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.     

Three-dimensional noncollinear antiferromagnetic order in single-crystalline FeMn ultrathin films

We present experimental evidence for a three-dimensional noncollinear antiferromagnetic spin structure in ultrathin single-crystalline fcc Fe50Mn50 layers using magnetic circular dichroism photoelectron emission microscopy and x-ray magnetic linear dichroism. Layer-resolved as-grown domain images of epitaxial trilayers grown on Cu(001) in which FeMn is sandwiched between ferromagnetic layers with different easy axes reveal the presence of antiferromagnetic spin components in the film plane and normal to the film plane. An FeMn spin structure with no collinear order in the film plane is consistent with the absence of x-ray magnetic linear dichroism in Fe L3 absorption in FeMn/Co bilayers.     

X-ray directional dichroism of a polar ferrimagnet

In a polar ferrimagnet GaFeO3, we have found a novel magneto-optical effect, termed x-ray nonreciprocal directional dichroism (XNDD), that the x-ray absorption at around the K edge of an Fe ion depends on whether the x-ray propagation vector is parallel or antiparallel to the outer product of the magnetization and electric-polarization vectors. The XNDD spectroscopy as demonstrated here can be a useful tool to probe the local magnetism in noncentrosymmetric systems such as magnetic interfaces and nanostructures.     

Nonreciprocal directional dichroism in multiferroics

Nonreciprocal directional dichroism in multiferroics, namely magnetoelectric coupling in the dynamic regime, is endowed with rich physics and promising applications, which are entangled with fundamental physical components, such as spin, orbital,lattice, charge, and topology. Such a linear nonreciprocal response behavior in the GHz-THz frequency range, represented by optical magnetoelectric effect and magnetochiral dichroism, occurs ubiquitously in material systems with the spontaneous breaking of space-time symmetry, and is subject to Onsager's reciprocal theorem in the thermodynamic limit. Microscopically,these nonreciprocal responses are usually encoded by toroidization(chirality) and electromagnon(quasiparticle), thus establishing a comprehensive understanding of magnetoelectric coupling and irreversible dynamics. Herein, the basic mechanisms and emergent nonreciprocal directional dichroism in single-phase multiferroics are summarized. We expect that the present review will stimulate diverse possibilities toward nonreciprocal directional dichroism within and beyond multiferroics.     

Microscopic nature of ferro- and antiferromagnetic interface coupling of uncompensated magnetic moments in exchange bias systems

Exchange bias in layered CoO/Fe structures is investigated by x-ray resonant magnetic reflectivity (XRMR) measurements. Element-specific hysteresis loops are obtained from x-ray magnetic circular dichroism effects in the XRMR spectra. Evidence is provided for the existence of different types of uncompensated moments in the antiferromagnetic material. Explanations are given for the microscopic nature of these moments and the complex exchange interactions that determine the magnetization reversal in exchange bias systems.     

Ferrimagnetism in EuFe4Sb12 due to the interplay of f-electron moments and a nearly ferromagnetic host

We combine x-ray magnetic circular dichroism spectroscopy at Fe L2,3 edges, at Eu M4,5 edges, x-ray absorption spectroscopy (XAS) investigation of Eu valence, and local spin density calculations, to show that the filled skutterudite Eu0.95Fe4Sb12 is a ferrimagnet in which the Fe 3d moment and the Eu2+ 4f moment are magnetically ordered with dominant antiferromagnetic coupling. From Eu L3 edge XAS, we find that about 13% of the Eu have a formal valence of 3+. We ascribe the origin of ferrimagnetism at a relatively high transition temperature TC of 85 K in Eu0.95Fe4Sb12 to f-electron interaction with the nearly ferromagnetic [Fe4Sb12]2.2- host lattice.     

Crystal-field level inversion in lightly Mn-doped Sr3Ru2O7

Sr3(Ru(1-x)Mnx)2O7, in which 4d-Ru is substituted by the more localized 3d-Mn, is studied by x-ray dichroism and spin-resolved density functional theory. We find that Mn impurities do not exhibit the same 4+ valence of Ru, but act as 3+ acceptors; the extra eg electron occupies the in-plane 3d(x2-y2) orbital instead of the expected out-of-plane 3d(3z2-r2). We propose that the 3d-4d interplay, via the ligand oxygen orbitals, is responsible for this crystal-field level inversion and the material's transition to an antiferromagnetic, possibly orbitally ordered, low-temperature state.     

Spin-flop ordering from frustrated ferro- and antiferromagnetic interactions: a combined theoretical and experimental study of a Mn/Fe(100) monolayer

The occurrence of a noncollinear magnetic structure at a Mn monolayer grown epitaxially on Fe(100) is predicted theoretically, using spinor density-functional theory, and observed experimentally, using x-ray magnetic circular dichroism (XMCD) and linear dichroism (XMLD) spectroscopies. The combined use of XMCD and XMLD at the Mn-absorption edge allows us to assess the existence of ferromagnetic and antiferromagnetic order at the interface, and also to determine the moment orientations with element specificity. The experimental results thus obtained are in excellent agreement with the magnetic structure determined theoretically.     

Field cooling induced changes in the antiferromagnetic structure of NiO films

The magnetic anisotropy in antiferromagnetic 500 A thick NiO films, before and after the establishment of an exchange bias field with Co84Fe16 ferromagnetic layers, was measured using magnetic linear dichroism in soft x-ray absorption. Both <111> textured NiO and untextured NiO films show exchange-bias induced in-plane magnetic anisotropy of nearly equal magnitude and with the Ni moment axis being nearly parallel to the exchange bias field direction. These results represent the first observation of the key step in the exchange biasing process, namely, repopulation of the antiferromagnetic domains whose magnetization axis is closest to the exchange bias field direction.     

Orbital ordering in La0.5Sr1.5MnO4 studied by soft X-ray linear dichroism

We found that the conventional model of orbital-ordering of 3x(2)-r(2)/3y(2)-r(2) type in the e(g) states of La0.5Sr1.5MnO4 is incompatible with measurements of linear dichroism in the Mn 2p-edge x-ray absorption, whereas these e(g) states exhibit predominantly cross-type orbital ordering of x(2)-z(2)/y(2)-z(2). LDA+U band-structure calculations reveal that such a cross-type orbital-ordering results from a combined effect of antiferromagnetic structure, Jahn-Teller distortion, and on-site Coulomb interactions.     

Linear nonreciprocal dichroism in boracite Co3B7O13I

Linear nonreciprocal dichroism that is odd in magnetic field B was observed in the transverse geometry and studied for cubic (symmetry class T _d ) phase of boracite Co₃B₇O₁₃I. Nonreciprocal dichroism was observed in the range of absorption bands corresponding to the transitions of the Co²⁺ ion in the energy range ΔE=1.2–3.2 eV. The sign and magnitude of nonreciprocal dichroism depend on the mutual orientation of the magnetic field and crystallographic axes. Nonreciprocal dichroism refers to the phenomena of magnetically induced spatial dispersion, and its anisotropy is typical for the manifestation of the second-order magnetoelectric susceptibility in the optical range.     

Novel pressure-induced magnetic transition in magnetite (Fe3O4)

Fe K-edge x-ray magnetic circular dichroism of magnetite (Fe3O4) powders was measured with synchrotron radiation under variable pressure and temperature conditions in diamond anvil cell. The magnetic dichroism was observed to decrease discontinuously by approximately 50% between 12 and 16 GPa, independent of temperature. The magnetic transition is attributed to a high-spin to intermediate-spin transition of Fe2+ ions in the octahedral sites and could account for previously observed structural and electrical anomalies in magnetite at this pressure range. The interpretation of x-ray magnetic circular dichroism data is supported by x-ray emission spectroscopy and theoretical cluster calculations.     

Voigt位型下电介质/反铁磁/电介质结构二次谐波生成非倒易性研究

利用非线性传递矩阵方法研究了Voigt位型下电介质/反铁磁/电介质 结构二次谐波生成的非倒易性. 研究发现外加静磁场反向和电介质层排序翻转均对二次谐波输出产生影响, 出现了二次谐波生成的非倒易性. 二次谐波生成非倒易性频率区域在反铁磁共振区, 此区间正处于THz频段. 随着入射角度的增加, 非倒易性的效果越来越明显. 研究二次谐波生成的非倒易性, 可为反铁磁器件的设计加工提供理论支持.     

Magnetic moments at the surface of antiferromagnetic NiO(100)

The orientation of magnetic moments at the (100) surface of antiferromagnetic NiO single crystals is studied by x-ray linear magnetic dichroism in photoemission microscopy. T domains are observed terminating at the surface, with domain boundaries running mostly along in-plane [10] directions. From the detailed polarization dependence we find that the magnetic surface structure of a cleaved crystal is bulk terminated. This is in contrast to sputtered surfaces, where magnetic moments lie within the surface plane, forming a magnetically relaxed structure. These findings are of importance for understanding the exchange bias phenomenon.     

Fragile magnetic ground state in half-doped LaSr2Mn2O7

We investigated the orbital and antiferromagnetic ordering behaviors of the half-doped bilayer manganite La(2-2x)Sr(1+2x)Mn2O7 (x ? 0.5) by using Mn L(2,3)-edge resonant soft x-ray scattering. Resonant soft x-ray scattering reveals the CE-type orbital order below T(oo) ? 220 K, which shows partial melting behavior below T(m) ? 165 K. We also found coexistence CE- and A-type antiferromagnetic orders. Both orders involve the CE-type orbital order with nearly the same orbital character and are coupled with each other. These results manifest that the ground state with the CE-type antiferromagnetic order is easily susceptible to destabilization into the A-type one even with a small fluctuation of the doping level, as suggested by the extremely narrow magnetic phase boundaries at x ? 0.5±0.005.     

X-ray optical activity: Applications of sum rules

Edge-selective sum rules are proposed for a variety of X-ray dichroisms related to natural or nonreciprocal optical activity. Four spherical operators are identified that mix orbitals of different parities in what is assumed to be the ground state. The orbital anapole moment Ω⁽¹⁾ is primarily responsible for the magnetochiral dichroism; the time-even rank-2 tensor N⁽²⁾=[L, Ω]⁽²⁾ for natural circular dichroism; the time-odd rank-2 tensor W⁽²⁾=[L, n]⁽²⁾ for nonreciprocal magnetic linear dichroisms. At higher orders, the time-odd rank-3 tensor Γ⁽³⁾=[L, L, Ω]⁽³⁾ can also contribute to all nonreciprocal dichroisms. The physical content of these operators is analyzed. For every magnetoelectric group, one can predict which dichroic effect can be measured with either a single crystal or a powdered sample. Experimental spectra are produced to illustrate the value of the sum rules and the practical conditions of their application. Regarding nonreciprocal activity, one should be cautious about discussing magnetic symmetry because the deep core hole can couple the true ground state with low-lying excited states.     

Correlation between exchange bias and pinned interfacial spins

Using x-ray magnetic circular dichroism, we have detected the very interfacial spins that are responsible for the horizontal loop shift in three different exchange bias sandwiches, chosen because of their potential for device applications. The "pinned" uncompensated interfacial spins constitute only a fraction of a monolayer and do not rotate in an external magnetic field since they are tightly locked to the antiferromagnetic lattice. A simple extension of the Meiklejohn and Bean model is proposed to account quantitatively for the exchange bias fields in the three studied systems from the experimentally determined number of pinned moments and their sizes.     

X-ray linear dichroism dependence on ferroelectric polarization

X-ray absorption spectroscopy and photoemission electron microscopy are techniques commonly used to determine the magnetic properties of thin films, crystals, and heterostructures. Recently, these methods have been used in the study of magnetoelectrics and multiferroics. The analysis of such materials has been compromised by the presence of multiple order parameters and the lack of information on how to separate these coupled properties. In this work, we shed light on the manifestation of dichroism from ferroelectric polarization and atomic structure using photoemission electron microscopy and x-ray absorption spectroscopy. Linear dichroism arising from the ferroelectric order in the PbZr0:2Ti0:8O3 thin films was studied as a function of incident x-ray polarization and geometry to unambiguously determine the angular dependence of the ferroelectric contribution to the dichroism. These measurements allow us to examine the contribution of surface charges and ferroelectric polarization as potential mechanisms for linear dichroism. The x-ray linear dichroism from ferroelectric order revealed an angular dependence based on the angle between the ferroelectric polarization direction and the x-ray polarization axis, allowing a formula for linear dichroism in ferroelectric samples to be defined.     

Suppression of antiferromagnetic interactions through Cu vacancies in Mn-substituted CuInSe2 chalcopyrites

Stoichiometric and Cu-poor Cu(0.95-x)Mn(0.05)InSe(2) (x = 0-0.20) compounds were synthesized by high-temperature, solid-state reactions. The presence of copper vacancies is revealed by Rietveld refinements of combined neutron and x-ray powder diffraction data. The antiferromagnetic interaction is depressed by the copper deficiency, which may be explained as the competition between the antiferromagnetic Mn-Se-Mn superexchange interaction and the hole-mediated ferromagnetic exchange induced by the copper vacancy. The introduction of copper vacancies is proposed to be a viable route to impart carrier-mediated ferromagnetic exchange in the chalcopyrite-based dilute magnetic semiconductors.