Spiral orientational order in quantum Hall skyrmion lattices

Abstract

We investigate the existence of spiral ordering in the planar spin orientation of skyrmions localised on a face centered rectangular lattice (FCRL). We use the non-linear sigma model (NLSM) to numerically calculate the minimum energy configurations of this lattice around the $ν=1$ quantum Hall ground state. Our variational ansatz contains an angle $θ$, characterising the FCRL and an angle $q$, characterising the orientational order. As $ν$ is increased towards one, there is a smooth transition from the triangular lattice (TL) characterised by $(θ,q) = (120^o,120^o)$ to FCRLs with spiral orientational order. The novel feature we find is that these phases are characterised by $θ, q)$ values such that $θ+q = 240^o$ (same as the TL phase). As $ν$ incresaes further towards one, there is a sharp transition from the FCRLs to the square lattice (SL), characterised by $(θ,q)=(90^o,180^o)$. Consequently, the parameter $θ+q$ jumps sharply at the FCRL-SL transition and can serve as an order parameter to characterise it.