Spin excitation anisotropy in the optimally isovalent-doped superconductor ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right)}_2$

We use neutron polarization analysis to study spin excitation anisotropy in the optimally isovalent-doped superconductor ${\mathrm{BaFe}}_2$(${\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}$)${}_2$ ($T_c=30$ K). Different from optimally hole- and electron-doped ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, where there is a clear spin excitation anisotropy in the paramagnetic tetragonal state well above $T_c$, we find no spin excitation anisotropy for energies above 2 meV in the normal state of ${\mathrm{BaFe}}_2$(${\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}$)${}_2$. Upon entering the superconducting state, significant spin excitation anisotropy develops at the antiferromagnetic (AF) zone center ${\mathbf{Q}}_{\mathrm{AF}}=(1,0,L=\mathrm{odd})$, while the magnetic spectrum is isotropic at the zone boundary $\mathbf{Q}=(1,0,L=\mathrm{even})$. By comparing the temperature, wave vector, and polarization dependence of the spin excitation anisotropy in ${\mathrm{BaFe}}_2$(${\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}$)${}_2$ and hole-doped ${\mathrm{Ba}}_{0.67}{\mathrm{K}}_{0.33}{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($T_c=38$ K), we conclude that such anisotropy arises from spin-orbit coupling and is associated with the nearby AF order and superconductivity.

Figure 1

(a) Chemical (dotted line with the orthorhombic lattice parameters of $a,b$, and $c$) and magnetic (cyan area) unit cells of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ in the AF orthorhombic phase. The arrows depict the stripe magnetic structure with ordered moments aligned along the $a$ axis. (b) The reciprocal space of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, where orange dots indicate in-plane AF ordering wave vector (${\mathbf{Q}}_{\mathrm{AF}}$). The presence of a magnetic peak at $(0,\pm 1)$ is due to twinning. Magenta and blue arrows indicate spin excitations polarized along the in-plane longitudinal ($M_a$) and transverse ($M_b$) directions. (c) $[H,0,L]$ scattering plane used in this experiment. Cyan arrows indicate the measured $\mathbf{Q}$, the solid orange dots are the AF ZCs, and the orange circles are at the zone boundaries along the $c$ axis. Neutron polarization directions ($\alpha =x,y,z$) and deduced three components ($M_{a,b,c}$) of magnetic excitations are marked by colored arrows. The equations show the relationship of $M_{a,b,c}$ and ${\sigma }_{\alpha }^{\mathrm{NSF}}$ at different wave vectors. (d) The schematic electronic phase diagram of ${\mathrm{BaFe}}_2$(${\mathrm{As}}_{1-x}{\mathrm{P}}_x$)${}_2$ [45]. The black arrow marks ${\mathrm{BaFe}}_2$(${\mathrm{As}}_{0.70}{\mathrm{P}}_{0.30}$)${}_2$ in the phase diagram. No AF order is found at the ${\mathbf{Q}}_{\mathrm{AF}}=(1,0,3)$ position as shown in the inset.

Figure 2

Energy scans for the neutron SF channels under different neutron polarization directions, marked as ${\sigma }_{x,y,z}^{\mathrm{SF}}$, at $T=2$ K and $\mathbf{Q}=(1,0,L)$ for (a) $L=1$, (b) $L=5$, (d) $L=0$, (e) $L=2$; and (c) at 35 K with $\mathbf{Q}=(1,0,1)$. (f) The neutron SF scattering ${\sigma }_x^{\mathrm{SF}}$ at $T=2$ K with $L=1$, and 0.

Figure 3

The differences between ${\sigma }_x^{\mathrm{SF}}$ and ${\sigma }_{y,z}^{\mathrm{SF}}$ at different $\mathbf{Q}=(1,0,L)$ and temperatures. (a), (b) $L=1$. (c), (d) $L=5$. (e), (f) $L=0$. (g), (h) $L=2$. The solid lines are guides to the eye. The dashed and dashed-dotted lines in (b-d) are the solid lines in (a) and (b), respectively.

Figure 4

Temperature dependence of ${\sigma }_{x,y,z}^{\mathrm{SF}}$ at (a) $\mathbf{Q}(=1,0,1)$ and $E=6$ meV, (b) $\mathbf{Q}=(1,0,5)$ and $E=6$ meV, and (c) $\mathbf{Q}=(1,0,1)$ and $E=10$ meV. (d)–(f) show the corresponding $M_y$ and $M_z$. (g) The energy dependence $M_a,M_b$, and $M_c$ at $T=2$ K obtained using data in Figs. 2 and 2 [27]. The vertical dashed lines mark $T_c$. The solid lines are guides to the eye.