Collective Excitations, NMR, and Phase Transitions in Skyrme Crystals

At Landau level filling factors near $\nu =1\mathrm{}$, quantum Hall ferromagnets form a Skyrme crystal state with quasi-long-range translational and noncollinear magnetic order. We develop an effective low energy theory which explains the presence of magnetic excitations in these systems at energies below the Larmor gap ( $\Delta$) and that predicts a dramatic enhancement of the nuclear spin relaxation rate by a factor of ${10}^3$. The effective theory predicts a rich set of quantum and classical phase transitions. Based in part on accurate time-dependent Hartree-Fock calculations of the ordered state collective excitation spectrum, we discuss aspects of the $T-\nu -\Delta$ Skyrme crystal phase diagram.