Uncommonly High Upper Critical Field in the Superconducting KOs$_2$O$_6$ Pyrochlore

The entire temperature dependence of the upper critical field H c2 in the β -pyrochlore KOs 2 O 6 is obtained from high-field resistivity and magnetic measurements. Both techniques identically give H c2 ( T ≃ 0 K) not only surprisingly high ( ∼ 33 T), but also the approach to it unusually temperature- linear all the way below T c (= 9.6 K). We show that, while H c2 (0) exceeds a simple spin-singlet paramagnetic limit H P , it is well below an H P enhanced due to the missing spatial inversion symmetry reported recently in KOs 2 O 6 , ensuring that the pair-breaking here is executed by orbital degrees. Ab initio calculations of orbital H c2 show that the unusual temperature dependence is reproduced if dominant s -wave superconductivity resides on the smaller closed Fermi surfaces.