Upper critical fields and two-band superconductivity in Sr${}_{1-x}$Eu${}_x$(Fe${}_{0.89}$Co${}_{0.11}$)${}_2$As${}_2$ ($x=0.20$ and $0.46$)

The upper critical fields $H_{c2}\left(T\right)$ of single crystals of Sr${}_{1-x}$Eu${}_x$(Fe${}_{0.89}$Co${}_{0.11}$)${}_2$As${}_2$ ($x=0.20$ and $0.46$) were determined by radio-frequency penetration depth measurements in pulsed magnetic fields. $H_{c2}\left(T\right)$ approaches the Pauli limiting field but shows an upward curvature with an enhancement from the orbital limited field, as inferred from the Werthamer-Helfand-Hohenberg theory. We discuss the temperature dependence of the upper critical fields and the decreasing anisotropy using a two-band BCS model.

Figure 1

(a) Low-temperature magnetic susceptibility measured in a magnetic field of 100 Oe applied in the $ab$ plane and resistivity in the zero field. The inset shows an expanded view of the field-cooled curve. The arrow indicates the antiferromagnetic transition. (b) Inverse in-plane magnetic susceptibility measured in 10 kOe.

Figure 2

Frequency shift ($\Delta F$) as a function of magnetic field for $H\parallel ab$ and $H\parallel c$ for the Eu20 sample at selected temperatures. Open symbols are $\Delta F$ taken at 19 K as a normal-state background signal. Solid line in (a) shows the criterion used to determine $H_{c2}\left(T\right)$.

Figure 3

$\Delta F$ as a function of the magnetic field for $H\parallel ab$ and $H\parallel c$ for Eu46. The inset in (b) shows the measurements up to 60 T at the base temperature of 0.51 K.

Figure 4

Anisotropic $H_{c2}\left(T\right)$ for Eu20 and Eu46 single crystals. The green circles in (b) are obtained from the resistivity measurement, which is in excellent agreement with the pulsed-field rf shift measurement. The dotted lines are fits to the WHH formula. The solid lines are fits to the two-band model. The insets show the temperature dependence of the anisotropy $\gamma =H_{c2}^{ab}/H_{c2}^c$, and the solid lines are the calculated curve of the two-band model fits.