  Red optical and near-infrared spectroscopy are presented for SDSS
J125637.13-022452.4, one of only four L subdwarfs reported to date. These data
confirm the low-temperature, metal-poor nature of this source, as indicated by
prominent metal-hydride bands, alkali lines, and collision-induced H2
absorption. The optical and near-infrared spectra of SDSS J1256-0224 are
similar to those of the sdL4 2MASS J16262034+3925190, and we derive a
classification of sdL3.5 based on the preliminary scheme of Burgasser, Cruz, &
Kirkpatrick. The kinematics of SDSS J1256-0224 are consistent with membership
in the Galactic inner halo, with estimated $UVW$ space velocities indicating a
slightly prograde, eccentric and inclined Galactic orbit (3.5 <~ R <~ 11 kpc;
|Zmax| = 7.5 kpc). Comparison to synthetic spectra computed with the Phoenix
code, including the recent implementation of kinetic condensate formation
(Drift-Phoenix), indicate Teff ~ 2100-2500 K and [M/H] ~ -1.5 to -1.0 for logg
~ 5.0-5.5 (cgs), although there are clear discrepancies between model and
observed spectra particularly in the red optical region. The stronger
metal-oxide bands present in the Drift-Phoenix model spectra, a result of
phase-non-equilibrium abundances of grain species, appears to contradict prior
suggestions that grain formation is inhibited in metal-poor atmospheres;
conclusive statements on the metallicity dependence of grain formation
efficiency are as yet premature. In addition, an apparent shift in the
temperature scale of L subdwarfs relative to L dwarfs may obviate the need for
modified grain chemistry to explain some of the former's unique spectral
characteristics.
