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

Abstract

Abstract. The thermodynamic and magnetocaloric properties of a generalized spin-(1/2, s) Fisher's super-exchange antiferromagnet are exactly investigated by using the decoration-iteration mapping transformation. Besides the critical temperature, sublattice magnetization, total magnetization, entropy and specific heat, the isothermal entropy change and adiabatic temperature change are rigorously calculated in order to examine cooling efficiency of the model in a vicinity of the first-and second-order phase transitions. It is shown that an enhanced inverse magnetocaloric effect occurs around the temperature interval T c (B = 0) T < T c (B = 0) for any magnetic-field change ∆B : 0 → B. The most pronounced inverse magnetocaloric effect can be found nearby the critical field, which corresponds to the zero-temperature phase transition from the long-range ordered ground state to the paramagnetic one. The observed phenomenon increases with the increasing value of decorating spins. Furthermore, sufficiently high values of decorating spins have also linked to a possibility of observing reentrant phase transitions at finite temperatures.

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

“…Let us begin with the finite-temperature phase diagrams of the mixed spin-1/2 and spin-S (S > 1/2) Ising model on a decorated square lattice, which are depicted in Figure 2 for four selected values of the spin magnitude S in the form of plots the critical temperature k B T c /|J| versus the transverse magnetic field Ω/|J|. It is worth mentioning that the critical temperature was calculated according to the critical condition (12), which is invariant with respect to a sign change of the coupling constant J → −J implying the identical critical behavior of the ferromagnetic (J > 0) and ferrimagnetic (J < 0) model system. The lines displayed in Figure 2 bring insight into the functional dependence of the dimensionless critical temperature k B T c /|J| on a relative size of the transverse magnetic field Ω/|J|.…”

“…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].…”

Magnetic and magnetocaloric properties of the exactly solvable mixed-spin Ising model on a decorated triangular lattice in a magnetic field

“…On the other hand, a rigorous investigation of the magneticfield effect on magnetic properties of the 2D Ising models still remains an open topic due to the lack of closed-form exact solution for the partition function at finite magnetic fields. At present, there are known just a few mixed-spin Ising models which allow an exact study of the magnetic-field effect in 2D, namely, the spin-1/2 Ising model on a kagomé lattice [5][6][7], the spin-1/2 Fisher super-exchange model on a square lattice [8,9] and its another extensions [10][11][12][13]. All these models involve the action of the longitudinal magnetic field on two-thirds of all the lattice sites.…”

“…In fact, the generalized decoration-iteration and star-triangle transformations establish a rigorous mapping correspondence between the aforementioned models and the spin-1/2 Ising lattices with known exact analytical solutions [29,32,33], which gives the oppor-tunity to gain a comprehensive picture on the critical behaviour as well as thermodynamics of these systems. Moreover, it has been demonstrated in our recent works [13] and [34] that the Fisher super-exchange model and its another variants represent excellent tools for a rigorous theoretical investigation of the magnetocaloric effect (MCE) in a proximity of the continuous (second-order) phase transitions. Thanks to its exact solvability, important MCE quantities such as the isothermal entropy change and the adiabatic temperature change may be straightforwardly calculated.…”

“…Taking into account the aforementioned facts, we propose in this paper a novel mixed-spin Ising model on a decorated triangular lattice in a longitudinal magnetic field for which the closed-form exact solution can be derived. The proposed model is somewhat reminiscent of the generalized Fisher super-exchange model on a square lattice [8][9][10][11][12][13], but its main novelty lies in definition on a non-bipartite triangular lattice, which provides a possible playground for a new type of spin frustration. Besides the ground-state analysis, our attention is focused on the study of the zero-temperature magnetization process, critical behaviour and magnetocaloric properties of the system.…”