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Physical review. B, Condensed matter

Bulk and surface spin-flop transitions in an antiferromagnetic XYZ chain

J. Karadamoglou, N. Papanicolaou

Published Oct 1, 1999• 9 citations
Publisher

Abstract

Spin-flop transitions are studied within a spin-$\frac{1}{2}$ antiferromagnetic XYZ chain immersed in a uniform bias magnetic field. For a special choice of anisotropy the bulk spin-flop transition occurs at a critical field ${H}_{b}$ characterized by the onset of ``accidental'' degeneracy in the energy spectrum that may indicate a hidden symmetry. On an open chain the bulk transition is preceded by a surface spin-flop transition induced by a surface magnon that turns soft at a new critical field ${H}_{s}<{H}_{b},$ while an antiferromagnetic domain wall is realized in the ground state as the bias field approaches ${H}_{b}.$ These $T=0$ phase transitions could be observed through electron-spin resonance on magnetic chains doped with nonmagnetic ions.

DOI
10.1103/physrevb.60.9477

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Spin-flop transitions are studied within a spin-12\frac{1}{2}21​ antiferromagnetic XYZ chain immersed in a uniform bias magnetic field. For a special choice of anisotropy the bulk spin-flop transition occurs at a critical field Hb{H}_{b}Hb​ characterized by the onset of ``accidental'' degeneracy in the energy spectrum that may indicate a hidden symmetry. On an open chain the bulk transition is preceded by a surface spin-flop transition induced by a surface magnon that turns soft at a new critical field Hs<Hb,{H}_{s}<{H}_{b},Hs​<Hb​, while an antiferromagnetic domain wall is realized in the ground state as the bias field approaches Hb.{H}_{b}.Hb​. These T=0T=0T=0 phase transitions could be observed through electron-spin resonance on magnetic chains doped with nonmagnetic ions.
A special limit of an antiferromagnetic XYZ\mathrm{XYZ}XYZ chain was recently shown to exhibit interesting bulk as well as surface spin-flop transitions at T=0.T=0.T=0. Here we provide a complete calculation of the thermodynamics of the bulk transition using a transfer-matrix renormalization-group method that addresses directly the thermodynamic limit of quantum spin chains. We also shed some light on certain spin-wave anomalies at low temperature predicted earlier by Johnson and Bonner.
The ground-state magnetization process of the S=1S=1S=1 antiferromagnetic chain with the easy-axis single-ion anisotropy described by negative DDD is investigated. It is numerically found that a phase transition between two different gapless phases occurs at an intermediate magnetic field between the starting and saturation points of the magnetization for $\ensuremath{-}1.49<D<\ensuremath{-}0.35.$ The transition is similar to the spin flopping, but it is second order and not accompanied with any significant anomalous behaviors in the magnetization curve. We also present the phase diagrams in the $m\ensuremath{-}D$ and $H\ensuremath{-}D$ planes which reveal a possible re-entrant transition.
At T = 0 and in a sufficiently large field, the nearest-neighbor antiferromagnetic Ising chain undergoes a first-order spin-flop transition into the ferromagnetic phase. We consider its smearing under the random-bond disorder such that all independent random bonds are antiferromagnetic (AF). It is shown that the ground-state thermodynamics of this random AF chain can be described exactly for an arbitrary distribution P(J) of AF bonds. Moreover, the site magnetizations of finite chains can be found analytically in this model. We consider a continuous P(J) that is zero above some −J 1 and behaves near it as (−J 1−J)λ, λ > −1. In this case, the ferromagnetic phase emerges continuously in a field H > H c = 2J 1. At 0 > λ > −1, it has the usual second-order anomalies near H c with the critical indices obeying the scaling relation and depending on λ. At λ > 0, higher-order transitions occur (third, fourth, etc.), marked by a divergence of the corresponding nonlinear susceptibilities. In the chains with an even number of spins, the intermediate “bow-tie” phase with linearly modulated AF order exists between the AF and ferromagnetic phases at J 1 < H < H c . Its origin can be traced to the infinite correlation length of the degenerate AF phase from which it emerges. This implies the existence of similar inhomogeneous phases with size- and form-dependent order in a number of other systems with infinite correlation length. The possibility to observe the signs of the “bow-tie” phase in low-T neutron diffraction experiments is discussed.
Abstract A great triumph of statistical physics in the latter part of the 20th century was the understanding of critical behavior and universality at second-order phase transitions. In contrast, first-order transitions were believed to have no common features. However, we argue that the classic, first-order “spin-flop” transition (between the antiferromagnetic and the rotationally degenerate, canted state) in an anisotropic antiferromagnet in a magnetic field exhibits a new kind of universality. We present a finite-size scaling theory for a first-order phase transition where a continuous symmetry is broken using an approximation of Gaussian probability distributions with a phenomenological degeneracy factor “q” included, where “q” characterizes the relative degeneracy of the ordered phases. Predictions are compared with high resolution Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field to study the finite-size behavior for L×L×L simple cubic lattices. The field dependence of all moments of the order parameters exhibit universal intersections at the spin-flop transition. Our Monte Carlo data agree with theoretical predictions for asymptotic large L behavior. Our theory yields q = π, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality.
We investigate the phase diagram of an anisotropic ferrimagnetic spin-(1/2, 1) in the presence of a non-commuting (transverse) magnetic field. We find a magnetization plateau for the isotropic case while there is no plateau for the anisotropic ferrimagnet. The magnetization plateau can appear only when the Hamiltonian has the U (1) symmetry in the presence of the magnetic field. The anisotropic model is driven by the magnetic field from the Néel phase for low fields to the spin-flop phase for intermediate fields and then to the paramagnetic phase for high fields. We find the quantum critical points and their dependence on the anisotropy of the aforementioned field-induced quantum phase transitions. The spin-flop phase corresponds to the spontaneous breaking of Z 2 symmetry. We use the numerical density matrix renormalization group and analytic spin wave theory to find the phase diagram of the model. The energy gap, sublattice magnetization and total magnetization parallel and perpendicular to the magnetic field are also calculated. The elementary excitation spectra are obtained via the spin wave theory in the three different regimes depending on the strength of the magnetic field.
This thesis is devoted to the study of a class of antifferomagnetic spin–1 chains with astrong easy plane anisotropy in the presence of magnetic field H. At zero temperature thesystem undergoes two quantum phase transitions at critical fields H1 and H2. Reliableand detailed theoretical analysis is provided on the Electron Spin Resonance (ESR)spectrum, thermodynamics and the thermal transport of the model. The tools at handrange from exact analytical solutions and to numerical simulation techniques. The S = 1antiferromagnet in a magnetic field can be systematically mapped onto an S = 1/2XXZ chain in a longitudinal magnetic field. This effective S = 1/2 description has beenextensively used in order to gain a better physical understanding of the original S = 1chain.For the Electron Spin Resonance spectrum, apart from the theoretical analysis, high-field ESR experimental studies of the compound N iCl2 − 4SC(NH2)2 (abbreviatedas DTN) are presented and found consistent with theoretical predictions. The mostinteresting feature is the experimental signature of the single–ion two–magnon boundstate.Part of this thesis is devoted to the magnetic–field and temperature dependence ofmagnetization and specific heat for the whole field–region and a wide range of temperatures,with special emphasis at the critical behaviour of these quantities at the criticalfields. Finally, the calculation of dynamic correlation functions pertinent to the studyof thermal transport is addressed for the S = 1 model with easy plane anisotropy andthe S = 1/2 XXZ model in the presence of finite magnetic field.