Thermal conductivity inlarge−Jtwo-dimensional antiferromagnets: Role of phonon scattering

Abstract

Motivated by the recent heat transport experiments in 2D antiferromagnets, such as La2CuO4, where the exchange coupling J is larger than the Debye energy ΘD, we discuss different types of relaxation processes for magnon heat current with a particular focus on coupling to 3D phonons. We study thermal conductivity by these in-plane magnetic excitations using two distinct techniques, Boltzmann formalism within the relaxation-time approximation and memory-function approach. Within these approaches, a close consideration is given to the scattering of magnons by both acoustic and optical branches of phonons. A remarkable accord between the two methods with regards to the asymptotic behavior of the effective relaxation rates is demonstrated. Additional scattering mechanisms, due to grain boundaries, impurities, and finite correlation length in the paramagnetic phase, are discussed and included in the calculations of the thermal conductivity κ(T ). Again, we demonstrate a close similarity of the results from the two techniques of calculating κ(T ). Our complementary approach strongly suggests that scattering from optical or zone-boundary phonons is important for magnon heat current relaxation in a high temperature window of ΘD T J.

Heat Transport in Spin Chains with Weak Spin-Phonon Coupling

“…Within this picture, the transport relaxation time is the same as spin-boson scattering time and the corresponding meanfree path fits excellently the available experimental data. Further systematic extensions of our theory to include multi-phonon scattering that can influence thermal conductivity at higher temperature are briefly discussed.Finally, we emphasize an important physical constraint on the strength of spin-phonon coupling of magnetoelastic nature [31,32], which is weak in the materials of interest. While an estimate of this coupling can be made microscopically, a simple piece of phenomenological evidence for this criterion is the absence of the spinPeierls transition in real compounds down to very low temperatures.…”

“…Self-energy and relaxation rate.-Assuming the spinphonon coupling to be small, a conjecture discussed below in detail [32], one can consider only the second-order spin-boson self-energy in Fig. 2(a) given by…”

“…where we introduced a naturally appearing dimensionless spin-phonon coupling constant g sp = λ/(aJ √ 2mω 0 ) [31,32]. For the spin-boson scattering rate, we need the imaginary part of the self-energy that is analytically continued to real frequencies.…”

“…As discussed in Refs. [31,32], the constant is a product of two parameters, with one characterizing the change of J by atomic displacement, γ = λ/J = a(∂J/∂x)/J, and the other representing an amplitude of zero-point atomic motion relative to a lattice constant [36], α = / √ 2ma 2 ω 0 , where is made explicit and m is the reduced mass associated with the phonon mode ω 0 . Parameter α is small, while γ can be large [31,43] because the superexchange is sensitive to the interatomic distance.…”

Thermal conductivity of local moment models with strong spin-orbit coupling

“…58 Previous studies of thermal transport in insulating magnetic materials indicated that the magnetic and thermal contributions to the thermal conductivity can be comparable. [59][60][61][62][63][64] Our main result in this work is to show that the spatially anisotropic magnetic states that can arise from strong spin-orbit coupling can dramatically affect the thermal transport, or have a rather small effect depending on the relative size of magnon and phonon thermal conductivities. In some cases, the thermal transport may help identify the symmetries of the magnetically ordered state if other measurements are difficult or problematic.…”