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)].
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