Magnetocaloric Effect in Two-Dimensional Diluted Ising Model: Appearance of Frustrations in the Ground State
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Magnetocaloric Effect in Two-Dimensional Diluted Ising Model: Appearance of Frustrations in the Ground State A. V. Shadrina, *, V. A. Ulitkoa, and Yu. D. Panova a Ural
Federal University Named after the First President of Russia B.N. Yeltsin, Yekaterinburg, Russia *e-mail: [email protected] Received March 26, 2020; revised March 26, 2020; accepted April 2, 2020
Abstract—The magnetocaloric effect in a two-dimensional Ising model is considered for different ratios between parameters of inter-site repulsion of nonmagnetic impurities and exchange coupling. Classical Monte Carlo simulations on a square lattice show that in case of weak coupling and at sufficiently high concentrations of nonmagnetic impurities the long-range ferromagnetic ordering breaks down to give isolated spin clusters in the ground state of the system. This leads to appearance of a paramagnetic response in the system at the zero temperature and nonzero entropy of the ground state. The feasibility to detect frustration of ground state using data on the magnetic entropy variation is discussed. Keywords: diluted Ising model, frustrations, magnetocaloric effect DOI: 10.1134/S1063783420090267
1. INTRODUCTION The magnetocaloric effect (MCE) consists in release or absorption of heat as a result of variation of an external magnetic field applied to a material. Initially, the effect was used to reach temperatures below 1 K, but, since materials exhibiting MCE at near room temperature have been discovered, magnetic cooling has become an area of very active research. The MCE in frustrated and low-dimensional systems attracts a special interest [1–4]. In Ising-type two-dimensional systems, the dependence of MCE on the parameter of magnetoelastic interaction for a square lattice was investigated in [5], while the effects of shape and size of geometrically frustrated Ising spin clusters in a triangular lattice have on the MCE were addressed in [6]. In this work, we consider a two-dimensional Ising system with a fixed concentration of mobile nonmagnetic charged impurities. The dilute Ising model is one key model [7, 8] in the theory of magnetic systems with quenched or annealed disorder as well as in the thermodynamic theory of binary alloys and mixtures of classical and quantum liquids. To describe our system, we use the pseudo-spin formalism (S = 1) in which for a given lattice site the states with pseudo-spin projections Sz = ±1 correspond to two magnetic states with spin projections sz = ±1/2, while the state with Sz = 0 corresponds to a charged nonmagnetic impurity. Write the Hamiltonian as follows:
H = −J
S ij
zi S zj
+V
P P
0i 0 j
ij
S
−h
i
zi ,
(1)
where Szi is the z-projection of pseudo-spin operator on a site, P0i = 1 – S zi2 is the projection operator on state Szi = 0, J = Js2, J is an exchange integral, s = 1/2, V is the inter-site interaction between impurities, h is an external magnetic field, ij are the nearest neighbors, and the sum is taken over all sites of the twodimensional square lattice. The concentratio
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