Effect of magnetic field on spontaneous Fermi-surface symmetry breaking

Abstract

We study magnetic field effects on spontaneous Fermi-surface symmetry breaking with $d$-wave symmetry, the so-called $d$-wave ``Pomeranchuk instability.'' We use a mean-field model of electrons with a pure forward scattering interaction on a square lattice. When either the majority or the minority spin band is tuned close to the van Hove filling by a magnetic field, the Fermi-surface symmetry breaking occurs in both bands, but with a different magnitude of the order parameter. The transition is typically of second order at high temperature and changes to first order at low temperature; the end points of the second order line are tricritical points. This qualitative picture does not change even in the limit of a large magnetic field, although the magnetic field substantially suppresses the transition temperature at the van Hove filling. The field produces neither a quantum critical point nor a quantum critical end point in our model. In the weak coupling limit, typical quantities characterizing the phase diagram have a field-independent single energy scale, while its dimensionless coefficient varies with the field. The field-induced Fermi-surface symmetry breaking is a promising scenario for the bilayer ruthenate ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$, and open questions are discussed to establish such a scenario.