Research area:

Theoretical investigation of the phase transition and dynamical properties of the rare-earth magnetics.

The main results:

1. An explicit form of an invariant tensor representation for Hamiltonian electrostatically interacting electrons in solids was obtained with irreducible operators of Hubbard transition (in collaboration with V.A.Popov).
2. The breakdown of Adler principle for processes of certain types in isotropic antiferromagnets was found within the framework of magnon-magnon and exiton-magnon interaction theory. (in collaboration with V.A.Popov).
3. The spectrum structure of one-fermion states of the finite non-closed XY-chain in the whole range of anisotropy parameters and transverse field magnitudes was investigated. The nature of ordering for a certain class of systems with non-degenerate ground state and finite volume was explained (in collaboration with Yu.V.Pereverzev).
4. For the antiferromagnetic Ising model (S=1) with easy-plane anisotropy under magnetic field a phase diagram in the temperature-field-anisotropy coordinates was built within mean-field approximation. (in collaboration with Yu.V.Pereverzev).
5. Mechanisms of the structural phase transition in the rare-earth magnetics induced by the magnetic field were investigated numerically within the vibronic model. The transition observed in KEr(MoO₄)₂ corresponds qualitatively to the model with two lattice vibration active modes which kinds of interaction with the electronic excitations are different.

Selected publications:

1. V. A. Popov and A. A. Loginov, Generalization of the Heisenberg Hamiltonian for the Case of an Atomic System with a Variable Atomic Spin Value, phys. stat. sol. (b) 84, 83 (1977) pp. 83-91.
2. A. A. Loginov and V. A. Popov, Tensor Structure of  Electrostatic Interaction Hamiltonian in the Hubbard Representation. Applications to Magnetically Ordered Crystals, FNT, 1978, 4 N4, pp. 497-510.
3. A. A. Loginov and V. A. Popov, On Adler Principle for Antiferromagnet Crystals,Ukrainian Physical Journal, 1988, 33, N9, pp. 1393-1401.
4. A. A. Loginov and Yu. V. Pereverzev, Classification of States and Macroscopic Degeneracy of an Open XY-Chain in a Transverse Field, FNT, 1997, 23, N7, pp.712-720.
5. A. A. Loginov and Yu. V. Pereverzev, Phase Diagram of Ising Model (S=1) with Easy-Plane Anisotropy at Magnetic Field, FNT, 1998, 24, N9, pp. 867-874.
6. A. A. Loginov, Magnetic Field Induced Phase Transitions in a Vibronic Model for KEr(MoO4)2, FNT, 2002, 28, N10. pp. 1056-1064.