Lifetime of Gapped Excitations in a Collinear Quantum Antiferromagnet

We demonstrate that local modulations of magnetic couplings have a profound effect on the temperature dependence of the relaxation rate of optical magnons in a wide class of antiferromagnets in which gapped excitations coexist with acoustic spin waves. In a two-dimensional collinear antiferromagnet with an easy-plane anisotropy, the disorder-induced relaxation rate of the gapped mode, Γᵢₘₚ≈Γ₀+A(TlnT)², greatly exceeds the magnon-magnon damping, Γ_m-m≈BT⁵, negligible at low temperatures. We measure the lifetime of gapped magnons in a prototype $XY$ antiferromagnet BaNi₂(PO₄)₂ using a high-resolution neutron-resonance spin-echo technique and find experimental data in close accord with the theoretical prediction. Similarly strong effects of disorder in the three-dimensional case and in noncollinear antiferromagnets are discussed.