  We consider the Neumann Laplacian with constant magnetic field on a regular
domain. Let $B$ be the strength of the magnetic field, and let $\lambda_1(B)$
be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is
proved that $B \mapsto \lambda_1(B)$ is monotone increasing for large $B$.
Combined with the results of \cite{FournaisHelffer3}, this implies that all the
`third' critical fields for strongly Type II superconductors coincide.
