Multi-k spin ordering in CaFe₃Ti₄O₁₂ stabilized by spin-orbit coupling and further-neighbor exchange

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.