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Journal of Applied Physics

Solitons in ferromagnetic spin-1 chains?

T. Schneider, E. Stoll

Published Nov 1, 1982• 11 citations
Publisher

Abstract

We report finite-ring calculations revealing that spin-1 ferromagnetic easy-plane chains in a symmetry-breaking field are well described by a weakly interacting Bose gas. The thermally-induced central peak (CP) previously observed by neutron scattering from CsNiF3, and interpreted in terms of solitons, is traced back to annihilation/creation processes of the excitations. Its temperature variation shows a pronounced interaction-mediated saturation. The essential features of the spin dynamics and of the field and temperature dependence of the specific heat can be explained without solitons. We predict corresponding CP phenomena in a large variety of spin systems.

DOI
10.1063/1.330294

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We report finite-ring calculations revealing that spin-1 ferromagnetic easy-plane chains in a symmetry-breaking field are well described by a weakly interacting Bose gas. The thermally-induced central peak (CP) previously observed by neutron scattering from CsNiF3, and interpreted in terms of solitons, is traced back to annihilation/creation processes of the excitations. Its temperature variation shows a pronounced interaction-mediated saturation. The essential features of the spin dynamics and of the field and temperature dependence of the specific heat can be explained without solitons. We predict corresponding CP phenomena in a large variety of spin systems.
A variational estimate of the free energy of a quantum spin chain based on the stochastic behavior of the quantization axes is proposed. It allows a description of the nonlinear excitations and quantum spin waves within the same framework. For an easy-plane ferromagnet with an external field in the plane it reveals that the nonlinear excitations (solitons) are predominantly described by the classical degrees of freedom. Considerable effort has been devoted to the theoretical description1 and experimental verification of the existence of nonlinear excitations. In this field magnetic chain systems have played an important part.2 Chain systems with an easy-plane anisotropy, such as (C6 H11 NH3 )CuBr3 (CHAB) and CsNiF3 , which are subjected to a symmetry breaking field, were found to be soliton bearing.3 Theoretically the description of the nonlinear effect is based on the mapping of the spin dynamics on a sine-Gordon model. Further research4 indicated that the interpretation of the thermodynamical properties of real systems in terms of the sine-Gordon model required however quantum and anisotropy corrections. Since the dipolar interactions between the spins in the chain are considered to be negligible, the direction of the spin chain in configuration space with respect to any preferred direction in spin space does not enter explicitly in the Hamiltonian. This makes it interesting to define a site-dependent z direction in spin space which makes an angle (Θn ,φn ) with the z direction in configuration space. The model Hamiltonian can then be written in terms of the spin operators defined with respect to the site-dependent quantization axis. The representation with equal quantization axis for all the sites is related to the representation with different quantization axes at each site by a rotation in spin space. The unitary transformation that describes the rotation contains the angles (Θn ,φn ), which we have treated as random variables. Based on this observation we have proposed a new variational approach for the quantum spin chain. We will outline the main results here. A full account is published elsewhere.5 In our approach the free energy of the system can be separated in a quantum part and a classical part. The free energy F of the chain is then approximated by an upper bound F<Fcl +Fqm , where βFcl =−ln[E(exp−βVcl )] and βFqm =−ln Tr(exp−β〈Hqm 〉). The first part is a configurational classical free energy, depending on the choice of the probability distribution for the quantization axes via the expectation E. The second contribution is the free energy of a modified quantum chain, whose parameters are classical averages and can be obtained from the configurational classical free energy. For easy-plane ferromagnetic chains, the nonlinear excitations are comprised in the classical part, whereas the quantum part contains predominantly linear excitations. For those thermodynamical quantities that are insensitive to the contribution of the quantum excitations, the chain is thermodynamically equivalent with a classical sine-Gordon system. The out-of-plane corrections are incorporated in the quantum part of the free energy. This behavior is corroborated experimentally by measurements of the excess heat capacity of CHAB for different magnetic fields with the same in-plane component.6 The validity of our approach is, however, not restricted to easy-plane ferromagnetic chains. Also for more complex systems with, for example, an orthorhombic or helical symmetry, the introduction of stochastic quantization axes can shed new light on some of the thermodynamical properties of these quantum systems in terms of their classical equivalent.
The excitation spectrum of the ferromagnetic s=12s=\frac{1}{2}s=21​ Ising-Heisenberg chain as probed by dynamic form factors is studied. Exact results are presented for zero temperature, and the modifications introduced by thermally induced transitions are elucidated by finite-chain calculations. A particularly interesting result is the occurrence of a thermally induced resonance around zero frequency for an Ising-like model. Its origin is traced back to transitions involving magnon bound states. The resonance structure of the dynamic form factors associated with a Heisenberg-like system turns out to be less spectacular, because the contributions of different induced transitions nearly overlap on the frequency scale; so that rather broad resonance structures result. Our findings have an important bearing on related models with s>12s>\frac{1}{2}s>21​, such as CsNiF3{\mathrm{F}}_{3}F3​, and on the soliton aspect of the classically treated systems.
We find the conditions under which the normal state of a spin-1 Bose gas is unstable toward condensation, ferromagnetism, liquid crystalline-like nematicity, and Bardeen-Cooper-Schrieffer-like pairing. When the spin-dependent interactions are much weaker than the density-density interaction there is direct transition from a featureless normal state to a fully ordered Bose-Einstein condensate with either ferromagnetic or nematic order. When the spin-independent and spin-dependent interactions are of comparable magnitude, we find several different symmetry breaking transitions at intermediate temperatures above the Bose-condensation transition temperature. We make predictions for the Tc{T}_{c}Tc​ for these transitions, and assess the role of magnetic field and finite system size.
Spinon, soliton and breather in the spin-1/2 antiferromagnetic chain KCuGaF6_66​
Elementary excitations of the S=1/2 one-dimensional antiferromagnet KCuGaF_6 were investigated by inelastic neutron scattering in zero and finite magnetic fields perpendicular to the (1, 1, 0) plane combined with specific heat measurements. KCuGaF6_66​ exhibits no long-range magnetic ordering down to 50 mK despite the large exchange interaction J/k_B=103 K. At zero magnetic field, well-defined spinon excitations were observed. The energy of the des Cloizeaux and Pearson mode of the spinon excitations is somewhat larger than that calculated with the above exchange constant. This discrepancy is mostly ascribed to the effective XY anisotropy arising from the large Dzyaloshinsky-Moriya interaction with an alternating D vector. KCuGaF_6 in a magnetic field is represented by the quantum sine-Gordon model, for which low-energy elementary excitations are composed of solitons, antisolitons and their bound states called breathers. Unlike the theoretical prediction, it was found that the energy of a soliton is smaller than that of the first breather, although the energy of the first breather coincides with that observed in a previous ESR measurement.
At sufficiently high phase space densities, the many-body state of a degenerate Bose gas can be described by a single macroscopic wavefunction that undergoes nonlinear dynamics. Ultracold Bose gases are a prominent platform in the field of nonlinear physics, enabling the study of stable stationary wavepackets, known as solitons. In these platforms, atom interactions are often weak and treated within a mean-field approach. However, interactions play a crucial role in the physics of these Bose gases and explain for example the formation mechanism of solitons or the emergence of a remarkable phase of matter: superfluidity. This thesis describes investigations on peculiar dynamics of ultracold Bose gases, which are approximated by zero-temperature physics. After introducing our experimental setup and its theoretical characterization, we discuss the survival of the superfluid property in spatially modulated systems, in connection with Leggett's seminal work in 1970 and the spectacular supersolid phase of matter. We then explore the physics of a specific type of 1D soliton that emerges in a weakly-immiscible two-component mixture, known as the magnetic soliton. Its name originates from its appearance in 1D ferromagnetic spin chains. Magnetic solitons exhibit a captivating periodic motion under a uniform force field, similar to the Bloch oscillations of electrons in solids. Finally, we introduce a new experimental setup for studying Rydberg excitations and the realization of an all-optical Bose-Einstein-Condensate.