Transdimensional anomalous Hall effect in rhombohedral thin graphite

Anomalous Hall effect (AHE), occurring in materials with broken time-reversal symmetry, epitomizes the interplay between magnetic order and electron orbital motions^1-4. In two-dimensional (2D) systems, AHE is coupled with out-of-plane orbital magnetization associated with in-plane chiral orbital motions. In three-dimensional (3D) systems, in which sample thickness far exceeds a vertical coherence-transport length l_z, the AHE is effectively a thickness-averaged 2D counterpart⁴-still governed by out-of-plane orbital magnetization arising from in-plane orbital motions. Here we report the experimental observation of a fundamentally new type of AHE that couples both in-plane and out-of-plane orbital magnetizations in multilayer rhombohedral graphene, shown by pronounced Hall resistance hysteresis under both in-plane and out-of-plane magnetic fields. This state emerges from a peculiar metallic phase that spontaneously breaks time-reversal, mirror and rotational symmetries driven by electron-electron interactions. By measuring multiple devices spanning 3-15 layers, we find that this phenomenon emerges only within an intermediate thickness of 2-5 nm. Theoretical calculations show that carriers within this window can sustain coherent orbital motions both within and across the 2D plane. Together, these identify an uncharted 'transdimensional' regime between 2D and 3D, in which the sample thickness is much larger than atomic spacing yet remains comparable to l_z, for the emergence of this new state of matter-transdimensional AHE. Our findings point to a distinct class of AHE, opening an unexplored model for correlated and topological physics in transdimensional landscapes.