Skyrmion Flux Lattices and their $\mu$SR signature

Recently, topological excitations known as skyrmions were predicted to exist in p-wave superconductors [1]. The elastic theory of an induced skyrmion lattice was developed in [2], and its melting curve was found to be qualitatively different from that for vortex lattices. Here we show that the muon spin resonance ($\mu$SR) signatures of the two types of lattices are also very different. $\mu$SR has been applied extensively to study the magnetic properties of vortex flux lattices [3]. The observable in this technique is the $\mu$SR line shape $n(B)$, which is the probability density that a muon experiences a local magnetic induction $B$. In a vortex lattice, for small $B$, $n(B) \propto \ln(1/B)/B$. By contrast, for a skyrmion lattice we predict $n(B) \propto B^ (-3/2)$. This difference provides another way to easily distinguish between vortex and skyrmion flux lattices, and can thus help to identify p-wave superconductors. [1] A. Knigavko, B. Rosenstein, and Y.F. Chen, Phys. Rev. B 60, 550 (1999). [2] Qi Li, John Toner, and D. Belitz, Phys.Rev. Lett. 98, 187002 (2007). [3] J. E. Sonier, J.H. Brewer, and R. F. Kiefl, Rev. Mod. Phys. 72, 769 (2000).