Effects of C substitution on the pinning mechanism of ${\text{MgB}}_2$

The temperature and magnetic field of the critical current density of four selected pure and C-doped ${\text{MgB}}_2$ samples have been investigated in detail and the flux pinning mechanism has been analyzed. It was found that the sintering temperature and the substitution of carbon can significantly modify the flux pinning mechanism. Below 30 K, the reduced field dependences of the reduced pinning force for all investigated samples were found to closely obey one scaling law, reflecting the presence of only one dominant pinning mechanism. A $\delta T_c$ pinning mechanism was found to be mainly responsible in pure ${\text{MgB}}_2$ samples while the $\delta l$ pinning mechanism becomes dominant for C-doped samples.

Figure 1

(Color online) X-ray diffraction pattern $\left(\text{Cu}K\alpha \right)$ of sample 485 along with the refined and difference patterns. The markers indicate the Bragg peak positions for ${\text{MgB}}_2$ (upper row) and MgO (lower row), respectively (see text).

Figure 2

(Color online) $J_c\left(H\right)$ at various temperatures for samples (a) 185 and (b) 485. The insets show the temperature dependence of the irreversibility field ${\mu }_0{H}_{\text{irr}}$ for these samples, with the solid line standing for the fitting result obtained by using the ${\left[1-{\left(T/T_c\right)}^2\right]}^{3/2}$ law.

Figure 3

(Color online) Field dependence of the reduced pinning force with the fitting results obtained by using $h^n{\left(1-h\right)}^m$ for samples (a) 165, (b) 185, (c) 485, and (d) 495, respectively. The insets plot the behavior of the maximum pinning force $F_{p\text{max}}$ vs the irreversibility field ${\mu }_0{H}_{\text{irr}}$ with the solid line showing the fitting result obtained by using $F_{p\text{max}}\propto H^{\alpha }$.

Figure 4

(Color online) $J_c$ of sample 485 at $T<30\text{K}$ in a double-logarithmic plots of $-{\text{log}}_{10}\left[J_c\left(B\right)/J_c\left(B=0\right)\right]$ vs the applied field. The inset shows the determination of the crossover fields $B_{\text{sb}}$ and $B_{\text{th}}$, where $B_{\text{sb}}$ stands for the crossover field from single vortex pinning to small bundle pinning and $B_{\text{th}}$ is the crossover field to the thermal fluctuations dominated regime.

Figure 5

(Color online) Temperature dependence of the crossover fields $B_{\text{sb}}$ and $B_{\text{th}}$ for samples (a) 165, (b) 185, (c) 485, and (d) 495, with the dotted and solid lines standing for the fitting results based on the $\delta l$ and $\delta T_c$ pinning mechanisms, respectively. The inset shows the temperature dependence of the critical current density at $B=0.1\text{T}$, with the dotted and solid lines for the calculated curves based on $\delta l$ and $\delta T_c$ pinning, respectively.

Figure 6

(Color online) Temperature dependence of the resistivity of samples 165, 185, 485, and 495 at zero field.