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arXiv:2009.04970 · Physical review. B./Physical review. B

Current jumps in flat-band ladders with Dzyaloshinskii-Moriya interactions

Santiago Acevedo, Pierre Pujol, Carlos Alberto Lamas

Published Nov 20, 2020• 4 citations
arXivHTMLPDF

Abstract

Localized magnons states, due to flat bands in the spectrum, is an intensely studied phenomenon and can be found in many frustrated magnets of different spatial dimensionality. The presence of Dzyaloshinskii-Moriya (DM) interactions may change radically the behavior in such systems. In this context, we study a paradigmatic example of a one-dimensional frustrated antiferromagnet, the sawtooth chain in the presence of DM interactions. Using both path integrals methods and numerical density matrix renormalization group, we revisit the physics of localized magnons and determine the consequences of the DM interaction on the ground state. We have studied the spin current behavior, finding three different regimes. First, a Luttinger-liquid regime where the spin current shows a step behavior as a function of parameter $D$, at a low magnetic field. Increasing the magnetic field, the system is in the Meissner phase at the $m=1/2$ plateau, where the spin current is proportional to the DM parameter. Finally, further increasing the magnetic field and for finite $D$ there is a small stiffness regime where the spin current shows, at fixed magnetization, a jump to large values at $D=0$, a phenomenon also due to the flat band.

DOI
10.1103/physrevb.102.195139

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Localized magnons states, due to flat bands in the spectrum, is an intensely studied phenomenon and can be found in many frustrated magnets of different spatial dimensionality. The presence of Dzyaloshinskii-Moriya (DM) interactions may change radically the behavior in such systems. In this context, we study a paradigmatic example of a one-dimensional frustrated antiferromagnet, the sawtooth chain in the presence of DM interactions. Using both path integrals methods and numerical density matrix renormalization group, we revisit the physics of localized magnons and determine the consequences of the DM interaction on the ground state. We have studied the spin current behavior, finding three different regimes. First, a Luttinger-liquid regime where the spin current shows a step behavior as a function of parameter DDD, at a low magnetic field. Increasing the magnetic field, the system is in the Meissner phase at the m=1/2m=1/2m=1/2 plateau, where the spin current is proportional to the DM parameter. Finally, further increasing the magnetic field and for finite DDD there is a small stiffness regime where the spin current shows, at fixed magnetization, a jump to large values at D=0D=0D=0, a phenomenon also due to the flat band.
We consider a generalization of the XXZ model on the sawtooth spin chain with Dzyaloshinskii-Moriya interactions in which all exchange constants (symmetric, antisymmetric, and axial anisotropy) are different for the three different bonds of each triangle. We derive and resolve algebraic constraints on the exchange constants ensuring the appearance of a flat band in the one-magnon spectrum. The properties of the corresponding flat magnon bands and localized magnon states are analyzed. We further construct the mapping of the flat-band conditions for the Dzyaloshinskii-Moriya constants onto the Katsura-Nagaosa-Balatsky parameters. Based on the mapping, the possibility of the electric-field-driven flat bands with the aid of the magnetoelectric coupling is examined.
A small value of the spin gap in quantum antiferromagnets with strong frustration makes them susceptible to nominally small deviations from the ideal Heisenberg model. One such perturbation, the anisotropic Dzyaloshinskii-Moriya (DM) interaction, is an important perturbation for the S=1/2S=1/2S=1/2 kagome antiferromagnet, one of the current candidates for a quantum-disordered ground state. We study the influence of the DM term in a related one-dimensional system, the sawtooth chain, which has valence-bond order in its ground state. Through a combination of analytical and numerical methods, we show that a relatively weak DM coupling, 0.115J0.115J0.115J, is sufficient to destroy the valence-bond order, close the spin gap, and turn the system into a Luttinger liquid with algebraic spin correlations. A similar mechanism may be at work in the kagome antiferromagnet.
We study the low-energy properties and, in particular, the magnetization process of a spin-1/2 Heisenberg ${J}_{1}\ensuremath{-}{J}_{2}$ sawtooth and frustrated chain (also known as a zigzag ladder) with a spatially modulated ggg factor. We treat the problem both analytically and numerically while keeping the J2/J1{J}_{2}/{J}_{1}J2​/J1​ ratio generic. Numerically, we use complete and Lanczos diagonalization as well as the infinite time-evolving block decimation method. Analytically, we employ (non-)Abelian bosonization. Additionally, for the sawtooth chain, we provide an analytical description in terms of flat bands and localized magnons. By considering a specific pattern for the ggg-factor modulation for both models, we show that a small inhomogeneity significantly enhances a magnetization plateau at half saturation. For the magnetization of the frustrated chain, we show the destruction of one-third of the full saturation plateau in favor of the creation of a plateau at half saturation. For large values of the inhomogeneity parameter, the existence of an additional plateau at zero magnetization is possible. Here and at higher magnetic fields, the system is locked in the half-saturation plateau, never reaching full saturation.
Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at m=1∕2m=1∕2m=1∕2. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaus. In particular, anisotropic interactions generically open a gap in the region between the plateaus, but we show that this gap closes upon entering fractional plateaus. All of these conclusions, based on analytical arguments, are supported by extensive density matrix renormalization group calculations.
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 consider analytically and numerically an anisotropic $\text{spin}\ensuremath{-}\frac{1}{2}$ delta chain (sawtooth chain) with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interactions. For certain values of the interactions a lowest one-particle band becomes flat and there is a class of localized-magnon eigenstates which form a ground state with a macroscopic degeneracy. In this case the model depends on a single parameter which can be chosen as the anisotropy of the exchange interactions. When this parameter changes from zero to infinity the model interpolates between the one-dimensional isotropic ferromagnet and the frustrated Ising model on the delta chain. It is shown that the low-temperature thermodynamic properties in these limiting cases are governed by the specific structure of the excitation spectrum. In particular, the specific heat has one or infinite number of low-temperature maxima for the small or the large anisotropy parameter, correspondingly. Qualitative features of such behavior survive when the interaction parameters deviate from the relations providing the local magnon ground state.