Figure 1

(a) Absorption coefficient, $\alpha$($\omega$), of $\alpha$-Fe${}_2$O${}_3$ in the range of on-site Fe${}^{3+}$ d-d excitations at 300 and 4.2 K. Inset: rhombohedral lattice[27] and low temperature four sublattice spin structure.[18] (b) Close up view of the fine structure on the leading edge of the ${}^6{A}_{1g}$ $\to$ ${}^4{T}_{1g}$ on-site excitation at 4.2 K in the $\alpha$, $\sigma$, and $\pi$ polarizations. Inset: close-up view of the excitons. (c) Comparison of the $\sigma$-polarized magnon sideband absorption spectrum with the calculated density of states. Inset: Calculated magnon density of states using optimized exchange constants $J_1=7.6$ K, $J_2=2.0$ K, $J_3=-27.7$ K, and $J_4=-22.2$ K.[28] The frequency channel width was taken to be 1 cm${}^{-1}$. The nature of the critical points in Brillouin zone are indicated.[29] (d) Temperature dependence of $E1$ ($\pi$) exciton and magnon sideband (MS1, $\alpha$) peak positions, expressed as the ratio of $\frac{{\omega }_e\left(T\right)}{{\omega }_e\left(0\right)}$ and $\frac{{\omega }_m\left(T\right)}{{\omega }_m\left(0\right)}$, respectively. The latter compares well with the calculated sublattice magnetization[11, 30] using the same exchange constants listed above. Inset: $\alpha$($\omega$) of the $\sigma$-polarized magnon sideband at different temperatures.Reuse & Permissions

Figure 2

(a) Absorption difference spectra [$\alpha$(B) - $\alpha$(B $=$ 0 T)] of $\alpha$-Fe${}_2$O${}_3$ at 4.2 K for the $\alpha$-polarization and B $\parallel$ [111] at selected magnetic fields: 5, 10, 15, 35 T. The corresponding low temperature zero field absorption spectrum is shown as a blue solid curve for comparison. Inset: oscillator strength change in the range of the magnon sideband and ${}^6{A}_{1g}$ $\to$ ${}^4{T}_{1g}$ on-site excitation as a function of magnetic field. (b, c) Close-up view of the excitons and magnon sideband at selected fields. (d) Peak position vs. magnetic field for the exciton and magnon sideband features. Error bars of these positions are smaller than the symbol size and not shown.Reuse & Permissions

Figure 3

(a) Schematic view of the high temperature[18]/field magnetic structure of $\alpha$-Fe${}_2$O${}_3$. The $C2$ rotational axis is indicated. (b) View of the magnetic ordering pattern looking down the [111] axis showing only the Fe centers. Blue arrows denote the collinear spin arrangement, and purple arrows schematically show the noncollinear state. The canting angle is on the order of $\sim$10${}^{-4}$ degrees and arises due to Dzyaloshinskii-Moriya interactions.[19, 20] Canting induces a weak ferromagnetic moment ${\mathrm{M}}_{\mathrm{weak}}$ along the direction of the $C2$ rotational axis (red arrow). This symmetry is clarified on the central Fe site, where the spin vector on the site of interest is shown along with that on the site below.Reuse & Permissions