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We analyze an effective model on a square lattice with two types of forwardscattering interactions, which, respectively, drive ferromagnetism (FM) andelectronic nematic order via a d-wave Pomeranchuk instability (dPI). The FM anddPI in general compete with each other and they are typically separated by afirst order phase boundary in the plane of the chemical potential andtemperature. Nevertheless there is a parameter region where the dPI occursinside the FM phase, leading to their coexistence. We also study the effect ofa magnetic field by choosing a chemical potential where the ground state isparamagnetic without a field. In this case, instead of FM, the dPI competeswith a metamagnetic instability. The latter occurs above a threshold strengthof the FM interaction and otherwise the dPI is stabilized with a dome-shapedphase diagram in the plane of a magnetic field and temperature. The FMinteraction shifts the center of the dome to a lower field, accompanied by asubstantial reduction of the field range where the dPI is stabilized and by anextension of the first order part of the transition line, although the maximalcritical temperature does not change. The experimental phase diagram of thebilayer ruthenate Sr3Ru2O7 can be well captured by the present theory.

Mean-field theory on a coupled system of ferromagnetism and electronic nematic order