Orbital multiferroicity in pentalayer rhombohedral graphene

Ferroic orders describe spontaneous polarization of spin, charge and lattice degrees of freedom in materials. Materials exhibiting multiple ferroic orders, known as multiferroics, have important parts in multifunctional electrical and magnetic device applications(1-4). Two-dimensional materials with honeycomb lattices offer opportunities to engineer unconventional multiferroicity, in which the ferroic orders are driven purely by the orbital degrees of freedom and not by electron spin. These include ferro-valleytricity corresponding to the electron valley(5) and ferro-orbital-magnetism(6) supported by quantum geometric effects. These orbital multiferroics could offer strong valley-magnetic couplings and large responses to external fields-enabling device applications such as multiple-state memory elements and electric control of the valley and magnetic states. Here we report orbital multiferroicity in pentalayer rhombohedral graphene using low-temperature magneto-transport measurements. We observed anomalous Hall signals R-xy with an exceptionally large Hall angle (tanTH > 0.6) and orbital magnetic hysteresis at hole doping. There are four such states with different valley polarizations and orbital magnetizations, forming a valley-magnetic quartet. By sweeping the gate electric field E, we observed a butterfly-shaped hysteresis of R-xy connecting the quartet. This hysteresis indicates a ferro-valleytronic order that couples to the composite field E . B (where B is the magnetic field), but not to the individual fields. Tuning E would switch each ferroic order independently and achieve non-volatile switching of them together. Our observations demonstrate a previously unknown type of multiferroics and point to electrically tunable ultralow-power valleytronic and magnetic devices.