Variety of Types of Magnetic Ordering: The Method of Random Exchange Interaction Fields
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TRICAL AND MAGNETIC PROPERTIES
Variety of Types of Magnetic Ordering: The Method of Random Exchange Interaction Fields V. I. Belokona, *, O. I. Dyachenkoa, R. V. Lapenkova, and E. V. Chibiriaka a
School of Natural Sciences, Far Eastern Federal University, Vladivostok, 690090 Russia *e-mail: [email protected] Received October 29, 2019; revised January 14, 2020; accepted January 16, 2020
Abstract—Various types of magnetic ordering in two-sublattice magnetic materials with exchange interaction were studied using the method of random exchange interaction fields and the Ising model. The conditions for the magnetization of such systems were identified. Equations for the temperatures of phase transitions were derived. Keywords: random field method, Ising model, magnetic ordering DOI: 10.1134/S0031918X20060034
INTRODUCTION Magnetism has been known since ancient times, but it remains the subject of extensive study. This is primarily related to the emergence of new magnetic materials (spin glass, spin ice) used in various technical devices (including computing devices). The molecular field theory is the simplest classical method for characterizing the properties of magnetic systems with exchange interaction. However, it is not suitable for certain types of magnetic ordering. The theory of random exchange interaction fields [1, 2] is one of the approaches that expand the applicability of the molecular field theory while retaining its simplicity. The field distribution function in this theory depends on the particle interaction law. Specifically, this may be the direct exchange interaction or the RKKY interaction. This approach has an advantage over the common molecular field theory in that it provides a quantitative description of phase transitions in systems with any exchange law and allows one to estimate the critical (minimum) concentration of interacting particles needed for a phase transition [3]. For example, the problem of concentration phase transitions in two-sublattice magnetic systems was solved in [4]. Magnetic phase transitions in thin films were examined in [5]. Since many magnetic materials are alloys consisting of various types of atoms, the research into magnetic ordering in such materials is of special interest. The aim of this study is to examine various types of magnetic ordering in two-sublattice magnetic materials with exchange interaction within the theory of random interaction fields and the Ising model.
THEORY OF RANDOM INTERACTION FIELDS It is assumed in the random interaction fields method that was developed further in [6–8], that effective (molecular) interaction field H is a random quantity distributed in accordance with a certain law. Its randomness may be associated both with the random distribution of impurities (at concentration p < 1 of interacting atoms) and with the orientation of magnetic moments of neighbors. The corresponding (approximate) field distribution function H for the Ising model takes the form [H − H 0M ]2 (1) W ( H ) = 1 exp − . πB B2 Mean value H = H0M a
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