Anisotropy of the sommerfeld coefficient in magnesium diboride single crystals

The anisotropic field dependence of the Sommerfeld coefficient γ has been measured down to B→0 by combining specific heat and Hall probe magnetization measurements in MgB2 single crystals. We find that γ(B,θ) is the sum of two contributions arising from the σ and π band, respectively. We show that γσ(B,θ)=B/Bc2(θ) where Bc2(θ)=Bc2ab/sin 2θ+Γ2cos 2θ with Γ∼5.4 (θ being the angle between the applied field and the c axis) and γπ(B,θ)=γπ(B)=B/Bπ(B). The "critical field" of the π band Bπ is fully isotropic but field dependent increasing from ∼0.25T for B≤0.1T up to 3 T ∼Bc2c for B→3T. Because of the coupling of the two bands, superconductivity survives in the π band up to 3 T but is totally destroyed above for any orientation of the field.