Spin Vorticity on the Octahedral Lattice

Recent developments have led to the theoretical discovery of spin ice’s sister phase of matter, spin vorticity [1]. Rather than the divergence free tetrahedrons, as seen in spin ice, spin vorticity hosts curl-free plaquettes. This constraint leads to an antisymmetric rank-2 U(1) gauge theory. Such a theory hosts string excitations that live on the boundary of membranes in the indirect dual lattice. We intend to extend work done by Szabo [2] on the octahedral lattice to see if the novel spin vorticity phase can be realized in this system. The vorticity is defined as the circulation of the spins on the void square plaquettes between the corner-sharing octahedra. We consider first and second neighbor interactions between the Ising spins pointing in or out of the octahedra. Using Monte-Carlo and Self Consistent Gaussian Approximation, we find evidence of the spin vorticity phase, which prevails in a larger parameter space beyond the special point where the Hamiltonian reduces to the square of the spin vorticity. Our exact diagonalization results support the existence of a quantum spin vorticity phase.

[1] K. T. K. Chung and M. J. P. Gingras, arXiv:2310.17607

[2] A. Szabo, F. Orlandi, and P. Manuel, Phys. Rev. Lett. 129, 247201