Magnetic-Field Effects on the Size of Vortices below the Surface of ${\mathrm{NbSe}}_2$ Detected Using Low Energy $\beta$-NMR

A low energy radioactive beam of polarized ${}^8\mathrm{Li}$ has been used to observe the vortex lattice near the surface of superconducting ${\mathrm{NbSe}}_2$. The inhomogeneous magnetic-field distribution associated with the vortex lattice was measured using depth-resolved $\beta$-detected NMR. Below $T_c$, one observes the characteristic line shape for a triangular vortex lattice which depends on the magnetic penetration depth and vortex core radius. The size of the vortex core varies strongly with the magnetic field. In particular, in a low field of 10.8 mT, the core radius is much larger than the coherence length. The possible origin of these giant vortices is discussed.

Figure 1

$\beta$-NMR spectra in a magnetic field of 300 mT and with beam energy of 20 keV, corresponding to a mean implantation depth $⟨z⟩=85\mathrm{nm}$. (a) In the normal state at 10 K and (b) field cooled to 3.5 K or $0.5T_c$.

Figure 2

$\beta$-NMR spectra in a low magnetic field of 10.8 mT. (a) In the normal state at 10 K with a beam energy which corresponds to $⟨z⟩=8\mathrm{nm}$. (b) The same conditions as (a) except field cooled to $0.5T_c$. (c) The same temperature as (b), but $⟨z⟩$ is about 10 times larger.

Figure 3

Depth dependence of (a) the cusp frequency ${\Delta }_c$ and (b) vortex core frequency ${\Delta }_v$ relative to the normal state frequency. The open circles are measured in a magnetic field of 10.8 mT, while the filled circles are taken at 300 mT. In all cases, the temperature is 3.5 K which corresponds to $0.5T_c$. The solid curves are from the vortex line shape model with a single depth independent ${\lambda }_{ab}$ and $\rho$.