$^{27}$Al-NMR Study of the Spinel Compound CoAl$_{2}$O$_{4}$*

CoAl$_{2}$O$_{4}$, a geometrically frustrated magnet, is believed to be located in the vicinity of a quantum melting point of the AFM ordered state. In CoAl$_{2}$O$_{4}$, magnetic frustration originates from Co$^{2+}(S =$ 3/2) spins on the tetrahedral A-site via non-magnetic Al ions occupying the octahedral B-site. To study the magnetic properties of CoAl$_{2}$O$_{4}$ from a microscopic point of view, we have carried out $^{27}$Al-NMR measurements using a well-characterized powder sample of CoAl$_{2}$O$_{4}$. The temperature dependence of the magnetic susceptibility $\chi $ shows a broad peak around 15 K and does not show any difference in zero-field-cooled and field-cooled measurements. $^{27}$Al-NMR spectra at 9.3 MHz ($H =$ 0.84 T) show seven peaks characterized by quadrupolar splitting with $\nu_{\mathrm{Q}}=$ 0.55 MHz at temperatures above 10 K. Below 10 K, the spectrum broadens suddenly. We also observe a peak of 1/$T_{1}$ of $^{27}$Al at 10 K. These NMR results clearly indicate magnetic ordering at 10 K, although $\chi $ does not exhibit any signature of long-range magnetic ordering.