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ARTICLE
Received 11 Jun 2015 |Accepted 17 Dec 2015 |Published 28 Jan 2016
Magnetic ground state of an individual Fe2þion
in strained semiconductor nanostructure
T. Smolen
´ski1, T. Kazimierczuk1, J. Kobak1, M. Goryca1, A. Golnik1, P. Kossacki1& W. Pacuski1
Single impurities with nonzero spin and multiple ground states offer a degree of freedom that
can be utilized to store the quantum information. However, Fe2þdopant is known for having
a single nondegenerate ground state in the bulk host semiconductors and thus is of little use
for spintronic applications. Here we show that the well-established picture of Fe2þspin
configuration can be modified by subjecting the Fe2þion to high strain, for example,
produced by lattice mismatched epitaxial nanostructures. Our analysis reveals that high strain
induces qualitative change in the ion energy spectrum and results in nearly doubly degenerate
ground state with spin projection S
z
¼±2. We provide an experimental proof of this concept
using a new system: a strained epitaxial quantum dot containing individual Fe2þion.
Magnetic character of the Fe2þground state in a CdSe/ZnSe dot is revealed in
photoluminescence experiments by exploiting a coupling between a confined exciton and the
single-iron impurity. We also demonstrate that the Fe2þspin can be oriented by
spin-polarized excitons, which opens a possibility of using it as an optically controllable
two-level system free of nuclear spin fluctuations.
DOI: 10.1038/ncomms10484 OPEN
1Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland. Correspondence and requests for materials
should be addressed to T.S. (email: Tomasz.Smolenski@fuw.edu.pl) or to T.K. (email: Tomasz.Kazimierczuk@fuw.edu.pl) or to W.P.
(email: Wojciech.Pacuski@fuw.edu.pl).
NATURE COMMUNICATIONS | 7:10484 | DOI: 10.1038/ncomms10484 | www.nature.com/naturecommunications 1
Spin configurations of transition metal ions in various host
semiconductors have been well-established already a few
decades ago1–8. It has been found that ions such as
Cr2þ(d4), Mn2þ(d5), Co2þ(d7) exhibit nonzero spin in their
ground states, which makes them useful in spintronics9,10. For
example, spin degree of freedom can be utilized in memories
based on giant magnetoresistance11,12 or to process information
using spin-transistor13. A fundamental requirement for
manipulation of the spin is the availability of at least two
different spin levels in the considered system. However, the
ground state of the Fe2þ(d6) ion in zinc-blende or wurtzite II–VI
semiconductors like ZnS, ZnSe, CdTe or CdSe has been found to
be nondegenerate14–22 with average spin hS
z
i¼0 and thus termed
nonmagnetic23.ToinduceFe
2þmagnetic moment, high-magnetic
field has to be applied, as for Van Vleck paramagnets24,25.
The physics of the transition metal ions has been recently
brought back into the spotlight owing to the possibility to access
the properties of single dopants26–33. The main motivation of
optoelectronics with single-dopant atoms—solotronics34—is
related to its potential for quantum information processing.
Among other achievements, optical orientation35–40,
readout26,27,32,41 and coherent precession42,43 of a single
magnetic ion spin were demonstrated. Current development of
the field benefits greatly from the fundaments of the early
findings. However, the physics of the transition metal ions in
semiconductor nanostructures goes far beyond the limits
established in the earlier works on bulk materials.
Here we demonstrate that, contrary to the well-established
knowledge on a Fe2þion in the semiconductor matrix, it is
possible to qualitatively change its low-field behaviour from
nonmagnetic to magnetic (by magnetic we consider a state which
splits linearly upon application of a magnetic field of magnitude
equivalent to ion-carrier exchange interaction, that is, of up to
1 T). In particular, we show that the magnetic behaviour of the
Fe2þion can be induced by placing such an ion in a highly
strained nanostructure. In order to elucidate this fact, we analyse
the Fe2þenergy spectra for the cases of weak and strong strain,
showing a clear hierarchy of the energy scales, relevant both to
zinc-blende and wurtzite structures. The magnetic behaviour of
the Fe2þion is experimentally evidenced by analysing the
magnetic field dependence of the photoluminescence spectrum of
an individual CdSe/ZnSe quantum dot (QD) containing a single
Fe2þimpurity. The nonzero spin ground state of the Fe2þion
even at low magnetic field opens the possibility of using it as a
two-level system in quantum information technology9.
Results
Fe2þenergy spectrum in bulk and in a strained nanostructure.
The dominant effect defining energy spectrum of a transition
metal ion in the bulk semiconductor is the crystal field2,20.Fe
2þ
has configuration d6, which means that the d-shell electrons have
combined orbital angular momentum of L¼2 and spin of S¼2.
The crystal field affects only orbital part of the wave function and
splits five orbital states of the ion into two subspaces: twofold
degenerate 5Eand threefold degenerate 5T
2
, with 5Ebeing lower
energy in T
d
symmetry (Fig. 1a). For Fe2þin CdSe or ZnSe this
splitting is about 10|Dq|E0.3 eV (refs 6,22,44). Thus, the 5T
2
level
is not populated even at room temperature and the properties of
the Fe2þion are defined only by the states in the 5Esubspace.
These states are not affected by a static Jahn–Teller distortion, as
it was shown for many Fe-doped semiconductors5,14–16.
Consequently, the second effect in order of strength is the
spin–orbit interaction lLS. It results in splitting of 5Elevels into
five equidistant groups, as shown in Fig. 1a. The value of the
splitting K
LS
is determined by the effective strength lof the
spin–orbit interaction and the crystal field splitting 10|Dq|
according to K
LS
¼6l2/10|Dq|E2 meV (refs 19,21). The
presence of a dynamical Jahn–Teller effect or application of
additional stress in experimentally accessible range results in only
small shifts of those energy levels and can be treated
perturbatively21,22,45–48. In any case, the lowest energy group
consists of a single nondegenerate state, which determines the
nonmagnetic character of the Fe2þion ground state.
We find that strong structural strain of a QD changes hierarchy
of the Fe2þenergy scales known from the bulk. The dominant
effect is still the crystal field, but the second effect becomes the
biaxial strain. It lifts orbital degeneracy of the 5Esubspace,
splitting it into Ejiand |yistates of symmetries corresponding to
single-electron dx2y2and dz2orbitals, respectively (Fig. 1b). The
ordering of those states is determined by the sign of the strain,
which, given the CdSe/ZnSe lattice mismatch, has compressive
character. Qualitatively, such strain pulls the tetrahedral lattice
bonds away from x–y plane (for details, see Supplementary Fig. 1)
and thus lowers the energy of the Ejiorbital while increasing the
energy of the |yione (as schematically depicted in Figs 1c,d).
More strict analysis leading to the same-level ordering is
presented in Supplementary Note 1. This analysis reveals also
that the strain-induced splitting of the Fe2þstates significantly
exceeds the strength of the spin–orbit interaction, which
determines the spin part of the wave function. The spin–orbit
interaction contributes to the energy of spin states of E
jiorbital in
the second order. It favours high-spin states according to the
effective spin Hamiltonian DS2
zwith Do0 (for details, see
Supplementary Note 2). In this approximation, (within the
discussed second order of the lLS interaction) the ground state is
doubly degenerate with the spin part of S
z
¼±2. Since the integer
spin of the Fe2þion does not warrant exact Kramers degeneracy,
further analysis and experimental results presented below reveal
that two low-energy states are in fact separated by small energy,
but still they can be easily split by an external magnetic field, in a
clear contrast to previously described case of the Fe2þembedded
in bulk semiconductor.
Photoluminescence of a strained QD with a single Fe2þion.
The experiment evidencing actual behaviour of the Fe2þion in a
strained nanostructure is carried out on a number (430) of
single QDs, each incorporating an individual iron ion. Such
structures are presented here for the first time. Self-assembled
zinc-blende CdSe:Fe QDs in ZnSe barrier are grown using
molecular beam epitaxy. Low-temperature (down to 1.5 K) pho-
toluminescence experiments on individual QDs are performed in
a setup providing spatial resolution of 0.5 mm without the need
for mesas or masks. More details on sample preparation and
experiment are given in the Methods section.
As expected for random character of low-density doping, in the
same sample we find QDs incorporating single Fe2þions and
undoped QDs for reference purposes. Photoluminescence spectra
corresponding to both of these cases are shown in Fig. 2.
Figure 2a presents a typical spectrum of an undoped QD. The
spectrum exhibits all standard features of epitaxial QDs32,49–51.
The sharp emission lines originate from recombination of
different excitonic complexes, including neutral exciton (X),
negatively charged exciton (X ) and biexciton (2X). The X and
2X lines are split owing to anisotropic part of electron-hole
exchange interaction. In the case of QD shown in Fig. 2a this
splitting yields d
1
¼370 meV, which is a typical value for
self-assembled CdSe/ZnSe QDs50,51. On the other hand, the
charged exciton line does not exhibit any splitting, in accordance
with the Kramers rule for systems with odd number of fermions.
In comparison, introduction of a single Fe2þion into a QD
leads to distinctive changes in the photoluminescence spectrum,
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10484
2NATURE COMMUNICATIONS | 7:10484 | DOI: 10.1038/ncomms10484 | www.nature.com/naturecommunications
as shown in Fig. 2b. The emission lines still correspond to
recombination of the same excitonic complexes, however, their
structure is determined by the s,pdexchange interaction with
the resident ion. The main effect is a strong splitting of each of
the observed emission lines. It is particularly striking for the
typically degenerate charged exciton, but also for the neutral
exciton it is significantly stronger than the typical value of d
1
.
Such a physical picture is similar for a large number of studied
Fe-doped QDs, as proven by distribution of measured s,pd
exchange splittings presented in the inset of Fig. 2b. The presence
of such s,pdsplitting is a direct confirmation of the magnetic
character of the Fe2þion. It originates from the fact that the
Fe2þspin may be aligned either parallel or anti-parallel to the
exciton angular momentum, which would not be possible in the
case of nonmagnetic ground state.
Magneto-photoluminescence of a QD with a single Fe2þion.
In order to provide the final proof of the magnetic character of
the Fe2þion in a QD, we measured the evolution of the X
photoluminescence spectrum in external magnetic field applied
along the growth direction (quantization axis of the magnetic ion
and QD excitons). Typical results obtained in spolarization of
detection are shown in Fig. 3a. We note that the observed pattern
is quite similar to the one obtained for InAs/GaAs QD containing
a complex of a single Mn2þion and a bound hole27,31,39,52,53,
despite different electronic and spin configurations.
Magneto-photoluminescence results in Fig. 3a seem complex,
however, they originate from quite simple behaviour of the initial
and final energy levels of the transitions, as illustrated in Fig. 3c.
First effect of the magnetic field is the Zeeman splitting between
S
z
¼2 and S
z
¼2 states of the Fe2þion. Unfortunately, the
photoluminescence spectrum does not show this splitting
directly, since, in general, exciton recombination does not affect
the ion spin state and thus the energy of emitted photon does not
depend on the ion Zeeman splitting. However, in the vicinity of
the level anticrossings the Fe2þspin states are mixed and this
selection rule is relaxed. Indeed, data in Fig. 3a feature several
weaker lines in the anticrossing range (that is, 0–2 T). Before we
discuss the origin of the anticrossings, let us analyse the behaviour
of these weak lines, in particular the cross-like feature. The two
cb
Spin–orbit
coupling
5D
(25)
(15)
(10)
10|Dq |
Crystal
field
Spin–orbit
coupling
(5)
(5)
(5)
(10)
ΔS(5T2)
ΔS(5E)
QD
strain
(2)
(2)
3|D|
|D| (1)
a
5D
(25)
5E5E
5T25T2
(15)
(10)
10|Dq |
Crystal
field
(1)
KLS (3)
KLS (2)
KLS (3)
KLS (1)
Fe
2+
in bulk
Fe2+ in a nanostructure
|〉,|〉
d
|〉
|〉
|〉
dx2–y2 corresponding to |
〉
dz2 corresponding to |〉
[ ··· ]
[ ··· ]
[ ··· ]
[ ··· ]
Figure 1 | Energy levels of the Fe2þion in crystal environment. Energy spectra of the Fe2þion in (a) a bulk zinc-blende semiconductor and
(b) a nanostructure with a strong in-plane compressive strain. Numbers in parentheses denote the degeneracy of the energy levels. Six-electron Fe2þ
orbital states split by the QD strain are denoted as E
ji
,|yi,|zi,|Ziand |xiafter Vallin et al.16 (these orbital states can be also referred to as single-electron
dorbitals of corresponding symmetries, as described in Supplementary Table 1). (c,d) Visualization of |yiand E
jiorbital states forming the 5Esubspace
with single-electron dz2and dx2y2orbitals of the same symmetries. Arrows schematically mark the shift of the neighbouring anions owing to the strain
of the QD.
Nonmagnetic QD
2,390 2,400 2,410
Energy (meV)
QD with a single Fe2+ ion
Photoluminescence
Intensity
Photoluminescence
Intensity
2,360 2,370 2,380
Energy (meV)
12
8
4
0
0.0 0.4 0.8 1.2
Number of dots
Δs,p–d (meV)
2X
X
X–
X–
2X
X
1
1
a
b
1
2 + Δ2
s,p–d
1
2 + Δ2
s,p–d
Δs,p–d
Figure 2 | Photoluminescence spectra of CdSe/ZnSe QDs with and
without a single Fe2þion. (a) A photoluminescence spectrum of a typical
CdSe QD showing X, X and 2X lines. Neutral complexes exhibit
anisotropic splitting of d
1
¼370 meV. (b) A photoluminescence spectrum of
a QD with a single Fe2þion. The photoluminescence lines are split mainly
owing to s,pdexchange interaction between confined carriers and the
d-shell electrons of the ion. For both spectra continuous background was
subtracted. Inset is a histogram of the s,pdexchange splitting of the
Xemission line. The cutoff at D
s,pd
t0.3 meV is because of our
selection procedure, which is limited by the resolution of our experimental
setup—only dots with larger zero-field splitting were tested in the magnetic
field to verify the presence of the Fe2þion.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10484 ARTICLE
NATURE COMMUNICATIONS | 7:10484 | DOI: 10.1038/ncomms10484 | www.nature.com/naturecommunications 3
crossing lines correspond to transitions involving the change of
the ion spin from S
z
¼±2toS
z
¼2. The splitting between
them depends almost linearly on the magnetic field with a slope
of about 0.84 meV T 1. More precise fitting including non-
linearity owing to proximity of the anticrossings gives slightly
larger value of 0.92 meV T 1. Taking into account that |DS
z
|¼4
for both the initial and the final states, this slope corresponds to
g-factor g
Fe
¼2.0, exactly as expected for the Fe2þspin.
Let us now focus on the nature of the observed anticrossings.
The first, relatively weak anticrossing occurs around 0 T. It is a
signature of the fact that the S
z
¼±2 states of the Fe2þion are
not perfectly degenerate, but are split by a small energy a,as
shown in Fig. 3c. This splitting varies between different studied
dots and its typical value yields about 50 meV. Consequently, this
splitting is much smaller than the X–Fe2þexchange or Zeeman
energy above 1 T. Such a splitting arises because of the spin–orbit
coupling, acting either in the fourth order, or lower orders in the
presence of an in-plane anisotropy of the QD27,53,54 (for details,
see Supplementary Note 2). In both cases, the resulting zero-field
eigenstates of the Fe2þare 1ffiffi2
pSz¼2
ji
Sz¼2
ji
ðÞ.
The second anticrossing around 2 T is closely related to the first
one. It occurs when the effective magnetic field acting on the
Fe2þspin in the presence of the s-emitting exciton vanishes.
Since exchange field of this exciton increases the energy of the
state corresponding to S
z
¼2 ion spin projection (Fig. 3c), the
anticrossing of the Fe2þion is effectively shifted from 0 T to a
higher field.
Finally, there is also the third, stronger anticrossing around
±9 T. This anticrossing is observed for both negative and
positive magnetic field (or equivalently: in sþand s
polarization), which clearly indicates that it is owing to mixing
of the exciton part of the total wave function. Indeed, the states
involved in the anticrossing correspond to s-and sþ-emitting
excitons coupled with S
z
¼2 spin projection of the Fe2þion
("+;2
ji
and #*;2
ji
). The anticrossing occurs when the
excitonic Zeeman effect reduces the ion-related exchange splitting
of the involved states and the anisotropic electron-hole exchange
interaction becomes dominant source of the splitting. It should be
noted that this anticrossing does not mix different states of the
Fe2þion and thus in this range of magnetic field the optical
recombination preserves the spin of the ion.
In order to quantitatively verify our interpretation of the
magneto-photoluminescence results, we performed a numerical
simulation of the expected field dependence of X photolumines-
cence spectrum. The simulation is based on the spin Hamiltonian
of an ion-exciton system described in the Methods section. As
8
4
0
–4
–8
X experiment X model X– experiment
8
4
0
–4
–8
8
4
0
–4
–8
B (T)
B (T)
B (T)
2,403 2,404 2,403 2,404 2,381 2,382
Energy (meV)Energy (meV)Energy (meV)
6
3
0
0.0 0.2 0.4
Number of dots
⏐Ae/3Ah
⏐
Fe2+
Fe2+
0Bc
E
a
a
Δs,p–d
Δs,p–d
⎜↑⇓,–2〉
⎜↑⇓,+2〉
⎜↑⇓,+2〉
⎜↑⇓,–2〉
⎜–2〉
⎜+2〉
⎜+2〉
⎜–2〉
B
–––
3Ah/2gFeB
Ae/2gFeB
|/|
abd
e
c
Figure 3 | Magneto-optical spectroscopy of X and X in a QD with a single Fe2þion. Magnetic field dependence of the photoluminescence spectrum of
aX:(a) experimental data and (b) simulation assuming strain-induced magnetism of the Fe2þion, as described in the text. The spectra were measured
and simulated in scircular polarization. (c) Schematic field dependence of the initial and final energy levels of the X recombination together with the
indicated s-polarized X optical transitions observed in photoluminescence measurements. The upper pair of levels corresponds to "+
ji
exciton coupled
with the ion spin (where mand +represent the spin projection of the electron and the heavy hole on the growth axis, respectively), while the bottom pair
represents the energies of the ion states in the empty dot. The excitonic transitions preserving (altering) the ion spin projection are marked with solid
(dashed) arrows. (d) Magnetic field evolution of a X photoluminescence spectrum measured in scircular polarization. Red and orange dashed lines
indicate magnetic field values B¼3A
h
/(2g
Fe
m
B
) and B¼A
e
/(2g
Fe
m
B
), respectively, which correspond to the end points of the cross-like feature in
Xmagneto-photoluminescence. (e) Histogram of experimentally determined ratio of ion-electron to ion-hole exchange integrals for the Fe2þin a QD.
Dashed line indicates the ratio |a/b|ofs-d and p-d exchange constants known from the bulk Cd
1x
Fe
x
Se.
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10484
4NATURE COMMUNICATIONS | 7:10484 | DOI: 10.1038/ncomms10484 | www.nature.com/naturecommunications
shown in Fig. 3b, such a model reproduces all features of the
experimental results. The simulation correctly captures even the
observed thermalization of the ion spin at increasing magnetic
field by taking into account the effective Fe2þspin temperature
of 15 K. Such a good overall agreement provides a strong proof of
correct identification of all relevant effects.
In the experiments reported so far we have used the X to probe
the properties of the Fe2þion. To determine both exchange
integrals between the ion and each confined carrier (the electron
and the hole), one needs to probe the Fe2þion using single
carriers. Experimentally, it is realized with a negatively charged
exciton (refs 27,53), the magneto-photoluminescence of which is
presented in Fig. 3d. In the initial state of X recombination the
Fe2þinteracts only with the hole (owing to spin-pairing of the
two electrons), while in the final state the ion interacts only with
the remaining electron. As such, the Fe2þion experiences an
exchange field in both of these states, which reduces a mixing
between the Fe2þspin states S
z
¼±2atB¼0 T. To bring these
two spin states into an anticrossing, one needs to apply a
magnetic field, which compensates either ion-hole or ion-electron
exchange interaction (in the initial or final state of the Xoptical
transitions). Such values of the magnetic field correspond to the
end points of the cross-like feature in X magneto-photolumi-
nescence, which is thus shifted with respect to previously
considered case of the X, as seen in Figs 3a,d. Indeed, the
cross-pattern for the X begins at zero magnetic field, while the
end points of this pattern for the X are given by B¼A
e
/(2g
Fe
m
B
)
and B¼3A
h
/(2g
Fe
m
B
), where A
e
and 3A
h
denote the ion-electron
and ion-hole exchange integrals, respectively. Both of these
integrals might be thus directly determined based on the
magnetic field dependence of the X photoluminescence
spectrum. The results of such an analysis performed for a
number of QDs are presented in Fig. 3e. They evidence that ion-
hole exchange constant clearly dominates over one of ion-
electron interaction. It can be directly related to the differences in
values of bulk Cd
1x
Fe
x
Se s-d and p-d exchange constants55
N
0
a¼0.26 eV and N
0
b¼1.53 eV. In particular, the ratio A
e
/
3A
h
should be equal to ratio a/bif only the local densities of
electron and hole wave functions at the Fe2þsite in the QD are
equal. Centring of the results in the Fig. 3e around a marked a/b
ratio is fully consistent with this prediction.
It is noteworthy that the field evolution of X photolumines-
cence spectrum does not feature an anticrossing at high-magnetic
fields, which arises for the X because of the electron-hole
exchange interaction. This observation is a direct confirmation
that such an interaction affects neither the initial nor the final
state of the X recombination.
Optical orientation of the spin of a single Fe2þion. Zero-field
splitting of the Fe2þspin may raise concerns whether the iron
spin can be controlled optically. In order to address this issue we
performed a proof-of-concept measurement of the optical
orientation35–40. Experimentally, we induce a polarization of the
Fe2þspin by injecting spin-polarized excitons to the QD under
circularly polarized non-resonant excitation (at E¼2.54 eV). The
spin state of the Fe2þion is monitored using the relative
intensities of the photoluminescence lines of the 2X. The
advantage of using the 2X instead of the X as a probe of the
ion spin state lies in the fact that the 2X is a spin-singlet and
therefore allows us to circumvent the issue of excitonic spin
relaxation40.
The intensities of the 2X lines corresponding to different Fe2þ
spin states vary depending on the polarization of the excitation, as
shown in Fig. 4a presenting the 2X photoluminescence spectra
measured at B¼4 T. Such a variation can be explained only by
the optically induced change in the occupation of the Fe2þstates
and thus is a direct evidence of an optical control over the Fe2þ
spin. The comparison of the two spectra allows us to quantify the
effect of the polarization of the excitation. In the presented case,
switching the polarization from sþto schanges the mean spin
of the Fe2þby DhS
z
iE0.4, that is by about 10%. Similar
efficiency was observed previously for non-resonant pumping of
the Mn2þspin in CdSe QDs40 and its value is most likely limited
by depolarization of the itinerant carriers during the energy
relaxation towards the ground state in a QD.
Figure 4b shows the dependence of the optical spin orientation
efficiency on the magnetic field. It exhibits a pronounced close-to-
linear increase, which is similar as in the case of previously
studied Mn2þion40. However, for the Fe2þwe also observe a
sharp drop of the orientation efficiency at B¼0 T. This effect is a
result of a mismatch between s±-polarized pumping and the
mixed character of Fe2þspin states in the absence of the
magnetic field. In other words, the ion spin-polarization induced
by the exciton cannot be maintained after the recombination,
since the Fe2þspin undergoes oscillations between two mixed
eigenstates at B¼0 T. Consequently, future experiments on zero-
field optical manipulation of the Fe2þspin should use a resonant
initialization protocol and temporally resolved spin readout37,42
rather than rely on continuous-wave non-resonant pumping with
circularly polarized light.
Discussion
All the presented results clearly show that the structural strain of
the QD induces magnetic character of the Fe2þion in its ground
state. Thus, a CdSe QD with a single Fe2þion joins other
solotronic QD systems like CdTe, InAs and CdSe QDs doped
with single manganese or cobalt ions26,27,32, which grant optical
access to the spin degree of freedom of a single transition metal
ion. In contrast to rich, but vulnerable S¼5/2 Mn2þspin in
CdTe and CdSe QDs, the Fe2þin a CdSe dot can be regarded as
a robust two-level system. Its spectroscopic properties are very
similar to InAs QD doped with a single Mn2þion
antiferromagnetically coupled to a hole27,31,39,52,53. In both
cases, the magnetic field dependence of the excitonic photo-
2,373.0 2,373.5
Energy (meV)
01234
Magnetic field (T)
0%
5%
10%
Efficiency of
Fe2+ optical orientation
Photoluminescence
Intensity
exc +
exc –
Sz
Fe = +2
Sz
Fe = –2
ba
Figure 4 | Optical orientation of the Fe2þspin. (a) Photoluminescence
spectra of the 2X measured in spolarization at B¼4 T using circularly
polarized excitation of different helicity (solid lines represent multi-peak
Gaussian fits to the measured spectra). Upon sþ-polarized excitation the
emission line corresponding to the Fe2þspin projection S
z
¼2 is weaker,
while the two lines corresponding to S
z
¼2 are stronger as compared
with the s-polarized excitation. The lines corresponding to S
z
¼2 are
mixed owing to anisotropic fine structure of the exciton, which does not
affect the Fe2þspin. (b) Efficiency of optical orientation of the Fe2þspin as
a function of the magnetic field (the data points were averaged over several
measurements of the 2X photoluminescence spectra at each field).
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10484 ARTICLE
NATURE COMMUNICATIONS | 7:10484 | DOI: 10.1038/ncomms10484 | www.nature.com/naturecommunications 5
luminescence spectrum is a result of an interplay between the
uniaxial anisotropy of the ion spin, its zero-field splitting and the
Ising coupling with the excitons. This observation is valid
regardless of the differences between these systems, such as
different electronic configuration of the ions or differences in
possible mechanisms leading to the zero-field splitting of the ion
states. The latter differences stem mostly from different effective
spins of the two ions: S¼2 in case of the Fe2þand J¼1 for the
Mn2þ-hole complex. As such, the Fe2þground states are
associated with a larger difference DS
z
¼4, and thus they cannot
be coupled by an in-plane anisotropy S2
xS2
yacting in the first
order. Practical conclusion from this consideration is that the
Fe2þspin is promising as a two-level system since it offers
additional protection from the perturbations in the environment.
On top of that, CdSe/ZnSe QDs with single Fe2þions, in contrast
to the systems mentioned earlier, can be grown free of any
nuclear spins: the natural iron has nuclear spin I¼0 and all the
elements of the host lattice have significant abundance of isotopes
without nuclear spins. Altogether these properties make the Fe2þ
in CdSe QDs an ideal system for quantum information
technology. However, the importance of our results is not
limited to this particular system. It is a general example of the fact
that even well-established textbook knowledge of energy
spectrum of various dopants should be carefully re-evaluated in
the world of semiconductor nanostructures.
Methods
Sample preparation.Samples with self-assembled zinc-blende CdSe:Fe QDs in
ZnSe barrier are grown using molecular beam epitaxy double-chamber system
manufactured by SVT Associates. About two monolayers of CdSe:Fe are deposited
without any growth interruptions on 1.5-mm thick ZnSe buffer grown on GaAs
(100) substrate. QDs are covered by a 50-nm thick ZnSe cap layer. Iron doping
density is adjusted in order to optimize the probability of finding a QD with exactly
one Fe2þion.
Experiment.Photoluminescence experiments on individual QDs are performed in
a micro- photoluminescence setup providing a spatial resolution of 0.5 mm. Low-
temperature (down to 1.5 K) photoluminescence is excited non-resonantly either at
405 or 488 nm in the case of the measurements of optical spin orientation of the
Fe2þion. The sample is placed in the split-coil superconducting magnet producing
a magnetic field of up to 10 T either in Faraday or Voigt configuration.
Modelling of magneto-photoluminescence.The X magneto-photoluminescence
from Fig. 3a is quantitatively described by a model of a X inside a QD with a single
Fe2þion. Our simulation is based on the standard procedure of finding the
eigenstates of the exciton complex and the empty (that is, without the exciton) QD
and subsequent calculation of allowed optical transitions. For simplicity, we assume
that the spatial part of excitonic wave function is not substantially modified by the
magnetic field and restrict our analysis to the spin degree of freedom. The possible
initial states of X–Fe2þcomplex are found by diagonalization of the Hamilto-
nian26,27,32:
Hi¼AeSrþ3AhSzJzþ
2d0szJzþd1sxJxþsyJy
þ
þmBBg
FeSzþgeszþghJz
ðÞ
þgB2þHFe ;
where Sand rare the spin operators of the Fe2þand the electron, while Jis
effective 1/2 spin operator in the two-dimensional subspace of lowest-energy heavy
hole states. The first two terms in Hidescribe the s,pdexchange interaction
between the iron ion and confined carriers55–59 with A
e
and 3A
h
being the ion-
electron and ion-hole exchange integrals. The next two terms represent isotropic
and anisotropic contributions to the electron-hole exchange interaction49 with
characteristic energies of d
0
and d
1
. The parameters g
Fe
,g
e
and g
h
are g-factors of
the Fe2þion, electron and hole, respectively, while gis the excitonic diamagnetic
shift constant. The last term HFe is the Hamiltonian of the Fe2þion leading to
energy spectrum as in Fig. 1b. Within the lowest-energy orbital state subspace, the
spin part of HFe might be expressed as
HFe ¼DS
2
z1
3SSþ1ðÞ
a
48 S4
þþS4
;ð2Þ
where the first term leads to a splitting of three spin subspaces corresponding to
different |S
z
|, while adenotes a small splitting between the two Fe2þlowest energy
spin states 1ffiffi2
pSz¼2
ji
Sz¼2
ji
ðÞ. This splitting is directly determined
from the photoluminescence studies and yields typically about 50 meV. Conversely,
the value of |D| is much larger, as we find no spectral signatures of |S
z
|o2 states
in our experiments. A quantitative estimation of the value of this splitting
3Do2.5 meV is obtained in Supplementary Note 3 based on the measurements
of X magneto-photoluminescence in Voigt configuration (the results of which
are shown in Supplementary Fig. 2).
The oscillator strengths of X optical transitions are calculated between
eigenstates of the Hamiltonian Hiand the Hamiltonian Hf¼H
Fe þmBBgFeSz
describing the final state of the recombination (that is, an empty QD). The relevant
parameters of both of these Hamiltonians are found by fitting the field dependence
of the photoluminescence spectrum. Additional parameter E
0
is introduced later to
plot the simulation in the same energy range as the experimental results. The
optical spectrum is simulated as a series of peaks at energies corresponding to
possible transitions between possible initial and final states. The intensity of a given
peak is the product of calculated oscillator strength and the Boltzmann factor
corresponding to thermalization of the ion spin at an effective temperature of 15 K.
For the sake of the presentation, the peaks are plotted as gaussians with FWHM of
0.1 meV. Strictly speaking, such procedure gives us the low-power absorption
spectrum, but it is also similar to the photoluminescence spectrum if only the
exciton states have the same lifetime and if it is shorter than the thermalization of
the excited state.
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Acknowledgements
We thank A. Twardowski, T. Dietl and M. Nawrocki for helpful discussions as well as
M. Dobrowolski and M. Koperski for experimental assistance in the first measurements.
This work was supported by the Polish National Science Centre under decisions DEC-
2011/01/B/ST3/02406, DEC-2011/02/A/ST3/00131, DEC-2013/09/B/ST3/02603, DEC-
2013/09/D/ST3/03768, DEC-2012/05/N/ST3/03209 and DEC-2012/07/N/ST3/03130, by
the Polish Ministry of Science and Higher Education in years 2012–2016 as research
grant ‘Diamentowy Grant’, by the Polish National Centre for Research and Development
project LIDER, and by the Foundation for Polish Science through MISTRZ programme.
One of us (T.S.) was supported by the Foundation for Polish Science through START
programme. This study was carried out with the use of CePT, CeZaMat and NLTK
infrastructures financed by the European Union—the European Regional Development
Fund within the Operational Programme ‘Innovative economy’ for 2007–2013.
Author contributions
W.P. grew the samples. T.S., J.K., A.G. and W.P. performed the magneto-optical
experiments. T.S., T.K. and J.K. analysed the data under P.K. and W.P. supervision. T.S.,
T.K. and M.G. calculated the effect of strain on energy levels of Fe2þion. T.S., T.K. and
W.P. prepared the manuscript in consultation with all authors.
Additional information
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How to cite this article: Smolen
´ski, T. et al. Magnetic ground state of an individual Fe2þ
ion in strained semiconductor nanostructure. Nat. Commun. 7:10484 doi: 10.1038/
ncomms10484 (2016).
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