Theory of ESR dipolar splitting of a spin pair in the presence of avalanche phonons

Abstract

The ESR spectrum of a pair of paramagnetic spins $S=\frac{1}{2}$, interacting via dipolar magnetic forces, is calculated in the presence of an incoherent phonon avalanche, which is coupled to the spin pair by linear spin-phonon interaction. The problem is approximately solved by a Green's-function approach. Two cases are discussed, the first for an infinitely narrow phonon spectrum, and the second for finite bandwidth of the avalanche phonons. When the ESR frequency falls out of the avalanche band, the spectrum of the pair is shown to consist of two lines shifted from the no-avalanche resonant field and more closely spaced than in the no-avalanche situation. When the ESR frequency is within the avalanche band, a sharp decrease of the ESR intensity is expected. These results are interpreted in terms of ac Stark shift and of screening of dipolar interaction by the avalanche phonons. Their relationships to electromagnetic power narrowing of ESR lines and to the "magic angle" effect in NMR are discussed. Finally the theoretical results are examined in connection with phonon-avalanche experiments on ${\mathrm{Ce}}^{3+}$-doped lanthanum magnesium nitrate.