Nuclear Spin Relaxation in Molybdenum Metal

Abstract

The ${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}$ and ${}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}$ nuclear spin-spin and spin-lattice relaxation rates in molybdenum metal have been studied in the temperature range $1\le T\le 4$°K. The transverse relaxation process is found to have an exponential time dependence (corresponding to a Lorentzian line shape) with characteristic times $T_2\left({}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}\right)=10\mathrm{}\pm 1$ msec and $T_2\left({}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}\right)=14\mathrm{}\pm 1$ msec which are independent of temperature. At 4.0°K the longitudinal relaxation times are $T_1\left({}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}\right)=8.9\mathrm{}\pm 0.2$ sec and $T_1\left({}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}\right)=7.6\mathrm{}\pm 0.2$ sec. The ratio $\frac{T_1\left({}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}\right)}{T_1\left({}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}\right)}=1.17\mathrm{}\pm 0.03$ is larger than the square of the nuclear moment ratio, ${\left(\frac{{\mu }^{97}}{{\mu }^{95}}\right)}^2=1.0424\mathrm{}$. This anomaly is attributed to an electric quadrupole process due to $d$-band conduction electrons. This process contributes significantly to the relaxation rate of ${}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}$ but not to that of ${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}$ because of the large difference in nuclear quadrupole moments ($\frac{Q^{97}}{Q^{95}}=9.2\mathrm{}$). The known moment ratios are used to partition the observed rates into nuclear magnetic dipole ($R_{\mu }$) and nuclear electric quadrupole ($R_Q$) contributions. The resulting values of $R_Q$ yield quadrupole moment estimates $Q^{95}=(0.12\mathrm{}\pm 0.03)\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$ and $Q^{97}=(1.1\mathrm{}\pm 0.2)\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$. An approximate separation of $R_{\mu }$ into contact, core-polarization, and orbital rates has been achieved. The principal contribution to the Knight shift and to the conduction-electron susceptibility is shown to arise from the orbital magnetization of the $d$ band. The results of this study provide an upper-limit estimate of about 3 for the electron-phonon enhancement of the $s$-electron specific heat.