Condensed Matter Physics, 2020, Vol. 23, No 4, 43704: 1–11 DOI: 10.5488/CMP.23.43704 http://www.icmp.lviv.ua/journal Influence of XY anisotropy on a magnetoelectric effect in spin-1/2 XY chain in a transverse magnetic field V. Ohanyan Laboratory of Theoretical Physics, and Joint Laboratory of Theoretical Physics — ICTP Affiliated Centre in Armenia, Yerevan State University, 1 Alex Manoogian Str., 0025 Yerevan, Armenia Received June 15, 2020, in final form July 28, 2020 A magnetoelectric effect according to Katsura-Nagaosa-Balatsky mechanism in spin-1/2 XY chain in transverse magnetic field is considered. A spatial orientation of the electric field is chosen to provide an exact solution of the model in terms of free spinless fermions. The simplest model of quantum spin chain demonstrating a magnetoelectric effect, a zero temperature case of the spin-1/2 XX chain in a transverse magnetic field with Katsura-Nagaosa-Balatsky mechanism, is considered. The model has the simplest possible form of the magnetization, polarization and susceptibility functions, depending on electric and magnetic fields in a most simple form. For the case of arbitrary XY anisotropy, a non-monotonous dependence of magnetization on the XY anisotropy parameter is figured out. This non-uniform behaviour is governed by the critical point which is connected with the possibility to drive the system gapless or gapped by the electric field. Singularities of the magnetoelectric susceptibility at the critical value of system parameters are shown. Key words: KNB mechanism, magnetoelectric effect, XY chain, free spinless fermions 1. Introduction Magnetoelectrics are materials having both dielectric polarization and magnetization in a single phase and exhibiting a magnetoelectric effect (MEE), a vast class of phenomena of intercoupling of magnetization and polarization in matter [1–4]. These materials are particularly important for their application in spintronic devices [5, 6]. The MEE is a class of phenomena in solids, which can be detected as magnetic field dependance of dielectric polarization and electric field dependance of magnetization. In most interesting cases of non-trivial MEE, the magnetization (dielectric polarization) can be induced by only applying an electric (magnetic) field. Nowadays, several microscopic mechanisms of the MEE are known [1–4]. One of these mechanisms is based on the so-called spin-current model or inverse Dzyaloshinskii-Moriya (DM) model and was proposed in a seminal paper by Katsura, Nagaosa and Balatsky [7]. The Katsura-Nagaosa-Balatsky (KNB) mechanism establishes a connection between the dielectric polarization of the crystal structure unit consisting of two magnetic ions chemically bonded to one or more p-elements and the spin states of the ions [7, 8]. The dielectric polarization that induces into the bond between two spins in this model is given by the following expression: P ij = μe ij × S i × S j , (1.1) here, e ij is the unit vector pointing from site i to site j , and μ is a microscopic constant characterizing the quantum chemical features of the bond between two metallic ions and p-element(s) [7, 8]. S i and S j are the spin operators of the corresponding ion states. The simplest case of the KNB mechanism is the linear arrangement of magnetic ions (spins), the geometrically linear spin chain. If we suppose the chain to be directed toward the x -axis, then the local polarization according to equation (1.1) acquires the following This work is licensed under a Creative Commons Attribution 4.0 International License . Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. 43704-1