Multi-k spin ordering in CaFe_{3}Ti_{4}O_{12} stabilized by spin-orbit coupling and further-neighbor exchange

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 CaFe_{3}Ti_{4}O_{12}, where only the S=2 Fe^{2+} 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 FeO_{4} 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. CaFe_{3}Ti_{4}O_{12} provides a rare example of how nontrivial long-range spin order can arise when near-neighbor Heisenberg superexchange is quenched.