Vortex matter properties of carbon-substitutedMgB2single crystals

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We have studied the vortex matter phase diagram in two carbon doped ${\mathrm{MgB}}_{2\ensuremath{-}x}{\mathrm{C}}_{x}$ ($x=0.04$ and 0.1) single crystals. We have found that, as in pristine ${\mathrm{MgB}}_{2}$, the peak effect is also present in carbon doped crystals. The regime where the peak effect is developed is more extended in comparison to the undoped crystal. The enhancement of the peak effect regime, combined with the higher ${H}_{c2}^{c}(0)$, makes doped ${\mathrm{MgB}}_{2}$ more favorable for practical applications. The absence of significant bulk pinning below the line ${H}_{\mathrm{on}}(T)$, which denotes the onset points of the peak effect, implies that the Bragg glass phase is present for $H<{H}_{\mathrm{on}}(T)$. Interestingly the end points ${H}_{\mathrm{ep}}(T)$ of the peak effect are placed well below the upper critical fields ${H}_{c2}(T)$. The unexpected absence of bulk pinning above the end-point line ${H}_{\mathrm{ep}}(T)$ of the peak effect implies the presence of a slightly pinned vortex phase in the regime ${H}_{\mathrm{ep}}(T)<H<{H}_{c2}(T)$.