Difference between Al and C doping in anisotropic upper critical field development in $\mathrm{Mg}{\mathrm{B}}_2$

The temperature dependence of the upper critical field $H_{c2}$ for both field directions in partially substituted polycrystalline $\mathrm{Mg}{\mathrm{B}}_2$ was determined. Whereas the suppression of $T_c$ is similar for aluminum and carbon substituted samples, $H_{c2}$ is affected by the substitution in profoundly different ways. In the case of Al substitution changes can tentatively be described by intrinsic effects (shift of the Fermi level). In the C substituted samples, $H_{c2}$ is increased drastically, and extrinsic effects (disorder) have to play a major role. The strong contrast between the two substitutions is discussed, taking into account three relevant scattering rates.

Figure 1

(Color online.) (a) Magnetization $M$ vs temperature $T$ in 20 Oe (both zero field cooled and field cooled) of Al or C substituted polycrystalline $\mathrm{Mg}{\mathrm{B}}_2$ samples. (b) Transition temperature $T_c$ vs number of additional electrons per unit cell due to Al (full symbols) or C (open symbols) substitution. The open square is from Ref. 14.

Figure 2

(Color online.) Upper critical field $H_{c2}$ of ${\mathrm{Mg}}_{0.9}{\mathrm{Al}}_{0.1}{\mathrm{B}}_2$. Inset: Second derivative ${\mathrm{d}}^{2}M∕\mathrm{d}{H}^2$ of the magnetization as a function of field $H$ at different temperatures on ${\mathrm{Mg}}_{0.9}{\mathrm{Al}}_{0.1}{\mathrm{B}}_2$. The location of the minimum upper critical field (see Ref. 21), i.e., $H_{c2}^{\Vert c}$ is indicated by arrows.

Figure 3

(Color online.) Zero temperature upper critical field vs number of additional electrons per unit cell due to Al (full symbols) or C (open symbols) substitution. Grey symbols are unsubstituted $\mathrm{Mg}{\mathrm{B}}_2$. (a) $H_{c2}^{\Vert c}\left(0\right)$. (b) $H_{c2}^{\Vert ab}\left(0\right)$. Squares in both panels are single crystal results from Refs. 14, 22, open circles in panel (a) are from Refs. 8, 9.

Figure 4

(Color online.) Upper critical field anisotropy ${\gamma }_H$ vs temperature $T$, for unsubstituted, aluminum substituted, and carbon substituted $\mathrm{Mg}{\mathrm{B}}_2$. The results from 6.3% C substituted (single crystalline) $\mathrm{Mg}{\mathrm{B}}_2$ are from Ref. 14.