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The spin-orbit coupled double perovskite iridate Ba$_2$YIrO$_6$ with $d^4$occupancy of Ir is considered as a candidate material for a non-magnetic $J=0$ground state. The issue of existence of such a state in Ba$_2$YIrO$_6$ howeverhas opened up intense debates both in experimental and theoretical studies. Inthis study, we revisit the issue using \textit{ab-initio} density functionalcombined with dynamical mean-field theory to investigate the magneticproperties of Ba$_2$YIrO$_6$ down to zero temperature. To reach the groundstate, a recently developed impurity solver based on tensor-product statesworking directly at zero temperature is employed. We find that Ba$_2$YIrO$_6$has a small instantaneous non-zero magnetic moment, both at $T=0$ K as well asat room temperature. We did not observe any evidence of magnetic ordering, noteven at $T=0$ K. From the calculated local magnetic susceptibility we see thatthe quantum fluctuations are very strong and effective in screening theinstantaneous moments. This dynamical screening, together with frustrationeffects in the fcc lattice that can lead to almost degenerate magnetic groundstates, prevents any long-range ordering.

Small moments without long-range magnetic ordering in the zero-temperature ground state of the double-perovskite iridate Ba$_2$YIrO$_6$