Effects of Magnetic and Non-Magnetic Impurities in MgB$_2$: A Point-Contact Study of Single Crystals

We studied the effects of chemical substitutions, either magnetic (Mn) or non-magnetic (Al, C), on the energy gaps of MgB$_2$ by means of directional point-contact spectroscopy (PCS) in state-of-the-art single crystals. Here we discuss two noticeable cases, i.e. Mg$_{1-x}$Mn$_{x}$B$_2$ crystals with $x$ up to 0.015, and Mg$_{1-x}$Al$_x$B$_2$ crystals with $x$ up to 0.32. In both cases, we used a pressure-less PCS technique in which a thin Au wire is put in contact with the side surface of the crystal by means of a small drop of Ag paint. The gaps $\Delta_{\sigma}$ and $\Delta_{\pi}$ were obtained through a two-band Blonder-Tinkham-Klapwijk (BTK) fit of the Andreev-reflection conductance curves of the resulting contacts. Both in Mn- and Al-doped MgB$_2$, the gaps decrease on decreasing the critical temperature of the contacts, $T_{c}^{A}$ (at which the Andreev-reflection structures disappear), but remain clearly distinct down to $T_{c}^{A}\simeq 10$ K. Once analysed within the two-band Eliashberg theory, the $\Delta_{\sigma}$ and $\Delta_{\pi}$ vs. $T_{c}^{A}$ curves give information about the effects of Mn and Al substitutions on the different scattering channels (interband and intraband, magnetic or non-magnetic). It turns out that the main effect of Mn is to increase the spin-flip scattering within the $\sigma$ band (with smaller contributions from either the $\pi-\pi$ or the $\sigma-\pi$ channels), as also confirmed by first-principle bandstructure calculations. In the case of Al, the band-filling effect is largely dominant. An increase in non-magnetic interband scattering is possible, but small enough not to give rise to gap merging. \newline \newline In collaboration with G.A. Ummarino, A. Calzolari, M. Tortello, D. Delaude, R.S. Gonnelli, Dipartimento di Fisica and CNISM, Politecnico di Torino, Italy; V.A. Stepanov, P.N. Lebedev Physical Institute, RAS, Moscow, Russia; N.D. Zhigadlo, J. Karpinski, Laboratory for Solid State Physics, ETHZ, Zurich, Switzerland; and S. Massidda, Dipartimento di Fisica, Universit\`{a} di Cagliari, Italy.