Single-chain magnets: Beyond the Glauber model

Abstract

Single-chain magnets (SCMs) are one-dimensional (1D) slow-relaxing magnetic chains with interesting fundamental properties and applications, such as information storage. The mechanism underlying the slow relaxation of SCMs is Glauber dynamics, in which R. J. Glauber proposed about 50 years ago that the 1D correlation of ferromagnetically coupled Ising spins causes very slow magnetic relaxation at a finite temperature. Since the first experimental observation of SCM dynamics of a cobalt(II)–organic radical alternating chain in 2001, several SCM systems have been reported, supporting and expanding the Glauber model. In this review, we present the recent advances concerning SCMs with the main focus on SCM systems beyond the Ising limit, SCMs constructed with non-collinear or canted antiferromagnetic intrachain interactions, the relation between SCM dynamics and interchain interactions, and some SCMs with chirality, porosity, spin-crossover, photo-switchable states, and so on.

Full text

Cite this: RSC Advances, 2013, 3, 3772
Single-chain magnets: beyond the Glauber model
Received 29th October 2012,
Accepted 5th December 2012
DOI: 10.1039/c2ra22675h
www.rsc.org/advances
Wei-Xiong Zhang,*
ab
Ryuta Ishikawa,
a
Brian Breedlove
a
and Masahiro Yamashita*
a
Single-chain magnets (SCMs) are one-dimensional (1D) slow-relaxing magnetic chains with interesting
fundamental properties and applications, such as information storage. The mechanism underlying the
slow relaxation of SCMs is Glauber dynamics, in which R. J. Glauber proposed about 50 years ago that the
1D correlation of ferromagnetically coupled Ising spins causes very slow magnetic relaxation at a finite
temperature. Since the first experimental observation of SCM dynamics of a cobalt(
II)–organic radical
alternating chain in 2001, several SCM systems have been reported, supporting and expanding the
Glauber model. In this review, we present the recent advances concerning SCMs with the main focus on
SCM systems beyond the Ising limit, SCMs constructed with non-collinear or canted antiferromagnetic
intrachain interactions, the relation between SCM dynamics and interchain interactions, and some SCMs
with chirality, porosity, spin-crossover, photo-switchable states, and so on.
1. Introduction
Slow-relaxing low-dimensional magnetic systems, such zero-
dimensional (0D) single-molecule magnets (SMMs) and one-
dimensional (1D) single-chain magnets (SCMs), are important
from the viewpoints of fundamental and applied research, and
have several potential applications such as information
storage and quantum computing.
1,2
These low-dimensional
magnets do not have long-range thermodynamic ordering,
which is usually found in high-dimensional magnets, at a
finite temperature. However, their magnetization can be
frozen below the blocking temperature (T
B
) in the absence of
an applied magnetic field. This superparamagnetic behaviour
is caused by slow dynamics and metastability, in which an
energy barrier (D) must be overcome in order to reach the true
equilibrium state. Thus, their magnetization dynamics follow
a
Department of Chemistry, Graduate School of Science, Tohoku University, 6-3
Aramaki-Aza-Aoba, Aobaku, Sendai 980-8578, Japan.
E-mail: yamasita@agnus.chem.tohoku.ac.jp
b
MOE Key Laboratory of Bioinorganic and Synthetic Chemistry, School of Chemistry
and Chemical Engineering, Sun Yat-Sen University, Guangzhou 510275, China.
E-mail: zhangwx6@mail.sysu.edu.cn
Wei-Xiong Zhang
Wei-Xiong Zhang was born in
Guangdong, China in 1981. He
obtained his BSc in 2004, and his
PhD in 2009 from Sun Yat-Sen
University (SYSU) under the
supervision of Prof. Xiao-Ming
Chen. He was a JSPS postdoc-
toral fellow in Prof. Masahiro
Yamashita’s group at Tohoku
University in Japan. He is an
associate professor at Sun Yat-
Sen University. His current
research activities include sin-
gle-chain magnets, microporous
magnets, and molecule-based
dielectric/ferroelectric materials.
Ryuta Ishikawa
Ryuta Ishikawa was born in
Fukuoka, Japan, in 1982. He
completed his PhD studies in
2012 under the guidance of
Prof. Masahiro Yamashita at
Tohoku University, Japan, where
he studied the field of molecule-
based magnets, especially single-
molecule magnets and single-
chain magnets. After a brief
postdoctoral stay at Tohoku
University, he has recently taken
up a postdoctoral fellowship
position at the Institute of
Molecular Science (ICMol) at
the University of Valencia,
Spain, where he continues to
pursue his research interests in
molecule-based materials science
and its application.
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a Arrhenius law:
t(T)~t
0
e
D=k
B
T
(1)
where k
B
is the Boltzmann constant, t(T) is the temperature-
dependent magnetization relaxation time, and t
0
is a pre-
exponential factor. It is obvious that increasing D is crucial for
increasing T
B
in order to produce samples compatible with
industrial applications.
The value of D for the reversal of the magnetization in
SMMs is typically the combined result of high-spin ground
states (S) and uniaxial magnetic anisotropy (namely the zero-
field splitting (ZFS) parameter, D, is negative) of a single
molecule: D =|D|S
2
for integer spin, and |D|(S
2
2 1/4) for half-
integer spin.
1
On the other hand, Glauber dynamics, in which
1D correlation of ferromagnetically coupled Ising spins causes
very slow magnetic relaxation, describes the slow dynamics of
SCMs at finite temperatures.
3
In comparison with SMMs, D for
the reversal of the magnetization in SCMs is affected not only
by the magnetic anisotropy of the spins but also their
intrachain magnetic interactions (vide infra). From this view-
point, it should be easier to increase D for SCMs than it is for
SMMs. Moreover, it is easier to study the static and dynamic
properties of 1D cooperative systems than it is to study those
of higher dimensional cooperative systems in which a
magnetic phase transition is possible. Thus, since the first
observation of the slow relaxation of the magnetization in an
alternating cobalt(
II)–organic radical chain, [Co
II
(hfac)
2
(NITPhOMe)] (hfac = hexafluoroacetylacetonate, NITPhOMe =
49-methoxy-phenyl-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide)
(CoPhOMe), by D. Gatteschi and co-workers in 2001,
4
the
chemistry and physics of SCMs have become very active fields
of research, and Glauber’s model has been experimentally
supported and expanded by the great efforts of chemists and
physicists.
In the following review, we are going to summarize the
recent developments concerning SCMs, especially factors that
expand Glauber’s model for dealing with experimental
systems. In section 2, we will introduce the Glauber model,
as well as the theoretical and experimental understanding of
some typical SCMs. Then we will focus on SCMs systems
beyond the Glauber model, namely, SCMs with |D/J| , 4/3 or D
> 0, SCMs constructed with non-collinear or canted
antiferromagnetic intrachain coupling, and the relation
between SCM dynamics and interchain interactions, in
sections 3–5 respectively. In section 6, some multifunctional
SCMs or switchable SCMs, such as chiral SCMs, porous SCMs,
SCMs with spin crossover (SCO), and SCMs with photo-
switchable states, etc., are presented. A brief perspective is
given in section 7.
Brian K. Breedlove was born in
Kansas City, KS, USA in 1969.
After earning a PhD in Inorganic
Chemistry from Purdue University
in 1999, he became a JSPS post-
doctoral fellow at Osaka City
University, Japan. Currently, he
is an associate professor in the
Chemistry Department of Tohoku
University, studying coordination
comple xe s.
Masahiro Yamashita was born in
1954 in Saga, Japan. He received
his BSc degree in 1977, his MSc in
1979, and his DSc in 1982 from
Kyushu University, working under
the supervision of Prof. S. Kida.
After his graduation, he joined the
Institute for Molecular Science
(IMS). In 1985, he was appointed
an Assistant Professor at Kyushu
University. In 1989, he was
appointed an Associate Professor
at Nagoya University, and he was
promoted to full Professor at the
same university in 1998. He was a full Professor at Tokyo
Metropolitan University from 2000 to 2004. He is now a full
Professor in the Department of Chemistry at Tohoku University. He
worked on the Core Research for Evolutional Science and Technology
(CREST) project at the Japan Science and Technology Corporation
(JST) from 2012. He also worked as the project leader of a Grant-in-
Aid for Creative Scientific Research from the Ministry of Education,
Culture, Sports, Science and Technology (S) from 2008. His current
interests include the multi-functional nanoscience of advanced metal
complexes, as well as quantum molecular spintronics based on single-
molecule quantum magnets and single-chain quantum magnets. He
has been honored with the Inoue Scientific Award (2002), and The
Chemical Society of Japan Award for Creative Work (2005).
Brian Breedlove Masahiro Yamashita
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2. Simple theory and background of SCMs
2.1 1D Ising chain
In 1963, R. J. Glauber analyzed the dynamics of a closed
L-membered chain by assuming two conditions:
3
1) L fixed
Ising spins make transitions randomly between the values of
¡1 because of the interaction of the spins with an external
stimuli, e.g. a heat reservoir, and 2) its transition probabilities
depend on the momentary spin values of its neighbouring
spins and tends to be the same value as its neighbouring spins
in the case of ferromagnetic coupling. The model can be
simplified to a 1D ferromagnetic Ising chain with the following
Hamiltonian:
H
^
~{2J
X
L
i~1
s
i
s
iz1
{gm
B
H
X
L
i~1
s
i
where J is a positive value of the ferromagnetic exchange
constant between spin units s, g is the gyromagnetic factor, m
B
is the Bohr magneton, and H is the magnetic field. The
influence of a uniform, time-varying H upon the model has
been discussed, and a frequency-dependent magnetic suscept-
ibility has been predicted in the weak-field limit.
In a 1D Ising chain, spin–spin correlations decay exponen-
tially with the spin separation r: ,s
i
s
i + r
>=e
2r/j
. This quantity
indicates the probability that the (i + r)th spin has the same
value as the ith spin. The characteristic length, j, which is
defined as the correlation length of this spatial decay, is
temperature dependent:
j~e
4J=k
B
T
.
2~e
D
j
=k
B
T
.
2 (3)
In a 1D chain consisting of L spins, if T >4J/(k
B
ln(L)), the chain
behaves as a collection of independent segments of j, in which
all of the spins are iso-oriented, separated by L/j domain walls
(the word ‘‘domain’’ is used in a soft sense in a 1D system,
since a rigid magnetic domain is found in higher-dimensional
magnetically ordered phases). The energy barrier, D
j
=4J,
which is the energy difference between the uniform state and a
single-wall state, could be regarded as the energy needed to
create a new single domain wall. t is then the average time to
flip all of the spins contained in a segment. For each flipping,
the probability that a domain wall moves to the left side is
same as the probability that it moves to the right side, and
thus t is proportional to j
2
, from a statistical argument for a
random walk mechanism;
5
in other words, D for magnetiza-
tion reversal is:
D
Glauber
=2D
j
(4)
At low temperature, j diverges exponentially, and thus t
becomes very large, resulting in a very slow relaxation.
2.2 Anisotropic Heisenberg chains
The Glauber model can be used to obtain fundamental
knowledge of the dynamic processes in cooperative systems.
However, the strict conditions for Ising-type states are difficult
for real systems to meet.
6
Thus, an anisotropic Heisenberg
chain model is used to describe most real SCMs:
H
^
~{2J
X
L
i~1
S
i
S
iz1
zD
X
L
i~1
S
2
i
{gm
B
H
X
L
i~1
S
i
where a negative value of D is assumed for the case of a
uniaxial anisotropic spin (S), and S
i,z
is the projection of the S
i
spin on its easy axis. As long as |D/J| is larger than 4/3, the
nature of the low temperature magnetic excitations is the same
as for the Ising model, namely large oriented domains
separated by sharp domain walls (a thickness equal to a
single unit cell) with D
j
=4|J|S
2
. The width of a domain wall is
larger than a unit cell for smaller anisotropies (|D/J| , 4/3),
and D
j
is a complicated function of D and J. When the
anisotropy is small, i.e.,|D| % |J|, D
j
approximates to
4S
2
(|JD|)
1/2
.
7,8
Moreover, another difference between the Ising model and
the anisotropic Heisenberg model is that S of each magnetic
unit causes a magnetic anisotropic energy value (D
A
=|D|S
2
),
as in the SMM case. In other words, each magnetic unit is by
itself a thermally-activated relaxing object. As a result, D in eqn
(1) for the reversal of spin should have contributions from
both intrachain magnetic interactions and the magnetic
anisotropy of each unit:
D
1
= D
Glauber
+ D
A
=8|J|S
2
+|D|S
2
(6)
On the other hand, it has been found that for a uniform
ferromagnetic Heisenberg chain, the static magnetic suscept-
ibility at low temperature is directly related to j:
xT=C~2j~e
D
j
=k
B
T
(7)
where C is the Curie constant per magnetic unit and equals
g
2
m
B
2
S(S + 1)/(3k
B
). Thus, the slope obtained from a linear
analysis of a ln(xT) vs. T
21
plot is directly related to D
j
.
2
This
equation is very important, since it links the static magnetic
susceptibility (xT) and relaxation dynamics for ferromagnetic
SCMs, and we will come back to this point later.
2.3 Finite-size effect
Ideally, L is infinite. However, defects such as non-magnetic or
exchange-breaking impurities, lattice defects, etc., naturally
occur in real materials. A real magnetic chain is thus a
collection of segments whose average length, ,L>, depends on
the number of defects. If j is shorter than ,L>, the system can
still be treated as an infinite chain, and thus eqn (4) and (6) are
Fig. 1 A scheme for a single-spin-flip in infinite and finite chains.
(2)
(5)
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valid. However, j increases exponentially with a decrease in
temperature. Below the crossover temperature, j becomes
much larger than ,L>, and the system behaves like a
collection of finite segments (Fig. 1). For this ‘‘open’’ Ising
chain,
9
t is proportional to j but not j
2
. Therefore, the
intrachain-interaction-contributed D is half for a finite chain,
D
Glauber
= D
j
, and the total D in eqn (1) for a finite chain
becomes:
D
2
= D
Glauber
+ D
A
=4|J|S
2
+|D|S
2
(8)
This fact is supported by the mechanism for the creation and
propagation of domain walls. For a finite L spin segment,
creating a new domain wall close to a defect site only costs half
the energy needed to create a domain wall inside the chain.
5
In
addition, the propagation process for reversing all of the spins
in the segments implies that t also depends linearly on , L>,
and a collective reversal process can occur in finite chains,
which has been experimentally observed in Zn
II
-doped
CoPhOMe samples.
10
The finite-size effect on the dynamics
of CoPhOMe in the presence of a static magnetic field was also
theoretically investigated.
11
Moreover, in some isolated chains
consisting of antiferromagnetically coupled SMM units, in
which all spin should be compensated ideally, SCM dynamics
were still observed due to the intrinsic defects of the material
that cut the chain into finite segments containing either an
odd or even spin number.
12,13
2.4 Examples of SCMs
Although CoPhOMe, reported in 2001, was the first 1D system
with slow magnetic relaxation, detailed discussion of its
magnetic properties using Glauber dynamics is difficult
because it is a non-collinear ferrimagnetic chain (vide infra).
The 1D ferromagnetic-like complex [Mn
2
(saltmen)
2
Ni
(pao)
2
(py)
2
](ClO
4
)
2
, (saltmen
22
= N,N9-(1,1,2,2-tetramethylethy-
lene)bis(salicylideneiminate); pao
2
= pyridine-2-aldoxime; py =
pyridine), which was reported by R. Cle
´
rac, H. Miyasaka and
co-workers in 2002,
14,15
was the first example showing
universal dynamics of Ising-like chains. Later, by finely
modifying the precursor building units, they obtained a large
family of SCMs with the general formula [Mn
2
(5-
Rsaltmen)
2
Ni(oxime)
2
(L)
x
]A
2
, where 5-Rsaltmen
22
= N,N9-
(1,1,2,2-tetramethylethylene)bis(5-R-salicylideneiminate) with
R = H and MeO; oxime = pao, 1-methylimidazole-2-aldoximate
(miao), and 1-ethylimidazole-2-aldoximate (eiao); L = mono-
dentate N ligands such as pyridine, 4-picoline, 4-tert-butylpyr-
idine, and N-methylimidazole with x = 2, or bidentate N
ligands such as 2,29-bipyridine and 1,10-phenanthroline with x
=1;A
2
= ClO
4
2
,BF
4
2
,PF
6
2
, ReO
4
2
, and BPh
4
2
(Mn
2
Ni).
16–18
In the Mn
2
Ni SCM family, as shown in Fig. 2, the out-of-plane
dimers [Mn
2
(5-Rsaltmen)
2
]
2+
are linked by the mononuclear
[Ni(oxime)
2
] units, forming an alternating chain with the
repeating trimer unit [–Mn–(O)
2
–Mn–ON–Ni–NO–]
n
. In this
form, the Jahn–Teller axes and the corresponding uniaxial
anisotropic axes of the Mn
III
ions are collinear with each other.
Each chain is well separated with a minimum intermetallic
distance of more than 10.0 Å and without interchain p–p
interactions. Above 30 K, xT is explained by trimeric magnetic
units (S
T
= 3) with strong intra-trimer antiferromagnetic Mn–
Ni coupling (via the oximate bridge, 224.2 , J
trimer
/k
B
,220.8
K) connected by inter-trimer ferromagnetic coupling (via the
phenolate bridge, J
chain
/k
B
is usually in the range of +0.4 to
+0.9 K). Two related compounds with magnetically isolated
[Mn–Ni–Mn] trimers display SMM behaviour with D values (D/
k
B
= 22.3 to 22.4 K) close to the estimated value for the trimer
units in these SCMs (about 22.5 K).
19
Thus, these SCMs can be
regarded as 1D systems made of ferromagnetically coupled
SMMs with collinear magnetic easy axes and D
A
y 20 K. Above
6 K, the linear region of the ln(xT) vs. T
21
plot confirmed the
1D nature of this system and its Ising-like magnetic
anisotropy, and D
j
values agree with the expected value
calculated using 4J
chain
S
2
. D
eff
values for these compounds,
obtained from ac magnetic susceptibility data, are related to
J
chain
by the equation D
eff
/k
B
= 22.4 + 64.4J
chain
/k
B
, which agrees
with the expected correlation (eqn (6)) for the infinite-chain
regime: D
1
=2D
j
+ D
A
=8J
chain
S
2
+|D|S
2
# 72J
chain
/k
B
+ 21.
20
In
other words, these materials illustrated the expected Glauber
dynamics in the Ising limit, filling the gap between theoretical
predictions and real experimental systems.
In the last decade, a growing number of SCMs with homo- or
hetero-spins linked by ferromagnetic, ferrimagnetic or canted
antiferromagnetic intrachain interactions have been
reported.
21–34
Many techniques, i.e. NMR, ESR, high pressure,
etc., have been used to study the dynamics of SCMs.
35–38
Similar to SMMs, quantum effects on the magnetic properties
were also observed in SCMs.
39
A few reviews covering the
theoretical interpretation of the dynamics of magnetization in
earlier reported SCMs,
2,40,5
synthetic strategies using building
blocks,
41–43
intrachain interactions,
44
and tuning intermole-
cular interactions of SMMs are available.
45,46
Thus, the aim of
this review article is to summarize the most recent advances
concerning SCMs, especially examples which can only be
described using the expanded Glauber model, and we will
Fig. 2 Drawing of 1D ferromagnetically coupled [Mn
2
Ni] trimer units, and the
corresponding arrangement in the ground state. (
2009 America n Chemical
Society).
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focus on three important factors for the rational design of
SCMs: magnetic anisotropy of spin units, intrachain interac-
tions and interchain interactions.
3. SCMs with |D/J| , 4/3 or D >0
3.1 SCMs beyond the Ising limit (|D/J| % 4/3)
When SCMs strictly satisfy the Ising limit (|D/J| & 4/3),
Glauber dynamics can be used to explain the experimental
data (vide supra ). However, even when |D| is much less than
|J|, i.e., less than the Ising limit (|D/J| % 4/3), as well as in the
intermediate regime (|D/J| # 4/3) between the Ising and
Heisenberg limits (vide infra), SCM behavior has been
observed. In such SCMs, the slow relaxation dynamics are
not well understood. For |D/J| & 4/3, the width of the domain
wall is sharp and/or narrow, whereas for |D/J| % 4/3, the
domain wall has a finite thickness, i.e., a ‘‘broad domain
wall’’.
47,5,48
The mechanism for the slow magnetic relaxation
of SCMs in this regime needs to be fully elucidated in order to
develop an applicable unified description of SCM behaviour.
However, the Glauber model cannot be used in this region
and, thus, must be revised for SCMs with a broad domain wall.
Along this line, in 2011, Billoni and co-workers reported
theoretical studies of the mechanism for the slow magnetic
relaxation of SCMs with a broad domain wall using transfer
matrix calculations and time-quantified Monte Carlo simula-
tions on molecular ferromagnetic 1D chains.
48
According to
this theory, the energy of the broad domain wall is described
by the following relation for 1D alternating chains consisting
of magnetic uniaxial anisotropic spins (S
A
) and isotropic spins
(S
B
):
D
j
Heisenberg
~2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 D
A
J
A{B
jj
S
3
A
S
B
q
(9)
where D
A
is much smaller than J
A–B
, and S
A
> S
B
.
3.2 Mn
III
–radical alternating 1D chains
One way to achieve strong magnetic exchange coupling is
through the use of organic radicals with diffuse spin orbits,
which can strongly overlap with the core electron density of
the paramagnetic metal ions as bridging ligands, as well as
magnetic mediators. Miller and co-workers have reported
anisotropic quasi-1D ferrimagnetic chains composed of
charge-transfer complexes of Mn
III
(porphyrin) derivatives (D
+
)
and organic anion radicals (A
?
2
), such as the tetracyanoethe-
nide radical anion (TCNE
?
2
) and related organic radical
anions,
…
D
+
A
?
2
D
+
A
?
2
…
(Fig. 3).
49–51
The magnetic exchange
interactions between the high-spin (HS) Mn(
III) ions (S = 2) and
TCNE
?
2
(S = 1/2) are considerably strong due to the s–d
z
2
–p*
type overlap defining the antiferromagnetic interaction. In
addition, the ac susceptibilities of some of their ferrimagnetic
1D complexes depend on the frequency, which is a key piece of
evidence of the slow relaxation process in SCMs. In other
words, Mn
III
(porphyrin)–TCNE
?
2
derivatives are good models
for SCMs beyond the Ising limit. However, Epstein and co-
workers have suggested that their viscous magnetic behaviour
is caused by disorder, leading to quasi-1D clusters coupled
through dipole–dipole interactions between chains to form 3D
domains.
49–51
Moreover, the crystal lattices of most
Mn
III
(porphyrin)–TCNE
?
2
derivatives contain interstitial sol-
vent molecules, which affect their magnetic behavior due to
absorption/desorption processes known as magnetic sponge
effects.
52–54
As mentioned above, however, it is difficult to
determine whether they are spin glasses or superparamag-
nets.
55
In 2006, Miyasaka and Cle
´
rac et al. reported an alternating
Mn
III
–radical 1D chain by elucidating the slow relaxation
mechanism of a family of 1D Mn
III
–radical chains (Fig. 4a).
56
They assembled an alternating 1D chain complex, [Mn
III
(5-
TMAMsaltmen)(TCNQ)](ClO
4
)
2
(5-TMAMsaltmen = N,N9-
(1,1,2,2-tetramethylethylene)bis(5-trimethylammoniomethyl-
salicylideneiminato); TCNQ = tetracyano-p-quinodimethane),
which has same ferrimagnetic alternating chain topology as
the family of Mn
III
(porphyrin)–TCNE
?
2
compounds, using a
Mn
III
salen derivative unit instead of a Mn
III
(porphyrin) unit
and TCNQ instead of TCNE. No interstitial solvent molecules,
only ClO
4
2
counter anions occupy the void spaces between
each chain. This complex is excellent for probing the intrinsic
magnetic properties of alternating Mn
III
–radical 1D chains
because of its high stability in air. xT versus T data are usually
fitted using the Seiden model
57
to obtain the intrachain
interaction (J
Mn–Rad
) between the HS Mn(III) ion (classical spin)
and the organic radical anion such as TCNE
?
2
(quantum spin)
for the family of alternating Mn
III
–radical 1D chains. J
Mn–Rad
/k
B
was determined to be 296.1 K, and D
Mn
/k
B
was estimated to be
22.4 K using single crystal magnetic measurements. D
j
/k
B
was
determined to be 26.5 K in the temperature range of 50–15 K
(Fig. 4b). Below 10 K, strong frequency dependence of the ac
susceptibilities was observed for both x9 and x99 signals,
suggesting the presence of slow magnetic relaxation in this
chain complex. Fitting the data using the Arrhenius law gave
D
t1
= 94.1 K with t
01
= 2.1 6 10
210
s (infinite-size regime) and
D
t2
= 67.7 K with t
02
= 6.8 6 10
28
s (finite-size regime) with a
crossover temperature of 4.5 K (Fig. 4d). Cole–Cole diagrams
fitted using a generalized Debye model, in which a parameter a
is assumed in the range of 0–1 and a smaller a value indicates
a narrow distribution of t,
58
show only one relaxation process
with a , 0.1 (Fig. 4c). Moreover, heat-capacity calorimetry
Fig. 3 Segment of a uniform 1D
…
D
+
A
?
2
D
+
A
?
2
…
chain of Mn
III
(TPP)–TCNE
?
2
,
TPP = meso-tetraphenylporphyrin. (
2011 The Royal Society of Chemistry).
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measurements showed no abnormalities in the values of C
p
at
low temperatures down to 0.5 K. Therefore, detailed magnetic
analysis of these dynamic properties shows unambiguously
that this complex is SCM.
[Mn
III
(To-FPP)(TCNE)]?2PhMe
47,59
and [Mn
III
(TBPP)(TCNE)]?
4m-PhCl
2
(where To-FPP
22
= meso-tetra(ortho-fluorophenyl)
porphyrinate, PhMe = toluene, TBPP
22
= meso-tetra(para-
biphenyl)porphyrinate, and m-PhCl
2
= meta-dichloroben-
zene)
60
are analogous Mn
III
–radical 1D chains showing slow
magnetic relaxation. In 2006
47
and 2011,
59
Tomkowicz and co-
workers carefully showed that one of the TCNE
?
2
salts of
phenylfluoro-substituted [Mn
III
(TPP)]
+
, [Mn
III
(To-FPP)(TCNE)]?
2PhMe, has interesting magnetic properties, such as SCM-like
behavior. Previously, Miller and Epstein reported that TCNE
?
2
salts of phenyl substituted [Mn
III
(TPP)]
+
, especially ortho-
substituted [Mn
III
(TPP)]
+
(Fig. 5a), exhibit a magnetic phase
transition at 12.5 K.
49–51
However, they could not confirm the
presence of any antiferromagnetic transitions. By using the
Seiden model with a ZFS parameter, J
Mn–Rad
/k
B
was deter-
mined to be 2108.5 K, and D
Mn
/k
B
was determined to be 22.95
K, assuming that the single-ion anisotropy comes from the HS
Mn
III
ion. D
j
/k
B
was determined to be 60 K at low temperatures
(Fig. 5b). The relaxation of the magnetization follows the
Arrhenius law, giving D
2
/k
B
= 117 K with t
0
= 1.4 6 10
210
s
(Fig. 5d), in which j is much greater than L (finite-size regime).
Cole–Cole plots for this complex have a quasi-semicircular
shape (average a = 0.12, as shown in Fig. 5c). In addition,
they reported that the magnetic relaxation in
[Mn
III
(To-FPP)(TCNE)]?2PhMe originates from a magnetic
soliton, that is, the domain wall motion of the 1D complexes
propagates as p solitons along the chains. Very recently, in
relation to [Mn
III
(Tm-FPP)(TCNE)]?xPhMe (where Tm-FPP
22
=
meso-tetra(meta-fluorophenyl)porphyrinate), which shows a
magnetic transition to a glassy ferromagnetic state at a critical
temperature (T
c
) of 10 K, the slow relaxation involving soliton
spin reversals and spin wave excitations for this complex were
experimentally determined using high-field/multi-frequency
EPR techniques by the same group. It was concluded that the
soliton excitations were higher in energy than the spin wave
excitations in SCMs with broad domain walls.
61
In addition,
the domain wall energy for the anisotropic Heisenberg type,
D
j
Heisenberg
/k
B
, was estimated to be 101.2 K for this complex
using eqn (9), whereas D
A
can be estimated from the simple
difference by using eqn (6), D
A
/k
B
=(D
2
2 D
j
Heisenberg
)/k
B
#
15.8 K, the value of which is similar to that estimated from
EPR data (D
EPR
/k
B
# 15 K).
In 2012, a new SCM with predetermined topologies,
[Mn(TBPP)(TCNE)]?4m-PhCl
2
, in which the interchain interac-
tions are suppressed was reported, extending the range of
available SCMs with broad domain walls (Fig. 6a and 6b).
60
Fig. 4 (a) Alternating zigzag 1D chain structure of [Mn
III
(5-TMAMsaltmen)(TCNQ)](ClO
4
)
2
. (b) Plot of ln(x9T) versus 1/T, where square and circle symbols have been
obtained with dc (1 kOe dc field) and ac (1 Hz ac frequency, 3 Oe ac field and zero dc field) techniques, respectively. (c) Cole–Cole plots. The solid red curves represent
the least squares fit to a generalized Debye model with a , 0.1. (d) Relaxation time (t) versus 1/T plot, where blue and red dots were obtained from ac and dc
measurements, respectively. (
2006 Wiley-VCH).
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Moreover, this compound is highly stable in air. Magnetic
exchange in the family of Mn
III
(porphyrin)–TCNE
?
2
chains
occurs through the TCNE
?
2
trans-m-N-s bounds. A comparison
of the static magnetic properties of this compound with other
related Mn
III
(porphyrin)–TCNE
?
2
chains indicates that J
Mn–Rad
increases linearly with a decrease in /Mn–N
…
C.
49–51
Specifically, this compound has the smallest /Mn–N
…
Cin
the family of Mn
III
(porphyrin)–TCNE
?
2
chains (Fig. 6c). The
intrachain interaction between magnetic spins (J
Mn–Rad
/k
B
) was
estimated to be 2136.1 K using the Seiden model, the value of
which is the largest value in the family of Mn
III
(porphyrin)–
TCNE
?
2
chains (Fig. 6c). D
Mn
/k
B
was estimated to be 23.7 K,
assuming single-ion anisotropy from the HS Mn
III
ion. This
value falls within the typical range reported for related five-
coordinate and six-coordinate HS Mn
III
(porphyrin) deriva-
tives.
62–70
D
j
/k
B
was determined to be 70.8 K in the
temperature range 60–18 K (Fig. 6d). Below 16 K, x9 and x99
signals were strongly dependent on the frequency. From
Arrhenius plots derived from Cole–Cole plots for this
compound, D
t
/k
B
= 146.3 K and t
0
= 4.1 6 10
210
s were
obtained (Fig. 6f). In addition, from Cole–Cole plots, clearly
only one relaxation process is present since the quasi-
semicircle shape could be fitted using the generalized Debye
model with a small a value of 0.04–0.16 (Fig. 6e). The
relaxation barrier and magnetization hysteresis at low tem-
peratures (coercive field, H
c
= 2.7 T at 1.8 K) are the largest yet
reported for Mn
III
(porphyrin)–TCNE
?
2
chains. Moreover, they
have shown that recent theoretical models for SCMs with
broad domain walls can be used to understand their
experimental results. On the basis of these considerations,
48
D
j
Heisenberg
/k
B
for this complex was estimated to be 126.9 K
using eqn (9), whereas the value of D
j
obtained from eqn (7)
was 70.8 K, the value of which is more than half that of
D
j
Heisenberg
/k
B
. On the other hand, the values of D
A
could not
be determined because, for SCMs with a broad domain wall,
there is no perfect analytical expression using local magnetic
parameters (J, D
Mn
, S
Mn
and s
Rad
) due to alternating
ferrimagnetic behaviour, i.e., hetero-spin 1D systems.
Nevertheless, the relationships D
1
=2D
j
+ D
A
and D
2
= D
j
+
D
A
, remain applicable for any SCM systems in infinite- and
finite-size regimes, respectively. Thus, the value of D
A
can be
estimated simply from the difference of D
2
and D
j
, D
A
= D
2
2
D
j
, for the complex in the finite-size regime. D
A
/k
B
was
estimated to be 75.5 K (using D
j
/k
B
= 70.8 K), the value of
which is much larger than the single-ion anistropy energy (D
A
/
k
B
=|D
Mn
|S
Mn
2
= 14.8 K) for the Ising limit situation, whereas
using the previously obtained D
j
Heisenberg
of 126.9 K calculated
from eqn (9), D
A
/k
B
= 19.4 K, the value of which is comparable
Fig. 5 (a) Structure of [Mn
III
(To-FPP)(TCNE)]. Three positions (R = para,R9 = meta and R 99 = ortho) for F substitutions are shown. (b) Temperature dependence of m
eff
.
Inset: Plot of ln(x9T) versus 1/T. (c) Cole–Cole plots. (d) Relaxation time (t) versus 1/T(
2006 The American Physical Society and 2011 IOP science).
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to |D
Mn
|S
Mn
2
. This result confirms that the value of D
A
for non-
Ising ferrimagnetic SCMs with a broad domain wall is more
complicated using local magnetic and structural parameters.
3.3 SCMs between the Ising and Heisenberg limits
In 2012, Miyasaka and Cle
´
rac et al. reported a series of isostructural
hetero-spin SCMs, [Mn
HS
III
(5-TMAMsalen)M
LS
III
(CN)
6
]?4H
2
O(LS=
low-spin, M = Co (S
Co
=0),Fe(S
Fe
=1/2),Mn(S
Mn
=1),Cr(S
Cr
=3/2),
and 5-TMAMsalen = N,N9-ethylenebis(5-trimethylammonio-
methylsalicylideneiminate)) with alternating cyano bridges
[–Mn
III
–NC–M
III
–CN–], except for the Mn
III
–Co
III
compound,
which is only paramagnetic due to the diamagnetic LS Co
III
ion
(Fig. 7).
71
In other words, the Mn
III
–Co
III
complex could be used
to probe the intrinsic D
Mn
parameter of the building unit
[Mn
III
(5-TMAMsalen)]
3+
(S
Mn
= 2) in the chain. D for the HS
Mn
III
site for this compound was determined to be 25.3 K,
meaning that the site exhibits significant uniaxial magnetic
anisotropy. On the other hand, the intrachain magnetic
interactions J
Mn–M
of the other three SCMs, Mn
III
–Fe
III
,Mn
III
–
Mn
III
and Mn
III
–Cr
III
, were estimated to be +4.5 K, +1.4 K and
29.0 K, respectively. In other words, Mn
III
–Fe
III
and Mn
III
–Mn
III
are ferromagnetic SCMs, whereas Mn
III
–Cr
III
is a ferrimagnetic
SCM. The values of D
j
/k
B
for Mn
III
–Fe
III
,Mn
III
–Mn
III
and Mn
III
–
Cr
III
were experimentally determined to be 14.1, 7.3, and 13.8 K
by linear analysis of the ln(xT) vs. T
21
plot. The temperature
dependence of t for this series of complexes systematically
indicates that a crossover between two Arrhenius laws,
corresponding to infinite-chain and finite-chain regimes,
occurs. Fitting with the Arrhenius law, D
t1
= 32.0 K, 25.0 K
and 48.1 K with t
01
=5.26 10
210
s, 1.7 6 10
29
s and 2.9 6
10
210
s (infinite-size regime) and D
t2
= 16.0 K, 17.4 K and 34.9 K
with t
02
= 8.0 6 10
25
s, 2.5 6 10
27
s and 1.9 6 10
27
s (finite-
size regime) with crossover temperatures of 1.47 K, 1.56 K and
2.05 K for the Mn
III
–Fe
III
,Mn
III
–Mn
III
and Mn
III
–Cr
III
SCMs,
respectively. Considering the estimated J
Mn–M
values and D
Mn
of
the Mn
III
–Co
III
complex, the values of D
j
for both the Ising
Fig. 6 (a) 1D chain motif of Mn
III
(TBPP)–TCNE
?
2
. (b) Representation of adjacent chains in the crysta l packing. The light yellow sphere indicates the 1D channel formed
by four adjacent chains. (c) Correlation between the Mn
III
–N
…
C angle defined in Mn
III
(porphyrin)–TCNE
?
2
and the J value. Labels a–f and ‘‘1’’, are explained in ref. 60.
(d) Plot of x9T with a semilogarithmic scale versus 1/T. (e) Cole–Cole plots. (f) Arrhenius plot of the relaxation time t determined from variable temperature (black) and
variable frequency (blue) ac susceptibilities. (
2012 American Chemical Society).
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(D
j
Ising
=4|J
Mn–M
|S
Mn
S
M
= 18 K, 11 K and 108 K) and Heisenberg
limits (D
j
Heisenberg
= 14.1 K, 7.3 K and 13.8 K) for Mn
III
–Fe
III
,
Mn
III
–Mn
III
and Mn
III
–Cr
III
complexes do not match the
respective experimetal D
j
values. The differences show that
these SCMs do not follow pure Glauber dynamics, but follow an
intermediate regime between the Ising and the Heisenberg
limits. Unfortunately, analytical expressions for D
j
in the
intermediate regime are still unknown. However, these iso-
structural hetero-spin SCMs will make it possible to test
theoretical SCM models between the Ising and Heisenberg
limits.
Currently, efforts are underway to prepare SCMs with broad
domain walls, as well as walls with widths between the sharp/
narrow domain and the broad domain. However, further
theoretical and experimental studies are necessary. In order to
understand non-Ising type SCMs, it is important that (i) better
models for such SCMs and (ii) a general theory including the
estimation of the anistropy energy etc. for hetero-spin 1D
chains are developed.
3.4 SCMs with easy-plane type magnetic anisotropy
As mentioned earlier, it is a generally held principle that
negative D values (D , 0) are essential in the design of SCMs as
well as SMMs. Thus, it usually believed that positive D values
(D > 0) will not lead to slow magnetic relaxation behavior in
SCMs and SMMs. However, a small number of subsequent
studies have reported the presence of slow magnetic relaxation
in SCMs as well as SMMs
72–75
with D >0.
3.4.1 SCMs with a mutually orthogonal arrangement of HS
Fe
II
ions and easy-plane magnetic anisotropy. In 2005,
Kajiwara et al. reported novel SCMs constructed using a
twisted arrangement of spin carrier components with easy-
plane type magnetic anisotropy, namely hard-axis or XY plane
anisotropy with D > 0, which generally helps avoiding the
bistability that leads to a ‘‘double-well potential’’.
76–79
The
mixed valence 1D chain complex catena-
[Fe
II
(ClO
4
)
2
{Fe
III
(bpca)
2
}]ClO
4
?3MeNO
2
(Hbpca = bis-(2-pyridyl-
carbonyl)amine) and its derivatives
80,81
) has an alternating
arrangement of HS Fe
II
ions and low-spin (LS) Fe
III
ions along
the chain axis connected in a ferrimagnetic manner (top of
Fig. 8a). The SCM character of these complexes is due to the
twisted arrangement, i.e., a mutually orthogonal arrangement
of easy-planes of Fe
II
ions along the chain axis, which
generates easy-axis anisotropy. The arrangement induces
Ising interactions along the chain axis (bottom of Fig. 8a). J/
k
B
between the HS Fe
II
and LS Fe
III
ions in the chain and D/k
B
Fig. 7 (a) X-ray crystal structure and the 1D chain motif of [Mn
III
(5-TMAMsalen)M
III
(CN)
6
]?4H
2
O (M = Co, Fe, Mn, Cr). (b) Temperature dependence of xT measured
from polycrystalline samples. (c) x9T vs. 1/T plots on a semi-logarithmic scale ( x9 is the in-phase ac susceptibility at 1 Hz, 3 Oe of ac field modulation in a zero dc field).
(d) Magnetization relaxation time (t) versus 1/T in a zero dc field. (
2012 Wiley-VCH).
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of the HS Fe
II
single-ion site for this compound were
determined to be 210.0 K and +14.9 K, respectively (Fig. 8b).
D
j
/k
B
was determined to be 5.16 K. In ac susceptibility
measurements on this complex, a strong frequency depen-
dence of both x9 and x99 components was observed (Fig. 8c).
Cole–Cole plots clearly indicate that relaxation occurs via a
single process with small a values in the range of 0.09–0.13.
From Arrhenius plots, D
t
/k
B
= 27 K with t
0
= 1.6 6 10
28
s, the
values of which do not follow the Glauber model. This
suggests that the transverse magnetization of HS Fe
II
spins
with an easy-plane-type magnetic anisotropy is responsible for
the slow magnetic relaxation in the SCMs.
3.4.2 SCMs induced by transverse ZFS of Re
IV
ions. In 2010
and 2011, Long et al. reported a series of cyano-bridged hetero-
spin SCMs, [(DMF)
4
M
II
Re
IV
Cl
4
(CN)
2
] (M = Mn, Fe, Co, Ni),
82
and their derivatives,
83
using a magnetically anisotropic
building unit, [Re
IV
Cl
4
(CN)
2
]
22
(Fig. 9a). Magnetic analyses
revealed that these 1D chains do not follow simple Glauber
dynamics. In other words, they are non-Ising SCMs. In
addition, in 2012, Long et al. found that
[(DMF)
4
Mn
II
Re
IV
Cl
4
(CN)
2
] has interesting magnetic properties,
such as SCM behaviour induced by a large transverse ZFS (E),
by using high-field/multi-frequency ESR techniques.
84
Previous fits to Arrhenius plots of this compound gave
parameters of D
t
/k
B
= 45 K with t
0
= 1.3 6 10
210
s. D
t
/k
B
was determined to be 27 K by linear analysis of the ln(xT) vs.
T
21
plot. Since the direct observation of D for Re
IV
sites within
the 1D chain complex was difficult, the authors prepared the
isostructural 1D complex [(DMF)
4
Zn
II
Re
IV
Cl
4
(CN)
2
], in which
the paramagnetic Mn
II
ions were replaced by diamagnetic Zn
II
ions to probe the intrinsic anisotropy of the Re
IV
centers in the
chain. To exclude the possibility that magnetic exchange
coupling may act to invert the sign of D in
[(DMF)
4
Mn
II
Re
IV
Cl
4
(CN)
2
] relative to its constituent
[Re
IV
Cl
4
(CN)
2
]
22
moiety, the authors prepared the discrete
trinuclear compound [(PY5Me
2
Mn)
2
ReCl
4
(CN)
2
](PF
6
)
2
(PY5Me
2
= 2,6-bis(1,1-bis(2-pyridyl)ethyl)pyridine), which is one part of
the magnetic unit in [(DMF)
4
Mn
II
Re
IV
Cl
4
(CN)
2
]. These EPR
studies clearly indicated the presence of a positive D value
(D
Re
/k
B
# 30 K) with a non-zero E value (E
Re
/k
B
# 3.0 K) for the
Re
IV
ion. Here the authors proposed a relevant D
A
scale, which
is the value determined using E rather than D. Therefore, the
D
A
value associated with the reversal of a single Re
IV
spin
Fig. 9 (a) Heterometallic 1D chain of [(DMF)
4
M
II
Re
IV
Cl
4
(CN)
2
] (M = Mn, Fe, Co,
Ni). (b) Classical magneto-anisotropy energy surface corresponding to the zero-
field operator equivalent terms given in H
ˆ
= DS
ˆ
z
+ E(S
ˆ
x
2 S
ˆ
y
)+m
B
gS
ˆ
, with D >0
and |E/D| equal to the ratio found from the present EPR experiments on
[(DMF)
4
Zn
II
Re
IV
Cl
4
(CN)
2
]. The radial distance to the surface represents the
energy of a spin as a function of its orientation; zero energy has been chosen to
correspond to the case when the spin is parallel to y, and only the z > 0 surface is
shown to aid viewing of the cross-section in the xy plane. As can be seen, the
spin experiences an anisotropic kinetic barrier against reversal from +y to 2y,
with the barrier minimum occurring along ¡x.(
2010 & 2012 American
Chemical Society).
Fig. 8 (a) Alternating 1D chain motif of catena-[Fe
II
(ClO
4
)
2
{Fe
III
(bpca)
2
}]ClO
4
?
3MeNO
2
and its spin arrangement of high-spin Fe
II
and low-spin Fe
III
ions along
the chain. (b) Temperature dependence of m
eff
for the powder sample and
oriented single crystal in a dc field applied along the chain and perpendicular to
the chain (inset). (c) Temperature dependence of ac susceptibility (x99: imaginary
part) for the powder sample. (
2005 American Chemical Society).
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within the chain is given by D
A
=2|E
Re
|S
Re
2
(Fig. 9b). On the
basis of these considerations, D
A
/k
B
was estimated to be 14 K.
Considering the previously obtained D
j
/k
B
value of 27 K, the
D
t
/k
B
value of this complex was estimated to be 41 K, which
agrees with the experimentally determined value of D
t
/k
B
=45
K in the finite-size regime.
4. SCMs with canted antiferromagnetic or
non-collinear intrachain interactions
The Glauber model only accounts for collinear ferromagnetic
intrachain interactions. In real molecular systems, however,
the symmetry on the metal site is very frequently lower than
that of the crystal space group. Thus, the 1D structure
generated by either a glide plane or a screw axis usually
induces non-collinearity of the anisotropy axes. In addition,
the lack of an inversion centre between two anisotropic metal
ions usually results in canted magnetic interactions, leading to
a spin-canting arrangement.
85–87
Thus, these non-collinear
spin arrangements cause uncompensated moments that
produce an observable magnetic susceptibility. Therefore, it
should be not a surprise that SCM behaviour could be
observed for complexes with a non-collinear 1D spin arrange-
ment, which in most cases involves canted antiferromagnetic
interactions. A modified Glauber model was theoretically
investigated, taking into account the non-collinearity of local
anisotropy axes, by Vindigni and Pini in 2009.
88
They found
that SCM behaviour was not only a feature of collinear ferro-
and ferrimagnetic chains, but also of canted antiferromagnetic
chains. However, they also found that the occurrence of slow
relaxation was dependent on the experimental geometry. In
other words, the resonant behaviour of the ac susceptibility in
response to an oscillating magnetic field is only possible for
fields applied in a direction where the magnetic moments are
uncompensated. Recently, a theoretical investigation on a 1D
heteronuclear {Fe
II
Nb
IV
} SCM, where alternate units are
isotropic (Nb
IV
ion, S = 1/2) and anisotropic (Fe
II
ion, S =2)
with non-collinear axes, was carried out using a transfer matrix
method and also supported the SCM dynamics arising from
non-collinearity of local anisotropy axes.
31,89
In comparison to collinear ferromagnetic interactions, in
real molecular magnets antiferromagnetic interactions are
more common and usually have a larger intensity because of
the overlap of the magnetic orbits, which implies an
antiferromagnetic interaction is more easily obtained than
the orbital orthogonality that leads to ferromagnetism.
90
Moreover, canted antiferromagnetic systems can be easily
designed by using asymmetrical bridge ligands, such as single
carboxylate and phosphinate bridges. Thus, more SCMs with
non-collinear spin arrangements are expected in the future.
4.1 Non-collinear ferrimagnetic Co
II
–radical SCM
As mentioned before, the first experimental magnetic slow-
relaxing 1D system CoPhOMe has a non-collinear ferrimag-
netic topology with a 3
1
helical screw axis.
4
As shown in
Fig. 10a, the magnetism comes from the cobalt ions, which
have Ising character and an effective spin of 1/2, and the
NITPhOMe organic radical ions, which have a magnetically
isotropic spin of 1/2. Spins are arranged in a helical structure,
as shown in Fig. 7b. Since the gyromagnetic factors of Co
II
and
NITPhOMe are different (g
Co
? g
R
), the strong antiferromag-
netic nearest-neighbour cobalt–radical exchange interaction
(ca. 2110 K) causes a compensated moment along the chain.
The primitive cell contains three Co
II
metal ions alternating
with three radicals. Each Co
II
ion is geometrically related to
the other two through a 120u rotation around the c axis and
has a local axis of easy anisotropy, z, which makes an angle of
y50u with the c axis (Fig. 10b). Vindigni and Pini have
theoretically investigated this six-fold helix model with
Fig. 10 (a) Simplified view of the 3
1
-helical chain of CoPhOMe. All hydrogen atoms, fluorine atoms, and methyl groups are omitted for clarity. (b) Location of even
and odd local axes (dashed lines) and magnetic moments (thick arrows) in CoPhOMe in the view along (left) and perpendicular (right) to the chain axis (
2009, IPO
Publishing Ltd).
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alternating spins and Ising exchange coupling, and they have
shown that, in order to qualitatively reproduce the dynamic
behaviour of this complex, a field must be applied along the c
axis, which causes the resonant behaviour of the ac suscept-
ibility.
88
Indeed, in the frequency range of 1–10
5
Hz, no out-of-
phase ac susceptibility was observed when the field was
applied in the plane perpendicular to the chain axis.
91
Thus,
resonant behaviour in the plane perpendicular to the chain
axis is not possible for an Ising spin chain arranged in an
n-fold helix with n >2.
4.2 Diphosphonate-bridged Co(
II) zigzag chain
The first example of a SCM with 1D antiferromagnetically
coupled homo-spin centres is the zigzag-chain cobalt(
II)
compound Co(4-Me-C
6
H
4
-CH
2
N(CH
2
PO
3
H)
2
))(H
2
O),
92–94
in
which the Co
II
ions are antiferromagnetically coupled via
diphosphonate bridges, as shown in Fig. 11a. The strong
tetragonal field around the Co
II
ions stabilizes the orbital
doublet degeneracy of the Co
II
ions, and thus an effective
pseudo-spin-1/2 Hamiltonian has been proposed to describe
the interaction between the Co
II
ions in their ground Ising-type
Kramers doublet states. Although only antiferromagnetic
interactions exist between the neighbouring Co
II
ions, as
shown in Fig. 11b, the tilting of the tetragonal axes of the
neighbouring Co
II
units in the zigzag structure gives rise to
spin canting and consequently to a non-vanishing magnetiza-
tion. Thus, frequency dependence of the ac susceptibilities
was observed below 2.4 K, and a D
t
/k
B
of 45.2 K was obtained.
In order to understand the unusual magnetic properties of this
complex, initially a simple model based on the mean-field
approach was used to obtain a qualitative explanation of all of
the observed characteristic features.
93
In 2008, a quantitative
description of the magnetic susceptibility and the SCM
behaviour was achieved by using a quantum-mechanical
approach incorporating strong uniaxial magnetic anisotropy,
spin–orbit interactions, antiferromagnetic exchange, and the
topology of the chain.
94
This model can be applied to more SCMs
since it is applicable not only to the spin-canted Co
II
chains but
also to chains of other Kramers ions. Moreover, it can be applied
not only to chains with intrachain antiferromagnetic exchange,
but also to both ferro- and canted-antiferromagnetic chains.
4.3 Phosphinate-bridged Mn(
III) SCM
In 2008, a canted antiferromagnetic SCM with phosphinate
bridges, [Mn(TPP)O
2
PHPh]?H
2
O, was reported by Sessoli and
co-workers.
95
It was synthesized by reacting manganese(III)
acetate, TPP, and phenylphosphinic acid, and it crystallizes in
the monoclinic space group C2/c. The magnetism comes from
the glide plane, resulting in Jahn–Teller elongation axes of the
Mn(
III) octahedron, which alternate along the chain with a
spin-canting angle (d) of 34.6u between the two different easy-
anisotropy axes (Fig. 12a). The sizable antiferromagnetic
exchange interactions pass through the phosphinate bridges,
interplaying with the uniaxial anisotropy of the Mn
III
ions,
resulting in a canted antiferromagnetic arrangement of the
spins (Fig. 12a and b). J and D were estimated to be 20.68(4) K
and 24.7(2) K, respectively, by analyzing static single-crystal
magnetic properties with a classical Monte Carlo approach.
Below 5.0 K, remarkable frequency dependence of the out-of-
phase signal was observed along the b axis, along which the
uncompensated spins align (Fig. 12c). The D value deduced
from the experimental temperature-dependent t value was
36.8 K, which is consistent with the calculated value of 37(2) K,
estimated using the equation taking into account the spin-
canting angle d (D
cal
=8S
2
|J|cos(d)+|D|S
2
). Moreover, as
shown in Fig. 12d, it was found that the commonly employed
linear analysis of ln(xT) vs. T
21
by eqn (7) leads to a large error
in the estimation of the exchange contribution of the SCM
dynamics. This fact indicates that eqn (7), which was deduced
from the 1D collinear ferromagnetic chain model,
2
should be
used carefully when estimating the exchange contribution for
non-collinear SCMs.
4.4 Dy
III
–radical non-collinear SCM
The molecular magnetic compound [Dy(hfac)
3
(NITPhOPh)]
belongs to a family of quasi-1D magnets, in which rare earth
(RE) ions and organic radical ions (with spin s = 1/2) alternate
along the chain axis, i.e. the b axis (Fig. 13a).
96,97
In this type of
lanthanide–radical chain, nearest-neighbour ferromagnetic
metal–radical and next-nearest-neighbour antiferromagnetic
metal–metal or radical–radical magnetic coupling (J
Mr
, J
MM
,
and J
rr
, respectively) are present. Static measurements on
single crystals suggested that J
MM
was dominant.
98
Furthermore, strong angular dependence of x
m
and inversion
between maxima and minima of the angular dependence of x
m
were found when the temperature was increased. This
"anisotropy inversion" was ascribed to weak 1D ferromagnet-
ism along the chain axis, since the easy anisotropy axes of
neighbouring Dy(
III) ions are canted by forming an angle h of
y80u with respect to the b axis (along the chain axis). This
arrangement leads to an uncompensated moment along the b
axis, whereas the components in the ac plane are compen-
sated. Moreover, the situation in this complex is more
Fig. 11 (a) 1D chain of Co(4-Me-C
6
H
4
-CH
2
N(CH
2
PO
3
H)
2
))(H
2
O). (b) Non-collinear
spin structure of neighbouring spins A and B (left) and of the chain with illustration
for a single spin flip-flop process (right). (
2008 American Chemical Society).
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Fig. 13 (a) View of the crystal structure of [Dy(hfac)
3
(NITPhOPh)] ( 2006 American Chemical Society). (b) Representation of the Ising axes of the Dy
III
ions (left), and
view along the b axis of the crystal packing, showing the two symmetry-related chains (right). (
2009 The American Physical Society).
Fig. 12 (a) Schematic views of the magnetic chain of [Mn(TPP)O
2
PHPh]?H
2
O along the a (left) and c (right) axes. (b) xT vs. T plot of the powder sample. The field-
dependent magnetizations for the powder sample at 1.6 K (full line) and 4.0 K (dashed line) are shown in the inset. (c) Plot of the real (x9) and imaginary (x99) molar
susceptibility against temperature measured in a zero static field on crystals oriented along the a (open triangles), b (circles), and c (squares) axes. The measurements
were performed with logarithmic spaced frequencies ranging from 4 Hz (red) to 20 00 Hz (blue). The black symbols are for the zero field quasi-static susceptibility
measured at 0.1 Hz. (d) Semilogarithmic plot of the correlation length (j) versus T
21
simulated by a classical Monte Carlo method along the b-axis (empty circles),
along the c-axis (empty squares), and the average length of the spin domains (gray filled squares). Full circles represent the experimental zero field xT along the b-axis.
(
2008 American Chemical Society).
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complicated, since the chain crystallizes in the P 2
1
2
1
2
1
space
group with three twofold screw axes as symmetry elements,
and all the Dy(
III) ions are symmetry related. Viewing along the
chain direction of the crystal packing, shown in Fig. 13b, it is
clear that the two types of chains (A and B) are related by a 2
1
screw axis (in the ac plane). However, each of these chains is
generated by its own 2
1
screw axis (along the b axis). By
keeping these structural features in mind, the angle-resolved
magnetometry experimental data could be reproduced using a
combined theoretical approach, in which single Dy(
III) ion
anisotropy is described at the quantum-chemical level and the
thermodynamic properties of the coupled ions are computed
with a classical-spin Hamiltonian. Thus, these studies provide
methodological guidelines to rationalize the magnetic proper-
ties of RE-based SCMs. It should be mentioned that the
magnetic properties of RE–radical systems are determined by
the competition between nearest-neighbour and next-nearest-
neighbour interactions. It is very interesting that, when the
contribution of the radicals to the static properties is almost
negligible, they still actively contribute to j even when the
Dy(
III) ions are partially substituted with diamagnetic ions. In
other words, by doping with diamagnetic ions, the interactions
between the segments of the chains would be tuneable.
4.5 Spin-canting SCM constructed from 1D supramolecular p–
p interacting manganese(
III) corroles units
Recently, B.-W. Wang, S. Gao and co-workers reported
[Mn(tpfc)(MeOH)]?H
2
O(H
3
tpfc = 5,10,15-tris(pentafluorophe-
nyl)corrole), which was obtained by slowly evaporating a
MeOH solution of [Mn(tpfc)] under ambient conditions.
99
It
crystallized in the orthorhombic Pna2
1
space group. The
manganese ion has an elongated square-pyramidal structure
with four equatorial corrole nitrogen atoms and one axial
oxygen atom from a methanol molecule. As shown in Fig. 14a,
the magnetic chain lies in a zigzag fashion along the c axis via
p–p interactions between aromatic corrole rings of neighbour-
ing molecules. The mean distance between adjacent corrole N
4
planes is 3.7 Å. The angle between consecutive N
4
planes is
30.5u, and the angle of inclination of each axial Mn–O bond
with respect to the c axis is roughly 20u. The shortest
intrachain and interchain Mn
…
Mn separations were 6.69 Å
and 15.37 Å, respectively.
The static magnetic susceptibility data in the temperature
range of 20–300 K were fitted by assuming that all J values
between adjacent Mn(
III) ions were the same, giving best-fit
parameters of J/k
B
= 20.45 K, D/k
B
= 23.73 K, and g = 2.00. The
negative J values indicate that antiferromagnetic interactions
dominate. In the lower temperature region (T , 2.15 K), xT
increased with a decrease in the temperature, and magnetiza-
tion hysteresis with a coercive field of 400 Oe was observed at
0.5 K. The data were explained on the basis of 1D spin-canted
antiferromagnetism with h # 40u between neighbouring
anisotropy axes within the chain, which is consistent with
the structural features. Furthermore, frequency dependence of
the ac magnetic susceptibilities was observed in a zero dc field
(Fig. 14b), and t obeyed eqn (1) with D/k
B
= 16.1 K and t
0
= 1.8
Fig. 14 (a) Local spin vector (black arrows) and canted antiferromagnetic coupling between adjacent molecules along the chain in [Mn(tpfc)(MeOH)]?H
2
O. (b) ac
magnetic susceptibility at zero dc field. (c) Hysteresis loop recorded at 0.5 K. (d) Cole–Cole plots (points) and the fits to a generalized Debye model (solid lines) in the
temperature range of 1.2–1.6 K. (e) ln(xT) vs. T
21
plot. Inset: the linear region in the temperature region of 1.2–1.8 K. ( 2012 Wiley-VCH).
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6 10
28
s. Cole–Cole plots (Fig. 14d) were fitted by using the
generalized Debye model, resulting in a values in the range of
0.14–0.18. The values suggest a narrow distribution of t.As
shown in Fig. 14e, the ln(xT) vs. T
21
plot in the temperature
range of 1.2–1.8 K showed a linear correlation, confirming that
the slow relaxation dynamics arise from the 1D magnetic
correlation. It should be mentioned that the slope of 2.5 K
obtained from the linear fitting is smaller than the calculated
one (5.5 K) for estimating the exchange contribution using D
j
/
k
B
=4|J/k
B
|cos(h). This fact is similar to that observed for
[Mn(TPP)O
2
PHPh]?H
2
O, mentioned in section 4.3.
4.6 Carboxylate-bridged salen-type Mn
III
chain with alternating
ferromagnetic and canted antiferromagnetic interactions.
Recently, two new SCMs,
100
[Mn
2
(naphtmen)
2
(cea)]
(ClO
4
)?2Et
2
O?2MeOH?H
2
O(MnNA-1) and [Mn
2
(naphtmen)
2
(Hcea)](ClO
4
)
2
?MeOH (MnNA-2) (naphtmen
22
= N,N9-(1,1,2,2-
tetramethylethylene)bis(naphthylideneiminato) and Hcea = 9-
(2-carboxylethyl)adenine) were reported. They were synthe-
sized by using Hcea as a bridging ligand with an adenine
moiety, and a salen-type Mn(
III) dinuclear complex,
[Mn
2
(naphtmen)
2
(H
2
O)
2
](ClO
4
)
2
. In these SCMs, as shown in
Fig. 15a, two crystallographically independent quasi-planar
chelated Mn(naphtmen) units are bridged by a carboxylate
group in a syn–anti mode. The carboxylate-bridged Mn
III
dinuclear units are alternately linked by two kinds of weak
Mn
…
O interactions, resulting in a 1D chain structure with a
repeating [
…
Mn–(CO
2
)–Mn
…
(O
Ph
)
2
…
] unit. H-bonds in differ-
ent modes between adenine moieties from adjacent chains
were found in both MnNA-1 and MnNA-2, since the adenine
moiety was protonated in MnNA-2 but not in MnNA-1. These
well-defined interchain H-bonds, together with the counter-
anions and the disordered solvent molecules, effectively
separate the chains, with a closest interchain Mn
…
Mn
distance of 12.642(3) Å in MnNA-1 and 10.905(1) Å in MnNA-
2, in contrast to their analogues with no H-bonds and solvent
molecules between magnetic chains.
101
From static magnetic measurements on powder samples,
there are canted antiferromagnetic interactions (J
1
) passing
through carboxylate bridges, and ferromagnetic interactions
(J
2
) passing through phenolate bridges alternating along the
chains, as shown in Fig. 15b, leading to a 1D chain with non-
cancellation of anisotropic spins. Analysis of the data above 14
K by using a Heisenberg dimer model with S = 2 and D for each
Mn
III
ion (spin Hamiltonian H = 22J
1
S
1
S
2
+2D[S
z
2
2 S(S + 1)/
3], S
1
= S
2
= 2) afforded g = 1.99, J
1
/k
B
= 20.97 K, D/k
B
= 23.21 K
for MnNA-1 and g = 2.01, J
1
/k
B
= 21.48 K, D/k
B
= 21.46 K for
MnNA-2. The estimated canting angle in the carboxylate-
bridged dimer was 29u for MnNA-1 and 7.7u for MnNA-2. The
ac susceptibilities for MnNA-1 and MnNA-2 in a zero dc field
were frequency dependent. The data at low temperature in a
zero field were fitted with a generalized Debye model,
affording an a value in the range of 0.04–0.14 for MnNA-1
and 0.12–0.28 for MnNA-2, which indicate relatively narrow
distributions of t values. The temperature-dependent t were
fitted with an Arrhenius law, affording a D
exp
value of 34 K for
MnNA-1 and 30 K for MnNA-2, which are consistent with the
calculated values (D
cal
= 30 K for MnNA-1 and 32 K for MnNA-
2), using D
cal
= 4(|J
1
|cos(d)+J
2
)S
2
+|D|S
2
with J
2
= 0.2 K.
2
The
slope D
j
(5.0 K for MnNA-1 and 20.38 K for MnNA-2), obtained
from the linear analysis of ln( xT) vs. T
21
, is smaller than the
true exchange contribution (y11 K for MnNA-1 and 12 K for
MnNA-2) in these spin-canted SCMs. The results are roughly
explained in Fig. 15b, in which the spin vector S is
decomposed into an uncompensated part [S?sin(d/2)] (blue
dashed line) and a compensated part [S?cos(d/2)] (red dashed
line). As T was lowered, xT increased due to the 1D
ferromagnetic uncompensated component, whereas it mono-
tonically decreased due to the compensated component. The
experimentally observed xT behaviour for a powder sample is
affected by this competition, and it will monotonically
decrease with a decrease in T if d is too small to produce a
large enough uncompensated component, which is the case
for MnNA-2. On the other hand, ln(j) along the chain is
proportional to |J
1
|cos(d)+J
2
. Thus, analysis of xT values
seriously underestimates the exchange contribution in spin-
canted SCMs, especially in the case of a small d. The
observations on these two SCMs and the other spin-canted
SCMs mentioned in Section 4.3 and 4.5 clearly show that,
although a linear regime of ln(xT) vs. T
21
still exists, the slope
Fig. 15 (a) View of 1D magnetic chains organized by H-bonds between adenine
moieties (in green ellipses), shown on the right. (b) Diagram of the spin canting
in MnNA-1 and MnNA-2. The green arrows represent the spins of the Mn
III
ions,
which could be divided into uncompensated and compensated components,
shown as blue and red dashed arrows, respectively. The resulting net magnetic
moments (black arrows) in the AF dimers are parallel to each other in a 1D
arrangement. (c) Field-dependent relaxation times for MnNA-1 and MnNA-2 at
1.8 K. (b) ln(xT) vs. T
21
plots for MnNA-1 and MnNA-2 in applied dc magnetic
fields of 0–400 Oe. The solid lines were fitted to the linear portion of the data in
a zero field for MnNA-1 (red) and MnNA-2 (blue). (
2012 American Chemical
Society).
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could not be used to estimate the exchange contribution for
spin-canted SCMs.
Moreover, an anomaly was observed in the field-dependent t
of MnNA-1 at 1.8 K (Fig. 15c), implying that it has an
antiferromagnetically ordered ground state. ln(xT) vs. T
21
plots (Fig. 15d) and field-cooling curves of MnNA-1 in various
dc fields further confirmed that antiferromagnetic ordering
occurs below 2.2 K. For MnNA-2, no magnetic ordering was
found above 1.8 K. Since MnNA-1 and MnNA-2 have similar
intrachain topologies and interchain magnetic separations, d
is the key factor affecting the magnetic ordering phase
transition temperatures. The larger d in MnNA-1 causes the
divergence of xT of the chain to be much steeper than that of
MnNA-2, leading to a higher phase transition temperature in
MnNA-1 ( vide infra). In other words, this fact indicates that a
smaller d hinders 3D ordering in favour of SCM dynamics.
5. SCM dynamics and interchain interactions
In the Glauber model, no interchain interactions exist. In
1980, S. Z
ˇ
umer treated a simple kinetic model for the weakly
coupled linear Ising chains and found that the slow relaxation
dynamics were not affected by a perturbation from the weak
interchain interactions.
102
Larger interchain interactions
(usually antiferromagnetic in nature) should lead to a long-
range antiferromagnetic ordered state, and it has been
generally believed that slow relaxation of the magnetization
does not occur in this ordered phase. However, a few years ago,
C. Coulon and co-workers demonstrated unambiguously that
slow relaxation of the magnetization occurred in an anti-
ferromagnetic phase of SCMs by experimentally and theoreti-
cally studying the magnetic properties of [Mn
2
(5-
MeOsaltmen)
2
Ni(pao)
2
(phen)](PF
6
)
2
, which belongs to the
Mn
2
Ni SCM family.
103
More recently, H. Miyasaka, R. Cle
´
rac
and co-workers reported the effects of the interchain coupling
on the magnetization dynamics and on the occurrence of slow
magnetic dynamics in antiferromagnetic phases.
104
[Mn(3,5-
Cl
2
saltmen)Ni(pao)
2
(phen)]PF
6
(MnNi-PF
6
) and [Mn(5-
Clsaltmen)Ni(pao)
2
(phen)]BPh
4
(MnNi-BPh
4
), where 3,5-
Cl
2
saltmen
22
= N,N9-(1,1,2,2-tetramethylethylene)bis(3,5-
dichlorosalicylideneiminate), 5-Clsaltmen
22
= N,N9-(1,1,2,2-
tetramethylethylene)-bis(5-chlorosalicylideneiminate), pao
2
=
pyridine-2-aldoximate, and phen = 1,10-phenanthroline, have
similar alternating linear ferrimagnetic chain structures, with
a [–Mn
III
–ON–Ni
II
–NO–] repeating motif, as shown in Fig. 16a
and b. In MnNi-PF
6
, with a small PF
6
2
counteranion, there
were interchain p–p contacts between the saltmen phenyl
rings, whereas in MnNi-BPh
4
with a bulky BPh
4
2
counter-
anion, there were none (Fig. 16c and d).
Dc magnetic susceptibility data in the temperature range of
300–50 K revealed the presence of intrachain Mn
III
–Ni
II
Fig. 16 ORTEP views of the 1D chain motifs in (a) MnNi-PF
6
and (b) MnNi-BPh
4
with 50% probability thermal ellipsoids. Packing of (c) MnNi-PF
6
and (d) MnNi-BPh
4
:
the top and bottom figures are side and top views of the chains, respectively. The temperature-dependent ac magnetic susceptibilities for (e) MnNi-PF
6
and (f) MnNi-
BPh
4
in zero dc field at different ac frequencies in a 3Oe ac field. ( 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim).
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antiferromagnetic interactions with similar amplitudes
(21.5(2) K for MnNi-PF
6
and 21.1(2) K for MnNi-BPh
4
). ln(xT)
vs. T
21
plots were linear between 40 and 11 K with a D
j
value of
33.6 K for both complexes, supporting anisotropic Heisenberg
1D behaviour. D
A
values of y10 K for MnNi-PF
6
and 11.5 K for
MnNi-BPh
4
were determined from the field-dependent mag-
netization data at 1.8 K. The similar values of D
j
and D
A
show
that both chains have the same intrinsic magnetic properties.
Indeed, as shown in Fig. 16e and f, both components of the ac
magnetic susceptibility of both complexes showed strong
frequency dependence below y6 K, suggesting slow magnetic
dynamics with almost the same D values (55 and 54 K).
However, as shown in Fig. 16e, a transition from a
paramagnetic phase to an antiferromagnetic phase clearly
occurred at 9.4 K for MnNi-PF
6
but not for MnNi-BPh
4
.
Namely, MnNi-BPh
4
is a normal SCM, whereas MnNi-PF
6
is an
antiferromagnet of SCMs due to the stronger interchain
coupling caused by the interchain p–p contacts.
The unambiguous discovery of the coexistence of slow
dynamics and a long-range antiferromagnetic ordered phase is
a newcomer in this research field, and suggests a new
approach to design high temperature SCMs-based magnets.
Moreover, it shows that detailed static measurements are
crucial for assigning the "true" ground state of a magnetic
system.
104
In this sense, some of the previously reported
systems, which have been described as SCMs, likely have an
antiferromagnetic ground state. To date, many examples of
antiferromagnetically ordered phases of SCMs have been
reported, and the number is growing.
105–114,34
It is interesting
that some of them were obtained by dehydration, which
caused a structural transformation.
115–117
On the other hand, the fact that slow dynamics can occur
"robustly" in ordered phases shows that it is the interchain
coupling, not the apparent slow dynamics, which separates the
superparamagnetism-like properties of the SCMs from the
classical magnetic properties of 3D-ordered bulk magnets.
Reducing the interchain interactions is crucial in the rational
design of SCMs. However, it is well known that interchain
coupling (J9) cannot be eliminated completely in a real bulk
material because the chains are actually packed in a 3D crystal,
and the dipole–dipole interchain magnetic interactions always
occur. In this case, the susceptibility of the whole crystal, x
3D
,
above the magnetic phase transition temperature, T
3D
, is given
by:
118
x
3D
(T)=x
1D
(T)/[1 2 nJ9x
1D
(T)]
(10)
where x
1D
(T) is the susceptibility of an isolated chain, and n is
the number of the chains to which the J9 interaction extends.
For a given J9, a steeper increase in x
1D
with T leads to a steeper
divergence in x
3D
and, thus, a higher T
3D
. As shown by eqn (7),
x
1D
is proportional to j/T and, thus, is exponentially divergent
at low temperature. That is, the 1D j gives rise to not only the
SCM dynamics but also 3D ordering at a finite temperature, so
long as an interchain interaction exists. That is why a very high
ratio of |J/J9| is required to maintain a paramagnetic state for
an SCM.
One effective way to reduce the interchain interactions is to
increase the distance r between the magnetic chains by using
longer organic ligands, diamagnetic shells, bulk ions, larger
solvent molecules, and so on, since the exchange and dipolar
interactions vary with the distance according to r
210
and r
23
,
respectively.
119
Indeed, some SCMs were obtained by this
strategy from their analogues exhibiting 3D ordering. For
example, using the radical NITPhOPh instead of NIT(Et)
resulted in a longer interchain shortest metal–metal distance
(10.76 Å in [Dy(hfac)
3
(NIT(Et))] to 11.35 Å in
[Dy(hfac)
3
(NITPhOPh)]), and thus, 3D ordering occurred in
[Dy(hfac)
3
(NIT(Et))] at 4.3 K,
120
whereas [Dy(hfac)
3
(NIT(Et))]
exhibited SCM dynamics.
96
However, it should be emphasized
that the dipole interactions can occur over a long distance, and
more importantly, they can be enhanced via 1D correlation as
the magnetic moment of each segment exponentially increases
with a decrease in the temperature in the case of collinear
ferro- or ferrimagnetic systems. It was found that T
3D
could be
higher than 20 K in some Mn-porphyrin-based magnets,
121
in
which the ferrimagnetic chains are well separated in space (up
to 30 Å apart) such that only dipolar interchain coupling
dominates.
An alternative to decrease T
3D
while keeping SCM dynamics
is to slow down the divergence of x
1D
with T while maintaining
the 1D correlation for developing SCM dynamics. This strategy
has been employed in many non-collinear 1D magnetic
systems, consciously or unconsciously. For instance, in 2008,
Ishida and co-workers reported an analogous derivative in
which the methyl group of the NITPhO-R radical (CoPhOMe)
was substituted by the longer n-butyl group (CoPhO-nBu).
122
CoPhOMe showed SCM dynamics without 3D ordering,
whereas CoPhO-nBu ordered magnetically around 45 K.
Later, Sessoli proposed that the different mutual orientations
of the Co(
II) easy-axes, which form a trigonal helical chain in
CoPhOMe and a binary screw in CoPhO-nBu, respectively, as
shown in Fig. 17, caused the different magnetic behaviors.
123
In other words, the non-collinear spin arrangement in
CoPhOMe effectively reduces the interchain dipolar interac-
tion. As shown in section 4.6, this strategy is effective for
canted antiferromagnetic SCMs, namely, interchain dipolar
interactions and T
3D
were reduced by carefully reducing d.
100
This means that using non-collinear or spin-canting interac-
tions is advantageous for designing SCMs.
6. Some examples of multi-functional SCMs
In the past few decades, considerable efforts in field of solid
state chemistry and physics have been focused on the
development of multifunctional molecular materials, which
are compounds exhibiting more than one physical property
within the same molecule, and/or two or more different
molecules in a hybrid system.
124,125
A variety of these systems,
such as magnetism/electroconductivity,
126–128
magnetism/
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polarization,
129–132
and magnetism/proton conduction,
133–136
have been studied from the multifunctional molecular
material point of view. Moreover, the physical properties of
some of these showed brilliant cooperative and synergistic
effects. As a basic cooperative system, 1D SCM cooperative
systems are designable, and thus a variety of functionalities
can be rationally combined with SCM dynamics. In this
section, we present some examples combining SCM dynamics
with other interesting physical properties, such as porosity,
chirality, spin crossover (SCO), photo-switchable states, and so
on.
6.1 Microporous SCMs
Combining porosity and magnetism is a promising way to
obtain magnetic sensors, low-density magnets, or magnetic
separation media, because the magnetic flux within the pores
of the solid will selectively attract paramagnetic molecules
while repelling diamagnetic ones.
137
Notable examples of
microporous solids with a high magnetic ordering tempera-
ture have been reported,
137–142
although the porosity and
magnetic ordering are hardly compatible since magnetic
exchange requires short bridges between the spin carriers
while porosity relies on the use of long diamagnetic linkers.
143
Some of them have both porosity and SMM-like slow-
relaxation behaviour.
140
However, examples of microporous
magnets exhibiting SCM-like dynamics are still rare.
144
A
microporous material exhibiting SCM magnetism,
[Co
2
(H
0.67
bdt)
3
]]?20H
2
O(H
2
bdt = 5,59-(1,4-phenylene)bis
(1H-tetrazole)), which was obtained using a hydrothermal
reaction involving CoSO
4
?7H
2
O, Hbdt, HF, and H
2
O, was
reported by K. R. Dunbar, J. Zubieta and co-workers in 2008.
145
As shown in Fig. 18a–c, the complex is constructed of
[Co(tetrazolate)]
n
chains running parallel to the a axis and
linked through the phenyl tethers of the bdt ligands, resulting
in a 3D metal–organic framework with a considerable solvent-
accessible volume (about 47.1% of space), which is occupied
by H
2
O molecules. After removing these solvent molecules, the
3D framework remains stable and, thus, exhibits a micropor-
ous character with a BET surface area of 729 m
2
g
21
and a
Langmuir surface area of 833 m
2
g
21
(Fig. 18e). In addition, it
exhibited a considerable H
2
uptake (1.49% by weight at 120
kPa). Moreover, although the two cobalt centres in the chain
have identical coordination environments of six nitrogen
atoms, the ligand octahedra are rotated with respect to each
other. Thus, the tilting of the anisotropy axes of the
antiferromagnetically coupled neighbouring Co
II
ions gives
rise to an uncompensated magnetic moment, causing typical
slow SCM magnetic relaxation behaviour, with D/k
B
= 43.4 K, t
0
= 5.1 6 10
29
s, and a = 0.1 (Fig. 18d). However, the SCM
character is lost after desolvation, and only partly recovered by
resolvation.
Fig. 18 (a) Ball-and-stick representation of the [Co(tetrazolate)]
n
chains of [Co
2
(H
0.67
bdt)
3
]?20H
2
O. Views of the linking of chains through the phenyl tethers of the
bdt ligands in (b) the ab plane and (c) the ac plane. (d) Temperature dependence of ac magnetic susceptibility. (e) BET N
2
sorption isotherm at 77.4 K. ( 2009 Wiley-
VCH Verlag GmbH & Co. KGaA, Weinheim).
Fig. 17 Top: Schematic view of the chemical structure of the compounds
[Co(hfac)
2
NITPhO-R], where R = Me for CoPhOMe, and R = n-butyl for CoPhO-
nBu. Bottom: 1D arrangement of Co(
II) spin centers (blue ellipsoids) and radical
centers (orange spheres). (
2008 Wiley-VCH Verlag GmbH & Co. KGaA,
Weinheim).
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6.2 Chiral SCMs
Chiral compounds have been used in asymmetric catalysis,
non-linear optics, ferroelectrics, and of course magnetism.
Combining ferromagnetism and chirality can result in
magneto-chiral dichroism
146,130
and chiral magneto-structural
effects.
147–150
In enantiopure 1D SCMs, the large magnetic
moment of a 1D array of magnetic ions, which are also the
chiral centres, should give rise to strong coupling between
chiral and magnetic properties, providing excellent possibi-
lities for the study of the magneto-chiral dichroism effect.
However, reports of chiral SCMs are still rare.
151–153
One
effective way to obtain enantiopure chiral coordination
complexes is to employ enantiopure chiral ligands. For
instance, the first chiral SCM was prepared by using an
enantiomerically pure (M)-1,19-binaphtalene-2,29-bis(oxamate)
[(M)-binaba] ligand.
151
As shown in Fig. 19a, one
N,N9,O,O9-tetradentate site of (M)-binaba can trap a Cu
II
ion,
resulting in a dianionic copper(
II) complex. This complex was
further employed as a bisbidentate metalloligand to construct
a hetero-metal Cu
II
–Co
II
chain complex, Cu[(M)-
binaba]Co(DMF)
2
?DMF, by chelating solvated Co
II
ions
through the cis carbonyl oxygen atoms. This synthesis process
was named the "complex-as-ligand" strategy.
154
The resulting
chain compound crystallizes in the non-centrosymmetric
C222
1
space group with an enantiopure chiral chain running
along a 2
1
screw axis which is parallel to the [001] direction
(Fig. 19b). The absolute configuration of the entire crystal was
assigned using X-ray diffraction with synchrotron radiation,
and its chirality and enantiomerically pure nature were
confirmed using solid circular dichroism.
A xT vs. T plot showed typical 1D ferrimagnetic bimetallic
chain behaviour. A relatively strong intrachain antiferromag-
netic coupling between the Co
II
and Cu
II
ions through the
oxamato bridge (241.6 K) was estimated by fitting the
experimental data in the temperature range of 40–300 K. The
shortest interchain metal ion distance was determined to be
9.195(1) Å due to the effective shielding afforded by the bulky
binaphthalene groups, implying that the chains are magneti-
cally isolated. Indeed, the absence of a l-peak in the heat
capacity measurements on a powder sample ruled out the
occurrence of 3D magnetic ordering. Therefore, it was not
surprising that SCM slow-relaxation behaviour was observed
for this chiral complex at low temperature, since Co
II
ions
usually possess relatively strong uniaxial magnetic anisotropy
(Fig. 19d). By fitting the temperature-dependent t with an
Arrhenius law, the D/k
B
value of 13.2 K and t
0
value of 2.2 6
10
28
s were obtained.
Later, using this "complex-as-ligand" strategy, a series of
neutral oxamato-bridged M
II
Cu
II
(M = Mn and Co) chiral
chains were obtained.
152
All of the Mn
II
Cu
II
and Co
II
Cu
II
chains were found to exhibit ferrimagnetic behaviour, but only
two of the enantiopure Co
II
Cu
II
chains showed slow magnetic
relaxation at low temperature, which was ascribed to the
Fig. 19 (a) Scheme of the so-called "complex-as-ligand" synthesis strategy. (b) View of a fragment of the chain of Cu[(M)-binaba]Co(DMF)
2
?DMF. Hydrogen atoms
have been omitted for clarity. (c) Temperature dependence of xT of Cu[(M)-binaba]Co(DMF)
2
?DMF in a dc magnetic field. (d) Temperature dependence of x99 of
Cu[(M)-binaba]Co(DMF)
2
?DMF in a zero applied dc field. The inset shows the Arrhenius plot. ( 2010 The Royal Society of Chemistry).
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magnetic anisotropy of the HS Co
II
ions. Interestingly, no
evidence for SCM behaviour was found for the racemic
Co
II
Cu
II
chain analogue, because the SCM behaviour was
suppressed by significant antiferromagnetic interchain inter-
actions as a consequence of the much shorter interchain
Co
…
Co distance.
By using a similar enantiomerically pure ligand with a
binaphtalene group, the chiral SCM catena-[Ni
II
((R)-
pabn)][Fe
III
(tp)(CN)
3
]PF
6
?2MeOH ((R)-pabn = (R)-N
2
,N
20
-bis
(pyridin-2-ylmethyl)-1,10-binaphthyl-2,20-diamine and Htp =
hydrotris(pyrazolyl)borate) (NiFe-Rpabn?2MeOH) was obtained
by H. Oshio and co-workers in 2010.
153
This complex crystal-
lized in the chiral space group P2
1
2
1
2
1
with a Flack’s
parameter of 0.01(1), which indicated the enantiomerically
pure nature of the entire crystal. As shown in Fig. 20a, Fe
III
and
Ni
II
ions alternate along the chain and are bridged by cyanide
ions, resulting in a 1D chain with intrachain ferromagnetic
interactions (J/k
B
= 9.2 K) due to the magnetic orbital
orthogonality of the LS Fe
III
and Ni
II
ions. Frequency
dependence of the ac magnetic susceptibility was observed
at low temperature (inset of Fig. 20b), confirming the existence
of slow relaxation of the magnetization. SCM dynamics were
observed, with D/k
B
= 40.4 K, t
0
=96 10
211
s, and a = 0.35.
Further study on the possible magneto-chiral dichroism of
these chiral SCMs is required.
6.3 Hybrid salt exhibiting SCM and SCO behaviours
SCO complexes can switch magnetic spin states of a molecule
between high-spin and low-spin, which respond to external
perturbations such as temperature, light, pressure and
magnetic field in both the solid state and in solution.
155–159
The combination of a SCO complex as the magnetic switchable
part and another complex with other physical properties is
interesting. One of the most useful approaches to obtain
multi-component materials is assembling molecules into
stable and non-covalently-joined aggregates spontaneously.
For instance, a hybrid salt with SCM and SCO properties,
[Fe
II
{HC(3,5-Me
2
pz)
3
}
2
][Mn
III
(5-Brsalcy)Mo
V
(CN)
8
]?2MeOH?5H
2
O
(HC(3,5-Me
2
pz)
3
= tris(3,5-dimethylpyrazolyl)methane, and
5-Brsalcy
22
= rac-N,N9-(1,2-cyclohexanediylethylene)bis(5-bromo-
salicylideneiminate)), was obtained by assembling the SCM part
and the SCO part into aggregates (Fig. 21a).
160
The SCM part was
constructed with an alternating arrangement of the monocatio-
nic [Mn
III
(5-Brsalcy)]
+
and the trianionic [Mo
V
(CN)
8
]
32
,forminga
dianionic cyano-bridged linear-like [–Mn
III
–NC–Mo
V
–CN–] chain.
Thus the organized chain requires cationic parts to maintain
charge balance, and a cationic [Fe
II
{HC(3,5-Me
2
pz)
3
}
2
]
2+
part is
inserted into the[Mn
III
(5-Brsalcy)Mo
V
(CN)
8
]
22
chains (Fig. 21b).
Many hydrogen-bonding interactions between interstitial H
2
O,
MeOH, and non-coordinated cyanide groups separate the
[Mn
III
(5-Brsalcy)Mo
V
(CN)
8
]
22
chains due to the long pathways
through the hydrogen-bonding. Besides, there is no p–p
interaction in the crystal structure. In the dc magnetic properties
of this complex, upon cooling, the xT values decrease mono-
tonically with decreasing temperature, and reach a plateau at 60
K, the value of which remained constant over the temperature
range 6–60 K. Below that temperature, xT undergoes an abrupt
rise (Fig. 21c). In order to understand the magnetic anomaly of
this compound, the authors prepared the isostructural hybrid
salt [Cd
II
{HC(3,5-Me
2
pz)
3
}
2
][Mn
III
(5-Brsalcy)Mo
V
(CN)
8
]?2H
2
O,
where the paramagnetic Fe
II
ions were replaced by diamagnetic
Cd
II
ions to probe the intrinsic SCO behaviour of the Fe
II
centers
in the crystal lattice. Indeed, magnetic anomalies were not
observed in [Cd
II
{HC(3,5-Me
2
pz)
3
}
2
][Mn
III
(5-Brsalcy)Mo
V
(CN)
8
]?
2H
2
O, confirming that the unusual signal stems solely from
the Fe
II
centres. Namely, this magnetic behaviour clearly
indicates a SCO phenomenon. Compared to the other
[Fe
II
{HC(3,5-Me
2
pz)
3
}
2
]
2+
salt with a sharp SCO phenomenon,
the rather gradual and incomplete spin transition in this
compound, in which Fe
II
centres are well isolated from one
another, that is, weak cooperativity, consequently leads to
gradual SCO behaviour. Moreover, the hydrostatic pressure
affected the SCO behaviour of this compound (Fig. 21c). On the
other hand, HS Mn
III
(S
Mn
= 2) and LS Mo
V
(S
Mo
=1/2)ionsinthe
[Mn
III
(5-Brsalcy)Mo
V
(CN)
8
]
22
chain are connected in a ferromag-
netic manner. The intrachain interaction between two magnetic
centers in the chain was determined using the Seiden model to
be J
Mn–Mo
/k
B
= +4.0 K, with a small interchain magnetic
Fig. 20 ORTEP diagram of 1D chain (a), temperature-dependent dc (b) and ac (inset of b) magnetic susceptibilities of NiFe-Rpabn?2MeOH. ( 2010 The Royal Society
of Chemistry).
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interaction (zJ9/k
B
= +0.039 K). Ac susceptibility measurements for
this compound reveal a strong frequency dependence of both x9
and x99 components at lower temperature (Fig. 21d). Fits to
Arrhenius plots for this compound gave D
t
/k
B
= 23.2 K with t
0
=
1.23 6 10
29
s. In addition, Cole–Cole diagrams clearly showed
that only one relaxation process occurred, since the quasi-
semicircle shape could be fitted using the generalized Debye
model with a small a value of less than 0.21.
6.4 Photo-switchable {Fe
2
Co} double-zigzag SCMs
Switchable materials, whose physical properties can be
controlled by external stimuli such as exchange of guest
molecules, heating, light, pressure, electric field and so on, are
actively sought after for a variety of applications, such as
sensors and switches. Several switchable nanomagnets have
been reported. However, only a few examples of SCM proper-
ties being controlled by external stimuli, such as host–guest
interactions, mentioned in Section 6.1, pressure,
37,38
and light,
have been reported.
161,162
{[Fe(2,29-bipyridine)(CN)
4
]
2
Co
(4,49-bipyridine)}?4H
2
O(Fe
2
Co-bipy) with a photo-switchable
{Fe
2
Co} double-zigzag chain (Fig. 22a) was reported by O. Sato
and co-workers.
161
As shown in Fig. 22b, temperature-induced
metal-to-metal charge transfer (MMCT) from a high-tempera-
ture (HT) phase with Fe
III
LS
(S = 1/2) and Co
II
HS
(S = 3/2) ions to
a low-temperature (LT) phase with diamagnetic Fe
II
LS
(S =0)
and Co
III
LS
(S = 0) ions occurred. At low temperature,
irradiation caused a transformation from diamagnetic
Fe
II
LS
(m-CN)Co
III
LS
to metastable paramagnetic Fe
III
LS
(m-CN)Co
II
HS
units, which could be stable for long periods at
low temperature. In the latter state, slow magnetic relaxation
was found to co-exist with 3D ordering due to interchain
interactions (Fig. 22c). Later, T. Liu, O. Sato, C.-Y. Duan and co-
workers synthesized the analogue {[Fe(pzTp)(CN)
3
]
2
Co
(4-styrylpyridine)
2
}?2H
2
O?2CH
3
OH (pzTp = tetrakis(pyrazolyl)
borate) (Fe
2
Co-pzTp)withthesame{Fe
2
Co} double-zigzag chain
topology and similar temperature-induced MMCT (Fig. 22d and
e).
162
Since a larger organic ligand was used in Fe
2
Co-pzTp,the
shortest interchain metal–metal distance was 11.945 Å, which is
longer than the value of 8.849 Å in Fe
2
Co-bipy.Becauseofthe
effective magnetic separation provided by the larger organic
ligand, Fe
2
Co-pzTp behavesasanSCMwithout3Dorderingatlow
temperature after irradiation (Fig. 22f).
Fig. 21 (a) 1D alternating chain motif of [Fe
II
{HC(3,5-Me
2
pz)
3
}
2
][Mn
III
(5-Brsalcy)Mo
V
(CN)
8
]?2MeOH?5H
2
O and (b) its crystal packing. (c) Left: Temperature dependence
of xT and field dependence of magnetization at 2 K (inset). Right: Plots of xT versus T at different pressures. (d) Temperature dependence of ac susceptibility (x99:
imaginary part). (
2011 The Royal Society of Chemistry).
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6.5 Photo-induced SCM behaviour of a cyanide-bridged [CoFe]
chain with multifaceted switchable states
Very recently, an analogue of NiFe-Rpabn?2MeOH, [Co
II
((R)-
pabn)][Fe
III
(tp)(CN)
3
](BF
4
)?MeOH?2H
2
O(CoFe-Rpabn?MeOH?
2H
2
O), was reported by H. Oshio and co-workers. CoFe-
Rpabn?MeOH?2H
2
O exhibited multifaceted switchable
states.
163
As shown in Fig. 23a, the cobalt and iron building
blocks in CoFe-Rpabn?MeOH ?2H
2
O alternate along the chain
and are bridged by cyanide ions in a square-wave type of
structure, which is similar to that observed in NiFe-
Rpabn?2MeOH mentioned in Section 6.2. The corresponding
S-complex CoFe-Spabn?2H
2
O was obtained by using enantio-
pure (S)-pabn. Both complexes crystallize in the chiral space
group P2
1
2
1
2
1
with a Flack’s parameter of 0.01, indicating that
they are enantiopure, which was further confirmed using CD
spectroscopy (Fig. 23b). When a racemic mixture of (R)- and
(S)-pabn ligands was used, a non-chiral polynuclear complex
formed, crystallizing in the centrosymmetric space group
Fddd.
Structural analysis revealed that the solvent molecules in
CoFe-Rpabn?MeOH?2H
2
O are changeable. A single-crystal-to-
single-crystal transformation from CoFe-Rpabn?MeOH?2H
2
O
to CoFe-Rpabn?H
2
O occurred on drying in a N
2
flow. Drying
CoFe-Rpabn?MeOH?2H
2
O in air yielded CoFe-Rpabn?3H
2
O, in
which the methanol molecule was replaced by a water
molecule, and drying CoFe- Rpabn?3H
2
O in an inert atmo-
sphere caused desolvation to occur, yielding CoFe-Rpabn ?H
2
O.
Similar to the observations concerning Fe
2
Co-bipy and Fe
2
Co-
pzTp, mentioned in Section 6.4, a so-called electron-transfer
coupled spin transition (ETCST) between LT [Co
III
LS
Fe
II
LS
]to
HT [Co
II
HS
Fe
III
LS
] phases due to electron transfer from Fe
II
to
Co
III
ions, followed by spin-state transition at the Co sites, was
found in the temperature range of 240–320 K for these
complexes with different solvent molecules. Moreover, the
phase-transition temperature (T
1/2
) was found to be solvent-
molecule dependent (Fig. 23c) in the following order: CoFe-
Rpabn?3H
2
O>CoFe-Rpabn?MeOH?2H
2
O>CoFe-Rpabn?H
2
O.
The hydrogen bonds between the methanol/water molecules
and nitrogen atoms of the iron centre’s terminal cyanide
ligand increase the stability of the Fe(
II) state and shift the
hysteresis to a higher phase-transition temperature.
Temperature-dependent dc conductivity measurements
were performed on CoFe-Rpabn?H
2
O in its thermal ETCST
region (240–320 K), revealing a transition from an insulator
(LT phase) to a semiconductor (HT phase). Moreover, a large
thermal hysteresis of the conductivity was observed between
250 and 285 K, similar to that observed in the magnetic
susceptibility measurements (Fig. 23e). This fact indicates that
both the electric and magnetic switching arise from the same
thermo-induced ETCST.
In addition, ETCST can be induced by irradiation at low
temperature. At 5.0 K, CoFe-Rpabn?H
2
O in the LT diamagnetic
Fig. 22 (a) Side view of the 1D double zigzag chain and (b) temperature-dependent dc and (c) ac magnetic susceptibilities of Fe
2
Co-bipy ( 2010 American Chemical
Society). Side view of the 1D double zigzag chain (d), temperature-dependent dc (e) and ac (f) magnetic susceptibilities of Fe
2
Co-pzTp ( 2012 American Chemical
Society).
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LS state was irradiated with an 808 nm laser for ten hours,
resulting in a rapid increase in the xT value upon ETCST from
a diamagnetic LS state to a paramagnetic metastable HS state
(Fig. 23d). As the temperature was raised from 4.0 K, the xT
values decreased up to 72 K, indicating the presence of
intrachain ferromagnetic interactions, and they then
decreased to zero as the metastable HS state relaxed back to
the stable LS ground state at 78 K. For this metastable HS
state, the ac magnetic susceptibility data in the temperature
range of 1.8–5.0 K showed frequency-dependent in- and out-of-
phase signals composed of major and minor components.
Cole–Cole plots showed two semicircular regions, which is
indicative of two relaxation processes. By fitting the data for
these two relaxation processes with the Arrhenius law, D/k
B
=
65.5 K and t
0
= 3.1 6 10
210
s were determined for the major
species, and D/k
B
= 33.3 K and t
0
= 3.3 6 10
28
s were
determined for the minor species. The major species in the
photo-induced HS phase was an SCM, whereas the minor
species was ascribed to the slight fragmentation of the HS
species. This kind of double slow relaxation of the magnetiza-
tion has also been observed in a 1D assembly of {Dy(nitronyl
nitroxide)
2
} units,
164
an oxamato-bridged Cu
II
Co
II
chain,
165
a
cyanide-bridged W
V
Mn
III
chain,
166
and a 4,2-wavelike Fe
III
2
Co
II
heterobimetallic chain.
167
However, the mechanism is still not
clear. More detailed static measurements in non-zero static
magnetic fields are necessary to fully understand the double
relaxation process.
7. A brief perspective
Although there have been notable advances in the research on
SCMs, there are still many questions remaining, like what is
the relaxation mechanism for SCM-related chain compounds
with geometrical spin-frustration, how do SCMs organize on
substrates, and how can the physics of slow relaxing systems
involving several parameters beyond the pure Glauber model
be explained.
As mentioned in the introduction, increasing D and, thus,
T
B
for SCMs is easier than for SMMs. Is it really possible to
create a SCM with a high T
B
(> 77 K)? In order to obtain high D
for SCMs, both intrachain interactions and the anisotropy of
the magnetic unit must be increased. Some lanthanide ions
with high uniaxial anisotropies are good choices for preparing
SCMs with high T
B
, and some chain compounds involving 3d
and 4f ions were found to exhibit slow relaxation dynamics at
low temperature.
168–170
However, their slow relaxation
Fig. 23 (a) Heterometallic cyanide-bridged [CoFe] complex CoFe-Rpabn with a square-wave type of structure. (b) UV-vis spectra (black) of CoFe-Rpabn, the CD
spectra of CoFe-Rbapn?3H
2
O (red) and CoFe-Sbapn (blue). (c) Magnetic susceptibility data collected for CoFe-Rbapn?3H
2
O (red) and CoFe-Rbapn?1H
2
O (blue) in the
temperature region of 240–320 K. (d) Thermal magnetic susceptibility measurements (blue) and the susceptibility after light irradiation (red) as the temperature
increased. Inset: Frequency dependence of the out-of-phase magnetic susceptibility at low temperature after irradiation. (e) Temperature dependence of the dc
conductivity (red) and magnetic susceptibility (blue) of CoFe-Rbapn?1H
2
O in the thermal ETCST region.
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dynamics mainly resulted from the magnetic anisotropy of the
4f ions, not from 1D intrachain correlation, since the magnetic
exchange interactions between 4f ions and 3d or other 4f ions
through the common organic bridges are usually very weak
due to the localization of the 4f electrons. In 2011, J. R. Long
and co-workers reported two N
2
32
-radical-bridged dinuclear
Ln
III
(Ln = Gd, Dy) complexes,
171
in which a strong magnetic
exchange was found between Ln
III
ions due to the diffuse spin
of the N
2
32
radical bridge. The high anisotropy of the Dy
III
ion
gave rise to a Dy
III
SMM with a record T
B
of 8.3 K, inspiring a
new approach to constructing SCMs with higher T
B
. On the
other hand, on the basis of eqn (1), besides D, t
0
is also an
important factor determining t. However, theoretical and
experimental understanding of t
0
is limited, and its structure
relation is still unknown.
Interchain interactions must be considered for real
magnetic systems. Thus, the role of neighbouring chains is
crucial for understanding SCMs, although we are interested in
the dynamics of single chains arising from 1D correlation.
Since SCM dynamics can occur in the presence of magnetic
ordering, several interesting questions exist: how can "robust"
SCM dynamics occur in a magnetically ordered phase?
Moreover, what happens if T
B
is close to T
3D
? Finally, can an
interchain interaction be used as a perturbation for SCMs,
similar to SMMs? For a single chain, interchain interactions
with neighbouring chains could be regarded as an effective
field created from its neighbouring chains. In this sense, the
study of the dynamics of an SCM chain in a non-zero static
magnetic field is crucial for further understanding of the
relation between SCM dynamics and interchain interactions.
The effect of an applied magnetic field on t of ferromagnetic
SCMs, which was investigated theoretically and experimentally
by C. Coulon and co-workers in 2007,
172
will be very helpful in
answering these questions. In addition, the relation between
1D chain slow-relaxation dynamics and the interchain inter-
actions is important for distinguishing SCM and spin-glass-
like dynamics. In comparison with SCMs, a spin-glass under-
goes a phase transition from a paramagnetic state to a
disordered, frozen state of the magnetization, which results in
a relatively broad distribution of t. A spin-glass is usually
associated with randomness and/or spin-frustration, and thus,
is related to not only intrachain defects but also interchain
interactions.
55
Finally, combining SCM dynamics with other functional-
ities is a promising direction in which to expand this field. As
mentioned in section 6, there has been some success in
constructing SCMs with other functions, i.e., chirality,
porosity, photo-switchability, etc., and the possibility that the
SCM dynamics interact with these functions must be explored.
The cyanide-bridged [CoFe] chain with multifaceted switch-
able states discussed in section 6.5 is an inspiring example for
preparing multifunctional materials, in which these function-
alities interact with each other such that one functionality
switches the other. Since a variety of functionalities can be
easily introduced into 1D cooperative systems, a variety of
multifunctional materials combining SCMs with other func-
tionalities will be available in the near future. Thus, the
discovery of the next generation of multifunctional magnetic
materials is a real possibility.
Acknowledgements
This work was financially supported by a Grant-Aid for Science
(S) (Grant no. 20225003) from the Ministry of Education,
Culture, Sports, Science, and Technology, Japan. W. Z. is
grateful to JSPS for a postdoctoral fellowship.
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