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An ongoing challenge in the study of quantum materials, is to reveal and explain collective quantum effects in spin systems where interactions between different mode types are important. This talk will focus on this problem through a combined experimental and theoretical study of interacting transverse and longitudinal modes in an S=1 easy-planar quantum magnet, Ba₂FeSi₂O₇ [1,2]. Our inelastic neutron scattering measurements show that Ba₂FeSi₂O₇ is a quasi-two-dimensional antiferromagnet with large single-ion anisotropy (D>5J), and the extended spin wave theory analysis demonstrates its close proximity to a quantum critical point. The measured spectrum reveals the emergence, decay, and renormalization of a longitudinal mode throughout the Brillouin zone. The decay of the longitudinal mode is particularly pronounced at the zone center where the decay channels to the transverse modes are most active. A generalization of the standard spin-wave theory is used to account for the many-body effects of the interacting transverse and longitudinal modes in Ba₂FeSi₂O₇. The measured mode decay and renormalization are reproduced by including one-loop corrections, where the kinematic conditions for the interactions are satisfied.

[1] S.-H. Do, H. Zhang, et al., Nat. Commun. 12 5331 (2021)

[2] T.-H. Jang, S.-H. Do et al., PRB 104 214434 (2021)