  We investigated the unoccupied part of the electronic structure of the
oxygen-deficient hafnium oxide (HfO$_{\sim1.8}$) using soft x-ray absorption
spectroscopy at O $K$ and Hf $N_3$ edges. Band-tail states beneath the
unoccupied Hf 5$d$ band are observed in the O $K$-edge spectra; combined with
ultraviolet photoemission spectrum, this indicates the non-negligible
occupation of Hf 5$d$ state. However, Hf $N_3$-edge magnetic circular dichroism
spectrum reveals the absence of a long-range ferromagnetic spin order in the
oxide. Thus the small amount of $d$ electron gained by the vacancy formation
does not show inter-site correlation, contrary to a recent report [M.
Venkatesan {\it et al.}, Nature {\bf 430}, 630 (2004)].
