On thermodynamics of the two-dimensional Heisenberg ferromagnet

Under general assumptions about the magnon dispersion for the model quoted in the title it is stated that at low temperatures T the specific heat is linear in T and the susceptibility is proportional to exp(const/T).     

Stripe-like topological excitations in a two-dimensional Heisenberg ferromagnet

For a two-dimensional Heisenberg ferromagnet, a class of steady-state nonlinear excitations above the ground state is considered. The excitations have the form of stripes and exhibit quasiparticle properties. The effect of an external magnetic field on the basic characteristics of these nonlinear topological excitations is investigated. The magnetic field is found to destroy the instanton-type solutions (kinks) and to generate new particles with the properties of vortex-antivortex pairs: each particle has a zero topological charge and an energy close to the double skyrmion energy 8πJS². The dispersion of the quasiparticles and the dependences of their energy and momentum on the number of magnons localized by one excitation are discussed.     

Three-magnon bound states in the two-dimensional isotropic and anisotropic Heisenberg ferromagnet

The existence is shown of bound complexes of three magnons in a two-dimensional simple cubic Heisenberg ferromagnet. The Heisenberg spin hamiltonian is replaced by Dyson's boson hamiltonian. The spurious features of this hamiltonian are treated explicitly. Using Faddeev's formalism, detailed calculations of the three-magnon bound state energy curves have been performed both for the isotropic and the longitudinally anisotropic ferromagnet. Attention is paid to the possibility of observing these three-magnon bound states experimentally.     

Comparative study between a two-dimensional anisotropic Heisenberg antiferromagnet with easy-axis single-ion anisotropy and one with easy-axis exchange anisotropy

Generally, in literature, easy-axis single ion anisotropy and easy-axis exchange anisotropy was treated in indistinct way. In this work we propose to perform a comparative study of the effects of these two easy-axis anisotropies on the behavior of the magnetization and the critical temperature (_Tc)$(T_{\mathrm{c}})$ in the 2D classical Heisenberg antiferromagnetic model. In order to study the low-temperature thermodynamics of this model, we should consider the contribution of anisotropic spin waves, using a self-consistent harmonic approximation (SCHA) theory. We compare the predictions of SCHA with numerical simulations on L×L$L\times L$ square lattices using Monte Carlo (MC) simulations, which include effects due to all thermodynamically allowed excitations. Our SCHA results are in good agreement with our MC simulations results and have shown that the strong K$K$ limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of _Tc$T_{\mathrm{c}}$ on anisotropic parameter K$K$ becomes linear and in the single-ion anisotropic case, _Tc$T_{\mathrm{c}}$ becomes independent of K$K$. Also, using MC simulations and finite size scaling, we show that the critical exponents in the two anisotropic case are compatible with the 2D Ising values α=0.125$\alpha =0.125$ and γ=1.75$\gamma =1.75$.     

Critical exponents for two-dimensional Heisenberg ferromagnet with long-range interaction

Summary Using renormalization group technique, the critical exponents are determined for two-dimensional Heisenberg ferromagnet in the presence of a magnetic field. Critical exponents are expressed as a function of potential range σ. For the long-range interaction potential between the spins, the spontaneous magnetization exponent β takes the poorer value of mean-field result. The other exponents agree with the known values of exponents. The susceptibility eigenvalue equation arising from renormalization group is also solved and eigenfunctions are determined.

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Riassunto Usando la tecnica del gruppo di rinormalizzazione si determinano gli esponenti critici per un ferromagnete di Heisenberg bidimensionale in presenza di un campo magnetico. Si esprimono gli esponenti critici in funzione di un intervallo di potenziale σ. Per un potenziale d’interazione a largo raggio tra gli spin, l’esponente di magnetizzazione spontanea β assume il valore più scarso del risultato del campo medio. Gli altri esponenti si accordano con i valori noti degli esponenti. Si risolve anche l’equazione degli autovalori di suscettibilità proveniente dal gruppo di rinormalizzazione e si determinano le autofunzioni.

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Резюме Используя технику грушы перенормировки, определяются критические экспоненты для двумерного ферромагнетика Гайзенберга в присутствии магнитного поля. Критические экспоненты выражаются через радиус действия потенциала. Для длиннодействующго потенциала взаимодействия между спинами зкспонента спонтанного нмагничивания β дает меньшую величину для среднего поля. Другие экспоненты согласуются с известными величинами для экспонент. Решается уравнение для собоственных значений восприимчивости, возникающее из группы перенормировки, и определяются собственные функции.

     

Local magnon modes and the dynamics of a small-radius two-dimensional magnetic soliton in an easy-axis ferromagnet

The internal dynamics of a small-radius precession magnetic soliton is considered. A variational formulation of the problem on the soliton-magnon interaction is proposed and used to calculate the frequency of a truly local mode. It is shown that this mode, as well as the conventional translational mode, remains localized in the small soliton radius limit. The presence of the local mode is confirmed by the numerical solution of the scattering problem.     

Spin-wave analysis of easy-axis quantum antiferromagnets on the triangular lattice

We perform the standard spin wave analysis of the triangular Heisenberg quantum antiferromagnet with nearest neighbour coupling. The exchange interaction is taken to be J _{z=J x=J y} (0<1). We give a simple explanation of the non-trivial classical degeneracy pointed out by Miyashita and Kawamura and show that it is removed by quantum fluctuations, but that the degeneracy manifests itself through the appearance of a second gapless spin-wave branch. The existence of a second gapless mode has a drastic influence on the quasiclassical behaviour near the Ising limit: the energy gain with respect to the Ising state energy is found to be linear in , and the reduction of the sublattice magnetization on two of the three sublattices remains finite as 0. These findings essentially invalidate the original qualitative arguments [14] in favour of a spin-liquid ground state of the anisotropic triangular antiferromagnet.     

Spin-wave relaxation in a quantum hall ferromagnet

We study spin wave relaxation in quantum Hall ferromagnet regimes. Spin-orbit coupling is considered as a factor determining spin nonconservation, and external random potential as a cause of energy dissipation making spin-flip processes irreversible. We compare this relaxation mechanism with other relaxation channels existing in a quantum Hall ferromagnet. The article is published in the original.     

Dynamical toroidal Hopfions in a ferromagnet with easy-axis anisotropy

Three-dimensional toroidal precession solitons with a nonzero Hopf index, which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have been found. The structure and existence region of the solitons have been numerically determined by solving the Landau-Lifshitz equation.     

Green function theory of a Heisenberg ferromagnet with dipole-octupole interactions

The effect of dipole-octupole interaction on different magnetic parameters for the spinS=3/2 system in the presence of biquadratic exchange has been investigated. The Green function technique with random phase approximation (RPA) has been employed to obtain analytical results. These results are in good agreement with the results of the molecular field approzimation (MFA).     

Two-phonon processes in Heisenberg ferromagnet

Using the method of double-time retarded Green function, an expression for the spin energy spectrum including the contributions of one-phonon and two-phonon processes has been derived. Calculations have been performed using the spin wave approximation. The broadening of the energy level is roughly estimated in a peculiar case.I would like to thank Dr. Dagmat Fraitová for her advice and help.     

Correlation inequality in Heisenberg ferromagnet

In a three-spin ferromagnetic system, Griffiths' second inequality is shown to hold for the Heisenberg model, provided every bond is strictly positive.     

Correlation inequality in Heisenberg ferromagnet

In a four-spin Heisenberg ferromagnetic system, it is found computationally that Griffiths' second inequality, ?〈σ_r·σ_s〉/?J_mn?0, m, n, r, s distinct, is violated, and conditions are obtained under which it holds.     

Structurally disordered Heisenberg ferromagnet

The effect of structural disorder on the properties of a Heisenberg ferromagnet is considered within the Bethe-Peierls-Weiss approximation. It is concluded that the details of the structural disorder, and its effect on the exchange interactions between localized spins, determine the direction of change in the Curie temperature with respect to the crystalline case.     

On some additional effects in Heisenberg ferromagnet caused by the presence of dipole-dipole interactions

The Heisenberg ferromagnet with dipole-dipole interactions was studied. It was shown that the presence of dipole-dipole interactions changes the direction of the quantization axis, gives the anharmonical correction to the low temperature magnetization proportional to the square of the temperature, increases the critical point and leads to a fusion process of elementary excitations. All the results obtained are valid only in the presence of an external magnetic field. The absence of the field requires a qualitatively new approach.     

Quantization of the continuous Heisenberg ferromagnet

The quantization of the continuous anisotropic Heisenberg ferromagnet with uniaxial anisotropy is performed by means of the quantum inverse scattering method. The space of quantum states is shown to possess the positive metric only in the su(1, 1) case (the magnet on the hyperboloid). The requirement of complete integrability leads, in the anisotropic case, to a deformation of the algebra of observables. The problem of local integrals of motion is discussed. The Hamiltonian is constructed for two-particle states.