A new class of altermagnetic materials has been added to usual ferro- and antiferro- magnetic classes by extending the concept of spin-momentum locking  to the case of weak spin-orbit coupling, i.e. to the non-relativistic groups of magnetic symmetry. For altermagnetics, the small net magnetization is accompanied by alternating spin-momentum locking in the k-space, so the unusual spin splitting is predicted.

For example, RuO2 altermagnet consists of two spin sublattices with orthogonal spin directions. In the k-space, the up-polarized subband can be obtained by π/2 rotation of the down-polarized subband, so RuO2 altermagnet is characterized by d-wave order parameter. Experimental  investigations can be conveniently performed for MnTe altermagnetic candidate, which is characterized by accessible (2–3 T) magnetic field range in contrast to RuO2 altermagnetic.

For some altermagnetic candidates,  anomalous Hall effect (AHE) has been experimentally demonstrated in a few early experiments,  despite of the expected zero non-relativistic net magnetization. It has been  argued theoretically, that the spontaneous nature of the AHE still requires relativistic spin-orbit interaction. Thus, inconsistency between the expected zero non-relativistic net magnetization and ambiguous experimental behavior requires comprehensive magnetization measurements in altermagnetics in wide temperature and magnetic field ranges.

Here, we experimentally study magnetization reversal curves for MnTe single crystals, which is the altermagnetic candidate.  Below 85 K, we observe the sophisticated angle dependence of magnetization M(α)  with beating pattern as the interplay between M (α) maxima and minima in the external magnetic field. This angle dependence is the most striking result of our experiment, while it cannot be expected for standard magnetic systems. We claim that our experiment shows the effect of weak spin-orbit coupling in MnTe, with crossover from relativistic to non-relativistic net magnetization, and, therefore, we experimentally confirm altermagnetism in MnTe.

Crossover from ferromagnetic to antiferromagnetic behavior shown as M(α) curves in different  magnetic fields. In low fields (around 0.2 kOe), M(α) shows ferromagnetic-like 180◦ periodicity. At high magnetic fields (around 15 kOe), the periodicity is changed to the antiferromagnetic 90◦ one. For the intermediate fields (around 6 kOe), one can see interplay between the maxima and the minima in M(α) curves.

Orlova N.N., Avakyants A.A., Timonina A.V., Kolesnikov N.N., Deviatov E.V.,
JETP Letters 120, issue 5 (2024)