Spontaneous Formation of a Superconducting and Antiferromagnetic Hybrid State in ${\mathrm{SrFe}}_2{\mathrm{As}}_2$ under High Pressure

We report a novel superconducting (SC) and antiferromagnetic (AF) hybrid state in ${\mathrm{SrFe}}_2{\mathrm{As}}_2$ revealed by ${}^{75}\mathrm{As}$ nuclear magnetic resonance (NMR) experiments on a single crystal under highly hydrostatic pressure up to 7 GPa. The NMR spectra at 5.4 GPa indicate simultaneous development of the SC and AF orders below 30 K. The nuclear spin-lattice relaxation rate in the SC domains shows a substantial residual density of states, suggesting proximity effects due to the spontaneous formation of a nanoscale SC-AF hybrid structure. This entangled behavior is a remarkable example of a self-organized heterogeneous structure in a clean system.

Figure 1

${}^{75}\mathrm{As}$-NMR spectra of 48.31 MHz at various $P$. (a) The spectra in the PM tetragonal normal state (slightly above $T_N$ or $T_c$) for $H\parallel c$ (green) and $H\perp c$ (sky blue). Although the central line for $H\perp c$ becomes broader at higher $P$ due to distribution of the second-order quadrupole shift, it remains sharp up to 7.2 GPa for $H\parallel c$. The vertical dashed line represents the unshifted resonance position $f_{\mathrm{res}}{\gamma }^{-1}$ ($=6.63\mathrm{T}$). (b) The spectra in the AF state for $H\parallel c$ (red) and $H\perp c$ (blue). The gray arrows indicate the splitting ($H\parallel c$) or the shift ($H\perp c$) induced by the hyperfine fields $\pm \Delta$ along the $c$ axis, transferred from the stripe-type AF Fe moments [illustrated at the right-top corner in (a)]. There are four satellite lines for $H\perp c$, indicating the twinned orthorhombic structure with asymmetric electric field gradients.

Figure 2

(a) The AF transition detected by tracking the peak intensity of the PM central line for $H\parallel c$. The rates for the $T$ sweep were kept slower than 0.05, 0.1, $0.3\mathrm{K}/\min$. for 1.9, 3.2, 4.2 GPa, respectively. Sharp transition with hysteresis demonstrates good homogeneity of the sample and the first-order AF transition. (b) $(T_{1}T{)}^{-1}$ in the PM state for $H\perp c$ (the plots in dark blue to sky blue with higher values) and for $H\parallel c$ (the lower plots in brown to green). The inset shows the $P\mathrm{\text{−}}T$ phase diagram. $T_N$ is determined from the 50% recovery of the PM intensity on warming in (a) (open diamonds). The bulk SC transition (open squares) is detected in our NMR experiment only at 5.4 GPa. $T_c$ is determined from the peak in $(T_{1}T{)}^{-1}$ at 11 T for $H\perp c$. The SC transition is absent below 4.2 and at 7.2 GPa. Crosses represent the data reported based on the resistivity (for AF) and the ac susceptibility (for SC) measurements [11].

Figure 3

${}^{75}\mathrm{As}$-NMR spectra at 5.4 GPa showing the coexistence of the AF and SC states. The insets show the color plots indicating the $T$ dependence of the spectral intensity distribution near the central line. The white dashed lines indicate the $T$ values of the spectra in the main panels. (a) The NMR spectra for $H\parallel c$ at 11 T measured at 28 K (above $T_c$), 18 K (below $T_c$), and 4.2 K. At 4.2 K, the spectrum shows contributions both from the commensurate stripe-type AF domains (gray arrows) and from the PM-SC domains (red arrows). (b) The PM (SC or normal) central lines for $H\parallel c$ at 6.6 T. Anomalous line shape with asymmetric broad tail is observed for $18\mathrm{K}<T<T_c$ (see the inset). Standard models of vortex lattices are unable to fit the spectrum at 25 K even if an extremely short penetration depth $\lambda$ is assumed. An example, is shown by the red line calculated with the modified London model for a rectangular vortex lattice [19, 22, 23]. (c) The spectra for $H\perp c$ at 11 T. At 4.2 K, the satellite lines from the AF domains split into two sets. The azimuth angle dependence of the satellite positions in the $ab$-plane are reproduced by the asymmetry parameter $|({\nu }_a-{\nu }_b)/{\nu }_c|=0.15$ as shown by the dashed lines. This proves the twinned orthorhombic structure of the AF domains. The broadened spectrum at 26 K from the AF domains indicates modulation of AF moments and the structure, most likely an incommensurate spin-density-wave type.

Figure 4

Evidence for bulk SC state at 5.4 GPa. (a) The $T$ dependence of $(T_{1}T{)}^{-1}$ in the PM state for $H\perp c$ at 11 T (blue) and for $H\parallel c$ at 11 T (orange) and at 6.6 T (red). The blue and the red data are identical to those shown in Fig. 2b. Opening of the SC gap causes sudden decrease of $(T_{1}T{)}^{-1}$ below $T_c$. Also shown are $(T_{1}T{)}^{-1}$ data in the AF state for $H\perp c$ at 11 T (sky blue). All measurements were made on the central line, whose positions are shown by the arrows in Fig. 3. (b) The $T$ dependence of the Knight shift for $H\parallel c$ at 6.6 and 11 T. The reduction below $T_c$ indicates the spin-singlet pairing in the SC state. (c) The ac susceptibility measured by the self resonance method using the NMR coil. The change of the resonating frequency $-\Delta f$ represents the Meissner shielding. (d)–(f) Typical recovery curves of the nuclear magnetization during the $T_1$ measurement at 28 K (immediately above $T_c$), 22 K, and 4.2 K (below $T_c$) for $H\parallel c$ at 11 T. Each curve is fit very well to the formula for spin $3/2$ nuclei, $\{\exp (-t/T_1)+9\exp (-6t/T_1)\}/10$, with a single value of $T_1$, supporting uniform relaxation process.