Strong depression of superconductivity in VN by spin fluctuations

In this paper we argue that spin fluctuations prevent VN from being a superconductor with a transition temperature of about 30 K instead of the experimental value of 8.6 K. Thus, besides V and Nb for which similar results have been reported recently, VN provides a further and even more pronounced example for spin-fluctuation-limited high-$T_c$ superconductivity. Our results are obtained from microscopic calculations of $T_c$ for the refractory compounds TiN, ZrN, VN, and NbN and from magnetic susceptibility data. Among these four compounds VN is exceptional in exhibiting both a large theoretical overestimate of $T_c$, if spin fluctuations are omitted, and a high magnetic susceptibility. Incorporating spin fluctuations within the theory of Berk and Schrieffer, the theoretical value of $T_c$ can be brought into agreement with experiment. Calculations of the magnetic susceptibility and of $T_c$ in nonstoichiometric $\mathrm{V}{\mathrm{N}}_x$ ($0.75<~x<~1.0$) and their comparison to experimental results of Ajami and MacCrone provide further support for our ideas.