Theoretical evidence of spin-orbital-entangled $J_{\mathbf{eff}}$=1/2 state in the 3$d$ transition metal oxide CuAl$_2$O$_4$

TL;DR

This paper provides theoretical and experimental evidence that CuAl$_2$O$_4$, a 3$d$ transition metal oxide, hosts a $J_{eff}=1/2$ spin-orbital-entangled state, challenging the notion that such states are exclusive to heavier elements with stronger spin-orbit coupling.

Contribution

It demonstrates the existence of a $J_{eff}=1/2$ state in a 3$d$ oxide, supported by synthesis, DFT, and DMFT calculations, expanding the understanding of spin-orbital entanglement in transition metals.

Findings

CuAl$_2$O$_4$ exhibits a $J_{eff}=1/2$ Mott insulating state.

The $J_{eff}=1/2$ state persists despite competing orbital quenching.

Spectroscopic data align with the $j_{eff}$=1/2 hole state.

Abstract

Transition metal oxides exhibit various competing phases and exotic phenomena depending on how their reaction to the rich degeneracy of the $d$-orbital. Large spin-orbit coupling (SOC) reduces this degeneracy in a unique way by providing a spin-orbital-entangled ground state for 4$d$ and 5$d$ transition metal compounds. In particular, the spin-orbital-entangled Kramers doublet, known as the $J_{\mathbf{eff}}$=1/2 pseudospin, appears in layered iridates and $\alpha$-RuCl$_3$, manifesting a relativistic Mott insulating phase. Such entanglement, however, seems barely attainable in 3$d$ transition metal oxides, where the SOC is small and the orbital angular momentum is easily quenched. From experimental and theoretical evidence, here we report on the CuAl$_2$O$_4$ spinel as the first example of a $J_{\mathbf{eff}}$=1/2 Mott insulator in 3$d$ transition metal compounds. Based on the experimental study, including synthesis of the cubic CuAl$_2$O$_4$ single crystal, density functional theory and dynamical mean field theory calculations reveal that the $J_{\mathbf{eff}}$=1/2 state survives the competition with an orbital-momentum-quenched $S$=1/2 state. The electron-addition spectra probing unoccupied states are well described by the $j_{\mathbf{eff}}$=1/2 hole state, whereas electron-removal spectra have a rich multiplet structure. The fully relativistic entity found in CuAl$_2$O$_4$ provides new insight into the untapped regime where the spin-orbital-entangled Kramers pair coexists with strong electron correlation.