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.

Imprinting magnetic information in manganites with x rays.

The effect of x rays on an orbital and charge ordered epitaxial film of a Pr0.5Ca0.5MnO3 is presented. As the film is exposed to x rays, the antiferromagnetic response increases and concomitantly the conductivity of the film improve. These results are discussed in terms of a persistent x-ray induced doping, leading to a modification of the magnetic structure. This effect allows writing electronic and magnetic information in the film and represents a novel way of manipulating magnetism.

Origin of the large polarization in multiferroic YMnO3 thin films revealed by soft- and hard-X-ray diffraction.

We investigated the magnetic structure of an orthorhombic YMnO(3) thin film by resonant soft x-ray and hard x-ray diffraction. We observed a temperature-dependent incommensurate magnetic reflection below 45 K and a commensurate lattice-distortion reflection below 35 K. These results demonstrate that the ground state is composed of coexisting E-type and cycloidal states. Their different ordering temperatures clarify the origin of the large polarization to be caused by the E-type antiferromagnetic states in the orthorhombic YMnO(3) thin film.

Femtosecond dynamics of the collinear-to-spiral antiferromagnetic phase transition in CuO.

We report on the ultrafast dynamics of magnetic order in a single crystal of CuO at a temperature of 207 K in response to strong optical excitation using femtosecond resonant x-ray diffraction. In the experiment, a femtosecond laser pulse induces a sudden, nonequilibrium increase in magnetic disorder. After a short delay ranging from 400 fs to 2 ps, we observe changes in the relative intensity of the magnetic ordering diffraction peaks that indicate a shift from a collinear commensurate phase to a spiral incommensurate phase. These results indicate that the ultimate speed for this antiferromagnetic reorientation transition in CuO is limited by the long-wavelength magnetic excitation connecting the two phases.

Probing spin fluctuations in NaOsO3by muon spin rotation and NMR spectroscopy.

We have used muon spin rotation and relaxation (µSR) and23Na nuclear magnetic resonance (NMR) spectroscopic methods in the NaOsO3antiferromagnetic phase to determine the temperature evolution of the magnetic order parameter and the role of the magnetic fluctuations at the Néel temperature. Additionally, we performed muon spin relaxation measurements in the vicinity ofTA= 30 K, where the appearance of an anomaly in the electrical resistivity was suggested to be due to a progressive reduction of the Os magnetic moment associated with spin fluctuation. Our measurements suggest the absence of prominent change in the spin fluctuations frequency atTA, within the muon probing time scale and the absence of a reduction of the localized Os magnetic moment reflected by the stability within few permille of the local magnetic field strength sensed by the muons below 50 K.

Imaging three-dimensional magnetic systems with x-rays.

Recent progress in nanofabrication and additive manufacturing have facilitated the building of nanometer-scale three-dimensional (3D) structures, that promise to lead to an emergence of new functionalities within a number of fields, compared to state-of-the-art two dimensional systems. In magnetism, the move to 3D systems offers the possibility for novel magnetic properties not available in planar systems, as well as enhanced performance, both of which are key for the development of new technological applications. In this review paper we will focus our attention on 3D magnetic systems and how their magnetic configuration can be retrieved using x-ray magnetic nanotomography. We will start with an introduction to magnetic materials, and their relevance to our everyday life, along with the growing impact that they will have in the coming years in, for example, reducing energy consumption. We will then briefly introduce common methods used to study magnetic materials, such as electron holography, neutron and x-ray imaging. In particular, we will focus on x-ray magnetic circular dichroism (XMCD) and how it can be used to image magnetic moment configurations. As a next step we will introduce tomography for 3D imaging, and how it can be adapted to study magnetic materials. Particular attention will be given to explaining the reconstruction algorithms that can be used to retrieve the magnetic moment configuration from the experimental data, as these represent one of the main challenges so far, as well as the different experimental geometries that are available. Recent experimental results will be used as specific examples to guide the reader through each step in order to make sure that the paper will be accessible for those interested in the topic that do not have a specialized background on magnetic imaging. Finally, we will describe the future prospects of such studies, identifying the current challenges facing the field, and how these can be tackled. In particular we will highlight the exciting possibilities offered by the next generation of synchrotron sources which will deliver diffraction limited beams, as well as with the extension of well-established methodologies currently implemented for the study of two-dimensional magnetic materials to achieve higher dimensional investigations.

Effects of dispersion and absorption in resonant Bragg diffraction of x-rays.

Resonant diffraction of x-rays by crystals with anisotropic optical properties is investigated theoretically, to assess how the intensity of a Bragg spot is influenced by effects related to dispersion (birefringence) and absorption (dichroism). Starting from an exact but opaque expression, simple analytic results are found to expose how intensity depends on dispersion and absorption in the primary and secondary beams and, also, the azimuthal angle (rotation of the crystal about the Bragg wavevector). If not the full story for a given application, our results are more than adequate to explore consequences of dispersion and absorption in the intensity of a Bragg spot. Results are evaluated for antiferromagnetic copper oxide, and low quartz. For CuO, one of our results reproduces all salient features of a previously published simulation of the azimuthal-angle dependence of a magnetic Bragg peak. It is transparent in our analytic result that dispersion and absorption effects alone cannot reproduce published experimental data. Available data for the azimuthal-angle dependence of space-group forbidden reflections (0,0, l), with l ≠ 3n, of low quartz depart from symmetry imposed by the triad axis of rotation symmetry. The observed asymmetry can be induced by dispersion and absorption even though absorption coefficients are constant, independent of the azimuthal angle, in this class of reflections.

Large-amplitude spin dynamics driven by a THz pulse in resonance with an electromagnon.

Multiferroics have attracted strong interest for potential applications where electric fields control magnetic order. The ultimate speed of control via magnetoelectric coupling, however, remains largely unexplored. Here, we report an experiment in which we drove spin dynamics in multiferroic TbMnO3 with an intense few-cycle terahertz (THz) light pulse tuned to resonance with an electromagnon, an electric-dipole active spin excitation. We observed the resulting spin motion using time-resolved resonant soft x-ray diffraction. Our results show that it is possible to directly manipulate atomic-scale magnetic structures with the electric field of light on a sub-picosecond time scale.

Melting of chiral order in terbium manganate (TbMnO3) observed with resonant x-ray Bragg diffraction.

Resonant Bragg diffraction of soft, circularly polarized x-rays has been used to observe directly the temperature dependence of chiral-order melting in a motif of Mn ions in terbium manganate. The underlying mechanism uses the b-axis component of a cycloid, which vanishes outside the polar phase. Melting is witnessed by the first and second harmonics of a cycloid, and we explain why the observed temperature dependence differs in the two harmonics. Conclusions follow from an exact treatment of diffraction by using atomic multipoles in a circular cycloid, since a standard treatment of the diffraction, based on a single material-vector identified with the magnetic dipole, does not reproduce correctly observations at the second harmonic.

Acentric magnetic and optical properties of chalcopyrite (CuFeS2).

The absence of spatial inversion symmetry at both local (point group 4) and global (crystal class (4)2m) levels greatly influences the electronic properties of chalcopyrite (CuFeS(2)). The predicted dichroic signals (natural circular, non-reciprocal and magneto-chiral) and resonant, parity-odd Bragg diffraction patterns at space-group forbidden reflections portray the uncommon, acentric symmetry. Despite extensive experimental investigations over several decades, by mineralogists, chemists and physicists, there is no consensus view about the electrical and magnetic properties of chalcopyrite. New spectroscopic and diffraction data, gathered at various temperatures in the vicinity of the copper and iron L(2,3) edges, provide necessary confidence in the magnetic motif used in our analytic simulations of x-ray scattering. With the sample held at 10 and 65 K, our data establish beyond reasonable doubt that there is no valence transition, and ordering of the copper moments as the origin of the low-temperature phase (T(c) ≈ 53 K) is ruled out.

Triakontadipole and high-order dysprosium multipoles in the antiferromagnetic phase of DyB2C2.

Resonant soft x-ray Bragg diffraction at the Dy M(4,5) edges has been used to study Dy multipoles in the combined magnetic and orbitally ordered phase of DyB(2)C(2). The analysis incorporates both the intra-atomic magnetic and quadrupolar interactions between the 3d core and 4f valence shells. Additionally, we introduce to the formalism the interference of magnetic and nonmagnetic oscillators. This allows a determination of the higher-order multipole moments of rank 1 (dipole) to 6 (hexacontatetrapole). The strength of the Dy 4f multipole moments have been estimated as being up to 80% of the quadrupolar moment.

Observation of orbital currents in CuO.

Orbital currents are proposed to be the order parameter of the pseudo-gap phase of cuprate high-temperature superconductors. We used resonant x-ray diffraction to observe orbital currents in a copper-oxygen plaquette, the basic building block of cuprate superconductors. The confirmation of the existence of orbital currents is an important step toward the understanding of the cuprates as well as materials lacking inversion symmetry, such as magnetically induced multiferroics. Although observed in the antiferromagnetic state of cupric oxide, we show that orbital currents can occur even in the absence of long-range magnetic moment ordering.

Direct observation of charge order and an orbital glass state in multiferroic LuFe2O4.

Geometrical frustration of the Fe ions in LuFe2O4 leads to intricate charge and magnetic order and a strong magnetoelectric coupling. Using resonant x-ray diffraction at the Fe K edge, the anomalous scattering factors of both Fe sites are deduced from the (h/3 k/3 l/2) reflections. The chemical shift between the two types of Fe ions equals 4.0(1) eV corresponding to full charge separation into Fe2+ and Fe3+. The polarization and azimuthal angle dependence of the superlattice reflections demonstrate the absence of differences in anisotropic scattering revealing random orientations of the Fe2+ orbitals characteristic of an orbital glass state.

Orbital order at Mn and O sites and absence of Zener polaron formation in manganites.

We report the doping dependence of the ground state of A-site ordered manganites below and above half doping. Energy and polarization dependence of the orbital reflection, taken by resonant soft-x-ray powder diffraction, at both Mn L(2,3) and O K edges, provides direct evidence for orbital order at Mn(3+) and oxygen sites and absence of Zener polaron formation. For x > or = 0.2 anomalous melting of the orbital order is observed, which is coupled neither to magnetic ordering nor to a structural transition, indicating a two-dimensional character of the interactions.

Polarization analysis in soft X-ray diffraction to study magnetic and orbital ordering.

An experimental approach to the analysis of charge, magnetic and orbital ordering in 3d transition-metal oxides is presented. The technique combines two important components: azimuthal rotations around the Bragg wavevector and polarization analysis of the Bragg intensities in the range 500-900 eV. The polarization analysis is performed using graded multilayers, which are translated and rotated in the vacuum chamber. It is shown why these two components are important to determine the origin of the Bragg scattered signals and how they allow us to separate the different contributions. Examples are given for the oxygen K and the Mn, Co, Ni and Cu L(2,3)-edges, and the advantages and drawbacks of this experimental technique are discussed.

Direct observation of oxygen superstructures in manganites.

We report the observation of superstructures associated with the oxygen 2p states in two prototypical manganites using x-ray diffraction at the oxygen K edge. In the stripe order system Bi0.31Ca0.69MnO3, hole-doped O states are orbitally ordered, at the same propagation vector as the Mn orbital ordering, but no oxygen charge stripes are found at this periodicity. In La7/8Sr1/8MnO3, we observe a 2p charge ordering described by alternating hole-poor and hole-rich MnO planes that is consistent with some of the recent predictions.