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arXiv:2002.07190 · Physical review. B./Physical review. B

Enhancement of magnetization plateaus in low-dimensional spin systems

Alexandros Metavitsiadis, Christina Psaroudaki, Wolfram Brenig

Published Jun 18, 2020• 25 citations
arXivHTMLPDF

Abstract

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 $g$ factor. We treat the problem both analytically and numerically while keeping the ${J}_{2}/{J}_{1}$ 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 $g$-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.

DOI
10.1103/physrevb.101.235143

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We study the low-energy properties and, in particular, the magnetization process of a spin-1/2 Heisenberg J1\ensuremath−J2{J}_{1}\ensuremath{-}{J}_{2}J1​\ensuremath−J2​ 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.
The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/21/21/2 ladder, and a two-legged spin-1/21/21/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ\mathrm{XXZ}XXZ spin-1/21/21/2 chain in a magnetic field; the second-order terms give corrections to the XXZ\mathrm{XXZ}XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.
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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 study the T=0T=0T=0 magnetization of frustrated two-leg spin ladders with arbitrary value of the spin SSS. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins SSS and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for $S\ensuremath{\le}2$. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.
In contrast to strongly frustrated classical systems, their quantum counterparts typically have a non-degenerate ground state. A counterexample is the celebrated Heisenberg sawtooth spin chain with ferromagnetic zigzag bonds J1J_1J1​ and competing antiferromagnetic basal bonds J2J_2J2​. At a quantum phase transition point ∣J2/J1∣=1/2|J_2/J_1|=1/2∣J2​/J1​∣=1/2, this model exhibits a flat one-magnon excitation band leading to a massively degenerate ground-state manifold which results in a large residual entropy. Thus, for the spin-half model, the residual entropy amounts to exactly one half of its maximum value lim⁡T→∞S(T)/N=ln⁡2\lim_{T\to\infty} S(T)/N = \ln2limT→∞​S(T)/N=ln2. In the present paper we study in detail the role of the spin quantum number sss and the magnetic field HHH in the parameter region around the transition (flat-band) point. For that we use full exact diagonalization up to N=20N=20N=20 lattice sites and the finite-temperature Lanczos method up to N=36N=36N=36 sites to calculate the density of states as well as the temperature dependence of the specific heat, the entropy and the susceptibility. The study of chain lengths up to N=36N=36N=36 allows a careful finite-size analysis. At the flat-band point we find extremely small finite-size effects for spin s=1/2s=1/2s=1/2, i.e., the numerical data virtually correspond to the thermodynamic limit. In all other cases the finite-size effects are still small and become visible at very low temperatures. In a sizeable parameter region around the flat-band point the former massively degenerate ground-state manifold acts as a large manifold of low-lying excitations leading to extraordinary thermodynamic properties at the transition point as well as in its vicinity such as an additional low-temperature maximum in the specific heat. Moreover, there is a very strong influence of the magnetic field on the low-temperature thermodynamics including an enhanced magnetocaloric effect.
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