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HUE UNIVERSITY JOURNAL OF SCIENCE NATURAL SCIENCE

Effect of Dzyaloshinskii-Moriya Interaction on Heisenberg Antiferromagnetic Spin Chain in the Presence of a Longitudinal Magnetic Field

Thảo Hương Phạm, T. Thuan Ngo, Thanh Le, Dinh Long Hoang, T. H. Ny Phan, H. Canh Nguyen

Published Jan 27, 2022• 3 citations
Publisher

Abstract

Using functional integral method for the Heisenberg antiferromagnetic spin chain with the added Dzyaloshinskii-Moriya Interaction in the presence of the longitudinal magnetic field, we find out expression for free energy of the spin chain via spin fluctuations, from which quantities characterize the antiferromagnetic order and phase transition such as staggered and total magnetizations derived. From that, we deduce the significant effect of the Dzyaloshinskii-Moriya interaction on the reduction of the antiferromagnetic order and show that the total magnetization can be deviated from the initial one under the influence of canting of the spins due to a combination of the Dzyaloshinskii-Moriya interaction and the magnetic field. Besides, the remarkable role of the transverse spin fluctuations due to the above factors on the antiferromagnetic behaviours of the spin chain is also indicated.

DOI
10.26459/hueunijns.v130i1d.6423

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Using functional integral method for the Heisenberg antiferromagnetic spin chain with the added Dzyaloshinskii-Moriya Interaction in the presence of the longitudinal magnetic field, we find out expression for free energy of the spin chain via spin fluctuations, from which quantities characterize the antiferromagnetic order and phase transition such as staggered and total magnetizations derived. From that, we deduce the significant effect of the Dzyaloshinskii-Moriya interaction on the reduction of the antiferromagnetic order and show that the total magnetization can be deviated from the initial one under the influence of canting of the spins due to a combination of the Dzyaloshinskii-Moriya interaction and the magnetic field. Besides, the remarkable role of the transverse spin fluctuations due to the above factors on the antiferromagnetic behaviours of the spin chain is also indicated.
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.
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 investigate an antiferromagnetic spin-1 Heisenberg chain in the presence of Dyzaloshinskii-Moriya interactions (DMI) and an external magnetic field. We study the resulting spin chain using a combination of numerical and analytical techniques. Using DMRG simulations to determine the spectral gap and the entanglement spectrum, we map out the phase diagram as a function of magnetic field strength and DMI strength. We provide a qualitative interpretation for these numerical findings by mapping the spin-1 chain on a spin-1/21/21/2 ladder and using a bosonization approach.
We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including D z and D x , on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters ( D z and D x ) have remarkably different influences on the entanglement. Different from the case D z , there is the non-monotonic variation of the concurrence with temperature in the case D x , and additionally the DM interaction D x can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case D x is larger than that of the case D z .
We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a gapful phase into a gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalization studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of a staggered component of the magnetic field vapes the composite (C1) in favor of the composite gapped (C2) phase.