Anisotropic Bilinear Research Articles

Ab initiodetermination of spin Hamiltonians with anisotropic exchange interactions: The case of the pyrochlore ferromagnetLu2V2O7

We present a general framework for deriving effective spin Hamiltonians of correlated magnetic systems based on a combination of relativistic ab initio density functional theory calculations, exact diagonalization of a generalized Hubbard Hamiltonian on finite clusters, and spin projections onto the low-energy subspace. A key motivation is to determine anisotropic bilinear exchange couplings in materials of interest. As an example, we apply this method to the pyrochlore ${\mathrm{Lu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{7}$ where the vanadium ions form a lattice of corner-sharing spin-1/2 tetrahedra. In this compound, anisotropic Dzyaloshinskii-Moriya interactions (DMIs) play an essential role in inducing a magnon Hall effect. We obtain quantitative estimates of the nearest-neighbor Heisenberg exchange, the DMI, and the symmetric part of the anisotropic exchange tensor. Finally, we compare our results with experimental ones on the ${\mathrm{Lu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{7}$ compound.

Influence of magnetic dipole and magnetoelastic interactions on the phase states of 2D non-Heisenberg ferromagnetic with complex exchange interactions

The phase states of the 2D non-Heisenberg ferromagnetic with anisotropic bilinear and biquadratic exchange interactions are investigated. The limiting cases of the system under consideration are the two-dimensional XY-model with biquadratic exchange interaction and the isotropic Heisenberg ferromagnetic. The account of the magnetic dipole interaction leads to the realization of spatially inhomogeneous quadrupolar phase. The stability regions of various phase transitions for different values of the material parameters are studied. The phase diagram is built. Besides, the temperature phase transitions are investigated. The influence of the magnetoelastic interaction on the formation of the long-range quadrupolar order is determined.

Linkage of Fields in Characteristic 2

Let F be a field with 2 = 0 and ϕ = ⟨⟨a 1,…,a n ⟩⟩ an n-fold anisotropic bilinear Pfister form over F with function field F(ϕ). In this paper we compute ker where I F ⊂ W(F) is the maximal ideal in the Witt ring W(F) of F. We use this computation to prove an n-linkage property of the subfields F 2(a 1,…,a n ).

Magnetic ordering near crossover in singlet paramagnets

The Zeeman effect, magnetization and differential magnetic susceptibility near the energy level crossing are calculated both in the isothermal and adiabatic regimes for a number of singlet paramagnets HoBa 2Cu 3O 7− δ ( δ=0, 1.0), HoVO 4, TmPO 4 with regard to the anisotropic bilinear interaction. A magnetic ordering is shown to appear in HoBa 2Cu 3O 7− δ ( δ=0, 1.0) and TmPO 4 for external magnetic field H||[0 0 1] near crossover, resulting in a deviation of the magnetic moment out of the magnetic field direction. A dependence of the phase diagram on the values of parameters of the anisotropic bilinear and quadrupolar interactions, temperature, etc. is explored.

Four-spin exchange in Bi2CuO4 (abstract)

Magnetic properties of Bi2CuO4 single crystals are of interest owing to their relationship to the high-Tc superconductor problem. Earlier we carried out the magnetic and neutron scattering investigations on high quality large single crystals. The Bi2CuO4 crystal belongs to the space group P4/ncc and the magnetic group is the collinear plane antiferromagnet with a Neel temperature of 45.8 K. The three-dimensional character of the antiferromagnetic ordering is reflected by the value of the critical magnetization exponent 0.352. The sublattice magnetization depends very little on temperature up to about 15 K. The spin-wave spectrum contains two branches with energy gaps of 2.1 and 3.4 meV. The theoretical interpretation of the experimental data shows the necessity of introducing the tensor four-site exchange in the S=1/2 spin Hamiltonian with the tetragonal anisotropic bilinear exchange. This provides the gap characteristics of the acoustic branch of spin waves and the correct temperature dependence of the sublattice magnetization. This result shows the importance of the four-site exchange for the formation of Bi2CuO4 magnetic properties. From the similarity of magnetic subsystems, Bi2CuO4, and high-Tc superconductors it is suggested that the four-site exchange is responsible for magnetic ordering of the square spin S=1/2 lattice. We also suggest a thermodynamic theory of the temperature dependence of magnetic properties of Bi2CuO4.

Magnetic neutron scattering in single crystal Bi2CuO4

The spin-wave excitations and the critical behavior of the sublattice magnetization in Bi2CuO4 have been investigated by means of neutron scattering. The three-dimensional character of the antiferromagnetic ordering with propagation vector K=(1,0,0) below TN=45.83(8) K is reflected by the value of the critical exponent β=0.352(3). The spin-wave excitations have been measured along the symmetry directions [100] and [001]. The spin-wave dispersion is found to split into two branches with energy gaps Δ1=2.1 meV and Δ2=3.4 meV at the zone center. The data analysis is based on an S=1/2 spin Hamiltonian of tetragonal symmetry with anisotropic bilinear exchange including a four-site exchange interaction term.

Curie temperature of anisotropic Heisenberg mixed spin system

The Curie temperature T c of an anisotropic Heisenberg ferromagnet with mixed spins of S = 1 and σ = 1 2 has been calculated using simple Green function decoupling theories. Assuming anisotropic bilinear and biquadratic exchange interactions ( J and α J) between nearest neighbours of the different spins, variations of T c and γ (= <S z> <σ z> ) at T c with α for simple cubic and body ce for various values of the anisotropy parameter η of the exchange interaction have been investigated. Anisotropy parameters for which biquadratic exchange interaction has no effect on T c were determined. The results are compared with those in the pair model approximation.

A neutron study of the anomalous magnetic interactions in CeSb

The magnetic excitations of CeSb in the ferromagnetic and the type IA antiferromagnetic state have been measured by inelastic neutron scattering experiments. A generalized random-phase-approximation (RPA) formalism taking into account anisotropic bilinear exchange interactions consistently describes the magnetic excitations as well as the critical behavior of the system. For CeSb anisotropic exchange interactions emerge which are very similar to CeAs. Undoubtedly, the static behavior of CeSb is not forced by the bilinear exchange, but, is due to higher-degree magnetic interactions. Furthermore, evidence for a strong reduction of the crystal field in the ordered state is obtained.

Anisotropic exchange and spin dynamics in the type-I (-IA) antiferromagnets CeAs, CeSb, and USb: A neutron study.

The anomalous anisotropic magnetic interactions and the spin dynamics of the fcc type-I or -IA antiferromagnetic cerium and uranium monopnictides CeAs, CeSb, and USb have been studied by inelastic and diffuse critical neutron scattering experiments. The diffuse scattering above the antiferromagnetic ordering temperature largely corresponds to longitudinal spin fluctuations which are highly anisotropic. In the ordered state the dispersion curves of the spin-wave excitations strongly depend on the actually realized spin structure. For the antiferromagnets the spin waves split into transverse modes with different polarizations due to the exchange anisotropy. In CeAs one of these modes exhibits nearly zero energy gap and quadratic dispersion which has not previously been observed in antiferromagnets. The wave-vector-dependent susceptibility tensor has been calculated within the random-phase-approximation (RPA) by taking account of crystal-field, anisotropic bilinear exchange, and isotropic quadrupolar interactions. General expressions including all levels of the ground-state multiplet are derived for single-q and triple-q type-I as well as for type-IA antiferromagnets, and detailed formulas of the magnetic excitation spectrum are given for the particularly interesting case of effective two-level systems which are often realized in f-electron magnets. The RPA formalism consistently describes the transverse magnetic excitations for T${T}_{N}$ as well as the longitudinal spin fluctuations for Tg${T}_{N}$ for all compounds under study. For CeAs and CeSb the bilinear exchange interactions turn out to be similar, and evidence for important effects of higher-order magnetic interactions is found. The latter are shown to be the driving mechanism for the realization of the various magnetic phases in CeSb. For CeAs the magnetic excitation spectrum unambiguously demonstrates that a collinear single-q type-I spin structure is realized, whereas for USb a noncollinear triple-q type-I spin structure emerges from the observed magnetic excitations.

The curie temperature of an anisotropic heisenberg ferromagnet with mixed spins

AbstractFor the anisotropic Heisenberg ferromagnet with mixed spins of S = 1/2 and S = 3/2 and of S = 1/2 and S = 2, the Curie temperature TC is calculated with the use of pair model approximation. Assuming an anisotropic bilinear exchange interaction J between nearest neighbors of different spins and a uniaxial single‐ionic anisotropy D‐term for the spins of S = 3/2 and S = 2, the behavior of Tc as a function of these parameters J and D is investigated for some types of the spin system with various values of the anisotropy parameter α of the exchange interaction.

AB-initio calculation of indirect anisotropic bilinear interactions in DyZn

In metallic rare-earth systems, conduction electrons having a non-spherical orbital character may produce an anisotropic bilinear exchange coupling between 4f ions in addition to the usual isotropic Heisenberg term. An ab-initio calculation of such a coupling has been performed for the cubic compound DyZn, using APW band wavefunctions. The magnitude of the tetragonal-type coupling J γ( q ) is far from negligible and arises mainly from d-e g conduction electrons.

The Curie Temperature of Anisotropic Heisenberg Ferromagnet with Mixed Spins ofS=1/2 andS=1

For the anisotropic Heisenberg ferromagnet with mixed spins of S =1/2 and S =1, the Curie temperature T c has been calculated with the use of pair model approximation. Assuming the anisotropic bilinear and biquadratic exchange interactions ( J and J ') between nearest neighbors of the different spins, and the uniaxial single-ionic anisotropy D for each spin of S =1, the behaviors of T c as a function of these exchange parameters and the uniaxial anisotropy parameter are investigated for some types of the spin system with various values of the anisotropy parameter α of the exchange interaction. For small values of the exchange anisotropy parameter α it has turned out that T c decreases with D in the range of 0≦ D ≦0.5 J 1 . Furthermore, the biquadratic exchange interaction turns out to give little effect on the Curie temperature of the anisotropic Heisenberg ferromagnet with mixed spins when the exchange anisotropy parameters are in the range of 0.48≦α≦0.55.

Exchange-coupled pairs of Cr3+ions in emerald (in EPR spectra)

The EPR spectra of synthetic and natural samples of chromium-doped beryllium aluminium silicate (emerald) show a large number of resonance lines in addition to those arising from isolated Cr3+ ions occupying Al3+ sites. The angular and temperature dependence of the spectra indicate that most of the additional lines arise from three types of exchange-coupled pairs of Cr3+ ions occupying first, second and third nearest neighbour Al3+ sites, with antiferromagnetic exchange coupling constants of approximately 2.260, 0.195 and 0.026 cm-1 respectively. The spectra have been fitted with a spin Hamiltonian which includes anisotropic bilinear exchange, Zeeman and crystal field terms. Dynamic strain experiments for the first nearest-neighbour Cr3+ ion pair suggest that the magnetostriction contribution to the biquadratic exchange is negligible, and so the upper limit of 1% refers to intrinsic biquadratic exchange.

Effect of Biquadratic Exchange Upon Ferromagnetic Two-Magnon Bound States. II. Anisotropic Exchange

We have investigated the two-magnon bound state spectrum of a ferromagnetically ordered system for which the Hamiltonian contains an anisotropic bilinear exchange term, an anisotropic biquadratic exchange term, and a single-ion anisotropy term. The bound states, labelled by a wave vector q which we have taken to be in the [111] direction, were calculated by using zero-temperature Green functions. The principal results are: (i) the existence of single-ion bound states in the absence of single-ion anisotropy and conversely, their absence in the presence of such anisotropy, in contrast to the case in which the exchange interactions are isotropic; (ii) the appearance of an S mode for values of q, [Formula: see text]; (iii) the ordering of bound states for isotropic exchange interactions wherein the S0 mode lies below the S1-mode, D-mode pair and where the S1 mode lies below (above) the D mode if they lie below (above) the band, no longer holds.