Absence of a boron isotope effect in the magnetic penetration depth of MgB$_{2}$

Abstract

The magnetic penetration depth $\lambda(0)$ in polycrystalline MgB$_{2}$ for different boron isotopes ($^{10}$B/$^{11}$B) was investigated by transverse field muon spin rotation. No boron isotope effect on the penetration depth $\lambda(0)$ was found within experimental error: $\Delta\lambda(0)/\lambda(0) = -0.8(8)%$, suggesting that MgB$_{2}$ is an adiabatic superconductor. This is in contrast to the substantial oxygen isotope effect on $\lambda(0)$ observed in cuprate high-temperature superconductors.