Bistable self-organization of nuclear spins in conducting solids

Abstract

Under suitable conditions the dynamic nuclear polarization by the Overhauser effect in conductors is responsible for a bistable hysteresis of the electron spin resonance (ESR) line of conduction electrons [Phys. Rev. B 47, 15 023 (1993)]. We study in this work the dynamics of the phenomenon in terms of the bistable self-organization of nuclear spins and the microwave field. The deterministic evolution of the nuclear field is described as an overdamped motion in a potential $U$. It is shown that the shape of the ESR line, in both monostable and bistable regimes, is proportional to the second derivative of this potential. By taking into account the fluctuations of the nuclear field, a Schr\odinger equation for the self-organized spin-field system is derived. For the monostable Overhauser effect, this equation is that of the quantum mechanical harmonic oscillator. The self-organized spin-field system can thus be compared with a vibrating molecule in the nuclear field space, in which the steady state nuclear field corresponds to the equilibrium interatomic distance. With this analogy, the bistable spin-field system may also be compared to a mixed valence molecular complex, in which the two stable configurations of the complex correspond to the two stable steady states of the nuclear field.