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 lend 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) similar to B(0) + cH(alpha), with alpha approximate to 0.72: For weak disorder, we predict the SV solid is a topologically ordered glass, in the "columnar elastic glass" universality class.