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arXiv:1912.06637 · Physical review. E

Enhanced magnetoelectric effect near a field-driven zero-temperature quantum phase transition of the spin-1/2 Heisenberg-Ising ladder

Jozef Strečka, Lucia Gálisová, Taras Verkholyak

Published Jan 3, 2020• 8 citations
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Abstract

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.

DOI
10.1103/physreve.101.012103

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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.
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.
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.
We study the interplay of electric and magnetic order in the one-dimensional Heisenberg spin-12\frac{1}{2}21​ XXZ chain with large Ising anisotropy in the presence of the Dzyaloshinskii-Moriya (DM) interaction and with longitudinal and transverse magnetic fields, interpreting the DM interaction as a coupling between the local electric polarization and an external electric field. We obtain the ground state phase diagram using the density matrix renormalization group method and compute various ground state quantities like the magnetization, staggered magnetization, electric polarization and spin correlation functions, etc. In the presence of both longitudinal and transverse magnetic fields, there are three different phases corresponding to a gapped N\'eel phase with antiferromagnetic (AF) order, gapped saturated phase, and a critical incommensurate gapless phase. The external electric field modifies the phase boundaries but does not lead to any new phases. Both external magnetic fields and electric fields can be used to tune between the phases. We also show that the transverse magnetic field induces a vector chiral order in the N\'eel phase (even in the absence of an electric field) which can be interpreted as an electric polarization in a direction parallel to the AF order.
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.
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 investigate quantum entanglement in a spin-1/2 Heisenberg trimer with spin-induced electric polarization described by the Katsura-Nagaosa-Balatsky (KNB) mechanism in the presence of external magnetic and electric fields. The electric field is assumed to lie in the plane of the magnetic ions, allowing its strength and orientation to be tuned independently. We analyze both bipartite and tripartite entanglement and demonstrate that the spin-electric-field coupling provides an efficient mechanism for controlling quantum correlations within the molecular nanomagnet. Depending on the electric-field parameters, the bipartite entanglement can be significantly enhanced or suppressed, while the multipartite entanglement exhibits a rich dependence on the microscopic spin-electric coupling. Most notably, we demonstrate that a rotating in-plane electric field of constant magnitude induces a controllable transfer of bipartite entanglement between different spin pairs. In the symmetric case of homogeneous exchange interactions and uniform KNB coupling, this transfer is found to be nearly ideal, with the bipartite negativity approaching its theoretical maximum for one spin pair while simultaneously vanishing for the remaining pairs. We show that the efficiency of the transfer can be tailored through the exchange interactions, bond geometry, and nonuniform spin-electric coupling. These results establish molecular nanomagnets with KNB spin-electric coupling as a promising platform for the electrical manipulation, steering, and localization of quantum entanglement at the molecular scale.