Magnetic and non-magnetic substitutions in MgB$_{2}$ single crystals: influence on superconducting properties and structure

Pure and substituted single crystals of MgB$_{2 }$have been grown at high pressure (30 kbar) using the cubic anvil technique. The crystals have very low residual resistivity $\rho _{o}$(40 K)$\approx $0.5 and a sharp transition $\Delta $T$_{c}\approx $0.2 K. Magnetic (Mn, Fe) and non-magnetic (Al, C) ions have been substituted to study their effect on superconductivity and on the impurity scattering in and between the $\sigma $ and $\pi $ bands. Single-phase Mg$_{1-x}$Al$_{x}$B$_{2}$ and MgB$_{2-x}$C$_{x}$ crystals were grown for x=0-0.3. Al and C cause a similar moderate decrease of T$_{c}$. Magnetic ions, such as Fe$^{3+}$ and Mn$^{2+}$ suppress T$_{c}$ very effectively, due to magnetic pair breaking. Superconductivity is completely suppressed for by 2{\%} Mn. Fe substitution decreases T$_{c}$ less rapidly than Mn but much faster than Al and C. Carbon substitution increases the H$_{c2}$ twice, while Al, Fe and Mn substitutions decrease this field. H$_{c2}$ anisotropy decreases with all substitutions, but the temperature dependence of the anisotropy is different, due to different scattering rates in the $\pi $ and $\sigma $ bands. For Mn and Al, $\pi $ and $\sigma $ energy gaps exist up to the highest substitution level, while for C substitution, merging of these gaps is observed indicating interband scattering.