"Soft" Anharmonic Vortex Glass in Ferromagnetic Superconductors

Abstract

Ferromagnetic order in superconductors can induce a {\em spontaneous} vortex (SV) state. For external field ${\bf H}=0$, 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 anharmonic effects lead to elastic moduli that are wavevector-dependent out to arbitrarily long length scales, and non-Hookean elasticity. The latter implies that for weak external fields $H$, the magnetic induction scales {\em universally} like $B(H)\sim B(0)+ c H^α$, with $α\approx 0.72$. For weak disorder, we predict the SV solid is a topologically ordered vortex glass, in the ``columnar elastic glass'' universality class.