  We show that magnetic fluctuations can destroy the Hebel-Slichter peak in
conventional superconductors. The Hebel-Slichter peak has previously been
expected to survive even in the presence of strong electronic interactions.
However, we show that antiferromagnetic fluctuations suppress the peak at
$\bf{q}=0$ in the imaginary part of the magnetic susceptibility,
$\chi_{+-}''\left(\bf{q},\omega\right)$, which causes the Hebel-Slichter peak.
This is of general interest as in many materials superconductivity is found
near a magnetically ordered phase, and the absence of a Hebel-Slichter peak is
taken as evidence of unconventional superconductivity in these systems. For
example, no Hebel-Slichter peak is observed in the $\kappa$-(BEDT-TTF)$_2X$
organic superconductors but heat capacity measurements have been taken to
indicate $s$-wave superconductivity. If antiferromagnetic fluctuations destroy
the putative Hebel-Slichter peak in organic superconductors then the peak
should be restored by applying a pressure, which is known to suppress
antiferromagnetic correlations in these materials.
