Ferroelectric-ferromagnetic multiferroicity driven by 3d-electrons in a TiCrO₄ monolayer

It is well known that dilute magnetic doping in semiconductors can establish long-range magnetism, yet the strategy is seldom used in multiferroics. This is probably because the empirical d⁰ rule states that partially filled d-electrons hinder ferroelectric polarization. In this work, first-principles calculations predict a thermally, dynamically, and mechanically stable two-dimensional monolayer TiCrO₄, which is ferroelectric-ferromagnetic multiferroic with both ferroic orders associated with partially filled Cr-3d electrons. Their Jahn-Teller interaction induces structural distortions that break the inversion symmetry and generate spontaneous out-of-plane polarization. Also, they form long-range ferromagnetism mediated by oxygen atoms. Thus, TiCrO₄ is a single-phase multiferroic oxide that violates the d⁰ rule. In addition, TiCrO₄ has a modest ferroelectric switching barrier and a ferromagnetic critical temperature near room temperature. These findings not only add a new member to the family of rare ferroelectric-ferromagnetic multiferroics, but also provide new insights into their rational design.