Staggered Dzyaloshinskii-Moriya inducing weak ferromagnetism in centrosymmetric altermagnets and weak ferrimagnetism in noncentrosymmetric altermagnets

Abstract

The Dzyaloshinskii-Moriya interaction (DMI) has explained successfully the weak ferromagnetism in {\it some} centrosymmetric antiferromagnets. However, in the last years, it was generally claimed that the DMI is not effective in such systems. We reconciled these views by separating the conventional antiferromagnets from altermagnets. Altermagnets are collinear magnets having zero magnetization preserved by crystal symmetries in the non-relativistic limit. The spin-up and spin-down sublattices can be connected either by a proper rotation or by a combination of a rotation and a mirror or an inversion symmetry. Consequently, the system shows even-parity wave spin order in the k-space lifting the Kramer's degeneracy in the non-relativistic band structure leading to unconventional magnetism. The DMI can create weak ferromagnetism or weak ferrimagnetism in centrosymmetric and in noncentrosymmetric altermagnets while it is not effective in conventional antiferromagnets. Once the spin-orbit coupling is included in an altermagnetic system (where the time-reversal symmetry is broken), the components of spin moments of the two sublattices along the Néel vector are antiparallel but the other two spin components orthogonal to the Néel vector can be null, parallel or antiparallel. In cases where we have different bands showing parallel and antiparallel spin components at the same time, the magnetic order results in weak ferrimagnetism. If we restrain to high-symmetry directions for the Néel vector, we find weak ferrimagnetism only in the noncentrosymmetric compound MnSe among the examined cases.

19 pages, 12 figure

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• Dominant orbital magnetization in the prototypical altermagnet MnTe
• Non-linear anomalous Edelstein response at altermagnetic interfaces
• Tunability of the magnetic properties in Ni intercalated transition metal dichalcogenide NbSe${}_2$
• Design and theory of switchable linear magnetoelectricity by ferroelectricity in Type-I multiferroics
• Persistent spin textures, altermagnetism and charge-to-spin conversion in metallic chiral crystals TM${}_3$X${}_6$
• Epitaxial growth and transport properties of a metallic altermagnet CrSb on a GaAs (001) substrate
• Relativistic Spin-momentum locking in altermagnets
• Nature of field-induced transitions and hysteretic magnetoresistance in non-collinear antiferromagnet EuIn2As2
• Dirac edge states as signature of two-dimensional altermagnetic topological crystalline phase
• Theory of bound magnetic polarons in cubic and uniaxial antiferromagnets
• Sign competing sources of Berry curvature and anomalous Hall conductance humps in topological ferromagnets
• Quantum anomalous Hall conductivity in altermagnets under applied magnetic field
• Staggered Dzyaloshinskii-Moriya and canting angle in centrosymmetric altermagnetic and ferromagnetic phases: influence on the anomalous Hall effect and Weyl points
• Relativistic spin-momentum locking in ferromagnets
• Wurtzite MnSe as a barrier for CdSe quantum wells with built-in electric field
• Altermagnetism Induced Bogoliubov Fermi Surfaces Form Topological Superconductivity
• Altermagnetism from the viewpoint of chemistry