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arXiv:1907.06542 · Physical Review Letters

Tunable Magnon Interactions in a Ferromagnetic Spin-1 Chain

Prashant Chauhan, Fahad Mahmood, Hitesh J. Changlani, S. M. Koohpayeh, N. P. Armitage

Published Jan 23, 2020• 28 citations
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Abstract

NiNb_{2}O_{6} is an almost ideal realization of a 1D spin-1 ferromagnetic Heisenberg chain compound with weak unidirectional anisotropy. Using time-domain THz spectroscopy, we measure the low-energy electrodynamic response of NiNb_{2}O_{6} as a function of temperature and external magnetic field. At low temperatures, we find a magnonlike spin excitation, which corresponds to the lowest energy excitation at q∼0. At higher temperatures, we unexpectedly observe a temperature-dependent renormalization of the spin-excitation energy, which has a strong dependence on field direction. Using theoretical arguments, exact diagonalizations, and finite temperature dynamical Lanczos calculations, we construct a picture of magnon-magnon interactions that naturally explains the observed renormalization. We show how magnetic field strength and direction may be used to directly tune the sign of the magnon-magnon interaction. This unique scenario is a consequence of the spin-1 nature and has no analog in the more widely studied spin-1/2 systems.

DOI
10.1103/physrevlett.124.037203

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NiNb_{2}O_{6} is an almost ideal realization of a 1D spin-1 ferromagnetic Heisenberg chain compound with weak unidirectional anisotropy. Using time-domain THz spectroscopy, we measure the low-energy electrodynamic response of NiNb_{2}O_{6} as a function of temperature and external magnetic field. At low temperatures, we find a magnonlike spin excitation, which corresponds to the lowest energy excitation at q∼0. At higher temperatures, we unexpectedly observe a temperature-dependent renormalization of the spin-excitation energy, which has a strong dependence on field direction. Using theoretical arguments, exact diagonalizations, and finite temperature dynamical Lanczos calculations, we construct a picture of magnon-magnon interactions that naturally explains the observed renormalization. We show how magnetic field strength and direction may be used to directly tune the sign of the magnon-magnon interaction. This unique scenario is a consequence of the spin-1 nature and has no analog in the more widely studied spin-1/2 systems.
Quasiparticles are physically motivated mathematical constructs for simplifying the seemingly complicated many-body description of solids. A complete understanding of their dynamics and the nature of the effective interactions between them provides rich information on real material properties at the microscopic level. In this paper, we explore the dynamics and interactions of magnon quasiparticles in a ferromagnetic spin-1 Heisenberg chain with easy-axis on-site anisotropy, a model relevant for the explanation of recent terahertz optics experiments on NiNb2O6{\mathrm{NiNb}}_{2}{\mathrm{O}}_{6}NiNb2​O6​ [P. Chauhan et al., Phys. Rev. Lett. 124, 037203 (2020)], and nonequilibrium dynamics in ultracold-atomic settings [W. C. Chung et al., Phys. Rev. Lett. 126, 163203 (2021)]. We build a picture for the properties of clouds of a few magnons with the help of exact diagonalization and density matrix renormalization group calculations supported by physically motivated Jastrow wave functions. We show how the binding energy of magnons effectively reduces with their number and explain how this energy scale is of direct relevance for dynamical magnetic susceptibility measurements. This understanding is used to make predictions for ultracold-atomic platforms, which are ideally suited to study the thermalization of multimagnon states. We simulate the nonequilibrium dynamics of these chains using the matrix product state based time-evolution block decimation algorithm and explore the dependence of revivals and thermalization on magnon density and easy-axis on-site anisotropy (which controls the strength of effective magnon interactions). We observe behaviors akin to those reported for many-body quantum scars, which we explain with an analytic approximation that is accurate in the limit of small anisotropy.
Abstract Motivated by recent experimental progress on the quasi-one-dimensional quantum magnet NiNb2O6, we study the spin dynamics of an S = 1 ferromagnetic Heisenberg chain with single-ion anisotropy by using a semiclassical molecular dynamics approach. This system undergoes a quantum phase transition from a ferromagnetic to a paramagnetic state under a transverse magnetic field, and the magnetic response reflecting this transition is well described by our semiclassical method. We show that at low temperature the transverse component of the dynamical structure factor depicts clearly the magnon dispersion, and the longitudinal component exhibits two continua associated with single- and two-magnon excitations, respectively. These spin excitation spectra show interesting temperature dependence as effects of magnon interactions. Our findings shed light on the experimental detection of spin excitations in a large class of quasi-one-dimensional magnets.
We report on an electron spin resonance (ESR) study of a nearly one-dimensional (1D) spin-12\frac{1}{2}21​ chain antiferromagnet, Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​, with extremely weak magnetic ordering. The ESR spectra at T>TNT>{T}_{N}T>TN​, in the disordered Luttinger-spin-liquid phase, reveal nearly ideal Heisenberg-chain behavior with only a very small, field-independent linewidth, $\ensuremath{\sim}1/T$. In the ordered state, below TN{T}_{N}TN​, we identify field-dependent antiferromagnetic resonance modes, which are well described by pseudo-Goldstone magnons in the model of a collinear biaxial antiferromagnet. Additionally, we observe a major resonant mode with unusual and strongly anisotropic properties, which is not anticipated by the conventional theory of Goldstone spin waves. We propose that this unexpected magnetic excitation can be attributed to a field-independent magnon mode renormalized due to its interaction with the high-energy amplitude (Higgs) mode in the regime of weak spontaneous symmetry breaking.
The magnetic and thermodynamic properties of a ferrimagnetic decorated spin-(12,1)(\frac{1}{2},1)(21​,1) Heisenberg chain with spin-1 pendant spins are investigated for three cases: (A) J1,J2>0{J}_{1},{J}_{2}>0J1​,J2​>0; (B) J1>0{J}_{1}>0J1​>0 and J2<0{J}_{2}<0J2​<0; and (C) J1<0{J}_{1}<0J1​<0 and J2>0{J}_{2}>0J2​>0, where J1{J}_{1}J1​ and J2{J}_{2}J2​ are the exchange couplings between spins in the chain and along the rung, respectively. The low-lying and magnetic properties are explored jointly by the real-space renormalization group, spin wave, and density-matrix renormalization-group methods, while the transfer-matrix renormalization-group method is invoked to study the thermodynamics. It is found that the magnon spectra consist of a gapless and two gapped branches. Two branches in case (C) have intersections. The coupling dependence of low-energy gaps are analyzed. In a magnetic field, a m=32m=\frac{3}{2}m=23​ (mmm is the magnetization per unit cell) plateau is observed for case (A), while two plateaux at m=12m=\frac{1}{2}m=21​ and 32\frac{3}{2}23​ are observed for cases (B) and (C). Between the two plateaux in cases (B) and (C), the sublattice magnetizations for the spins coupled by ferromagnetic interactions have decreasing regions with increasing the magnetic field. At finite temperature, the zero-field susceptibility temperature product $\ensuremath{\chi}T$ and specific heat exhibit distinct exotic features with varying the couplings and temperature for different cases. $\ensuremath{\chi}T$ is found to converge as $T\ensuremath{\rightarrow}0$, which is different from the divergent behavior in the spin-(12,1)(\frac{1}{2},1)(21​,1) mixed-spin chain without pendants. The observed thermodynamic behaviors are also discussed with the help of their low-lying excitations.
We study theoretically the Raman-scattering spectra in the one-dimensional (1D) quantum spin-1/2 antiferromagnets. The analysis reveals that their low-energy dynamics is exquisitely sensitive to various perturbations to the Heisenberg chain with nearest-neighbor exchange interactions, such as magnetic anisotropy, longer-range exchange interactions, and bond dimerization. These weak interactions are mainly responsible for the Raman scattering and give rise to different types of spectra as functions of frequency, temperature, and external field. In contrast to the Raman spectra in higher dimensions in which the two-magnon process is dominant, those in 1D antiferromagnets provide much richer information on these perturbations.
We study few-magnon excitations in a finite-size spin-SSS chain with ferromagnetic nearest-neighbor (NN) interaction J>0J>0J>0 and antiferromagnetic next-nearest-neighbor (NNN) interaction ${J}^{\ensuremath{'}}<0$, in the presence of the single-ion (SI) anisotropy DDD. We first reveal the condition for the emergence of zero-excitation-energy states. In the isotropic case with $\mathrm{\ensuremath{\Delta}}={\mathrm{\ensuremath{\Delta}}}^{\ensuremath{'}}=1$ ($\mathrm{\ensuremath{\Delta}}$ and ${\mathrm{\ensuremath{\Delta}}}^{\ensuremath{'}}$ are the corresponding anisotropy parameters), a threshold of $J/|{J}^{\ensuremath{'}}|$, above which the ground state is ferromagnetic, is determined by exact diagonalization for short chains up to 12 sites. Using a set of exact two-magnon Bloch states, we then map the two-magnon problem to a single-particle one on an effective open chain with both NN and NNN hoppings. The whole two-magnon excitation spectrum is calculated for large systems, and the commensurate-incommensurate transition in the lowest-lying mode is found to exhibit different behaviors between S=1/2S=1/2S=1/2 and higher spins due to the interplay of the SI anisotropy and the NNN interaction. For the commensurate momentum $k=\ensuremath{-}\ensuremath{\pi}$, the effective lattice is decoupled into two NN open chains that can be exactly solved via a plane-wave ansatz. Based on this, we analytically identify in the ${\mathrm{\ensuremath{\Delta}}}^{\ensuremath{'}}\ensuremath{-}D/|{J}^{\ensuremath{'}}|$ plane the regions supporting the SI or NNN exchange two-magnon bound states near the edge of the band. In particular, we prove that there always exists a lower-lying NN exchange two-magnon bound state near the band edge for arbitrary $S\ensuremath{\ge}1/2$. Finally, we numerically calculate the nnn-magnon spectra for S=1/2S=1/2S=1/2 with $n\ensuremath{\le}5$ by using a spin-operator matrix element method. The corresponding nnn-magnon commensurate instability regions are determined for finite chains, and consistent results with prior literature are observed.