LiOsO 3 is the first experimentally confirmed polar metal with ferroelectric-like distortion. One puzzling experimental fact is its paramagnetic state down to very low temperature with negligible magnetic moment, which is anomalous considering its 5d 3 electron configuration since other osmium oxides (e.g., NaOsO 3 ) with 5d 3 Os ions are magnetic. Here the magnetic and electronic properties of LiOsO 3 are re-investigated carefully using the first-principles density functional theory. The calculations reveal that the magnetic state of LiOsO 3 can be completely suppressed by the spin-orbit coupling. The subtle balance between significant spin-orbit coupling and weak Hubbard U of 5d electrons can explain both the nonmagnetic LiOsO 3 and magnetic NaOsO 3 . This work provides a reasonable understanding of the long-standing puzzle of magnetism in some osmium oxides.Correlated electron systems with appreciable Coulomb repulsion are one of the most attractive platforms for accessing a series of emerging physical properties such as metal-insulator transition (MIT), superconductivity, colossal magnetoresistance, multiferroicity, and so on, which are often technologically useful. Such a Coulomb repulsion is usually characterized by the on-site Hubbard U. On the other hand, spin-orbit coupling (SOC) in condensed matters is becoming highly concerned, evidenced within a lot of emergent quantum materials such as topological insulators, Weyl semi-metals, and Kitaev systems, [1][2][3][4] where SOC can be the core ingredient of physics underlying their novel physical phenomena. On one hand, SOC can be strong for heavy ions, and even comparable to U for 5d electrons. For example, SOC is believed to play a decisive role in determining the unconventional properties in those 5d 5 transition metal oxides, [5] such as the J eff ¼ 1/2 Mott state for iridates (Ir 4þ ). [6] On the other hand, the wavefunctions of 5d electrons are more extended than those of 3d and 4d electrons, which effectively reduces the on-site Coulomb repulsion U. Therefore, the competitive and/or cooperative effect of SOC plus Coulomb repulsion provide a unique playground for novel 5d electronic properties.Here we consider a specific 5d perovskite system: LiOsO 3 , which is known as the first experimentally confirmed polar metal with ferroelectric-like structural transition, [7] as predicted by Anderson and Blount. [8] Certainly, the major concern with such an unusual ferroelectric-like metallic state is not only the potential functionality but more importantly possible competition and coupling between the ferroelectricity and metallicity which are usually mutually exclusive.A well-known but yet unsolved puzzling issue of LiOsO 3 is its magnetic ground state. In LiOsO 3 , each Os ion is surrounded by an oxygen octahedron, which splits Os's 5d orbitals into the t 2g and e g sectors by the crystalline field. In the ideal limit, the three 5d electrons of Os 5þ ion will occupy the t 2g orbitals in the half filling manner. If the SOC effect is negligible, the half-filled...