Variation of charge dynamics upon antiferromagnetic transitions in the Dirac semimetal ${\mathrm{EuMnBi}}_2$

We have investigated the temperature- and field-variation of electronic state for the Dirac semimetal of ${\mathrm{EuMnBi}}_2$ by means of optical spectroscopy and theoretical calculation. The optical conductivity spectra show a clear Drude peak in the paramagnetic phase, which gradually diminishes in the Mn-$3d$ antiferromagnetic phase with decreasing temperature. Meanwhile, the absorption peaks due to the interband transition grow at low temperatures, resulting in a pseudogap feature with an energy scale of 0.07 eV. The analysis of Drude weight shows that the Drude response is nearly governed by the Dirac electrons at low temperatures. On the contrary, both the antiferromagnetic transition and spin reorientation of Eu-$4f$ moment do not significantly change the spectra except the moderate variation of Drude weight. As a comparison, we have also investigated the charge dynamics for ${\mathrm{EuZnBi}}_2$, which is an analog without the Mn-$3d$ antiferromagnetic ordering. In ${\mathrm{EuZnBi}}_2$, the optical conductivity spectra do not show the pseudogap structure, but show an intense Drude peak at all temperatures. Combined with the results of ab initio calculation, in ${\mathrm{EuMnBi}}_2$, it is likely that the reconstruction of electronic state driven by the Mn-$3d$ antiferromagnetic ordering causes the Dirac semimetallic state with tiny hole pockets, wherein electronic states other than the Dirac band are nearly gapped-out from the Fermi level.

Figure 1

The crystal and magnetic structure of ${\mathrm{EuMnBi}}_2$ (a) in the antiferromagnetic phase below $H_{\mathrm{f}}$ (=5.3 T) and (b) the spin-flopped phase above $H_{\mathrm{f}}$. The green (yellow) arrow denotes the Eu-$4f$ moment (Mn-$3d$ spin), respectively. The illustration is drawn by using VESTA [43]. (c) The resistivity along the $c$ axis (red) and that perpendicular to the $c$ axis (blue), respectively. The dashed (dotted) line denotes the antiferromagnetic transition temperature of Mn $3d$-spin (Eu-$4f$ moment), respectively. The resistivity shows a jump or kink at $T_{\mathrm{N}}\left(\mathrm{Eu}\right)$.

Figure 2

(a) Reflectivity spectra and (b) optical conductivity spectra of ${\mathrm{EuMnBi}}_2$ at 10 K for the polished sample and cleaved sample.

Figure 3

(a) The reflectivity and (b) optical conductivity $\sigma \left(\omega \right)$ spectra for ${\mathrm{EuMnBi}}_2$ measured with the light polarization perpendicular to the $c$ axis. The vertical dotted line denotes the energy of isosbestic point (0.094 eV). (c) The spectral intensity below the cut-off energy ${\omega }_c$ = 0.094 eV (circle) and 0.4 eV (triangle) and their difference $\mathrm{\Delta }{N}_{\mathrm{eff}}$. The dotted (dashed) line denotes the antiferromagnetic transition temperature of Eu-$4f$ moment (Mn-$3d$ spin), respectively.

Figure 4

(a) The fitting of optical conductivity spectra by the Drude-Lorentz model. The blue curve denotes the Drude response, and the green and yellow curves correspond to the absorption peak A and B, respectively. (b) The temperature dependence of Drude weight estimated from the Drude peak $N_{\mathrm{eff}}\left(\sigma \right)$ (circle) and plasma frequency $N_{\mathrm{eff}}\left({\omega }_p\right)$ (triangle). (c) The temperature dependence of width of Drude peak ${\gamma }_D$. (d) The loss function spectra Im[$-1/\epsilon \left(\omega \right)]$. Each spectrum is offset for clarity. The triangle denotes the peak of plasmon resonance. The dashed line is the fitting curve of plasmon resonance at 10 K (see also the Apendix).

Figure 5

(a) Temperature dependence of resistivity along the $c$ axis and that perpendicular to the $c$ axis. (b) The reflectivity spectra and (c) optical conductivity spectra at various temperatures. (d) The spectral intensity below the cut-off energy ${\omega }_c$ = 0.094 eV (circle) and 0.4 eV (triangle). The dotted line denotes the antiferromagnetic transition temperature of Eu-$4f$ moment.

Figure 6

First-principles band structure for (a) ${\mathrm{EuMnBi}}_2$ and (c) ${\mathrm{EuZnBi}}_2$. (Partial) density of states for ${\mathrm{EuMnBi}}_2$ and ${\mathrm{EuZnBi}}_2$ are shown in panels (b) and (d), respectively. The inset to (c) shows the illustration of the Brillouin zone and $k$ path.

Figure 7

(a) The reflectivity spectra measured at various magnetic fields along the $c$ axis and at 6 K. The triangle denotes the dip structure due to the plasma resonance. (b) The loss function spectra at 10 K under zero magnetic field. (c) The square of resonance energy (${\omega }_r^{*2}$) as a function of magnetic field. The vertical-dashed line represents the spin-flop transition of Eu-$4f$ moment ($H_f$). The dotted curve (hatched curve) denote the fitting results with the formula ${\omega }_r^2={\omega }_p^{2*}+{\omega }_c^2$ (the guide to eyes).