Magnetic anisotropy in hole-doped superconducting Ba${}_{0.67}$K${}_{0.33}$Fe${}_2$As${}_2$ probed by polarized inelastic neutron scattering

We use polarized inelastic neutron scattering (INS) to study spin excitations of optimally hole-doped superconductor Ba${}_{0.67}$K${}_{0.33}$Fe${}_2$As${}_2$ ($T_c=38$ K). In the normal state, the imaginary part of the dynamic susceptibility, ${\chi }^{\prime \prime }(Q,\omega )$, shows magnetic anisotropy for energies below $\sim$7 meV with $c$-axis polarized spin excitations larger than that of the in-plane component. Upon entering into the superconducting state, previous unpolarized INS experiments have shown that spin gaps at $\sim$5 and 0.75 meV open at wave vectors $Q=(0.5,0.5,0)$ and $(0.5,0.5,1)$, respectively, with a broad neutron spin resonance at $E_r=15$ meV. Our neutron polarization analysis reveals that the large difference in spin gaps is purely due to different spin gaps in the $c$ axis and in-plane polarized spin excitations, resulting in a resonance with different energy widths for the $c$-axis and in-plane spin excitations. The observation of spin anisotropy in both optimally electron- and hole-doped BaFe${}_2$As${}_2$ is due to their proximity to the AF ordered BaFe${}_2$As${}_2$ where spin anisotropy exists below $T_N$.

Figure 1

Neutron polarization analysis determined $c$-axis (${\chi }_c^{\prime \prime }\propto M_{001}$) and in-plane (${\chi }_{a/b}^{\prime \prime }\propto M_{110}$) components of spin excitations in Ba${}_{0.67}$K${}_{0.33}$Fe${}_2$As${}_2$ from raw SF constant-$Q$ scans at $\mathbf{Q}=(0.5,0.5,0)$ and and $(0.5,0.5,2)$. To extract $M_{001}$ and $M_{110}$, we use methods described in Ref. 23 and assume $M_{1\overline{1}0}=M_{110}$ in the tetragonal crystal. (a) Energy dependence of $M_{001}$ and $M_{110}$ at $T=45$ K. (b) Identical scans at $T=2$ K. (c) The solid and open circles show the temperature difference (2–45 K) for $M_{001}$ and $M_{110}$, respectively. (d) The sum of ${\sigma }_{xx}^{\mathrm{SF}}+{\sigma }_{yy}^{\mathrm{SF}}+{\sigma }_{zz}^{\mathrm{SF}}$ at 45 and 2 K. Since background scattering is not expected to change between these temperatures,[16] such a procedure will increase the statistics of magnetic scattering. The black data points are collected at $\mathbf{Q}=(0.5,0.5,0)$ with $k_f=2.66$ Å${}^{-1}$, while the red data points are at $\mathbf{Q}=(0.5,0.5,1)$ with $k_f=3.84$ Å${}^{-1}$. The solid and dashed lines are guided to the eyes.

Figure 2

Constant-$Q$ scans at $\mathbf{Q}=(0.5,0.5,1)$ below and above $T_c$. (a) Energy dependence of $M_{001}$ and $M_{110}$ at $T=45$ K and (b) at 2 K. The superconductivity-induced spin gaps are at $\le 2$ and 7 meV for $M_{001}$ and $M_{110}$, respectively. At resonance energy of $E_r=15$ meV, the scattering is isotropic. (c) The solid and open circles show the temperature difference (2$-$45 K) for $M_{001}$ and $M_{110}$, respectively. (d) The sum of ${\sigma }_{xx}^{\mathrm{SF}}+{\sigma }_{yy}^{\mathrm{SF}}+{\sigma }_{zz}^{\mathrm{SF}}$ at 45 and 2 K. The solid and dashed lines are guides to the eye.

Figure 3

Energy dependence of spin anisotropy as determined by the difference between $M_{001}-M_{110}$ for temperatures (a) 45 K and (b) 2 K at wave vector $\mathbf{Q}=(0.5,0.5,0)$ and $\mathbf{Q}=(0.5,0.5,2)$. Similar differences above (c) and below (d) $T_c$ at $\mathbf{Q}=(0.5,0.5,1)$. The energy width is broader in (d) compared with (b). The solid and dashed lines are guides to the eye.

Figure 4

Constant-energy scans along the $[H,H,0]$ and $[H,H,1]$ directions at an energy transfer of $E=4$ meV for different neutron polarization directions. (a) Neutron SF scattering cross sections ${\sigma }_{xx}^{\mathrm{SF}}$, ${\sigma }_{yy}^{\mathrm{SF}}$, and ${\sigma }_{zz}^{\mathrm{SF}}$ at 45 K along the $[H,H,0]$ direction. Similar scans along the $[H,H,1]$ direction at (b) 2 K and (c) 45 K. All data are obtained with $k_f=2.66{\AA }^{-1}$. The solid lines are fit by Gaussian.