  Ferroic orders describe spontaneous polarization of spin, charge, and lattice
degrees of freedom in materials. Materials featuring multiple ferroic orders,
known as multiferroics, play important roles in multi-functional electrical and
magnetic device applications. 2D materials with honeycomb lattices offer
exciting opportunities to engineer unconventional multiferroicity, where the
ferroic orders are driven purely by the orbital degrees of freedom but not
electron spin. These include ferro-valleytricity corresponding to the electron
valley and ferro-orbital-magnetism supported by quantum geometric effects. Such
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 valley and magnetic
states. Here we report orbital multiferroicity in pentalayer rhombohedral
graphene using low temperature magneto-transport measurements. We observed
anomalous Hall signals Rxy with an exceptionally large Hall angle (tan{\Theta}H
> 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 Rxy connecting the quartet. This hysteresis
indicates a ferro-valleytronic order that couples to the composite field E\cdot
B, but not the individual fields. Tuning E would switch each ferroic order
independently, and achieve non-volatile switching of them together. Our
observations demonstrate a new type of multiferroics and point to electrically
tunable ultra-low power valleytronic and magnetic devices.
