Electron-spin resonance in insulating doped semiconductors

Spin dynamics of shallow impurity electrons in the insulating phase of $n$-doped semiconductors is examined within the framework of the scaling theory of a disordered spin-½ Heisenberg antiferromagnet. Quantum fluctuations of the donor nuclear spins are included and found to be important in determining the ESR line shape and position. With use of the known hyperfine constant, a quantitative fit to the experimental results is obtained, including the dramatic temperature and frequency dependence of the linewidth and resonance field seen in phosphorus-doped silicon at millikelvin temperatures.