Density Wave Mediated Dzyaloshinskii-Moriya Interactions

Abstract

We investigate the effect that density wave states have on the localized spins of a square lattice. We find that topologically nontrivial density wave states can induce stable Dzyaloshinskii-Moriya (DM) interactions among the localized spins of the lattice in the presence of an external magnetic field, and we study the resulting spin models for both antiferromagnetic and ferromagnetic backgrounds. While the density wave state itself can contribute to the the thermal Hall effect, as shown by Li & Lee (arXiv:1905.04248v3), symmetry considerations preclude the resulting spin excitations from inducing a further thermal Hall effect. We utilize a Holstein-Primakoff (HP) substitution about the classical mean-field ground state to calculate the magnon dispersion for LSCO and find that the density wave induces a weak $d_{x^2-y^2}$ anisotropy; upon calculating the non-Abelian Berry curvature for this magnon branch we show explicitly that the magnon contribution to ${\kappa }_{xy}$ is zero. Finally, we calculate corrections to the magnetic ground state energy, spin canting angles, and the spin-wave dispersion due to the topological density wave for ferromagnetic backgrounds. We find that terms linear in the HP bosons can affect the critical behavior, a point previously overlooked in the literature.

arXiv comment10 pages, 8 figures

References in corpus (35)

• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Hidden Order in the Cuprates
• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor
• The pseudogap: friend or foe of high Tc?
• Theoretical prediction of rotating magnon wavepacket in ferromagnets
• Topological chiral magnonic edge mode in a magnonic crystal
• Polar Kerr Effect Measurements of YBa2Cu3O6+x: Evidence for Broken Symmetry Near the Pseudogap Temperature
• A Theory of the Pseudogap State of the Cuprates
• A Phenomenological Theory of The Pseudogap State
• Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals
• A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor
• Density Wave States of Non-Zero Angular Momentum
• Energy Magnetization and Thermal Hall Effect
• A global inversion-symmetry-broken phase inside the pseudogap region of YBa${}_2$Cu${}_3$O${}_y$
• Berry Curvature and Phonon Hall Effect
• Giant thermal Hall conductivity from neutral excitations in the pseudogap phase of cuprates
• Doppler shift picture of the Dzyaloshinskii--Moriya interaction
• Fermi pockets and quantum oscillations of the Hall coefficient in high temperature superconductors
• Effective gauge field theory of spintronics
• Thermal Hall effect and topological edge states in a square lattice antiferromagnet
• Correlated band theory of spin and orbital contributions to Dzyaloshinskii-Moriya interactions
• Hartree-Fock Computation of the High-Tc Cuprate Phase Diagram
• Spin Rotation Technique for Non-Collinear Magnetic Systems: Application to the Generalized Villain Model
• Competing ferromagnetism in high temperature copper oxide superconductors
• Phonon Hall thermal conductivity from Green-Kubo formula
• Competing phases in the extended U-V-J Hubbard model near the van Hove fillings
• Competing phases in the extended U-V-J Hubbard model near the van Hove fillings: 2-patch approach
• Thermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study
• Universal behavior of the thermal Hall conductivity
• Ferromagnetic order beyond the superconducting dome in a cuprate superconductor
• Consideration of Thermal Hall Effect in Undoped Cuprates
• Topological density wave states of non-zero angular momentum
• The thermal Hall conductance of two doped symmetry-breaking topological insulators
• Onsager rule, quantum oscillation frequencies, and the density of states in the mixed-vortex state of cuprates