Lower Critical Field at Odds with A S-Wave Superconductivity in The New Superconductor $MgB_2$

The lower critical field H c 1 has been carefully measured on a well shaped cylindrical sample of the new superconductor MgB 2 fabricated by high pressure synthesis. The penetration depth λ is calculated from the H c 1 data. It is found that a linear relation of H c 1 ( T ) appears in whole temperature region below T c . Furthermore a finite slope of dH c 1 /dT and dλ ( T ) /dT remains down to the lowest temperature ( 2 K ). These are inconsistent with the expectation for a widely thought s-wave superconductivity in MgB 2 .