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Cooling Field Dependence of Exchange Bias in Phase-Separated La0.88Sr0.12CoO3

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Yan-kun Tang
Yan-kun Tang
Yan-kun Tang
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Young Sun at Chinese Academy of Sciences
Young Sun
Zhao-Hua Cheng at Chinese Academy of Sciences
Zhao-Hua Cheng
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Abstract and Figures

We report the observation of exchange bias phenomena in the hole-doped perovskite cobaltite La0.88Sr0.12CoO3 in which a spontaneous phase separation occurs. When the sample is cooled in a static magnetic field through a freezing temperature, the magnetization hysteresis loops shift to the negative field. Moreover, the exchange bias strongly depends on the cooling field. These results highlight the important role of a glassy interface between the intrinsic inhomogeneous phases in a phase-separated system.
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Cooling field dependence of exchange bias in phase-separated
La0.88Sr0.12CoO3
Yan-kun Tang, Young Sun,a兲and Zhao-hua Cheng
State Key Laboratory of Magnetism and Beijing National Laboratory for Condensed Matter Physics,
Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
共Received 9 December 2005; accepted 13 May 2006; published online 31 July 2006兲
We report the observation of exchange bias phenomena in the hole-doped perovskite cobaltite
La0.88Sr0.12CoO3in which a spontaneous phase separation occurs. When the sample is cooled in a
static magnetic field through a freezing temperature, the magnetization hysteresis loops shift to the
negative field. Moreover, the exchange bias strongly depends on the cooling field. These results
highlight the important role of a glassy interface between the intrinsic inhomogeneous phases in a
phase-separated system. © 2006 American Institute of Physics.关DOI: 10.1063/1.2219698兴
I. INTRODUCTION
The exchange bias phenomenon refers to a shift of the
magnetization hysteresis loop away from zero field due to an
unidirectional anisotropy. This anisotropy is usually caused
by the exchange coupling at the interface between ferromag-
netic 共FM兲and antiferromagnetic 共AFM兲spin structures after
the system is cooled in a static magnetic field through the
Néel temperature of the AFM.1So far the research on ex-
change bias has been mainly focused on FM/AFM thin films
where a well defined and controllable interface exists.2,3 In
addition to FM/AFM interfaces, exchange bias has also been
observed in other types of interfaces involving a ferrimagnet
共FI兲共e.g., FI/AFM and FI/FM兲共Refs. 4 and 5兲or a spin glass
共SG兲phase 共e.g., FM/SG, AFM/SG, and FI/SG兲.6–9 These
interfaces are usually achieved through artificially designed
phase inhomogeneity, for example, by making artificial mag-
netic bilayers or mixing magnetic particles with a different
matrix 共granular systems兲. In this paper, we report the obser-
vation of exchange bias phenomenon in a spontaneously
phase-separated cobaltite in which intrinsic phase inhomoge-
neity plays a crucial role.
The hole-doped cobaltites La1−xSrxCoO3共LSCO兲have
been proved to exhibit a particularly clear form of phase
separation for a broad range of doping level xby many ex-
perimental evidences obtained using various techniques in-
cluding electron microscopy,10,11 nuclear magnetic resonance
共NMR兲,12,13 and small-angle neutron scattering 共SANS兲.14 It
has been well recognized that the phase separation in LSCO
is in the form of coexistence of FM metallic regions and
non-FM insulating regions. Furthermore, with this form of
phase separation, it has been proposed that the spontaneously
phase-separated LSCO is analog to the artificial granular
films that are composed of FM particles embedded in a
non-FM matrix.14 In this work, we have studied the magne-
tization hysteresis loops of a La0.88Sr0.12CoO3sample with
zero-field-cooling and field-cooling processes. Our results
demonstrate exchange bias phenomena that strongly depend
on the cooling field.
II. EXPERIMENTS
The La0.88Sr0.12CoO3sample was prepared with solid
state reaction method. A stoichiometric mixture of SrCO3,
Co3O4, and La2O3powders was well ground and calcined
twice at 800 and 950 ° C for 24 h. Then, the resulting powder
was pressed into pellets and sintered at 1100 and 1150 °C
for 24 h, respectively. X-ray diffraction patterns show that
the sample is single phase with rhombohedral structure. The
magnetization measurements were performed using a com-
mercial Quantum Design superconducting quantum interfer-
ence device 共SQUID兲magnetometer.
III. RESULTS AND DISCUSSION
Figure 1 shows the temperature dependence of magneti-
zation in a low magnetic field 共H=10 Oe兲with the zero-
field-cooled 共ZFC兲and field-cooled 共FC兲processes for
La0.88Sr0.12CoO3. At 240 K, the magnetization starts to in-
crease rapidly with decreasing temperature. Below 240 K,
the ZFC and FC magnetizations separate with each other.
These results imply that the onset of FM ordering within the
a兲Author to whom correspondence should be addressed; electronic mail:
youngsun@aphy.iphy.ac.cn
FIG. 1. Temperature dependence of magnetization with ZFC and FC
processes for La0.88Sr0.12CoO3. The inset illustrates the freezing temperature
of 50 K with ZFC process for La0.88Sr0.12CoO3.
JOURNAL OF APPLIED PHYSICS 100, 023914 共2006兲
0021-8979/2006/100共2兲/023914/3/$23.00 © 2006 American Institute of Physics100, 023914-1
Downloaded 01 Aug 2006 to 159.226.36.159. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
clusters occurs at Tc=240 K. As illustrated in the inset of
Fig. 1, the ZFC magnetization exhibits a peak around 50 K
共Tf兲and a wide shoulder around 170 K. The wide shoulder
could be due to the intercluster interactions, and the sharp
peak around Tfindicates a collective freezing of magnetic
moments.15
Figure 2 shows the hysteresis loops of La0.88Sr0.12CoO3
at 5 K with both the ZFC and FC processes. For the ZFC
process, the sample was cooled in zero magnetic field from
360 to 5 K. For the FC process, the sample was cooled in
10 kOe magnetic field from 360 to 5 K. Then the hysteresis
loops were measured between ±50 kOe. While the ZFC
magnetization has a normal hysteresis loop centered at zero
field, it is clear that the FC hysteresis loop shifts to the nega-
tive field. The magnitude of the shift is known as exchange
bias HE=−共HC1+HC2兲/2, where HC1and HC2are the left
and right coercive fields, respectively. With the coercive
fields obtained from the FC loop, we get the value of ex-
change bias, HE⬇500 Oe. The FC hysteresis loop also has
an increased coercivity, HC=兩HC1−HC2兩/2 =6640 Oe, com-
pared to the coercivity of 5430 Oe for the ZFC loop. All
these behaviors are the characteristics of exchange bias
phenomenon.
The appearance of exchange bias in La0.88Sr0.12CoO3in-
dicates that an unidirectional anisotropy is built up after the
sample is cooled in a magnetic field. In some compounds,
such as Gd2CuO4,16 a shift of hysteresis loops is also ob-
served, which is interpreted as the presence of unidirectional
anisotropies due to Dzyaloshinskii-Moriya interactions.
However, it seems that this mechanism is not appropriate for
our sample considering the large magnetization of our
sample and the shape of the initial magnetization curve. We
argue that this unidirectional anisotropy in La0.88Sr0.12CoO3
is due to interfacial exchange interaction associated with
phase separation. As we already mentioned above, the phase-
separated LSCO is analogous to the artificial granular films
that are composed of FM particles embedded in a non-FM
matrix. It has been well known that a spin-disordered
interface/surface layer is usually formed when a FM particle
is embedded in a non-FM matrix8or the magnetic particle is
small enough 共the finite size effect兲.7Such spin-disordered
interfaces/surfaces lead to exchange bias in many artificial
granular systems.9,17 Similarly, we believe that spin-
disordered regions could exist at the interfaces between the
FM clusters and the non-FM matrix in phase-separated
LSCO. In fact, 59Co NMR and magnetic relaxation experi-
ments have revealed that SG regions coexist with FM and
non-FM regions in LSCO.12,13,18 Therefore, the exchange
bias in LSCO can be qualitatively understood with the fol-
lowing picture. When the sample is cooled in the presence of
a magnetic field, an energy favorable spin configuration at
the interface will be selected through the exchange interac-
tion between the spin glass regions and the FM clusters. The
exchange interaction competes with thermal fluctuation. As a
result, the interfacial spin configuration is frozen below the
freezing temperature and becomes more stable at lower tem-
peratures. When the measuring field is reversed, the spins of
FM particles start to rotate. However, the spin configuration
at the interface may remain unchanged. Therefore, the spins
at interface exert a microscopic torque on the FM spins to
keep them in their original position. Thus, the field needed
to reverse the FM spins will be larger because an extra
field is required to overcome the microscopic torque. As a
result, the magnetization hysteresis loop shifts toward the
negative field. Based on this picture, exchange bias in
La0.88Sr0.12CoO3can be qualitatively interpreted in terms of
the interfacial coupling associated with intrinsic phase inho-
mogeneity. We also measured the FC hysteresis loops at
60 K 共above Tf兲. No exchange bias is observed, which is
consistent with the above picture. We note that this effect
was also recently observed in other phase-separated perov-
skite oxides,19,20 which indicates that the exchange bias as-
sociated with phase separation is an intrinsic property.
We then studied the influence of cooling field on the
exchange bias in La0.88Sr0.12CoO3. The sample was cooled
down from 360 to 5 K under different applied fields 0
艋Hcool艋50 kOe. After the temperature was stable, the field
was set to H=50 kOe and the hysteresis loop was measured.
Figure 3 shows the cooling field dependence of the loop
parameters, exchange bias HE, remanent magnetization Mr,
coercivity HC, and magnetization at H=50 kOe M50 kOe.At
small cooling field, Mr,HC, and HEincrease with increasing
cooling field whereas M50 kOe remains nearly constant. The
constant M50 kOe indicates that the proportion of FM clusters
changes little at small cooling fields. With the increase of
cooling field, the alignment degree of the moments of FM
clusters along a preferential direction is enhanced, which re-
duces the effect of averaging of the anisotropy due to ran-
domness. Therefore, Mr,HC, and HEincrease with the in-
crease of cooling field. At high cooling field, Mrtends to be
saturated but HCand HEdecrease with increasing cooling
field. The decrease in HEis accompanied with the increase in
M50 kOe. This indicates that the growth of FM clusters in high
cooling field could contribute partly to the decay of HE.At
high cooling field, not only the alignment degree of the mo-
ments of FM clusters is enhanced but also the size of FM
clusters increases. As the FM clusters grow up, exchange
FIG. 2. Hysteresis loops of La0.88Sr0.12CoO3at 5 K measured after zero-
field cooling and field cooling in 10 kOe field. Inset: enlarged view of the
central region of the loops.
023914-2 Tang, Sun, and Cheng J. Appl. Phys. 100, 023914 共2006兲
Downloaded 01 Aug 2006 to 159.226.36.159. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
bias is reduced. This effect is qualitatively analogous to that
in FM/AFM thin films where exchange bias is inversely pro-
portional to the thickness of the FM layer and becomes neg-
ligible when the FM layer is too thick.1Meanwhile, the spins
at the interfaces between the FM clusters and the surround-
ing non-FM matrix also tend to orient along the field direc-
tion when the Zeeman coupling overcomes the interfacial
exchange coupling. Both the growth of FM clusters and the
diminishment of spin disorder at the interfaces weaken the
exchange bias.
IV. CONCLUSIONS
In summary, we have discovered exchange bias phenom-
ena associated with phase separation in LSCO. The exchange
bias is strongly dependent on cooling field. These results
suggest that, in a spontaneously phase-separated system, the
exchange coupling at the interfaces between the FM regions
and the surrounding non-FM phase may create an exchange
anisotropy when the sample is cooled in a static magnetic
field.
ACKNOWLEDGMENTS
The authors are grateful to Professor Jian-wang Cai for
helpful discussion and Professor Tong-yun Zhao for assis-
tance in experiments. This work was supported by the State
Key Project of Fundamental Research and the National
Natural Science Foundation of China.
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FIG. 3. The cooling field dependence of 共a兲exchange bias HE,共b兲remanent
magnetization Mr,共c兲coercivity HC,and共d兲magnetization at 50 kOe
M50 kOe at 5 K.
023914-3 Tang, Sun, and Cheng J. Appl. Phys. 100, 023914 共2006兲
Downloaded 01 Aug 2006 to 159.226.36.159. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
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  • Apr 2020
  • J ALLOY COMPD
Effects of Manganese (Mn) substitution on the magnetic and dielectric properties of spinel phase Co1−xMnxCr2O4 (0.0 ≤ x ≤ 1) nanoparticles (NPs) have been studied. X-ray diffraction and Fourier transform infrared spectroscopy analysis showed the normal spinel structure for all the samples. Average crystallite size showed increasing trend with Mn doping and lies in the range 32–47 nm. The undoped CoCr2O4 NPs displayed a typical phase transition from paramagnetic (PM) to ferrimagnetic (FiM) state at TC = 100 K along with conical spiral magnetic state at TS = 27 K and lock-in transition state at TL = 13 K. The TC, TS and TL values were shifted towards lower temperatures with increasing Mn content and finally an antiferromagnetism (AFM) is obtained for MnCr2O4 NPs at TN = 20 K. A magnetic phase diagram was developed which showed the presence of different phases in these nanoparticles and attributed it to change in magnetic interactions with increasing Mn content. Saturation magnetization (MS) showed an increasing trend with Mn content due to the large magnetic moment of Mn ions. Nanoparticles showed an overall increasing trend of the dielectric constant with Mn concentration which is due to possible hopping of Mn²⁺ to Mn³⁺ and as well as increasing average crystallite size with Mn doping. In summary, increase in Mn doping revealed reduction in TC, TS, and TL values, an increasing MS trend, an AFM phase introduction and improved dielectric properties for Co1−xMnxCr2O4 NPs.
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Magnetic Structured Nickel Core-Shell @ Silica/PMMA Nanocomposites from Synthesis to Applications
Article
Full-text available
  • Jul 2020
  • J INORG ORGANOMET P
Incorporating Ni@SiO2 nanoparticles on poly-methyl methacrylate (PMMA) can alter electrical, optical, and magnetic properties of Ni nanoparticles to be used for energy storage applications, photo electronic devices and spintronic applications. The Ni@SiO2/PMMA nanocomposite samples are prepared by casting method. The morphology of the prepared nanoparticles was examined through high resolution transition electron microscope revealed the formation of SiO2 coating on ni nanoparticles. Furthermore, the topography of nanocomposites was characterized by the field emission scanning electron microscope. We investigated the formation of crystalline phase of Ni nanoparticles through X-ray diffraction. The Complex dielectric permittivity, electrical conductivity, electric modulus and impedance spectra of the PNC films were investigated in the frequency range from 0.1 Hz to 10 MHz. The real and imaginary parts of the permittivity decrease with increasing frequency due to an increase in Ni@SiO2 content. All the nanocomposites showed relatively low conductivity values and high impedance that could be used for nano-dielectrics. UV–Vis spectrophotometer was used to measure optical properties such as transmittance, and absorbance at normal incidence in the wavelength range of 200–1100 nm. The transmittance was found to decrease while the absorbance increases with increasing Ni@SiO2 nanoparticles. The indirect optical band gap of the composite films was calculated, and it was sharply decreased. Magnetic hysteresis plots at room temperature of composites Ni@SiO2/PMMA were studied. All samples demonstrate ferromagnetic behavior with well pronounced magnetic hysteresis.
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F – -Induced Tunable Perovskite Structure and Impressive Spin Polarization in SrCoO 3
Article
  • Oct 2019
Tailoring the reciprocity between the charge and spin degrees of freedom in perovskites is effective in designing and realizing novel spintronic functionalities. Recently, it has been proposed that this type of quantum correlation can be intensively engineered via structure modulation, such as introducing protons into SrCoO3 and SmNiO3. To this end, we describe a new structure modulating strategy via F⁻ substitution, e.g., the perovskite oxyfluoride, SrCoO2.9-δF0.1 (SCOF-0.1), against hexagonal Sr2Co2O5. Co K-edge X-ray absorption spectra reveal that a large amount of oxygen vacancies and a desirable structural distortion are generated with the evolution of the hexagonal to cubic structure induced by F⁻ substitution at a low dose. Distinctively, SrCoO2.9-δF0.1 demonstrates a much enhanced magnetic transition temperature of up to 350 K and realizes a remarkable exchange bias effect (HEB=1745 Oe) at room temperature that is driven by the strong interplay among the structure, oxygen vacancies, and charge and spin degrees of freedom. This work describes a simple F⁻ substitution approach to design and regulate spintronics, which leads to a complex correlation among the order parameters by modulating oxygen vacancies.
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Glassy magnetic behavior in the phase-separated perovskite cobaltites
Article
Full-text available
  • Jan 2006
In this paper we demonstrate that the origin of the glassy behaviors (memory, aging, etc.) in the phase-separated perovskite cobaltites cannot be simply ascribed to intercluster interactions as the phase-separated manganites can. Instead, our study indicates that both the intercluster interactions and a spin glasslike phase contribute to the glassy behaviors. Thus, this study distinguishes the picture of phase separation between manganites and cobaltites.
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Structural details and magnetic order of La1-xSrxCoO3 (x ≤ 0.3)
Article
Full-text available
  • Jan 1999
The crystallographic structure and the magnetic order of the distorted perovskite La1-xSrxCoO3 (0.10≤x ≤0.30) has been studied by neutron diffraction, high-resolution electron microscopy, and magnetic-susceptibility measurements. The results give direct evidence for an inhomogeneous distribution of the Sr2+ ions and the segregation of the material into hole-rich ferromagnetic regions and a hole-poor semiconducting matrix at lower values of x. The holes introduced by Sr doping are attracted to the Sr2+ ions where they stabilize to lowest temperatures an intermediate-spin state at neighboring trivalent cobalt. The antibonding e electrons so stabilized increase the mean unit-cell volume and are delocalized over the cobalt atoms of the cluster where they couple the localized t5 configurations ferromagnetically. Long-range ferromagnetic order between clusters is realized even for Sr doping as low as x=0.10. The transition to a spin glass state is observed only for Sr concentrations smaller than 0.10. The volume of a hole-rich cluster grows in a magnetic field, and the origin of the large negative magnetoresistance observed near Tc for 0.15 ≤ x ≤ 0.25 appears to be due to a growth of the clusters to a percolation threshold. For x=0.30, the σ* band of the intermediate-spin state below Tc is at the threshold of a transition from itinerant to polaronic conduction and, above Tc, the system transforms smoothly to a cluster state.
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Alternating current magnetic susceptibility measurements in La1-xSrxCoO3 (X≤0.30) below 300 K
Article
  • Apr 1997
A dynamical magnetic susceptibility study on La1−xSrxCoO3 samples obtained by a coprecipitation method is reported for x ⩽ 0.30. For x<0.20 differences between zero field cooled and field cooled dc magnetic susceptibility appear at a temperature Ta below the Curie point, TC ≈ 240 K, as well as a magnetic freezing point at a temperature Tb<Ta. Alternating current magnetic susceptibility shows two maxima at these temperatures, which is interpreted as the evidence of different interaction processes between ferromagnetic clusters mediated by a matrix of changing spin-state Co3+ ions. For x ≥ 0.20 an unique blocking process seems to take place due to the percolation of the ferromagnetic clusters, making unimportant the contribution of the matrix.
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Exchange Bias
Article
  • Feb 1999
  • J MAGN MAGN MATER
We review the phenomenology of exchange bias and related effects, with emphasis on layered antiferromagnetic (AFM)–ferromagnetic (FM) structures. A compilation of materials exhibiting exchange bias and some of the techniques used to study them is given. Some of the applications of exchange bias are discussed. The leading theoretical models are summarized. Finally some of the factors controlling exchange bias as well as some of the unsolved issues associated with exchange bias are discussed.
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Exchange bias associated with phase separation in the perovskite cobaltite La1-xSrxCoO3
Article
  • May 2006
  • PHYS REV B
We report the observation of exchange bias phenomena in the hole-doped perovskite cobaltites La1-xSrxCoO3 ( x=0.12 , 0.15, 0.18, and 0.30) in which a spontaneous phase separation occurs. When the La1-xSrxCoO3 samples are cooled in a static magnetic field through a freezing temperature, the magnetization hysteresis loops exhibit both horizontal and vertical shifts. We also observed training effect of the exchange bias, which can be interpreted by a spin configurational relaxation model. Moreover, exchange bias in La1-xSrxCoO3 is strongly dependent on the measuring field and the cooling field due to the influence of magnetic field on the relative proportion of the coexisting phases. These results suggest that the intrinsic phase inhomogeneity in a spontaneously phase-separated system may induce an interfacial exchange anisotropy.
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A study of the magnitude of exchange biasing in [111] Fe 3O 4/CoO bilayers
Article
  • Jul 1995
  • J MAGN MAGN MATER
Exchange biasing has been studied for a series of [111]-oriented Fe3O4/CoO bilayers with constant Fe3O4 and varying CoO thicknesses. The magnitude of exchange biasing in this oxidic system is compared with the value calculated under the assumption of nearest-neighbour exchange at a flat and magnetically uncompensated interface.
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Spin dynamics in La1-xSrxCoO3
Article
  • Dec 2003
  • Phys Rev B
The spin dynamics of Sr-doped cobaltite La1-xSrxCoO3 (x=0.14 and x=0.4) has been investigated in both zero magnetic field and high field by NMR. The results are consistent with microscopically phase-separated regions of ferromagnetic and nonferromagnetic materials. Nuclear spin-lattice and spin-spin relaxation in the ferromagnetic regions is attributed to fluctuating hyperfine fields produced by double exchange between Co ions. The linear temperature dependence of the correlation time, obtained from the data analysis, suggests that lattice excitations modify the double-exchange process as the temperature is raised. In the nonferromagnetic regions, a distribution of nuclear spin-lattice relaxation times is found. It is likely that low-frequency fluctuating localized moments, such as small spin clusters, in spin-glass regions provide the relaxation mechanism for both the spin-glass and low-spin (S=0) regions. A simple model involving these ideas can account for the stretched exponential nuclear magnetization recovery in the nonferromagnetic regions, and permits an estimate to be made of the mean size of low-spin regions.
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Magnetothermal Behavior of Nanoscale Fe/Fe-Oxide Granular System
Article
  • Nov 2002
The low-temperature magnetic properties of samples obtained by cold-compacting core-shell Fe/Fe oxide nanoparticles have been investigated, and their dependence on the structure, composition, and mean particle size D has been discussed. Samples with different D, varying from 6 to 15 nm, and different Fe to oxide ratio were analyzed by means of transmission electron microscopy, x-ray diffraction, and magnetization measurements in the 5–300-K temperature range. The results support the existence of a low-temperature (below T1∼20K) frozen, disordered magnetic state, characterized by a strong exchange coupling between the structurally disordered, spin-glass-like oxide matrix and the Fe nanocrystallites. Above T1, a different regime is distinguished, characterized by the coexistence of a quasi-static, ferromagnetic component, given by the Fe particles, and a relaxing component, represented by regions of exchange-interacting spins of the oxide matrix. As the temperature is increased above T1, the net moments of the oxide magnetic regions become able to thermally fluctuate and they tend to be polarized by the Fe particle moments. The above picture well accounts for the composition, particle size, and thermal dependence of the coercivity and of the exchange field, which strongly increase with reducing temperature in correspondence with the freezing of most of the moments of the oxide magnetic regions.
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Field-Cooling Dependence of Exchange Bias in a Granular System of Fe Nanoparticles Embedded in an Fe Oxide Matrix
Article
  • Aug 2004
  • PHYS REV B
The exchange bias properties of a granular system composed of Fe nanoparticles (mean size ˜6nm ) embedded in an Fe oxide matrix have been studied. The effect of the cooling field on the exchange field, coercivity and remanent magnetization at T=5K has been investigated. The observed variations are explained in terms of interfacial exchange coupling between a ferromagnetic phase (the Fe particles) and a disordered magnetic phase (the oxide matrix), whose spin configuration is strongly affected by the cooling field.
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Finite Size Effects in Antiferromagnetic NiO Nanoparticles
Article
  • Aug 1997
  • PHYS REV LETT
Antiferromagnetic NiO nanoparticles exhibit anomalous magnetic properties, such as large moments, and coercivities and loop shifts of up to 10 kOe. This behavior is difficult to understand in terms of 2-sublattice antiferromagnetic ordering which is accepted for bulk NiO. Numerical modeling of spin configurations in these nanoparticles yields 8-, 6-, or 4-sublattice configurations, indicating a new finite size effect, in which the reduced coordination of surface spins causes a fundamental change in the magnetic order throughout the particle. The relatively weak coupling between the sublattices allows a variety of reversal paths for the spins upon cycling the applied field, resulting in large coercivities and loop shifts.
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