Abstract:
Experimental studies of magnetic properties of a topological van der Waals antiferromagnet insulator MnBi$_2$Te$_4$ demonstrated not only an anomalous behavior of magnetization before and after the spin-flop transition but also its strong temperature dependence. To interpret these effects, we present a quantum theory of layered antiferromagnet with a trigonal symmetry of the triangular lattice. Using atomic representations for spin operators and the diagram technique for Hubbard operators, we obtain a dispersion equation describing the temperature dependence of the excitation spectrum. In the anisotropic self-consistent field approximation, we derive a transcendent equation establishing an interrelation between the Néel temperature and model parameters. For the weak-anisotropy case, we obtain its analytical solution. We describe the temperature evolution of magnetization as a function of magnetic field and construct a phase diagram showing regions where different configurations of MnBi$_2$Te$_4$ magnetic sublattices are realized. We observe that quantum effects induced by the trigonal component of the single-ion anisotropy essentially affect the thermodynamic properties of antiferromagnets.
Keywords:single-ion anisotropy, spin 5/2, trigonal component of the crystalline field, quantum
effects, diagram technique for Hubbard operators, Matsubara Green's functions,
spin-flop transition, antiferromagnet magnetization, saturation field, Néel
temperature, MnBi$_2$Te$_4$.
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