Solitons in an easy plane ferromagnet

Dynamical solitons in a uniaxial ferromagnet are considered. The second constant of magnetic anisotropy is taken into account. In the case of easy plane anisotropy the explicit form for the magnetization is found. The dispersion laws for obtained solitons are discussed.     

Localised spin wave modes in a Heisenberg ferromagnet with biquadratic interaction

The presence of biquadratic exchange in a one-dimensional ferromagnetic Heisenberg chain with an impurity spin is shown to change the nature of the impurity modes and its eigenvalues considerably which can be observed experimentally.     

Solitons in a deformed ferromagnet with anisotropy of the easy plane type

Soliton dynamics is studied in a compressed ferromagnetic chain having anisotropy of the “easy plane” type. It is shown that there exists a soliton wave of lattice deformation which follows the magnetic soliton. Two models are considered for the connection between deformation and spins. The soliton renormalization constant is found. The effect of lattice anharmonicity is studied.     

Spiral-logarithmic structures in a Heisenberg ferromagnet

Spiral-logarithmic structure is suggested as a stationary solution of a modified equation for the Heisenberg model, and the single-and N-soliton solutions are constructed on this base.     

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.     

Phonon renormalization and damping in a Heisenberg ferromagnet

A theoretical study of spin-phonon interaction in a Heisenberg ferromagnet is made on the basis of a Green function technique. We have calculated below and aboveT _c the renormalized phonon energy and the phonon damping for the first time beyond the RPA. The obtained temperature and magnetic field dependence of the phonon relaxation time is in good agreement with the experimental data.     

Analogue of surface reconstruction in a Heisenberg ferromagnet

When the exchange interaction between spins in the surface of a Heisenberg ferromagnet is antiferromagnetic in sign, the surface region may order in an anti-ferromagnetic manner, even though the bulk is ferromagnetic. We discuss the properties of a model which exhibits this behavior from a theoretical point of view. The properties of the model are examined to see if by this means one can understand some aspects of recent observations of spin polarized photoemission from the surface of EuO.     

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.     

Susceptibility of compressible Heisenberg ferromagnet

The spin-phonon spin $\text{1}\text{2}$ Heisenberg system is found to have the same critical index for the susceptibility as the ideal, rigid lattice ferromagnet. This is in accordance with the criterion for critical index renormalisation expounded by Fisher in terms of the sign of the specific heat index.     

Surface spin waves in Heisenberg ferromagnet

The existence conditions and the dispersion laws for surface spin waves in Heisenberg ferromagnet are obtained for any orientation of the surface and any exchange constant or anisotropy field in the surface plane. It is shown that purely decaying modes, both of accoustical or optical types, can occur only for surface having special properties of rotational symmetry.     

Dynamic critical behavior of the Heisenberg model with strong easy plane anisotropy

The dynamic critical behavior of the Heisenberg model with a strong anisotropy of the exchange constant in the z direction is investigated. The main features of the time evolution of this model are revealed. The static and dynamic critical behavior of planar magnetic models is shown to be described well by the Heisenberg model with strong easy plane anisotropy.     

Dyson equation for Heisenberg ferromagnet

An exact representation for the self-energy operator of the two-time Green function for the transverse spin components for the Heisenberg ferromagnet is obtained.     

The Heisenberg ferromagnet as a quantum field theory

We consider a lattice of spin 1/2 ions, described by the discrete form of the current commutation relationsJ _i J _(i) =1/2, [J _i ,J _i ]=i _ij J _i where =1, 2, 3 andi label the lattice sites. The algebra is realized as the Clifford algebra over a Hilbert space. The equations of motion are specified by a formal Hamiltonian of the Heisenberg form: , wheref _ij 0 and only a finite numberQ of ions are linked to any given lattice site. We prove that the Hamiltonian is non-negative in a representation of , and has a ground state exhibiting ferromagnetism. The time displacement group acts continuously on , inducing automorphisms. is asymptotically abelian with respect to the space translations of the lattice.The model is an example of an algebraic quantum field theory and possesses a broken symmetry, the rotation group 0(3). The consequent Goldstone theorem is proved, namely, there is no energy gap in the spectrum ofH.