Magnetic eightfold nodal-point and nodal-network fermions in MnB2

Realizing topological semimetal states with novel emergent fermions in magnetic materials is a focus of current research. Based on first-principles calculations and symmetry analysis, we reveal interesting magnetic emergent fermions in an existing material MnB₂. In the temperature range from 157 K to 760 K, MnB₂ is a collinear antiferromagnet. We find the coexistence of eightfold nodal points and nodal network close to the Fermi level, which are protected by the spin group in the absence of spin-orbit coupling. Depending on the N\'eel vector orientation, consideration of spin-orbit coupling will either open small gaps at these nodal features, or transform them into magnetic linear and quadratic Dirac points and nodal rings. Below 157 K, MnB₂ acquires weak ferromagnetism due to spin tilting. We predict that this transition is accompanied by a drastic change in anomalous Hall response, from zero above 157 K to ~2004pt0exΩ0.16em0excm^-1 below 157 K.