Resonant x-ray scattering experiments at the vanadium K edge demonstrate the existence of orbital ordering in V 2 O 3 . Bragg peaks due to the long-range order of 3d orbitals occupancy are observed when the photon energy is tuned to the threshold of the vanadium 3d bands. The azimuthal dependence of the resonant intensities confirms that the resonance arises from the ordering of the vanadium orbital occupancy. The observed orbital structure accounts for the complex magnetic structure of V 2 O 3 . The measured magnetic and orbital responses have the same critical temperature T N .[S0031-9007 (99)09287-X] PACS numbers: 78.70.Ck, 71.30. + h, 75.50.EeTwenty years ago, Castellani et al. [1] proposed that long-range order in the occupancy of the vanadium 3d orbitals was responsible for the complex magnetic properties of V 2 O 3 . Upon doping with Cr and/or under the application of hydrostatic pressure [2,3] V 2 O 3 exhibits both insulating and metallic phases with peculiar magnetic correlations [4][5][6]. It was suggested [1] that the spatial ordering of the occupancy of degenerate electronic orbitals accounts for the anisotropic exchange integrals found in the antiferromagnetic insulator phase (AFI) [5]. Furthermore, fluctuations in the orbital occupancy have been invoked to explain the evolution of the magnetic correlations in various phases of the V 2 O 3 system [6]. It appears that orbital occupancy plays a central role in the physics of V 2 O 3 , but no direct proof for orbital order could be produced experimentally since the original proposal in the late 1970s.In this Letter we present resonant x-ray scattering (RXS) experiments at the K edge of vanadium that demonstrate unambiguously the existence of orbital order in V 2 O 3 and provide information on the type of ordering. RXS is sensitive to the occupancy of electronic orbitals because it probes the symmetry of vacant electronic states through resonant multipole electric transitions; the variation of the orbital resonant scattering cross section with the direction of the incident polarization (azimuthal angle F) reflects the spatial symmetry of ordered orbitals. Furthermore, RXS may be tuned to probe selectively the electronic shells where orbital order takes place. In the case of V 2 O 3 , theoretical calculations [7] have shown that the resonance at the vanadium K edge provides observable cross sections arising from the order of the 3d vanadium states.RXS experiments were performed at the ID20 magnetic scattering undulator beam line at the European Synchrotron Radiation Facility [8]. A double crystal, Si(111), monochromator located between two focusing mirrors defined a narrow energy band around the vanadium K edge (FHWM 0.8 eV) with a high degree of linear s polarization. The x-ray beam was diffracted by the sample onto a pyrolitic graphite crystal analyzer [(004) reflection] to separate the s and p components of the scattered radiation. The sample was mounted with beeswax in a closed cycle refrigerator which could be rotated about the scattering vector to p...

The calculation of the amplitude of X-rays scattered by a magnetically ordered substance, carried out in the relativistic quantum theory (i.e. taking the spin into account), is detailed. The effect of the orbital momentum is described in an appendix. The practical formulae dealing with the polarization of the beams are given both in a simple form for the usual experiments and in a complete form, using the Stokes vectors, for the most general case. The experiments show a change in the intensity of the X-rays diffracted by a ferromagnetic (pure iron) or a ferrimagnetic (zinc-substituted magnetite) powder when the magnetization, perpendicular to the diffraction plane, is reversed. The relative values of these intensity changes range from 10 -4 to 5 x 10 -3 and agree in sign and magnitude with the predictions. They are proportional to the spin-density structure factor multiplied by the imaginary part of the chargedensity structure factor; the large anomalous scattering of the Cu Ka radiation in the iron-containing samples is used in the present experiments. moment associated with the spin does interact with the magnetic field of the radiation (Fig. 1). This effect can Driving force Reradiation-eE E -e E-dipol.-eE H -e ~ H-quadr. E grad/~.H --e~ffj ~C_.,~ ~ ~H $ E-dipol. IntroductionX-ray diffraction is usually interpreted through the Thomson scattering mechanism, i.e. the interaction between the electromagnetic radiation and the charge of the electrons. X-rays therefore seem to give information about the charge density only and not about the spin density. If one examines the phenomenon more thoroughly, it appears that the electronic spin also plays some role; the magnetic 0567-7394/81/030314-11 $01.00Tor qUeHx/ z ~; ~H H-dipol. be treated with relativistic quantum theory. The Klein & Nishina (1929) formula for the Compton effect takes this effect into account, but only implicitly since it concerns mean values taken over all spin states. In relativistic theory space and spin wave functions cannot be separated as they can be in the nonrelativistic limit. A perturbation on the movement of an electron has an effect which depends upon the spin. During the collision with a photon of momentum k(0 (k¢f) after collision) the electron is accelerated. One may admit that the effect of this acceleration depends upon the direction of the spin by some term of the order of I k(f) -k(0 I/mc, which expresses the relativistic character of the acceleration undergone by the electron (Fig. 2a). This is analogous to the Mott asymmetry (Tolhoek, 1956) observed in the scattering of an electron by the electric field of a nucleus, or to the Schwinger (1948) scattering (see a recent review by Felcher & Peterson, 1975), which is similar to the Mott assymetry but concerns neutrons instead of electrons (Fig. 2b). These effects can also be compared to the spin-orbit coupling (Fig. 2c), the magnitude of which is still determined by the ratio I pl/mc (p is the electron momentum). One should not forget that these comparisons do not account f...

The spin-and orbital-moment magnetization form factors in NiO have been measured using magnetic x-ray scattering. The polarization analysis of nonresonant magnetic-scattering intensities has evidenced a large contribution from the orbital moment to the total magnetization. In the antiferromagnetic phase, the orbital moment contributes 17Ϯ3% to the magnetization density. ͓S0163-1829͑98͒05313-2͔

Magneto-electric multiferroics exemplified by TbMnO 3 possess both magnetic and ferroelectric long-range order. The magnetic order is mostly understood, whereas the nature of the ferroelectricity has remained more elusive. Competing models proposed to explain the ferroelectricity are associated respectively with charge transfer and ionic displacements. Exploiting the magneto-electric coupling, we use an electric field to produce a single magnetic domain state, and a magnetic field to induce ionic displacements. Under these conditions, interference charge-magnetic X-ray scattering arises, encoding the amplitude and phase of the displacements. When combined with a theoretical analysis, our data allow us to resolve the ionic displacements at the femtoscale, and show that such displacements make a significant contribution to the zero-field ferroelectric moment.The discovery of spin-cycloid multiferroics, in which the onset of non-collinear magnetic order leads to a spontaneous ferroelectric polarization, has generated considerable interest in 1 arXiv:1110.2875v1 [cond-mat.str-el] 13 Oct 2011 the control of electric polarization by magnetic fields, and vice versa (1, 2). While comprehensive, microscopic descriptions of their magnetic structures have been obtained (3-11), our understanding of the ferroelectric state is still emerging. Two competing theoretical scenarios have been proposed: one purely electronic, without ionic displacements (12); one based on anti-symmetric exchange interactions, with ionic displacements (13). Experiments have been unable to resolve the individual ionic displacements (14).Spin-cycloid multiferroics exhibit an exceptionally strong cross-coupling between the different types of order, as demonstrated when the electric (magnetic) field E (H) was used to control magnetization M (ferroelectric polarization P) (1,5,(15)(16)(17)(18). Interest in this class of multiferroic has been generated both by the potential for novel devices, and the challenge they represent to our fundamental understanding of ordering phenomena in solids. TbMnO 3 is the prototypical spin-cycloid multiferroic (1). Diffraction studies have established that in its ferroelectric phase below ∼30 K the Mn magnetic moments form a cycloid in the bc plane (3), while the Tb moments order sinusoidally (5), Fig. 1A,B. Formation of the cycloid removes the centre of inversion at the Mn sites and generates a spontaneous P along c. The scenario in which P is generated by ionic displacements has been investigated by ab-initio density functional theory (DFT) (19,20) which makes definite predictions for the displacements of the constituent ions. Experimentally, only an upper limit (of ∼500 fm) has been estimated for the ionic displacements from EXAFS measurements (14); EXAFS has been used to obtain femtoscale displacements in other systems (21). Application of a sufficiently strong magnetic field along either the a or b axis results in the flopping of P from the c to a axis (6, 15). Conventional X-ray scattering in an applied magnetic fie...