We study self-energy effects induced by strong magnetic fluctuations in the paramagnetic phase of strongly correlated itinerant magnets within the density-functional theory combined with the dynamical mean-field theory ($\mathrm{DFT}+\mathrm{DMFT}$ approach) and its nonlocal extension. We show that both local and nonlocal magnetic correlations yield a splitting of the electronic spectrum in the paramagnetic phase, such that it closely resembles the DFT band structure in the ordered phase. We demonstrate these effects on $\alpha$-iron, half-metal ${\mathrm{CrO}}_2$, van der Waals material ${\mathrm{CrTe}}_2$, and altermagnet CrSb. Although the obtained split bands do not possess a certain spin projection, their splitting suppresses spectral weight at the Fermi level. Even when originating from local magnetic correlations, the splitting is strongly momentum dependent as a consequence of the orbital selectivity of nonquasiparticle states. The relative importance of nonlocal vs local correlations depends on the proximity to half filling of $d$ states: closer to half filling, the role of local correlations increases.

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• Altermagnetism
• Magnetic order
• Spin fluctuations
• Van Hove singularity
• Altermagnets
• Half-metals
• Paramagnets
• van der Waals systems
• DFT+DMFT
• Dynamical mean field theory