Spin Waves in Detwinned ${\mathrm{BaFe}}_2{\mathrm{As}}_2$

Understanding magnetic interactions in the parent compounds of high-temperature superconductors forms the basis for determining their role for the mechanism of superconductivity. For parent compounds of iron pnictide superconductors such as $A{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($A=\mathrm{Ba}$, Ca, Sr), although spin excitations have been mapped out throughout the entire Brillouin zone, the respective measurements were carried out on twinned samples and did not allow for a conclusive determination of the spin dynamics. Here we use inelastic neutron scattering to completely map out spin excitations of $\sim 100\%$ detwinned ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. By comparing observed spectra with theoretical calculations, we conclude that the spin excitations can be well described by an itinerant model when taking into account moderate electronic correlation effects.

Figure 1

Summary of neutron-scattering results and theoretical calculations of spin waves of detwinned ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. (a) Spin arrangement of ${\mathrm{Fe}}^{2+}$ in the FeAs plane and the definition of the effective magnetic exchange couplings $J_{1a}$, $J_{1b}$ and $J_2$. The pink area marks the AF unit cell of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. (b) Reciprocal space of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ with twin domains. The green and red dots mark the magnetic Bragg peak positions for twin domains. The pink rectangular area is the AF Brillouin zone. The black diamonds centered at (1,0) and (0,1) are the integration region for calculating energy-dependent local dynamic susceptibility. (c) Spin-wave dispersions of a detwinned ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ extracted from constant-energy cuts collected at $T=7\mathrm{K}$. The black curves are obtained from a Heisenberg model ($J_{1a}\text{−}{J}_{1b}\text{−}{J}_2$) fit of twinned ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ [13]. The background shows the spectral weight from the RPA calculation (renormalized with $z=0.7$) with $U=1.02/z\mathrm{eV}$ and $J=U/4$ [19]. (d) Energy-dependent local susceptibility ${\chi }^{\prime \prime }(E)$ for AF Brillouin zones at (1,0) and (0,1). The green and red dashed lines are spin-wave fits from a Heisenberg Hamiltonian obtained from a twinned sample (with arbitrary units) [13]. The green and red solid lines are from $\mathrm{MF}+\mathrm{RPA}$ calculations, which were multiplied by 2.8 for clear comparison. (e) Spin-wave anisotropy $\psi (E)$. The purple and black solid lines are calculated spin-wave anisotropy from the Heisenberg Hamiltonian and $\mathrm{MF}+\mathrm{RPA}$, respectively. The blue line is a guide for the eye of the experimental data. The vertical error bars in (c) and horizontal error bars in (d) and (e) mark the integrating energy ranges. The vertical error bar in (c) indicates a $1\sigma$ confidential interval for the fitting of the momentum position. The ones in (d) and (e) originate from the uncertainty of the scattered neutrons and the propagation of the uncertainty for the calculation of ${\chi }^{\prime \prime }(E)$ and $\psi$, respectively.

Figure 2

Projection of the magnetic scattering intensity ($(d^2\sigma /d\mathbf{\Omega }dE)(k_i/k_f)$) onto energy and momentum planes. (a)–(d) Magnon dispersions along the (a) $[1,K]$, (b) $[H,1]$, (c) $[H,0]$, and (d) $[0,K]$ directions measured with $E_i=81\mathrm{meV}$. These four directions are marked by red dashed lines in (h). (e)–(l) Constant-energy slices in the $[H,K]$ plane. (e) is measured with $E_i=30\mathrm{meV}$, (f),(g) with $E_i=81\mathrm{meV}$, (h)–(j) with $E_i=250\mathrm{meV}$, and (k),(l) with $E_i=450\mathrm{meV}$. All the data in this figure were collected at $T=7\mathrm{K}$.

Figure 3

Theoretical $\mathrm{MF}+\mathrm{RPA}$ calculations of the magnetic scattering intensity as shown in Fig. 2 with $U=1.02/z\mathrm{eV}$ and Hund’s coupling $J=0.255/z\mathrm{eV}$ ($z=0.7$). The intensity for magnetic scattering in this figure is obtained from ${\chi }^{\prime \prime }(\mathbf{q},\omega )$ calculated using $\mathrm{MF}+\mathrm{RPA}$, taking into account magnetic form factor, Bose factor, etc. [19]. To facilitate the comparison, the intensity from calculation was multiplied by a factor of 2.8.

Figure 4

Temperature and energy dependence of the nematic spin correlations of uniaxial-strained ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. (a) Temperature dependence of the spin-excitation anisotropy ($\psi$) between (1,0) and (0,1) for energy transfers of $10.6\pm 2.8$, $15.7\pm 2.3$, $61\pm 3$, and $97\pm 7\mathrm{meV}$. (b) $\psi$ as a function of energy transfer measured at various temperatures from 7 K to 197 K. The solid line marks the anisotropy for 7 K as shown in Fig. 1. The dashed lines in (a) and (b) are guides to the eye.