Spin-lattice relaxation time of conduction electrons in $\mathrm{Mg}{\mathrm{B}}_2$

The spin-lattice relaxation time, $T_1$, of conduction electrons is measured as a function of temperature and magnetic field in $\mathrm{Mg}{\mathrm{B}}_2$ in the normal and superconducting states. The method is based on the detection of the $z$ component of the conduction electron magnetization under electron-spin-resonance conditions with amplitude-modulated microwave excitation. Measurement of $T_1$ below $T_c$ at $0.32\mathrm{T}$ allows us to disentangle contributions from the two Fermi surfaces of $\mathrm{Mg}{\mathrm{B}}_2$, as this field restores the normal state on the part of the Fermi surface with $\pi$ symmetry only.

Figure 1

CESR linewidth of $\mathrm{Mg}{\mathrm{B}}_2$ as a function of temperature for the $15\mathrm{T}$ CESR measurement (∎). Open circles (엯) show the homogeneous linewidth $\left(\Delta H_{\mathrm{hom}}\right)$ after correcting for the field-dependent broadening as explained in the text. Representative error bars are shown at the lowest temperature.

Figure 2

ESR linewidth of $\mathrm{Mg}{\mathrm{B}}_2$ as a function of magnetic field measured at $40\mathrm{K}$ (∎). Solid curve is a linear fit to the data with parameters given in the text.

Figure 3

Inhomogeneous CESR line broadening in $\mathrm{Mg}{\mathrm{B}}_2$ below $T_c$ at $0.32\mathrm{T}$. Full and open symbols show the CESR linewidth for up and down magnetic field sweeps, respectively. Inset shows the data near $T_c$. Note the line narrowing below $T_c$ and the field sweep direction dependent linewidths below the irreversibility temperature $T_{\mathrm{irr}}$.

Figure 4

ESR (a), (b) and LOD ESR (c), (d) spectra of $\mathrm{Mg}{\mathrm{B}}_2$ at $9.1\mathrm{GHz}$ $\left(0.32\mathrm{T}\right)$. (a) and (c) at $40\mathrm{K}$ in the normal state, and (b) and (d) in the superconducting state at $15\mathrm{K}$. Solid and dashed curves are the in- and out-of-phase LOD signals, respectively, and are offset for clarity. Vertical solid lines indicate the resonance field above $T_c$. Note the diamagnetic shift and broadening for both kinds of spectra below $T_c$. Also note the rotated phase of the in-phase and out-of-phase channels upon cooling.

Figure 5

Spin-lattice relaxation time as a function of the reduced temperature in $\mathrm{Mg}{\mathrm{B}}_2$ at 0.32 (∎) and $1.27\mathrm{T}$ (엯) magnetic fields. Representative error bars are shown for some of the data. Dashed curve shows $T_1$ corresponding to $\Delta H_{\mathrm{hom}}$ in the $15\mathrm{T}$ measurement as in Fig. 1, with the reduced temperature normalized to $39\mathrm{K}$.