Magnetothermal Transport in Spin-Ladder Systems

TL;DR

This paper develops a theoretical model for magnetothermal conductivity in spin-1/2 ladder systems, emphasizing spinon-phonon interactions and their impact on heat transport under strong magnetic fields.

Contribution

It introduces a low-energy theory mapping the ladder Hamiltonian to an XXZ spin-chain, accounting for spinon-phonon hybridization and scattering mechanisms affecting thermal conductivity.

Findings

The model explains the magnetic field dependence of thermal conductivity.

Hybridization of spinons and phonons enhances scattering effects.

Results are consistent with experimental measurements in BPCB.

Abstract

We study a theoretical model for the magnetothermal conductivity of a spin-1/2 ladder with low exchange coupling ($J\ll\Theta_D$) subject to a strong magnetic field $B$. Our theory for the thermal transport accounts for the contribution of spinons coupled to lattice phonon modes in the one-dimensional lattice. We employ a mapping of the ladder Hamiltonian onto an XXZ spin-chain in a weaker effective field B_{eff}=B-B_{0}$, where $B_{0}=(B_{c1}+B_{c2})/2$ corresponds to half-filling of the spinon band. This provides a low-energy theory for the spinon excitations and their coupling to the phonons. The coupling of acoustic longitudinal phonons to spinons gives rise to hybridization of spinons and phonons, and provides an enhanced $B$-dependant scattering of phonons on spinons. Using a memory matrix approach, we show that the interplay between several scattering mechanisms, namely: umklapp, disorder and phonon-spinon collisions, dominates the relaxation of heat current. This yields magnetothermal effects that are qualitatively consistent with the thermal conductivity measurements in the spin-1/2 ladder compound ${\rm Br_4(C_5H_{12}N)_2}$ (BPCB).