We present near-infrared spectroscopic observations of 20 previously known DAZ white dwarfs obtained at the NASA Infrared Telescope Facility. Two of these white dwarfs (G29-38 and GD 362) are known to display significant K-band excesses due to circumstellar debris disks. Here we report the discovery of excess K-band radiation from another DAZ white dwarf WD0408041 (GD56). Using spectroscopic observations, we show that the excess radiation cannot be explained by a stellar or substellar companion, and is likely to be caused by a warm debris disk. Our observations strengthen the connection between the debris disk phenomena and the observed metal abundances in cool DAZ white dwarfs. However, we do not find any excess infrared emission from the most metal rich DAZs with Teff = 16,000 20,000 K. This suggests that the metal abundances in warmer DAZ white dwarfs may require another explanation.