Erratum: Dzyaloshinskii-Moriya interaction in the cuprates [Phys. Rev. B44, 10 112 (1991)]

Abstract

There are errors in our derivation of the detailed expressions for the Dzyaloshinskii-Moriya (DM) couplings for the cuprates. The contribution to the DM coupling from the virtual process involving the Cu 3d orbital r -3z should vanish. This becomes transparent when one evaluates the spin-orbit coupling using axes oriented along the tilted Cu-0 octahedra.Consequently, all the terms involving the hopping integral t 2 2 in Ref. 1 should be suppressed. These terms appear in Eqs. (10), (13), and (16). As a result, for LazCu04, in the low-temperature orthogonal phase, one of the DM components d, =0, while in the low-temperature tetragonal phase, d4=0.

New magnetic phase of the chiral skyrmion material Cu 2 OSeO 3

“…The DM interaction originates from the antisymmetric anisotropic exchange between Cu spins, which is the first-order correction to the Heisenberg exchange in powers of λ: D ~ Jζ , where , Δ being the typical electron excitation energy on Cu sites ( 25 , 32 ). The first three anisotropy terms in Eq.…”

Spin dynamics of a canted antiferromagnet in a magnetic field

“…(2) and (3) to evaluate d a / dB and d b / dB at zero field and by using the SW frequencies 14 to perform a small q expansion of q 2 . After a lengthy calculation, we obtain…”

Nonlocal Coulomb interactions and the magnetic anisotropies in the low-temperature phases of the cuprates

“…These comprise the antisymmetric Dzyaloshinskii-Moriya interaction 3 as well as symmetric anisotropies which are equally important for the determination of the magnetic ground state. 4 Generally, the study of these magnetic anisotropies [5][6][7][8][9][10][11] is based on Moriya's extension 12 of Anderson's theory 13 of kinetic superexchange. The importance of the on-site Coulomb exchange interactions within the theory of kinetic superexchange has been noted recently.…”