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Odd Number of Coupled Antiferromagnetic Anisotropic Heisenberg Chains with Dzyaloshinskii-Moriya Interaction

A. Benyoussef, Abderrazak Boubekri, Hamid Ez-zahraouy A

Published Apr 1, 1999• 1 citation
Publisher

Abstract

Using the linear spin-wave analysis, we have studied the effect of the Dzyaloshinskii-Moriya interaction on the stability of the Néel phase and the energy gap for the XXZ Heisenberg model on the odd number of coupled chains. We have found that the instability of the Néel state occurs below a critical value of the easy-axis anisotropy and the energy gap vanishes above a critical value of the DM interaction.

DOI
10.1002/(sici)1521-3951(199904)212:2<317::aid-pssb317>3.0.co;2-v

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Using the linear spin-wave analysis, we have studied the effect of the Dzyaloshinskii-Moriya interaction on the stability of the Néel phase and the energy gap for the XXZ Heisenberg model on the odd number of coupled chains. We have found that the instability of the Néel state occurs below a critical value of the easy-axis anisotropy and the energy gap vanishes above a critical value of the DM interaction.
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In this paper the effect of Dzyaloshinskii-Moriya interaction and anisotropy on the entanglement of Heisenberg chain has been studied. While the anisotropy suppresses the entanglement due to favoring of the alignment of spins, the DM interaction restores the spoiled entanglement via creation of the quantum fluctuations. Thermodynamic limit of the model and emerging of nonanalytic behavior of the entanglement have also been probed. The singularities of the entanglement correspond to the critical boundary separating different phases of the model. The singularity of the entanglement derivative approaches the critical point from the gapped phase and will be symmetric if both phases on the boundary are gapped.
Dzyaloshinskii–Moriya (DM) interactions cause many interesting physical features, such as topologically nontrivial magnetic skyrmions and chiral domain walls. These interactions become more pronounced in low-dimensional systems. We investigated a one-dimensional Heisenberg spin-1/2 chain with an asymmetric DM interaction. The results show that, upon applying a nonzero DM interaction, the Néel ground state transitions to a spin chiral phase. Moreover, using the mean-field approximation, we obtain the dispersion of the energy spectrum, from which the z-axis spin chirality is calculated as a function of the strength of the DM interaction for low-lying excitations. The results indicate that the DM interaction facilitates chirality for Dz ≤ J and induces a spin-gapped chiral state.
Abstract The dynamic analysis of quantum coherence of a polarized 1/2 − XXZ Heisenberg spins chain model with modulated Dzyaloshinskii-Moriya interaction and applied magnetic field, is investigated using quantum renormalization group approaches. In a thermodynamic limits, we derived the coherence factor and the monogamy of entanglement of a bipartite and tripartite states of the modulated system. We find that with increasing the anisotropy factor and decreasing the Dzyaloshinsky-Moriya factor Dz, the quantum coherence and the monogamy of entanglement decrease for the considered model of antiferromagnetic materials and exhibits non-analyticity around the critical point △ = 1 of the anisotropy factor. Note that, the decreasing is more important in the weak regime of the external magnetic field when applied. In addition, we perceive that the non-analytical behavior around the critical value of the anisotropy factor translate quantum phase transition from spin liquid to Néel phase and vice-versa depending on whether spin is localised on an even or odd site in the chain. The application of an external electric tens play a role in stabilizing the spins in preferred orientations and reenforce correlations beneficial for ferroelectricity that opens a route to switch magnetoelectricity with electric polarazation and vice-versa.
We have studied the phase diagram of the one dimensional XXZ model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has three phases, ferromagnetic, spin-fluid and Néel phases which are separated by a critical line which depends on the DM coupling constant. We have shown that the staggered magnetization is the order parameter of the system and investigated the influence of DM interaction on the chiral ordering as a helical magnetic order.