Study of ${}^{11}\mathrm{B}$ and ${}^{13}\mathrm{C}$ NMR on doped ${\mathrm{MgB}}_2$ in the normal and in the superconducting state

We have studied carbon-doped magnesium diboride nanoparticles using ${}^{13}\mathrm{C}$ and ${}^{11}\mathrm{B}$ NMR in the normal and superconducting states. Measurements of the line shape reveal the role of carbon as a flux-pinning center and, combined with Knight shift measurements, suggest the doping procedure favors the chemical substitution scenario. We perform ab initio calculations on a structure with a single carbon-boron substitution which yield results that match the experimental data. The ${}^{13}\mathrm{C}$ and ${}^{11}\mathrm{B}$ Knight shift data are used to extract the spin susceptibility, which indicates a BCS pairing mechanism; however, we do not observe the Hebel-Slichter coherence peak from 1/$T_1$ data, which we hypothesize is due to a pair-breaking mechanism present in the boron planes.

Figure 1

(a) Magnetic-susceptibility measurements on ${\mathrm{MgB}}_{1.95}{}^{13}\mathrm{C}_{0.05}$. $T_c$ was determined to be 37 K at 0.01 T. (b) TEM images of carbon chemical-vapor-coated ${\mathrm{MgB}}_{1.95}{}^{13}\mathrm{C}_{0.05}$ powder particles reacted at 850 ${}^{\mathrm{o}}\mathrm{C}$.

Figure 2

(a) ${}^{11}\mathrm{B}$ MAS-NMR direct acquisition spectrum recorded with 80-kHz pulse amplitude; spectra are the result of 40 transients with 4 s between scans, and the sample is in a 4.0-mm rotor, spinning at 8 kHz in a constant field of 9.4 T. (b) ${}^{13}\mathrm{C}$ MAS-NMR spectrum recorded with 80-kHz pulse amplitude and a Hahn echo sequence with $\tau =50\mu \mathrm{s}$; the spectrum is the result of 131 000 transients with 1 s between scans on 10 mg of ${\mathrm{MgB}}_{1.95}{}^{13}\mathrm{C}_{0.05}$ packed into a 2.5-mm zirconium oxide rotor spinning at 30 kHz at 14.1 T. (c) MQMAS spectrum of ${\mathrm{MgB}}_{1.95}{}^{13}\mathrm{C}_{0.05}$ . (d) MQMAS spectrum of ${\mathrm{MgB}}_2$.

Figure 3

NMR peak shape of ${\mathrm{MgB}}_{1.95}{}^{13}\mathrm{C}_{0.05}$ as a function of temperature. (a) ${}^{11}\mathrm{B}$ NMR spectra at fields of 8.5 and 4.7 T. (b) ${}^{13}\mathrm{C}$ NMR spectra at fields of 8.5 and 4.7 T.

Figure 4

Knight shift (%) of ${}^{13}\mathrm{C}$ and ${}^{11}\mathrm{B}$ on ${\mathrm{MgB}}_{1.95}{}^{13}\mathrm{C}_{0.05}$ as a function of temperature at 4.7 and 8.5 T. Normalized spin susceptibility was obtained by subtracting Knight shifts as described in text.

Figure 5

Spin-lattice relaxation rate of ${\mathrm{MgB}}_{1.95}{}^{13}\mathrm{C}_{0.05}$. (a) ${}^{11}\mathrm{B}$ NMR. (b) ${}^{13}\mathrm{C}$ NMR. The black dotted line is the Korringa product. Values are 155 and 200 s K for boron and carbon, respectively.