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arXiv:cond-mat/9808100 · Physical Review Letters

Instability of Antiferromagnetic Magnons in Strong Fields

Mike E. Zhitomirsky, A. L. Chernyshev

Published May 31, 1999• 91 citations
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Abstract

We predict that spin waves in an ordered quantum antiferromagnet in a strong magnetic field become unstable with respect to spontaneous two-magnon decays. At zero temperature, the instability occurs between the threshold field ${H}^{*}$ and the saturation field ${H}_{c}$. As an example, we investigate the high-field dynamics of a Heisenberg antiferromagnet on a square lattice and show that the single-magnon branch of the spectrum disappears in most of the Brillouin zone.

DOI
10.1103/physrevlett.82.4536

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We predict that spin waves in an ordered quantum antiferromagnet in a strong magnetic field become unstable with respect to spontaneous two-magnon decays. At zero temperature, the instability occurs between the threshold field H∗{H}^{*}H∗ and the saturation field Hc{H}_{c}Hc​. As an example, we investigate the high-field dynamics of a Heisenberg antiferromagnet on a square lattice and show that the single-magnon branch of the spectrum disappears in most of the Brillouin zone.
We study the field dependence of the antiferromagnetic spin-12\frac{1}{2}21​ Heisenberg model on the square lattice by means of exact diagonalizations. In the first part, we calculate the spin-wave velocity ccc, the spin stiffness ${\ensuremath{\rho}}_{s}$, and the magnetic susceptibility ${\ensuremath{\chi}}_{\ensuremath{\perp}}$, and thus determine the microscopic parameters of the low-energy long-wavelength description. In the second part, we present a comprehensive study of dynamical spin-correlation functions for magnetic fields ranging from zero up to saturation. We find that, at low fields, magnons are well defined in the whole Brillouin zone but the dispersion is substantially modified by quantum fluctuations compared to the classical spectrum. At higher fields, decay channels open and magnons become unstable with respect to multimagnon scattering. Our results directly apply to inelastic neutron-scattering experiments.
We investigate the spontaneous disintegration of magnons in two-dimensional ferromagnets and antiferromagnets dominated by long-range dipolar interactions. Analyzing kinematic constraints, we show that the unusual dispersion of dipolar ferromagnets in a uniform magnetic field precludes magnon decay at all fields, in sharp contrast to short-range exchange-driven magnets. However, in a staggered magnetic field, magnons can decay in both dipolar ferromagnets and antiferromagnets. Remarkably, such decays do not require a minimum threshold field, and happen over a nearly fixed fraction of the Brillouin zone in the XY limit, highlighting the significant role played by dipolar interactions. In addition, topological transitions in the decay surfaces lead to singularities in the magnon spectrum. Regularizing such singular behavior via a self-consistent approach, we make predictions for dynamical spin correlations accessible to near-term quantum simulators and sensors.
We discuss spin-12\frac{1}{2}21​ Heisenberg antiferromagnet on simple square lattice in magnetic field HHH using a recently proposed bond-operator technique. It is well known that magnetically ordered phases of quantum magnets are well described at least qualitatively by the conventional spin-wave theory that only introduces quantum corrections into the classical solution of the problem. We observe that quantum fluctuations change drastically dynamical properties of the considered model at HHH close to its saturation value: the dynamical structure factor shows anomalies corresponding to Green's function poles which have no counterparts in the spin-wave theory. That is, quantum fluctuations produce multiple short-wavelength magnon modes not changing qualitatively the long-wavelength spin dynamics. Our results are in agreement with previous quantum Monte Carlo simulations and exact diagonalization of finite clusters.
Quantum phase transition at the saturation field is studied for a class of frustrated quantum antiferromagnets. The considered models include (i) the ${J}_{1}\mathrm{\text{\ensuremath{-}}}{J}_{2}$ frustrated square-lattice antiferromagnet with J2=12J1{J}_{2}=\frac{1}{2}{J}_{1}J2​=21​J1​ and (ii) the nearest-neighbor Heisenberg antiferromagnet on a face centered cubic lattice. In the fully saturated phase the magnon spectra for the two models have lines of degenerate minima. Transition into a partially magnetized state is treated via a mapping to a dilute gas of hard-core bosons and by complementary spin-wave calculations. Momentum dependence of the exact four-point boson vertex removes the degeneracy of the single-particle excitation spectra and selects the ordering wave vectors at $(\ensuremath{\pi},\ensuremath{\pi})$ and $(\ensuremath{\pi},0,0)$ for the two models. We predict a unique form for the magnetization curve $\ensuremath{\Delta}M=S\ensuremath{-}M\ensuremath{\simeq}{\ensuremath{\mu}}^{(d\ensuremath{-}1)/2}(\mathrm{log}\ensuremath{\mu}{)}^{(d\ensuremath{-}1)}$, where $\ensuremath{\mu}$ is a distance from the quantum critical point.
We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 XXZ model in a z-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magnetic-field driven Berezinskii-Kosterlitz-Thouless phase transition which occurs at low temperatures.
We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 XXZ model in a z-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magnetic-field driven Berezinskii–Kosterlitz– Thouless phase transition which occurs at low temperatures.