Spin-Wave Renormalization Applied to Ferromagnetic CrBr3

Abstract

Nuclear-magnetic-resonance-domain magnetization data for ferromagnetic Cr${\mathrm{Br}}_3$ have been extended over the range 1-20°K. Using the low-temperature (≤5.25°K) data and Holstein-Primakoff spin-wave theory without the usual long-wavelength approximation, we have shown that exchange constants reported by Gossard, Jaccarino, and Remeika are in error by about 40%. This error resulted from the long-wavelength approximation, which causes, even at temperatures $\frac{1}{9}\mathrm{th}$ the Curie temperature, errors much larger than experimental errors. In the low-temperature range, we have found a 20% range for the values of the exchange constants which will explain the experimental results. However, by using spin-wave renormalization techniques to interpret the intermediate temperature data, the acceptable range in values for the exchange constants is narrowed to less than 2%. We have been able to fit the experimental NMR frequencies, throughout the temperature range of 1-20°K, with the renormalized spin-wave theory. The resulting rms error of 16.2 kc/sec lies within the mean experimental error, thereby giving experimental verification to the approximations used in developing the spin-wave renormalization. This data fit gives 8.25°K for the intralayer exchange constant, 0.497°K for the interlayer exchange constant, and 58.099 Mc/sec for the 0°K, zero-field ${\mathrm{Cr}}^{53}$ resonance frequency.