The extra energy needed to point a material’s magnetisation in a direction it does not prefer. In that preference is what keeps the magnetic order from falling apart.
Going deeper
Magnetic anisotropy is the energy cost of pointing the magnetisation away from the direction the crystal prefers. In two dimensions it is not a detail: it opens a gap in the spin-wave spectrum, and without that gap thermal fluctuations would destroy the magnetic order entirely.
Where the preference comes from
Exchange decides whether neighbouring moments align, but it says nothing about which direction they should point; on its own it is isotropic. The preference comes from , which ties the to the orbital motion and so to the crystal axes. In an magnet this appears as single-ion – the energy of a magnetic ion depends on the orientation of its moment relative to the ligands around it – and as between neighbours.
A second, usually weaker contribution is magnetostatic: the dipolar field of a thin film favours in-plane magnetisation. In CrI3 the heavy iodine ligands make the exchange itself anisotropic, and that, far more than the single-ion term, points the easy axis out of the plane.
Why 2D order depends on it
The forbids long-range order at finite temperature in a two-dimensional magnet with continuous symmetry, because of arbitrarily low energy are always excited. Anisotropy breaks that continuous symmetry: the spin-wave spectrum acquires a gap proportional to the anisotropy, so few magnons are excited at low temperature and order survives.
The practical consequence is a ranking. CrI3, strongly Ising-like, keeps order to 45 K as a , close to its bulk value. Cr2Ge2Te6, much more isotropic, loses order rapidly as it is thinned and needed a small applied field to stabilise it in the thinnest layers. CrSBr orders with an in-plane easy axis, and Fe3GeTe2 is a metallic magnet with strong out-of-plane anisotropy. The anisotropy, not the exchange strength, is what predicts which materials survive thinning.
Measuring and changing it
Anisotropy is measured by the field required to pull the magnetisation into a hard direction, by ferromagnetic resonance, or – most directly for a 2D magnet – from the spin-wave gap seen in or infrared spectroscopy. Calculations obtain it from the total-energy difference between magnetisation directions, a small number that demands careful convergence and a proper treatment of spin–orbit coupling.
It can also be engineered. changes the ligand field and with it the single-ion term; electric fields and change it in thin ; proximity to another layer or to a heavy metal adds interfacial anisotropy. Since the of a 2D magnet depends on the anisotropy, this is one of the more promising routes to raising it.
For specialists
The energy difference between magnetisation directions, arising from spin–orbit coupling and dipolar effects; it opens the spin-wave gap that allows 2D magnetic order.