“Soft” Anharmonic Vortex Glass in Ferromagnetic Superconductors

Ferromagnetic order in superconductors can induce a spontaneous vortex (SV) state. For external field H � 0, rotational symmetry guarantees a vanishing tilt modulus of the SV solid, leading to drastically different behavior than that of a conventional, external-field-induced vortex solid. We show that quenched disorder and anharmoinc effects lead to elastic moduli that are wave-vector dependent out to arbitrarily long length scales, and non-Hookean elasticity. The latter implies that for weak external fields H , the magnetic induction scales universally like B�H� � B�0� 1 cH , with a � 0.72. For weak disorder, we predict the SV solid is a topologically ordered glass, in the “columnar elastic glass” universality class.