  We study an interacting electronic system exhibiting a spin nematic
instability. Using a phenomenological form for the spin fluctuation spectrum
near the spin-density-wave (SDW) phase, we compute the spin nematic
susceptibility in energy and momentum space as a function of temperature and
the magnetic correlation length xi. The spin nematic instability occurs when xi
reaches a critical value xi_{cr}, i.e., its transition temperature T_{SN} is
always higher than the SDW critical temperature T_{SDW}. In particular, xi_{cr}
decreases monotonically with increasing T_{SN}. Concomitantly, low-energy
nematic fluctuations are present in a wider temperature region as T_{SN}
becomes higher. Approaching the spin nematic instability, the nematic spectral
function at zero momentum exhibits a central peak as a function of energy for a
finite temperature and a soft mode at zero temperature. These properties
originate from the general feature that the imaginary part of the
spin-fluctuation bubble has a term linear in energy and its coefficient is
proportional to the square of temperature. Furthermore we find that the nematic
spectral function exhibits a diffusive peak around zero momentum and zero
energy without clear dispersive features. A possible phase diagram for the spin
nematic and SDW transitions is also discussed.
