Current-induced Orbital and Spin Magnetizations in Crystals with Helical Structure

Observation of edge states derived from topological helix chains

Introducing the concept of topology has revolutionized materials classification, leading to the discovery of topological insulators and Dirac-Weyl semimetals1-3. One of the most fundamental theories underpinning topological materials is the Su-Schrieffer-Heeger (SSH) model4,5, which was developed in 1979-decades before the recognition of topological insulators-to describe conducting polymers. Distinct from the vast majority of known topological insulators with two and three dimensions1-3, the SSH model predicts a one-dimensional analogue of topological insulators, which hosts topological bound states at the endpoints of a chain4-8. To establish this unique and pivotal state, it is crucial to identify the low-energy excitations stemming from bound states, but this has remained unknown in solids because of the absence of suitable platforms. Here we report unusual electronic states that support the emergent bound states in elemental tellurium, the single helix of which was recently proposed to realize an extended version of the SSH chain9,10. Using spin- and angle-resolved photoemission spectroscopy with a micro-focused beam, we have shown spin-polarized in-gap states confined to the edges of the (0001) surface. Our density functional theory calculations indicate that these states are attributed to the interacting bound states originating from the one-dimensional array of SSH tellurium chains. Helices in solids offer a promising experimental platform for investigating exotic properties associated with the SSH chain and exploring topological phases through dimensionality control.

Quantification of chirality based on electric toroidal monopole

Chirality ubiquitously appears in nature; however, its quantification remains obscure owing to the lack of microscopic description at the quantum-mechanical level. We propose a way of evaluating chirality in terms of the electric toroidal monopole, a practical entity of time-reversal even pseudoscalar (parity-odd) objects reflecting relevant electronic wave functions. For this purpose, we analyze a twisted methane molecule at the quantum-mechanical level, showing that the electric toroidal monopoles become a quantitative indicator for chirality. In the twisted methane, we clarify that the handedness of chirality corresponds to the sign of the expectation value of the electric toroidal monopole and that the most important ingredient is the modulation of the spin-dependent imaginary hopping between the hydrogen atoms, while the relativistic spin-orbit coupling within the carbon atom is irrelevant for chirality.

Dominance of Extrinsic Scattering Mechanisms in the Orbital Hall Effect: Graphene, Transition Metal Dichalcogenides, and Topological Antiferromagnets

The theory of the orbital Hall effect (OHE), a transverse flow of orbital angular momentum (OAM) in response to an electric field, has concentrated on intrinsic mechanisms. Here, using a quantum kinetic formulation, we determine the full OHE in the presence of short-range disorder using 2D massive Dirac fermions as a prototype. We find that, in doped systems, extrinsic effects associated with the Fermi surface (skew scattering and side jump) provide ≈95% of the OHE. This suggests that, at experimentally relevant transport densities, the OHE is primarily extrinsic.

Optoelectronic Manifestation of Orbital Angular Momentum Driven by Chiral Hopping in Helical Se Chains

Chiral materials have garnered significant attention in the field of condensed matter physics. Nevertheless, the magnetic moment induced by the chiral spatial motion of electrons in helical materials, such as elemental Te and Se, remains inadequately understood. In this work, we investigate the development of quantum angular momentum enforced by chirality by using static and time-dependent density functional theory calculations for an elemental Se chain. Our findings reveal the emergence of an unconventional orbital texture driven by the chiral geometry, giving rise to a nonvanishing current-induced orbital moment. By incorporating spin-orbit coupling, we demonstrate that current-induced spin accumulation arises in the chiral chain, which fundamentally differs from the conventional Edelstein effect. Furthermore, we demonstrate optoelectronic detection of the orbital angular momentum in the chiral Se chain, providing an alternative to the interband Berry curvature, which is ill-defined in low dimensions.

Time-Reversal-Even Nonlinear Current Induced Spin Polarization

We propose a time-reversal-even spin generation in second order of electric fields, which dominates the current induced spin polarization in a wide class of centrosymmetric nonmagnetic materials, and leads to a novel nonlinear spin-orbit torque in magnets. We reveal a quantum origin of this effect from the momentum space dipole of the anomalous spin polarizability. First-principles calculations predict sizable spin generations in several nonmagnetic hcp metals, in monolayer TiTe_{2}, and in ferromagnetic monolayer MnSe_{2}, which can be detected in experiment. Our work opens up the broad vista of nonlinear spintronics in both nonmagnetic and magnetic systems.

Spin Polarization of Polyalanine Molecules in 2D and Dimer-Row Assemblies Adsorbed on Magnetic Substrates: The Role of Coupling, Chirality, and Coordination

Propagation of electrons along helical molecules adsorbed on surfaces comes along with a robust spin polarization effect called chirality induced spin selectivity CISS. However, experiments on the molecular scale that allow a true correlation of spin effects with the molecular structure are quite rare. Here we have studied the structure of self-assembled chiral molecules and the electronic transmission and spin polarization of the current through the system by means of ambient scanning tunneling microscopy and spectroscopy in heterostructures of various α-helix polyalanine-based molecules (PA) adsorbed on Al₂O₃/Pt/Au/Co/Au substrates with perpendicular magnetic anisotropy. We have found a phase separation of the molecules into well-ordered enantiopure 2D hexagonal phases and quasi-1D heterochiral-dimer structures, which allows for the analysis of the spin polarization with almost atomic precision of PA in different phases. The spin polarization reaches up to 75% for chemisorbed molecules arranged in a hexagonal phase. On the contrary, for weakly coupled PA molecules without cysteine anchoring groups in a quasi-1D phase, a spin polarization of around 50% was found. Our results show that both the intermolecular interaction as well as the coupling to the substrate are important and point out that collective effects within the molecules and at the interfaces are required to achieve a high chiral induced spin selectivity.

Direct visualization of Rashba-split bands and spin/orbital-charge interconversion at KTaO3 interfaces

Rashba interfaces have emerged as promising platforms for spin-charge interconversion through the direct and inverse Edelstein effects. Notably, oxide-based two-dimensional electron gases display a large and gate-tunable conversion efficiency, as determined by transport measurements. However, a direct visualization of the Rashba-split bands in oxide two-dimensional electron gases is lacking, which hampers an advanced understanding of their rich spin-orbit physics. Here, we investigate KTaO₃ two-dimensional electron gases and evidence their Rashba-split bands using angle resolved photoemission spectroscopy. Fitting the bands with a tight-binding Hamiltonian, we extract the effective Rashba coefficient and bring insight into the complex multiorbital nature of the band structure. Our calculations reveal unconventional spin and orbital textures, showing compensation effects from quasi-degenerate band pairs which strongly depend on in-plane anisotropy. We compute the band-resolved spin and orbital Edelstein effects, and predict interconversion efficiencies exceeding those of other oxide two-dimensional electron gases. Finally, we suggest design rules for Rashba systems to optimize spin-charge interconversion performance.

Visualization of the Rashbasplit bands in oxide two-dimensional electron gases is lacking, which hampers understanding of their rich spin-orbit physics. Here, the authors investigate KTaO₃ two dimensional electron gases and their Rashba-split bands.

Rotation, Electric-Field Responses, and Absolute Enantioselection in Chiral Crystals

The microscopic origin of chirality, possible electric-field induced static rotational lattice deformation, and rotation-field induced electric polarization are investigated. By building up a realistic tight-binding model for the elemental Te crystal in terms of a symmetry-adapted basis, we identify the microscopic origin of the chirality and essential couplings among polar and axial vectors with the same time-reversal properties. Based on this microscopic model, we elucidate quantitatively that an interband process, driven by nearest-neighbor spin-dependent imaginary hopping, is the key factor in the electric-field induced rotation and its inverse response. From the symmetry point of view, these couplings and responses are characteristic and common to any chiral material, leading to a possible experimental approach to achieve absolute enantioselection by simultaneously applied electric and rotation fields, or a magnetic field and electric current, and so on, as a conjugate field of the chirality.

Gate-tuneable and chirality-dependent charge-to-spin conversion in tellurium nanowires

Chiral materials are an ideal playground for exploring the relation between symmetry, relativistic effects and electronic transport. For instance, chiral organic molecules have been intensively studied to electrically generate spin-polarized currents in the last decade, but their poor electronic conductivity limits their potential for applications. Conversely, chiral inorganic materials such as tellurium have excellent electrical conductivity, but their potential for enabling the electrical control of spin polarization in devices remains unclear. Here, we demonstrate the all-electrical generation, manipulation and detection of spin polarization in chiral single-crystalline tellurium nanowires. By recording a large (up to 7%) and chirality-dependent unidirectional magnetoresistance, we show that the orientation of the electrically generated spin polarization is determined by the nanowire handedness and uniquely follows the current direction, while its magnitude can be manipulated by an electrostatic gate. Our results pave the way for the development of magnet-free chirality-based spintronic devices.

Orbital Dynamics in Centrosymmetric Systems

Orbital dynamics in time-reversal-symmetric centrosymmetric systems is examined theoretically. Contrary to common belief, we demonstrate that many aspects of orbital dynamics are qualitatively different from spin dynamics because the algebraic properties of the orbital and spin angular momentum operators are different. This difference generates interesting orbital responses, which do not have spin counterparts. For instance, the orbital angular momentum expectation values may oscillate even without breaking neither the time-reversal nor the inversion symmetry. Our quantum Boltzmann approach reproduces the previous result on the orbital Hall effect and reveals additional orbital dynamics phenomena, whose detection schemes are discussed briefly. Our work will be useful for the experimental differentiation of the orbital dynamics from the spin dynamics.

Detection of graphene's divergent orbital diamagnetism at the Dirac point

[Figure: see text].

Magneto-chiral anisotropy: From fundamentals to perspectives

The interplay between chirality and magnetic fields gives rise to a cross effect referred to as magneto-chiral anisotropy (MChA), which can manifest itself in different physical properties of chiral magnetized materials. The first experimental demonstration of MChA was by optical means with visible light. Further optical manifestations of MChA have been evidenced across most of the electromagnetic spectrum, from terahertz to X-rays. Moreover, exploiting the versatility of molecular chemistry toward chiral magnetic systems, many efforts have been made to identify the microscopic origins of optical MChA, necessary to advance the effect toward technological applications. In parallel, the replacement of light by electric current has allowed the observation of nonreciprocal electrical charge transport in both molecular and inorganic conductors as a result of electrical MChA (eMChA). MChA in other domains such as sound propagation, photochemistry, and electrochemistry are still in their infancy, with only a few experimental demonstrations, and offer wide perspectives for further studies with potentially large impact, like the understanding of the homochirality of life. After a general introduction to MChA, we give a complete review of all these phenomena, particularly during the last decade.

Kramers nodal line metals

Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.

Chirality-Dependent Circular Photogalvanic Effect in Enantiomorphic 2D Organic-Inorganic Hybrid Perovskites

The control of the optoelectronic properties of 2D organic-inorganic hybrid perovskite (2D-OIHP) lead halides is an increasingly prevalent topic. Herein, the observation of the circular photogalvanic effect (CPGE) in new enantiomorphic 2D-OIHP lead iodides is reported, which are synthesized as a first OIHP-related system belonging to a chiral space group by incorporating organic chiral cations into the inorganic layers of lead iodides. The CPGE is an optoelectronic phenomenon associated with the spin-orbit coupling of heavy atoms in noncentrosymmetric systems. Owing to the CPGE, light-helicity-dependent steady photocurrents are generated without an external bias voltage under the irradiation of circularly polarized light. Furthermore, the sign reversal of the CPGE photocurrent depending on the chirality of the designed 2D-OIHP lead iodides is observed. This result indicates formation of the theoretically predicted radial spin-polarized texture in k-space of chiral systems owing to spin-momentum locking. Hence, chiral 2D-OIHP lead halides can be a promising platform for engineering opto-spintronic functionalities.

Radial Spin Texture of the Weyl Fermions in Chiral Tellurium

Trigonal tellurium, a small-gap semiconductor with pronounced magneto-electric and magneto-optical responses, is among the simplest realizations of a chiral crystal. We have studied by spin- and angle-resolved photoelectron spectroscopy its unconventional electronic structure and unique spin texture. We identify Kramers-Weyl, composite, and accordionlike Weyl fermions, so far only predicted by theory, and show that the spin polarization is parallel to the wave vector along the lines in k space connecting high-symmetry points. Our results clarify the symmetries that enforce such spin texture in a chiral crystal, thus bringing new insight in the formation of a spin vectorial field more complex than the previously proposed hedgehog configuration. Our findings thus pave the way to a classification scheme for these exotic spin textures and their search in chiral crystals.

Chirality-Induced Spin-Polarized State of a Chiral Crystal CrNb_{3}S_{6}

Chirality-induced spin transport phenomena are investigated at room temperature without magnetic fields in a monoaxial chiral dichalcogenide CrNb_{3}S_{6}. We found that spin polarization occurs in these chiral bulk crystals under a charge current flowing along the principal c axis. Such phenomena are detected as an inverse spin Hall signal which is induced on the detection electrode that absorbs polarized spin from the chiral crystal. The inverse response is observed when applying the charge current into the detection electrode. The signal sign reverses in the device with the opposite chirality. Furthermore, the spin signals are found over micrometer length scales in a nonlocal configuration. Such a robust generation and protection of the spin-polarized state is discussed based on a one-dimensional model with an antisymmetric spin-orbit coupling.

Wannier90 as a community code: new features and applications

Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with high-throughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic source-code documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.

Radial Spin Texture in Elemental Tellurium with Chiral Crystal Structure

The chiral crystal is characterized by a lack of mirror symmetry and inversion center, resulting in the inequivalent right- and left-handed structures. In the noncentrosymmetric crystal structure, the spin and momentum of electrons are expected to be locked in the reciprocal space with the help of the spin-orbit interaction. To reveal the spin textures of chiral crystals, we investigate the spin and electronic structure in a p-type semiconductor, elemental tellurium, with the simplest chiral structure by using spin- and angle-resolved photoemission spectroscopy. Our data demonstrate that the highest valence band crossing the Fermi level has a spin component parallel to the electron momentum around the Brillouin zone corners. Significantly, we have also confirmed that the spin polarization is reversed in the crystal with the opposite chirality. The results indicate that the spin textures of the right- and left-handed chiral crystals are hedgehoglike, leading to unconventional magnetoelectric effects and nonreciprocal phenomena.

Strain Engineering of the Berry Curvature Dipole and Valley Magnetization in Monolayer MoS_{2}

The Berry curvature dipole is a physical quantity that is expected to allow various quantum geometrical phenomena in a range of solid-state systems. Monolayer transition metal dichalcogenides provide an exceptional platform to modulate and investigate the Berry curvature dipole through strain. Here, we theoretically demonstrate and experimentally verify for monolayer MoS_{2} the generation of valley orbital magnetization as a response to an in-plane electric field due to the Berry curvature dipole. The measured valley orbital magnetization shows excellent agreement with the calculated Berry curvature dipole, which can be controlled by the magnitude and direction of strain. Our results show that the Berry curvature dipole acts as an effective magnetic field in current-carrying systems, providing a novel route to generate magnetization.

Mixed topological semimetals driven by orbital complexity in two-dimensional ferromagnets

The concepts of Weyl fermions and topological semimetals emerging in three-dimensional momentum space are extensively explored owing to the vast variety of exotic properties that they give rise to. On the other hand, very little is known about semimetallic states emerging in two-dimensional magnetic materials, which present the foundation for both present and future information technology. Here, we demonstrate that including the magnetization direction into the topological analysis allows for a natural classification of topological semimetallic states that manifest in two-dimensional ferromagnets as a result of the interplay between spin-orbit and exchange interactions. We explore the emergence and stability of such mixed topological semimetals in realistic materials, and point out the perspectives of mixed topological states for current-induced orbital magnetism and current-induced domain wall motion. Our findings pave the way to understanding, engineering and utilizing topological semimetallic states in two-dimensional spin-orbit ferromagnets.

Topological quantum properties of chiral crystals

Chiral crystals are materials with a lattice structure that has a well-defined handedness due to the lack of inversion, mirror or other roto-inversion symmetries. Although it has been shown that the presence of crystalline symmetries can protect topological band crossings, the topological electronic properties of chiral crystals remain largely uncharacterized. Here we show that Kramers-Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin-orbit coupling and are guaranteed by structural chirality, lattice translation and time-reversal symmetry. Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. We identify representative chiral materials in 33 of the 65 chiral space groups in which Kramers-Weyl fermions are relevant to the low-energy physics. We determine that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin-orbit coupling carry non-trivial Chern numbers. Kramers-Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window.

Phonon Angular Momentum Induced by the Temperature Gradient

Phonon modes in crystals can have angular momenta in general. It nevertheless cancels in equilibrium when the time-reversal symmetry is preserved. In this Letter, we show that when a temperature gradient is applied and heat current flows in the crystal, the phonon distribution becomes off equilibrium, and a finite angular momentum is generated by the heat current. This mechanism is analogous to the Edelstein effect in electronic systems. This effect requires crystals with sufficiently low crystallographic symmetries, such as polar or chiral crystal structures. Because of the positive charges of the nuclei, this phonon angular momentum induces magnetization. In addition, when the crystal can freely rotate, this generated phonon angular momentum is converted to a rigid-body rotation of the crystal, due to the conservation of the total angular momentum. Furthermore, in metallic crystals, the phonon angular momentum will be partially converted into spin angular momentum of electrons.

Tellurene: its physical properties, scalable nanomanufacturing, and device applications

Tellurium (Te) has a trigonal crystal lattice with inherent structural anisotropy. Te is multifunctional, e.g., semiconducting, photoconductive, thermoelectric, piezoelectric, etc., for applications in electronics, sensors, optoelectronics, and energy devices. Due to the inherent structural anisotropy, previously reported synthetic methods predominantly yield one-dimensional (1D) Te nanostructures. Much less is known about 2D Te nanostructures, their processing schemes, and their material properties. This review focuses on the synthesis and morphology control of emerging 2D tellurene and summarizes the latest developments in understanding the fundamental properties of monolayer and few-layer tellurene, as well as the recent advances in demonstrating prototypical tellurene devices. Finally, the prospects for future research and application opportunities as well as the accompanying challenges of 2D tellurene are summarized and highlighted.

Giant antidamping orbital torque originating from the orbital Rashba-Edelstein effect in ferromagnetic heterostructures

Enhancing the in-plane current-induced torque efficiency in inversion-symmetry-breaking ferromagnetic heterostructures is of both fundamental and practical interests for emerging magnetic memory device applications. Here, we present an interface-originated magnetoelectric effect, the orbital Rashba–Edelstein effect, for realizing large torque efficiency in Pt/Co/SiO₂/Pt films with strong perpendicular magnetic anisotropy (PMA). The key element is a pronounced Co 3d orbital splitting due to asymmetric orbital hybridization at the Pt/Co and Co/SiO₂ interfaces, which not only stabilizes the PMA but also produces a large orbital torque upon the Co magnetization with current injection. The torque efficiency is found to be strongly magnetization direction- and temperature-dependent, and can reach up to 2.83 at room temperature, which is several times to one order of magnitude larger than those previously reported. This work highlights the active role of the orbital anisotropy for efficient torque generation and indicates a route for torque efficiency optimization through orbital engineering.

The emerging spintronics applications are hampered by low current-induced torque efficiency in, for example, inversion-symmetry-breaking ferromagnetic heterostructures. Here the authors demonstrate an orbital Rashba-Edelstein effect which can enhance the torque efficiency in Pt/Co/SiO₂/Pt films due to the intrinsic Co 3d orbital anisotropy.

Orbital Edelstein Effect as a Condensed-Matter Analog of Solenoids

We theoretically study current-induced orbital magnetization in a chiral crystal. This phenomenon is an orbital version of the Edelstein effect. We propose an analogy between the current-induced orbital magnetization and an Ampère field in a solenoid in classical electrodynamics. To quantify this effect, we define a dimensionless parameter from the response coefficients relating a current density with an orbital magnetization. This dimensionless parameter can be regarded as a number of turns within a unit cell when the crystal is regarded as a solenoid, and it represents how "chiral" the crystal is. By focusing on the dimensionless parameter, one can design a band structure that realizes the induction of large orbital magnetization. In particular, a Weyl semimetal with all of the Weyl nodes close to the Fermi energy can have a large value for this dimensionless parameter, which can exceed that of a classical solenoid.

Observation of current-induced bulk magnetization in elemental tellurium

The magnetoelectric effect in bulk matter is of growing interest both fundamentally and technologically. Since the beginning of the century, the magnetoelectric effect has been studied intensively in multiferroic materials. However, magnetoelectric phenomena in materials without any (anti-)ferroic order remain almost unexplored. Here we show the observation of a new class of bulk magnetoelectric effect, by revisiting elemental trigonal tellurium. We demonstrate that elemental tellurium, which is a nonmagnetic semiconductor, exhibits current-induced magnetization. This effect is attributed to spin splitting of the bulk band owing to the lack of inversion symmetry in trigonal tellurium. This finding highlights magnetoelectricity in bulk matter driven by moving electrons without any (anti-)ferroic order. Notably, current-induced magnetization generates a magnetic field that is not circular around but is parallel to the applied current; thus, this phenomenon opens a new area of magnetic field generation beyond Ampere’s law that may lead to industrial applications.

Electrical control of magnetic response in bulk material without electric or magnetic order is rare and potentially attractive for high efficient spintronics. Here, the authors report magnetization in elemental tellurium driven purely by current without any (anti-)ferroic order.

Toward surface orbitronics: giant orbital magnetism from the orbital Rashba effect at the surface of sp-metals

As the inversion symmetry is broken at a surface, spin-orbit interaction gives rise to spin-dependent energy shifts - a phenomenon which is known as the spin Rashba effect. Recently, it has been recognized that an orbital counterpart of the spin Rashba effect - the orbital Rashba effect - can be realized at surfaces even without spin-orbit coupling. Here, we propose a mechanism for the orbital Rashba effect based on sp orbital hybridization, which ultimately leads to the electric polarization of surface states. For the experimentally well-studied system of a BiAg₂ monolayer, as a proof of principle, we show from first principles that this effect leads to chiral orbital textures in k-space. In predicting the magnitude of the orbital moment arising from the orbital Rashba effect, we demonstrate the crucial role played by the Berry phase theory for the magnitude and variation of the orbital textures. As a result, we predict a pronounced manifestation of various orbital effects at surfaces, and proclaim the orbital Rashba effect to be a key platform for surface orbitronics.

Observation of re-entrant spin reorientation in TbFe1-xMnxO3

We report a spin reorientation from Γ4(Gx, Ay, Fz) to Γ1(Ax, Gy, Cz) magnetic configuration near room temperature and a re-entrant transition from Γ1(Ax, Gy, Cz) to Γ4(Gx, Ay, Fz) at low temperature in TbFe1-xMnxO3 single crystals by performing both magnetization and neutron diffraction measurements. The Γ4 - Γ1 spin reorientation temperature can be enhanced to room temperature when x is around 0.5 ~ 0.6. These new transitions are distinct from the well-known Γ4 - Γ2 transition observed in TbFeO3, and the sinusoidal antiferromagnetism to complex spiral magnetism transition observed in multiferroic TbMnO3. We further study the evolution of magnetic entropy change (-ΔSM) versus Mn concentration to reveal the mechanism of the re-entrant spin reorientation behavior and the complex magnetic phase at low temperature. The variation of -ΔSM between a and c axes indicates the significant change of magnetocrystalline anisotropy energy in the TbFe1-xMnxO3 system. Furthermore, as Jahn-Teller inactive Fe(3+) ions coexist with Jahn-Teller active Mn(3+) ions, various anisotropy interactions, compete with each other, giving rise to a rich magnetic phase diagram. The large magnetocaloric effect reveals that the studied material could be a potential magnetic refrigerant. These findings expand our knowledge of spin reorientation phenomena and offer the alternative realization of spin-switching devices at room temperature in the rare-earth orthoferrites.

Gyrotropic Magnetic Effect and the Magnetic Moment on the Fermi Surface

The current density j^{B} induced in a clean metal by a slowly-varying magnetic field B is formulated as the low-frequency limit of natural optical activity, or natural gyrotropy. Working with a multiband Pauli Hamiltonian, we obtain from the Kubo formula a simple expression for α_{ij}^{GME}=j_{i}^{B}/B_{j} in terms of the intrinsic magnetic moment (orbital plus spin) of the Bloch electrons on the Fermi surface. An alternate semiclassical derivation provides an intuitive picture of the effect, and takes into account the influence of scattering processes in dirty metals. This "gyrotropic magnetic effect" is fundamentally different from the chiral magnetic effect driven by the chiral anomaly and governed by the Berry curvature on the Fermi surface, and the two effects are compared for a minimal model of a Weyl semimetal. Like the Berry curvature, the intrinsic magnetic moment should be regarded as a basic ingredient in the Fermi-liquid description of transport in broken-symmetry metals.