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The magnetic and electronic properties of Ba$_4$Ru$_3$O$_{10}$ wereinvestigated by the ab-initio and model calculations. It is shown thatnonmagnetic ground state of the one-third Ru$^{4+}$ ions is not due to thecorrelation effects. It is rather caused by the charge disproportionationbetween crystallographically different Ru and the molecular orbital formationin the Ru's trimer.

Unconventional magnetism as a consequence of the charge disproportionation and the molecular orbital formation in Ba4Ru3O10