Green’s function theory of magnetism in Bi <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>2</mml:mn> </mml:msub>

Abstract

The Green's function theory of Lymar'and Rudoi [Theor. Math. Phys. vol. 21, 990 (1974)] is generalized to the case of multiple intra- and inter-sublattice magnetic interactions in a collinear spin-half antiferromagnet and applied to magnetic excitations in Bi$_2$CuO$_4$. The spin Hamiltonian includes both the out-of-plane and in-plane symmetric anisotropy terms and the Zeeman term, which describes the interaction with an external magnetic field $B$ applied along the N\'eel vector. Within the spin-wave approximation we calculate spin excitation dispersion, antiferromagnetic resonance frequencies and the critical field $B_c$ of the spin-flop metamagnetic transition. A weak in-plane anisotropy is shown to result in a gap in the acoustic-like branch of the excitations. The gap nonlinearly depends on the external field and closes at $B=B_c$. An expression for the Neel temperature in the Tyablikov random phase approximation at zero field is derived. For the parameters derived from the recent inelastic neutron scattering study by Yuan et al. [Phys. Rev. B vol. 103, 134436 (2021)] it gives $T_{\rm N}\approx 52$~K.