arXiv subjects

Giuseppe Cuono

Publications and source records attributed to Giuseppe Cuono.

At least 19 recordsLinked to original sources

arXiv2026

Contemporary Insights into Electronic Structure and Microscopic Transport in Nodal-Line Semimetals

Topological semimetals have emerged as an important class of quantum materials with novel electronic responses and unconventional transport phenomena. Among them, nodal-line semimetals are distinguished by band crossings that extend along one-dimensional lines in momentum space rather than occurring at discrete points, forming closed loops, chains, or extended lines. The stability of these nodal structures is governed by crystalline symmetries such as mirror, spin-rotation, and nonsymmorphic operations, which give rise to characteristic topological invariants and surface states, including drumhead-like bands. In this review, we present a comprehensive overview of the theoretical framework and experimental realization of nodal-line semimetals, with particular emphasis on symmetry protection and the consequences of symmetry breaking. We discuss the classification of nodal-line structures, their evolution into other topological phases, and their signatures in electronic structure measurements and transport phenomena. Special attention is given to insights obtained from angle-resolved photoemission spectroscopy and related probes. By bringing together symmetry analysis, band topology, and experimental observations, this review aims to clarify the relationship between topology, magnetism, and measurable electronic responses in nodal-line semimetals. These considerations highlight their potential as a versatile platform for next-generation topological electronic functionalities and emergent quantum phenomena beyond conventional paradigms.

cond-mat.mtrl-sci↗

arXiv2026

Charge and spin photogalvanic effects in the p-wave magnet NiI2

NiI2 is an exotic van der Waals material in which a noncollinear spin spiral breaks spatial inversion symmetry without sizeable structural distortion, generating improper ferroelectric polarization, and stabilizing p-wave magnetic states with electron-volt-scale odd-parity spin splitting. Using first-principles calculations, here we establish that nonlinear optical transport can directly probe and separate these effects. Magnetically-induced inversion breaking associated with the spin spiral produces a photogalvanic shift current under linearly polarized light, with conductivities exceeding those of conventional ferroelectrics. In contrast, a large photogalvanic injection current under circularly polarized light originates from helicity-selective transitions between spin-split states at opposite crystal momenta, directly exposing the nonrelativistic p-wave spin texture. We further predict pure spin photocurrents whose flow direction exchanges with that of the charge current under linear and circular excitation. The ability to generate and control pure spin currents without accompanying charge currents makes NiI2 a promising material platform for all-optical spin injection in van der Waals heterostructures.

cond-mat.mtrl-sci↗

arXiv2026

Interplay between Relativistic Spin-Momentum Locking and Breaking of Inversion Symmetry: conditions for p-wave magnetism

We investigate the interplay between relativistic spin-momentum locking arising from altermagnetism and various forms of inversion symmetry breaking. Depending on the symmetry breaking, this can give rise to Rashba-type spin-orbit coupling (SOC), Weyl-type SOC, or the coexistence of two distinct spin-momentum lockings. We focus on the altermagnetic Ca2RuO4 as a testbed material. Our results reproduce the experimentally observed ground state, which is an A-centered magnetic order with the Neel vector along the b-axis, hosting spin cantings along the a- and c-axes but without weak ferromagnetism. Ca2RuO4 exhibits relativistic spin-momentum locking, with different even-parity wave orders for the three spin components. We interpret the experimental results on doped samples as evidence for a transition from a pure altermagnetic phase to a weak ferromagnetic phase. Under ferroelectric- and antiferroelectric-like distortions, there are no qualitative changes in the non-relativistic spin-momentum locking and in the weak ferromagnetism. However, we observe the rise of the Rashba or Weyl-type SOC. Using numerical and analytical models, we investigate which nodal planes persist when inversion symmetry is broken in the relativistic case. The spin-momentum locking of the other components adopt a p-wave character in the case of Rashba; in contrast, Weyl-type SOC disrupts all nodal planes, leaving only nodal lines. Finally, to simulate a stripe phase with structural distortions along the z-axis, we studied a modulated electric field inducing atomic displacements within one Ca2RuO4 layer. This produces a magnetic phase transition to an exotic altermagnetic state with two non-relativistic spin-momentum lockings hosting weak ferromagnetism. Our research presents a comprehensive analysis of various possible scenarios in altermagnets with breaking of inversion symmetries under relativistic effects

cond-mat.mtrl-sci↗

arXiv2026

Staggered Dzyaloshinskii-Moriya and canting angle in centrosymmetric altermagnetic and ferromagnetic phases: influence on the anomalous Hall effect and Weyl points

We present a simple methodology to compute the anomalous Hall conductivity (AHC) as a function of the canting angles in ferromagnets and altermagnets, starting from a nonmagnetic Hamiltonian obtained from first-principles calculations that preserves the full symmetry of the crystal structure. Magnetism is introduced by including on-site spin splitting, spin-orbit coupling, and spin-canting angles. As a representative material, we study SrRuO$_3$, which supports spin canting and exhibits a sign change of the AHC. In the ferromagnetic phase, the low-energy AHC is found to be close to zero at the Fermi level, in agreement with experimental observations. We show that the dependence of the AHC on the relevant physical parameters is most pronounced in the central region of the electronic bandwidth. We determine the symmetry-allowed components of the AHC for different magnetic orders in the large family of transition-metal perovskite ABO$_3$ compounds with space group $62$, including the spontaneous in-plane anomalous Hall effect. Within density functional theory, we evaluate the range of spin-canting angles in SrRuO$_3$ and demonstrate that it is suppressed as electronic correlations increase. By analyzing the AHC as a function of the canting angle, we find that the collinear magnetic configurations contribute most to the AHC, while spin canting plays a secondary role in determining its magnitude in non-collinear ferromagnets and altermagnets. However, canting can become relevant and induce a sign change of the AHC when the collinear magnetic state exhibits an AHC close to zero. Finally, we investigate the locations of Weyl points in the Brillouin zone and their evolution as a function of the canting angle.

cond-mat.mtrl-sci↗

arXiv2025

Bulk photovoltaic effect in MoSe$_2$ and Janus MoSSe sliding ferroelectrics

We present a first-principles study of the nonlinear optical properties of sliding ferroelectric bilayers based on MoSe$_2$ and Janus MoSSe. Two Janus configurations are considered: i) one bilayer where the two intralayer polarizations caused by Janus chemical asymmetry cancel each other out, yielding photocurrent spectra comparable to pristine MoSe$_2$ bilayers; ii) another bilayer where the intralayer polarizations add up, for which the photoresponses are strongly enhanced. Our results show that photocurrent generation in the polar Janus structures is predominantly governed by vertical chemical asymmetry, with limited dependence on the sliding direction. These findings highlight complementary design strategies: interlayer sliding enables sensitivity to external tuning, while the Janus intralayer polarization enhances photoresponses in the visible range. The interplay between composition and stacking therefore provides a versatile platform for tailoring light-matter interactions in 2D ferroelectric materials.

cond-mat.mtrl-sci↗

arXiv2025

Dual topology and edge-reconstruction in $\alpha$-Sn

We formulate the tight-binding model for cubic $\alpha$-Sn based on the DFT calculations. In the model, we incorporate a variable bond angle, which allows us to simulate the effect of the in-plane strain. In the bulk, we demonstrate the presence of the $\mathbb{Z}_2$ topological invariant and a non-zero mirror Chern number, making $\alpha$-Sn one of the rare cases where dual topology can be observed. We calculate the topological phase diagram of multi-layer $\alpha$-Sn as a function of strain and number of layers. We find that a non-trivial quantum spin Hall state appears only for compressive strain above five layers of thickness. Quite surprisingly, both in the trivial and non-trivial phases, we find a plethora of edge-states with energies inside the bulk gap of the system. Some of these states are localized at the side surfaces of the slab, some of them prefer top/bottom surfaces and some are localized in the hinges. We trace the microscopic origin of these states back to a minimal model that supports chiral symmetry and multiple one-dimensional winding numbers that take different values in different directions in the Brillouin zone.

cond-mat.mes-hall↗

arXiv2025

AMaRaNTA: Automated First-Principles Exchange Parameters In 2D Magnets

Two-dimensional (2D) magnets host a wide range of exotic magnetic textures, whose low-energy excitations and finite-temperature properties are typically described by effective spin models based on Heisenberg-like Hamiltonians. A key challenge in this framework is the reliable determination, from ab initio calculations, of exchange parameters and their anisotropic components, crucial for stabilising long-range order. Among the different strategies proposed for this task, the energy-mapping method -- based on total-energy calculations within Density Functional Theory (DFT) -- is the most widely adopted, but it typically requires laborious, multi-step procedures. To overcome this limitation, we introduce AMaRaNTA (Automating Magnetic paRAmeters iN a Tensorial Approach), a computational package that systematically automates the energy-mapping method, specifically through its ``four-state'' formulation, to extract exchange and anisotropy parameters in 2D magnets. In its current implementation, AMaRaNTA returns the nearest-neighbour exchange tensor, complemented by scalar parameters for second- and third-nearest-neighbour exchange interactions as well as single-ion anisotropy. Together, these provide a minimal yet sufficient set of parameters to capture magnetic frustration and anisotropies, essential for stabilising several observed magnetic states in 2D materials. Applied to a representative subset of the Materials Cloud 2D Structure database, AMaRaNTA demonstrates robust, automated and reproducible screening of magnetic interactions, with clear potential for high-throughput simulations.

cond-mat.mtrl-sci↗

arXiv2025

Nature of field-induced transitions and hysteretic magnetoresistance in non-collinear antiferromagnet EuIn2As2

We examine the magnetic and electrical transport properties of the hexagonal EuIn2As2 compound, combining experimental and theoretical results. This compound is predicted to be an axion-insulator from an electronic point of view and an altermagnet while in the collinear magnetic phase. However, experiments indicate that the Fermi level lies within the valence band rather than in the topological gap, potentially leading to the dominance of magnetic properties. Our detailed studies on magnetization and electrical transport support the presence of a broken-helix antiferromagnetic state, which was previously identified by X-ray and neutron diffraction experiments. Notably, we observed within that state a field-induced metamagnetic transition marked by a large hysteresis in magnetoresistance, which turns into a sharp upturn for the magnetic field tilted by 15 degree from the c-axis of the crystal. Combined with theoretical calculations, it is explained that the application of a magnetic field changes the low-resistivity antiferromagnetic domain walls to the high-resistivity domain walls due to the reduction in the Fermi surface sheets interaction area in the domain walls, originating from p-orbitals of As. EuIn2As2, therefore, presents a new case study that broadens the understanding of complex magnetic structures and their influence on electrical transport.

cond-mat.mtrl-sci↗

arXiv2025

Dirac edge states as signature of two-dimensional altermagnetic topological crystalline phase

Two-dimensional (2D) metallic altermagnets present exciting opportunities for both fundamental research and practical innovations. Their ability to enhance tunneling magnetoresistance in magnetic tunnel junctions, combined with the direct control of spin currents via electric fields, makes them highly promising for spintronic devices. Moreover, the rich electronic structure of altermagnets can host nontrivial topological phases. In particular, topological crystalline insulators are compounds where the topological states are protected by both crystalline and time-reversal symmetries. Furthermore, manipulating the state of a system between topological and trivial phases through external parameters unlocks new possibilities for quantum materials and advanced electronics. We show the edge states of a 2D altermagnetic topological crystalline insulator, using as a representative example Cr$_2$BAl, a 2D MBene metallic altermagnet with a d$_{x^2-y^2}$ altermagnetic ordering. We find that the system can host an altermagnetic phase with extremely large ``weak ferrimagnetism" which is sizeable also with light atoms, only with an in-plane component of the N\'eel vector. The electronic structure of Cr$_2$BAl presents multiple crossings and anti-crossings in the vicinity of the Fermi level along [100] and [010] directions. When the spin-orbit coupling interaction is included, with the N\'eel vector along [001] direction, energy gaps open at the band crossing points, resulting in a pronounced peak in the spin Hall conductivity. The simulated Cr-B terminated [100] edge-projected band structure reveals Dirac dispersions at the bulk crossings and anti-crossings, which are absent in Cr-Al terminations.

cond-mat.mes-hall↗

arXiv2025

Coexistence of Rashba and Dirac dispersions on the surface of centrosymmetric topological insulator decorated with transition metals

The Dirac cone originates from the bulk topology, yet its primary contribution comes from the surface since spatially, the Dirac state emerges at the boundary between the trivial and topological phases. At the same time, the Rashba states emerge in regions where inversion symmetry is broken. On the surface of the centrosymmetric topological insulators, both Rashba and Dirac bands are present and their hybridization produces the giant Rashba effect, modifying both Rashba's and Dirac's bands. Therefore, pure Rashba and Dirac fermions are inherently incompatible on the surface of centrosymmetric topological insulators if the material is homogeneous. Inspired by recent experiments, we focused on the (111) polar surface of PbSe, which becomes a topological crystalline insulator under compressive strain, and we established the conditions under which a topological system can simultaneously host pure Rashba and Dirac surface states close to the Fermi level. The coexistence of pure Dirac and Rashba dispersions is only possible in a non-homogeneous centrosymmetric topological insulator, where the spatial origins of the two bands are effectively separated. In the experimentally observed case of PbSe, we demonstrate that a metallic overlayer induces a strong electrostatic potential gradient in the subsurface region, which in turn generates the electric field responsible for Rashba splitting in the subsurface layers. Consequently, in PbSe(111), the Rashba states arise from subsurface layers, while the Dirac states live mainly on the surface layers. Finally, we compare the properties of the Rashba in the trivial and topological phases; the calculated Rashba coefficient agrees qualitatively with the experimental results.

cond-mat.mes-hall↗

arXiv2025

Dirac surface states, multiorbital dimerization and superconductivity in Nb- and Ta-based A15 compounds

Using first-principle calculations, we investigate the electronic, topological and superconducting properties of Nb$_3$X (X = Ge, Sn, Sb) and Ta$_3$Y (Y = As, Sb, Bi) A15 compounds. We demonstrate that these compounds host Dirac surface states which are related to a nontrivial Z$_2$ topological value. The spin-orbit coupling (SOC) splits the eightfold degenerate R point close to the Fermi level enhancing the amplitude of the spin Hall conductance. Indeed, despite the moderate spin-orbit of the Nb-compounds, a large spin Hall effect is also obtained in Nb$_3$Ge and Nb$_3$Sn compounds. We show that the Coulomb interaction opens the gap at the R point thus making more evident the occurrence of Dirac surface states. We then investigate the superconducting properties by determining the strength of the electron-phonon BCS coupling. The evolution of the critical temperature is tracked down to the 2D limit indicating a reduction of the transition temperature which mainly arises from the suppression of the density of states at the Fermi level. Finally, we propose a minimal tight-binding model based on three coupled Su-Schrieffer-Heeger chains with t$_{2g}$ Ta- and Nb-orbitals reproducing the spin-orbit splittings at the R point among the $π$-bond bands in this class of compounds. We separate the kinetic parameters in $π$ and $δ$-bonds, in intradimer and interdimer hoppings and discuss their relevance for the topological electronic structure. We point out that Nb$_3$Ge might represent a Z$_2$ topological metal with the highest superconducting temperature ever recorded.

cond-mat.supr-con↗

arXiv2025

Giant non-reciprocal band structure effect in a multiferroic material

Multiferroic materials, characterized by the coexistence of ferroelectricity and ferromagnetism, may unveil band structures suggestive of complex phenomena and new functionalities. In this Letter, we analyze the band structure of EuO in its multiferroic phase. Using density functional theory calculations and detailed symmetry analysis, we reveal a previously overlooked non-reciprocal band structure effect, where the electronic energy bands exhibit asymmetry along opposite directions with respect to the special points in the Brillouin zone. This effect, which is enabled by spin-orbit coupling, is giant for the top valence Eu $4f$ bands, and can be switched by external electric or magnetic fields. Furthermore, this results in an enhanced bulk photovoltaic effect. Specifically, our predictions indicate the emergence of a large injection current response to linearly polarized light, resulting in a photoconductivity value several orders of magnitude higher than that reported in any other oxide material. Ultimately, this non-reciprocal band structure effect and the associated large bulk photovoltaic response may be general phenomena emerging not just in EuO but also in other multiferroics or magnetoelectrics, potentially providing new cross-functionalities.

cond-mat.mtrl-sci↗

arXiv2025

Conditions for orbital selective altermagnetism in Sr$_2$RuO$_4$: tight binding model, similarities with cuprates and implications on superconductivity

The vibrational modes in Sr$_2$RuO$_4$ easily induce octahedral rotations without tilting. Being on the verge of a magnetic instability, such propensity of octahedral rotation may also produce magnetic fluctuations. In this work, we analyze the long-range magnetic phase diagram incorporating such octahedral rotations and demonstrate the possibility of an altermagnetic phase in Sr$_2$RuO$_4$. Using ab-initio calculations, we first study single layer Sr$_2$RuO$_4$ with octahedral rotations, obtaining an orbital-selective $g$-wave altermagnetic phase. We further provide an effective $t_{2g}$ tight-binding model, demonstrating that the $g$-wave altermagnetism is primarily a product of second and third nearest neighbor interorbital hybridizations between the ${\gamma}z$ ($\gamma=x,y$) orbitals, but only a much longer range intraorbital hybridization in the $xy$ orbitals, establishing a strong orbital-selectiveness for the altermagnetism. Notably, by replacing the $xy$ orbital with the $x^2-y^2$ orbital, a similar tight-biding model may be used to investigate the hole-doped cuprate superconductors. We then study bulk Sr$_2$RuO$_4$, where we find the altermagnetic phase as the magnetic ground state for a range of finite octahedral rotations. In the bulk, interlayer hopping breaks some of the symmetries of the $g$-wave altermagnet, resulting in a $d_{xy}$-wave altermagnet, still with orbital selectiveness. We also include relativistic effects through spin-orbit coupling and obtain that an effective staggered Dzyaloshinskii-Moriya interaction generates weak ferromagnetism. Finally, we discuss the implications of the altermagnetic order on the intrinsic superconductivity of Sr$_2$RuO$_4$. Assuming in-plane and intraorbital pairing, the altermagnetism favors spin-singlet $d_{x^2-y^2}$-wave or $g$-wave pairing, or (nematic or chiral) combinations thereof.

cond-mat.supr-con↗

arXiv2024

Bulk photovoltaic effect in ferroelectric and antiferroelectric phases of antimony sulphoiodide investigated by means of ab-initio simulations

We employ first-principles calculations to investigate the ferroelectric properties and the bulk photovoltaic effect (BPVE) of antimony sulfur iodide (SbSI). The BPVE enables direct sunlight-to-electricity conversion in homogeneous materials and, in ferroelectric compounds, can be tuned via an electric field controlling the polarization. However, most ferroelectrics are oxides with large band gaps exceeding the energy of visible light, thereby limiting their photovoltaic performance. SbSI, featuring a visible-range band gap, combines remarkable photovoltaic capabilities with a spin-textured band structure, coupling charge and spin degrees of freedom. Our calculations predict ferroelectric and antiferroelectric phases with comparable band gaps but distinct spin textures, relevant for spintronics applications. The BPVE is driven by the linear and circular photogalvanic effects, exhibiting high photoconductivities under visible light. Furthermore, it serves as a diagnostic tool to identify the material phase, with the circular photogalvanic effect reflecting spin texture changes. Thanks to its multifunctional properties, SbSI emerges as a promising candidate for solar energy conversion and advanced electronics, with potential applications extending to spintronics.

cond-mat.mtrl-sci↗

arXiv2024

Emerging new phases in correlated Mott insulator Ca2RuO4

The Mott insulator Ca2RuO4 is a paradigmatic example among transition metal oxides, where the interplay of charge, spin, orbital, and lattice degrees of freedom leads to competing quantum phases. In this paper, we focus on and review some key aspects, from the underlying physical framework and its basic properties, to recent theoretical efforts that aim to trigger unconventional quantum ground states, using several external parameters and stimuli. Using first-principle calculations, we demonstrate that Ca2RuO4 shows a spin splitting in the reciprocal space, and identify it as an altermagnetic candidate material. The non relativistic spin-splitting has an orbital selective nature, dictated by the local crystallographic symmetry. Next, we consider two routes that may trigger exotic quantum states. The first one corresponds to transition metal substitution of the 4d4 Ru with isovalent 3d3 ions. This substitutional doping may alter the spin-orbital correlations favoring the emergence of negative thermal expansion. The second route explores fledgling states arising in a nonequilibrium steady state under the influence of an applied electric field. We show that the electric field can directly affect the orbital density, eventually leading to strong orbital fluctuations and the suppression of orbital imbalance, which may, in turn, reduce antiferromagnetism. These aspects suggest possible practical applications, as its unique properties may open up possibilities for augmenting existing technologies, surpassing the limitations of conventional materials.

cond-mat.str-el↗

arXiv2024

CdTe and HgTe doped with V, Cr, and Mn -- prospects for the quantum anomalous Hall effect

Using first principle calculations we examine properties of (Cd,V)Te, (Cd,Cr)Te, (Hg,V)Te, and (Hg,Cr)Te relevant to the quantum anomalous Hall effect (QAHE), such as the position of V- and Cr- derived energy levels and the exchange interactions between magnetic ions. We consider CdTe and HgTe, containing 12.5% of cation-substitutional V or Cr ions in comparison to the well-known case of (Cd,Mn)Te and (Hg,Mn)Te, and examine their suitability for the fabrication of ferromagnetic barriers or ferromagnetic topological quantum wells, respectively. To account for the strong correlation of transition metal d electrons we employ hybrid functionals with different mixing parameters aHSE focusing on aHSE = 0.32, which better reproduces the experimental band gaps in HgTe, CdTe, Hg0.875Mn0.125Te, and Cd0.875Mn0.125Te. We find that Cr, like Mn, acts as an isoelectronic dopant but V can be an in-gap donor in CdTe and a resonant donor in HgTe, similar to the case of Fe in HgSe. From the magnetic point of view, Cr-doping results in a ferromagnetic phase within the general gradient approximation (GGA) but interactions become antiferromagnetic within hybrid functionals. However, (Hg,V)Te is a ferromagnet within both exchange-correlation functionals in a stark contrast to (Hg,Mn)Te for which robust antiferromagnetic coupling is found theoretically and experimentally. Furthermore, we establish that the Jahn-Teller effect is relevant only in the case of Cr-doping. Considering lower defect concentrations in HgTe-based quantum wells compared to (Bi,Sb)3Te2 layers, our results imply that HgTe quantum wells or (Cd,Hg)Te barriers containing either V or Cr show advantages over (Bi,Sb,Cr,V)3Te2-based QAHE systems but whether (i) ferromagnetic coupling will dominate in the Cr case and (ii) V will not introduce too many electrons to the quantum well is to be checked experimentally

cond-mat.mtrl-sci↗

arXiv2024

Pentagonal nanowires from topological crystalline insulators: a platform for intrinsic core-shell nanowires and higher-order topology

We report on the experimental realization of Pb1-xSnxTe pentagonal nanowires (NWs) with [110] orientation using molecular beam epitaxy techniques. Using first-principles calculations, we investigate the structural stability in NWs of SnTe and PbTe in three different structural phases: cubic, pentagonal with [001] orientation and pentagonal with [110] orientation. Within a semiclassical approach, we show that the interplay between ionic and covalent bonds favors the formation of pentagonal NWs. Additionally, we find that this pentagonal structure is more likely to occur in tellurides than in selenides. The disclination and twin boundary cause the electronic states originating from the NW core region to generate a conducting band connecting the valence and conduction bands, creating a symmetry-enforced metallic phase. The metallic core band has opposite slopes in the cases of Sn and Te twin boundary, while the bands from the shell are insulating. We finally study the electronic and topological properties of pentagonal NWs unveiling their potential as a new platform for higher-order topology and fractional charge. These pentagonal NWs represent a unique case of intrinsic core-shell one-dimensional nanostructures with distinct structural, electronic and topological properties between the core and the shell region.

cond-mat.mtrl-sci↗

arXiv2023

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

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 N\'eel vector are antiparallel but the other two spin components orthogonal to the N\'eel 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 N\'eel vector, we find weak ferrimagnetism only in the noncentrosymmetric compound MnSe among the examined cases.

cond-mat.mtrl-sci↗