Evidence for strong-coupling s-wave superconductivity in MgB₂: ¹¹B-NMR study of MgB₂ and the related materials

We report the results of nuclear spin-lattice relaxation time, T₁ of ¹¹B in MgB₂, Al-doped MgB₂ and NbB₂. A T₁T = constant behavior was observed in the normal state, indicating the absence of strong magnetic correlation. In the superconducting (SC) state, 1/T₁ shows a tiny coherence peak just below T_c and decreases exponentially, demonstrating an s-wave superconductivity. The magnitude of SC gap is estimated as 2Δ/k_BT_c∼5, which is quite larger than the weak-coupling value in the BCS theory, 2Δ/k_BT_c = 3.5. This rules out a possibility for the multiple SC gaps that was suggested in many literatures. The anisotropy in the upper critical field was also corroborated by the T₁ measurement on a bulk polycrystalline sample. In NbB₂ with a low value of T_c = 5 K, the T₁ measurement revealed the distinct coherence peak just below T_c, followed by an exponential decrease with a magnitude of SC gap 2Δ/k_BT_c = 3.1. These data are consistent with the weak-coupling BCS theory. As Al³⁺ is substituted for Mg²⁺, 1/T₁T, which is proportional to the square of the density of states at the Fermi level N(E_F), decreases. The variation in T_c against the relative changes in N(E_F) deduced from 1/T₁T is well fitted in terms of the McMillan equation by assuming a characteristic phonon frequency ω ∼ 700 K and an electron-phonon coupling constant λ ∼ 0.87. Thus obtained values are in good agreement with the values suggested by the theoretical works. The high-T_c superconductivity in MgB₂ is shown to occur through the strong coupling with high frequency phonons.