Linear temperature dependence of lower critical field inMgB2

The lower critical field $H_{c1\mathrm{}}$ has been carefully measured on a well-shaped cylindrical dense sample of the new superconductor ${\mathrm{MgB}}_2$ fabricated by high-pressure synthesis. The penetration depth $\lambda$ is calculated from the $H_{c1\mathrm{}}$ data. It is found that a linear relation of $H_{c1\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ appears in the whole temperature region below $T_c.$ Furthermore, a finite slope of ${\mathrm{dH}}_{c1\mathrm{}}/dT$ and $d\lambda \mathrm{}\left(T\right)/dT$ remains down to the lowest temperature (2 K). These are inconsistent with the expectation for an isotropic s-wave superconductivity in ${\mathrm{MgB}}_2.$