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Exact results for itinerant ferromagnetism in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:math>-orbital system on cubic and square lattices
We study itinerant ferromagnetism in a ${t}_{2g}$ multiorbital Hubbard system in the cubic lattice, which consists of three planar oriented orbital bands of ${d}_{xy},\phantom{\rule{0.16em}{0ex}}{d}_{yz}$, and ${d}_{zx}$. Electrons in each orbital band can only move within a two-dimensional plane in the three-dimensional lattice parallel to the corresponding orbital orientation. Electrons of …