Giant non-reciprocal band structure effect in a multiferroic material

TL;DR

This work reveals a giant, SOC-enabled non-reciprocal band structure effect in EuO when it is driven into a multiferroic phase, with pronounced k-dependent asymmetries in the top Eu 4f valence bands that are switchable by external fields. Using DFT+U with SOC and symmetry-based k·p reasoning, the authors show MF-I (M ⟂ P) hosts a strong NRBE across the Brillouin zone, while MF-II (M ∥ P) exhibits much weaker effects, and SOC is essential for the NRBE in MF-I. They then connect this band-structure feature to an extraordinarily large bulk photovoltaic response, dominated by the injection current under linearly polarized light, yielding current densities on the order of 100 mA/cm^2 at visible energies. The results suggest that giant NRBE and enhanced BPE could be general phenomena in multiferroics or magnetoelectrics, enabling cross-functional optoelectronic and spintronic applications.

Abstract

Multiferroic materials, characterized by the coexistence of ferroelectricity and ferromagnetism, may unveil band structures suggestive of complex phenomena and new functionalities. In this Letter, we analyze the band structure of EuO in its multiferroic phase. Using density functional theory calculations and detailed symmetry analysis, we reveal a previously overlooked non-reciprocal band structure effect, where the electronic energy bands exhibit asymmetry along opposite directions with respect to the special points in the Brillouin zone. This effect, which is enabled by spin-orbit coupling, is giant for the top valence Eu $4f$ bands, and can be switched by external electric or magnetic fields. Furthermore, this results in an enhanced bulk photovoltaic effect. Specifically, our predictions indicate the emergence of a large injection current response to linearly polarized light, resulting in a photoconductivity value several orders of magnitude higher than that reported in any other oxide material. Ultimately, this non-reciprocal band structure effect and the associated large bulk photovoltaic response may be general phenomena emerging not just in EuO but also in other multiferroics or magnetoelectrics, potentially providing new cross-functionalities.

Figures (13)

• Figure 1: Schematic crystal and band structures for the FM and MF systems with $\bm{M}$$\parallel$ or $\perp c$.
• Figure 2: Band structure of MF-I. (a) Top valence bands along $\overline{\mathrm{Y}}-\Gamma-\mathrm{Y}$. Continuous (dotted) lines correspond to ${\bm M}\parallel (-)\hat{x}$. Inset: linear-in-$k$ behavior of $\Delta \epsilon_n$. (b) Band structure around the X. (d) Brillouin zone. (e) Constant energy cut at $E-E_\mathrm{F}=-0.4$ eV in the $k_z=0$ plane without SOC. (f) Same as (e) with SOC, also showing the spin polarizations.
• Figure 3: Injection photoconductivity. (a) Schematic of the band velocity weight factor for MF-I. (b) $\eta_\mathrm{S}^{yyy}$ and $\eta_\mathrm{S}^{xyz}$ for MF-I and MF-II. (c) Integrand of $\eta^{yyy}$, corresponding to v-c electronic transitions in the $k_z=0$ plane of the BZ.
• Figure S1: Valence bands of the (a) FM-I, (b) FM-II, (c) MF-I, and (d) MF-II structures, which are depicted in Fig. 1 of the Letter.
• Figure S2: The band structure of MF-II is symmetric along lines parallel to $k_y$ and around the special points $\Gamma$ (a), X (b), and Z (c) in the BZ. In contrast, an asymmetry emerges along low-symmetry lines, such as T$-$X$-$T$'$ (e), where T represents the center of the $\Gamma$PS triangle in the BZ and T$'$ is its mirror counterpart with respect to X (d).