Field-induced quasi-bound state within the two-magnon continuum of a square-lattice Heisenberg antiferromagnet

Quantum magnets in two dimensions display strong quantum interaction effects even when magnetically ordered. Using the metal-organic framework material CuF 2 (D 2 O) 2 (pyz), we investigate the field-dependent spin dynamics of the S = 1/2 square-lattice Heisenberg antiferromagnet by high-resolution inelastic neutron scattering to applied fields beyond one third of saturation. We discover an anomalously sharp, dispersive “shadow mode” residing within the two-magnon continuum, which shadows the dispersion of the transverse one-magnon branches across the Brillouin zone at an offset equal to the Larmor energy. We perform cylinder matrix-product-state (MPS) calculations that reproduce the field-induced spectrum quantitatively and apply a spectrally consistent 1/ S spin-wave theory to deduce that the “Larmor-shadow mode” is a composite two-magnon resonance: a dispersing magnon at wavevector Q couples to the uniform Larmor precession at Γ, its small intrinsic linewidth indicating a non-perturbative effect of attractive magnon-magnon interactions. Another quantum-fluctuation phenomenon, the zero-field (π, 0) anomaly, is lost at increasing fields, which tighten the spectral weight into the one-magnon and Larmor-shadow modes. To our knowledge, these results constitute the first observation of a sharp quasi-bound state embedded in the continuum of a gapless two-dimensional antiferromagnet.