Condensed Matter Theory

Abstract:

We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials, and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wavevectors. We find that at all non-zero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal symmetric and spatially non-uniform order. This order, which we dub the 'incommensurate Kekulé spiral' (IKS) order, spontaneously breaks both the emergent valley-charge conservation and moiré translation symmetries, but preserves a modified translation symmetry T^′ -- which simultaneously shifts the spatial coordinates and rotates the U(1) angle which characterizes the spontaneous inter-valley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.

Abstract:

Orthogonal spin ordering is rarely observed in magnetic oxides because nearest-neighbor symmetric Heisenberg superexchange interactions usually dominate. We have discovered that in the quadruple perovskite CaFe3Ti4O12, where only the S=2 Fe2+ ion is magnetic, long-range magnetic order consisting of an unusual arrangement of three interpenetrating orthogonal sublattices is stabilized. Each magnetic sublattice corresponds to a set of FeO4 square planes sharing a common orientation. This multi-k magnetic spin ordering is the result of fourth-neighbor spin couplings with a strong easy-axis anisotropy. In an applied magnetic field, each sublattice tends towards ferromagnetic alignment, but remains polarized by internal magnetic fields generated by the others, thus stabilizing in a noncollinear canted ferromagnetic structure. CaFe3Ti4O12 provides a rare example of how nontrivial long-range spin order can arise when near-neighbor Heisenberg superexchange is quenched.