Zero-FieldCr53Nuclear Magnetic Resonance in Ferromagnetic CrI3: Renormalized Spin-Wave and Green's-Function Analysis

Abstract

The zero-field ${}_{}{}^{53}{}_{}{}^{}\mathrm{Cr}$ nuclear magnetic resonance (NMR) has been studied in ferromagnetic Cr${\mathrm{I}}_3$ in the temperature range 1.6-27.5°K. The observed spectrum consists of a quadrupole triplet ($h^{-1\mathrm{}}{e}^{2}qQ=0.744\mathrm{}\pm 0.005$ Mc/sec) arising from nuclei within the ferromagnetic domains, and a broad absorption at lower frequencies due to nuclei in domain walls. The difference between the domain and wall frequencies follows the relation $\Delta \nu \left(\frac{\mathrm{Mc}}{sec}\right)=0.8(\pm 0.1)+0.248(\pm 0.005)T$ over the entire range of our experiments, where $T$ is the temperature in °K. The temperature dependence of the domain magnetization, as derived from the resonance data, is in excellent agreement with predictions of a renormalized spin-wave model using values for the intralayer and interlayer exchange constants of $\frac{J_T}{k_B}=13.5\mathrm{}\pm 0.5$ and $\frac{J_L}{k_B}=1.72\mathrm{}\pm 0.20$, respectively, and a published value for the uniaxial anisotropy constant. The extrapolated 0°K zero-field ½  -½ ${}_{}{}^{53}{}_{}{}^{}\mathrm{Cr}$ NMR frequency is $\nu \mathrm{}\left(0\right)=49.393\mathrm{}$ Mc/sec. The results of the spin-wave analysis are supported by calculations of the Curie temperatures for Cr${\mathrm{Br}}_3$ and Cr${\mathrm{I}}_3$ using the random-phase Green's-function method, based on the spin-wave-derived exchange constants. The calculated values of 33.6°K for Cr${\mathrm{Br}}_3$ and 68.2°K for Cr${\mathrm{I}}_3$ are in excellent agreement with reported experimental ordering temperatures of 32.5° and 68°K, respectively.