How Correlations and Spin–Orbit Coupling Work within Extended Orbitals of Transition-Metal Tetrahedra of 4d/5d Lacunar Spinels

Abstract

Spin–orbit quartet ground states are associated with rich phenomenology, ranging from multipolar phases in f1 rare-earth borides to magnetism emerging through covalency and vibronic couplings in d1 transition-metal compounds. The latter effect has been studied since the 1960s on t2g 1 octahedral ML 6 units in both molecular complexes and extended solid-state lattices. Here we analyze the J eff = 3/2 quartet ground state of larger cubane-like M 4 L 4 entities in lacunar spinels, composed of transition-metal (M) tetrahedra caged by chalcogenide ligands (L). These represent a unique platform where spin–orbit coupling acts on molecular-like, delocalized t2 orbitals. Using quantum chemical methods, we pin down the interplay of spin–orbit couplings in such a setting and many-body physics related to other molecular-like single-electron levels, both below and above the reference t2 1. We provide a different interpretation of resonant inelastic X-ray scattering data on GaTa4Se8 and, by comparing magnetic susceptibility data with calculated g factors, valuable insights into the important role of vibronic couplings.

Dressed jeff-1/2 objects in mixed-valence lacunar spinel molybdates

“…For such a CAS(5e,3o), which only incorporates the (… a 1 2 e 4 ) t 2 5 configuration, the j eff = 3/2 quartet is split by 100 meV from the j eff = 1/2 ground-state term, yielding a SOC constant . This value lies close to the SOC constant estimated for the (… a 1 2 e 4 ) t 2 1 compound GaNb 4 Se 8 , 18 . Compared to a Mo + single-ion value 10 , the SOC parameter is lower in GaMo 4 Se 8 , due to the more delocalized character of lacunar-spinel t 2 electrons – those orbit in lacunar spinels a four-site unit, not a single TM ion.…”

“…For insights into the correlated electronic structure of Mo 4 13+ units in GaMo 4 S 8 and GaMo 4 Se 8 , we adopt the embedded-cluster quantum chemical approach described in Ref. 18 and the lattice parameters and atomic positions determined by Powell et al . for GaMo 4 S 8 20 and Routledge et al .…”

“…Since the t 2 levels come at higher energy as compared to the a 1 and e components, the basic single-tetrahedron electronic structure in GaMo 4 X 8 would then imply filled a 1 and e states and one hole within the t 2 sector. However, given the results of state-of-the-art quantum chemical calculations on related "clustered" compounds, both d- [15][16][17][18] and p-electron 19 based, there are reasons to believe that the picture presently put forward for the single-tetramer electronic structure in GaMo 4 X 8 is somewhat too sketchy.…”

“…For insights into the correlated electronic structure of Mo 4 13+ units in GaMo 4 S 8 and GaMo 4 Se 8 , we adopt the embedded-cluster quantum chemical approach described in Ref. 18 and the lattice parameters and atomic positions determined by Powell et al for GaMo 4 S 8 20 and Routledge et al for GaMo 4 Se 8 21 . An [Mo 4 X 16 ] 19cluster was in each case embedded within a large array of point charges created with the Ewald program 22,23 ; capped effective core potentials (cECPs) were assigned to the 98 closest atoms.…”

Quantum chemical insights into hexaboride electronic structures: correlations within the boron p-orbital subsystem

“…While strong correlation effects within a whole manifold of electron configurations were already pointed out for the case of d-ion clusters [37][38][39][40][41], we here describe similar physics occurring on p-electron octahedral clusters as found in M B 6 hexaborides. In particular, we highlight the role of correlation effects on B 6 octahedral units.…”