Quasiparticle Excitations outside the Vortex Cores in MgB$_2$ Probed by Muon Spin Rotation

The magnetic penetration depth $\lambda$ in the mixed state of MgB$_2$ has been determined microscopically from the field distribution around magnetic vortices probed by muon spin rotation. Both the temperature and magnetic field dependence of $\lambda$ strongly suggest the presence of delocalized quasiparticles around the vortex cores. In particular, the effect of Doppler shift has been clearly observed as a finite gradient of the field dependence of $\lambda$, strongly suggesting an anisotropic order parameter with the region of a vanishingly small energy gap.