Quantum Heisenberg chain and square lattices are important paradigms of a low-dimensional magnetism. Their ground states are determined by the strength of quantum fluctuations. Correspondingly, the ground state of a rectangular lattice interpolates between the spin liquid and the ordered collinear Néel state with the partially reduced order parameter. The diversity of additional exchange interactions offers variety of quantum models derived from the aforementioned paradigms. Besides the spatial anisotropy of the exchange coupling, controlling the lattice dimensionality and ground-state properties, the spin anisotropy (intrinsic or induced by the magnetic field) represents another important effect disturbing a rotational symmetry of the spin system. The S = 1/2 easy-axis and easy-plane XXZ models on the square lattice even for extremely weak spin anisotropies undergo Heisenberg-Ising and Heisenberg-XY crossovers, respectively, acting as precursors to the onset of the finite-temperature phase transitions within the two-dimensional Ising universality class (for the easy axis anisotropy) and a topological Berezinskii–Kosterlitz–Thouless phase transition (for the easy-plane anisotropy). Experimental realizations of the S = 1/2 two-dimensional XXZ models in bulk quantum magnets appeared only recently. Partial solutions of the problems associated with their experimental identifications are discussed and some possibilities of future investigations in quantum magnets on the square and rectangular lattice are outlined.

The phase content and sequence, the crystal structure, and the magnetic properties of perovskite solid solutions of the (1−y)BiFeO₃–yBiZn_0.5Ti_0.5O₃ series (0.05 ≤ y ≤ 0.90) synthesized under high pressure have been studied. Two perovskite phases, namely the rhombohedral R3c and the tetragonal P4mm, which correspond to the structural types of the end members, BiFeO₃ and BiZn_0.5Ti_0.5O₃, respectively, were revealed in the as-synthesized samples. The rhombohedral and the tetragonal phases were found to coexist in the compositional range of 0.30 ≤ y ≤ 0.90. Magnetic properties of the BiFe_1−y[Zn_0.5Ti_0.5]_yO₃ ceramics with y < 0.30 were measured as a function of temperature. The obtained compositional variations of the normalized unit-cell volume and the Néel temperature of the BiFe_1−y[Zn_0.5Ti_0.5]_yO₃ perovskites in the range of their rhombohedral phase were compared with the respective dependences for the BiFe_1−yB³⁺_yO₃ perovskites (where B³⁺ = Ga, Co, Mn, Cr, and Sc). The role of the high-pressure synthesis in the formation of the antiferromagnetic states different from the modulated cycloidal one characteristic of the parent BiFeO₃ is discussed.

An experimental study of the magnetocaloric effect in tetraaquabis(hydrogen maleato)nickel(II), [Ni(C₄H₃O₄)₂(H₂O)₄] powder sample is presented. The magnetocaloric properties of the studied sample were investigated using specific heat and magnetization measurements in magnetic fields up to 9 T in the temperature range from 0.4 to 50 K. A large conventional magnetocaloric effect was found at a temperature of about 3.5 K, where −ΔS_M = 8.5 Jkg⁻¹K⁻¹ and 11.2 Jkg⁻¹K⁻¹ for a magnetic field of 5 T and 7 T, respectively. Assuming a substantial role of the crystal field, the temperature dependence of the magnetic specific heat in a zero magnetic field was compared with an S = 1 model with single-ion anisotropy parameters D and E (axial and rhombic). The best agreement was found for the parameters D/k_B = −7.82 K and E/k_B = −2.15 K. On the other hand, the experimental temperature dependence of −ΔS_M shows higher values compared to the theoretical prediction for the mentioned model, indicating the presence of additional factors in the system, such as an exchange interaction between magnetic ions. The first exchange pathway can be realized through maleic rings between the nearest Ni(II) ions. The second exchange pathway can be realized through water molecules approximately along the a crystallographic axis. Broken-symmetry DFT calculations performed using the computational package ORCA provided the values of ferromagnetic exchange interactions, J₁/k_B = 1.50 K and J₂/k_B = 1.44 K (using B3LYP functional). The presence of such ferromagnetic correlations in the studied system may explain the enhanced magnetocaloric effect compared with the model of an anisotropic spin-1 paramagnet.

An experimental study of the rotational magnetocaloric effect in Ni(en)(H₂O)₄SO₄∙2H₂O (en = ethylenediamine) single crystal is presented. The study was carried out at temperatures above 2 K and was associated with adiabatic crystal rotation between the easy plane and hard axis in magnetic fields up to 7 T. The magnetocaloric properties of the studied system were investigated by isothermal magnetization measurement. The experimental observations were completed with ab initio calculations of the anisotropy parameters. A large rotational magnetic entropy change ≈12 Jkg⁻¹K⁻¹ and ≈16.9 Jkg⁻¹K⁻¹ was achieved in 5 T and 7 T, respectively. The present study suggests a possible application of this material in low-temperature refrigeration since the adiabatic rotation of the single crystal in 7 T led to a cooldown of the sample from the initial temperature of 4.2 K down to 0.34 K. Finally, theoretical calculations show that S = 1 Ni(II)-based systems with easy-plane anisotropy can have better rotational magnetocaloric properties than costly materials containing rare-earth elements in their chemical structures.

The growth of sufficiently large single crystals of $\mathrm{Cu}\left(tn\right){\mathrm{Cl}}_2$ $(tn=1,3\text{−}\text{diaminopropane})$ enabled specific heat and susceptibility studies in various field orientations. The nearly invisible broad hump in zero-field specific heat at 0.6 K coincides with the change in the characteristic parameters of zero-field muon relaxation spectra. The lack of oscillations in the time spectra and their exponential character preserved down to 40 mK suggest the coexistence of static and fluctuating local fields associated with the prevalence of low-dimensional correlations. The extreme two-dimensionality is also manifested by the nonmonotonous character of the magnetic phase diagram. First-principle calculations of exchange couplings introduced a concept of a quasi-two-dimensional magnetic lattice with many couplings within the magnetic layers. The strongest ones lead to the model of a rectangular lattice with the intrachain coupling $J/k_{\mathrm{B}}=4.3$ K and the interchain coupling $J^{\prime }/J=0.46$, which provides excellent agreement with the zero-field specific heat. However, the susceptibility data suggest the importance of other weaker interactions in accord with first-principle studies. Significant broadening of field-induced specific heat anomalies may be ascribed to potential intrinsic partial magnetic disorder associated with the gradual modulation of $tn$ positions in the crystal structure.