Magnetic-Field-Induced Antiferromagnetism in Two-Dimensional Hubbard Model: Analysis of CeRhIn$_5$

We propose the mechanism for the magnetic-field-induced antiferromagnetic (AFM) state in a two-dimensional Hubbard model in the vicinity of the AFM quantum critical point (QCP), using the fluctuation-exchange (FLEX) approximation by taking the Zeeman energy due to the magnetic field $B$ into account. In the vicinity of the QCP, we find that the AFM correlation perpendicular to $B$ is enhanced, whereas that parallel to $B$ is reduced. This fact means that the finite magnetic field increases $T_N$, with the AFM order perpendicular to $B$. The increment in $T_N$ can be understood in terms of the reduction of both quantum and thermal fluctuations due to the magnetic field, which is caused by the self-energy effect within the FLEX approximation. The present study naturally explains the increment in $T_N$ in CeRhIn_5 under the magnetic field found recently.