Self-consistent T-matrix approach to gap renormalization in quantum magnets with bond disorder

•Self-consistent T-matrix approach is adapted for quantum magnets with bond disorder.•Density of states and gap described in both resonant and non-resonant regimes.•Theory successfully applied for experimental data on Ba(3-x)SrxCr2O8. The analytical theory of density of states (DOS) in three-dimensional quantum magnets with the bond disorder is proposed based on the self-consistent T-matrix approximation (SCTMA). It successfully describes the DOS both for resonant and non-resonant scattering, whose emergence is governed by the ratio of scattering length and the average distance between impurities, which concentration is denoted as c. Corrections to the quasiparticle band gap in these cases are shown to scale as c2/3 and c, respectively. Moreover, the theory yields a semi-circle form of the DOS for the bound states inside the gap, which results in highly nontrivial DOS in the intermediate parameter region between the two limiting cases when the band DOS and the semi-circle overlap. Long-wavelength excitations are discussed. In the resonant regime their damping scales as c2/3, which, according to Ioffe-Regel criterion, corresponds to their localization. Applicability of the theory is illustrated by its quantitative agreement with the recent experimental data on spin-dimer system Ba3−xSrxCr2O8.