**Ľubomíra Regeciová**

In the past decade, numerous theoretical and experimental studies have been dedicated to understand the underlying physics of rare-earth tetraborides in which a number of anomalous phenomena such as the fascinating sequence of magnetization plateaus at fractional values of the saturated magnetization, metamagnetic transitions or magnetocaloric effect were experimentally observed. Several models have already been proposed to describe these compounds, but none of them was able to explain satisfactorily all mentioned phenomena in details. In this thesis we have investigated properties of the extended Ising model with the first, second, third, fourth and fifth nearest-neighbor spin coupling, the Ising model with the long-range RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction and the model based on the coexistence of the spin and the electron subsystems. Our results have showed that even small values of the fourth and fifth nearest-neighbor spin couplings change significantly the shape of magnetization curve. This model is able to describe some of the partial sequences of fractional magnetization plateaus observed in rare-earth tetraborides. Furthermore, the model with the RKKY interaction mediated by conduction electrons forms, for different values of kF, various sequences of magnetization plateaus. For the value kF~2π/1.24, corresponding to the real situation in rare-earth tetraborides, we have found the main 1/2 plateau which perfectly accords with experimental measurements in ErB4 and TmB4 compounds. Finally we have showed that model based on the coexistence of electron and spin subsystem is able to qualitatively describe the magnetocaloric effect observed in the TmB4 compound.

**Matúš Lach**

The two-dimensional XY model is known to exhibit an unusual infinite order phase transition belonging to the Kosterlitz-Thouless (KT) universality class [1]. Introduction of a nematic coupling into the Hamiltonian leads to an additional phase transition belonging in the Ising universality class [2]. Recently, it has been shown that higher order harmonics can lead to a qualitatively different phase diagram, with additional ordered phases originating from the competition between the ferromagnetic and higher-order (pseudonematic) couplings [3]. The new phase transitions were identified to belong to the 2D Potts, Ising, or KT universality classes. In the present study we investigate effects of geometrical frustration on such a generalized XY model by considering it on a triangular lattice with antiferromagnetic (AF) coupling. The simplest generalization involving the second-order antinematic (AN2) coupling has been shown to display, besides the AF and AN2 phases, also an additional chiral phase above the KT line [4]. Here we modify this model by considering the AN3 term of the third instead of the second order AN2 and study how the phase diagram is affected by this change. Recent investigations of the ground-state properties of such a model suggested an interesting behavior with potential interdisciplinary applications [5]. We demonstrate that such a modification leads to the overall change of the phase diagram topology, compared to the model with the AN2 term. Namely, besides the AF and AN3 phases which appear in the limits of relatively strong AF and AN3 interactions, respectively, it includes an additional complex noncollinear quasi-long-range ordered phase at lower temperatures wedged between the AF and AN3 phases. This new phase originates from the competition between the AF and AN3 couplings, which is absent in the model with AN2.

[1] J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973).[2] D.H. Lee and G. Grinstein, Phys. Rev. Lett. 55, 541 (1985).

[3] F.C. Poderoso, J.J. Arenzon, and Y. Levin, Phys. Rev. Lett. 106, 067202 (2011).

[4] J.-H. Park, S. Onoda, N. Nagaosa, and J. H. Han, Phys. Rev. Lett. 101 167202 (2008).

[5] M. Žukovič, Phys. Rev. B 94 014438 (2016). URL:https://ktfa.science.upjs.sk/events/phd-students-talks-3/ ORGANIZER;CN=:MAILTO: CATEGORIES:KTFA seminar LOCATION:Jesenna 5, Košice END:VEVENT END:VCALENDAR