Saiko P. Quadrupole and quadrupole-ferromagnetic phases in uniaxial magnets with single-ion anisotropy and biquadratic exchange interaction

The thesis is devoted to the study of the properties of a spin-1 magnet with competing vector and tensor interactions with the most general form of uniaxial symmetry. Such types of tensor interactions as single-ion anisotropy (SIA) and biquadratic exchange interaction (BEI) are considered. It has been shown that the presence of several competing interactions in the system causes its high sensitivity to changes of the model Hamiltonian constants. There is a range of Hamiltonian parameters where only three symmetric phases can be realized: ferromagnetic phase with the ordering axis Z (FMP), planar quadrupole phase with the ordering plane XOY (PQP) and paramagnetic phase (PMP). The corresponding phase diagram in dimensionless field-temperature coordinates is constructed, and it contains a triple point. The dependence of the triple point coordinates on the Hamiltonian parameters is calculated. There is a range of Hamiltonian parameters where the phase diagram in the same coordinates in addition to the specified symmetric phases also includes two phases with broken symmetry: axial quadrupole phase with the ordering axis Z (AQP) and mixed quadrupole-ferromagnetic phase (QFP). There are two multicritical points on the phase diagram: triple and tetracritical. The competition of the FMP and PQP phases is considered and it is proved that the first-order phase transition between this phases is accompanied by the hysteresis phenomena. A corresponding hysteresis loop in the field-magnetization coordinates is constructed. The AQP phase has been studied in details and the spin excitation spectrum in presence of the longitudinal external magnetic field was obtained. The dependence of the quadrupole components of the order parameter on the temperature is constructed for this phase. It is proved that the critical temperature of the phase transition between the AQP and QFP phases strongly depends on the degree of BEI anisotropy. The phase transition between the AQP and PQP phases in the absence of the external magnetic field is investigated. It is determined that quadrupole components of the order parameter, which are functions of the single-ion anisotropy parameter, show hysteresis-like behavior. Thus, it has been shown that the behavior of the uniaxial spin-1 magnets in the presence of SIA and BEI significantly depends on the competition between different types of interactions. The BEI and its anisotropy degree play a significant role in this competition and at the properties of the magnetic system. The change of the BEI anisotropy constants affects the presence of certain phases in it. For the experimental check of the thesis results, it is advisable to use a magnet for which BEI plays a dominant role in the formation of magnetic ordering, where quadrupole and quadrupole-ferromagnetic phases are implemented along with FMP and PMP phases.