Anisotropic magnetic excitations of a frustrated bilinear-biquadratic spin model: Implications for spin waves of detwinned iron pnictides

Elucidating the nature of spin excitations is important to understanding the mechanism of superconductivity in the iron pnictides. Motivated by recent inelastic neutron scattering measurements in the nearly 100% detwinned ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, we study the spin dynamics of an $S=1$ frustrated bilinear-biquadratic Heisenberg model in the antiferromagnetic phase with wave vector $(\pi ,0)$. The biquadratic interactions are treated in a dynamical way using a flavor-wave theory in an $SU\left(3\right)$ representation. Besides the dipolar spin wave (magnon) excitations, the biquadratic interactions give rise to quadrupolar excitations at high energies. We find that the quadrupolar wave significantly influences, in an energy dependent way, the anisotropy between the spin excitation spectra along the $(\pi ,0)$ and $(0,\pi )$ directions in the wave vector space. Our theoretical results capture the essential behavior of the spin dynamics measured in the antiferromagnetic phase of the detwinned ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. More generally, our results underscore the importance of electron correlation effects for the microscopic physics of the iron pnictides.

Figure 1

(a) Reciprocal space of the detwinned ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ in the $(\pi ,0)$ AFM phase. The magnetic Bragg peak positions of the $(\pi ,0)$ magnetic order are marked as red dots. The integrated areas centered at $(\pi ,0)$ and $(0,\pi )$ in Eq. (22) are shown by red and green diamonds, respectively. (b) Dispersions of magnons (solid line) and quadrupolar wave (dashed line) of the bilinear-biquadratic model from the $SU\left(3\right)$ flavor-wave theory. See text for the model parameters. The dots with error bars show the measured dispersion data of a detwinned ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ at $T=7$ K, extracted from Ref. [48].

Figure 2

Constant energy cuts of the magnetic excitation spectrum in the wave vector space for the $(\pi ,0)$ AFM phase of the $J\text{−}K$ model [in (a)–(d)]. For comparison, the corresponding experimental results are shown in (e)–(h). The experimental plots are reproduced from Ref. [48].

Figure 3

(a) Comparison of the energy dependence for the local dynamical spin susceptibilities ${\chi }_{{\mathbf{Q}}_{1\left(2\right)}}$, as defined in Eq. (22), with ${\mathbf{Q}}_1=(\pi ,0)$ and ${\mathbf{Q}}_2=(0,\pi )$ respectively marked as (1,0) and (0,1), between the experimental data (symbols) and the $SU\left(3\right)$ flavor-wave theory results of the $J\text{−}K$ model (lines). (b) Comparison of the spin excitation anisotropy factor $\mathrm{\Psi }$ between the experimental data (symbols), the $SU\left(3\right)$ flavor-wave results of the $J\text{−}K$ model (black solid curve), and the $SU\left(2\right)$ spin-wave results of the $J_{1a}\text{−}{J}_{1b}\text{−}{J}_2$ model (pink dashed curve). The experimental data for ${\chi }_{{\mathbf{Q}}_{1\left(2\right)}}$ in (a) are from Ref. [48], from which the experimental data for $\mathrm{\Psi }$ in (b) are determined according to Eq. (23). The result (pink dashed curve) for $\mathrm{\Psi }$ from an $SU\left(2\right)$-based calculation of the $J_{1a}\text{−}{J}_{1b}\text{−}{J}_2$ model, shown in (b), is also from Ref. [48].

Figure 4

Energy dependence of the local susceptibilities ${\chi }^{″}$: comparing the experimental data (symbols), the $SU\left(3\right)$ flavor-wave theory of the $J\text{−}K$ model (solid lines), and the modified RPA results (dashed lines) in absolute units. The experimental data and the modified RPA results are from Ref. [48].