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Physical review. B./Physical review. B

Disentangling spin excitation continua in classical and quantum magnets using two-dimensional nonlinear spectroscopy

Emily Z. Zhang, Ciarán Hickey, Yong Baek Kim

Published Sep 9, 2024• 6 citations
Publisher

Abstract

Two-dimensional coherent spectroscopy ($2D\phantom{\rule{0}{0ex}}C\phantom{\rule{0}{0ex}}S$) has emerged as a powerful tool for probing nonlinear excitation dynamics in quantum magnets, overcoming the limitations of traditional inelastic neutron scattering as a linear probe. The authors use here classical molecular dynamics simulations to compare the $2D\phantom{\rule{0}{0ex}}C\phantom{\rule{0}{0ex}}S$ responses of various models with large Kitaev interactions, revealing distinct features between quantum spin liquids, classical spin liquids, and large unit cell magnetic orders. These findings underscore the potential for $2D\phantom{\rule{0}{0ex}}C\phantom{\rule{0}{0ex}}S$ in disentangling the complex dynamics of frustrated magnetic systems.

DOI
10.1103/physrevb.110.104415

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Two-dimensional coherent spectroscopy (2D\phantom{\rule{0}{0ex}}C\phantom{\rule{0}{0ex}}S) has emerged as a powerful tool for probing nonlinear excitation dynamics in quantum magnets, overcoming the limitations of traditional inelastic neutron scattering as a linear probe. The authors use here classical molecular dynamics simulations to compare the 2D\phantom{\rule{0}{0ex}}C\phantom{\rule{0}{0ex}}S responses of various models with large Kitaev interactions, revealing distinct features between quantum spin liquids, classical spin liquids, and large unit cell magnetic orders. These findings underscore the potential for 2D\phantom{\rule{0}{0ex}}C\phantom{\rule{0}{0ex}}S in disentangling the complex dynamics of frustrated magnetic systems.
Inelastic neutron scattering (INS) has traditionally been one of the primary methods for investigating quantum magnets, particularly in identifying a continuum of excitations as a hallmark of spin fractionalization in quantum spin liquids (QSLs). However, INS faces severe limitations due to its inability to distinguish between such QSL signatures and similar excitation continua arising from highly frustrated magnetic orders with large unit cells or classical spin liquids. In contrast, two-dimensional coherent spectroscopy (2DCS) has emerged as a powerful tool to probe nonlinear excitation dynamics, offering insights into the underlying mechanisms behind these broad spectral features. In this paper, we utilize classical molecular dynamics (MD) techniques to explore the 2DCS responses of frustrated magnets with dominant Kitaev interactions. Comparing the classical and quantum versions of the pure Kitaev model our results indicate both clear similarities, in the form of sharp line features, and clear distinctions, in the locations of these features and in selection rules. Moreover, in the extended KΓΓ′KΓΓ'KΓΓ′ model, we show that the 2DCS response of the Kitaev spin liquid is completely distinct from that of large unit cell magnetic orders, despite both generating a broad continuum in INS. Additionally, we demonstrate the extreme sensitivity of classical 2DCS to thermal fluctuations and discuss the potential significance of quantum coherence in experimental settings. Overall, our work illustrates the potential of 2DCS in resolving the complex physics underlying ambiguous spin excitation continua, thereby enhancing our understanding of the dynamics in these frustrated systems.
Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χyzx(2)(ω1,ω2)χ^{(2)}_{yzx}(ω_1, ω_2)χyzx(2)​(ω1​,ω2​) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z2\mathbb{Z}_2Z2​ flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wavefunctions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our work can guide future 2DCS experiments on Kitaev magnets.
Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χ_{yzx}^{(2)}(ω_{1},ω_{2}) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z_{2} flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wave functions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our Letter can guide future 2DCS experiments on Kitaev magnets.
Identifying quantum spin liquids, magnon breakdown, or fractionalized excitations in quantum magnets is an ongoing challenge due to the ambiguity in interpreting excitation continua occurring in linear-response probes. Recently, it was proposed that techniques measuring higher-order response, such as two-dimensional coherent spectroscopy (2DCS), could resolve such ambiguities. Numerically simulating nonlinear response functions can, however, be computationally very demanding. We present an efficient Lanczos-based method to compute second-order susceptibilities χ 2 ( ω t , ω τ ) directly in the frequency domain. Applying this to extended Kitaev models describing α − RuCl 3 , we find qualitatively different nonlinear responses between intermediate magnetic field strengths and the high-field regime. To put these results into context, we derive the general 2DCS response of partially polarized magnets within the linear spin-wave approximation, establishing that χ 2 ( ω t , ω τ ) is restricted to a distinct universal form if the excitations are conventional magnons. Deviations from this form, as predicted in our Lanczos-based simulations for α − RuCl 3 , can hence serve in 2DCS experiments as direct criteria to determine whether an observed excitation continuum is of conventional two-magnon type or of different nature.
Unambiguous identification of fractionalized excitations in quantum spin liquids has been a long-standing issue in correlated topological phases. Conventional spectroscopic probes, such as the dynamical spin structure factor, can only detect composites of fractionalized excitations, leading to a broad continuum in energy. Lacking a clear signature in conventional probes has been the biggest obstacle in the field. In this work, we theoretically investigate what kinds of distinctive signatures of fractionalized excitations can be probed in two-dimensional nonlinear spectroscopy by considering the exactly solvable Kitaev spin liquids. We demonstrate the existence of a number of salient features of the Majorana fermions and fluxes in two-dimensional nonlinear spectroscopy, which provide crucial information about such excitations.
Local moments with a spin S>1/2 can exhibit a rich variety of elementary quasiparticle excitations, such as quadrupolar excitations, that go beyond the dipolar magnons of conventional spin-1/2 systems. However, the experimental observation of such quadrupolar excitations is often challenging due to the dipolar selection rules of many linear response probes, rendering them invisible. Here we show that nonlinear spectroscopy, in the form of two-dimensional coherent spectroscopy (2DCS), can be used to reveal quadrupolar excitations. Considering a family of spin-1 Heisenberg ferromagnets with single-ion easy-axis anisotropy as an example, we explicitly calculate their 2DCS signature by combining exact diagonalization and generalized spin wave theory. We further demonstrate that 2DCS can provide access to the quadrupolar weight of an excitation, analogous to how linear response provides access to the dipolar weight. Our work highlights the potential of nonlinear spectroscopy as a powerful tool to diagnose multipolar excitations in quantum magnets.