Spiral orientational order in quantum Hall skyrmion lattices

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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) = (120ᵒ,120ᵒ) 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 = 240ᵒ (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)=(90ᵒ,180ᵒ). Consequently, the parameter θ+q jumps sharply at the FCRL-SL transition and can serve as an order parameter to characterise it.