Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids^1,2. It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology^3–7 to topological quantum matter^8–14. Traditionally, LKSD has been considered to originate from two possible internal symmetry-breaking mechanisms. The first refers to time-reversal symmetry breaking by magnetization of ferromagnets and tends to be strong because of the non-relativistic exchange origin¹⁵. The second applies to crystals with broken inversion symmetry and tends to be comparatively weaker, as it originates from the relativistic spin–orbit coupling (SOC)^16–19. A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic^20,21, that allows for LKSD without net magnetization and inversion-symmetry breaking. Here we provide the confirmation using photoemission spectroscopy and ab initio calculations. We identify two distinct unconventional mechanisms of LKSD generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization^20–23. Our observation of the altermagnetic LKSD can have broad consequences in magnetism. It motivates exploration and exploitation of the unconventional nature of this magnetic phase in an extended family of materials, ranging from insulators and semiconductors to metals and superconductors^20,21, that have been either identified recently or perceived for many decades as conventional antiferromagnets^21,24,25.

Nanoscale detection and control of the magnetic order underpins a spectrum of condensed-matter research and device functionalities involving magnetism. The key principle involved is the breaking of time-reversal symmetry, which in ferromagnets is generated by an internal magnetization. However, the presence of a net magnetization limits device scalability and compatibility with phases, such as superconductors and topological insulators. Recently, altermagnetism has been proposed as a solution to these restrictions, as it shares the enabling time-reversal-symmetry-breaking characteristic of ferromagnetism, combined with the antiferromagnetic-like vanishing net magnetization^1–4. So far, altermagnetic ordering has been inferred from spatially averaged probes^4–19. Here we demonstrate nanoscale imaging of altermagnetic states from 100-nanometre-scale vortices and domain walls to 10-micrometre-scale single-domain states in manganese telluride (MnTe)^{2,7,9,14–16,18,20,21}. We combine the time-reversal-symmetry-breaking sensitivity of X-ray magnetic circular dichroism¹² with magnetic linear dichroism and photoemission electron microscopy to achieve maps of the local altermagnetic ordering vector. A variety of spin configurations are imposed using microstructure patterning and thermal cycling in magnetic fields. The demonstrated detection and controlled formation of altermagnetic spin configurations paves the way for future experimental studies across the theoretically predicted research landscape of altermagnetism, including unconventional spin-polarization phenomena, the interplay of altermagnetism with superconducting and topological phases, and highly scalable digital and neuromorphic spintronic devices^3,14,22–24.

Entanglement of the spin–orbit and magnetic order in multiferroic materials bears a strong potential for engineering novel electronic and spintronic devices. Here, we explore the electron and spin structure of ferroelectric α-GeTe thin films doped with ferromagnetic Mn impurities to achieve its multiferroic functionality. We use bulk-sensitive soft-X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to follow hybridization of the GeTe valence band with the Mn dopants. We observe a gradual opening of the Zeeman gap in the bulk Rashba bands around the Dirac point with increase of the Mn concentration, indicative of the ferromagnetic order, at persistent Rashba splitting. Furthermore, subtle details regarding the spin–orbit and magnetic order entanglement are deduced from spin-resolved ARPES measurements. We identify antiparallel orientation of the ferroelectric and ferromagnetic polarization, and altering of the Rashba-type spin helicity by magnetic switching. Our experimental results are supported by first-principles calculations of the electron and spin structure.

Ferroelectric materials are used in actuators or sensors because of their non-volatile macroscopic electric polarization. GeTe is the simplest known diatomic ferroelectric endowed with exceedingly complex physics related to its crystalline, amorphous, thermoelectric, and—fairly recently discovered—topological properties, making the material potentially interesting for spintronics applications. Typically, ferroelectric materials possess random oriented domains that need poling to achieve macroscopic polarization. By using X-ray absorption fine structure spectroscopy complemented with anomalous diffraction and piezo-response force microscopy, we investigated the bulk ferroelectric structure of GeTe crystals and thin films. Both feature multi-domain structures in the form of oblique domains for films and domain colonies inside crystals. Despite these multi-domain structures which are expected to randomize the polarization direction, our experimental results show that at room temperature there is a preferential ferroelectric order remarkably consistent with theoretical predictions from ideal GeTe crystals. This robust self-poled state has high piezoelectricity and additional poling reveals persistent memory effects.

We present an angle- and spin-resolved photoemission study of half-metallic three-dimensional perovskite ${\mathrm{La}}_{2∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Mn}{\mathrm{O}}_3$ thin films grown with pulsed laser deposition. The experiments are performed in the (100) mirror plane. The experimental results are related to GGA+U calculations through simulations of photoemission spectra, which take into account the final state broadening in surface-perpendicular momentum and the initial-state broadening in energy. We demonstrate that due to the three-dimensional nature of ${\mathrm{La}}_{2∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Mn}{\mathrm{O}}_3$, these intrinsic mechanisms of the photoemission process give rise to deviations of the photoemission spectrum from the spectral function corresponding to the strict momentum conservation. In the spin-integrated data, we identify ghost spectral intensity coming from states with different momenta and, in particular, nonvanishing intensity filling the whole interior of the central Fermi surface spheroid. In the spin-resolved data, we find experimental polarization values near the Fermi surface of 55% at the normal emission and 80% at off-normal emission. Despite a seeming contradiction to the half-metallic picture, such a reduction in spin contrast is reproduced by our simulations as a result of the broadening mechanisms and is consistent with the half-metallic nature of ${\mathrm{La}}_{2∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Mn}{\mathrm{O}}_3$.

Ferroelectric $\alpha$-GeTe is unveiled to exhibit an intriguing multiple nontrivial topology of the electronic band structure due to the existence of triple-point and type-II Weyl fermions, which goes well beyond the giant Rashba spin splitting controlled by external fields as previously reported. Using spin- and angle-resolved photoemission spectroscopy combined with ab initio density functional theory, the unique spin texture around the triple point caused by the crossing of one spin-degenerate and two spin-split bands along the ferroelectric crystal axis is derived. This consistently reveals spin winding numbers that are coupled with time-reversal symmetry and Lorentz invariance, which are found to be equal for both triple-point pairs in the Brillouin zone. The rich manifold of effects opens up promising perspectives for studying nontrivial phenomena and multicomponent fermions in condensed matter systems.