Covalency and vibronic couplings make a nonmagnetic j=3/2 ion magnetic

For 4d ¹ and 5d ¹ spin-orbit-coupled electron configurations, the notion of nonmagnetic j=3/2 quartet ground state discussed in classical textbooks is at odds with the observed variety of magnetic properties. Here we throw fresh light on the electronic structure of 4d ¹ and 5d ¹ ions in molybdenum- and osmium-based double-perovskite systems and reveal different kinds of on-site many-body physics in the two families of compounds: although the sizable magnetic moments and g-factors measured experimentally are due to both metal d-ligand p hybridisation and dynamic Jahn-Teller interactions for 4d electrons, it is essentially d-p covalency for the 5d ¹ configuration. These results highlight the subtle interplay of spin-orbit interactions, covalency and electron-lattice couplings as the major factor in deciding the nature of the magnetic ground states of 4d and 5d quantum materials. Cation charge imbalance in the double-perovskite structure is further shown to allow a fine tuning of the gap between the t _2g and e _g levels, an effect of much potential in the context of orbital engineering in oxide electronics.