MATERIALS SCIENCE: Multiferroics as Quantum Electromagnets

Current Control of Spin Helicity and Nonreciprocal Charge Transport in a Multiferroic Conductor

A multiferroic state with both electronic polarity (P) and magnetization (M) shows the inherently strong P-M coupling when P is induced by cycloidal (Néel-wall like) spin modulation. The sign of P is determined by the clockwise or counterclockwise rotation of spin, termed the spin helicity. Such a multiferroic state is not limited to magnetic insulators but can be broadly observed in conductors. Here, the current control of the multiferroics is reported in a helimagnetic metal YMn6Sn6 and its detection through nonreciprocal resistivity (NRR). The underlying concept is the coupling of the current with the toroidal momentT ∼ P × M ∼ ( q ̂ × χ v ) × M $\bm{T}\sim \bm{P}\ensuremath{\times{}}\bm{M}\sim (\widehat{\bm{q}}\ensuremath{\times{}}{\bm{\chi}}_{v})\ensuremath{\times{}}\bm{M}$ as well as with the magneto-chirality χv · M, whereq ̂ $\hspace*{0.28em}\widehat{\bm{q}}$ and χv are the unit modulation wave vector and the vector spin chirality, respectively. An enhancement of NRR is furthermore observed by the spin-cluster scattering via χv and its fluctuation. These findings may pave the way to an exploration of multiferroic conductors and the application of the spin-helicity degree of freedom as a state variable.

Imaging of electric-field-induced domain structure in DyMnO 3 nanocrystals

Multiferroic materials that exhibit interacting and coexisting properties, like ferroelectricity and ferromagnetism, possess significant potential in the development of novel technologies that can be controlled through the application of external fields. They also exhibit varying regions of polarity, known as domains, with the interfaces that separate the domains referred to as domain walls. In this study, using three-dimensional (3D) bragg coherent diffractive imaging (BCDI), we investigate the dynamics of multiferroic domain walls in a single hexagonal dysprosium manganite (h-DyMnO3 ) nanocrystal under varying applied electric field. Our analysis reveals that domain wall motion is influenced by the pinning effects, and a threshold voltage of +3 V is required to overcome them. Using circular mean analysis and phase gradient mapping, we identified localised phase realignment and high-gradient regions corresponding to domain walls, providing insights into the behaviour of multiferroic systems under external stimuli.

Nonabelian Ginzburg-Landau theory for ferroelectrics

The Ginzburg-Landau theory, which was introduced to phenomenologically describe the destruction of superconductivity by a magnetic field at the beginning, has brought up much more knowledge beyond the original one as a mean-field theory of thermodynamics states. There the complex order parameter plays an important role. Here we propose a macroscopic theory to describe the features of ferroelectrics by a two-component complex order parameter coupled to nonabelian gauge potentials that provide more freedom to reflect interplays between different measurables. Within this theoretical framework, some recently discovered empirical static and time-independent phenomena, such as vortex, anti-vortex, spiral orders can be obtained as solutions for different gauge potentials. It is expected to bring in a new angle of view with more elucidation than the traditional one that takes the polarization as order parameter.

High Entropy Approach to Engineer Strongly Correlated Functionalities in Manganites

Technologically relevant strongly correlated phenomena such as colossal magnetoresistance (CMR) and metal-insulator transitions (MIT) exhibited by perovskite manganites are driven and enhanced by the coexistence of multiple competing magneto-electronic phases. Such magneto-electronic inhomogeneity is governed by the intrinsic lattice-charge-spin-orbital correlations, which, in turn, are conventionally tailored in manganites via chemical substitution, charge doping, or strain engineering. Alternately, the recently discovered high entropy oxides (HEOs), owing to the presence of multiple-principal cations on a given sub-lattice, exhibit indications of an inherent magneto-electronic phase separation encapsulated in a single crystallographic phase. Here, the high entropy (HE) concept is combined with standard property control by hole doping in a series of single-phase orthorhombic HE-manganites (HE-Mn), (Gd_0.25 La_0.25 Nd_0.25 Sm_0.25 )_{1- x} Sr_x MnO₃ (x = 0-0.5). High-resolution transmission microscopy reveals hitherto-unknown lattice imperfections in HEOs: twins, stacking faults, and missing planes. Magnetometry and electrical measurements infer three distinct ground states-insulating antiferromagnetic, unpercolated metallic ferromagnetic, and long-range metallic ferromagnetic-coexisting or/and competing as a result of hole doping and multi-cation complexity. Consequently, CMR ≈1550% stemming from an MIT is observed in polycrystalline pellets, matching the best-known values for bulk conventional manganites. Hence, this initial case study highlights the potential for a synergetic development of strongly correlated oxides offered by the high entropy design approach.

Record high-Tc and large practical utilization level of electric polarization in metal-free molecular antiferroelectric solid solutions

Metal-free antiferroelectric materials are holding a promise for energy storage application, owing to their unique merits of wearability, environmental friendliness, and structure tunability. Despite receiving great interests, metal-free antiferroelectrics are quite limited and it is a challenge to acquire new soft antiferroelectric candidates. Here, we have successfully exploited binary CMBrxI1-x and CMBrxCl1-x solid solution as single crystals (0 ≤ x ≤ 1, where CM is cyclohexylmethylammonium). A molecule-level modification can effectively enhance Curie temperature. Emphatically, the binary CM-chloride salt shows the highest antiferroelectric-to-paraelectric Curie temperature of ~453 K among the known molecular antiferroelectrics. Its characteristic double electrical hysteresis loops provide a large electric polarization up to ~11.4 μC/cm2, which endows notable energy storage behaviors. To our best knowledge, this work provides an effective solid-solution methodology to the targeted design of new metal-free antiferroelectric candidates toward biocompatible energy storage devices.

Metal-free ferroelectric halide perovskite exhibits visible photoluminescence correlated with local ferroelectricity

Perovskite materials with tunable electronic and structural characteristics can realize various physical properties including electrical/ionic conduction, ferroelectricity, and luminescence. Integrating and coupling these properties in a single perovskite material offer new possibilities for fundamental research and applications. In particular, coupling ferroelectricity and luminescence would enable novel applications. Here, we report that the metal-free ferroelectric perovskite MDABCO (N-methyl-N'-diazabicyclo[2.2.2]octonium)-ammonium triiodide exhibits coupled superior ferroelectricity and visible photoluminescence (PL). Besides strong second-harmonic generation (SHG) associated with its ferroelectricity, MDABCO-ammonium triiodide shows long-lifetime PL at room temperature. Remarkably, the PL intensity depends strongly on the polarization of the excitation light. We found that this anisotropy is coupled to the local crystal orientation that was determined by polarization-resolved SHG. Our results suggest that the anisotropic PL property can be tuned in response to its ferroelectric state via an external field and, thereby, presents a previosuly unobserved functionality in perovskites.

Magnetically Induced Polarization in Centrosymmetric Bonds

We reveal the microscopic origin of electric polarization P[over →] induced by noncollinear magnetic order. We show that in Mott insulators, such P[over →] is given by all possible combinations of position operators r[over →][over ^]_{ij}=(r[over →]_{ij}^{0},r[over →]_{ij}) and transfer integrals t[over ^]_{ij}=(t_{ij}^{0},t_{ij}) in the bonds, where r[over →]_{ij}^{0} and t_{ij}^{0} are spin-independent contributions in the basis of Kramers doublet states, while r[over →]_{ij} and t_{ij} stem solely from the spin-orbit interaction. Among them, the combination t_{ij}^{0}r[over →]_{ij}, which couples to the spin current, remains finite in the centrosymmetric bonds, thus yielding finite P[over →] in the case of noncollinear arrangement of spins. The form of the magnetoelectric coupling, which is controlled by r[over →]_{ij}, appears to be rich and is not limited to the phenomenological law P[over →]∼ε_{ij}×[e_{i}×e_{j}] with ε_{ij} being the bond vector connecting the spins e_{i} and e_{j}. Using density-functional theory, we illustrate how the proposed mechanism works in the spiral magnets CuCl_{2}, CuBr_{2}, CuO, and α-Li_{2}IrO_{3}, providing a consistent explanation for the available experimental data.

Controlling phase transition in monolayer metal diiodides XI2(X: Fe, Co, and Ni) by carrier doping

We applied the generalized Bloch theorem to verify the ground state (most stable state) in monolayer metal diiodides 1T-XI₂(X: Fe, Co, and Ni), a family of metal dihalides, using the first-principles calculations. The ground state, which can be ferromagnetic, antiferromagnetic, or spiral state, was specified by a wavevector in the primitive unit cell. While the ground state of FeI₂is ferromagnetic, the spiral state becomes the ground state for CoI₂and NiI₂. Since the multiferroic behavior in the metal dihalide can be preserved by the spiral structure, we believe that CoI₂and NiI₂are promising multiferroic materials in the most stable state. When the lattice parameter increases, we also show that the ground state of NiI₂changes to a ferromagnetic state while others still keep their initial ground states. For the last discussion, we revealed the phase transition manipulated by the hole-electron doping due to the spin-spin competition between the ferromagnetic superexchange and the antiferromagnetic direct exchange. These results convince us that metal diiodides have many benefits for future spintronic devices.

A Photoluminescent Lead Bromide Hybrid Perovskite Molecular Ferroelastic Semiconductor with Sequential High-Tc Phase Transitions

Organic-inorganic hybrid lead halide perovskites have attracted great interest for their use in promising optoelectronic applications. However, reports of photoluminescent perovskite molecular ferroelastic semiconductors with sequential high-T_c phase transitions have been scarce. In this work, a one-dimensional lead bromide hybrid perovskite [N,N-dimethylethanolammonium]PbBr₃ has been synthesized, undergoing high-T_c sequential phase transitions at around 351 and 444 K, higher than those of most previously discovered hybrid perovskite phase transition materials. The specific intermolecular hydrogen bond between cationic molecules provides the greatest contribution to its high T_c by increasing the barrier of molecular motion under the temperature stimuli. The prominent ferroelastic domain evolution is visually observed under orthogonally polarized light. In addition, [N,N-dimethylethanolammonium]PbBr₃ exhibits semiconducting and orange light emission characteristics. This finding opens up an avenue for designing high-performance ferroelastic materials and provides great motivation for discovering new multifunctional materials for the next generation of smart devices.

Phonon and magnetoelastic coupling in Al0.5Ga0.5FeO3: Raman, magnetization and neutron diffraction studies

The intriguing coupling phenomena among spin, phonon, and charge degrees of freedom in materials having magnetic, ferroelectric and/or ferroelastic order have been of research interest for the fundamental understanding and technological relevance. We report a detailed study on structure and phonons of Al_0.5Ga_0.5FeO₃ (ALGF), a lead-free magnetoelectric material, carried out using variable temperature dependent powder neutron diffraction and Raman spectroscopy. Neutron diffraction studies suggest that Al³⁺ ions are distributed in one tetrahedrally (BO₄) and three octahedrally (BO₆) coordinated sites of the orthorhombic (Pc2₁n) structure and there is no structural transition in the temperature range of 7-800 K. Temperature dependent field-cooled and zero-field-cooled magnetization studies indicate ferrimagnetic ordering below 225 K (T_N), and that is reflected in the low temperature powder neutron diffraction data. An antiferromagnetic type arrangement of Fe³⁺ ions with net magnetic moment of 0.13 μ_B/Fe³⁺ was observed from powder neutron diffraction analysis and it corroborates the findings from magnetization studies. At the magnetic transition temperature, no drastic change in lattice strain was observed, while significant changes in phonons were observed in the Raman spectra. The deviation of several mode frequencies from the standard anharmonicity model in the ferrimagnetic phase (below 240 K) is attributed to coupling effect between spin and phonon. Spin-phonon coupling effect is discernable from Raman bands located at 270, 425, 582, 695, 738, and 841 cm^-1. Their coupling strengths (λ) have been estimated using our phonon spectra and magnetization results. BO_n (n = 4, 6) libration (restricted rotation) mode at 270 cm^-1 has the largest coupling constant (λ∼ 2.3), while the stretching vibrations located at 695 and 738 cm^-1 have the lowest coupling constant (λ∼ 0.5). In addition to the libration mode, several internal stretching and bending modes of polyhedral units are strongly affected by spin ordering.

Magnetoelectricity in multiferroics: a theoretical perspective

The key physical property of multiferroic materials is the existence of coupling between magnetism and polarization, i.e. magnetoelectricity. The origin and manifestations of magnetoelectricity can be very different in the available plethora of multiferroic systems, with multiple possible mechanisms hidden behind the phenomena. In this review, we describe the fundamental physics that causes magnetoelectricity from a theoretical viewpoint. The present review will focus on mainstream physical mechanisms in both single-phase multiferroics and magnetoelectric heterostructures. The most recent tendencies addressing possible new magnetoelectric mechanisms will also be briefly outlined.

Spin-flop and magnetodielectric reversal in Yb substituted GdMnO3

The evolution of various spin structures in Yb doped GdMnO₃ distorted orthorhombic perovskite system was investigated from their magnetic, dielectric and magnetodielectric characteristics. The Gd_1-x Yb _x MnO₃ (0  ⩽  x  ⩽  0.15) revealed an enhanced magnetodielectric coupling when their magnetic structure is guided from ab to the bc-cycloidal spin structure upon Yb doping. The compounds exhibit magnetic field and temperature controlled spin-flop from c to a-axis. Additionally, magnetodielectric reversal is observed for the x  =  0.1 sample which depends on both magnetic field and temperature. The resultant correlation between magnetic and electric orderings is discussed in the frame of symmetric and antisymmetric exchange interaction models. These findings provide further insight in understanding the magnetoelectric materials and importantly show a way to tune the magnetic and magnetodielectric properties towards better application potential.

Quasielastic and low-energy inelastic neutron scattering study of HoCrO3 by high resolution time-of-flight neutron spectroscopy

In order to understand the origin of the huge quasielastic magnetic scattering observed previously with a back-scattering neutron spectrometer, we have re-investigated the low energy excitations in HoCrO₃ by inelastic neutron scattering in a much wider energy range with time-of-flight neutron spectrometers. The inelastic signals are due to the excitations between the ground state doublet of the Ho ion. The quasielastic signal is due to the fluctuation of the disordered Ho moments. At low temperature the intensity of quasielastic scattering is small. It starts increasing as the temperature increases above 30 K. At the same temperature, the elastic intensity due to Ho moment ordering decreases in a similar way. This observation strengthens the hypothesis that the quasielastic scattering is due the fluctuations of the disordered Ho moments. The time scale of fluctuations has been determine from the quasielastic scattering and was found to vary from about 22 ps at [Formula: see text] K to about 2.5 ps at [Formula: see text] K. The stretched exponential line shape indicates a distribution of decay rates at low temperatures.

Continuous Hydrothermal Synthesis of Inorganic Nanoparticles: Applications and Future Directions

Nanomaterials are at the leading edge of the emerging field of nanotechnology. Their unique and tunable size-dependent properties (in the range 1-100 nm) make these materials indispensable in many modern technological applications. In this Review, we summarize the state-of-art in the manufacture and applications of inorganic nanoparticles made using continuous hydrothermal flow synthesis (CHFS) processes. First, we introduce ideal requirements of any flow process for nanoceramics production, outline different approaches to CHFS, and introduce the pertinent properties of supercritical water and issues around mixing in flow, to generate nanoparticles. This Review then gives comprehensive coverage of the current application space for CHFS-made nanomaterials including optical, healthcare, electronics (including sensors, information, and communication technologies), catalysis, devices (including energy harvesting/conversion/fuels), and energy storage applications. Thereafter, topics of precursor chemistry and products, as well as materials or structures, are discussed (surface-functionalized hybrids, nanocomposites, nanograined coatings and monoliths, and metal-organic frameworks). Later, this Review focuses on some of the key apparatus innovations in the field, such as in situ flow/rapid heating systems (to investigate kinetics and mechanisms), approaches to high throughput flow syntheses (for nanomaterials discovery), as well as recent developments in scale-up of hydrothermal flow processes. Finally, this Review covers environmental considerations, future directions and capabilities, along with the conclusions and outlook.

Dielectric properties of complex magnetic field induced states in PbCuSO4(OH)2

Spin spirals, which coexist with collinear spin order in linarite PbCuSO₄(OH)₂, indicate electrical polarisation textures of spin-multipolar phases. We derive experimental evidence by a detailed investigation of the magnetic-field dependent dielectric and electric polarization properties at low temperatures. Linarite exhibits a quasi-one-dimensional frustrated S = ½ spin chain, which forms 3D spin-spiral order in zero magnetic field for T < 2.85 K. Recently, due to the monoclinic lattice of linarite with CuO₂ ribbon chains, complex magnetic field induced states were found. These spin-multipolar phases, which compete with spin-density waves at low magnetic fields, exist in close vicinity to the transition from the spin spiral into field induced spin polarized state. Via antisymmetric Dzyaloshinskii-Moriya interaction spin-driven ferroelectricity develops in the spin-spirals state. Via electric polarization measurements this allows to prove the transitions into complex magnetic field induced phases. Thorough analyses of the temperature and magnetic field dependent dielectric properties of a naturally grown single crystalline sample provide a detailed (T,H) phase diagrams for the three different crystallographic directions.

Doping effects on trimerization and magnetoelectric coupling of single crystal multiferroic (Y,Lu)MnO3

Hexagonal RMnO₃ is a multiferroic compound with a giant spin-lattice coupling at an antiferromagnetic transition temperature, Lee et al (2008 Nature 451 805). Despite extensive studies over the past two decades, the origin and underlying microscopic mechanism of strong spin-lattice coupling remain very much elusive. In this study, we have tried to address this problem by measuring the thermal expansion and dielectric constant of doped single crystals Y_1-x Lu _x MnO₃ where x  =  0, 0.25, 0.5, 0.75, and 1.0. From these measurements, we confirm that there is a progressive change in the physical properties with doping. At the same time, all our samples exhibit clear anomalies at T _N, even in the samples where x  =  0.5 and 0.75. This is opposed to some earlier ideas, which suggests an unusual doping dependence of the anomaly. Our work reveals yet another interesting facet of the spin-lattice coupling issue in hexagonal RMnO₃.

Magnetoelectric Response in Multiferroic SrFe12O19 Ceramics

We report here realization of ferroelectricity, ferromagnetism and magnetocapacitance effect in singleSrFe12O19ceramic at room temperature. The ceramics demonstrate a saturated polarization hysteresis loop, two nonlinear I-V peaks and large anomaly of dielectric constant near Curie temperature, which confirm the intrinsic ferroelectricity of SrFe12O19 ceramicswith subsequent heat-treatment in O2atmosphere. The remnant polarization of the SrFe12O19 ceramic is estimated to be 103μC/cm2. The ceramic also exhibits strong ferromagnetic characterization, the coercive field and remnant magnetic moment are 6192Oe and 35.8emu/g, respectively. Subsequent annealing SrFe12O19 ceramics in O2 plays a key role on revealing its intrinsic ferroelectricity and improving the ferromagnetism through transforming Fe2+ into Fe3+. By applying a magnetic field, the capacitance demonstrates remarkable change along with B field, the maximum rate of change in ε (Δε(B)/ε(0)) is 1174%, which reflects a giant magnetocapacitance effect in SrFe12O19. XPS and molecular magnetic moment measurements confirmed the transformation of Fe2+ into Fe3+ and removal of oxygen vacancies upon O2 heat treatment. These combined functional responses in SrFe12O19 ceramics opens substantial possibilities for applications in novel electric devices.

Electromagnon dispersion probed by inelastic X-ray scattering in LiCrO2

Inelastic X-ray scattering with meV energy resolution (IXS) is an ideal tool to measure collective excitations in solids and liquids. In non-resonant scattering condition, the cross-section is strongly dominated by lattice vibrations (phonons). However, it is possible to probe additional degrees of freedom such as magnetic fluctuations that are strongly coupled to the phonons. The IXS spectrum of the coupled system contains not only the phonon dispersion but also the so far undetected magnetic correlation function. Here we report the observation of strong magnon–phonon coupling in LiCrO₂ that enables the measurement of magnetic correlations throughout the Brillouin zone via IXS. We find electromagnon excitations and electric dipole active two-magnon excitations in the magnetically ordered phase and heavily damped electromagnons in the paramagnetic phase of LiCrO₂. We predict that several (frustrated) magnets with dominant direct exchange and non-collinear magnetism show surprisingly large IXS cross-section for magnons and multi-magnon processes.

Whilst terahertz optical spectroscopy allows for the study of coupled spin and lattice excitations, it is limited in momentum space. Here, the authors use inelastic x-ray scattering to demonstrate strong magnon-phonon coupling and electromagnon excitations across the Brillouin zone of LiCrO₂.

Electric-field control of spin-orbit torque in a magnetically doped topological insulator

Electric-field manipulation of magnetic order has proved of both fundamental and technological importance in spintronic devices. So far, electric-field control of ferromagnetism, magnetization and magnetic anisotropy has been explored in various magnetic materials, but the efficient electric-field control of spin-orbit torque (SOT) still remains elusive. Here, we report the effective electric-field control of a giant SOT in a Cr-doped topological insulator (TI) thin film using a top-gate field-effect transistor structure. The SOT strength can be modulated by a factor of four within the accessible gate voltage range, and it shows strong correlation with the spin-polarized surface current in the film. Furthermore, we demonstrate the magnetization switching by scanning gate voltage with constant current and in-plane magnetic field applied in the film. The effective electric-field control of SOT and the giant spin-torque efficiency in Cr-doped TI may lead to the development of energy-efficient gate-controlled spin-torque devices compatible with modern field-effect semiconductor technologies.

Magnetoelectric relaxor and reentrant behaviours in multiferroic Pb(Fe2/3W1/3)O3 crystal

Significant quenched disorder in crystal structure can break ferroic (magnetic or electric) long-range order, resulting in the development of ferroic glassy states at low temperatures such as magnetic spin glasses, electric dipolar glasses, relaxor ferroelectrics, etc. These states have been widely studied due to novel physical phenomena they reveal. Much less known are the effects of quenched disorder in multiferroics, i.e. the materials where magnetic and electric correlations coexist. Here we report an unusual behaviour in complex perovskite Pb(Fe2/3W1/3)O3 (PFW) crystals: the coexistence of electric relaxor, magnetic relaxor and antiferromagnetic (AFM) states. The most striking finding is the transformation of the AFM phase into a new reentrant-type magnetic glassy phase below Tg ≅ 10 K. We show that the behaviour at this transformation contrasts the typical behaviour of canonical spin glasses and is similar to the behaviour of relaxor ferroelectrics. Magnetoelectric effect is also observed in the AFM phase in the temperature range of the transition into electric relaxor phase at Tf ≅ 200. The mechanism of magnetic relaxor behaviour is supposed to arise from the frustrated interactions among the spins located at the AFM domain walls. Our results should inspire further studies of multirelaxor behaviour in other multiferroic systems.

Ferroelectric Metal in Tetragonal BiCoO3/BiFeO3 Bilayers and Its Electric Field Effect

By first-principles calculations we investigate the electronic structure of tetragonal BiCoO₃/BiFeO₃ bilayers with different terminations. The multiferroic insulator BiCoO₃ and BiFeO₃ transform into metal in all of three models. Particularly, energetically favored model CoO₂-BiO exhibits ferroelectric metallic properties, and external electric field enhances the ferroelectric displacements significantly. The metallic character is mainly associated to e_g electrons, while t_2g electrons are responsible for ferroelectric properties. Moreover, the strong hybridization between e_g and O p electrons around Fermi level provides conditions to the coexistence of ferroelectric and metallic properties. These special behaviors of electrons are influenced by the interfacial electronic reconstruction with formed Bi-O electrovalent bond, which breaks O_A-Fe/Co-O_B coupling partially. Besides, the external electric field reverses spin polarization of Fe/Co ions efficiently, even reaching 100%.

Pressure effect on the properties of magnetic moments and phase transitions in YMnO3 from first principles

We report the properties of magnetic, electronic, phonon frequencies and magnetic phase transitions in orthorhombic perovskite YMnO₃ by means of first-principles calculations.

Dynamical magnetoelectric phenomena of multiferroic skyrmions

Magnetic skyrmions, vortex-like swirling spin textures characterized by a quantized topological invariant, realized in chiral-lattice magnets are currently attracting intense research interest. In particular, their dynamics under external fields is an issue of vital importance both for fundamental science and for technical application. Whereas observations of magnetic skyrmions has been limited to metallic magnets so far, their realization was also discovered in a chiral-lattice insulating magnet Cu2OSeO3 in 2012. Skyrmions in the insulator turned out to exhibit multiferroic nature with spin-induced ferroelectricity. Strong magnetoelectric coupling between noncollinear skyrmion spins and electric polarizations mediated by relativistic spin-orbit interaction enables us to drive motion and oscillation of magnetic skyrmions by application of electric fields instead of injection of electric currents. Insulating materials also provide an environment suitable for detection of pure spin dynamics through spectroscopic measurements owing to the absence of appreciable charge excitations. In this article, we review recent theoretical and experimental studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulators. We argue that multiferroic skyrmions show unique coupled oscillation modes of magnetizations and polarizations, so-called electromagnon excitations, which are both magnetically and electrically active, and interference between the electric and magnetic activation processes leads to peculiar magnetoelectric effects in a microwave frequency regime.

Electric field control of magnetic states in isolated and dipole-coupled FeGa nanomagnets delineated on a PMN-PT substrate

We report observation of a 'non-volatile' converse magneto-electric effect in elliptical FeGa nanomagnets delineated on a piezoelectric PMN-PT substrate. The nanomagnets are first magnetized with a magnetic field directed along their nominal major axes. Subsequent application of a strong electric field across the piezoelectric substrate generates strain in the substrate, which is partially transferred to the nanomagnets and rotates the magnetizations of some of them away from their initial orientations. The rotated magnetizations remain in their new orientations after the field is removed, resulting in 'non-volatility'. In isolated nanomagnets, the magnetization rotates by <90° upon application of the electric field, but in a dipole-coupled pair consisting of one 'hard' and one 'soft' nanomagnet, which are both initially magnetized in the same direction by the magnetic field, the soft nanomagnet's magnetization rotates by [Formula: see text] upon application of the electric field because of the dipole influence of the hard nanomagnet. This effect can be utilized for a nanomagnetic NOT logic gate.

Nanometer-size hard magnetic ferrite exhibiting high optical-transparency and nonlinear optical-magnetoelectric effect

Development of nanometer-sized magnetic particles exhibiting a large coercive field (H_c) is in high demand for densification of magnetic recording. Herein, we report a single-nanosize (i.e., less than ten nanometers across) hard magnetic ferrite. This magnetic ferrite is composed of ε-Fe₂O₃, with a sufficiently high H_c value for magnetic recording systems and a remarkably high magnetic anisotropy constant of 7.7 × 10⁶ erg cm⁻³. For example, 8.2-nm nanoparticles have an H_c value of 5.2 kOe at room temperature. A colloidal solution of these nanoparticles possesses a light orange color due to a wide band gap of 2.9 eV (430 nm), indicating a possibility of transparent magnetic pigments. Additionally, we have observed magnetization-induced second harmonic generation (MSHG). The nonlinear optical-magnetoelectric effect of the present polar magnetic nanocrystal was quite strong. These findings have been demonstrated in a simple iron oxide, which is highly significant from the viewpoints of economic cost and mass production.

Dzyaloshinskii-Moriya Interaction and Spiral Order in Spin-orbit Coupled Optical Lattices

We show that the recent experimental realization of spin-orbit coupling in ultracold atomic gases can be used to study different types of spin spiral order and resulting multiferroic effects. Spin-orbit coupling in optical lattices can give rise to the Dzyaloshinskii-Moriya (DM) spin interaction which is essential for spin spiral order. By taking into account spin-orbit coupling and an external Zeeman field, we derive an effective spin model in the Mott insulator regime at half filling and demonstrate that the DM interaction in optical lattices can be made extremely strong with realistic experimental parameters. The rich finite temperature phase diagrams of the effective spin models for fermions and bosons are obtained via classical Monte Carlo simulations.

Microwave Magnetochiral Effect in Cu_{2}OSeO_{3}

We theoretically find that in the multiferroic chiral magnet Cu_{2}OSeO_{3} resonant magnetic excitations are coupled to the collective oscillation of the electric polarization, and thereby attain simultaneous activity to the ac magnetic field and ac electric field. Because of the interference between these magnetic and electric activation processes, this material hosts a gigantic magnetochiral dichroism for microwaves, that is, a directional dichroism at gigahertz frequencies in the Faraday geometry. The absorption intensity of a microwave differs by as much as ~30% depending on whether its propagation direction is parallel or antiparallel to the external magnetic field.

Room-temperature magnetoelectric coupling in nanocrystalline (Na1−xKx)0.5Bi0.5TiO3 (x = 0.1, 0.16, 0.20, 0.25)

Nanocrystalline (Na_1−xK_x)_0.5Bi_0.5TiO₃ (x = 0.1, 0.16, 0.20, 0.25) plates exhibit ferromagnetism at room temperature.

Multiferroic properties of o-LuMnO3 controlled by b-axis strain

Strain is a leading candidate for controlling magnetoelectric coupling in multiferroics. Here, we use x-ray diffraction to study the coupling between magnetic order and structural distortion in epitaxial films of the orthorhombic (o-) perovskite LuMnO(3). An antiferromagnetic spin canting in the E-type magnetic structure is shown to be related to the ferroelectrically induced structural distortion and to a change in the magnetic propagation vector. By comparing films of different orientations and thicknesses, these quantities are found to be controlled by b-axis strain. It is shown that compressive strain destabilizes the commensurate E-type structure and reduces its accompanying ferroelectric distortion.

Phase transition and phase separation in multiferroic orthorhombic Dy(1-x)Ho(x)MnO3 (0 ≤ x ≤ 1)

We report on structural, magnetic, ferroelectric, and thermodynamic properties of polycrystalline orthorhombic manganites Dy_1−xHo_xMnO₃ for Ho substitution levels 0 ≤ x ≤ 1. This system offers a possibility to systemically modulate the multiferroicity of RMnO₃ via tuning the A-site ionic radii as well as the A-site magnetism. The successive transition of the multiferroic ground state is traced from the bc-cycloidal (DyMnO₃) to the E-type antiferromagnetic phase (HoMnO₃). In the middle substitution range 0.4 < x < 0.5, the phase separation is prominent, which's residual may survive in an even wider range. Accompanied with the phase transition and phase separation, obvious enhancement of both the polarization and magnetoelectric response is observed. Our experimental study also confirmed that the rare earth (Dy/Ho)-Mn exchange striction is a crucial role in deciding the multiferroicity of manganites.

Electric field control of ferroelectric domain structures in MnWO4

Competing interactions make the magnetic structure of MnWO4 highly frustrated, and only the AF2 phase of the three magnetically ordered phases (AF1, AF2, AF3) is ferroelectric. The high frustration may thus allow a possibility to tune the magnetic structure by means of an electric field via magnetoelectric coupling. By using the pyroelectric current method, we measure the remnant ferroelectric polarization in MnWO4 upon application of a poling electric field via two different roadmaps. It is demonstrated that an electric field as low as 10 kV cm(-1) is sufficient to enhance the stability of a ferroelectric AF2 phase at the expense of a non-ferroelectric AF1 phase. This work suggests that electric field induced electrostatic energy, although small due to weak magnetically induced electric polarization, may effectively tune ferroelectric domain structures, and thus the magnetic structure of highly frustrated multiferroic materials.

Multiferroics of spin origin

Multiferroics, compounds with both magnetic and ferroelectric orders, are believed to be a key material system to achieve cross-control between magnetism and electricity in a solid with minute energy dissipation. Such a colossal magnetoelectric (ME) effect has been an issue of keen interest for a long time in condensed matter physics as well as a most desired function in the emerging spin-related electronics. Here we begin with the basic mechanisms to realize multiferroicity or spin-driven ferroelectricity in magnetic materials, which have recently been clarified and proved both theoretically and experimentally. According to the proposed mechanisms, many families of multiferroics have been explored, found (re-discovered), and newly developed, realizing a variety of colossal ME controls. We overview versatile multiferroics from the viewpoints of their multiferroicity mechanisms and their fundamental ME characteristics on the basis of the recent advances in exploratory materials. One of the new directions in multiferroic science is the dynamical ME effect, namely the dynamical and/or fast cross-control between electric and magnetic dipoles in a solid. We argue here that the dynamics of multiferroic domain walls significantly contributes to the amplification of ME response, which has been revealed through the dielectric spectroscopy. Another related issue is the electric-dipole-active magnetic resonance, called electromagnons. The electromagnons can provide a new stage of ME optics via resonant coupling with the external electromagnetic wave (light). Finally, we give concluding remarks on multiferroics physics in the light of a broader perspective from the emergent electromagnetism in a solid as well as from the possible application toward future dissipationless electronics.

Disappearance of Ising nature in Ca3ZnMnO6 studied by high-field ESR

High-field electron spin resonance measurements of an antiferromagnet Ca3ZnMnO6 isostructure, with the Ising-chain multiferroic Ca3CoMnO6, have been carried out. Two distinct resonance modes were observed below TN = 25 K, which is well explained by conventional antiferromagnetic resonance theory with easy-plane anisotropy. The zero-field spin gap is derived to be about 166 GHz, originating from the easy-plane anisotropy and exchange interaction. Our result suggests that the Dzyaloshinsky-Moriya interaction, which may induce spin canting, is absent. Disappearance of Ising anisotropy in Ca3ZnMnO6 suggests that the Co(4+) ion, as well as the Co-Mn superexchange, plays an important role for the Ising nature in Ca3CoMnO6.

Hydrothermal epitaxy and resultant properties of EuTiO3 films on SrTiO3(001) substrate

We report a novel epitaxial growth of EuTiO3 films on SrTiO3(001) substrate by hydrothermal method. The morphological, structural, chemical, and magnetic properties of these epitaxial EuTiO3 films were examined by scanning electron microscopy, transmission electron microscopy, high-resolution X-ray diffractometry, X-ray photoelectron spectroscopy, and superconducting quantum interference device magnetometry, respectively. As-grown EuTiO3 films with a perovskite structure were found to show an out-of-plane lattice shrinkage and room-temperature ferromagnetism, possibly resulting from an existence of Eu(3+). Postannealing at 1,000°C could reduce the amount of Eu(3+), relax the out-of-plane lattice shrinkage, and impact the magnetic properties of the films.

PACS

81.10.Aj; 81.15.-z; 61.05.-a.

Controlling magnetism on metal surfaces with non-magnetic means: electric fields and surface charging

We review the state of the art of surface magnetic property control with non-magnetic means, concentrating on metallic surfaces and techniques such as charge-doping or external electric field (EEF) application. Magneto-electric coupling via EEF-based charge manipulation is discussed as a way to tailor single adatom spins, exchange interaction between adsorbates or anisotropies of layered systems. The mechanisms of paramagnetic and spin-dependent electric field screening and the effect thereof on surface magnetism are discussed in the framework of theoretical and experimental studies. The possibility to enhance the effect of EEF by immersing the target system into an electrolyte or ionic liquid is discussed by the example of substitutional impurities and metallic alloy multilayers. A similar physics is pointed out for the case of charge traps, metallic systems decoupled from a bulk electron bath. In that case the charging provides the charge carrier density changes necessary to affect the magnetic moments and anisotropies in the system. Finally, the option of using quasi-free electrons rather than localized atomic spins for surface magnetism control is discussed with the example of Shockley-type metallic surface states confined to magnetic nanoislands.

Topological properties and dynamics of magnetic skyrmions

Magnetic skyrmions are particle-like nanometre-sized spin textures of topological origin found in several magnetic materials, and are characterized by a long lifetime. Skyrmions have been observed both by means of neutron scattering in momentum space and microscopy techniques in real space, and their properties include novel Hall effects, current-driven motion with ultralow current density and multiferroic behaviour. These properties can be understood from a unified viewpoint, namely the emergent electromagnetism associated with the non-coplanar spin structure of skyrmions. From this description, potential applications of skyrmions as information carriers in magnetic information storage and processing devices are envisaged.

Electric field control of terahertz polarization in a multiferroic manganite with electromagnons

All-electrical control of a dynamic magnetoelectric effect is demonstrated in a classical multiferroic manganite DyMnO3, a material containing coupled antiferromagnetic and ferroelectric orders. Because of intrinsic magnetoelectric coupling with electromagnons a linearly polarized terahertz light rotates upon passing through the sample. The amplitude and the direction of the polarization rotation are defined by the orientation of ferroelectric domains and can be switched by static voltage. These experiments allow the terahertz polarization to be tuned using the dynamic magnetoelectric effect.

Four-states multiferroic memory embodied using Mn-doped BaTiO3 nanorods

Multiferroics that show simultaneous ferroic responses have received a great deal of attention by virtue of their potential for enabling new device paradigms. Here, we demonstrate a high-density four-states multiferroic memory using vertically aligned Mn-doped BaTiO3 nanorods prepared by applying the dip-pen nanolithography technique. In the present nanorods array, the polarization (P) switching by an external electric field does not influence the magnetization (M) of the nanorod owing to a negligible degree of the P-M cross-coupling. Similarly, the magnetic-field-induced M switching is unaffected by the ferroelectric polarization. On the basis of these, we are able to implement a four-states nonvolatile multiferroic memory, namely, (+P,+M), (+P,-M) ,(-P,+M), and (-P,-M) with the reliability in the P and M switching. Thus, the present work makes an important step toward the practical realization of multistate ferroic memories.

The effect of magnetic anisotropy on the spin configurations of patterned La(0.7)Sr(0.3)MnO3 elements

We study the effect of magnetocrystalline anisotropy on the magnetic configurations of La0.7Sr0.3MnO3 bar and triangle elements using photoemission electron microscopy imaging. The dominant remanent state is a low energy flux-closure state for both thin (15 nm) and thick (50 nm) elements. The magnetocrystalline anisotropy, which competes with the dipolar energy, causes a strong modification of the spin configuration in the thin elements, depending on the shape, size and orientation of the structures. We investigate the magnetic switching processes and observe in triangular shaped elements a displacement of the vortex core along the easy axis for an external magnetic field applied close to the hard axis, which is well reproduced by micromagnetic simulations.