Two-sublattice System Research Articles

Possibility of the Appearance of a Tricritical Point in a Two-Sublattice System with an Asymmetric Double Minimum Potential

The ferroelectric transition in a two-sublattice system with an asymmetric double minimum potential is of the second or the first order according to the values of model parameters. It has turned out that the tricritical point can exist when such parameter values satisfy some conditions. Several possible phase diagrams are presented as examples, and discussed.

Molecular-field theory of the magnetic configurations and transverse magnetization processes in systems with high-order uniaxial anisotropy and strong antisymmetric exchange, with applications to some Sr-substituted hexagonal ferrites

We study in the molecular-field approximation the equilibrium configuration and the phase transitions of a magnetic model system consisting of two sets of moments of equal magnitude, coupled by isotropic, anisotropic, and antisymmetric exchange, in the presence of uniaxial anisotropy, under the effect of a transverse magnetic field. The anisotropy is developed up to the sixth-order terms, with no restricting conditions upon the relative strength of the different interactions. Two possible interpretations of the model are developed: as a two-sublattice system, and as a quasicontinuous distribution of magnetic moments, exhibiting spiral magnetic structures. The theoretical results are then applied to the interpretation of the unusual magnetic structures, magnetization curves, and phase transitions observed in some Sr-substituted hexagonal ferrites of the $Y$ and $Z$ families, allowing an estimation of all the interaction parameters.

Two-sublattice magnetic system with fourth-order uniaxial anisotropy and strong antisymmetric exchange in a transverse magnetic field

Discusses the equilibrium configurations and the phase transitions of a semi-classical model system consisting of two equal magnetic moments coupled by isotropic, anisotropic and antisymmetric exchange, with uniaxial anisotropy terms up to fourth order, in the presence of a transverse magnetic field. No restriction is imposed on the values of the interaction parameters. Magnetic configurations of the 'conical' type appear for non-negligible values of the antisymmetric exchange and of the fourth-order anisotropy term, and are found to be stable over a wide range of values of the physical parameters and the external field. The results of the theoretical model are applied to the interpretation of the neutron scattering data and the transverse magnetisation measurements on some diamagnetically substituted hexaferrites of the Y and Z types.

Exchange constant of calcium- and germanium-substituted yttrium-iron-garnet thin films

The room-temperature exchange constant of single-crystal calcium- and germanium-substituted yttrium-iron-garnet thin films has been measured using ferromagnetic resonance techniques. The germanium concentrations varied in the range of 0 to 1.4 moles per formula unit. The experimental results are compared with the predictions of a percolation model by Kirkpatrick and Harris and reasonable agreement is found when it is assumed that the germanium substitution is confined to the tetrahedral iron sublattice. The results are also compared with the predictions of a model by Slonczewski et al. which relates the exchange constant in a substituted garnet to the Curie temperature. In this case the agreement is qualitative at best and raises the question of whether the exchange constant can be related to the Curie temperature without considering the details of the substitution on the individual iron sublattices. Finally the effective $g$ value has been measured for all samples and the results are shown to be in agreement with the Wangsness model for a two-sublattice system. There is some indication of the existence of a high-field susceptibility in the heavily substituted samples.

Electron paramagnetic and antiferromagnetic resonance in LiCuCl 3.2H 2O

The 9.6 GHz antiferromagnetic and paramagnetic resonance spectrum of LiCuCl 3.2H 2O is studied as a function of temperature for various directions of the external magnetic field. The easy axis, e, is found to be in the a- c plane at an angle of 70.5° to the a axis and 38.5° to the c axis. Four AFMR lines are detected in the case H‖ e below the Néel temperature of 4.4 K. Each of these lines shows the characteristic temperature and angular dependence, as predicted by the theory of Nagamiya, Keffer and Kittel. Three new resonance lines are detected below 2.5 K, these lines are suggested to be the resonances due to the occurrence of a second, two-sublattice system in the compound. The critical line broadening of the paramagnetic resonance line above T N is also noted; various descriptions for this broadening are presented.

A large NMR lineshift due to induced-staggered magnetization in paramagnetic state

Antiferromagnetic staggered susceptibility is studied in a new way by the examination of the proton NMR lineshift above T N in a crystallographic two-sublattice system with different g-tensors. The lineshift has a large contribution from the staggered magnetization which is induced in the paramagnetic state by the action of a uniform external field. A large value of the staggered susceptibility derived from the experiment in a nearly two-dimensional Heisenberg antiferromagnet, Cu(HCOO) 2.4D 2O, can be ascribed to the existence of a highly developed short-range order above T N in this crystal.

Dipole and Quadrupole Phase Transitions in Spin-1 Models

A spin-1 Hamiltonian with arbitrary bilinear and biquadratic pair interactions has been studied in the molecular-field approximation by using one- and two-sublattice models. Various types of orderings and transitions are found for the Hamiltonians with different symmetries. For a system described by a one-sublattice Hamiltonian with Ising, isotropic, or cubic symmetry, only one phase transition is found; either from the paramagnetic phase to a ferromagnetic or to a ferroquadrupolar phase. (Parallel alignment of quadrupoles is denoted ferroquadrupolar.) For the one-sublattice Hamiltonian with axial symmetry, we find two separate phase transitions; first from the paramagnetic phase to a ferroquadrupolar phase and then to a ferromagnetic phase. A two-sublattice system described by an Ising or isotropic Hamiltonian can have a transition either from the paramagnetic phase to a ferromagnetic phase, or to a ferriquadrupolar phase. Additional transitions are also found from the ferromagnetic to a ferrimagnetic phase and then back to the ferromagnetic phase. The system can have as many as three successive transitions. For a two-sublattice Hamiltonian with cubic symmetry, besides the transitions found in Ising systems, there are "reorientation" phase transitions; i.e., transitions from a quadrupole ordering along the cube edge to an ordering along the cube diagonal. This system can have more than three successive phase transitions.

Contribution of the Demagnetizing Field near the Spin-Flopping Field for CuCl2·2H2O

A lack of symmetry in the susceptibility tensor χyx was found experimentally by Naiman and Lawrence over the spin-flopping region in CuCl2·2H2O when the external magnetic field was less than 10−3 rad away from the easy axis. This fact cannot be explained by considering the effective field acting on the two-sublattice system to be composed of exchange, anisotropy, and external magnetic fields. Additionally, the Dzialoshinski-Moriya interaction for CuCl2·2H2O appears analytically only as a shift in the critical field while the wander of the easy axis influences the shape but not the symmetry of χyx. The demagnetizing field has been included exactly using a 2×2 tensor, and it was found that for an ellipsoidal spin-flopping specimen the major effect on χyx is to shift the value of the critical field. According to Joseph and Schlömann, the demagnetizing tensor components for bodies with ``corners'' need not be constant, and this could possibly explain the observed asymmetry in χyx. To test this theory, single crystals were shaped into spheres and χyx was remeasured. The essential agreement between the results before and after shaping lead us to conclude that demagnetizing effects which depend on the crystal shape are not important. Possible crystalline inclusions and/or domain formation may play a significant role.

Experimental g′ and g Values of Fe, Co, Ni, and Their Alloys

The magnetomechanical ratio g′ and the spectroscopic factor g were measured on same samples of iron and nickel. The g factors were also measured for some Fe-Ni, Fe-Co, Co-Ni, alloys. The experimental values of g and g′ are used to check the Kittel-Van Vleck relations, whose exact form 1/g+1/g′ = 1 appears well satisfied. It is shown that the effective magnetomechanical ratio geff′ of an alloy, which is given by the quotient of the total magnetic moment to the total angular momentum of the system, converts itself by means of the relation 1/g+l/g′ = 1 to the formula of Tsuya and Wangsness, which gives the effective splitting factor geff of a two-sublattice system. The calculated curves of geff agree with the experimental points for the Fe-Ni, Fe-Co, Co-Ni alloys. Using the measured values of g and g′, one calculates the mean spin moment contribution of the ferromagnetics, with a mean electronic number higher than 26.8,which crystallize in fcc or hexagonal structures: the mean spin moment decreases linearly by increasing electronic number with a slope of −1.05μB/electron.

Effective Ferrimagnetic Resonance Parameters with Gilbert-Type Relaxation Terms

Steady-state effective parameters of the susceptibility tensor have been found for a two-sublattice system by using equations of motion with Gilbert-type relaxation terms. To the same order in the molecular field coefficient, these parameters differ from those previously found for Landau-Lifschitz type terms in that they have infinite discontinuities in the compensation region, there is no distinction between the effective gyromagnetic ratios characterizing the absorption and the Faraday effect, and there is no additional term appearing in the expression for the off-diagonal element.

Effective Parameters in Ferrimagnetic Resonance

The steady-state solution for the susceptibility tensor of a two-sublattice system has been found by using sublattice equations of motion which include complete Landau-Lifschitz relaxation terms with individual relaxation parameters and which describe relaxation toward the instantaneous total field acting on the sublattice. It is shown that one can define effective parameters describing the behavior of the system as a whole which remain finite throughout the compensation region and, in particular, insure that the absorption coefficient will remain positive. It is also found that the effective gyromagnetic ratios characterizing the absorption and Faraday effect are different in principle, and a new term is found in the expression for the off-diagonal element which is a consequence both of the sublattice structure and total field relaxation. In the case of small damping, many of these distinctions disappear and some parameters reduce to those previously obtained. It is shown that the inclusion of total field relaxation is necessary to obtain results which are unambiguous and correct in principle; the magnetization line width product is also shown to be continuous, but vanishing at the compensation point for angular momentum.

Theory of infra-red resonances in ferrimagnetics

The frequency dependence of the magnetic susceptibility for circular excitation of an uncompensated ferrimagnet is derived from the K ramers-K ronig relations for gyrotropic media. In the lossless case the susceptibility is completely determined by two sets of parameters: the resonance frequencies and the corresponding optical strengths. These parameters are calculated for systems of two and three sublattices. In agreement with the results of K aplan and K ittel it is found that the high-frequency mode of the two-sublattice system is optically inactive unless the splitting factors or the anisotropy fields are different for the two sublattices. A system of three sublattices, corresponding to the case of ordered ferrites, is discussed in detail. The infra-red resonance frequencies can be estimated from the Néel temperature. For representative cases the expected resonance frequencies are in the range of 10 13 sec −1. A method of detecting the high-frequency resonances by means of the magneto-optical Kerr effect is discussed.