A link between an electron’s – a tiny built-in magnet – and the way it moves. It is strongest in heavy atoms, and in some it is strong enough to split energy levels and make spin useful for devices.
Going deeper
Left: in the electron’s own frame the charged nucleus circles it, forming a current loop whose magnetic field acts on the electron’s spin – the origin of spin–orbit coupling. Right: in a TMDC monolayer this splits the top of the valence band at the K point into two bands with opposite spin, by about 150 meV in MoS2 and 450 meV in the heavier WSe2.
A relativistic effect you can measure in a crystal
An electron moving through the electric field of an atomic nucleus experiences, in its own reference frame, a magnetic field – because from the electron’s point of view it is the charged nucleus that moves. That magnetic field interacts with the electron’s spin, so the energy of a state depends on how spin and orbital motion are aligned. For hydrogen-like atoms the effect grows roughly as the fourth power of nuclear charge, which is why it is tiny in carbon and large in tungsten, bismuth or lead.
What it does in 2D materials
In a crystal, spin–orbit coupling splits bands that would otherwise hold both spin directions at the same energy. The effect is most striking in , whose symmetry lets the splitting appear at the : the valence band at K divides into two spin-polarised bands, about 150 meV apart in MoS2 and about 450 meV apart in WSe2. Because the K and K′ are related by time reversal, the spin order is opposite in the two valleys – , the basis of valley-selective optics and .
Strong spin–orbit coupling also drives in , produces the at surfaces and interfaces, and sets the that lets order at all.
Borrowing it from a neighbour
Graphene, built from light carbon, has spin–orbit coupling so weak that its predicted gap is far below anything measurable in ordinary devices – good for , useless for . Placing graphene on a TMDC changes that: its electrons pick up spin–orbit coupling from the neighbouring layer by proximity, with strengths many times the intrinsic value. Stacking thus lets spin–orbit coupling be added to a material that lacks it, and tuned by the choice and alignment of the neighbour.
For specialists
The relativistic interaction between an electron’s spin and its orbital motion, growing steeply with atomic number. In TMDC monolayers with broken inversion symmetry it splits the valence band by roughly 150–450 meV, producing spin–valley locking, and it underlies Ising superconductivity, topological gaps and magnetic anisotropy.