Entanglement and manipulation of the magnetic and spin-orbit order in multiferroic Rashba semiconductors

Theory of spin and orbital Edelstein effects

In systems with broken spatial inversion symmetry, such as surfaces, interfaces, or bulk systems lacking an inversion center, the application of a charge current can generate finite spin and orbital densities associated with a nonequilibrium magnetization, which is known as spin and orbital Edelstein effect (SEE and OEE), respectively. Early reports on this current-induced magnetization focus on two-dimensional Rashba systems, in which an in-plane nonequilibrium spin density is generated perpendicular to the applied charge current. However, until today, a large variety of materials have been theoretically predicted and experimentally demonstrated to exhibit a sizeable Edelstein effect, which comprises contributions from the spin as well as the orbital degrees of freedom, and whose associated magnetization may be out of plane, nonorthogonal, and even parallel to the applied charge current, depending on the system's particular symmetries. In this review, we give an overview on the most commonly used theoretical approaches for the discussion and prediction of the SEE and OEE. Further, we introduce a selection of the most intensely discussed materials exhibiting a finite Edelstein effect, and give a brief summary of common experimental techniques.

High Thermoelectric Performance in Rhombohedral GeSe-LiBiTe2

GeSe, an analogue of SnSe, shows promise in exhibiting exceptional thermoelectric performance in the Pnma phase. The constraints on its dopability, however, pose challenges in attaining optimal carrier concentrations and improving ZT values. This study demonstrates a crystal structure evolution strategy for achieving highly doped samples and promising ZTs in GeSe via LiBiTe2 alloying. A rhombohedral phase (R3m) can be stabilized in the GeSe-LiBiTe2 system, further evolving into a cubic (Fm3̅m) phase with a rising temperature. The band structures of GeSe-LiBiTe2 in the rhombohedral and cubic phases feature a similar multiple-valley energy-converged valence band of L and Σ bands. The observed high carrier concentration (∼1020 cm-3) reflects the effective convergence of these bands, enabling a high density-of-states effective mass and an enhanced power factor. Moreover, a very low lattice thermal conductivity of 0.6-0.5 W m-1 K-1 from 300 to 723 K is achieved in 0.9GeSe-0.1LiBiTe2, approaching the amorphous limit value. This remarkably low lattice thermal conductivity is related to phonon scattering from point defects, planar vacancies, and ferroelectric instability-induced low-energy Einstein oscillators. Finally, a maximum ZT value of 1.1 to 1.3 at 723 K is obtained, with a high average ZT value of over 0.8 (400-723 K) in 0.9GeSe-0.1LiBiTe2 samples. This study establishes a viable route for tailoring crystal structures to significantly improve the performance of GeSe-related compounds.

Magnetic parity violation and parity-time-reversal-symmetric magnets

Parity-time-reversal symmetry (PTsymmetry), a symmetry for the combined operations of space inversion (P) and time reversal (T), is a fundamental concept of physics and characterizes the functionality of materials as well asPandTsymmetries. In particular, thePT-symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leavesPTsymmetry intact, the simultaneous violation ofPandTsymmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagneticP-symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion.

Persistence of Structural Distortion and Bulk Band Rashba Splitting in SnTe above Its Ferroelectric Critical Temperature

The ferroelectric semiconductor α-SnTe has been regarded as a topological crystalline insulator, and the dispersion of its surface states has been intensively measured with angle-resolved photoemission spectroscopy (ARPES) over the past decade. However, much less attention has been given to the impact of the ferroelectric transition on its electronic structure, and in particular on its bulk states. Here, we investigate the low-energy electronic structure of α-SnTe with ARPES and follow the evolution of the bulk-state Rashba splitting as a function of temperature, across its ferroelectric critical temperature of about Tc ≈ 110 K. Unexpectedly, we observe a persistent band splitting up to room temperature, which is consistent with an order-disorder contribution of local dipoles to the phase transition that requires the presence of fluctuating dipoles above Tc. We conclude that no topological surface state can occur under these conditions at the (111) surface of SnTe, at odds with recent literature.

Efficient magnetic switching in a correlated spin glass

The interplay between spin-orbit interaction and magnetic order is one of the most active research fields in condensed matter physics and drives the search for materials with novel, and tunable, magnetic and spin properties. Here we report on a variety of unique and unexpected observations in thin multiferroic Ge1-xMnxTe films. The ferrimagnetic order parameter in this ferroelectric semiconductor is found to switch direction under magnetostochastic resonance with current pulses many orders of magnitude lower as for typical spin-orbit torque systems. Upon a switching event, the magnetic order spreads coherently and collectively over macroscopic distances through a correlated spin-glass state. Utilizing these observations, we apply a novel methodology to controllably harness this stochastic magnetization dynamics.

Experimental Band Structure of Pb(Zr,Ti)O3 : Mechanism of Ferroelectric Stabilization

Pb(Zr,Ti)O₃ (PZT) is the most common ferroelectric (FE) material widely used in solid-state technology. Despite intense studies of PZT over decades, its intrinsic band structure, electron energy depending on 3D momentum k, is still unknown. Here, Pb(Zr_0.2 Ti_0.8 )O₃ using soft-X-ray angle-resolved photoelectron spectroscopy (ARPES) is explored. The enhanced photoelectron escape depth in this photon energy range allows sharp intrinsic definition of the out-of-plane momentum k and thereby of the full 3D band structure. Furthermore, the problem of sample charging due to the inherently insulating nature of PZT is solved by using thin-film PZT samples, where a thickness-induced self-doping results in their heavy doping. For the first time, the soft-X-ray ARPES experiments deliver the intrinsic 3D band structure of PZT as well as the FE-polarization dependent electrostatic potential profile across the PZT film deposited on SrTiO₃ and La_x SrMn_{1- x} O₃ substrates. The negative charges near the surface, required to stabilize the FE state pointing away from the sample (P+), are identified as oxygen vacancies creating localized in-gap states below the Fermi energy. For the opposite polarization state (P-), the positive charges near the surface are identified as cation vacancies resulting from non-ideal stoichiometry of the PZT film as deduced from quantitative XPS measurements.

Ferroelectric control of pseudospin texture in CuInP2S6monolayer

Spin-orbit coupling (SOC) plays an important role in condensed matter physics and has potential applications in spintronics devices. In this paper, we study the electronic properties of ferroelectric CuInP₂S₆(CIPS) monolayer through first-principles calculations. The result shows that CIPS monolayer is a potential for valleytronics material and we find that the in-plane helical and nonhelical pseudospin texture are induced by the Rashba and Dresselhaus effect, respectively. The chirality of helical pseudospin texture is coupled to the out-of-plane ferroelectric polarization. Furthermore, a large spin splitting due to the SOC effect can be found atKvalley, which can be regarded as the Zeeman effect under a valley-dependent pseudomagnetic field. The CIPS monolayer with Rashbaet aleffects provides a good platform for electrically controlled spin polarization physics.

Non-monotonic variation of the Kramers point band gap with increasing magnetic doping in BiTeI

Polar Rashba-type semiconductor BiTeI doped with magnetic elements constitutes one of the most promising platforms for the future development of spintronics and quantum computing thanks to the combination of strong spin-orbit coupling and internal ferromagnetic ordering. The latter originates from magnetic impurities and is able to open an energy gap at the Kramers point (KP gap) of the Rashba bands. In the current work using angle-resolved photoemission spectroscopy (ARPES) we show that the KP gap depends non-monotonically on the doping level in case of V-doped BiTeI. We observe that the gap increases with V concentration until it reaches 3% and then starts to mitigate. Moreover, we find that the saturation magnetisation of samples under applied magnetic field studied by superconducting quantum interference device (SQUID) magnetometer has a similar behaviour with the doping level. Theoretical analysis shows that the non-monotonic behavior can be explained by the increase of antiferromagnetic coupled atoms of magnetic impurity above a certain doping level. This leads to the reduction of the total magnetic moment in the domains and thus to the mitigation of the KP gap as observed in the experiment. These findings provide further insight in the creation of internal magnetic ordering and consequent KP gap opening in magnetically-doped Rashba-type semiconductors.

Triple-Point Fermions in Ferroelectric GeTe

Ferroelectric α-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.

Three-Dimensional Limit of Bulk Rashba Effect in Ferroelectric Semiconductor GeTe

Ferroelectric Rashba semiconductors (FERSCs) have recently attracted intensive attention due to their giant bulk Rashba parameter, α_R, which results in a locking between the spin degrees of freedom and the switchable electric polarization. However, the integration of FERSCs into microelectronic devices has provoked questions concerning whether the Rashba effect can persist when the material thickness is reduced to several nanometers. Here we find that α_R can keep a large value of 2.12 eV Å in the 5.0 nm thick GeTe film. The behavior of α_R with thickness can be expressed by the scaling law and provides a 3D thickness limit of the bulk Rashba effect, d_c = 2.1 ± 0.5 nm. Finally, we find that the thickness can modify the Berry curvature as well, which influences the polarization and consequently alters the α_R. Our results give insight into understanding the factors influencing α_R in FERSCs and pave a novel route for designing Rashba-type quantum materials.

Ferroelectric Switching of Pure Spin Polarization in Two-Dimensional Electron Gas

Two-dimensional electron gas (2DEG) created at compound interfaces can exhibit a broad range of exotic physical phenomena, including quantum Hall phase, emergent ferromagnetism, and superconductivity. Although electron spin plays key roles in these phenomena, the fundamental understanding and application prospects of such emergent interfacial states have been largely impeded by the lack of purely spin-polarized 2DEG. In this work, by first-principles calculations of the multiferroic superlattice GeTe/MnTe, we find the ferroelectric polarization of GeTe is concurrent with the half-metallic 2DEG at interfaces. Remarkably, the pure spin polarization of the 2DEG can be created and annihilated by polarizing and depolarizing the ferroelectrics and can be switched (between pure spin-up and pure spin-down) by flipping the ferroelectric polarization. Given the electric-field amplification effect of ferroelectric electronics, we envision multiferroic superlattices could open up new opportunities for low-power, high-efficiency spintronic devices such as spin field-effect transistors.

Relation between spin-orbit induced spin polarization, Fano-effect and circular dichroism in soft x-ray photoemission

A Feynman diagram analysis of photoemission probabilities suggests a relation between two final-state spin polarization effects, the optical spin-orientation originating from the interaction with circularly polarized light ([Formula: see text], Fano effect) and the spin polarization induced by the spin-orbit scattering ([Formula: see text], Mott effect). The analysis predicts that [Formula: see text] is proportional to the product of [Formula: see text] and the circular dichroism in the angular distribution (CDAD) of photoelectrons. To confirm this prediction, the spin polarization of photoelectrons excited by soft x-ray radiation from initial spin-degenerate bulk states of tungsten using time-of-flight momentum microscopy with parallel spin detection has been measured. By measurement of four independent photoemission intensities for two opposite spin directions and opposite photon helicity, CDAD, Fano, and Mott effect are distinguished. The results confirm the prediction from the Feynman diagram analysis.

Ferroelectric Rashba semiconductors, AgBiP2X6 (X = S, Se and Te), with valley polarization: an avenue towards electric and nonvolatile control of spintronic devices

The electric and nonvolatile control of spin in semiconductors represents a fundamental step towards novel electronic devices. In this work, using first-principles calculations we investigate the electronic properties of AgBiP2X6 (X = S, Se, and Te) monolayers, which may be a new member of ferroelectric Rashba semiconductors due to the inversion symmetry breaking arising from the ferroelectric polarization, thus allowing for the electric control of spin. The AgBiP2X6 monolayers are dynamically and thermodynamically stable up to room temperature. In the AgBiP2Te6 monolayer, the calculated band structure reveals the direct band-gap semiconducting nature in the presence of highly mobile two-dimensional electron gas near the Fermi level. The inclusion of spin-orbit coupling yields the giant Rashba-type spin splitting with a Rashba parameter of 6.5 eV Å, which is even comparable to that of some known bulk Rashba semiconductors. Except for the Rashba-type spin splitting, spin-orbit coupling together with inversion symmetry breaking also gives rise to valley polarization located at the edge of the conduction bands. The strength of the Rashba-type spin splitting and location of the conduction band minimum can be significantly tuned by applying the in-plane biaxial strain. Also, we demonstrate that these remarkable features can be retained in the presence of the BN substrate. The coexistence of the Rashba-type spin splitting (in-plane spin direction) and band splitting at the K/K' valleys (out-of-plane spin direction) makes the AgBiP2Te6 monolayer interesting for spintronics and valleytronics.

Evolution of Electronic States and Emergence of Superconductivity in the Polar Semiconductor GeTe by Doping Valence-Skipping Indium

GeTe is a chemically simple IV-VI semiconductor which bears a rich plethora of different physical properties induced by doping and external stimuli. Here, we report a superconductor-semiconductor-superconductor transition controlled by finely-tuned In doping. Our results reveal the existence of a critical doping concentration x_{c}=0.12 in Ge_{1-x}In_{x}Te, where various properties, including structure, resistivity, charge carrier type, and the density of states, take either an extremum or change their character. At the same time, we find indications of a change in the In-valence state from In^{3+} to In^{1+} with increasing x by core-level photoemission spectroscopy, suggesting that this system is a new promising playground to probe valence fluctuations and their possible impact on structural, electronic, and thermodynamic properties of their host.

Changing the magnetic states of an Fe/BaTiO3 interface through crystal field effects controlled by strain

The search for better and inexpensive magnetoelectric materials is now commonplace in solid state physics, using electric field induced strain to change the multiferroic magnetic state.

Rashba-like spin splitting along three momentum directions in trigonal layered PtBi2

Spin-orbit coupling (SOC) has gained much attention for its rich physical phenomena and highly promising applications in spintronic devices. The Rashba-type SOC in systems with inversion symmetry breaking is particularly attractive for spintronics applications since it allows for flexible manipulation of spin current by external electric fields. Here, we report the discovery of a giant anisotropic Rashba-like spin splitting along three momentum directions (3D Rashba-like spin splitting) with a helical spin polarization around the M points in the Brillouin zone of trigonal layered PtBi₂. Due to its inversion asymmetry and reduced symmetry at the M point, Rashba-type as well as Dresselhaus-type SOC cooperatively yield a 3D spin splitting with α_R ≈ 4.36 eV Å in PtBi₂. The experimental realization of 3D Rashba-like spin splitting not only has fundamental interests but also paves the way to the future exploration of a new class of material with unprecedented functionalities for spintronics applications.

Rashba type spin splitting – relevant for spintronics applications - is driven by inversion symmetry breaking but could so far not be realized in all momentum directions in a crystal. Here, the authors report on PtBi₂ that exhibits Rashba spin splitting in all three momentum directions.

Ferroelectricity and Rashba Effect in a Two-Dimensional Dion-Jacobson Hybrid Organic-Inorganic Perovskite

Hybrid organic-inorganic perovskites (HOIPs) are a new generation of high-performance materials for solar cells and light emitting diodes. Beyond these applications, ferroelectricity and spin-related properties of HOIPs are increasingly attracting interests. The presence of strong spin-orbit coupling, allied with symmetry breaking ensured by remanent polarization, should give rise to Rashba-type splitting of electronic bands in HOIP. However, the report of both ferroelectricity and Rashba effect in HOIP is rare. Here we report the observation of robust ferroelectricity and Rashba effect in two-dimensional Dion-Jacobson perovskites.

Ferroelectric Self-Poling in GeTe Films and Crystals

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.

Manipulation of dipolar magnetism in low-dimensional iron oxide nanoparticle assemblies

Trench-patterned iron oxide nanoparticles are switched between a superspin glass and a superferromagnetic state.

Current-driven magnetization switching in ferromagnetic bulk Rashba semiconductor (Ge,Mn)Te

Multiferroic materials with both ferroelectric and ferromagnetic orders provide a promising arena for the electrical manipulation of magnetization through the mutual correlation between those ferroic orders. Such a concept of multiferroics may expand to semiconductor with both broken symmetries of spatial inversion and time reversal, that is, polar ferromagnetic semiconductors. Here, we report the observation of current-driven magnetization switching in one such example, (Ge,Mn)Te thin films. The ferromagnetism caused by Mn doping opens an exchange gap in original massless Dirac band of the polar semiconductor GeTe with Rashba-type spin-split bands. The anomalous Hall conductivity is enhanced with increasing hole carrier density, indicating that the contribution of the Berry phase is maximized as the Fermi level approaches the exchange gap. By means of pulse-current injection, the electrical switching of the magnetization is observed in the (Ge,Mn)Te thin films as thick as 200 nm, pointing to the Rashba-Edelstein effect of bulk origin. The efficiency of this effect strongly depends on the Fermi-level position owing to the efficient spin accumulation at around the gap. The magnetic bulk Rashba system will be a promising platform for exploring the functional correlations among electric polarization, magnetization, and current.

Ferroelectric Control of the Spin Texture in GeTe

The electric and nonvolatile control of the spin texture in semiconductors would represent a fundamental step toward novel electronic devices combining memory and computing functionalities. Recently, GeTe has been theoretically proposed as the father compound of a new class of materials, namely ferroelectric Rashba semiconductors. They display bulk bands with giant Rashba-like splitting due to the inversion symmetry breaking arising from the ferroelectric polarization, thus allowing for the ferroelectric control of the spin. Here, we provide the experimental demonstration of the correlation between ferroelectricity and spin texture. A surface-engineering strategy is used to set two opposite predefined uniform ferroelectric polarizations, inward and outward, as monitored by piezoresponse force microscopy. Spin and angular resolved photoemission experiments show that these GeTe(111) surfaces display opposite sense of circulation of spin in bulk Rashba bands. Furthermore, we demonstrate the crafting of nonvolatile ferroelectric patterns in GeTe films at the nanoscale by using the conductive tip of an atomic force microscope. Based on the intimate link between ferroelectric polarization and spin in GeTe, ferroelectric patterning paves the way to the investigation of devices with engineered spin configurations.

Magnetic Skyrmionic Polarons

We study a two-dimensional electron gas exchange coupled to a system of classical magnetic ions. For large Rashba spin-orbit coupling, a single electron can become self-trapped in a skyrmion spin texture self-induced in the magnetic ions system. This new quasiparticle carries electrical and topological charge as well as a large spin, and we named it as magnetic skyrmionic polaron. We study a range of parameters; temperature, exchange coupling, Rashba coupling, and magnetic field, for which the magnetic skyrmionic polaron is the fundamental state in the system. The dynamics of this quasiparticle is studied using the collective coordinate approximation, and we obtain that in the presence of an electric field the new quasiparticle shows, due to the chirality of the skyrmion, a Hall effect. Finally, we argue that the magnetic skyrmionic polarons can be found in large Rashba spin-orbit coupling semiconductors as GeMnTe.

Bulk Rashba Semiconductors and Related Quantum Phenomena

Bithmuth tellurohalides BiTeX (X = Cl, Br and I) are model examples of bulk Rashba semiconductors, exhibiting a giant Rashba-type spin splitting among their both valence and conduction bands. Extensive spectroscopic and transport experiments combined with the state-of-the-art first-principles calculations have revealed many unique quantum phenomena emerging from the bulk Rashba effect in these systems. The novel features such as the exotic inter- and intra-band optical transitions, enhanced magneto-optical response, divergent orbital dia-/para-magnetic susceptibility and helical spin textures with a nontrivial Berry's phase in the momentum space are among the salient discoveries, all arising from this effect. Also, it is theoretically proposed and indications have been experimentally reported that bulk Rashba semiconductors such as BiTeI have the capability of becoming a topological insulator under the application of a hydrostatic pressure. Here, we overview these studies and show that BiTeX are an ideal platform to explore the next aspects of quantum matter, which could ultimately be utilized to create spintronic devices with novel functionalities.

Hosting of surface states in spin-orbit induced projected bulk band gaps of W(1 1 0) and Ir(1 1 1)

Spin-momentum locking of surface states has attracted great interest in recent years due to envisioned technological applications in the field of spintronics. Normal metal surfaces like W(1 1 0) and Ir(1 1 1) show surface states with energy dispersions and spin-polarization textures, which are reminiscent of topologically non-trivial surface states. In order to understand this phenomenon the connection of bulk and surface states has to be explored. Using time-of-flight momentum microscopy with soft x-ray excitation, we present a comprehensive analysis of the bulk bands of W and Ir. Surface states are determined by the same method with photon excitation in the vacuum ultraviolet region. The superposition of both spectral densities reveals the hosting of surface states within the gap structure of bulk bands projected on the surface Brillouin zone. Quantitative differences in the extension of experimental and theoretical local band gaps indicate an underestimation of electron correlation effects in theory.

Spin Orientation of Two-Dimensional Electrons Driven by Temperature-Tunable Competition of Spin-Orbit and Exchange-Magnetic Interactions

Finding ways to create and control the spin-dependent properties of two-dimensional electron states (2DESs) is a major challenge for the elaboration of novel spin-based devices. Spin-orbit and exchange-magnetic interactions (SOI and EMI) are two fundamental mechanisms that enable access to the tunability of spin-dependent properties of carriers. The silicon surface of HoRh₂Si₂ appears to be a unique model system, where concurrent SOI and EMI can be visualized and controlled by varying the temperature. The beauty and simplicity of this system lie in the 4f moments, which act as a multiple tuning instrument on the 2DESs, as the 4f projections parallel and perpendicular to the surface order at essentially different temperatures. Here we show that the SOI locks the spins of the 2DESs exclusively in the surface plane when the 4f moments are disordered: the Rashba-Bychkov effect. When the temperature is gradually lowered and the system experiences magnetic order, the rising EMI progressively competes with the SOI leading to a fundamental change in the spin-dependent properties of the 2DESs. The spins rotate and reorient toward the out-of-plane Ho 4f moments. Our findings show that the direction of the spins and the spin-splitting of the two-dimensional electrons at the surface can be manipulated in a controlled way by using only one parameter: the temperature.

GeTe: a simple compound blessed with a plethora of properties

A selection from the wide range of functional properties present in the binary compound, GeTe, are reviewed is this paper.