Magnetically controllable band splittings in Pnma ferromagnetic materials

The electric or magnetic control of band splitting in ferroelectric or ferromagnetic materials is one of the central themes in the context of spin orbitronics. The conventional controllable splitting patterns can be mainly categorized into three types including Rashba-, Dresselhaus-, and Zeeman-type spin splittings, which originate from either a spin-orbit interaction or magnetic exchange interaction. The discovery of new patterns of controllable band splittings and understanding their mechanisms are important not only from a fundamental perspective, but also for practical applications in the design of spin-orbitronic devices. Here, by first-principles calculations and a symmetry analysis, we identify the existence of a band splitting pattern in Pnma ferromagnetic YTiO3 that is controllable by a magnetic field. In sharp contrast to the conventional band splitting patterns (e.g., Rashba-, Dresselhaus-, and Zeeman-type splittings), the mechanism of our pattern is ascribed to the electrons' orbital degree of freedom. Such a mechanism can be generalized to various ferromagnets adopting the Pnma symmetry. We hope that our research will create another avenue for controlling band splittings and provide an alternative route towards designing magnetically based spin-orbitronic devices.