Signatures of coupling between spin waves and Dirac fermions in ${\mathrm{YbMnBi}}_2$

We present inelastic neutron scattering measurements of magnetic excitations in ${\mathrm{YbMnBi}}_2$, which reveal features consistent with a direct coupling of magnetic excitations to Dirac fermions. In contrast with the large broadening of magnetic spectra observed in antiferromagnetic metals such as the iron pnictides, here the spin waves exhibit a small but resolvable intrinsic width, consistent with our theoretical analysis. The subtle manifestation of spin-fermion coupling is a consequence of the Dirac nature of the conduction electrons, including the vanishing density of states near the Dirac points. Accounting for the Dirac fermion dispersion specific to ${\mathrm{YbMnBi}}_2$ leads to particular signatures, such as the nearly wave-vector-independent damping observed in the experiment.

Figure 1

Spin waves in ${\mathrm{YbMnBi}}_2$ at $T=4$ K. (a)–(c) INS spectra showing dispersion along the $\left[H,0,0\right]$ direction measured with incident energies $E_{\mathrm{i}}=35$, 100, and 200 meV, respectively. The dashed line in (a) indicates the spin gap $\mathrm{\Delta }$ (cf. Table 1 and Fig. S6). (d)–(f) INS spectra calculated using spin-wave dispersion and Eqs. (1) and (2), with the best fit parameters listed in Table 1. Intensity scales shown in the color bars are in arbitrary units, which differ for different $E_{\mathrm{i}}$.

Figure 2

INS spectra measured on ${\mathrm{YbMnBi}}_2$ with $E_{\mathrm{i}}=100$ meV at $T=320$, 270, 150, and 4 K, illustrating the spin-wave dispersions along two symmetry directions, (a)–(d) $\left[H,0,0\right]$ and (i)–(l) $\left[0,0,L\right]$. (e)–(h) and (m)–(p) INS spectra calculated using Eqs. (1) and (2) for the same wave vectors as the data, using the results of fits given in Table 1, and corrected for the instrument resolution (see Ref. [21] for details).

Figure 3

(a)–(d) The damping parameter $\gamma$ (magenta solid circles with white error bars) obtained from fitting 1D energy cuts using DHO response, and the low-energy part of spin-wave dispersion at $T=4$, 150, 270, and 320 K, respectively. Black circles show the corresponding spin-wave energy $E_{\mathbf{q}}$ which was fitted for all temperatures. White circles illustrate the dispersion obtained using the parameters in Table 1 for the corresponding temperature. The underdamped spin wave exists where $E_{\mathbf{q}}>\gamma /2$. (e)–(h) Open circles are fitted values from 1D data and magenta dashed lines are for 2D data given in Table 1. Error bars show one standard deviation.

Figure 4

(a) The Fermi surface resulting from the anisotropic Dirac cones and a shift of the crossing away from the Fermi surface. The Dirac cones are rotated with respect to each other as sketched to the right. The centers of the ${\mathbf{p}}_{+}$ and ${\mathbf{p}}_{-}$ cones are connected by the antiferromagnetic wave vector ${\mathbf{Q}}_{\mathrm{AFM}}=(\pi ,0)$. (b) Diagrammatic representation of the leading correction to the spin susceptibility through coupling to the Dirac electrons. Solid lines are Dirac propagators, and dashed lines are spin waves. (c) The polarization $\mathrm{Im}\mathrm{\Pi }(E,{\overline{q}}_1,{\overline{q}}_2)$ obtained by numerical integration for an energy $E>\sqrt{2}{v}_{\parallel }q$ and $v_{\parallel }/v_{\perp }=0.005$ as a function of ${\overline{q}}_i=v_{\perp }{q}_i$.