Magnetocaloric properties of a spin-1 anisotropic ferromagnetic Heisenberg system within the pair approximation

Abstract

The thermodynamics properties of a ferromagnetic Heisenberg model with the exchange anisotropy of a spin-1 system in presence of single-ion anisotropy (D) and external magnetic field (h) are studied here using the pair approximation approach. We treat the model in three-dimensional lattice with coordination number z=6. Other coordination numbers have been also examined. Within this approximation based on Gibbs free energy, we investigate the effect of both single-ion and exchange coupling anisotropies on the thermodynamic quantities such as magnetization, entropy, heat capacity, susceptibility and entropy change as in-process measures. The objective is to describe magnetocaloric effect (MCE) and relative cooling power aiming to optimize them. We find some interesting phenomena in these quantities due to external magnetic field, exchange anisotropy and single-ion anisotropy. For conflicting interactions, re-entrance behavior can occur. Interestingly, high spin size as well as strong exchange or single-ion anisotropy can improve the MCE performances. PA method [8,9]. It is clear from the above matrix elements that the matrix representation of H ij in this base is symmetric. Therefore, we need to determine the eigenvalues by diagonalizing the matrix of H . ij After performing calculations, we find the following eigenvalues: E J D D J J 2.4. Critical temperature The Curie temperature T C can be found by linearization of self-consistent equation (20) when 0 l  and external magnetic field h=0, leading to: z z J J w 1 2 e 2e cosh e 2e 4 cosh 2e cosh , 2 7 D J D J D J D J

The Pair Approximation method for the ferromagnetic Heisenberg model with spin $S=1$ and arbitrary range of interactions. Application for the magnetic semiconductor CrIAs

“…Regarding quantum models, apart from the pure Heisenberg [24,26], or mixed Heisenberg-Ising systems [28], the XXZ model with spin S = 1/2 [15] and the transverse Ising model with a random field [14] have been studied, together with XY model applied to describe a particular magnetocaloric material [32]. Recently, the anisotropic Heisenberg model with spin S = 1 has been investigated within this method [33] and also a mixed-spin system with spins 1/2 and 1 was investigated [34]. It is worth noticing that also some non-magnetic applications of PA have been developed, for example, for modelling of brain-computer interfaces [35].…”

“…The knowledge of the Gibbs energy is especially important for the 1st order phase transitions. Another merit is a possibility of calculation of spin-spin correlations, which are indispensable for investigations of such properties as magnetocaloric effect [27,31,33].…”

“…By contrast with the work of Boubekri at al. [33], where the anisotropic Heisenberg model with only nearest-neighbour (NN) interactions was studied, we consider the isotropic model but with the interactions of arbitrary range, extending up to the arbitrary coordination zone. Moreover, the molecular field acting on the pair-cluster has two components in the present approach, which is appropriate for the case of spin value S = 1.…”

“…Namely, it consists of the ordinary bilinear field, and the quadrupolar field. We take note of the fact that the quadrupolar field was neglected in the paper [33], therefore it can be treated as a simplified version of our full and systematic method which we intend to present here. Our variational approach exploits the maximal number of independent quantum mechanical operators based on spin operator which can be utilized to construct the trial density matrix.…”