Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3

Picosecond Spin Current Generation from Vicinal Metal-Antiferromagnetic Insulator Interfaces

We report the picosecond spin current generation from the interface between a heavy metal and a vicinal antiferromagnet insulator Cr_{2}O_{3} by laser pulses at room temperature and zero magnetic field. It is converted into a detectable terahertz emission in the heavy metal via the inverse spin Hall effect. The vicinal interfaces are apparently the source of the picosecond spin current, as evidenced by the proportional terahertz signals to the vicinal angle. We attribute the origin of the spin current to the transient magnetic moment generated by an interfacial nonlinear magnetic-dipole difference-frequency generation. We propose a model based on the in-plane inversion symmetry breaking to quantitatively explain the terahertz intensity with respect to the angles of the laser polarization and the film azimuth. Our work opens new opportunities in antiferromagnetic and ultrafast spintronics by considering symmetry breaking.

Light-induced electronic polarization in antiferromagnetic Cr2O3

In a solid, the electronic subsystem can exhibit incipient order with lower point group symmetry than the crystal lattice. Ultrafast external fields that couple exclusively to electronic order parameters have rarely been investigated, however, despite their potential importance in inducing exotic effects. Here we show that when inversion symmetry is broken by the antiferromagnetic order in Cr2O3, transmitting a linearly polarized light pulse through the crystal gives rise to an in-plane rotational symmetry-breaking (from C3 to C1) via optical rectification. Using interferometric time-resolved second harmonic generation, we show that the ultrafast timescale of the symmetry reduction is indicative of a purely electronic response; the underlying spin and crystal structures remain unaffected. The symmetry-broken state exhibits a dipole moment, and its polar axis can be controlled with the incident light. Our results establish a coherent nonlinear optical protocol by which to break electronic symmetries and produce unconventional electronic effects in solids.

Noncentrosymmetric Triangular Magnet CaMnTeO6: Strong Quantum Fluctuations and Role of s0 versus s2 Electronic States in Competing Exchange Interactions

Noncentrosymmetric triangular magnets offer a unique platform for realizing strong quantum fluctuations. However, designing these quantum materials remains an open challenge attributable to a knowledge gap in the tunability of competing exchange interactions at the atomic level. Here, a new noncentrosymmetric triangular S = 3/2 magnet CaMnTeO6 is created based on careful chemical and physical considerations. The model material displays competing magnetic interactions and features nonlinear optical responses with the capability of generating coherent photons. The incommensurate magnetic ground state of CaMnTeO6 with an unusually large spin rotation angle of 127°(1) indicates that the anisotropic interlayer exchange is strong and competing with the isotropic interlayer Heisenberg interaction. The moment of 1.39(1) µB, extracted from low-temperature heat capacity and neutron diffraction measurements, is only 46% of the expected value of the static moment 3 µB. This reduction indicates the presence of strong quantum fluctuations in the half-integer spin S = 3/2 CaMnTeO6 magnet, which is rare. By comparing the spin-polarized band structure, chemical bonding, and physical properties of AMnTeO6 (A = Ca, Sr, Pb), how quantum-chemical interpretation can illuminate insights into the fundamentals of magnetic exchange interactions, providing a powerful tool for modulating spin dynamics with atomically precise control is demonstrated.

Large nonlinear optical magnetoelectric response in a noncentrosymmetric magnetic Weyl semimetal

Weyl semimetals resulting from either inversion (P) or time-reversal (T) symmetry breaking have been revealed to show the record-breaking large optical response due to intense Berry curvature of Weyl-node pairs. Different classes of Weyl semimetals with both P and T symmetry breaking potentially exhibit optical magnetoelectric (ME) responses, which are essentially distinct from the previously observed optical responses in conventional Weyl semimetals, leading to the versatile functions such as directional dependence for light propagation and gyrotropic effects. However, such optical ME phenomena of (semi)metallic systems have remained elusive so far. Here, we show the large nonlinear optical ME response in noncentrosymmetric magnetic Weyl semimetal PrAlGe, in which the polar structural asymmetry and ferromagnetic ordering break P and T symmetry. We observe the giant second harmonic generation (SHG) arising from the P symmetry breaking in the paramagnetic phase, being comparable to the largest SHG response reported in Weyl semimetal TaAs. In the ferromagnetically ordered phase, it is found that interference between this nonmagnetic SHG and the magnetically induced SHG emerging due to both P and T symmetry breaking results in the magnetic field switching of SHG intensity. Furthermore, such an interference effect critically depends on the light-propagating direction. The corresponding magnetically induced nonlinear susceptibility is significantly larger than the prototypical ME material, manifesting the existence of the strong nonlinear dynamical ME coupling. The present findings establish the unique optical functionality of P- and T-symmetry broken ME topological semimetals.

Magnetoelectric coupling in multiferroics probed by optical second harmonic generation

Magnetoelectric coupling, as a fundamental physical nature and with the potential to add functionality to devices while also reducing energy consumption, has been challenging to be probed in freestanding membranes or two-dimensional materials due to their instability and fragility. In this paper, we report a magnetoelectric coupling probed by optical second harmonic generation with external magnetic field, and show the manipulation of the ferroelectric and antiferromagnetic orders by the magnetic and thermal fields in BiFeO₃ films epitaxially grown on the substrates and in the freestanding ones. Here we define an optical magnetoelectric-coupling constant, denoting the ability of controlling light-induced nonlinear polarization by the magnetic field, and found the magnetoelectric-coupling was suppressed by strain releasing but remain robust against thermal fluctuation for freestanding BiFeO₃.

Anomalous Second Harmonic Generation from Atomically Thin MnBi2Te4

MnBi₂Te₄ is a van der Waals topological insulator with intrinsic intralayer ferromagnetic exchange and A-type antiferromagnetic interlayer coupling. Theoretically, it belongs to a class of structurally centrosymmetric crystals whose layered antiferromagnetic order breaks inversion symmetry for even layer numbers, making optical second harmonic generation (SHG) an ideal probe of the coupling between the crystal and magnetic structures. Here, we perform magnetic field and temperature-dependent SHG measurements on MnBi₂Te₄ flakes ranging from bulk to monolayer thickness. We find that the dominant SHG signal from MnBi₂Te₄ is unexpectedly unrelated to both magnetic state and layer number. We suggest that surface SHG is the likely source of the observed strong SHG, whose symmetry matches that of the MnBi₂Te₄-vacuum interface. Our results highlight the importance of considering the surface contribution to inversion symmetry-breaking in van der Waals centrosymmetric magnets.

An optimized scheme for detecting magneto-optic effects in ultrathin films with Sagnac interferometry

Sagnac interferometry is advantageous in measuring time-reversal-symmetry breaking effects in ferromagnetic and antiferromagnetic materials as it suppresses time-reversal symmetric birefringent effects that are ubiquitous and often overwhelming in optical detection systems. When its sensitivity is limited only by the amplifier noise in the photo-detector, one needs to optimize the optical power that returns to the detector. We demonstrate an experimental scheme that maximizes the returning optical power in a Sagnac interferometry when detecting the magneto-optic effect in ultrathin films. In this scheme, the optical beam bearing the Faraday effect on a thin film is reflected at a second surface coated with a highly reflective gold film. The gold film increases the returned optical power by a factor of 4-5. For a normal-incidence Sagnac interferometer, this scheme yields an increase in the signal-to-noise ratio by the same factor. For an oblique-incidence Sagnac interferometer, this scheme should yield an increase in the signal-to-noise ratio by a factor of 20-25. For illustration, this scheme is used to measure magnetization curves and Kerr rotation images of 4.5-unit-cell thick SrRuO₃(001) grown on SrTiO₃(001).

Direct observation of antiferromagnetic parity violation in the electronic structure of Mn2Au

Using momentum microscopy with sub-µm spatial resolution, allowing momentum resolved photoemission on individual antiferromagnetic domains, we observe an asymmetry in the electronic band structure,E(k)≠E(-k), in Mn₂Au. This broken band structure parity originates from the combined time and parity symmetry,PT, of the antiferromagnetic order of the Mn moments, in connection with spin-orbit coupling. The spin-orbit interaction couples the broken parity to the Néel order parameter direction. We demonstrate a novel tool to image the Néel vector direction,N, by combining spatially resolved momentum microscopy withab-initiocalculations that correlate the broken parity with the vectorN.

Direct Imaging of Antiferromagnetic Domains and Anomalous Layer-Dependent Mirror Symmetry Breaking in Atomically Thin MnPS_{3}

We have developed a sensitive cryogenic second-harmonic generation microscopy to study a van der Waals antiferromagnet MnPS_{3}. We find that long-range Néel antiferromagnetic order develops from the bulk crystal down to the bilayer, while it is absent in the monolayer. Before entering the long-range antiferromagnetic ordered phase in all samples, an upturn of the second harmonic generation below 200 K indicates the formation of the short-range order and magnetoelastic coupling. We also directly image the two antiphase (180°) antiferromagnetic domains and thermally induced domain switching down to bilayer. An anomalous mirror symmetry breaking shows up in samples thinner than ten layers for the temperature both above and below the Néel temperature, which indicates a structural change in few-layer samples. Minimal change of the second harmonic generation polar patterns in strain tuning experiments indicate that the symmetry crossover at ten layers is most likely an intrinsic property of MnPS_{3} instead of an extrinsic origin of substrate-induced strain. Our results show that second harmonic generation microscopy is a direct tool for studying antiferromagnetic domains in atomically thin materials, and opens a new way to study two-dimensional antiferromagnets.

Magnetic Order and Symmetry in the 2D Semiconductor CrSBr

The advent of two-dimensional (2D) magnets offers unprecedented control over electrons and spins. A key factor in determining exchange coupling and magnetic order is symmetry. Here, we apply second harmonic generation (SHG) to probe a 2D magnetic semiconductor CrSBr. We find that monolayers are ferromagnetically ordered below 146 K, an observation enabled by the discovery of a large magnetic dipole SHG effect in the centrosymmetric structure. In multilayers, the ferromagnetic monolayers are coupled antiferromagnetically, and in contrast to other 2D magnets, the Néel temperature of CrSBr increases with decreasing layer number. We identify magnetic dipole and magnetic toroidal moments as order parameters of the ferromagnetic monolayer and antiferromagnetic bilayer, respectively. These findings establish CrSBr as an exciting 2D magnetic semiconductor and extend the SHG probe of magnetic symmetry to the monolayer limit, opening the door to exploring the applications of magnetic-electronic coupling and the magnetic toroidal moment.

Nonreciprocal second harmonic generation in a magnetoelectric material

Mirror symmetries are of particular importance because they are connected to fundamental properties and conservation laws. Spatial inversion and time reversal are typically associated to charge and spin phenomena, respectively. When both are broken, magnetoelectric cross-coupling can arise. In the optical regime, a difference between forward and backward propagation of light may result. Usually, this nonreciprocal response is small. We show that a giant nonreciprocal optical response can occur when transferring from linear to nonlinear optics, specifically second harmonic generation (SHG). CuB₂O₄ exhibits SHG transmission changes by almost 100% upon reversal of a magnetic field of just ±10 mT. The observed nonreciprocity results from an interference between magnetic-dipole and electric-dipole SHG. Although the former is inherently weaker than the latter, a resonantly enhanced magnetic-dipole transition has a comparable amplitude as a nonresonant electric-dipole transition, thus maximizing the nonreciprocity. Multiferroics and magnetoelectrics are an obvious materials platform to exhibit nonreciprocal nonlinear optical functionalities.

Signatures of Ultrafast Reversal of Excitonic Order in Ta_{2}NiSe_{5}

In the presence of electron-phonon coupling, an excitonic insulator harbors two degenerate ground states described by an Ising-type order parameter. Starting from a microscopic Hamiltonian, we derive the equations of motion for the Ising order parameter in the phonon coupled excitonic insulator Ta_{2}NiSe_{5} and show that it can be controllably reversed on ultrashort timescales using appropriate laser pulse sequences. Using a combination of theory and time-resolved optical reflectivity measurements, we report evidence of such order parameter reversal in Ta_{2}NiSe_{5} based on the anomalous behavior of its coherently excited order-parameter-coupled phonons. Our Letter expands the field of ultrafast order parameter control beyond spin and charge ordered materials.

Multiferroic heterostructures for spintronics

For next-generation technology, magnetic systems are of interest due to the natural ability to store information and, through spin transport, propagate this information for logic functions. Controlling the magnetization state through currents has proven energy inefficient. Multiferroic thin-film heterostructures, combining ferroelectric and ferromagnetic orders, hold promise for energy efficient electronics. The electric field control of magnetic order is expected to reduce energy dissipation by 2–3 orders of magnitude relative to the current state-of-the-art. The coupling between electrical and magnetic orders in multiferroic and magnetoelectric thin-film heterostructures relies on interfacial coupling though magnetic exchange or mechanical strain and the correlation between domains in adjacent functional ferroic layers. We review the recent developments in electrical control of magnetism through artificial magnetoelectric heterostructures, domain imprint, emergent physics and device paradigms for magnetoelectric logic, neuromorphic devices, and hybrid magnetoelectric/spin-current-based applications. Finally, we conclude with a discussion of experiments that probe the crucial dynamics of the magnetoelectric switching and optical tuning of ferroelectric states towards all-optical control of magnetoelectric switching events.

Rich information on 2D materials revealed by optical second harmonic generation

Two-dimensional (2D) materials have brought a spectacular revolution in fundamental research and industrial applications due to their unique physical properties of atomically thin thickness, strong light-matter interaction, unity valley polarization and enhanced many-body interactions. To fully explore their exotic physical properties and facilitate potential applications in electronics and optoelectronics, an effective and versatile characterization method is highly demanded. Among the many methods of characterization, optical second harmonic generation (SHG) has attracted broad attention because of its sensitivity, versatility and simplicity. The SHG technique is sufficiently sensitive at the atomic scale and therefore suitable for studies on 2D materials. More importantly, it has the capacity to acquire abundant information ranging from crystallographic, and electronic, to magnetic properties in various 2D materials due to its sensitivity to both spatial-inversion symmetry and time-reversal symmetry. These advantages accompanied by its characteristics of non-invasion and high throughput make SHG a powerful tool for 2D materials. This review summarizes recent experimental developments of SHG applications in 2D materials and also provides an outlook of potential prospects based on SHG.

Bulk-like dielectric and magnetic properties of sub 100 nm thick single crystal Cr2O3 films on an epitaxial oxide electrode

The manipulation of antiferromagnetic order in magnetoelectric Cr₂O₃ using electric field has been of great interest due to its potential in low-power electronics. The substantial leakage and low dielectric breakdown observed in twinned Cr₂O₃ thin films, however, hinders its development in energy efficient spintronics. To compensate, large film thicknesses (250 nm or greater) have been employed at the expense of device scalability. Recently, epitaxial V₂O₃ thin film electrodes have been used to eliminate twin boundaries and significantly reduce the leakage of 300 nm thick single crystal films. Here we report the electrical endurance and magnetic properties of thin (less than 100 nm) single crystal Cr₂O₃ films on epitaxial V₂O₃ buffered Al₂O₃ (0001) single crystal substrates. The growth of Cr₂O₃ on isostructural V₂O₃ thin film electrodes helps eliminate the existence of twin domains in Cr₂O₃ films, therefore significantly reducing leakage current and increasing dielectric breakdown. 60 nm thick Cr₂O₃ films show bulk-like resistivity (~ 10¹² Ω cm) with a breakdown voltage in the range of 150-300 MV/m. Exchange bias measurements of 30 nm thick Cr₂O₃ display a blocking temperature of ~ 285 K while room temperature optical second harmonic generation measurements possess the symmetry consistent with bulk magnetic order.

Switchable magnetic bulk photovoltaic effect in the two-dimensional magnet CrI3

The bulk photovoltaic effect (BPVE) rectifies light into the dc current in a single-phase material and attracts the interest to design high-efficiency solar cells beyond the pn junction paradigm. Because it is a hot electron effect, the BPVE surpasses the thermodynamic Shockley-Queisser limit to generate above-band-gap photovoltage. While the guiding principle for BPVE materials is to break the crystal centrosymmetry, here we propose a magnetic photogalvanic effect (MPGE) that introduces the magnetism as a key ingredient and induces a giant BPVE. The MPGE emerges from the magnetism-induced asymmetry of the carrier velocity in the band structure. We demonstrate the MPGE in a layered magnetic insulator CrI₃, with much larger photoconductivity than any previously reported results. The photocurrent can be reversed and switched by controllable magnetic transitions. Our work paves a pathway to search for magnetic photovoltaic materials and to design switchable devices combining magnetic, electronic, and optical functionalities.

Automatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server

Two new programs, MTENSOR and TENSOR, hosted on the open-access website known as the Bilbao Crystallographic Server, are presented. The programs provide automatically the symmetry-adapted form of tensor properties for any magnetic or non-magnetic point group or space group. The tensor is chosen from a list of 144 known tensor properties gathered from the scientific literature or, alternatively, the user can also build a tensor that possesses an arbitrary intrinsic symmetry. Four different tensor types are considered: equilibrium, transport, optical and nonlinear optical susceptibility tensors. For magnetically ordered structures, special attention is devoted to a detailed discussion of the transformation rules of the tensors under the time-reversal operation 1'. It is emphasized that for non-equilibrium properties it is the Onsager theorem, and not the constitutive relationships, that indicates how these tensors transform under 1'. In this way it is not necessary to restrict the validity of Neumann's principle. New Jahn symbols describing the intrinsic symmetry of the tensors are introduced for several transport and optical properties. In the case of some nonlinear optical susceptibilities of practical interest, an intuitive method is proposed based on simple diagrams, which allows easy deduction of the action of 1' on the susceptibilities. This topic has not received sufficient attention in the literature and, in fact, it is usual to find published results where the symmetry restrictions for such tensors are incomplete.

Magnetoelectric Force Microscopy on Antiferromagnetic 180∘ Domains in Cr₂O₃

Magnetoelectric force microscopy (MeFM) is characterized as methodical tool for the investigation of antiferromagnetic domain states, in particular of the 180∘ variety. As reference compound for this investigation we use Cr2O3. Access to the antiferromagnetic order is provided by the linear magnetoelectric effect. We resolve the opposite antiferromagnetic 180∘ domain states of Cr2O3 and estimate the sensitivity of the MeFM approach, its inherent advantages in comparison to alternative techniques and its general feasibility for probing antiferromagnetic order.

Multipolar interference for non-reciprocal nonlinear generation

We show that nonlinear multipolar interference allows achieving not only unidirectional, but also non-reciprocal nonlinear generation from a nanoelement, with the direction of the produced light decoupled from the direction of at least one of the excitation beams. Alternatively, it may allow inhibiting the specified nonlinear response in a nanoelement or in its periodic arrangement by reversing the direction of one of the pumps. These general phenomena exploit the fact that, contrary to the linear response case, nonlinear magneto-electric interference stems from a combination of additive and multiplicative processes and includes an interference between various terms within the electric and magnetic partial waves themselves. We demonstrate the introduced concept numerically using an example of a plasmonic dimer geometry with realistic material parameters.

High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection

We present a method of performing high-speed rotational anisotropy nonlinear optical harmonic generation experiments at rotational frequencies of several hertz by projecting the harmonic light reflected at different angles from a sample onto a stationary position-sensitive detector. The high rotational speed of the technique, 10(3) to 10(4) times larger than existing methods, permits precise measurements of the crystallographic and electronic symmetries of samples by averaging over low frequency laser-power, beam-pointing, and pulse-width fluctuations. We demonstrate the sensitivity of our technique by resolving the bulk fourfold rotational symmetry of GaAs about its [001] axis using second-harmonic generation.

Control of magnetic contrast with nonlinear magneto-plasmonics

The interaction between surface plasmons (SP) and magnetic behavior has generated great research interest due to its potential for future magneto-optical devices with ultra-high sensitivity and ultra-fast switching. Here we combine two surface sensitive effects: magnetic second-harmonic generation (MSHG) and SP to enhance the detection sensitivity of the surface magnetization in a single-crystal iron film. We show that the MSHG signal can be significantly enhanced by SP in an attenuated total reflection (ATR) condition, and that the magnetic contrast can be varied over a wide range by the angle-of-incidence. Furthermore, the magnetic contrast of transverse and longitudinal MSHG display opposite trends, which originates from the change of relative phase between MSHG components. This new effect enhances the sensing of magnetic switching, which has potential usage in quaternary magnetic storage systems and bio-chemical sensors due to its very high surface sensitivity and simple structure.

A low temperature nonlinear optical rotational anisotropy spectrometer for the determination of crystallographic and electronic symmetries

Nonlinear optical generation from a crystalline material can reveal the symmetries of both its lattice structure and underlying ordered electronic phases and can therefore be exploited as a complementary technique to diffraction based scattering probes. Although this technique has been successfully used to study the lattice and magnetic structures of systems such as semiconductor surfaces, multiferroic crystals, magnetic thin films, and multilayers, challenging technical requirements have prevented its application to the plethora of complex electronic phases found in strongly correlated electron systems. These requirements include an ability to probe small bulk single crystals at the μm length scale, a need for sensitivity to the entire nonlinear optical susceptibility tensor, oblique light incidence reflection geometry, and incident light frequency tunability among others. These measurements are further complicated by the need for extreme sample environments such as ultra low temperatures, high magnetic fields, or high pressures. In this review we present a novel experimental construction using a rotating light scattering plane that meets all the aforementioned requirements. We demonstrate the efficacy of our scheme by making symmetry measurements on a μm scale facet of a small bulk single crystal of Sr2IrO4 using optical second and third harmonic generation.

Surface plasmon-enhanced transverse magnetic second-harmonic generation

We present experimental studies on surface plasmon (SP) enhanced transverse magnetic second-harmonic generation (T-MSHG) in single-crystal iron films grown by molecular beam epitaxy at room temperature on MgO (001) substrates. We show that it is possible to achieve both strongly enhanced T-MSHG intensity and high magnetic contrast ratio under attenuated total reflection configuration without using complex heterostructures because MSHG is generated directly at the iron surface where SPs are present. The T-MSHG has a much larger contrast ratio than transverse magneto-optical Kerr effect (T-MOKE) and shows great potential for a new generation of bio-chemical sensors due to its very high surface sensitivity. In addition, by analyzing the experimental results and the simulations based on SP field-enhancement theory, we demonstrate that the second-order susceptibility of MSHG shows great anisotropy and the tensor χ(xzz)(odd) is dominant in our sample.

Electric control of exchange bias training

Voltage-controlled exchange bias training and tunability are introduced. Isothermal voltage pulses are used to reverse the antiferromagnetic order parameter of magnetoelectric Cr(2)O(3), and thus continuously tune the exchange bias of an adjacent CoPd film. Voltage-controlled exchange bias training is initialized by tuning the antiferromagnetic interface into a nonequilibrium state incommensurate with the underlying bulk. Interpretation of these hitherto unreported effects contributes to new understanding in electrically controlled magnetism.

Nonlinear interference and unidirectional wave mixing in metamaterials

When both electric and magnetic mechanisms contribute to a particular nonlinear optical process, there exists the possibility for nonlinear interference, often characterized by constructive or destructive interference in the radiation pattern of harmonics and mix waves. However, observation of a significant effect from nonlinear interference requires careful balancing of the various contributions. For this purpose, we propose an artificial metamaterial, using the formalism of nonlinear magnetoelectric coupling to simultaneously engineer the nonlinear polarization and magnetization. We confirm our predictions of nonlinear interference with both simulations and experiment, demonstrating unidirectional wave mixing in two microwave metamaterials. Our results point toward an ever wider range of nonlinear properties, in which nonlinear interference is just one of many potential applications.

Hexagonal Manganites—(RMnO3): Class (I) Multiferroics with Strong Coupling of Magnetism and Ferroelectricity

Hexagonal manganites belong to an exciting class of materials exhibiting strong interactions between a highly frustrated magnetic system, the ferroelectric polarization, and the lattice. The existence and mutual interaction of different magnetic ions (Mn and rare earth) results in complex magnetic phase diagrams and novel physical phenomena. A summary and discussion of the various properties, underlying physical mechanisms, the role of the rare earth ions, and the complex interactions in multiferroic hexagonal manganites, are presented in this paper.

Nonlinear Magnetooptical Effects Caused by Piezoelectric Ferromagnetism in F4̄3m-type Prussian Blue Analogues

The second harmonic generation (SHG) and magnetization-induced SHG (MSHG) of AMA[MB(CN)6]-type (F3m) Prussian blue analogues (i.e., CsCo[Cr(CN)6].0.5H2O and RbMn[Fe(CN)6]) were observed. A large interaction between the nonlinear optical response and magnetic spins was observed in CsCo[Cr(CN)6].0.5H2O. These observations of SHG and MSHG imply that AMA[MB(CN)6]-type Prussian blue analogues are piezoelectric above the Curie temperature (TC) and piezoelectric ferromagnet below TC.

Ultrafast manipulation of antiferromagnetism of NiO

Photoexcitation of antiferromagnetic NiO leads to ultrafast reorientation of Ni2+ spins due to change of the magnetic anisotropy. Recovery of the magnetic ground state occurs as coherent oscillation of the antiferromagnetic order parameter between hard- and easy-axis states manifesting itself as quantum beating. The coherence time is approximately 1 ns with the beating frequency being determined by the anisotropy energy.

Magnetic-field induced second harmonic generation in CuB2O4

Three types of optical magnetic-field induced second harmonic (MFISH) generation are observed in CuB2O4. Unusually sharp and intense electronic transitions in MFISH and linear absorption spectra provide selective access to the two nonequivalent Cu2+ sublattices. The magnetic phase diagram for both sublattices is determined by MFISH. Magnetic structure is dominated by antiferromagnetic order at the 4b site. Sublattice interactions transfer it to the 8d site where it coexists with a discoupled paramagnetic component.

Magnetization-induced second harmonic generation in a polar ferromagnet

Second harmonic generation (SHG) induced by spontaneous magnetization has been investigated for a polar ferromagnetic crystal of GaFeO3. The Kerr rotation of the second harmonic light becomes gigantic with decreasing temperature below the magnetic transition temperature (approximately =205 K), e.g., as large as 73 degrees at 100 K. The magnetic domains can be visualized by using that large nonlinear Kerr rotation. The spectrum of the magnetization-induced SHG as measured indicates the two-photon resonant electronic process on a Fe3+ ion in the crystal.

Anomalously broad Raman scattering spectrum due to two-magnon excitation in hexagonal YMnO3

A strong and broad Raman scattering (RS) spectrum is observed from two-magnon processes in YMnO3. The spectrum is analyzed by taking account (i) the magnon-exciton interaction and (ii) the magnon-phonon coupling in the intermediate state. Anomalous broadening of the RS is attributed to the large superexchange interaction between manganite ions and subsequent modification of magnons under the presence of the exciton and phonons in the intermediate state.

X-ray magnetochiral dichroism: a new spectroscopic probe of parity nonconserving magnetic solids

We report the first experimental detection of x-ray magnetochiral dichroism in magnetoelectric Cr2O3. This dichroism, which does not require any polarized x-ray beam, is related to the time-reversal odd part of the optical activity tensor dominated by electric dipole-electric quadrupole E1E2 interference terms. The experiments were carried out using either a single crystal or a powdered pellet required to grow a single antiferromagnetic domain by magnetoelectric annealing. This new element (edge) specific spectroscopy offers unique access to the atomic orbital anapole moment Omega-z.

Nonlinear magneto-optical properties of colossal magnetoresistive manganites

Pr(1--x)CaxMnO(3) and Nd(1--x)SrxMnO(3) were investigated with three-photon difference frequency generation (DFG). This method allows one to determine both the crystalline and the magnetic symmetry. In the highly ordered low-temperature phase of Nd(0.50)Sr(0.50)MnO(3), a DFG contribution coupling simultaneously to antiferromagnetic and charge ordering was observed and used to reveal the formation of domains. Thus, magnetically induced three-photon processes are introduced into the fields of both nonlinear magneto-optics and colossal magnetoresistance as a powerful new method.

First observation of nonreciprocal X-Ray gyrotropy

We report the first observation of a nonreciprocal x-ray linear dichroism caused by the time-reversal odd, real part zeta of the complex gyrotropy tensor zeta(*) which is dominated by electric dipole-electric quadrupole E1E2 interference terms. A nonreciprocal transverse anisotropy was observed in the low temperature insulating phase of a Cr doped V2O3 Mott crystal when a single antiferromagnetic domain was grown by magnetoelectric annealing along the hexagonal c axis. This new element (edge) specific spectroscopy could nicely complement x-ray magnetic circular dichroism which is silent for antiferromagnetic materials.

Determination of the magnetic symmetry of hexagonal manganites by second harmonic generation

Optical second harmonic spectroscopy is introduced as a powerful supplement for the determination of complex magnetic structures. Experimental efforts are simplified and new degrees of freedom are opened. Thereby, some principal or technical restrictions of neutron or magnetic x-ray diffraction experiments are overcome. High spatial resolution leads to additional information about magnetically ordered matter. As an example, the noncollinear magnetic structure of the hexagonal manganites RMnO3 ( R = Sc, Y, Ho, Er, Tm, Yb, Lu) is analyzed. The results show that some earlier conclusions on their magnetic symmetry and properties should be revised.

Nonlinear spatially resolved phase spectroscopy

A new method for the determination of spatially resolved phase differences of nonlinear susceptibilities is presented. The technique is based on the interference of the signal field with a reference field. A phase-shifting element that directly changes the phase difference between the two second-harmonic fields is introduced. The reliability of the method is tested by an experiment with two quartz crystals. As a first application, a measurement of the phase difference between domains in antiferromagnetic YMnO(3) is presented.