Nuclear Magnetic Resonance in Ferrimagnetic MnFe2O4

Abstract

The ${\mathrm{Mn}}^{55}$ nuclear magnetic resonance has been studied in Mn${\mathrm{Fe}}_{2}$${\mathrm{O}}_{4}$. The unpulled resonance frequency extrapolated to 0\ifmmode^\circ\else\textdegree\fi{}K is 587 Mc/sec. By studying the effect of an external magnetic field on the resonance it was determined that the main line at low temperatures arises from nuclei within the bulk of the single domains; and that the hyperfine coupling constant $A$ is negative. The form of the single-domain enhancement factor was verified. At higher temperatures, the signal comes from nuclei within the domain walls. Frequency pulling effects associated with both the wall nuclei and bulk nuclei are observed in the liquid-helium temperature range. The temperature dependence of the ${\mathrm{Mn}}^{55}$ frequency was used to study the temperature dependence of the $A$-site sublattice magnetization. The results are in excellent agreement with the predictions of spin-wave theory as applied to the spinel lattice. A precise cancellation of two ${T}^{\frac{5}{2}}$ terms arising, respectively, from the ${k}^{4}$ terms in the acoustic mode dispersion relation and the $k$-dependent transformation coefficients to diagonal spin-wave variables gives detailed information on $\ensuremath{\omega}(k)$ as well as a sensitive test of ferrimagnetic spin-wave theory. The effect on the nuclear resonance of very small anisotropy in the ferromagnetic system is discussed. In the event of a near crossover of the unperturbed nuclear and ferromagnetic uniform precession frequencies, the NMR line is shifted toward lower frequencies. This shift and the accompanying broadening are compared with the experimental observations in the vicinity of 250\ifmmode^\circ\else\textdegree\fi{}K where such a crossover is expected.