The effect of uniaxial crystal-field anisotropy on magnetic properties of the superexchange antiferromagnetic Ising model

Abstract

The generalized Fisher super-exchange antiferromagnetic model with uniaxial crystal-field anisotropy is exactly investigated using an extended mapping technique. An exact relation between partition function of the studied system and that of the standard zero-field spin-1/2 Ising model on the corresponding lattice is obtained applying the decoration-iteration transformation. Consequently, exact results for all physical quantities are derived for arbitrary spin values S of decorating atoms. Particular attention is paid to the investigation of the effect of crystal-field anisotropy and external longitudinal magnetic field on magnetic properties of the system under investigation. The most interesting numerical results for ground-state and finite-temperature phase diagrams, thermal dependences of the sublattice magnetization and other thermodynamic quantities are discussed.

Exact Results of the Mixed-Spin Ising Model on a Decorated Square Lattice With Two Different Decorating Spins of Integer Magnitudes

“…77 and references cited therein). Among the systems, which belong to the class of exactly solved decorated Ising models, one could mention, at least, the original ferrimagnetic model introduced by Syozi [99][100][101][102][103][104] as well as the models with higher decorating spins. 49,50 It is worth mentioning that exact solutions of these spin model systems have furnished answers to interesting questions from the academic point of view (scaling and universality hypothesis, re-entrant phase transitions) as well as from the experimental viewpoint (dilution, technological application of ferrimagnets).…”

Reentrant phenomenon and inverse magnetocaloric effect in a generalized spin-(1/2, s) Fisher’s super-exchange antiferromagnet

“…Finally, it is worthwhile to mention that the presented generalization of the Fisher's super-exchange antiferromagnet on a decorated lattice in terms of arbitrary decorating spins is just one of many possible. Other simple generalizations allowing rigorous investigation of an enhanced MCE in two-dimensional spin systems are the introduction of the second-neighbor interaction between nodal spins [35], the introduction of the chemical potential [36], the axial zero-field splitting [38], the transverse magnetic field as well as the rhombic zero-field splitting on decorating spins. Moreover, one may also consider other planar lattices with the even coordination number, such as the kagomé lattice and the triangular lattice.…”

“…Fisher has proposed a novel spin-1/2 super-exchange Ising antiferromagnet on a decorated square lattice, which permits a rigorous solution of the partition function in the presence of an external magnetic field [33,34]. The spin-1/2 Fisher's super-exchange model and its other variants [35][36][37][38] can thus be used for exact theoretical study of the effect of applied field on magnetic properties of a certain class of magnetic insulators, e.g., for investigation of the cooling or heating efficiency of the system in a vicinity of discontinuous (first-order) and continuous (second-order) phase transitions. In addition, these spin models may also bring a considerable insight into deficiencies of some approximative methods.…”

Weak Singularities of the Isothermal Entropy Change as the Smoking Gun Evidence of Phase Transitions of Mixed-Spin Ising Model on a Decorated Square Lattice in Transverse Field

“…Among these paradigmatic examples, one could for instance mention Fisher's superexchange antiferromagnet, which refers to a spin-1/2 Ising model on a decorated square lattice with spatially modulated ferromagnetic and antiferromagnetic interactions in a longitudinal magnetic field [7,8]. Exact solutions for several variants and extensions of the original Fisher's superexchange model have been found by considering higher spin values, crystal-field anisotropy or different lattice geometries [9][10][11][12][13][14]. A few additional special cases of 2D Ising models partially taking into consideration the longitudinal magnetic field were exactly solved by making use of a precise mapping correspondence with free-fermion 16-vertex or 32-vertex models [15][16][17][18][19][20][21].…”