Neutron Spin Resonance in the Heavily Hole-Doped ${\mathrm{KFe}}_2{\mathrm{As}}_2$ Superconductor

We report high-resolution neutron scattering measurements of the low energy spin fluctuations of ${\mathrm{KFe}}_2{\mathrm{As}}_2$, the end member of the hole-doped ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ family with only hole pockets, above and below its superconducting transition temperature $T_c$ ($\sim 3.5\mathrm{K}$). Our data reveal clear spin fluctuations at the incommensurate wave vector ($0.5\pm \delta$, 0, $L$), ($\delta =0.2$) (1-Fe unit cell), which exhibit $L$-modulation peaking at $L=0.5$. Upon cooling to the superconducting state, the incommensurate spin fluctuations gradually open a spin gap and form a sharp spin resonance mode. The incommensurability ($2\delta =0.4$) of the resonance mode ($\sim 1.2\mathrm{meV}$) is considerably larger than the previously reported value ($2\delta \approx 0.32$) at higher energies ($\ge \sim 6\mathrm{meV}$). The determination of the momentum structure of spin fluctuation in the low energy limit allows a direct comparison with the realistic Fermi surface and superconducting gap structure. Our results point to an $s$-wave pairing with a reversed sign between the hole pockets near the zone center in ${\mathrm{KFe}}_2{\mathrm{As}}_2$.

Figure 1

(a) The schematic crystal structure of ${\mathrm{KFe}}_2{\mathrm{As}}_2$. The dashed lines represent the 1-Fe unit cell. (b) dc magnetic susceptibility measurements on the ${\mathrm{KFe}}_2{\mathrm{As}}_2$ single crystal. A sharp superconducting transition is observed at $T_c\sim 3.5\mathrm{K}$ in the zero-field-cooled (ZFC) measurement in a magnetic field of $H=10\mathrm{Oe}$. The screening is slightly larger than $-1$ because of the demagnetization effect. (c) Temperature dependence of the in-plane resistivity of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ single crystal. The inset shows data around $T_c$ on an enlarged scale.

Figure 2

Momentum dependence of the magnetic excitations. (a),(b) Constant energy scans below and above $T_c$ at $E=1.2\mathrm{meV}$ along $(H,0,0.5)$ direction and at $E=1.6\mathrm{meV}$ along $(H,0,0)$ direction, respectively. (c) Constant energy scan along the $(0.3,0,L)$ direction at $E=1.2\mathrm{meV}$ below $T_c$. The spin fluctuations exhibit $L$ modulation and are peaked at the half-integer positions. Solid lines are Lorentz fits to the data.

Figure 3

Energy dependence of spin excitations for ${\mathrm{KFe}}_2{\mathrm{As}}_2$. (a),(b) Constant-$\mathbf{Q}$ scans in the superconducting state ($T=0.47\mathrm{K}$) and normal state ($T=4.5\mathrm{K}$) for $\mathbf{Q}=(0.3,0,0.5)$ and $\mathbf{Q}=(0.3,0,0)$, respectively. For comparison, the background scattering measured at $\mathbf{Q}=(0.2,0,0.5)$ and (0.5,0,0.5) is also shown. (c),(d) Temperature difference plot shows clear spin resonance at $E=1.2\mathrm{meV}$ for $\mathbf{Q}=(0.3,0,0.5)$ and $E=1.6\mathrm{meV}$ for $\mathbf{Q}=(0.3,0,0)$, respectively. The horizontal bars indicate the instrument resolution ($\sim 0.12\mathrm{meV}$). The FWHM of the resonance peaks at $L=0.5$ and $L=0$ are $\sim 0.27$ and $\sim 0.51\mathrm{meV}$, respectively.

Figure 4

(a) Temperature dependence of the scattering intensity at $\mathbf{Q}=(0.3,0,0.5)$ with $E=1.2\mathrm{meV}$, which clearly shows a kink at $T_c$. The data show clearly order-parameter-like increase below $T_c$, a hallmark of the neutron spin resonance. The solid line is a guide to the eyes. (b) Schematic of the hole Fermi pockets in ${\mathrm{KFe}}_2{\mathrm{As}}_2$ in the Brillouin zone, inferred from de Haas–van Alphen and ARPES measurements [17, 27, 28]. The purple arrows indicate the interband scattering.