Topologically protected magnetoelectric switching in a multiferroic.

Electric control of magnetism and magnetic control of ferroelectricity can improve the energy efficiency of magnetic memory and data-processing devices1. However, the necessary magnetoelectric switching is hard to achieve, and requires more than just a coupling between the spin and the charge degrees of freedom2-5. Here we show that an application and subsequent removal of a magnetic field reverses the electric polarization of the multiferroic GdMn2O5, thus requiring two cycles to bring the system back to the original configuration. During this unusual hysteresis loop, four states with different magnetic configurations are visited by the system, with one half of all spins undergoing unidirectional full-circle rotation in increments of about 90 degrees. Therefore, GdMn2O5 acts as a magnetic crankshaft that converts the back-and-forth variations of the magnetic field into a circular spin motion. This peculiar four-state magnetoelectric switching emerges as a topologically protected boundary between different two-state switching regimes. Our findings establish a paradigm of topologically protected switching phenomena in ferroic materials.

Structural phase purification of bulk HfO2:Y through pressure cycling.

We combine synchrotron-based infrared absorption and Raman scattering spectroscopies with diamond anvil cell techniques and first-principles calculations to explore the properties of hafnia under compression. We find that pressure drives HfO[Formula: see text]:7%Y from the mixed monoclinic ([Formula: see text]) [Formula: see text] antipolar orthorhombic ([Formula: see text]) phase to pure antipolar orthorhombic ([Formula: see text]) phase at approximately 6.3 GPa. This transformation is irreversible, meaning that upon release, the material is kinetically trapped in the [Formula: see text] metastable state at 300 K. Compression also drives polar orthorhombic ([Formula: see text]) hafnia into the tetragonal ([Formula: see text]) phase, although the latter is not metastable upon release. These results are unified by an analysis of the energy landscape. The fact that pressure allows us to stabilize targeted metastable structures with less Y stabilizer is important to preserving the flat phonon band physics of pure HfO[Formula: see text].

Observation of chiral surface excitons in a topological insulator Bi2Se3.

The protected electron states at the boundaries or on the surfaces of topological insulators (TIs) have been the subject of intense theoretical and experimental investigations. Such states are enforced by very strong spin-orbit interaction in solids composed of heavy elements. Here, we study the composite particles-chiral excitons-formed by the Coulomb attraction between electrons and holes residing on the surface of an archetypical 3D TI, [Formula: see text] Photoluminescence (PL) emission arising due to recombination of excitons in conventional semiconductors is usually unpolarized because of scattering by phonons and other degrees of freedom during exciton thermalization. On the contrary, we observe almost perfectly polarization-preserving PL emission from chiral excitons. We demonstrate that the chiral excitons can be optically oriented with circularly polarized light in a broad range of excitation energies, even when the latter deviate from the (apparent) optical band gap by hundreds of millielectronvolts, and that the orientation remains preserved even at room temperature. Based on the dependences of the PL spectra on the energy and polarization of incident photons, we propose that chiral excitons are made from massive holes and massless (Dirac) electrons, both with chiral spin textures enforced by strong spin-orbit coupling. A theoretical model based on this proposal describes quantitatively the experimental observations. The optical orientation of composite particles, the chiral excitons, emerges as a general result of strong spin-orbit coupling in a 2D electron system. Our findings can potentially expand applications of TIs in photonics and optoelectronics.

Total Angular Momentum Dichroism of the Terahertz Vortex Beams at the Antiferromagnetic Resonances.

Terahertz vortex beams with different superposition of the orbital angular momentum l=±1, ±2, ±3, and ±4 and spin angular momentum σ=±1 were used to study antiferromagnetic (AFM) resonances in TbFe_{3}(BO_{3})_{4} and Ni_{3}TeO_{6} single crystals. In both materials we observed a strong vortex beam dichroism for the AFM resonances that are split in external magnetic field. The magnitude of the vortex dichroism is comparable to that for conventional circular dichroism due to σ. The selection rules at the AFM resonances are governed by the total angular momentum of the vortex beam: j=σ+l. In particular, for l=±2, ±3, and ±4 the sign of l is shown to dominate over that for conventional circular polarization σ.

From One- to Two-Magnon Excitations in the S=3/2 Magnet ß-CaCr_{2}O_{4}.

We apply neutron spectroscopy to measure the magnetic dynamics in the S=3/2 magnet ß-CaCr_{2}O_{4} (T_{N}=21 K). The low-energy fluctuations, in the ordered state, resemble large-S linear spin waves from the incommensurate ground state. However, at higher energy transfers, these semiclassical and harmonic dynamics are replaced by an energy and momentum broadened continuum of excitations. Applying kinematic constraints required for energy and momentum conservation, sum rules of neutron scattering, and comparison against exact diagonalization calculations, we show that the dynamics at high-energy transfers resemble low-S one-dimensional quantum fluctuations. ß-CaCr_{2}O_{4} represents an example of a magnet at the border between classical Néel and quantum phases, displaying dual characteristics.

Terahertz Vortex Beam as a Spectroscopic Probe of Magnetic Excitations.

Circularly polarized light with spin angular momentum is one of the most valuable probes of magnetism. We demonstrate that light beams with orbital angular momentum (OAM), or vortex beams, can also couple to magnetism exhibiting dichroisms in a magnetized medium. Resonant optical absorption in a ferrimagnetic crystal depends strongly on both the handedness of the vortex and the direction of the beam propagation with respect to the sample magnetization. This effect exceeds the conventional dichroism for circularly polarized light. Our results demonstrate the high potential of the vortex beams with OAM as a new spectroscopic probe of magnetism in matter.

Asymmetric Splitting of an Antiferromagnetic Resonance via Quartic Exchange Interactions in Multiferroic Hexagonal HoMnO_{3}.

The symmetric splitting of two spin-wave branches in an antiferromagnetic resonance (AFR) experiment has been an essential measurement of antiferromagnets for over half a century. In this work, circularly polarized time-domain THz spectroscopy experiments performed on the low symmetry multiferroic hexagonal HoMnO_{3} reveal an AFR of the Mn sublattice to split asymmetrically in an applied magnetic field, with an ≈50% difference in g factors between the high and low energy branches of this excitation. The temperature dependence of the g factors, including a drastic renormalization at the Ho spin ordering temperature, reveals this asymmetry to unambiguously stem from Ho-Mn interactions. Theoretical calculations demonstrate that the AFR asymmetry is not explained by conventional Ho-Mn exchange mechanisms alone and is only reproduced if quartic spin interactions are also included in the spin Hamiltonian. Our results provide a paradigm for the optical study of such novel interactions in hexagonal manganites and low symmetry antiferromagnets in general.

Chiral Spin Mode on the Surface of a Topological Insulator.

Using polarization-resolved resonant Raman spectroscopy, we explore collective spin excitations of the chiral surface states in a three dimensional topological insulator, Bi_{2}Se_{3}. We observe a sharp peak at 150 meV in the pseudovector A_{2} symmetry channel of the Raman spectra. By comparing the data with calculations, we identify this peak as the transverse collective spin mode of surface Dirac fermions. This mode, unlike a Dirac plasmon or a surface plasmon in the charge sector of excitations, is analogous to a spin wave in a partially polarized Fermi liquid, with spin-orbit coupling playing the role of an effective magnetic field.

Hidden Antipolar Order Parameter and Entangled Néel-Type Charged Domain Walls in Hybrid Improper Ferroelectrics.

Hybrid improper ferroelectricity (HIF) denotes a new class of polar instability by the mixture of two octahedral-distortion modes and can feature the coexistence of abundant head-to-head and tail-to-tail polar domains, of which the domain walls tend to be charged due to the respective screening charges with an opposite sign. However, no such coexisting carriers are available in the materials. Using group-theoretical, microscopic, and spectroscopic analyses, we establish the existence of a hidden antipolar order parameter in model HIF (Ca,Sr)_{3}Ti_{2}O_{7} by the condensation of a weak, previously unnoticed antipolar lattice instability, turning the order-parameter spaces to be multicomponent with the distinct polar-antipolar intertwining and accompanied formation of Néel-type twinlike antipolar domain walls (few nanometers) between the head-to-head and tail-to-tail domains. The finite-width Néel walls and correlated domain topology inherently lift the polar divergences between the domains, casting an emergent exemplification of charged domain-wall screening by an antipolar ingredient.

Orphan Spins in the S=5/2 Antiferromagnet CaFe_{2}O_{4}.

CaFe_{2}O_{4} is an anisotropic S=5/2 antiferromagnet with two competing A (↑↑↓↓) and B (↑↓↑↓) magnetic order parameters separated by static antiphase boundaries at low temperatures. Neutron diffraction and bulk susceptibility measurements, show that the spins near these boundaries are weakly correlated and a carry an uncompensated ferromagnetic moment that can be tuned with a magnetic field. Spectroscopic measurements find these spins are bound with excitation energies less than the bulk magnetic spin waves and resemble the spectra from isolated spin clusters. Localized bound orphaned spins separate the two competing magnetic order parameters in CaFe_{2}O_{4}.

Toward the Intrinsic Limit of the Topological Insulator Bi_{2}Se_{3}.

Combining high resolution scanning tunneling microscopy and first principles calculations, we identified the major native defects, in particular the Se vacancies and Se interstitial defects, that are responsible for the bulk conduction and nanoscale potential fluctuations in single crystals of archetypal topological insulator Bi_{2}Se_{3}. Here it is established that the defect concentrations in Bi_{2}Se_{3} are far above the thermodynamic limit, and that the growth kinetics dominate the observed defect concentrations. Furthermore, through careful control of the synthesis, our tunneling spectroscopy suggests that our best samples are approaching the intrinsic limit with the Fermi level inside the band gap without introducing extrinsic dopants.

Solitary Magnons in the S=5/2 Antiferromagnet CaFe_{2}O_{4}.

CaFe_{2}O_{4} is a S=5/2 anisotropic antiferromagnet based upon zig-zag chains having two competing magnetic structures, denoted as the A (↑↑↓↓) and B (↑↓↑↓) phases, which differ by the c-axis stacking of ferromagnetic stripes. We apply neutron scattering to demonstrate that the competing A and B phase order parameters result in magnetic antiphase boundaries along c which freeze on the time scale of ∼1 ns at the onset of magnetic order at 200 K. Using high resolution neutron spectroscopy, we find quantized spin wave levels and measure 9 such excitations localized in regions ∼1-2 c-axis lattice constants in size. We discuss these in the context of solitary magnons predicted to exist in anisotropic systems. The magnetic anisotropy affords both competing A+B orders as well as localization of spin excitations in a classical magnet.

Direct visualization of magnetoelectric domains.

The coupling between the magnetic and electric dipoles in multiferroic and magnetoelectric materials holds promise for conceptually novel electronic devices. This calls for the development of local probes of the magnetoelectric response, which is strongly affected by defects in magnetic and ferroelectric ground states. For example, multiferroic hexagonal rare earth manganites exhibit a dense network of boundaries between six degenerate states of their crystal lattice, which are locked to both ferroelectric and magnetic domain walls. Here we present the application of a magnetoelectric force microscopy technique that combines magnetic force microscopy with in situ modulating high electric fields. This method allows us to image the magnetoelectric response of the domain patterns in hexagonal manganites directly. We find that this response changes sign at each structural domain wall, a result that is corroborated by symmetry analysis and phenomenological modelling, and provides compelling evidence for a lattice-mediated magnetoelectric coupling. The direct visualization of magnetoelectric domains at mesoscopic scales opens up explorations of emergent phenomena in multifunctional materials with multiple coupled orders.

Negative thermal expansion in hybrid improper ferroelectric Ruddlesden-Popper perovskites by symmetry trapping.

We present new results on the microscopic nature of the ferroelectricity mechanisms in Ca3 Mn2O7 and Ca3Ti2O7. To the first approximation, we confirm the hybrid improper ferroelectric mechanism recently proposed by Benedek and Fennie for these Ruddlesden-Popper compounds. However, in Ca3Mn2O7 we find that there is a complex competition between lattice modes of different symmetry which leads to a phase coexistence over a large temperature range and the "symmetry trapping" of a soft mode. This trapping of the soft mode leads to a large uniaxial negative thermal expansion (NTE) reaching a maximum between 250 and 350 K (3.6×10^(-6) K^{-1}) representing the only sizable NTE reported for these and related perovskite materials to date. Our results suggest a systematic strategy for designing and searching for ceramics with large NTE coefficients.

Optical Diode Effect at Spin-Wave Excitations of the Room-Temperature Multiferroic BiFeO_{3}.

Multiferroics permit the magnetic control of the electric polarization and the electric control of the magnetization. These static magnetoelectric (ME) effects are of enormous interest: The ability to read and write a magnetic state current-free by an electric voltage would provide a huge technological advantage. Dynamic or optical ME effects are equally interesting, because they give rise to unidirectional light propagation as recently observed in low-temperature multiferroics. This phenomenon, if realized at room temperature, would allow the development of optical diodes which transmit unpolarized light in one, but not in the opposite, direction. Here, we report strong unidirectional transmission in the room-temperature multiferroic BiFeO_{3} over the gigahertz-terahertz frequency range. The supporting theory attributes the observed unidirectional transmission to the spin-current-driven dynamic ME effect. These findings are an important step toward the realization of optical diodes, supplemented by the ability to switch the transmission direction with a magnetic or electric field.

Origin of first-order-type electronic and structural transitions in IrTe2.

We have explored the origin of unusual first-order-type electronic and structural transitions in IrTe2, based on the first-principles total energy density functional theory analysis. We have clarified that the structural transition occurs through the interplay among the charge density wavelike lattice modulation with q1/5=(1/5,0,1/5), in-plane dimer ordering, and the uniform lattice deformation. The Ir-Ir dimer formation via a molecular-orbital version of the Jahn-Teller distortion in the Ir-Ir zigzag stripe is found to play the most important role in producing the charge disproportionation state. Angle-resolved photoemission spectroscopy reveals the characteristic features of structural transition, which are in good agreement with the density functional theory bands obtained by the band-unfolding technique.

Successive Magnetic-Field-Induced Transitions and Colossal Magnetoelectric Effect in Ni_{3}TeO_{6}.

We report the discovery of a metamagnetic phase transition in a polar antiferromagnet Ni_{3}TeO_{6} that occurs at 52 T. The new phase transition accompanies a colossal magnetoelectric effect, with a magnetic-field-induced polarization change of 0.3 µC/cm^{2}, a value that is 4 times larger than for the spin-flop transition at 9 T in the same material, and also comparable to the largest magnetically induced polarization changes observed to date. Via density-functional calculations we construct a full microscopic model that describes the data. We model the spin structures in all fields and clarify the physics behind the 52 T transition. The high-field transition involves a competition between multiple different exchange interactions which drives the polarization change through the exchange-striction mechanism. The resultant spin structure is rather counterintuitive and complex, thus providing new insights on design principles for materials with strong magnetoelectric coupling.

Unfolding of vortices into topological stripes in a multiferroic material.

Multiferroic hexagonal RMnO(3) (R=rare earths) crystals exhibit dense networks of vortex lines at which six domain walls merge. While the domain walls can be readily moved with an applied electric field, the vortex cores so far have been impossible to control. Our experiments demonstrate that shear strain induces a Magnus-type force pulling vortices and antivortices in opposite directions and unfolding them into a topological stripe domain state. We discuss the analogy between this effect and the current-driven dynamics of vortices in superconductors and superfluids.

Temperature-dependent interplay of Dzyaloshinskii-Moriya interaction and single-ion anisotropy in multiferroic BiFeO3.

Low-energy magnon excitations in multiferroic BiFeO3 were measured in detail as a function of temperature around several Brillouin zone centers by inelastic neutron scattering experiments on single crystals. Unique features around 1 meV are directly associated with the interplay of the Dzyaloshinskii-Moriya interaction and a small single-ion anisotropy. The temperature dependence of these and the exchange interactions were determined by fitting the measured magnon dispersion with spin-wave calculations. The spectra best fit an easy-axis type magnetic anisotropy and the deduced exchange and anisotropy parameters enable us to determine the anharmonicity of the magnetic cycloid. We then draw a direct connection between the changes in the parameters of spin Hamiltonian with temperature and the physical properties and structural deformations of BiFeO3.

Dimerization-induced Fermi-surface reconstruction in IrTe2.

We report a de Haas-van Alphen (dHvA) oscillation study on IrTe2 single crystals showing complex dimer formations. By comparing the angle dependence of dHvA oscillations with band structure calculations, we show distinct Fermi surface reconstruction induced by a 1/5-type and a 1/8-type dimerizations. This verifies that an intriguing quasi-two-dimensional conducting plane across the layers is induced by dimerization in both cases. A phase transition to the 1/8 phase with higher dimer density reveals that local instabilities associated with intra- and interdimer couplings are the main driving force for complex dimer formations in IrTe2.