Magnetic-field-induced density of states in $\mathrm{Mg}{\mathrm{B}}_2$: Spin susceptibility measured by conduction-electron spin resonance

The magnetic-field dependence of the electron spin susceptibility ${\chi }_s$ was measured in the superconducting state of high-purity $\mathrm{Mg}{\mathrm{B}}_2$ fine powders from the intensity of the conduction-electron spin resonance at 3.8, 9.4, and $35\mathrm{GHz}$. The measurements confirm that a large part of the density of states is restored at low temperatures at fields below $1\mathrm{T}$ in qualitative agreement with the closing of the $\pi$ band gaps in the two-band model. However, the increase of ${\chi }_s$ with field and temperature is larger than expected from current superconductor models of $\mathrm{Mg}{\mathrm{B}}_2$.

Figure 1

Temperature dependence of the CESR signal of $\mathrm{Mg}{\mathrm{B}}_2$ fine powder sample (sample 1) at $9.4\mathrm{GHz}$ $\left(0.34\mathrm{T}\right)$. ∗ denotes the ESR signal of a tiny amount of paramagnetic impurity phase.

Figure 2

Temperature dependence of the diamagnetic shift (full symbols are up sweeps, open symbols are down sweeps) of the CESR (squares, $3.8\mathrm{GHz}$, $0.14\mathrm{T}$; circles, $9.4\mathrm{GHz}$, $0.34\mathrm{T}$; triangles, $35\mathrm{GHz}$, $1.28\mathrm{T}$) and diamagnetic magnetization measured by SQUID (solid, dashed, and dotted curves are at 0.14, 0.34, and $1.28\mathrm{T}$, respectively).

Figure 3

The temperature- and magnetic-field-dependent spin susceptibility of $\mathrm{Mg}{\mathrm{B}}_2$ below $T_c$ (squares, $3.8\mathrm{GHz}$, $0.14\mathrm{T}$; circles, $9.4\mathrm{GHz}$, $0.34\mathrm{T}$; triangles, $35\mathrm{GHz}$, $1.28\mathrm{T}$). Dashed and solid curves are ${\chi }_s$ in the absence of magnetic field as calculated for the isotropic BCS and two-gap models, respectively, as explained in the text.

Figure 4

Comparison of the measured field dependence of the low-temperature normalized susceptibility ${\chi }_s∕{\chi }_N$ (squares) to the predictions of the two-gap model of Ref. 26. The magnetic-field-dependent DOS (dashed line) is assumed to have independent contributions from a $\pi$ band with $H_{c2}^{\pi }=0.4\mathrm{T}$ and a $\sigma$ band with $H_{c2}^c=2.5\mathrm{T}$ and $H_{c2}^{ab}=16\mathrm{T}$. The solid line represents DOS calculated from single-crystal specific heat measurements (Ref. 8).