Ferrimagnetic State Research Articles

Magnetic evolution from the superparamagnetism in nanospinel chromites Cd1−xCoxCr2O4 (0 ≤ x ≤ 1.0)

Magnetic properties of the spinel-type Cd1−xCoxCr2O4 (0 ≤ x ≤ 1.0) nanocrystals are systematically studied. Complementary results of the inductively coupled plasma optical emission spectroscopy (ICP-OES) and the dispersive X-ray spectroscopy (EDX) indicate cations redistribution with increased Cr concentration from the nanoparticle core to the surface. Powder X-ray diffraction (XRD) reveals an obtained single spinel phase of average crystallite size of 7–10 nm that is in consistence with TEM particle size. The lattice constant exhibits a general decrease by incorporating the smaller Co atoms, however its behavior violates Vegard’s law. An observed kink anomaly in the lattice constant behavior at x ~ 0.4 is attributed to the cations redistribution and further preferred site occupations. Static magnetization and AC susceptibility measurements reveal competitive magnetic phases in the solid solution nanocrystals. A superparamagnetic state of the noninteracting and single domain CdCr2O4 nanoparticles expands first to higher blocking temperatures at x < 0.4 before it evolves to a core collinear ferrimagnetic (FIM) state with coexisting surface spin-glass freezing. The low-temperature core spiral spin orders survive in the FIM phase. A tentative magnetic phase diagram is presented and discussed in a frame of effects of the type and redistribution of cations as well as emergent uncompensated surface spins on the nearest and next nearest neighbor exchanges in chromite nanospinels.

Picosecond Creation of Switchable Optomagnets from a Polar Antiferromagnet with Giant Photoinduced Kerr Rotations

On-demand spin orientation with long polarized lifetime and easily detectable signal is an ultimate goal for spintronics. However, there still exists a trade-off between controllability and stability of spin polarization, awaiting a significant breakthrough. Here, we demonstrate switchable optomagnet effects in (Fe$_{1-x}$Zn$_{x}$)$_{2}$Mo$_{3}$O$_{8}$, from which we can obtain tunable magnetization, spanning from -40$\%$ to 40$\%$ of a saturated magnetization that is created from zero magnetization in the antiferromagnetic state without magnetic fields. It is accomplishable via utilizing circularly-polarized laser pulses to excite spin-flip transitions in polar antiferromagnets that have no spin canting, traditionally hard to control without very strong magnetic fields. The spin controllability in (Fe$_{1-x}$Zn$_{x}$)$_{2}$Mo$_{3}$O$_{8}$ originates from its polar structure that breaks the crystal inversion symmetry, allowing distinct on-site $d$-$d$ transitions for selective spin flip. By chemical doping, we exploit the phase competition between antiferromagnetic and ferrimagnetic states to enhance and stabilize the optomagnet effects, which result in long-lived photoinduced Kerr rotations. The present study, creating switchable giant optomagnet effects in polar antiferromagnets, sketches a new blueprint for the function of antiferromagnetic spintronics.

Interchain interaction effect on the magnetic properties of azurite material

Considering the interchain exchange interaction through dimer and monomer in the azurite, a two-dimensional Ising–Heisenberg model with dimer and monomer interlacing arrangement is established, and the magnetic and thermodynamic properties are calculated by Monte Carlo method. In the ground state, as the magnetic field increases from zero, the system changes from quantum antiferromagnetic (QAF) state with monomer in antiferromagnetic state and dimer in spin singlet to the quantum ferrimagnetism (QFI) state with monomer in saturated state and dimer in spin singlet, and finally reaches the saturated spin state (SP). In the QFI state, system shows 1/3 magnetization plateau. Starting from the QAF phase closing to the boundary with QFI phase, the specific heat and magnetic susceptibility of the system with temperature show beaks in the low temperature region, corresponding phase change, and in the whole range of temperature they may present double peak structure. Starting from the two phases of QFI and SP near the boundary between them, the magnetic susceptibility and specific heat with temperature also show peak, and the corresponding phase transition temperature is symmetry with respect to the phase boundary. Comparing with the specific heat data in the experiment, we conjecture the strength of the interchain interaction of azurite material is about half of the dimer interaction.

Magnetic Properties of Proton Irradiated Mn3Si2Te6 van der Waals Single Crystals

ABSTRACTThe bulk van der Waals crystal Mn3Si2Te6 (MST) has been irradiated with a proton beam of 2 MeV at a fluence of 1×1018 H+ cm-2. The temperature dependent magnetization measurements show a drastic decrease in the magnetization of 49.2% in the H//c direction observed in ferrimagnetic state. This decrease in magnetization is also reflected in the isothermal magnetization curves. No significant change in the ferrimagnetic transition temperature (75 K) was reflected after irradiation. Electron paramagnetic resonance (EPR) spectroscopy shows no magnetically active defects present after irradiation. Here, experimental findings gathered from MST bulk crystals via magnetic measurements, magnetocaloric effect, and heat capacity are discussed.

Cation ordering, ferrimagnetism and ferroelectric relaxor behavior in Pb(Fe1\u2212xScx)2\u22153W1\u22153O3 solid solutions

Ceramic samples of the multiferroic perovskite Pb(Fe1−xScx)2∕3W1∕3O3 with 0 ≤ x ≤ 0.4 have been synthesized using a conventional solid-state reaction method, and investigated experimentally and theoretically using first-principle calculations. Rietveld analyses of joint synchrotron X-ray and neutron diffraction patterns show the formation of a pure crystalline phase with cubic (Fm3̅m) structure with partial ordering in the B-sites. The replacement of Fe by Sc leads to the increase of the cation order between the B′ and B′′ sites. As the non-magnetic Sc3+ ions replace the magnetic Fe3+ cations, the antiferromagnetic state of PbFe2∕3W1∕3O3 is turned into a ferrimagnetic state reflecting the different magnitude of the magnetic moments on the B′ and B′′ sites. The materials remain ferroelectric relaxors with increasing Sc content. Results from experiments on annealed and quenched samples show that the cooling rate after high temperature annealing controls the degree of cationic order in Pb(Fe1−xScx)2∕3W1∕3O3 and possibly also in the undoped PbFe2∕3W1∕3O3.Graphical abstract

Electronic Structure, Optical, and Magnetic Properties of Mn100−xGex (x = 20, 25, and 30) Alloys Near Tetragonal–Orthorhombic Structural Phase Transition

Electronic, structural, optical, and magnetic properties of the Mn100−xGex alloys for x = 20, 25, and 30 are investigated near a tetragonal–orthorhombic structural phase transition. In the electronic structure calculations, the ferrimagnetic ground state is found which is in excellent agreement with the experimental observation of magnetic properties. The calculations reveal that the main contribution to the optical absorption is associated with the electronic transitions in the system of 3d manganese bands, these states significantly change near the Fermi energy. The optical conductivity of the alloys is also transformed with an increase of the low‐energy absorption values near structural phase transition due to the enhanced electronic transitions. Among different compositions of the studied Mn–Ge, the highest magnetization is observed for Mn70Ge30 whereas highest coercivity is observed for the Mn75Ge25 alloy. High coercivity can be ascribed to the highest magneto‐crystalline anisotropy of the sample whereas high magnetization of Mn70Ge30 can be due to the presence of a hexagonal ferromagnetic phase with higher magnetization. The effect of Mn–Ge composition on the structural phase transition and its relationship with the electronic structure, optical, and magnetic properties may allow for better designing of new Heusler alloys for various customized applications.

Influence of cooling field on field induced magnetic states in Ca3Co2O6 compound

Manifold degeneracy in the zero field cooled (ZFC) state of the Ising like spin system, Ca3Co2O6, is progressively alleviated by magnetic field (H) at low temperature (T). Field excursion after ZFC stabilizes ferrimagnetic (FIM) state above Tsf ~7K which converts to ferromagnetic (FM) state at high-H. Whereas, various metastable states have been created by H excursion of degenerate ZFC state below Tsf and finally it switches to FM state. In contrast, field cooling at 5kOe supports stable FIM ordering for all temperatures in low fields, which converts to the FM state at increasingly higher-H with decrease in T. This thermomagnetic irreversibility (TMI) below ~7K indicates non-ergodic nature of the ZFC state and it persists till the system fully saturates. It is obvious that both the hindered kinetics of H-T induced first order intermediate phase to FIM transformation and interplay of different interchain interactions like 1st nearest neighbor (nn) and 2nd nn with thermal energy are playing a crucial role in appearance of such type of TMI in this spin system.

Electron-Transfer Activity in a Cyanide-Bridged Fe42 Nanomagnet.

The ability to switch a molecule between different magnetic states is of considerable importance for the development of new molecular electronic devices. Desirable properties for such applications include a large-spin ground state with an electronic structure that can be controlled via external stimuli. Fe42 is a cyanide-bridged stellated cuboctahedron of mixed-valence Fe ions that exhibits an extraordinarily large S = 45 spin ground state. We have found that the spin ground state of Fe42 can be altered by controlling the humidity and temperature. Dehydration results in a 15 μB reduction of the saturation magnetization that can be partially recovered upon rehydration. The complementary use of UV-vis, IR, L2,3-edge X-ray absorption spectroscopy and X-ray magnetic circular dichroism is applied to uncover the mechanism for the observed dynamic behavior. It is identified that dehydration is concurrent with metal-to-metal electron transfer between Fe pairs via a cyanide π hybridization. Upon dehydration, electron transfer occurs from low-spin {FeII(Tp)(CN)3} sites to high-spin FeIII centers. The observed reduction in magnetization upon dehydration of Fe42 is inconsistent with a ferrimagnetic ground state and is proposed to originate from a change in zero-field splitting at electron-reduced high-spin sites.

Ab initio study on Pb2FeOsO6 and possible half metallicity via Na doping

Abstract Pb2FeOsO6, with an Fe-Os antisite occupancy of about 16%, was synthesized recently and measured to be a cubic ferrimagnetic semiconductor with a high magnetic ordering temperature (Tc) of 280 K. We performed an investigation on Pb2FeOsO6 by using the density functional theory. Our calculated results indicate that Pb2FeOsO6 crystallizes into tetragonal symmetry and is a C-type antiferromagnet. After doping with Na, the system experiences a transition from C-type antiferromagnetic state to ferrimagnetic state, and the half-filled Os5+ t2g orbitals cross the Fermi level owning to the injection of holes. Therefore, the Na-doped Pb2FeOsO6 exhibits a half metallic nature. Moreover, the Tc raises significantly by Na doping. Therefore, we expect that the Na-doped Pb2FeOsO6 would be promising candidates as spintronic material.

Electronic and Magnetic Structure and Elastic and Thermal Properties of Mn2-Based Full Heusler Alloys

Magnetism, electronic structure, elastic and thermal properties of Mn2YAl (with Y = Cr, V) have been investigated. The optimized lattice parameters, bulk modulus, and cohesive energy have been obtained. These alloys have the ferrimagnetic state as the most stable magnetic configuration, since the calculations showed a strong Mn-V antiferromagnetic coupling leading to the ferromagnetism of the Mn sublattices. A small and itinerant magnetic moment of Mn at the A site is found, which is antiparallel to the moment of Y at the B position in Mn2YAl (with Y = Cr, V) compounds. The calculated total spin moments are integral values and increase from − 2 μB/f.u. for Mn2VAl to – 1 μB/f.u. for Mn2CrAl with increasing the number of valence electrons. Band structure and total and partial density of states could be calculated via applying the modified Becke Johnson approximation (mBJ). Based on these results, Mn2YAl (with Y = Cr, V) are half-metallic ferrimagnets with the energy gap lies in the majority spin direction and a high-spin polarization (100%). The main difference between these two compounds is that the band gap is increased by 48% (0.210 eV for Mn2CrAl and 0.401 eV Mn2VAl). Elastic anisotropies, brittleness, and thermodynamic properties are determined for the Mn2YAl (with Y = Cr, V). The slight difference in the spatial distributions of Young’s moduli of Mn2YAl (with Y = Cr, V) reflects the small differences for the elastic anisotropies of the alloys under consideration. The mechanical stability of Mn2YAl (with Y = Cr, V) alloys are studied based on the elastic constants. The thermal properties are studied and investigated using the quasi-harmonic model, in addition, the temperature effect on heat capacities at constant pressure and volume, entropy, and thermal expansion are analyzed and discussed.

Magnetocaloric effect in single crystal GdTiO3

We studied the magnetocaloric effect in a single crystal GdTiO3. Single crystal GdTiO3 had a second order phase transition from a paramagnetic to ferrimagnetic state at 33 K. The maximum entropy change of -ΔS=0.10 J/cm3 K was observed in a 5 T field at the transition temperature. A small anisotropy was found in the magnetization and specific heat in low magnetic fields. The magnetization showed no hysteresis. Temperature dependencies of entropy, which are important for analyzing the refrigeration cycle, were calculated from the magnetization and specific heat measurements. These results indicate that GdTiO3 has the potential for applications as a magnetic refrigerant for hydrogen liquefaction.

Enhancement of Curie- and spin-spiral temperatures with doping Fe in multiferroic CoCr2O4 nanoparticles

Abstract Multiferroic, CoCr2O4 bulk material undergoes successive magnetic transitions such as paramagnetic to collinear ferrimagnetic state at Curie temperature (TC) and non-collinear spin-spiral ordering temperature TS followed by a lock-in-transition TL. In this paper, the rich sequence of magnetic transitions in CoCr2O4 nanoparticles after doping with iron ions are investigated by varying the concentration from x = 10 to 40%. With increasing iron concentration from 10 to 40%, while TC increases from 102 to 160 K higher than the TC of pure CoCr2O4, TS increases from 26 to 40 K. Later transition is clearly shown by sharp transition in specific heat measurement. While enhancement in TC is attributed to increase in lattice expansion and the exchange interaction between tetrahedral (A) and octahedral (B) sites, spin-spiral ordering is dictated by B-B interaction. Further, we have examined the magnetic transitions through neutron scattering using polarized neutron beam along three orthogonal directions. We observe that the para to ferrimagnetic transition is found to be continuous and the spiral ordering is diffused in nature irrespective of composition.

The Phase Diagram and Exotic Magnetostrictive Behaviors in Spinel Oxide Co(Fe1-xAlx)2O4 System.

We report the magnetic and magnetostrictive behaviors of the pseudobinary ferrimagnetic spinel oxide system (1−x)CoFe2O4–xCoAl2O4 [Co(Fe1−xAlx)2O4], with one end-member being the ferrimagnetic CoFe2O4 and the other end-member being CoAl2O4 that is paramagnetic above 9.8 K. The temperature spectra of magnetization and magnetic susceptibility were employed to detect the magnetic transition temperatures and to determine the phase diagram of this system. Composition dependent and temperature dependent magnetostrictive behaviors reveal an exotic phase boundary that separates two ferrimagnetic states: At room temperature and under small magnetic fields (∼500 Oe), Fe-rich compositions exhibit negative magnetostriction while the Al-rich compositions exhibit positive magnetostriction though the values are small (<10 ppm). Moreover, the compositions around this phase boundary at room temperature (x = 0.35, 0.4, 0.45, 0.5) exhibit near-zero magnetostriction and enhanced magnetic susceptibility, which may be promising in the applications for magnetic cores, current sensors, or magnetic shielding materials.

Thermoelectric, Structural, Optoelectronic and Magnetic properties of double perovskite Sr2CrTaO6: First principle Study

Using the full-potential linearized augmented plane wave method (FP-LAPW) based on the density functional theory (DFT) as implemented in the Wien2k package, first principles calculations were performed to investigate structural, electronic, magnetic, optical and for the first time thermoelectric properties of Sr2CrTaO6 double perovskite compound. The exchange correlation potential is treated by the generalized gradient approximation (GGA) and GGA + U where U is on-site Coulomb interaction correction. The trans-blaha-modified Becke–Johnson (TB-mBJ-GGA) is also used. Obtained results for the structural, electronic, and magnetic properties are in good agreement with the available experimental data. Structural and electronic properties show that our compound shows half-metallic ferrimagnetic phase ground state. Optical properties such dielectric function, absorption coefficient and reflectivity were computed and confirm that our compound is very suitable for device applications in the major parts of the spectrum (infrared, visible and ultraviolet). The novelty of our work is the study of thermoelectric properties of Sr2CrTaO6 double perovskite such as electrical conductivity, Seebeck coefficient and factor of merit.

Interplay between spin reorientation and magnetoelastic transitions, and anisotropic magnetostriction in the Mn1.95Cr0.05Sb single crystal

Abstract A single crystal of tetragonal Mn1.95Cr0.05Sb has been successfully grown by a modified-Bridgeman method with tiny amounts of hexagonal MnSb secondary phase distributed in the self-assembled mosaic boundaries. Under low magnetic fields, the consecutive occurrences of a spin-reorientation transition (SRT) and a magnetoelastic transition from ferrimagnetic (FRI) state to antiferromagnetic (AFM) state appear in c-axis, while these two transitions occur separately in a-axis. Such behavior can be ascribed to the asynchronous spin reorientation, which is resulted from the competition between the Zeeman energy and the magnetocrystalline anisotropy. More interestingly, the anisotropic magnetostrictions associated with the field-induced metamagnetic magnetoelastic transition have been observed. In the process of cooling, the maximum reversible values of ∼0.230% and ∼−0.125% are obtained at 165 K along c- and a-axes, respectively, for the application of cyclic magnetic fields up to 30 kOe. These values are consistent with those estimated by the difference in thermal expansion curves near the transition region. Moreover, it can be also found that the metamagnetic magnetoelastic transition shows either a narrow hysteresis (∼6 K) and a strong sensitivity to the magnetic field (∼−0.5 K/kOe). Therefore, the high reversible magnetostriction is spread over a wide temperature range for the studied sample. Our experimental findings indicate that the Mn2Sb-based intermetallics can be considered as a promising candidate with low-cost for magnetostriction.

High-pressure magnetism of the double perovskite Sr2FeOsO6 studied by synchrotron Fe57 Mössbauer spectroscopy

The pressure dependence of the magnetism of the double perovskite ${\mathrm{Sr}}_{2}{\mathrm{FeOsO}}_{6}$ was investigated by temperature- and magnetic-field-dependent synchrotron $^{57}\mathrm{Fe}$ M\ossbauer spectroscopy in the energy domain up to $\ensuremath{\sim}50$ GPa. ${\mathrm{Sr}}_{2}{\mathrm{FeOsO}}_{6}$ is known to feature antiferromagnetic ordering below ${T}_{\mathrm{N}}\ensuremath{\sim}140$ K and a change in spin structure from AF1 to AF2 near 70 K at ambient pressure. Previous Os ${L}_{2,3}$ x-ray magnetic circular dichroism (XMCD) spectra [Veiga et al., Phys. Rev. B 91, 235135 (2015)] indicated a pressure-driven change from the antiferromagnetic to the ferrimagnetic state. Raman spectra of ${\mathrm{Sr}}_{2}{\mathrm{FeOsO}}_{6}$ collected at room temperature and up to 34 GPa are in agreement with previous x-ray-diffraction studies which verified that the tetragonal ambient pressure crystal structure is retained at high pressure. The M\ossbauer investigations show that the Fe ions remain in the +3 high-spin $({{t}_{2g}}^{3}{e}_{g}^{2})$ state over the whole pressure range. The magnetic ordering is strongly stabilized by high pressure and for $pg30$ GPa the ordering temperature is increased to above room temperature. Broad magnetic hyperfine patterns as well as coexistence of magnetic and paramagnetic signals at high pressures indicate the formation of inhomogeneous magnetic states. The shapes of applied-field M\ossbauer spectra at low temperature are similar at 2 and 33 GPa and do not allow resolution of distinct antiferromagnetic and ferrimagnetic components. Pressure-induced spin canting in a basically antiferromagnetic spin structure or magnetic phase separation involving a pressure-induced minority ferrimagnetic phase may be the origin for the ferromagnetic XMCD signal.

Superspinglass behavior of maghemite nanoparticles dispersed in mesoporous silica

Abstract γ-Fe2O3 nanoparticles were dispersed in a mesoporous silica (SBA15) matrix using the co-precipitation method. While structural properties were investigated by X-ray diffraction, X-ray photoelectron spectroscopy, micro-Raman and transmission electron microscopy, magnetic studies were performed with DC and AC magnetometry. The γ-Fe2O3 nanoparticles have the regular cubic spinel structure. A strong reduction in the saturation magnetization (∼30 emu/gFe, 300 K) was measured and can be mainly attributed to the large fraction (60%) of surface spin disorder. This phenomenon was studied using the modified Kneller’s law and a modified Bloch spin wave model with a surface disorder term. Values of spin wave stiffness constant D of 391 meVA2 and exchange integral Jex equal to 1.12 meV were obtained, suggesting the presence of a block spinel ferrimagnetic state. The Vogel-Fulcher relation was applied to study the nanoparticles magnetic interactions. The values of zv = 5.3 (5), Tf = 184 K and τ 0 = 10 - 12 s suggest a superspinglass behavior. Thermoremanent experiments have also shown that magnetic relaxation occurs even below Tf (180 K) with an exponential decay with scale parameters in the range from 0.56 to 0.6, in agreement with the slowing down law. These facts indicate that the superspinglass effect is mainly caused by the strong surface spin disorder and frustrated collective state related to an interacting system with a broad particle size distribution.

Magnetic phase transitions induced by pressure and magnetic field: The case of antiferromagnetic USb2

Fascinating phenomena observed under applied pressure and magnetic field are attracting much research attention. Recent experiments have shown that application of the pressure or magnetic field to the ${\mathrm{USb}}_{2}$ compound induce the transformations of the ground-state antiferromagnetic (AFM) structure $(+\ensuremath{-}\ensuremath{-}+)$ to, respectively, ferromagnetic (FM) or ferrimagnetic structures. Remarkably, the magnetic critical temperature of the FM state, induced by pressure, is more than two times smaller than the N\'eel temperature of the AFM ground state. We performed density-functional theory (DFT) and DFT+$U$ studies to reveal the origin of the unusual magnetic ground state of the system and the driving mechanisms of the phase transitions. We investigate both the magnetic anisotropy properties and the parameters of the interatomic exchange interactions. To study pressure-induced effects we carry out calculations for reduced volume and demonstrate that the existence of the AFM-FM phase transformation depends on the peculiar features of the magnetic anisotropy. We discuss why the magnetic field that couples directly to the magnetic moments of atoms leads to the phase transition to the ferrimagnetic state whereas the pressure that does not couple directly to magnetic moments results in the FM structure. Our work demonstrates how the competition of different physical factors leads to variety of unusual properties of the antiferromagnetic ${\mathrm{USb}}_{2}$.

Spectra of Collective Excitations and Low-Frequency Asymptotics of Green’s Functions in Uniaxial and Biaxial Ferrimagnetics

The paper studies the dynamic description of uniaxial and biaxial ferrimagnetics with spin s=1/2 in alternative external field. The nonlinear dynamic equations with sources are obtained, on basis on which low-frequency asymptotics of two-time Green functions in the uniaxial and biaxial cases of the ferrimagnet are obtained. Energy models are constructed that are specific functions of Casimir invariants of the algebra of Poisson brackets for magnetic degrees of freedom. On their basis, the question of the stable magnetic states has been solved for the considered systems. These equations were linearized, an explicit form of the collective excitations spectra was found, and their character was analyzed. The article studies the uniaxial case of a ferrimagnet, as well as biaxial cases of an antiferromagnet, easy-axis and easy-plane ferrimagnets. It is shown that for a uniaxial antiferromagnet the spectrum of magnetic excitations has a Goldstone character. For biaxial ferrimagnetic materials, it was found that the spectrum has either a quadratic character or a more complex dependence on the wave vector. It is shown that in the uniaxial case of an antiferromagnet the Green function of the type Gsα,sβ(k,0), Gsα,nβ(k,0) and Gsα,sβ(0,ω) have regular asymptotic behavior, and the Green function of type Gnα,nβ(k,0)≈1/k2 and Gsα,nβ(0,ω)≈1/ω, Gnα,nβ(0,ω)≈1/ω2 have a pole feature in the wave vector and frequency. Biaxial ferrimagnetic states have another type of the features of low-frequency asymptotics of the Green's functions. In the case of a ferrimagnet, the “easy-axis” of the asymptotic behavior of the Green functions Gsα,sβ(0,ω), Gsα,nβ(0,ω), Gnα,nβ(0,ω), Gsα,sβ(k,0), Gsα,nβ(k,0), Gnα,nβ(k,0) have a pole character. For the case of the “easy-plane” type ferrimagnet, the asymptotics of the Green functions Gsα,nβ(0,ω), Gnα,nβ(0,ω), Gsα,nβ(k,0), Gnα,nβ(k,0), have a pole character, and the Green function Gsα,sβ(k,ω) contains both the pole component and the regular part. A comparative analysis of the low-frequency asymptotics of Green functions shows that the nature of magnetic anisotropy significantly effects the structure of low-frequency asymptotics for uniaxial and biaxial cases of ferrimagnet. Separately, we note the non-Bogolyubov character of the Green function asymptotics for ferrimagnet with biaxial anisotropy Gnα,nβ(k,0)≈1/k4.

Structural and Magnetic Property of Cr3+ Substituted Cobalt Ferrite Nanomaterials Prepared by the Sol-Gel Method.

Cobalt-chromium ferrite, CoCrxFe2−xO4 (x = 0–1.2), has been synthesized by the sol-gel auto-combustion method. X-ray diffraction (XRD) indicates that samples calcined at 800 °C for 3 h were a single-cubic phase. The lattice parameter decreased with increasing Cr concentration. Scanning electron microscopy (SEM) confirmed that the sample powders were nanoparticles. It was confirmed from the room temperature Mössbauer spectra that transition from the ferrimagnetic state to the superparamagnetic state occurred with the doping of chromium. Both the saturation magnetization and the coercivity decreased with the chromium doping. With a higher annealing temperature, the saturation magnetization increased and the coercivity increased initially and then decreased for CoCr0.2Fe1.8O4.