Weak orbital ferromagnetism in altermagnets

A couple of years ago, a new type of magnetic material was introduced, called altermagnets, which are quantum material with both ferromagnetic and antiferromagnetic properties. In ferromagnetic materials, the magnetic moments on different atoms are spontaneously arranged in the same direction and parallel to each other and the material becomes magnetic. In antiferromagnetic materials, on the other hand, the atoms are arranged antiparallel and the material as a whole becomes non-magnetic.

Altermagnets have, just like antiferromagnets, antiparallel magnetic atoms, but differ from antiferromagnets in the crystal structure around the magnetic atoms. If the crystal structure was rotate, for example 180 degrees, around one of the magnetic atoms in an ordinary antiferromagnet, it would be the same structure as around the other magnetic atoms in the material. If, on the other hand, the crystal structure were rotated in the same way in an altermagnet, the rotated crystal structure would differ from the non-rotated one.

This rotational difference between altermagnets and antiferromagnets also implies a difference in energy between spin up and spin down for the electrons movement in altermagnets, while the energy for spin up and spin down in antiferromagnets is the same. The relation between electron spin and crystal structure makes altermagnets suitable quantum materials with very interesting properties for electrical quantum transport and also unconventional transport by spin waves.

Altermagnets also react to external magnetic fields in a similar way like ferromagnets, but weaker. However, the reason for this behaviour in altermagnets has so far remained unsolved.

Weak ferromagnetic materials were discovered 65 years ago and the physicists Dzyaloshinskii and Moriya introduced the Dzyaloshinskii-Moriya interaction, which could explain the emergence of weak ferromagnetism in various materials, but not in all altermagnets.

The origin of the Dzyaloshinskii-Moriya interaction is fundamentally unrelated to the defining property of altermagnets, both in terms of their antiferromagnetic properties, in how the atoms are arranged antiparallel, and in terms of the crystal structure rotation. In several altermagnets, the Dzyaloshinskii-Moriya interaction is also mathematically forbidden.

In an international collaboration, Daegeun Jo and Peter Oppeneer at Uppsala University, have now found an explanation for altermagnets weak ferromagnetic reactions to external magnetic fields.

The researchers have discovered that different orbital moments arise on atoms in altermagnets and also on ordinary antiferromagnets due to the crystal structure around the magnetic atoms, which do not cancel each other out and produce a weak orbital ferromagnetic response. The researchers were also able to calculate that the weak orbital response is larger than the previously known antisymmetric Dzyaloshinskii-Moriya spin response in quite a few materials. This may provide an alternative explanation for how weak ferromagnetism arises in altermagnets and even ordinary antiferromagnets.

"It is astonishing that sixty-five years after Dzyaloshinskii and Moriya, we have found another mechanism to explain weak ferromagnetism that could even be larger than the already established Dzyaloshinskii-Moriya interaction in several materials," says Daegeun Jo, post doc at the Department of Physics and Astronomy.

Camilla Thulin