Bipolarons and the temperature dependence of exchange in the metal trihydrides

We analyze a two-particle, two-site, tight-binding model linearly coupled to a harmonic bath in order to describe the temperature dependence of exchange in the metal trihydrides. We present a variational calculation that predicts two regimes: coherent, motionally narrowed exchange, and incoherent, quenched exchange. We show for an ohmic bath that the behavior rapidly switches from unquenched to quenched at a finite temperature that scales linearly with the correlation energy U and logarithmically with both bath coupling parameters and the zero-temperature exchange 4t2/U. We show that Zilm’s description of the temperature dependence of the spin coupling (Ref. 1) can be derived asymptotically and shows a geometric dependence of the ‘‘activation’’ energy that is absent in a finite basis approximation. The model proposed explains the temperature dependence of the exchange splittings observed by nuclear magnetic resonance for the metal trihydrides.