Orbital Angular Momentum of Magnons in Ferromagnetic Zig-Zag Lattices

The past 13 years have seen remarkable advances in the field of ``magnonics,", which focuses on the quanta of spin excitations known as magnons. One of the main goals of magnonics is the storage and processing of information. In quick succession, experimentalists discovered that magnons can produce the thermal Hall and Seebeck effects. Almost all previous theoretical work in magnonics has been based on the Berry curvature, which produces a fictitious magnetic field in the presence of dipole-dipole or Dzyalloshinzkii-Moriya (DM) interactions, both associated with spin-orbit coupling. In recent work, we have focused directly on the orbital angular momentum (OAM) of magnons O_n(k) in band n with wavevector k. In order to create a gauge invariant and hence observable quantity, O_n(k) must be averaged over all angles f for k = (k,φ) in two dimensions. Even then, the angle-average OAM F_n(k) is nonzero only for special ferromagnetic (FM) lattices that break inversion symmetry and support DM or dipole interactions. The most well-known such case is the FM honeycomb lattice with exchange J > 0 and DM interaction D. Examples are CrSiTe₃, CrGeTe₃, CrI₃, and CrCl₃. We have recently discovered another case: a square lattice with two FM exchange couplings J₁ and J₂ (r = J₂/J₁ > 1) in a zig-zag pattern. Examples are spin-1/2 Heisenberg Vanadium chains in CdVO₃ (r » 5), spin-3/2 Chromium chains in LaCrOS₂ (r >> 1), and spin-3.4/2 Manganese chains in La₃MnAs₅ (r » 7.6).