Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

Abstract

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) "interrupted" ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically Tg ≃ 100 − 200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal and C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like τ typ ∼ τ0 exp (Tg/T ). The glass cross-over temperature Tg related to correlations among solitons is equal to the average energy barrier and scales like Tg ∼ 2xξ0∆. x is the concentration of defects, ξ0 the correlation length of the CDW or SDW and ∆ the charge or spin gap.

Interplay between Phase Defects and Spin Polarization in the Specific Heat of the Spin-Density-Wave Compound(TMTTF)2Brin a Magnetic Field

“…Larkin [4] and Ovchinnikov [5] have shown that a single strong pinning impurity leads to a bound state of an electronlike soliton and a hole-like antisoliton. This results in a potential V (ϕ(y i )) with multiple minima [6], leading to slow relaxation in agreement with the very low temperature heat relaxation experiments [5].…”

“…This allows a systematic study of the equilibrium energy relaxation over almost one decade in temperature and a direct comparison to the local model of strong pinning without introducing an additional time scale related to ageing [6,11].…”

“…Collective pinning is however frozen below a glass transition of order ∼ 50 K, as shown by dielectric susceptibility experiments [2]. At very low temperature, the residual degrees of freedom in a zero magnetic field correspond to the local defects of the local model of strong pinning [3,4,5,6,7,8]. Larkin [4] and Ovchinnikov [5] have shown that a single strong pinning impurity leads to a bound state of an electronlike soliton and a hole-like antisoliton.…”