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

We use inelastic neutron scattering to study the temperature and energy dependence of spin excitations in an optimally P-doped ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$ superconductor ($T_c=30$ K) throughout the Brillouin zone. In the undoped state, spin waves and paramagnetic spin excitations of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ stem from an antiferromagnetic (AF) ordering wave vector ${\mathbf{Q}}_{\text{AF}}=(\pm 1,0)$, and peak near the zone boundary at $(\pm 1,\pm 1)$ around 180 meV. Replacing 30% As by smaller P to induce superconductivity, low-energy spin excitations of ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$ form a resonance in the superconducting state and high-energy spin excitations now peak around 220 meV near $(\pm 1,\pm 1)$. These results are consistent with calculations from a combined density functional theory and dynamical mean field theory, and suggest that the decreased average pnictogen height in ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$ reduces the strength of electron correlations and increases the effective bandwidth of magnetic excitations.

Figure 1

(a) The crystal structure of ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right){}_2$. The purple, silvery, and blue balls indicate Fe, As/P, and Ba positions, respectively. (b), (c) Schematic diagrams of the FeAs tetrahedron, showing the average iron-pnictogen height decreased from 1.36 Å for ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ to 1.28 Å for ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$ [37]. (d) The energy dependence of $S(Q,E)$ of spin waves of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ along the $(1,K)$ direction (with integration of $H$ from 0.9 to 1.1 r.l.u.) after subtracting the background integrated from $1.8<H<2.2$ and from $-0.25<K<0.25$ r.l.u. with $E_i=450$ meV at $T=10$ K measured on MAPS [30]. (e) Identical projection for spin excitations of ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$ obtained on MAPS with $E_i=450$ meV. The negative scattering below $\sim 50$ meV is due to errors in background subtraction. Energy dependence of wave vector integrated [integration range is shown in the shaded box in the inset of (g)] dynamic susceptibility ${\chi }^{\prime \prime }\left(E\right)$ for (f) ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and (g) ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$. The vertical dashed lines in (d) and (e) show the wave vector integration range along the $[0,K]$ direction. (h) Energy dependence of the local dynamic spin susceptibility ${\chi }^{\prime \prime }\left(E\right)$ for ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ (solid cyan line) and ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$ below (solid red triangle and solid red line) and above (open purple circles) $T_c$ with corrected magnetic form factor. Dashed cyan and red lines are DFT+DMFT calculations for ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$, respectively.

Figure 2

(a), (b) Calculated Fermi surfaces of the $d_{xz},d_{yz}$, and $d_{xy}$ orbitals for ${\mathrm{BFe}}_2{\mathrm{As}}_2$ and ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$, respectively. (c), (d) The corresponding wave vector dependence of the low-energy ($E=25$ meV) spin excitations. The color bars represent the vanadium-normalized absolute spin-wave intensity in units of mbar/sr/meV/Fe. The temperature differences of constant-wave vector scans at (e) $\mathbf{Q}=(1,0,0)$ and (f) $(1,0,1)$ below (2 K) and above (42 K) $T_c$ obtained using the EIGER triple-axis spectrometer. The modulation of resonance (superconductivity-induced intensity gain) with $L$ is consistent with previous experiments [40]. Constant-energy slices of the spin excitations as a function of increasing energy (g) at 40 K and (h) 10 K. (i) Temperature difference between 10 and 40 K, showing clearly the intensity gain in the energy region of 8–11 meV.

Figure 3

Wave vector dependence of spin waves of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ at 7 K and spin excitations of ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$ at 10 K for energy transfers of (a), (k) $E=30\pm 5$ meV $[E_i=80$ meV and $\mathbf{q}=(H,K,3)]$; (b), (i) $E=50\pm 5$ meV $[{\mathit{E}}_i=250$ meV and $\mathbf{q}=(H,K,3)]$; (c), (m) $E=95\pm 5$ meV $[E_i=250$ meV and $\mathbf{q}=(H,K,5)]$; (d), (n) $E=157\pm 10$ meV $[{\mathit{E}}_i=450$ meV and $\mathbf{q}=(\mathit{H},\mathit{K},6)]$; (e), (o) $\mathit{E}=225\pm 10$ meV $[{\mathit{E}}_i=450$ meV and $\mathbf{q}=(\mathit{H},\mathit{K},9)]$. In all cases, the $\pm$ meV indicates the energy integration range. The red boxes in (d), (e), (n), and (o) indicate regions that contain nonduplicate data from fourfold symmetrizing of the raw data (meaning only the data within the red box are statistically significant, and data in other regions of reciprocal space are mirror images of the red box data). (f)–(j) and (p)–(t) Calculations of identical energy slices from the DFT+DMFT method [46].

Figure 4

(a) Calculated total dynamic magnetic structure factor $S(Q,E)$ for (a) ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and (b) ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{0.7}{\mathrm{P}}_{0.3}\right){}_2$ using DFT+DMFT. The solid red points in (b) are data from cuts to Fig. 3 and the solid line is the dispersion of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ from Ref. [30]. (c), (d) Calculated dynamic magnetic structure factors from the $d_{xy}\text{−}{d}_{xy}$ and $d_{yz}\text{−}{d}_{yz}$ intraorbital contributions, respectively.