High-order one-dimensional (1D) fermion in ferromagnetic RbFeF3

Abstract

Nodal line semimetals/metals (NLSMs), hosting band-crossings in one dimension, are expected to exhibit exotic physical phenomena, like drumhead surface states. The conventional NLSMs host a linear energy dispersion around it. Recently, it has been predicted that NLs hosting a high-order energy dispersion may also be stabilized in nonmagnetic systems. However, it still remains challenges to find their counterpart in magnetic systems. Here, based on first-principles calculation and theoretical analysis, we predict for the first-time that RbFeF3, a ferromagnetic material, has a high-order NL without spin-orbital coupling (SOC). We give the symmetry conditions which stabilizes the quadratic nodal lines (QNLs), thus an effective Hamiltonian is constructed to demonstrate its existence. Different from the nonmagnetic nodal lines, they come from the same single spin channel, achieving a 100% spin polarization. Interestingly, it exhibits a “torus” drumhead surface states in the whole Brillouin zone, which is quite different from that of linear NL. Under symmetry breaking, the QNL could be reduced into a pair of linear type-II NLs by tuning the magnetization direction. Our work provides a ideal magnetic material with high-order NL which has not been observed before.