Exchange narrowing of the one- and two-phonon contributions to the electron spin resonance linewidth in Co 3 O 4

Abstract We investigate the temperature dependence of the electron spin resonance (ESR) linewidth above the critical region in Co 3 O 4 . The focus is on the temperature dependence of the one and two-phonon processes. We express the linewidth as a sum of three terms, a constant, associated with spin-spin interactions, a one-phonon term, and a two-phonon term, and use a least-squares fit over the temperature range 50 K  ≤ T ≤  500 K in analyzing the data. It is found that the spin-spin mechanism is dominant below 100 K, while the two-phonon mechanism is most important above 250 K. In the intermediate region, all three mechanisms make significant contributions. The success of the high temperature approximation for the phonon terms, which occurs well below the Debye temperature of 525 K, is attributed to the exchange narrowing of the bandwidth of the phonons contributing to the linewidth. The phonon mechanisms for the ESR linewidth in magnetic insulators are compared with the phonon linewidth mechanisms for magnetic impurities in non-magnetic crystals.