Effect of interionic anisotropy on the phase states and spectra of a non-Heisenberg magnet with S = 1
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DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
Effect of Interionic Anisotropy on the Phase States and Spectra of a Non-Heisenberg Magnet with S = 1 O. A. Kosmachev, A. V. Krivtsova, and Yu. A. Fridman Vernadskii Crimea Federal University, Simferopol, Crimea Republic, 295077 Russia e-mail: [email protected] Received August 4, 2015
Abstract—We study the effect of interionic anisotropy on the phase states of a non-Heisenberg ferromagnet with magnetic ion spin S = 1. It is shown that depending on the relation between the interionic anisotropy constants, uniaxial and angular ferromagnetic and nonmagnetic phases exist in the system. We analyze the dynamic properties of the system in the vicinity of orientational phase transitions, as well as a phase transition in the magnetic moment magnitude. It is shown that orientational phase transitions in ferromagnetic and nematic phases can be first- as well as second-order. DOI: 10.1134/S1063776116020060
1. INTRODUCTION Ordering in spin systems is usually associated with the standard magnetic order for which mean spin values 〈Sn〉 at the sites differ from zero and form various magnetic structures (ferromagnetic, antiferromagnetic, etc.; see [1–3]). The main property of magnetically ordered systems is time-reflection symmetry breaking, 〈Sn〉 → –〈Sn〉 for t → –t. Most publications devoted to linear and nonlinear dynamics of the magnetic moment are based on the Landau–Lifshitz equation for the unit (normalized) magnetization vector (see [1, 2]). The validity of the Landau–Lifshitz equation can be substantiated for a ferromagnet that can be described by the Heisenberg exchange Hamiltonian including the isotropic bilinear interaction of spins of the type JS1S2. This Hamiltonian contains only the first powers of spin operators (at a given site), and it is natural to use spin coherent states (generalized coherent states for group SU(2) ~ SO(3)) for its analysis (see review [4]). It turns out that in the case of pure states of interest (in fact, at T → 0), the evolution of the system occurs within these states; in particular, average value 〈S〉 of the spin (magnetization) vector has a constant length. This condition in fact coincides with that observed for the Landau–Lifshitz equation disregarding dissipation. However, the possibility of a spin nematic state, in which average values of spins 〈Sn〉 at lattice sites are equal to zero, but spontaneous symmetry breaking of the spin system is associated with anisotropy of some higher-order correlators of spin projections, was indicated long ago [5]. For such systems, specific modes of spin oscillations including longitudinal spin dynamics also exist. Such effects appear due to non-Heisenberg
interactions, i.e., the presence of higher-order spin invariants of the type (SnSn')2S (S is the spin of a magnetic ion) in the exchange Hamiltonian. If a situation does not fit the Heisenberg model (e.g., higher-order invariants of the isotropic interaction are taken into account), the condition |〈S〉| = const does not hold and coherent states can
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