Valleytronic and magneto-optical properties of Janus and conventional TiBrI / Cr I 3 and Ti X 2 / Cr I 3 ( X = Br , I ) heterostructures

We report magnetic proximity effect, valley splitting (VS), and magneto-optical properties of polar $(\mathrm{TiBrI}/\mathrm{Cr}{\mathrm{I}}_{3})$ and nonpolar ($\mathrm{Ti}{X}_{2}/\mathrm{Cr}{\mathrm{I}}_{3}$, $X=\mathrm{Br},\mathrm{I}$) magnetic van der Waals heterostructures. To properly handle many-body effects, the band structure and excitonic effects are considered on the same footing by carrying out first-principles calculations together with resolving the Bethe-Salpeter equation. We find that an atypical type-III band alignment leads to a sizable magnetic proximity effect as well as giant VS (126 meV). In addition, they can be largely tuned by the polarity of TiXY crystal structure and stacking configuration. Moreover, such a giant magnetic proximity effect drives a switch of spin-band (spin-up and spin-down) ordering of TiBrI, not only in the conduction band, but also surprisingly in the valence band in the vicinity of $K$ or $K$\ensuremath{'} points, which brings out a significant change in exciton emissions. Our results open an avenue for spintronics and nano-optics applications.