What it does
An altermagnet is a magnet whose up and down spins cancel, like an antiferromagnet, yet whose electron bands are split by spin, as in a ferromagnet. The splitting changes sign around the Brillouin zone: up spins sit higher for electrons moving one way and lower for electrons moving at 90° to it. The Altermagnet checker tells you whether a crystal’s symmetry allows this. This explorer shows what it looks like, using the simplest models that have it.
You get four pictures:
- Bands along the path Y–Γ–X–M–Γ, spin up solid and spin down dashed. Along Γ–X and Γ–Y the spins split in opposite ways; along Γ–M they lie on top of each other.
- Fermi contours: the shape of the filled states at the Fermi level for each spin. The two shapes are rotated copies of each other.
- A splitting map of E↑ − E↓ over the whole zone, showing the d-wave (four lobes) or g-wave (eight lobes) pattern.
- The spin-resolved density of states, identical for both spins, which is why there is no net magnetisation.
How to use it
- Pick the two-sublattice model (the physical picture) or the one-band model (the splitting form written in directly).
- In the two-sublattice model, ta and tb set how easily each sublattice’s electrons hop along x and y. Atoms on sublattice A prefer one axis and atoms on B the other. t1 links the two sublattices.
- J is the exchange splitting from the local moments; μ moves the Fermi level, filling more or fewer states.
- Change one value at a time and watch the bands and contours respond.
Things to try
- Set ta = tb. The sublattices become alike apart from their spins, a translation can now swap them, and the splitting vanishes: a plain antiferromagnet.
- Set J = 0. No magnetism, no splitting.
- In the one-band model, switch from d-wave to g-wave: the nodes (lines of zero splitting) double from two to four.
- Raise μ to see the Fermi contours grow and change shape.
Worked example
With the default made-up values (t1 = 1, ta = 0.3, tb = −0.1, J = 0.8, μ = 0.2), the largest splitting is 1.6, that is 2J, at the zone edge points X and Y. At X the spin-up bands are at −1.8 and 1.4 while the spin-down bands meet near −0.2. At Γ and everywhere along kx = ±ky the two spins have the same energy. Each spin holds 1.007 electrons per cell, so the net moment is zero.
FAQ
Is this a real material? No. These are teaching models with made-up numbers. Real altermagnets such as RuO₂-type rutiles or MnTe need first-principles calculations, and their measured splittings are the subject of current research.
Why is there no spin-orbit coupling? Altermagnetism is defined without it: the spin splitting comes from the exchange field and the crystal’s symmetry alone. Spin-orbit coupling adds smaller effects such as the anomalous Hall effect.
What does the splitting do? It lets a current carry spin without a net magnetisation (a spin-splitter effect) and gives large magnetoresistance in tunnel junctions, which is why altermagnets are studied for fast, robust memory devices.
Where the numbers come from
- Model: a standard two-sublattice tight-binding model on a square lattice, in which the two spin sublattices have opposite hopping anisotropy and are related only by a 90° rotation, as used to introduce altermagnetism in the literature since 2022. The equations are written out and solved by fibub; no paper's figures or fitted parameters are reproduced.
- One-band forms cos kx − cos ky, sin kx sin ky and sin kx sin ky (cos kx − cos ky): the lowest lattice harmonics of d- and g-wave symmetry on a square lattice (textbook group theory).
- All parameters are made-up model values in units of the hopping, not measured materials. Eigenvalues are checked against NumPy in the tests.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.