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arXiv:1805.08442 · Physical review. B./Physical review. B

Spin-1/2 XY chain magnetoelectric: Effect of zigzag geometry

O. R. Baran, Vadim Ohanyan, Taras Verkholyak

Published Aug 20, 2018• 13 citations
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Abstract

A spin-1/2 $XY$ chain model of magnetoelectrics on a zigzag chain is considered rigorously. The magnetoelectric coupling is described within the Katsura-Nagaosa-Balatsky mechanism. In the zigzag geometry it leads to the staggered Dzyaloshinskii-Moriya interaction. Using nonuniform spin rotations, the model is reduced to a dimerized $XY$ chain and solved exactly using the Jordan-Wigner transformation. We analyze the ground-state phase diagram of the model and the zero- and finite-temperature magnetoelectric effects and obtain the magnetization and polarization curves versus magnetic and electric fields, as well as the parameters of anisotropic dielectric and magnetoelectric response. It is also shown that the electric field may enhance the magnetocaloric effect in the model.

DOI
10.1103/physrevb.98.064415

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A spin-1/2 XYXYXY chain model of magnetoelectrics on a zigzag chain is considered rigorously. The magnetoelectric coupling is described within the Katsura-Nagaosa-Balatsky mechanism. In the zigzag geometry it leads to the staggered Dzyaloshinskii-Moriya interaction. Using nonuniform spin rotations, the model is reduced to a dimerized XYXYXY chain and solved exactly using the Jordan-Wigner transformation. We analyze the ground-state phase diagram of the model and the zero- and finite-temperature magnetoelectric effects and obtain the magnetization and polarization curves versus magnetic and electric fields, as well as the parameters of anisotropic dielectric and magnetoelectric response. It is also shown that the electric field may enhance the magnetocaloric effect in the model.
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We consider a simple integrable model of a spin chain exhibiting the magnetoelectric effect (MEE). Starting from the periodic S=1/2S=1/2S=1/2 XXZ chain with Dzyaloshinskii-Moriya terms, which we consider as a local electric polarization in the spirit of the Katsura-Nagaosa-Baladsky (KNB) mechanism, we perform the mapping onto the conventional XXZ chain with twisted boundary conditions. Using the techniques of quantum transfer matrix and nonlinear integral equations we obtain the magnetization, electric polarization, and magnetoelectric tensor as functions of magnetic and electric field for arbitrary temperatures. We investigate these dependencies as well as the thermal behavior of the above-mentioned physical quantities, especially in the low-temperature regime. We found several regimes of polarization. Adjusting the magnetic field one can switch the system from one regime to another. The features of the critical properties connected with the MEE are also illustrated.
We illustrate the magnetoelectric effect conditioned by the Katsura-Nagaosa-Balatsky (KNB) mechanism within the frames of exactly solvable spin-1/2XY1/2 XY1/2XY chains. Due to three-spin interactions which are present in our consideration, the magnetization (polarization) is influenced by the electric (magnetic) field even in the absence of the magnetic (electric) field. We also discuss a magnetoelectrocaloric effect examining the entropy changes under the isothermal varying of the magnetic and/or electric field.
The magnetoelectric effect of a spin-1/2 Heisenberg-Ising ladder in the presence of external electric and magnetic fields is rigorously examined by taking into account the Katsura-Nagaosa-Balatsky mechanism. It is shown that an applied electric field may control the quantum phase transition between a Néel (stripy) ordered phase and a disordered paramagnetic phase. The staggered magnetization vanishes according to a power law with an Ising-type critical exponent 1/8, the electric polarization exhibits a weak singularity, and the dielectric susceptibility shows a logarithmic divergence at this particular quantum phase transition. The external electric field may alternatively invoke a discontinuous phase transition accompanied with abrupt jumps of the dielectric polarization and susceptibility on the assumption that the external magnetic field becomes nonzero.
The linear perturbation renormalization group (LPRG) is used to study coupled XYXYXY chains with Dzyaloshinskii-Moriya (DM) and three-spin interactions in a magnetic field. Starting with a minimal model exhibiting the magnetoelectric effect, a spin-12XY\frac{1}{2} XY21​XY chain with nearest, next-nearest (J2x)({J}_{2}^{x})(J2x​), and DM (D1y)({D}_{1}^{y})(D1y​) interactions in a magnetic field, the recursion relations for all effective interactions generated by the LPRG transformation are found. The evaluation of these relations allows us to analyze, among others, the influence of J2x,D1y{J}_{2}^{x},\phantom{\rule{0.16em}{0ex}}{D}_{1}^{y}J2x​,D1y​, three-spin (${S}_{i}^{x}{S}_{i+1}^{y}{S}_{i+2}^{z}\ensuremath{-}{S}_{i}^{y}{S}_{i+1}^{x}{S}_{i+2}^{z}$), and interchain interactions on the thermodynamic properties. The field and temperature dependences of the polarization, specific heat, and correlation functions are found. It is shown that an interchain coupling triggers a phase transition indicated by the divergence of the renormalized coupling parameters.
We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya exchange interaction in an external magnetic field. Based on the exact solution derived by means of Jordan-Wigner transformation, we study the excitation gap, spin correlations, ground-state degeneracy, and critical properties at phase transitions. The phase diagram at finite electric and magnetic field consists of three phases: ferromagnetic, canted antiferromagnetic, and chiral. Dzyaloshinskii-Moriya interaction induces an electrical polarization in the ground state of the chiral phase, where the nonlocal string order and special features of entanglement spectra arise, while strong chiral correlations emerge at finite temperature in the other phases and are controlled by a gap between the nonchiral ground state and the chiral excitations. We further show that the magnetoelectric effects in all phases disappear above a typical temperature corresponding to the total bandwidth of the effective fermionic model. To this end we explore the entropy, specific heat, magnetization, electric polarization, and the magnetoelectric tensor at finite temperature. We identify rather peculiar specific-heat and polarization behavior of the compass model which follows from highly frustrated interactions.