Altermagnetic lifting of Kramers spin degeneracy

Lifted Kramers spin-degeneracy has been among the central topics of condensed-matter physics since the dawn of the band theory of solids. It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology to topological quantum matter. Traditionally, lifted Kramers spin-degeneracy has been considered to originate from two possible internal symmetry-breaking mechanisms. The first one refers to time-reversal symmetry breaking by magnetization of ferromagnets, and tends to be strong due to the non-relativistic exchange-coupling origin. The second mechanism applies to crystals with broken inversion symmetry, and tends to be comparatively weaker as it originates from the relativistic spin-orbit coupling. A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic, that allows for lifting the Kramers spin degeneracy 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 lifted Kramers spin degeneracy generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization. Our observation of the altermagnetic lifting of the Kramers spin degeneracy 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, that have been either identified recently or perceived for many decades as conventional antiferromagnets

Altermagnetic lifting of Kramers spin degeneracy

Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids1,2. It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology3–7 to topological quantum matter8–14. 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 altermagnetic20,21, 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 magnetization20–23. 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 superconductors20,21, that have been either identified recently or perceived for many decades as conventional antiferromagnets21,24,25

Photosynthesis as a discrete biochemical process

It is shown that the existence of a multioscillatory and chaotic regime observed in the photosynthesis could be explained on the basis of logistic equations, i.e., using a discrete approach. Transforming known phenomenological differential equations describing the photosynthesis into the discrete formalism it is possible to demonstrate that by change of control parameters such equations generate the very well known Feigenbaum‘s scenario of the duplication of states including the possibility of the transition into a chaotic regime. The multioscillatory states characterised by even, and what is surprising, also by odd number of “subcycles” are generated at some special combinations of values of control parameters

Unveiling the complete dispersion of the giant Rashba split surface states of ferroelectric α-GeTe(111) by alkali doping

α-GeTe(111) is a noncentrosymmetric ferroelectric material for which a strong spin-orbit interaction gives rise to giant Rashba split states in the bulk and at the surface. The detailed dispersions of the surface states inside the bulk band gap remains an open question because they are located in the unoccupied part of the electronic structure, making them inaccessible to static angle-resolved photoemission spectroscopy. We show that this difficulty can be overcome via in situ potassium doping of the surface, leading to a rigid shift of 80 meV of the surface states into the occupied states. Thus, we resolve, in great detail, their dispersion and highlight their crossing at the ̄ point, which, in comparison with density functional theory calculations, definitively confirms the Rashba mechanis

Disentangling bulk and surface Rashba effects in ferroelectric α-GeTe

Identifikace bulkových a povrchových Rashba stavů v ferroelektrickém GeTeMacroscopic ferroelectric order in α-GeTe with its noncentrosymmetric lattice structure leads to a giant Rashba spin splitting in the bulk bands due to strong spin-orbit interaction. Direct measurements of the bulk band structure using soft x-ray angle-resolved photoemission (ARPES) reveals the three-dimensional electronic structure with spindle torus shape. By combining high-resolution and spin-resolved ARPES as well as photoemission calculations, the bulk electronic structure is disentangled from the two-dimensional surface electronic structure by means of surface capping, which quenches the complex surface electronic structure. This unravels the bulk Rashba-split states in the ferroelectric Rashba α-GeTe(111) semiconductor exhibiting a giant spin splitting with Rashba parameter αR around 4.2 eV A°, the highest of so-far known materials

Approximate Entropy as a measure of complexity in sap flow temporal dynamics of two tropical tree species under water deficit

Approximate Entropy (ApEn), a model-independent statistics to quantify serial irregularities, was used to evaluate changes in sap flow temporal dynamics of two tropical species of trees subjected to water deficit. Water deficit induced a decrease in sap flow of G. ulmifolia, whereas C. legalis held stable their sap flow levels. Slight increases in time series complexity were observed in both species under drought condition. This study showed that ApEn could be used as a helpful tool to assess slight changes in temporal dynamics of physiological data, and to uncover some patterns of plant physiological responses to environmental stimuli.<br>Entropia Aproximada (ApEn), um modelo estatístico independente para quantificar irregularidade em séries temporais, foi utilizada para avaliar alterações na dinâmica temporal do fluxo de seiva em duas espécies arbóreas tropicais submetidas à deficiência hídrica. A deficiência hídrica induziu uma grande redução no fluxo de seiva em G. ulmifolia, enquanto que na espécie C. legalis manteve-se estável. A complexidade das séries temporais foi levemente aumentada sob deficiência hídrica. O estudo mostrou que ApEn pode ser usada como um método para detectar pequenas alterações na dinâmica temporal de dados fisiológicos, e revelar alguns padrões de respostas fisiológicas a estímulos ambientais