The recent identification of a new class of antiferromagnets represents a paradigm shift in quantum and topological materials physics [see, C. Autieri, New type of magnetism splits from convention, Nature 626, 482 (2024), and references cited therein]. Antiferromagnets exhibit zero net magnetization preserved by crystal symmetries in the non-relativistic limit. If, however, the spin-up and spin-down Néel sublattices are connected by rotational symmetries (proper or improper, symmorphic or nonsymmorphic), the time-reversal symmetry is broken, and a non-zero spin-splitting of bands can appear. Such systems, the so-called altermagnets, offer prospects for fast and energy efficient spintronic functionalities without stray-field coupling between magnetic cells.
Building on the expertise gained from pioneering studies of bulk altermagnets [1], MagTop’s researchers computationally searched for the presence of band spin-splittings at surfaces of three representative antiferromagnets belonging to the orthorhombic (LaMnO3), hexagonal (α-MnTe), and tetragonal (RuO2) space groups [2]. Furthermore, altermagnetism was predicted and examined for various 2D transition metal borides (Mbene), such as monolayers of a topological crystalline insulator Cr2BAl [3] and structures of two distinct monolayers (Janus materials), like Cr4B3N [4].
Figure 1 shows schematically examples of two surface antiferromagnetic configurations: one which is incompatible with altermagnetism, as surface net magnetization is non-zero, and one where altermagnetism, i.e., non-relativistic spin-splitting, in the absence of net magnetization, can be searched for.
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Figure 1.: Schematic representation of surface layers in antiferromagnets with a non-zero (a) and compensated (b) net magnetic moment. Brillouin zone with high-symmetry points for the tetragonal antiferromagnetic RuO2 (c). With subscripts 1 and 2, we indicate the two points in the k-space that have opposite non-relativistic spin-splitting, that are S1 and S2 in this example. We project the bulk Brillouin zone on the principal surfaces (100), (010) and (001). The projected high-symmetry points have an overline. Given the geometrical position of the k-points with opposite non-relativistic spin-splitting, the altermagnetic surface states survive on the (001) surface (colored in green). Adapted from ref. [2].
Looking at three principal surface orientations <100>, we found that for several cases two surfaces are blind to altermagnetism, while altermagnetism survives for one surface orientation (see Figure 1). We demonstrated qualitatively that an electric field orthogonal to the blind surface can activate the altermagnetism. Our results indicate, therefore, which surfaces or interfaces should show non-relativistic band spin-splitting in spin-resolved ARPES, and offer guidelines for designing novel spintronic applications [2].
Our ab initio investigation of the structural, electronic, magnetic, and topological properties of the Mbene Cr2BAl monolayer pointed to an altermagnetic ground state over a wide range of lattice parameter values [3]. In this configuration, Cr2BAl is a dx2−y2 altermagnet, showing non-relativistic spin-splitting in the band structure, with opposite splittings along Γ-X and Γ-Y and with degenerate bands along Γ-M. When the spin-orbit coupling is taken into account, the compound is an altermagnetic topological crystalline insulator with the splitting that produces a peak in the spin Hall conductivity and generates Dirac dispersions visible along the [100] surface.
Combining spin-resolved band structure and charge transport ab initio approaches, we proposed with Chinese co-workers a new altermagnet of Cr4B3N Janus bilayer, and predicted a giant magnetoresistance in tunnel junctions with Cr4B3N electrodes [4].
Altermagnets often show the anomalous Hall effect and non-zero magnetization, phenomena that allow the generation of non-dissipative currents as well as to probe and affect the Néel vector orientation – a critical asset for, e.g., tunneling magnetoresistance devices. MagTop researchers considered an altermagnetic hexagonal semiconductor α-MnTe, grown and studied experimentally also in Warsaw [e.g., Kluczyk et al., Phys. Rev. B 110, 155201 (2024)], and identified theoretically three possible origins of weak spontaneous magnetization below Néel temperature: the staggered Dzyaloshinskii-Moriya interaction [5,6], orbital magnetization[7], and bound magnetic polarons [8].
In altermagnets, exchange coupling between magnetic ion pairs contains a cross-product component, known as the Dzyaloshinskii–Moriya interaction (DMI), even in the absence of inversion asymmetry in the crystal structure, the case of α-MnTe. As shown in Figure 2, the DMI vector is staggered [5,6] (i.e., its direction alternates) but the resulting spin canting produces non-zero net magnetization of the order of 10-5 Bohr magneton per magnetic ion along the c axis [1], as experimentally observed in MnTe.
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Fig. 2: Canting of spins out of the x direction (a) by staggered DMI vectors D (b) results in non-zero spin magnetization along the c-axis in α-MnTe (a, b). Positive (red) and negative (blue) Sz components in valence band (c) (after ref. [5]).
However, non-zero Berry phase in altermagnetic systems results not only in the anomalous Hall effect but also in orbital magnetization. This magnetization is also oriented along the c-axis and its magnitude, according to our ab initio studies, is significantly greater than the spin counterpart [7].
An interesting aspect concerns the role of magnetic domains present in real samples. According to the aforementioned theories, magnetization changes sign with the reversal of the Néel vector direction, so that its value tends to zero in the multidomain case. So, in another MagTop’s work we studied the role played by bound magnetic polarons that consist of a carrier bound by an impurity or defect accompanied by a ferromagnetic spin cloud produced by sp-d exchange coupling [8]. Such a system behaves as a superparamagnetic particle, and shows hysteresis if magnetic anisotropy is sufficiently large, independently of the Néel vector direction.
[1] A. Fakhredine, R. M. Sattigeri, G. Cuono, C. Autieri, Interplay between altermagnetism and nonsymmorphic symmetries generating large anomalous Hall conductivity by semi-Dirac points induced anticrossings, Phys. Rev. B 108, 115138 (2023).
[2] R. M. Sattigeri, G. Cuono, C. Autieri, Altermagnetic surface states: towards the observation and utilization of altermagnetism in thin films, interfaces and topological materials, Nanoscale 15, 16998 (2023).
[3] R. M. Sattigeri, X. Gong, A. Fakhredine, C. Autieri, G. Cuono, Dirac edge states of two-dimensional altermagnetic topological crystalline insulators, arxiv:2506.10782.
[4] W. Sun, M. Wang, L. Sun, B. Sa, S. Dong, C. Autieri, Z. Chen, Altermagnetizing the FeSe-like two-dimensional materials and approaching to giant tunneling magnetoresistance with Janus Cr4BN(B2) MBene electrode, arXiv:2502.03165 (2025).
[5] C. Autieri, R. M. Sattigeri, G. Cuono and A. Fakhredine, Staggered Dzyaloshinskii-Moriya interaction inducing weak ferromagnetism in centrosymmetric altermagnets and weak ferrimagnetism in noncentrosymmetric altermagnets, Phys. Rev. B 111, 054442 (2025)
[6] C. Autieri, G. Cuono, D. Chakraborty, P. Gentile, and A. Black-Schaffer, Conditions for orbital-selective altermagnetism in Sr2RuO4: tight-binding model, similarities with cuprates and implications for the superconductivity, Phys. Rev. B 112, 014412 (2025)
[7] C. C. Ye, K. Tenzin, J. Slawińska and C. Autieri. Dominant orbital magnetization in the prototypical altermagnet MnTe. Preprint available at https://arxiv.org/abs/2505.08675
[8] D. Bugajewski, C. Autieri and T. Dietl, Theory of bound magnetic polarons in cubic and uniaxial antiferromagnets. Preprint available at https://arxiv.org/abs/2506.10208