Upper critical field of isoelectron substituted SrFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$

The upper critical field $H_{c2}$ of optimally doped, iron-based superconductor SrFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ ($x$ $=$ 0.35, $T_c$ $=$ 25 K) was measured as a function of temperature down to 1.6 K for two principal directions of magnetic field $H\parallel c$ and $H\parallel a$. Measurements were performed in pulsed magnetic fields up to 65 T using a tunnel-diode resonator technique on as-grown and heavy-ion-irradiated single crystals, with columnar defect density corresponding to a matching field $B_{\varphi }$ $=$ 25 T. The $H_{c2,c}\left(T\right)$ is close to $T$ linear, while clear saturation is observed for $H_{c2,a}\left(T\right)$, leading to a strongly temperature-dependent anisotropy parameter $\gamma$. The linear shape of $H_{c2,c}\left(T\right)$ is very similar to that observed in nodal KFe${}_2$As${}_2$, but very different from full-gap LiFeAs. Irradiation does not introduce any additional features on the $H_{c2}\left(T\right)$ line corresponding to the matching field. Instead, it suppresses uniformly both $T_c$ and $H_{c2}$, keeping their ratio constant.

Figure 1

(a) Temperature-dependent in-plane resistivity of the representative sample of pristine SrFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$, $x=$ 0.35. Close to perfect $T$-linear dependence is observed in the temperature range from $T_c$ up to 400 K. Resistive transition ends at $\sim$25 K, close to the magnetic transition observed in zero-field TDR measurements (b). The bottom panel (c) shows TDR frequency shift (in arbitrary units) measured as a function of magnetic field during pulsed field experiments at indicated temperatures. The lines show the way the $H_{c2}$ was defined from the data as a crossover point of linear extrapolation of the rapid frequency drop to the level of the background signal.

Figure 2

The temperature-dependent upper critical fields for pristine (black open symbols) and irradiated (closed blue symbols) samples of optimally doped SrFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ with $x$ $=$ 0.35, as determined from pulsed field measurements in magnetic fields parallel to the $c$ axis (squares) and to the conducting $ab$ plane (circles). The lines connect data points and do not show the true position of zero-field $T_c$, determined in separate experiments.

Figure 3

The temperature-dependent anisotropy parameter $\gamma \left(T\right)\equiv H_{c2,a}\left(T\right)/H_{c2,c}\left(T\right)$ in pristine (open circles) and irradiated (closed circles) samples of SrFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$, $x=$ 0.35.

Figure 4

The $H-T$ phase diagram of SrFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$, $x=$ 0.35 (red). Normalized $H/H_{c2}\left(0\right)$ is plotted vs normalized temperature, $T/T_c\left(0\right)$. Solid symbols show $H_{c2}\parallel c$ axis and open symbols show $H_{c2}\parallel ab$ plane. For reference we show similar plots for full-gap superconductor LiFeAs (green up-triangles)[45] and nodal KFe${}_2$As${}_2$ (blue circles).[48]

Figure 5

The temperature-dependent anisotropy parameter $\gamma \left(T\right)\equiv H_{c2,a}\left(T\right)/H_{c2,c}\left(T\right)$ normalized to its value at $T=0$ in pristine SrFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$, $x=$ 0.35 (filled red circles). For the reference we show $\gamma (T/T_c)/\gamma \left(0\right)$ in clean iron-pnictide superconductors, nodal KFe${}_2$As${}_2$ (blue squares),[48] and full-gap LiFeAs (green triangles).[45]