The spin-Peierls transition beyond the adiabatic approximation

TL;DR

This paper presents a new theoretical approach to the spin-Peierls transition that accounts for three-dimensional phonon effects without relying on adiabatic approximations, explaining experimental observations in CuGeO3.

Contribution

It introduces a non-adiabatic, exact phonon integration method combined with a mean field interchain analysis for the spin-Peierls transition, improving upon previous models.

Findings

Spin gap and critical temperature are reduced by finite phonon frequency effects.

The theory explains the absence of a soft mode in CuGeO3.

Results are applicable to inorganic spin-Peierls compounds.

Abstract

We develop a theory of the spin-Peierls transition taking into account the three dimensional character of the phonon field. Our approach does not rely on the adiabatic or mean field treatment for the phonons. It is instead based in the exact integration of the phonon field, the exact long wavelength solution of the one chain spin problem, and then a mean field approximation for the interchain interaction. We show that the spin gap and the critical temperature are strongly reduced due to the finite frequency effects of the phonon coupling transverse to the magnetic chains. We claim that our results should be applicable to the inorganic spin-Peierls compound CuGeO$_3$. We show that the long standing discussion on absence of a soft mode in this compound can be naturally resolved within our theory.