Two-sublattice Ferrimagnet Research Articles

Theoretical and Numerical Modeling of Optical Switching of Epitaxial Nanostructures Based on Iron-Garnet Films

The paper presents a theoretical analysis of magnetization switching in a gadolinium ferrite garnet film due to the demagnetizing effect of a femtosecond laser pulse. Using the Lagrange formalism for a two-sublattice ferrimagnet, the effective Lagrangian, thermodynamic potential, and Rayleigh dissipative function are obtained. The phase diagram of the ferrite film is analyzed, and the main states of the system are identified. Magnetization switching diagrams and trajectories of the order parameter dynamics of the magnet are constructed. The ranges of magnetic fields, temperatures, and demagnetization values for the most efficient magnetization switching are analyzed.

Алгоритм определения намагниченностей подрешеток двухподрешеточного ферримагнетика с точкой компенсации. Часть 2. Степенное приближение

The calculation algorithm of sublattice magnetizations in two-sublattice ferrimagnet with compensation point is proposed. On the consideration of magnetic as the combination of spin with two orientations it is found the dependence of magnetization from the temperature in the firm of transcendent equation. The calculated decision of this equation make the coincidence the calculated dependence with experiment in precision about 10%. For the analytic presentation of magnetization temperature dependence in obviously view it is proposed the power index approximation which consist of relation magnetic temperature to curie temperature in six power index. On the basis of power index approximation the phase diagram of two-sublattice ferrimagnet with compensation point is constructed. It is shown the scheme of sublattice magnetization determination on the basis of using meanings by temperature character points of phase diagram lower branch. It is found the equation system which connects the character points parameters with magnetizations in initial point and in the point of maximum of diagram in the temperature more than compensation. By solving this equation system it is found the enough simple analytical expressions which determine the saturation magnetizations both sublattices through parameters of character points on lower brunch of phase diagram. The proposed methods is applied to determination of sublattice magnetizations in experiments by measuring summary magnetization which are curried out on the films of two different compositions using the vibration magnetometer. For the examination of determined meanings the comparison with constructed on its basis phase diagram with the diagram determined in experiment was carried out. The examination shows the coincidence calculated data with experiment in limits from 8 to 40%. The analysis of correspondence determined diagram data with experimental data. It is found the good (to part of percent) coincidence of whole magnetization meaning in the beginning of diagram and also the coincidence of compensation temperature and Curie temperature. For the interpretation of visible deflections it is proposed the hypothesis about influence of third sublattice which changes the magnetizations of main sublattices. It is proposed some recommendations for further development of investigations.

Алгоритм определения намагниченностей подрешеток двухподрешеточного ферримагнетика с точкой компенсации. Часть 1. Фазовая диаграмма

The calculation algorithm of sublattice magnetizations in two-lattice ferromagnet with compensation point is proposed. On the basis of preceding works review it is put the task about calculation of sublattices in individuality. It is investigated the general scheme of whole ferrimagnet magnetization forming which contains two magnetic sublattices both connected by exchange interaction. In geometry of axis symmetry along constant field direction it is investigated the orientational dependence of sublattices magnetization from applied field. It is found the forming conditions of anti-parallel and parallel collinear phases and corner phase between its. It is proposed the model presentation of magnetization dependence from temperature which contain the degree index dependence of general temperature to Curie temperature relation for each sublattice individual. For the simplicity and clear appearance of presentation the power index was choose. It is established the conditions which are necessary for forming the temperature compensation point. It is found the dependencies of deflection corners of each sublattices magnetization from field direction in accounting the given temperature. The decision of proposed excitation for magnetic field allows to find the boundaries of sublattice system transition between phases. On the basis of proposed temperature dependencies of critical transition fields it is drawing the phase diagram of two-sublattice ferrimagnet. It is found two settled on field one above other branches. The lower branch correspond to anti-parallel phase and upper branch correspond to parallel phase. It is found that lower branch contain sufficient quantity of information for to determine the individual both sublattice magnetization. It is proposed the methodic for calculation the individual sublattice magnetization based on the character temperature values and summary magnetizations. On the lower branch marked four character points which correspond to four temperatures and two values of summary magnetization. With using these points it is founded the equation system which allows to determinate the individual magnetizations values. It is proposed some recommendations for further development of investigations.

Giant widening of interface magnetic layer in almost compensated iron garnet

A two-sublattice ferrimagnet undergoes a transition from a collinear to the canted magnetic phase at magnetic field oriented along an easy magnetization direction. In this work, we study the transition by means of the magneto-optical Faraday effect in a thin film of compensated iron garnet (Lu3−xBix)(Fe5−y−zGayAlz)O12 grown on the Gd3Ga5O12 substrate. In the immediate vicinity of the compensation temperature, a precursor of the transition with a complex shape was observed. Using a special sample with variable thickness, we demonstrate an interfacial origin of the precursor. Diffusion of gadolinium from the substrate into the film forms a thin intermixed layer with enhanced magnetization. It induces an extended inhomogeneous magnetic structure in the film. A two-step shape of the precursor appears due to an easy-plane anisotropy of the intermixed magnetic layer. We emphasize that an effective width of the inhomogeneous magnetization distribution in the film grows enormously while approaching the compensation temperature.

Domain wall dynamics of ferrimagnets influenced by spin current near the angular momentum compensation temperature

We report on a theoretical study of the spin-current excited dynamics of domain walls (DWs) in ferrimagnets in the vicinity of the angular momentum compensation point. Effective Lagrangian and nonlinear dynamic equations are derived for a two-sublattice ferrimagnet taking into account both spin-torques and external magnetic field. The dynamics of the DW before and after the Walker breakdown is calculated for any direction of the spin current polarization. It is shown that for the in-plane polarization of the spin current, the DW mobility reaches a maximum near the temperature of the angular momentum compensation. For the out-of-plane spin polarization, in contrast, a spin current with the densities below the Walker breakdown does not excite the dynamics of the DW. After overcoming the Walker breakdown, the domain wall velocity increases linearly with increasing the current density. In this spin-current polarization configuration the possibility of a gigahertz oscillation dynamics of the quasi-antiferromagnetic vector under the action of a damping-like torque in the angular momentum compensation point is demonstrated. Possible structures for experimental demonstration of the considered effects are discussed.

Magnetostriction and thermal expansion of nonstoichiometric TbCo2Mnx compounds

The magnetostriction and thermal expansion of the TbCo2Mnx compounds (0 ≤ x ≤ 0.6) have been investigated. The compounds crystallize in the cubic MgCu2-type lattice in spite of the Tb to 3d-metal (Co + Mn) ratio deviates from the stoichiometry. The spontaneous and forced volume magnetostriction as well as anisotropic magnetostriction were determined for various temperatures. The intra- and intersublattice Tb-Tb, Tb-3d and 3d-3d exchange interactions were estimated within the molecular field model for a two-sublattice ferrimagnet. It was found that the compounds have a large volume and anisotropic magnetostriction in a wide temperature range. At room temperature, TbCo2Mn0.4 compound possesses high linear magnetostriction of 400 ppm in magnetic field of 5 kOe, which makes it possible to consider the nonstoichiometric compounds as promising materials for magnetostrictive applications.

Ferrimagnetism in a system of two antiferromagnetically coupled Heisenberg models

We phenomenologically investigate the phase diagram of some ferrimagnetic materials on the basis of two bilinearly coupled Heisenberg models sitting on two interpenetrating simple magnetic cubic lattices. Computations were performed with the help of the Landau free energy obtained through applying the Hubbard-Stratonovich transformation to the initial microscopic Heisenberg Hamiltonian. The transitions to the magnetically ordered phases within the model are found to be of second order with the occurrence of a compensation point at lower temperatures for some values of the system’s parameters. It is found that the main stable phase is a two-sublattice collinear ferrimagnet in addition to a metastable non-collinear phase. The numerical results give a detailed description of temperature dependence of magnetization on the strength of intersublattice interaction and the difference between the effective exchanges of two ferromagnetically ordered sublattices. Our results are in qualitative agreement with the experimental results on Y3Fe5O12 in the strong coupling limit and the compounds ErFe2 and GdCo12B6 for weak couplings.

Entropy and magnetocaloric effect in ferrimagnets RCo2

The equations of state for the magnetic and elastic subsystems of a ferrimagnet are obtained in terms of the exchange–striction model. In the formulas derived for magnetic entropy, it is represented as the sum of the contributions of two magnetic sublattices of the ferrimagnet. One of the main characteristics of the magnetocaloric effect, viz., isothermal variation ΔS iso of the entropy in a magnetic field, is calculated for compounds RCo2 (R = Er, Ho, Dy) that experience a first-order magnetic phase transition and TbCo2 that experiences a second-order magnetic phase transition. It is shown that the calculated values of ΔS iso for these compounds are in satisfactory quantitative agreement with experimental results. The change in the entropy of a ferrimagnet in a strong magnetic field upon a transition from the ferrimagnetic to ferromagnetic ordering is calculated. The peculiarities in the magnetic field dependences of the magnetic entropy of a two-sublattice ferrimagnet are analyzed.

Magnetic-field induced phase transitions in intermetallic rare-earth ferrimagnets with a compensation point

The behavior of highly anisotropic f-d ferrimagnets in strong magnetic fields is studied. HoFexAl12-x (x = 5,6) compounds, which have compensation temperatures Tcomp > 0 for x = 5 and Tcomp ≈ 0 K for x = 6, are used as examples. Magnetic phase diagrams for these substances in a two-sublattice (f-d) ferrimagnet with a compensation point are constructed and analyzed with exchange interactions and anisotropy taken into account. Special attention is devoted to the influence of the rare-earth anisotropy on the form and properties of the phase diagram.

Longitudinal spin dynamics in ferrimagnets: Multiple spin wave nature of longitudinal spin excitations

Motivated by the existing controversy about the physical mechanisms that govern longitudinal magnetization dynamics under the effect of ultrafast laser pulses, in this paper we study the microscopic model of longitudinal spin excitations in a two-sublattice ferrimagnet using the diagrammatic technique for spin operators. The diagrammatic approach provides us with an efficient procedure to derive graphical representations for perturbation expansion series for different spin Green's functions and thus to overcome limitations typical for phenomenological approaches. The infinite series involving all distinct loops built from spin wave propagators are summed up. These result in an expression for the longitudinal spin susceptibility ${\ensuremath{\chi}}^{zz}(\mathbf{q},\ensuremath{\omega})$ applicable in all regions of frequency $\ensuremath{\omega}$ and wave vector q space beyond the hydrodynamical and critical regimes. A strong renormalization of the longitudinal spin oscillations due to processes of virtual creation and annihilation of transverse spin waves has been found. We have shown that the spectrum of longitudinal excitations consists of a quasirelaxation mode forming a central peak in ${\ensuremath{\chi}}^{zz}(\mathbf{q},\ensuremath{\omega})$ and two (acoustic and exchange) precessionlike modes. As the main result, it is predicted that both acoustic and exchange longitudinal excitations are energetically above similar modes of transverse spin waves at the same temperature and wave vector. The existence of the exchange longitudinal mode at such frequencies can result in a new form of excitation behavior in ferrimagnetic system, which could be important for understanding the physics of nonequilibrium magnetic dynamics under the effect of ultrafast laser pulses in multisublattice magnetic materials.

Specific features of the properties of half-metallic ferromagnetic Heusler alloys Fe2MnAl, Fe2MnSi, and Co2MnAl

The structural, magnetic, and electrical properties of half-metallic Heusler alloys Fe2MnAl, Fe2MnSi, and Co2MnAl have been investigated in the temperature range of 4–900 K. According to the X-ray diffraction analysis, these alloys have the B2 and L21 structures with different degrees of atomic order. The magnetic state of the alloys is considered as a two-sublattice ferrimagnet. The electrical resistivity and thermoelectric power have been discussed in the framework of the two-current conduction model taking into account the existence of an energy gap in the electronic spectrum of the alloys near the Fermi level for the subband with spin-down (minority) electrons.

Magnetization dynamics of a two-sublattice ferrimagnet near the angular momentum compensation point

The high-frequency properties of two-sublattice ferrimagnets are examined near the temperature TL at which the angular momentum of the sublattices is compensated. A diagram technique for spin operators is used, along with analytic expressions that are valid over the entire temperature range of the magnetically ordered state of the system. It is shown that near TL longitudinal fluctuations in the magnetization have a significant influence on the resonance properties of the magnet, with different temperature behaviors of the in-phase and out-of-phase precessions of the sublattice magnetization. As TL is approached the frequency of the in-phase precession increases simultaneously with a rise in the line width, while the frequency of the out-of-phase oscillations falls off significantly, so the two modes become equivalent. These results may be important for understanding the microscopic mechanisms of magnetic reversal by ultrashort laser pulses in rare earth ferrimagnets.

Exchange relaxation as a mechanism of the ultrafast reorientation of spins in a two-sublattice ferrimagnet

In the exchange approximation, an exact solution is obtained for the sublattice magnetizations evolution in a two-sublattice ferrimagnet. Nonlinear regimes of spin dynamics are found that include both the longitudinal and precessional evolution of the sublattice magnetizations, with the account taken of the exchange relaxation. In particular, those regimes describe the spin switching observed in the GdFeCo alloy under the influence of a femtosecond laser pulse.

Domain structure of a thin single-crystal plate of terbium iron garnet near the magnetic compensation point

The domain structure of a thin single-crystal plate of the iron garnet Tb3Fe5O12 has been investigated using the magneto-optical method in the temperature range near the magnetic compensation point of this ferrimagnet Tc = 248.6 K. It has been shown that, when the temperature of the sample approaches the magnetic compensation point, the domain width significantly increases, but remains finite at T = Tc. The magnetic H-T phase diagram, which determines the boundary between the multidomain and domain-free (uniformly magnetized) states of the sample, has been constructed using the data on visual observations of the transformation of the domain structure with variations in the temperature and external magnetic field. The results obtained have been interpreted in terms of the thermodynamic theory of stability of different magnetic phases of a two-sublattice cubic ferrimagnet near Tc.

Magnetic properties of a DyFe 5Al 7 single crystal

A single crystal of DyFe 5Al 7 (tetragonal ThMn 12 structure) has been studied. DyFe 5Al 7 orders ferrimagnetically at T C = 231 K and has a compensation of the Dy and Fe sublattices at T comp = 93 K. Magnetization isotherms measured along the principal axes of the single crystal indicate that the magnetic moments lie in the basal plane of the tetragonal lattice. Strong magnetic anisotropy is observed not only between the basal plane and the [0 0 1] axis but also within the basal plane, with the [1 0 0] axis being the easy magnetization direction with the spontaneous magnetic moment 2.1 μ B. A very high coercivity with H c values up to 3 T was found at 2 K. In the temperature range 75–100 K, the compound exhibits a field-induced magnetic transition along the easy [1 0 0] direction. Temperature dependence of the critical field H cr of the transition is very strong, the value of H cr evidently exceeds 14 T below 75 K. A model for the magnetization process of a two-sublattice ferrimagnet with a weak intersublattice exchange interaction has been developed to explain the magnetic transition. The model reproduces the temperature behavior of H cr near the compensation point.

High-field low-temperature magnetisation curves of anisotropic ferrimagnets

Possible shapes of high-field magnetisation curves of two-sublattice ferrimagnets are analysed within a model with two anisotropy constants for the subdominant sublattice. The model is relevant to 3 d–4 f intermetallic compounds. For the purpose of classification the magnetisation curves are regarded as ordered sequences of horizontal, slanted and vertical sections, without reference to quantitative details. Every shape type corresponds to a domain in the plane of relative anisotropy parameters κ 1 and κ 2. The κ 1 κ 2 diagram proves rather complicated; however, in the limiting cases of very weak or very strong anisotropy (in relation to intersublattice exchange) it takes the same universal form characteristic of simple ferromagnets.

Inhomogeneous magnetic states in Mn2 − x Zn x Sb (0.6 ≤ x ≤ 1.0) solid solutions

Mn2 − xZnxSb (0.6 ≤ x ≤ 1.0) solid solutions are shown to undergo magnetic phase separation (coexistence of two magnetic phases in a structurally homogeneous material) using a combination of characterization techniques (magnetometry, X-ray diffraction, neutron diffraction, Mossbauer spectroscopy, and resistivity measurements). A model is presented for the coexistence of two magnetic phases in the two-sublattice ferrimagnet Mn2Sb diamagnetically diluted with zinc.

Microwave absorption in the frustrated ferrimagnet Cu2OSeO3

The resonance properties of a new Cu2OSeO3 ferrimagnet have been investigated in a wide range of frequencies (17–142GHz) at liquid helium temperature. The resonance data were used to plot the frequency-field curve of the ferromagnetic spectrum described in the model of an anisotropic two-sublattice ferrimagnet. The effective magnetic anisotropy corresponding to the gap in the spin wave spectrum was estimated (3GHz). It was found that the spectrum has a multicomponent structure due to the diversity of the types of magnetization precession. As the amplitude of the high-frequency magnetic field increased, additional absorption was observed in an external magnetic field below the main resonance field. The addition absorption detected corresponds to a nonuniform nonlinear parametric resonance due to the nonuniformity of the magnetic structure in the ferrimagnetic crystal Cu2OSeO3.

Deducing model parameters of ferrimagnets from high-field magnetization curves

The maximum magnetic field available for acquisition of quality magnetization data has risen significantly in recent times, the current limit being just short of a megaoersted. This opens possibilities for determining model parameters of various magnets by way of expressions containing directly observable quantities. Here such expressions are derived for anisotropic two-sublattice ferrimagnets.

Quantum effects in an anisotropic ferrimagnet

A model of a two-sublattice collinear ferrimagnet with direct exchange interaction and unequal values of the partial magnetization has been investigated. The condition of existence of the compensation point is determined from material parameters of the system at low temperatures. The excitation spectra are obtained. An analysis is made of the spectra as a function of the total magnetization of the two sublattices.