Type-I superconductivity in YbSb${}_2$ single crystals

We present evidence of type-I superconductivity in YbSb${}_2$ single crystals from dc and ac magnetization, heat capacity, and resistivity measurements. The critical temperature and critical field are determined to be $T_c\approx$ 1.3 K and $H_c\approx$ 55 Oe. A small Ginzburg-Landau parameter $\kappa =$ 0.05, together with typical magnetization isotherms of type-I superconductors, small critical field values, a strong differential paramagnetic effect signal, and a field-induced change from second- to first-order phase transition, confirms the type-I nature of the superconductivity in YbSb${}_2$. A possible second superconducting state is observed in the radio-frequency susceptibility measurements, with $T_c^{\left(2\right)}\approx$ 0.41 K and $H_c^{\left(2\right)}\approx$ 430 Oe.

Figure 1

Powder XRD pattern of YbSb${}_2$ (black line), with peak positions (vertical marks) calculated based on space group $Cmcm$ and lattice parameters $a=4.554$ Å, $b=16.715$ Å, and $c=4.267$ Å. A small amount of residual Sb flux is marked by a blue asterisk.

Figure 2

Temperature-dependent susceptibility of YbSb${}_2$, measured in a dc field parallel to the crystal plate. The ZFC and FC data are plotted as solid and dashed lines, respectively.

Figure 3

(a) Isothermal magnetization and (b) full $M\left(H\right)$ loops of YbSb${}_2$ for $T=$ 0.5 K (squares) and 1 K (triangles) in the $H\parallel$ plate. Solid and open symbols correspond to data before (top axis) and after (bottom axis) the demagnetization correction, respectively (see text).

Figure 4

Temperature-dependent ac susceptibility of YbSb${}_2$, measured in fields $H$ up to 60 Oe.

Figure 5

Field-dependent ac susceptibility of YbSb${}_2$, measured for various temperatures from 0.06 to 1.28 K.

Figure 6

Temperature-dependent heat capacity of YbSb${}_2$ for $H=$ 0, 10, 20, 30, 40, 50, 60 Oe and 20, 60 kOe. The left inset shows $C_p/T$ vs $T^2$ for $H=0$, 60 Oe, 20 kOe, and 60 kOe, showing a field-dependent Sommerfeld coefficient $\gamma$. The right inset shows the superconducting (squares) and normal (black line) electronic specific heat for $H=0$, plotted as $C_{el}/T$ vs $T$. An entropy conservation construct (red lines) is used to determine the jump in the electronic specific heat at $T_c$.

Figure 7

The ac resistivity of YbSb${}_2$ for $H=$ 0 and $i\parallel$ plate. The top inset shows a zoomed-in view of the low-temperature resistivity around $T_c$; the bottom inset shows $\Delta \rho =\rho -{\rho }_0$ vs $T^2$ (symbols), together with a linear fit (solid line).

Figure 8

Shift of resonant frequency $\Delta f=-G4\pi \chi \left(T\right)$, measured in fields up to 400 Oe. The ZFC and FC data are shown as solid and dashed lines, respectively; the inset shows a zoomed-in view of the low-temperature data for $H=$ 0, with ZFC and FC data shown as solid and open symbols.

Figure 9

Superfluid density calculated as $\rho ={\lambda }^2\left(0\right)/{\lambda }^2\left(T\right)$. The solid red line shows a fit to the typical behavior of an $s$-wave BCS superconductor.

Figure 10

$H$-$T$ phase diagram of YbSb${}_2$. Points determined from ${\chi }^{\prime }\left(T\right)$, ${\chi }^{\prime }\left(H\right)$, $C_p\left(T\right)$, and $\Delta f\left(T\right)$ data are marked by black squares, red triangles, blue diamonds, and green circles. The superconductive phase boundary determined from thermodynamic data is illustrated by a purple line. The possible new superconducting state observed in the rf magnetization measurement is marked with a dashed line; the inset shows a zoomed-in view of the data points from thermodynamic measurements.