Orientation-dependent readout in a model altermagnetic junction
Can the orientation of a momentum-dependent spin splitting determine how a junction distinguishes two magnetic states? A simple transport model gives a direct answer. A 90° rotation reverses the readout, while a 45° rotation makes the two states indistinguishable. The cancellation follows from symmetry and is reproduced by the conductance calculation.
1. Model and observable
The model is deliberately minimal. Two magnetic electrodes couple through a single spin-independent resonant level, each electrode a pair of semi-infinite chains with an angular coordinate φ that labels independent transport channels. Both spin splittings take a d-wave form.
hR(φ, χ) = Δ cos[2(φ − χ)].
Here χ is the relative orientation of the two spin textures. This is distinct from the relative direction of their magnetic order. For each χ, the conductance is calculated with parallel (P) and antiparallel (AP) Néel vectors. Their electrical distinguishability is measured by
The conductance is obtained from the lead self-energies and the device Green function using the NEGF transmission formula. An isotropic ferromagnetic electrode with the same root-mean-square splitting, and a nonmagnetic electrode, serve as controls.
2. Numerical result
Select the resonant-level energy below. The left panel compares the three models. The right panel shows the two magnetic-state conductances in the d-wave model.
Resonant-level gate
Gate = 0 eV
37 orientations · 3 magnetic controls
Gate = 0.15 eV
37 orientations · 3 magnetic controls
Gate = 0.3 eV
37 orientations · 3 magnetic controls
Gate = 0.5 eV
37 orientations · 3 magnetic controls
Figure 1. Computed contrast and conductance versus texture orientation. The contrast axis is fixed across gates, while the conductance axis adapts to each gate. Conductance is spin-summed and normalized per angular channel.
At zero gate energy, the contrast changes from −1.5844% at χ = 0° to +1.5844% at χ = 90°. At χ = 45°, it vanishes to numerical precision. The matched ferromagnetic control has a similar initial contrast but no dependence on χ. Changing the gate can also reverse the sign of the readout.
3. Why the cancellation occurs
A 90° rotation changes the sign of the right-electrode splitting.
This exchanges the two magnetic configurations, giving GP(χ + π/2) = GAP(χ) and therefore C(χ + π/2) = −C(χ).
At χ = π/4, the right texture is Δ sin(2φ). Reflecting φ → −φ leaves the left texture unchanged and reverses the right one. Because the junction weights these reflected channels equally, the channel-averaged parallel and antiparallel conductances must coincide.
Within this model, the 45° cancellation follows from a symmetry of the transport channels. It does not require tuning the resonant-level energy to a particular value or assuming a weak-tunneling approximation.
4. Connection to magnetic fluctuations
I came at this from a different angle first. An earlier calculation of mine asked whether gate tuning could suppress the response to small Néel-vector fluctuations, and it did find a zero of the local angular curvature near 0.24 eV. But the same zero showed up in the ferromagnetic control, and it drifted whenever I changed the model parameters. So it was not telling me anything about altermagnets.
That failure motivated a sharper question. Could the momentum-dependent spin texture impose a relation on the readout itself, rather than on its curvature? This time the answer comes from an exact symmetry of the model, not a fitted gate value. The two cancellations are not the same thing. Vanishing curvature is a local response to small rotations, while C = 0 means the parallel and antiparallel states carry equal conductance. One does not imply the other.
5. Interpretation and scope
So the picture is simple. A momentum-dependent spin texture can set the polarity of magnetic-state readout and pin a single orientation where that readout vanishes. What makes it worth reporting is the chain it closes, from electrode symmetry, to a transport observable, to a numerical calculation that actually tests the analytical prediction.
The present calculation is an effective d-wave model. Rotating χ changes the spin texture, but it does not reconstruct an atomistic interface. Equal channel weighting and the absence of spin–orbit coupling or disorder are model assumptions. No material-specific Hamiltonian, switching dynamics or experimental signal-to-noise ratio is inferred from these curves.
Transport equations and numerical parameters
Gr = [E − H − ΣLr − ΣRr]−1
T = Tr[ΓLGrΓRGa]
Lead hopping t = 1 eV, contact hopping tc = 0.45 eV, splitting Δ = 0.5 eV, electronic kBT = 0.005 eV. The ferromagnetic control uses Δ/√2. Conductance integrates T against −∂f/∂E over ±12 kBT. The supplied refined dataset uses 257 energy points and 128 angular channels. The maximum contrast change from the coarser grid is 2.78 × 10−11.
Tabulated contrast
| Gate / eV | C at 0° | C at 45° | C at 90° |
|---|---|---|---|
| 0 | -1.5844% | +0.0000% | +1.5844% |
| 0.15 | -0.7298% | -0.0000% | +0.7298% |
| 0.3 | +0.4334% | +0.0000% | -0.4334% |
| 0.5 | +0.8996% | +0.0000% | -0.8996% |