A generalized Landau–Lifshitz equation for an isotropic SU(3) magnet

Abstract

In this paper we obtain equations for large-scale fluctuations of a mean field (the field of magnetization and quadrupole moments) in a magnetic system realized by a square (cubic) lattice of atoms with spin s 1 at each site. We use the generalized Heisenberg Hamiltonian with a biquadratic exchange as a quantum model. A quantum thermodynamical averaging gives classical effective models, which are interpreted as Hamiltonian systems on coadjoint orbits of the Lie group SU(3).

Topological excitations in a two-dimensional spin system with high spin s ≥1

“…where η a is a quadratic form in {µ a }, η a = √ 5 d abc µ b µ c (see [9] for more details). The Hamiltonian systems on coadjoint orbits of SU (3) serve as classical effective models for the system with spin s ≥ 1 and a biquadratic exchange.…”

“…The corresponding mean-field configuration is obtained by substituting (13) in (9). The behavior of the components µ 3 and µ 8 is shown in Fig.…”

Longitudinal spin dynamics in nickel fluorosilicate

“…[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] Nowadays, many examples are known of the unconventional properties of magnetic materials containing the lanthanide and actinide ions, which also exhibit the effects of spin reduction. 26,27 This unconventional magnetism has been found not only for crystalline magnets, but also for the Bose-Einstein condensates of atoms with a nuclear spin of unity.…”

The SU(3) symmetry and macroscopic dynamics of magnets with spin s = 1

“…These, in particular, can be the means of the SU (2s+1) Lie group generators. The spin-(s=1) magnets with this number of parameters were studied in [19]- [21]. In [21], new integrable models were obtained that describe the dynamics and soliton states of magnets for the spin value s = 1.…”