Breakdown of single spin-fluid model in the heavily hole-doped superconductor ${\mathrm{CsFe}}_2{\mathrm{As}}_2$

Although Fe-based superconductors are correlated electronic systems with multiorbital, previous nuclear magnetic resonance (NMR) measurement suggests that a single spin-fluid model is sufficient to describe its spin behavior. Here, we first observed the breakdown of single spin-fluid model in a heavily hole-doped Fe-based superconductor ${\mathrm{CsFe}}_2{\mathrm{As}}_2$ by site-selective NMR measurement. At high-temperature regime, both Knight shift and nuclear spin-lattice relaxation at ${}^{133}\mathrm{Cs}$ and ${}^{75}\mathrm{As}$ nuclei exhibit distinct temperature-dependent behavior, suggesting the breakdown of the single spin-fluid model in ${\mathrm{CsFe}}_2{\mathrm{As}}_2$. This is ascribed to the coexistence of both localized and itinerant spin degree of freedom at $3d$ orbitals, which is consistent with the orbital-selective Mott phase. With decreasing temperature, the single spin-fluid behavior is recovered below $T^{*}\sim 75$ K due to a coherent state among $3d$ orbitals. The Kondo liquid scenario is proposed to understand the low-temperature coherent state.

Figure 1

(a) Illustration of the microscopic process of the dominated contribution on Knight shift due to transferred hyperfine interaction at ${}^{75}\mathrm{As}$ and ${}^{133}\mathrm{Cs}$ sites. The crystalline structure of ${\mathrm{CsFe}}_2{\mathrm{As}}_2$ is shown in the side view along Fe-Fe direction. The hyperfine interaction contributed to Knight shift of ${}^{75}\mathrm{As}$ and ${}^{133}\mathrm{Cs}$ are dominated by the transferred hyperfine interaction through the hybridization of on-site $4s$ or $6s$ orbital with $3d$ orbitals at the nearest-neighbor Fe atoms. We performed NMR measurements on both ${}^{75}\mathrm{As}$ and ${}^{133}\mathrm{Cs}$ nuclei. The full spectrum at 2 K are shown in (b) for ${}^{133}\mathrm{Cs}$ nuclei and (c) for ${}^{75}\mathrm{As}$ nuclei.

Figure 2

(a) Temperature-dependent Knight shift for both ${}^{75}\mathrm{As}$ and ${}^{133}\mathrm{Cs}$ nuclei. The blue triangles represent the Knight shift of ${}^{133}\mathrm{Cs}$ nuclei. The red squares represents the Knight shift of ${}^{75}\mathrm{As}$. The red dash line is a guiding line for temperature-dependent ${}^{75}\mathrm{K}$ at high temperature, indicating a decreasing of ${}^{75}\mathrm{K}$ with increasing temperature, which is also confirmed by bulk susceptibility measurement [22]. Both Knight shifts below $T^{*}$ follow a same temperature-dependent behavior, which is also confirmed by the ${}^{133}\mathrm{K}\text{−}{}^{75}\mathrm{K}$ plot in the inset. (b) Temperature-dependent nuclei spin-lattice relaxation for both ${}^{75}\mathrm{As}$ and ${}^{133}\mathrm{Cs}$ nuclei. The blue triangles represent the nuclei spin-lattice relaxation of ${}^{133}\mathrm{Cs}$ nuclei. The red squares represents the nuclei spin-lattice relaxation of ${}^{75}\mathrm{As}$. Both nuclei spin-lattice relaxation below $T^{*}$ follow a same power-law behavior, which is also confirmed by the $\frac{1}{{}^{133}{T}_1}\text{−}\frac{1}{{}^{75}{T}_1}$ plot in the inset. The fitting formula of spin-lattice relaxation decay is $I\left(t\right)=I_0+I_1(0.1e^{-{\left(\frac{t}{T_1}\right)}^r}+0.9e^{-{\left(\frac{6t}{T_1}\right)}^r})$ for ${}^{75}\mathrm{As}$ nuclei and $I\left(t\right)=I_0+I_1{e}^{-{\left(\frac{t}{T_1}\right)}^r}$ for ${}^{133}\mathrm{Cs}$ nuclei.

Figure 3

(a) Schematic phase diagram of Fe-based superconductors tuned by on-site Coulomb repulsion $U$ and Hund's coupling $J_H$ [16, 17]. When both of $U$ and $J_H$ are small, the system is a normal metal. When $J_H$ is moderate but $U$ is enough large, the system will enter into Mott insulating phase. When $J_H$ become enough large, an orbital-selective Mott phase will replace the Mott insulating phase in the phase diagram. (b) Illustration of microscopic picture for the incoherent-to-coherent crossover. At high temperature, the system behaves as an orbital-selective Mott phase with both localized and itinerant $3d$ electrons. Below $T^{*}$, the system enters into a Kondo liquid state, in which all $3d$ electrons become coherent through Kondo-type coupling.