Anisotropy and internal-field distribution of $\mathrm{Mg}{\mathrm{B}}_2$ in the mixed state at low temperatures

Magnetization and muon spin relaxation on $\mathrm{Mg}{\mathrm{B}}_2$ were measured as a function of the applied magnetic field at $2\mathrm{K}$. Both indicate an inverse-squared penetration depth strongly decreasing with increasing field $H$ below about $1\mathrm{T}$. Magnetization also suggests the anisotropy of the penetration depth increases with increasing $H$, interpolating between a low $H_{c1}$ and a high $H_{c2}$ anisotropy. Measurements of the torque as a function of the angle between the field and the $c$ axis of the crystal are in agreement with this finding, while also ruling out drastic differences between the mixed state anisotropies of the two basic length scales penetration depth and coherence length.

Figure 1

(Color online) Magnetization $M$ vs field ${\mu }_{0}H$ at $2\mathrm{K}$ on a $\mathrm{Mg}{\mathrm{B}}_2$ single crystal with $H\Vert c$ and $H\Vert \mathit{ab}$.

Figure 2

(Color online) Comparison of $1∕{\lambda }^2$ vs $H$ obtained from $\mathrm{d}M∕\mathrm{d}\left(\ln H\right)$ of Fig. 1, and from the muon spin depolarization rate measured on unaligned powder (circles). The shaded box indicates fields close to or lower than $H_{c1}$ (see text).

Figure 3

(Color online) Angle $\theta$ dependence of torque $\tau$ in $0.2\mathrm{T}$ at $8\mathrm{K}$ (symbols) (Ref. 27). Dashed line, theoretical description (Ref. 17) assuming ${\gamma }_{\lambda }⪡{\gamma }_H$; full line, description with ${\gamma }_{\lambda }={\gamma }_H$.

Figure 4

(Color online) Anisotropy determined from an analysis of the torque data (Fig. 3) with Eq. (1) (Ref. 17), at various low temperatures, as a function of field $H$ (Ref. 29). Also shown is the anisotropy determined from Fig. 2 (open circle) and the anisotropy very close to $T_c$ (dotted line, see text).