Anisotropic Diamagnetic Response in Type-II Superconductors with Gap and Fermi-Surface Anisotropies

The effects of anisotropic gap structures on a diamagnetic response are investigated in order to demonstrate that the field-angle-resolved magnetization [$M_L(\chi )$] measurement can be used as a spectroscopic method to detect gap structures. Our microscopic calculation based on the quasiclassical Eilenberger formalism reveals that $M_L(\chi )$ in a superconductor with a fourfold gap displays a fourfold oscillation reflecting the gap and Fermi-surface anisotropies, and the sign of this oscillation changes at a field between $H_{c1}$ and $H_{c2}$. As a prototype of unconventional superconductors, magnetization data for borocarbides are also discussed.

Figure 1

The coordinates $(x,y,z)$ and the crystal axes $(a,b,c)$. The induction $\mathbf{B}$ is rotated from the $a$ axis by an angle $\chi$.

Figure 2

Logarithmic field dependence of longitudinal magnetization $M_L$ at $T/T_c=0.6$ for $\mathbf{B}\parallel$ node (filled circles) and $\mathbf{B}\parallel$ antinode (open circles). The used anisotropy parameters are $\alpha =1$ and $\beta =0$. $H_{\mathrm{o}\mathrm{r}\mathrm{b}}=1.037{\Phi }_0/2\pi {\xi }_0^2$ (${\xi }_0=v_0/2\pi T_c$) is the orbital limiting field in the isotropic case. Inset: Field dependence of $M_L^{\mathrm{a}\mathrm{v}}=[M_L(\chi =0)+M_L(\chi =\pi /4)]/2$ for the same parameters.

Figure 3

Field-angle dependences of $M_L(\chi )$ for (a) $\alpha =1,\beta =0$ and (b) $\alpha =1,\beta =0.4$ at $T/T_c=0.6$ for several inductions. The data at different $B$ are vertically shifted.

Figure 4

Logarithmic field dependence of $\delta M_L=M_L(\chi =\pi /4)-M_L(\chi =0)$ for $\alpha =1,\beta =0.4$ at $T/T_c=0.6$. Inset: The sign reversal field $B^{*}$ in the $B$-$T$ phase diagram. The $H_{c2}$ is determined through linear extrapolations of $M_L$.