Nuclear-Magnetic-Resonance Study of Impurity Effects in a Heisenberg Antiferromagnet

Abstract

Experimental and theoretical impurity-magnon-mode studies have been made using the ${\mathrm{F}}^{19}$ NMR in the impure antiferromagnet $\mathrm{Mn}{\mathrm{F}}_{2}:X$ (where $X=\mathrm{V},\phantom{\rule{0ex}{0ex}}\mathrm{F}\mathrm{e},\phantom{\rule{0ex}{0ex}}\mathrm{C}\mathrm{o},\phantom{\rule{0ex}{0ex}}\mathrm{N}\mathrm{i},\phantom{\rule{0ex}{0ex}}\mathrm{o}\mathrm{r}\phantom{\rule{0ex}{0ex}}\mathrm{Z}\mathrm{n}$, usually in concentrations of 1% or less). Fixed-frequency spin-echo techniques were employed with a variable external field applied parallel to the unique axis. At low temperatures, the frequency position and relative intensity of a given, discrete impurity-associated ${\mathrm{F}}^{19}$ resonance were used to identify the position in the lattice of that particular ${\mathrm{F}}^{\ensuremath{-}}$ ion relative to the impurity. Both the homogeneous and inhomogeneous linewidths of these resonances were examined, and their magnitudes were interpreted. From the temperature dependence of the many resonances associated with a specific impurity, the temperature dependence of the impurity, near-neighbor (nn), and next-near-neighbor (nnn) spin magnetizations ${M}_{i}(t)$ could be determined. It was found that a sizable nn host-impurity exchange interaction ${J}_{\mathrm{nn}}$ is required to fit the ${M}_{i}(t)$ data in the $\mathrm{Mn}{\mathrm{F}}_{2}:X$, whereas in pure Mn${\mathrm{F}}_{2}$ and Fe${\mathrm{F}}_{2}$, $|{J}_{\mathrm{nn}}|\ensuremath{\ll}|{J}_{\mathrm{nnn}}|$. Good agreement between experiment and the Hone-Walker (HW) thermodynamic Green's-function theory was found for ${M}_{\mathrm{nnn}}(T)$ for the case of a spinless impurity (${\mathrm{Zn}}^{2+}$); a corresponding theory does not yet exist for which both ${S}_{\mathrm{imp}}\ensuremath{\ne}0$ and ${J}_{\mathrm{nn}}\ensuremath{\ne}0$. From the field dependence of the ${\mathrm{F}}^{19}$ resonances in Mn${\mathrm{F}}_{2}$: Zn at elevated temperatures, the parallel susceptibility ${{\ensuremath{\chi}}_{\mathrm{nnn}}}^{\ensuremath{'}\ensuremath{'}}(T)$ of a nnn to a spinless impurity was determined. Experiment and a modified spin-wave theory, which uses the HW impurity spectral weight function, agree well. The magnitude and temperature dependence of the nuclear spin-lattice relaxation rates ${({T}_{1})}_{i}^{\ensuremath{-}1}$ for several of the impurity-associated ${\mathrm{F}}^{19}$ resonances was measured. Using the same theoretical approach as was made for ${{\ensuremath{\chi}}_{i}}^{\ensuremath{'}\ensuremath{'}}(T)$, the nuclear relaxation via two-magnon scattering was obtained. Comparison between theory and experiment is not possible, as this requires a detailed knowledge of the spatial dependence of the phase of the impurity-magnon wave functions which are unknown at present. In addition to the single-impurity studies, several crystals with larger impurity concentrations were examined. Their resonances gave information on the tendency of impurities to cluster. Finally, a detailed, albeit crude, model of strain effects on the local ${\mathrm{F}}^{19}$ transferred hyperfine fields in an imperfect Mn${\mathrm{F}}_{2}$ crystal is given, which yields reasonable results for the displacements of specific resonances from their expected positions.