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arXiv:2205.11770 · npj Quantum Materials

Understanding temperature-dependent SU(3) spin dynamics in the S = 1 antiferromagnet Ba2FeSi2O7

Seung-Hwan Do, Hao Zhang, David Dahlbom, Travis J. Williams, Vasile Ovidiu Garlea, Tao Hong, Tae-Hwan Jang, Sang‐Wook Cheong, Jae‐Hoon Park, Kipton M. Barros, Cristian D. Batista, Andrew D Christianson

Published Jan 12, 2023• 18 citations
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Abstract

Abstract Quantum magnets admit more than one classical limit and N-level systems with strong single-ion anisotropy are expected to be described by a classical approximation based on SU(N) coherent states. Here we test this hypothesis by modeling finite temperature inelastic neutron scattering (INS) data of the effective spin-one antiferromagnet Ba2FeSi2O7. The measured dynamic structure factor is calculated with a generalized Landau-Lifshitz dynamics for SU(3) spins. Unlike the traditional classical limit based on SU(2) coherent states, the results obtained with classical SU(3) spins are in good agreement with the measured temperature-dependent spectrum. The SU(3) approach developed here provides a general framework to understand the broad class of materials comprising weakly coupled antiferromagnetic dimers, trimers, or tetramers, and magnets with strong single-ion anisotropy.

DOI
10.1038/s41535-022-00526-7

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Abstract Quantum magnets admit more than one classical limit and N-level systems with strong single-ion anisotropy are expected to be described by a classical approximation based on SU(N) coherent states. Here we test this hypothesis by modeling finite temperature inelastic neutron scattering (INS) data of the effective spin-one antiferromagnet Ba2FeSi2O7. The measured dynamic structure factor is calculated with a generalized Landau-Lifshitz dynamics for SU(3) spins. Unlike the traditional classical limit based on SU(2) coherent states, the results obtained with classical SU(3) spins are in good agreement with the measured temperature-dependent spectrum. The SU(3) approach developed here provides a general framework to understand the broad class of materials comprising weakly coupled antiferromagnetic dimers, trimers, or tetramers, and magnets with strong single-ion anisotropy.
We introduce a classical limit of the dynamics of quantum spin systems based on coherent states of SU(N)\mathrm{SU}(N)SU(N), where NNN is the dimension of the local Hilbert space. This approach, which generalizes the well-known Landau-Lifshitz dynamics from SU(2) to SU(N)\mathrm{SU}(N)SU(N), provides a better approximation to the exact quantum dynamics for a large class of realistic spin Hamiltonians, including $S\ensuremath{\ge}1$ systems with large single-ion anisotropy and weakly coupled multispin units, such as dimers or trimers. We illustrate this idea by comparing the spin structure factors of a single-ion S=1S=1S=1 model that are obtained with the SU(2) and SU(3) classical spin dynamics against the exact solution.
Simulating quantum spin systems at finite temperatures is an open challenge in many-body physics. This work studies the temperature-dependent spin dynamics of a pivotal compound, FeI2{\mathrm{FeI}}_{2}FeI2​, to determine if universal quantum effects can be accounted for by a phenomenological renormalization of the dynamical spin structure factor $S(\mathbf{q},\ensuremath{\omega})$ measured by inelastic neutron scattering. Renormalization schemes based on the quantum-to-classical correspondence principle are commonly applied at low temperatures to the harmonic oscillators describing normal modes. However, it is not clear how to extend this renormalization to arbitrarily high temperatures. Here we introduce a temperature-dependent normalization of the classical moments, the magnitude of which is determined by imposing the quantum sum rule, e.g., $\ensuremath{\int}d\ensuremath{\omega}d\mathbf{q}S(\mathbf{q},\ensuremath{\omega})={N}_{S}S(S+1)$ for NS{N}_{S}NS​ dipolar magnetic moments. We show that this simple renormalization scheme significantly improves the agreement between the calculated and measured $S(\mathbf{q},\ensuremath{\omega})$ for FeI2{\mathrm{FeI}}_{2}FeI2​ at all temperatures. Due to the coupled dynamics of dipolar and quadrupolar moments in that material, this renormalization procedure is extended to classical theories based on SU(3) coherent states, and by extension, to any SU(N)\mathrm{SU}(N)SU(N) coherent state representation of local multipolar moments.
Quantum to classical crossover in generalized spin systems -- the temperature-dependent spin dynamics of FeI2_22​
Simulating quantum spin systems at finite temperatures is an open challenge in many-body physics. This work studies the temperature-dependent spin dynamics of a pivotal compound, FeI2_22​, to determine if universal quantum effects can be accounted for by a phenomenological renormalization of the dynamical spin structure factor S(q,ω)S(\mathbf{q}, ω)S(q,ω) measured by inelastic neutron scattering. Renormalization schemes based on the quantum-to-classical correspondence principle are commonly applied at low temperatures to the harmonic oscillators describing normal modes. However, it is not clear how to extend this renormalization to arbitrarily high temperatures. Here we introduce a temperature-dependent normalization of the classical moments, whose magnitude is determined by imposing the quantum sum rule, i.e. ∫dωdqS(q,ω)=NSS(S+1)\int dωd\mathbf{q} S(\mathbf{q}, ω) = N_S S (S+1)∫dωdqS(q,ω)=NS​S(S+1) for NSN_SNS​ dipolar magnetic moments. We show that this simple renormalization scheme significantly improves the agreement between the calculated and measured S(q,ω)S(\mathbf{q}, ω)S(q,ω) for FeI2_{2}2​ at all temperatures. Due to the coupled dynamics of dipolar and quadrupolar moments in that material, this renormalization procedure is extended to classical theories based on SU(3) coherent states, and by extension, to any SU(N) coherent state representation of local multipolar moments.
We employ a classical limit grounded in SU(4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the S=1/2S=1/2S=1/2 ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical approximation with density matrix renormalization group and exact diagonalization calculations in finite-size ladders, we demonstrate that the classical dynamics offers an accurate approximation across the entire temperature range when the interdimer coupling is weak and a good approximation in the high-temperature regime even when the interdimer coupling is strong. This agreement is achieved after appropriately rescaling the temperature axis and renormalizing expectation values to satisfy a quantum sum rule, following D. Dahlbom et al. [Phys. Rev. B 109, 014427 (2024)]. We anticipate the method will be particularly effective when applied to 2D and 3D lattices composed of weakly coupled dimers, situations that remain challenging for alternative numerical methods.
Using finite temperature Lanczos technique on finite clusters we calculate dynamical spin structure factor of the quasi-two-dimensional dimer spin liquid SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}SrCu2​(BO3​)2​ as a function of wave vector and temperature. At low temperatures the peak belonging to the lowest spin excitations is split due to spin anisotropy, in accord with the experimental data. Unusual temperature dependence of calculated spectra is as well in agreement with inelastic neutron scattering measurements. Normalized peak intensities of the single-triplet peak are q\mathbf{q}q independent, their temperature dependence is analyzed in terms of thermodynamic quantities.
Quasi-one-dimensional magnetic materials provide important test beds for rigorous models of interacting many-body systems. Nevertheless, there have been few studies of finite temperature effects on spin correlations in low-spin systems, though these are most likely to exhibit quantum effects. Copper benzoate, Cu(C6D5COO)2⋅3D2O, is a good realization of the S=1/2 Heisenberg antiferromagnetic chain (HAFC). We have performed ac susceptibility and inelastic neutron scattering experiments on this material which establish the Hamiltonian and an excitation spectrum which is consistent with the spinon continuum ansatz of Müller et al. We present inelastic neutron scattering measurements of the temperature evolution of the dynamic spin–spin correlation function Szz(π,ω). Comparison will be made to the classical prediction and to a finite temperature field theory of Schulz as applied to this S=1/2 HAFC.