Orbital Effects in Solids: Basics, Recent Progress, and Opportunities

Quantum materials with strong spin–orbit coupling: challenges and opportunities for materials chemists

“…Figures reprinted/adapted with permission from (a) Nature 7 , © 2018; (b) 8 (c) 9 (d) 10 American Chemical Society, © 2013, 2019, 2017. gular momentum L of the electrons, which is expressed in terms of a new quantum number J that redefines the energy levels of the electrons. 11 Spin-orbit coupling perturbs the wavefunctions of the electrons under its influence and the magnetic forces acting on them, affecting their spatial distributions and magnetic moments. We will discuss it in the context of its effect on the magnetic and electronic states of transition metal compounds, which strengthens on moving from 3d to 4d and 5d systems.…”

“…12,13 For 4d and 5d species, orbital effects are even more significant. The crystal field splitting ∆ O (the lifting of the degeneracy of the valence d orbitals of an ion in a perfect octahedral coordination environment) becomes larger, 11 increasing from 1.5-2 eV in 3d oxides to 2.5-3 eV and 3-4 eV in 4d and 5d oxides, respectively -hence the valence electrons in the latter two almost exclusively adopt a low-spin configuration. However, the spin-orbit coupling experienced by those electrons increases even more significantly, having a dependence on the atomic number Z between Z 2 and Z 4 , 14 and the spin-orbit coupling constant λ SO increases from 0.02-0.07 eV for 3d species to 0.1-0.2 eV for 4d species and 0.3-0.5eV for 5d ones.…”

“…However, the spin-orbit coupling experienced by those electrons increases even more significantly, having a dependence on the atomic number Z between Z 2 and Z 4 , 14 and the spin-orbit coupling constant λ SO increases from 0.02-0.07 eV for 3d species to 0.1-0.2 eV for 4d species and 0.3-0.5eV for 5d ones. 11 Consequently it can become large enough to be comparable to other energy scales, such as additional splitting of the t 2g orbitals induced by distortions of the coordination octahedron, and can therefore play a pivotal role in determining the electronic ground state. 11,[15][16][17] As such, materials featuring 4d or 5d transition metal cations with t 1 2g , t 2 2g , t 4 2g or t 5 2g electron configurations, such as Ir 4+ and Ru 3+ , are sought after as hosts for the exotic electronic states that can result from strong spin-orbit coupling.…”

“…11 Consequently it can become large enough to be comparable to other energy scales, such as additional splitting of the t 2g orbitals induced by distortions of the coordination octahedron, and can therefore play a pivotal role in determining the electronic ground state. 11,[15][16][17] As such, materials featuring 4d or 5d transition metal cations with t 1 2g , t 2 2g , t 4 2g or t 5 2g electron configurations, such as Ir 4+ and Ru 3+ , are sought after as hosts for the exotic electronic states that can result from strong spin-orbit coupling. It is worth noting that many of the materials in which such states have been found have actually been known for decades, 18 but the development of new theoretical frameworks and experimental probes was required before their electronic and magnetic properties could be properly described.…”

Na9Bi5Os3O24: A Diamagnetic Oxide Featuring a Pronouncedly Jahn–Teller‐Compressed Octahedral Coordination of Osmium(VI)

“…In anormal situation for asingle d electron or hole the decrease in one-electron energy due to JT effect is Àgd (where, d is distortion and g is the coupling constant);itcompetes with the elastic energy % Bd 2 /2, and this would result in JT distortions d = g/B and aJTenergy gain of E JT = Àg 2 /2 B. [13] Forthe lowspin state of d 2 configuration we of course lose Hunds coupling energy,but it can be readily seen that in this case the JT distortion is much stronger, d = 2 g/B,and the energy gain is 4t imes larger, E JT = À2 g 2 /B (the gain in the one-electron energy is in general Àgdn,where nisthe number of electrons at the lower orbital).…”