Systematic Effects of Carbon Doping on the Superconducting Properties of $\mathrm{Mg}({\mathrm{B}}_{1-x}{\mathrm{C}}_x{)}_2$

The upper critical field, $H_{c2}$, of $\mathrm{Mg}({\mathrm{B}}_{1-x}{\mathrm{C}}_x{)}_2$ has been measured in order to probe the maximum magnetic field range for superconductivity that can be attained by C doping. Carbon doped ${\mathrm{MgB}}_2$ filaments were prepared, and for carbon levels below $4\%$ the transition temperatures are depressed by about $1\mathrm{K}/\%$ C and $H_{c2}(T=0)$ rises by about $5\mathrm{T}/\%$ C. This means that $3.8\%$ C substitution will depress $T_c$ from 39.2 to $36.2\mathrm{K}$ and raise $H_{c2}(T=0)$ from $16.0$ to $32.5\mathrm{T}$. These rises in $H_{c2}$ are accompanied by a rise in resistivity at $40\mathrm{K}$ from about $0.5$ to about $10\mu \Omega \mathrm{cm}$.

Figure 1

(a) Selected regions of powder x-ray diffraction data from $\mathrm{Mg}({\mathrm{B}}_{1-x}{\mathrm{C}}_x{)}_2$ wire segments synthesized from boron filaments with $0\%$, $0.5\%$, $1\%$, and $2\%$ nominal carbon substitution. Note that whereas there is no detectable shift of $(002)$ peak, the $(110)$ peak shifts systematically with carbon substitution. (b) Shift in the $a$-lattice parameter as a function of carbon content from neutron diffraction data [6] shown as a dashed line with our shift in the $a$-lattice parameter shown as large triangles on the $y$ axis. Projection of our $\Delta a$ data onto the $\Delta a(x)$ line (shown as dotted lines) indicates that the our three carbon substituted $\mathrm{Mg}({\mathrm{B}}_{1-x}{\mathrm{C}}_x{)}_2$ samples have $x\approx 0.0047$, 0.021, and 0.038. The inset shows data for an enlarged carbon range, $x<0.15$, and includes the $x\sim 0.10$ sample [5, 6] as well as data from Lee et al. [13] showing their nominal carbon concentrations (*) as well as Auger electron spectroscopy data (+).

Figure 2

Superconducting transition temperature as a function of carbon content. Data inferred from temperature dependent resistivity (shown in lower inset) is shown as squares and data inferred from temperature dependent, low field magnetization (shown in upper inset) is shown as circles. Data from Ribeiro et al. [5] for $x\approx 0.10$ are also shown. Insets: squares indicate $x=0$; circles, $x=0.0042$; triangles, $x=0.021$; stars, $x=0.038$. The carbon content error bars are projections of the Avdeev et al. error bars for $x\sim 0.10$ back toward $x=0$ (see inset of Fig. 1).

Figure 3

Temperature (a) and magnetic field (b) dependent electrical resistivity of $\mathrm{Mg}({\mathrm{B}}_{1-x}{\mathrm{C}}_x{)}_2$ with $x=0.038$. The data presented in (a) are for $H\le 14\mathrm{T}$ and taken in a Quantum Design PPMS system. The data in (b) are for $H\le 33\mathrm{T}$ and were taken at the NHMFL, Tallahassee.

Figure 4

Superconducting upper critical field $H_{c2}$ as a function of temperature for $\mathrm{Mg}({\mathrm{B}}_{1-x}{\mathrm{C}}_x{)}_2$, $x\le 0.038$ samples. Inset: $H_{c2}(T)$ closer to $T_c$ determined from temperature dependent resistivity (solid squares), field dependent resistivity (triangles), and field dependent magnetization (open squares).

Figure 5

Superconducting upper critical field $H_{c2}$ and superconducting transition temperature $T_c$ as a function of $x$ for $\mathrm{Mg}({\mathrm{B}}_{1-x}{\mathrm{C}}_x{)}_2$ samples. $T_c(x)$ data is shown as open circles for this study and for $x\approx 0.10$ from Ribeiro et al. [5], stars for single crystal samples from Kazakov et al. [19], and the asterisk/cross pairs show the nominal and inferred carbon content given by Lee et al. [13]. $H_{c2}(0)$ data are shown as solid circles for this work and for $x\approx 0.10$ from Holanova et al. [8].