Determination of superconducting anisotropy from magnetization data on random powders as applied to ${\mathrm{LuNi}}_2{\mathrm{B}}_2\mathrm{C},$ ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C},$ and ${\mathrm{MgB}}_2$

The recently discovered intermetallic superconductor ${\mathrm{MgB}}_2$ appears to have a highly anisotopic upper critical field with $H_{c2\mathrm{}}^{\max }{/H}_{c2\mathrm{}}^{\min }\equiv \gamma >5.\mathrm{}$ In order to determine the temperature dependence of both $H_{c2\mathrm{}}^{\max }$ and $H_{c2\mathrm{}}^{\min }$ we propose a method of extracting the superconducting anisotropy from the magnetization $M(H,T)\mathrm{}$ of randomly oriented powder samples. The method is based on two features in $(\partial M/\partial {T)}_H:$ the onset of diamagnetism at $T_c^{\max },$ that is commonly associated with $H_{c2\mathrm{}},$ and a kink in $\partial M/\partial T$ at a lower temperature $T_c^{\min }.$ Results for ${\mathrm{LuNi}}_2{\mathrm{B}}_2\mathrm{C}$ and ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$ powders are in agreement with anisotropic $H_{c2\mathrm{}}$ obtained from magnetotransport measurements on single crystals. Using this method on four different types of ${\mathrm{MgB}}_2$ powder samples we are able to determine $H_{c2\mathrm{}}^{\max }\mathrm{}\left(T\right)\mathrm{}$ and $H_{c2\mathrm{}}^{\min }\mathrm{}\left(T\right)\mathrm{}$ with $\gamma \approx 6.$