The field of research: (experimental) study of amorphous semiconductors based on As₂S₃ at low temperatures. Interpretation of experimental heat capacity data from the point of view of fracton excitation model. Fractons in quasiparticle formalism correspond to the vibrations of fractals - random clusters of atoms-clusters that are characteristic of the structure of amorphous materials.
Another area of interest are (quasi) low-dimensional magnetic materials and their lattice subsystem. We deal with the following materials:

Heisenberg chains with spin 1 (based on nickel ion) where we study the influence of the crystal field on the ground state including the so-called large-D systems (e.g. NENC), Haldane systems (NENP) and XY systems (CsNiF₃).

Ising chains and layers with the effective spin 1/2 based on rare earth ions (AR(MoO₄)₂, A=Cs,K, R=Dy, Gd, Lu, Er) where we investigate the effect of dipolar interaction, crystal field and lattice vibrations on the state of a low-dimensional magnetic system. We were the first who showed in the system KEr(MoO₄)₂ the possibility of applying a large rotational cryo-magnetocaloric effect without the need for a phase transition.

metalo-organic frameworks (MOFs) – strongly porous materials based on transition metal ions

Heisenberg two-dimensional systems with spatially anisotropic square lattice and spin 1/2. In such grids, the central spin has four nearest neighbors with which it can interact as follows:

1. with equally strong exchange interaction J (square lattice)
2. with two neighbors opposite interacts through J and with two others is coupled with J' (two-dimensional array of coupled chains = rectangular lattice)
3. interacts with two adjacent neighbors via J and with other two adjacent neighbors via J' (two-dimensional array of coupled zigzag chains = zigzag square lattice, two-dimensional array of coupled tetramers,….)
4. interacts with one neighbor via J and with the other three via J '(dvarious dimerized square lattices)

By rotating the basic clusters (2J '+ 2J, J' + 3J, J + 3J ') it is possible to obtain a large number of two-dimensional lattices, which differ from each other by the nature of the ground state (ordered collinear Néel state, S = 0 non-magnetic state) and properties at finite temperatures. The research of such spatially anisotropic lattices does not have a long tradition, since from a theoretical point of view it was difficult to run calculations on large grids to exclude "finite size effects". From an experimental point of view, the first systems also appear relatively late, as the lack of theoretical predictions and the difficulty of preparing high-quality and sufficiently large single crystals did not allow a more accurate identification of the system. In this respect, calculations from the first principles are very helpful, which, based on the knowledge of the crystal structure, can provide the estimates of the interaction constants Ji around the central atom. Our study of the compound Cu(en)(H₂O) ₂SO₄ (CUEN), (en=C₂H₈N₂) has also gone through such a complex process. CUEN was initially identified as the realization of a spatially anisotropic triangular lattice in the collinear Neel phase, which shares features with a square lattice [1]. A subsequent study of electron paramagnetic resonance refuted this assumption and pointed at the existence of a square lattice [2]. Only first principles calculations showed that CUEN is the first implementation of a zigzag square lattice, which was also confirmed by analyzes of thermodynamic data within the model, while theoretical predictions were numerically calculated by the quantum Monte Carlo method for 120x120 spin lattice [3]. In this work, we have also shown, that even in such a lattice, the magnetic field induces quantum spin vortices and the associated Berezinskii-Kosterlitz-Thouless (BKT) phase transition theoretically predicted for an ideal square lattice. In the context of vortices, the BKT transition is also observed in superconductors in the magnetic field and superfluid helium in the non-inertial system. Recent theoretical studies show that CUEN is a suitable system for observation of the spin Nernst effect. In addition, the substitution of H₂O by en a compound Cu(en) ₂SO₄ is prepared, which is characterized by strong dimerized square lattice. The spin subsystem undergoes a field induced phase transition into the ordered state in magnetic fields above 7 T.
On the example of the analysis of experimental data of CuenCl₂ developed a procedure how to extract information about low-dimensional magnetism despite the strong influence of interplanar interactions when applying magnetic fields higher than the saturation field if sufficient theoretical predictions are available [4].
In addition, we found that the Heisenberg models on the zigzag square lattice and rectangular lattice are equivalent at both the ground state and finite temperatures, in both zero and non-zero magnetic fields. Therefore, this equivalence will not enable to identify the real systems, unless first-principle calculations are made.

[1] M. Kajňaková, M. Orendáč, A. Orendáčová, et al., Phys. Rev. B 71, 014435 (2005).
[2] R. Tarasenko, A. Orendáčová, E. Čižmár et al, Phys. Rev. B 87, 174401 (2013).
[3] L. Lederová, A. Orendáčová, J. Chovan et al, Phys. Rev. B 95, 054436 (2017).
[4] L. Lederová, A. Orendáčová, R. Tarasenko, et al, Phys. Rev. B 100, 134416 (2019).

P.J. Šafárik University in Košice, 1984, Physics of Condensed Matter and Acoustics

P.J. Šafárik University in Košice, 1986, Physics of Condensed Matter and Acoustics

P.J. Šafárik University in Košice, Faculty of Science, 1999, Physics of Condensed Matter and Acoustics

P.J. Šafárik University in Košice, Faculty of Science, 2012, Physics of Condensed Matter and Acoustics

Comenius University, Faculty of mathematics, physics and informatics, 2007, Physics of Condensed Matter and Acoustics