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AIP Advances

Spin chirality driven by the Dzyaloshinskii–Moriya interaction in one-dimensional antiferromagnetic chain

Guo Xing, Yaojin Li, Zimeng Yao, Chenglong Jia, Lan Zhang

Published Apr 1, 2023• 6 citations
Publisher

Abstract

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.

DOI
10.1063/5.0146777

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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.
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.
The effects of the Dzyaloshinski—Moriya (DM) interaction on the ground-state properties of the anisotropic XY chain in a transverse field have been studied by means of correlation functions and entanglement. Different from the case without the DM interaction, the excitation spectra ∊ k of this model are not symmetrical in the momentum space and are not always positive. As a result, besides the ferromagnetic (FM) and the paramagnetic (PM) phases, a gapless chiral phase is induced. In the chiral phase, the von Neumann entropy is proportional to log 2 L ( L is the length of a subchain) with the coefficient A ≈ 1/3, which is the same as that of the XY chain in a transverse field without the DM interaction for γ = 0 and 0 < h ≤ 1. And in the vicinity of the critical point between the chiral phase and the FM (or PM) phase, the behaviors of the nearest-neighbor concurrence and its derivative are like those for the anisotropy transition.
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.
By using the density-matrix renormalization group method, the spin entanglement in the antiferromagnetic Heisenberg chain with the staggered Dzyaloshinskii-Moriya (DM) interactions is investigated. It is found that the staggered DM interactions remove the field-induced second order quantum phase transition of the system at the magnitude of magnetic field H＝2, and lead to the vanishing of the anomalous behavior of quantum entanglement. Also, the staggered DM interactions eliminate the divergence of entanglement range. It means the disappearance of the factorizing point in the model studied. Due to the presence of the staggered DM interactions, the system will never come to the state of saturated ferromagnetism under finite magnetic fields, thus maintaining the spin entanglement. The staggered DM interactions favor the tuning of the strength and range of spin entanglement.
The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii–Moriya (DM) interaction considered as Gaussian distribution, and the entanglement in one-dimensional random XY spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For the ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. (ii) For the antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.