Spin excitations of the correlated semiconductor FeSi probed by THz radiation

By direct measurements of the complex optical conductivity $\sigma \left(\nu \right)$ of FeSi, we have discovered a broad absorption peak centered at frequency ${\nu }_0\left(4.2\mathrm{K}\right)\approx 32{\mathrm{cm}}^{-1}$ that develops at temperatures below 20 K. This feature is caused by spin-polaronic states formed in the middle of the gap in the electronic density of states. We observe the spin excitations between the electronic levels split by the exchange field of $H_e=34\pm 6$ T. Spin fluctuations are identified as the main factor determining the formation of the spin polarons and the rich magnetic phase diagram of FeSi.

Figure 1

THz spectra of (a) optical conductivity ${\sigma }_1$ and (b) dielectric function ${\epsilon }_1$ of FeSi calculated from (c) transmission Tr and (d) normalized phase shift $\varphi /\nu$ at $T=4.2$, 10, and 16.3 K (solid, open, and cross-centered symbols, respectively). The $\varphi \left(\nu \right)/\nu$(4.2 K) data are out of scale and not shown in (d). Solid lines present the results of the least-square fitting by Eq. (1) (a),(b) or by interferometric equations (c),(d). The error bars for the 4.2-K data in (a) and (b) are within the symbols.

Figure 2

THz conductivity ${\sigma }_1$($T$) of FeSi measured at $\nu =21$ cm${}^{-1}$ (1) in comparison with the dc conductivity ${\sigma }_{\mathrm{dc}}$($T$) of etched (2) and polished (3) samples. Activation asymptotics of ${\sigma }_{\mathrm{dc}}$ and the squared plasma frequency ${\nu }_{\mathrm{pl}}^2$ (4) ${\sigma }_{\mathrm{dc}}$,${\nu }_{\mathrm{pl}}^2\propto \exp (-E_{\mathrm{g}}/2k_{B}T)$ are shown by solid lines. The inset presents the difference $\Delta \sigma \left(T\right)={\sigma }_1\left(T\right)-{\sigma }_{\mathrm{dc}}$($T$). The arrow points to a kink on $\Delta$$\sigma$($T$) at $T^{*}\sim 8$ K.

Figure 3

Wide range optical conductivity ${\sigma }_1$ and dielectric function ${\epsilon }_1$ of FeSi at temperatures 4.2–300 K. The dashed lines represent the results of least-square fitting by Eq. (1). The ${\sigma }_{\mathrm{dc}}$ values are shown by open circles at zero frequency. The shaded area shows the THz resonance contribution at $T=4.2$ K with the parameters given in Table .

Figure 4

The scaling of ${\sigma }_1(\nu ,T=4.2\mathrm{K})$ data by the relations ${\left({\sigma }_1\nu \right)}^2\propto (h\nu -E_{\mathrm{dir}})$ and ${\left({\sigma }_1\nu \right)}^{0.5}\propto (h\nu \pm E_{\mathrm{ph}}-E_{\mathrm{ind}})$ used to determine the direct and indirect gaps (see text) (Ref. 24). The solid lines correspond to the least-squares fits. The proposed band structure of FeSi is sketched in the inset.