Quantum Griffiths singularity in three-dimensional MoTiN superconducting films

Quantum Griffiths singularity (QGS) has been experimentally observed in a range of two-dimensional (2D) superconducting systems. Although it is theoretically suggested that the QGS also exists in three-dimensional (3D) superconductors, there is almost no experimental support to the theoretical prediction. In the present paper, we observe the occurrence of QGS in a series of -80-nm-thick Mo0.8Ti0.2Nx (0.84 <= x <= 1.12) superconducting films (with a NaCl structure) near the field-driven superconductor-metal transition (SMT). For each film, the low-temperature magnetoresistance isotherms, measured at magnetic fields being perpendicular or parallel to the film plane, do not cross at a single point but in a wide region. The dynamical critical exponents z nu 1 (for perpendicular field) and z nu 11 (for parallel field) obtained by analyzing the related magnetoresistance isotherms increase with decreasing temperature and tend to diverge as T 0 K. In addition, the corrected resistivities for the perpendicular and parallel field in the vicinity of the SMTs both obey an activated scaling based on the random transverse-field Ising model. Although these films are 3D with respect to the superconductivity, the activated scaling near the SMT for these films is as same as that for 2D superconductors with QGS. The QGS in the 3D Mo0.8Ti0.2Nx superconducting films originates from the slow dynamics of the rare regions in these systems. We also fabricate a -80-nm-thick (Mo0.8Ti0.2)2N1.06 superconducting film with face-centered cubic structure at low nitrogen partial pressure. It is found that the low-temperature magnetoresistance isotherms for the perpendicular (parallel) field cross at a single point and the resistivity data for the perpendicular (parallel) field in the vicinity of the field-induced SMT obey the power-law scaling deduced from the dirty-boson model. Our results provide unambiguous experimental evidence for the existence of QGS in 3D superconductors.