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Considering the growing interest in magnetic materials for unconventional computing, data storage, and sensor applications, there is active research not only on material synthesis but also characterisation of their properties. In addition to structural and integral magnetic characterisations, imaging of magnetization patterns, current distributions and magnetic fields at nano- and microscale is of major importance to understand the material responses and qualify them for specific applications. In this roadmap, we aim to cover a broad portfolio of techniques to perform nano- and microscale magnetic imaging using SQUIDs, spin center and Hall effect magnetometries, scanning probe microscopies, x-ray- and electron-based methods as well as magnetooptics and nanoMRI. The roadmap is aimed as a single access point of information for experts in the field as well as the young generation of students outlining prospects of the development of magnetic imaging technologies for the upcoming decade with a focus on physics, materials science, and chemistry of planar, 3D and geometrically curved objects of different material classes including 2D materials, complex oxides, semi-metals, multiferroics, skyrmions, antiferromagnets, frustrated magnets, magnetic molecules/nanoparticles, ionic conductors, superconductors, spintronic and spinorbitronic materials.

Resonant driving of electronic transitions with coherent laser sources creates quantum coherent superpositions of the involved electronic states. Most time-resolved studies have focused on gases or isolated subsystems embedded in insulating solids, aiming for applications in quantum information. Here, we demonstrate coherent control of orbital wavefunctions in pyrochlore $Tb_{2}Ti_{2}O_{7}$, which forms an interacting spin liquid ground state. We show that resonant excitation with a strong THz pulse creates a coherent superposition of the lowest energy Tb 4f states before the magnetic interactions eventually dephase them. The coherence manifests itself as a macroscopic oscillating magnetic dipole, which is detected by ultrafast resonant x-ray diffraction. The induced quantum coherence demonstrates coherent control of orbital wave functions, a new tool for the ultrafast manipulation and investigation of quantum materials.

Hexagonal YMnO$_{3}$ is a prototype antiferromagnet which exhibits multiferroic behavior with the ferroelectric and magnetic transitions occurring at different temperatures. We observe an out-of-plane canting of the Mn$^{3+}$ magnetic moments using resonant X-ray diffraction (RXD) in a single crystal of this material. These canted moments result in the symmetry-forbidden (0,0,1) magnetic Bragg reflection, which is observed at the Mn $L_{2,3}$ absorption edges. We also observe an unexpected difference in the RXD spectral shapes at different temperatures. Using ab initio calculations, we explore the possibility that this behavior arises due to the interference between scattering from the canted magnetic moments and parity-odd atomic multipoles on the Mn$^{3+}$ ions.

Ultrafast manipulation of the magnetic state of matter bears great potential for future information technologies. While demagnetisation in ferromagnets is governed by dissipation of angular momentum, materials with multiple spin sublattices, e.g. antiferromagnets, can allow direct angular momentum transfer between opposing spins, promising faster functionality. In lanthanides, 4$\it{f}$ magnetic exchange is mediated indirectly through the conduction electrons (the Ruderman-Kittel-Kasuya-Yosida interaction, RKKY), and the effect of such conditions on direct spin transfer processes is largely unexplored. Here, we investigate ultrafast magnetization dynamics in 4f antiferromagnets, and systematically vary the 4$\it{f}$ occupation, thereby altering the magnitude of RKKY. By combining time-resolved soft x-ray diffraction with ab-initio calculations, we find that the rate of direct transfer between opposing moments is directly determined by the magnitude of RKKY. Given the high sensitivity of RKKY to the conduction electrons, our results offer a novel approach for fine-tuning the speed of magnetic devices.

The interaction of many-body systems with intense light pulses may lead to novel emergent phenomena far from equilibrium. Recent discoveries, such as the optical enhancement of the critical temperature in certain superconductors and the photo-stabilization of hidden phases, have turned this field into an important research frontier. Here, we demonstrate nonthermal charge-density-wave (CDW) order at electronic temperatures far greater than the thermodynamic transition temperature. Using time- and angle-resolved photoemission spectroscopy and time-resolved X-ray diffraction, we investigate the electronic and structural order parameters of an ultrafast photoinduced CDW-to-metal transition. Tracking the dynamical CDW recovery as a function of electronic temperature reveals a behaviour markedly different from equilibrium, which we attribute to the suppression of lattice fluctuations in the transient nonthermal phonon distribution. A complete description of the system's coherent and incoherent order-parameter dynamics is given by a time-dependent Ginzburg-Landau framework, providing access to the transient potential energy surfaces., Comment: 23 pages, 14 figures

We report a soft x-ray resonant magnetic scattering study of the spin configuration in multiferroic thin films of Co$_{0.975}$Ge$_{0.025}$Cr$_2$O$_4$ (Ge-CCO) and CoCr$_2$O$_4$ (CCO), under low- and high-magnetic fields, from 0.2 T up to 6.5 T. A characterization of Ge-CCO at a low magnetic field is performed and the results are compared to those of pure CCO. The ferrimagnetic phase transition temperature $T_C \approx 95$ K and the multiferroic transition temperature $T_S \approx 27$ K in Ge-CCO are comparable to those observed in CCO. In Ge-CCO, the ordering wave vector $\textit{(qq0)}$ observed below $T_S$ is slightly larger compared to that of CCO, and, unlike CCO, the diffraction intensity consists of two contributions that show a dissimilar x-ray polarization dependence. In Ge-CCO, the coercive field observed at low temperatures was larger than the one reported for CCO. In both compounds, an unexpected reversal of the spiral helicity and therefore the electric polarization was observed on simply magnetic field cooling. In addition, we find a change in the helicity as a function of momentum transfer in the magnetic diffraction peak of Ge-CCO, indicative of the presence of multiple magnetic spirals., Comment: 20 pages, 12 figures

Orthorhombic HoMnO3 is a multiferroic in which Mn antiferromagnetic order induces ferroelectricity. A second transition occurs within the multiferroic phase, in which a strong enhancement of the ferroelectric polarization occurs concomitantly to antiferromagnetic ordering of Ho 4f magnetic moments. Using the element selectivity of resonant X-ray diffraction, we study the magnetic order of the Mn 3d and Ho 4f moments. We explicitly show that the Mn magnetic order is affected by the Ho 4f magnetic ordering transition. Based on the azimuthal dependence of the (0 q 0) and (0 1-q 0) magnetic reflections, we suggest that the Ho 4f order is similar to that previously observed for Tb 4f in TbMnO3, which resembles an ac-cycloid. This is unlike the Mn order, which has already been shown to be different for the two materials. Using non-resonant diffraction, we show that the magnetically-induced ferroelectric lattice distortion is unaffected by the Ho ordering, suggesting a mechanism through which the Ho order affects polarization without affecting the lattice in the same manner as the Mn order.

A central prospect of antiferromagnetic spintronics is to exploit magnetic properties that are unavailable with ferromagnets. However, this poses the challenge of accessing such properties for readout and control. To this end, light-induced manipulation of the transient ground state, e.g. by changing the magnetic anisotropy potential, opens promising pathways towards ultrafast deterministic control of antiferromagnetism. Here, we use this approach to trigger a $\it{coherent}$ rotation of the entire long-range antiferromagnetic spin arrangement about a crystalline axis in $GdRh_2Si_2$ and demonstrate $\it{deterministic}$ control of this rotation upon ultrafast optical excitation. Our observations can be explained by a displacive excitation of the Gd spins$'$ local anisotropy potential by the optical excitation, allowing for a full description of this transient magnetic anisotropy potential.

Critical behavior is very common in many fields of science and a wide variety of many-body systems exhibit emergent critical phenomena. The beauty of critical phase transitions lies in their scale-free properties, such that the temperature dependence of physical parameters of systems differing at the microscopic scale can be described by the same generic power laws. In this work we establish the critical properties of the antiferromagnetic phase transition in artificial square ice, showing that it belongs to the two-dimensional Ising universality class, which extends the applicability of such concepts from atomistic to mesoscopic magnets. Combining soft x-ray resonant magnetic scattering experiments and Monte Carlo simulations, we characterize the transition to the low temperature long range order expected for the artificial square ice system. By measuring the critical scattering, we provide direct quantitative evidence of a continuous magnetic phase transition, obtaining critical exponents which are compatible with those of the two-dimensional Ising universality class. In addition, by varying the blocking temperature relative to the phase transition temperature, we demonstrate its influence on the out-of-equilibrium dynamics due to critical slowing down at the phase transition.

The magnetic and electronic nature of the gamma-Al2O3/SrTiO3 spinel/perovskite interface is explored by means of x-ray absorption spectroscopy. Polarized x-ray techniques combined with atomic multiplet calculations reveal localized magnetic moments assigned to Ti3+ at the interface with equivalent size for in- and out-of-plane magnetic field directions. Although magnetic fingerprints are revealed, the Ti3+ magnetism can be explained by a paramagnetic response at low temperature under applied magnetic fields. Modeling the x-ray linear dichroism results in a delta0 = 1.9 eV splitting between the t2g and eg states for the Ti4+ 3d0 orbitals. In addition these results indicate that the lowest energy states have the out-of-plane dxz/dyz symmetry. The isotropic magnetic moment behavior and the lowest energy dxz/dyz states are in contrast to the observations for the two-dimensional electron gas at the perovskite/perovskite interface of LaAlO3/SrTiO3, that exhibits an anisotropic magnetic dxy ground state., Comment: 6 pages, 5 figures

The ability to control the structure of a crystalline solid on ultrafast timescales bears enormous potential for information storage and manipulation or generating new functional states of matter [1]. In many materials where the ultrafast control of crystalline structures has been explored, optical excitation pushes materials towards their less ordered high temperature phase [2{9] as electronically driven ordered phases melt and possible concomitant structural modifications relax. Nonetheless, for a few select materials it has been shown that photoexcitation can slightly enhance the amplitude of an electronic ordering phenomenon (i.e. its electronic order parameter) [9{13]. Here we show via femtosecond hard X-ray diffraction that photodoping of the perovskite EuTiO3 transiently increases the order parameter associated with a purely structural [14] phase transition represented by the antiferrodistortive rotation of the oxygen octahedra. This can be understood from an ultrafast charge-transfer induced reduction of the Goldschmidt tolerance factor [15], which is a fundamental control parameter for the properties of perovskites, Comment: 11 pages, 3 figures

We report the direct observation of a magnetic-feld induced long-wavelength spin spiral modulation in the chiral compound Ba3TaFe3Si2O14. This new spin texture emerges out of a chiral helical ground state, and is hallmarked by the onset of a unique contribution to the bulk electric polarization, the sign of which depends on the crystal chirality. The periodicity of the feld induced modulation, several hundreds of nm depending on the field value, is comparable to the length scales of mesoscopic topological defects such as skyrmions, merons and solitons. The phase transition and observed threshold behavior are consistent with a phenomenology based on the allowed Lifshitz invariants for the chiral symmetry of langasite, which intriguingly contain all the ingredients for the possible realization of topologically stable antiferromagnetic skyrmions.

We report on the ultrafast dynamics of charge order and structural response during the photoinduced suppression of charge and orbital order in a mixed-valence manganite. Employing femtosecond time-resolved resonant x-ray diffraction below and at the Mn K absorption edge, we present a method to disentangle the transient charge order and structural dynamics in thin films of Pr0.5Ca0.5MnO3. Based on the static resonant scattering spectra, we extract the dispersion correction of charge ordered Mn3+ and Mn4+ ions, allowing us to separate the transient contributions of purely charge order from structural contributions to the scattering amplitude after optical excitation. Our finding of a coherent structural mode at around 2.3 THz, which primarily modulates the lattice, but does not strongly affect the charge order, confirms the picture of the charge order being the driving force of the combined charge, orbital and structural transition.

The ultrafast dynamics of the octahedral rotation in Ca:SrTiO3 is studied by time resolved x-ray diffraction after photo excitation over the band gap. By monitoring the diffraction intensity of a superlattice reflection that is directly related to the structural order parameter of the soft-mode driven antiferrodistortive phase in Ca:SrTiO3, we observe a ultrafast relaxation on a 0.2 ps timescale of the rotation of the oxygen octahedron, which is found to be independent of the initial temperaure despite large changes in the corresponding soft-mode frequency. A further, much smaller reduction on a slower picosecond timescale is attributed to thermal effects. Time-dependent density-functional-theory calculations show that the fast response can be ascribed to an ultrafast displacive modification of the soft-mode potential towards the normal state, induced by holes created in the oxygen 2p states.

5d transition metal oxides offer new opportunities to test our understanding of the interplay of correlation effects and spin-orbit interactions in materials in the absence of a single dominant interaction. The subtle balance between solid-state interactions can result in new mechanisms that minimize the interaction energy, and in material properties of potential use for applications. We focus here on the 5d transition metal oxide NaOsO3, a strong candidate for the realization of a magnetically driven transition from a metallic to an insulating state exploiting the so-called Slater mechanism. Experimental results are derived from non-resonant and resonant x-ray single crystal diffraction at the Os L-edges. A change in the crystallographic symmetry does not accompany the metal-insulator transition in the Slater mechanism and, indeed, we find no evidence of such a change in NaOsO3. An equally important experimental observation is the emergence of the (300) Bragg peak in the resonant condition with the onset of magnetic order. The intensity of this space-group forbidden Bragg peak continuously increases with decreasing temperature in line with the square of intensity observed for an allowed magnetic Bragg peak. Our main experimental results, the absence of crystal symmetry breaking and the emergence of a space-group forbidden Bragg peak with developing magnetic order, support the use of the Slater mechanism to interpret the metal-insulator transition in NaOsO3. We successfully describe our experimental results with simulations of the electronic structure and, also, with an atomic model based on the established symmetry of the crystal and magnetic structure., Comment: 6 figures

We use femtosecond x-ray diffraction to study the structural response of charge and orbitally ordered Pr$_{1-x}$Ca$_x$MnO$_3$ thin films across a phase transition induced by 800 nm laser pulses. By investigating the dynamics of both superlattice reflections and regular Bragg peaks, we disentangle the different structural contributions and analyze their relevant time-scales. The dynamics of the structural and charge order response are qualitatively different when excited above and below a critical fluence $f_c$. For excitations below $f_c$ the charge order and the superlattice is only partially suppressed and the ground state recovers within a few tens of nanosecond via diffusive cooling. When exciting above the critical fluence the superlattice vanishes within approximately half a picosecond followed by a change of the unit cell parameters on a 10 picoseconds time-scale. At this point all memory from the symmetry breaking is lost and the recovery time increases by many order of magnitudes due to the first order character of the structural phase transition.

X-ray magnetic circular and linear dichroism (XMCD and XMLD) have been used to investigate the Fe magnetic response during the spin reorientation transition (SRT) in TmFeO3. These experiments are complemented with resonant magnetic diffraction experiments at the Tm M5 edge to study simultaneously the induced magnetic order in the Tm 4f shell and the behavior of the Tm orbitals through the SRT. Comparing the Fe XMLD results with neutron diffraction and magnetization measurements on the same sample indicate that the SRT has an enhanced temperature range in the near surface region. This view is supported by the resonant soft x-ray diffraction results at the Tm M5 edge. These find an induced magnetic moment on the Tm sites, which is well-described by a dipolar mean field model originating from the Fe moments. Even though such a model can describe the 4f response in the experiments, it is insufficient to describe the SRT even when considering a change in the 4f anisotropy. Moreover, the results of the Fe XMCD are indicative of a decoupling of spin canting and antiferromagnetic spin rotation in the near surface regime close to the SRT, which remains to be understood., Comment: 28 pages, 12 figures

We use ultrafast x-ray pulses to characterize the lattice response of SrTiO3 when driven by strong terahertz (THz) fields. We observe transient changes in the diffraction intensity with a delayed onset with respect to the driving field. Fourier analysis reveals two frequency components corresponding to the two lowest energy zone-center optical modes in SrTiO3. The lower frequency mode exhibits clear softening as the temperature is decreased while the higher frequency mode shows slight temperature dependence., Comment: 15 pages, 5 figures

Chiral multiferroic langasites have attracted attention due to their doubly-chiral magnetic ground state within an enantiomorphic crystal. We report on a detailed resonant soft X-ray diffraction study of the multiferroic Ba$_3$TaFe$_3$Si$_2$O$_{14}$ at the Fe $L_{2,3}$ and oxygen $K$ edges. Below $T_N$ ($\approx27K$) we observe the satellite reflections $(0,0,\tau)$, $(0,0,2\tau)$, $(0,0,3\tau)$ and $(0,0,1-3\tau)$ where $\tau \approx 0.140 \pm 0.001$. The dependence of the scattering intensity on X-ray polarization and azimuthal angle indicate that the odd harmonics are dominated by the out-of-plane ($\mathbf{\hat{c}}$-axis) magnetic dipole while the $(0,0,2\tau)$ originates from the electron density distortions accompanying magnetic order. We observe dissimilar energy dependences of the diffraction intensity of the purely magnetic odd-harmonic satellites at the Fe $L_3$ edge. Utilizing first-principles calculations, we show that this is a consequence of the loss of threefold crystal symmetry in the multiferroic phase.

Using resonant soft X-ray techniques we follow the magnetic behavior of a strained epitaxial film of CoCr2O4, a type-II multiferroic. The film is [110]-oriented, such that both the ferroelectric and ferromagnetic moments can coexist in plane. X-ray magnetic circular dichroism (XMCD) is used in scattering and in transmission modes to probe the magnetization of Co and Cr separately. The transmission measurements utilized X-ray excited optical luminescence from the substrate. Resonant soft X-ray diffraction (RSXD) was used to study the magnetic order of the low temperature phase. The XMCD signals of Co and Cr appear at the same ordering temperature Tc~90K, and are always opposite in sign. The coercive field of the Co and of Cr moments is the same, and is approximately two orders of magnitude higher than in bulk. Through sum rules analysis an enlarged Co2+ orbital moment (m_L) is found, which can explain this hardening. The RSXD signal of the (q q 0) reflection appears below Ts, the same ordering temperature as the conical magnetic structure in bulk, indicating that this phase remains multiferroic under strain. To describe the azimuthal dependence of this reflection, a slight modification is required to the spin model proposed by the conventional Lyons-Kaplan-Dwight-Menyuk theory for magnetic spinels. Lastly, a slight increase in reflected intensity is observed below Ts=27K when measuring at the Cr edge (but not at the Co edge)., Comment: 28 pages, 15 figures

We employ time-resolved resonant x-ray diffraction to study the melting of charge order and the associated insulator-metal transition in the doped manganite Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ after resonant excitation of a high-frequency infrared-active lattice mode. We find that the charge order reduces promptly and highly nonlinearly as function of excitation fluence. Density functional theory calculations suggest that direct anharmonic coupling between the excited lattice mode and the electronic structure drive these dynamics, highlighting a new avenue of nonlinear phonon control.

Multiferroic properties of orthorhombic HoMnO3 (Pbnm space group) are significantly modified by epitaxial compressive strain along the a-axis. We are able to focus on the effect of strain solely along the a-axis by using an YAlO3 (010) substrate, which has only a small lattice mismatch with HoMnO3 along the other in-plane direction (the c-axis). Multiferroic properties of strained and relaxed HoMnO3 thin films are compared with those reported for bulk, and are found to differ widely. A relaxed film exhibits bulk-like properties such as a ferroelectric transition temperature of 25 K and an incommensurate antiferromagnetic order below 39 K, with an ordering wave vector of (0 qb 0) with qb ~ 0.41 at 10 K. A strained film becomes ferroelectric already at 37.5 K and has an incommensurate magnetic order with qb ~ 0.49 at 10 K., Comment: submitted to Applied Physics Letters

Using femtosecond time-resolved resonant magnetic x-ray diffraction at the Ho L3 absorption edge, we investigate the demagnetization dynamics in antiferromagnetically ordered metallic Ho after femtosecond optical excitation. Tuning the x-ray energy to the electric dipole (E1, 2p -> 5d) or quadrupole (E2, 2p -> 4f) transition allows us to selectively and independently study the spin dynamics of the itinerant 5d and localized 4f electronic subsystems via the suppression of the magnetic (2 1 3-tau ) satellite peak. We find demagnetization timescales very similar to ferromagnetic 4f systems, suggesting that the loss of magnetic order occurs via a similar spin-flip process in both cases. The simultaneous demagnetization of both subsystems demonstrates strong intra-atomic 4f-5d exchange coupling. In addition, an ultrafast lattice contraction due to the release of magnetostriction leads to a transient shift of the magnetic satellite peak.

We introduce a mechanism in which coupling between fluctuating spin magnetic dipole moments and polar optical phonons leads to a non-zero ferroic ordering of quasi-static magnetoelectric multipoles. Using first-principles calculations within the LSDA$+U$ method of density functional theory, we calculate the magnitude of the effect for the prototypical cuprate superconductor, HgBa$_2$CuO$_4$. We show that our proposed mechanism is consistent, to our knowledge, with all experimental data for the onset of the pseudo-gap phase and therefore propose the quasi-static magnetoelectric multipole as a possible pseudo-gap order parameter. Finally, we show that our mechanism embraces some key aspects of previous theoretical models, in particular the description of the pseudo-gap phase in terms of orbital currents., Comment: 11 pages, 6 figures

We performed ultrafast time-resolved near-infrared pump, resonant soft X-ray diffraction probe measurements to investigate the coupling between the photoexcited electronic system and the spin cycloid magnetic order in multiferroic TbMnO3 at low temperatures. We observe melting of the long range antiferromagnetic order at low excitation fluences with a decay time constant of 22.3 +- 1.1 ps, which is much slower than the ~1 ps melting times previously observed in other systems. To explain the data we propose a simple model of the melting process where the pump laser pulse directly excites the electronic system, which then leads to an increase in the effective temperature of the spin system via a slower relaxation mechanism. Despite this apparent increase in the effective spin temperature, we do not observe changes in the wavevector q of the antiferromagnetic spin order that would typically correlate with an increase in temperature under equilibrium conditions. We suggest that this behavior results from the extremely low magnon group velocity that hinders a change in the spin-spiral wavevector on these time scales., Comment: 9 pages, 4 figures

We investigate the structural and magnetic origins of the unusual ultrafast second-harmonicgeneration (SHG) response of femtosecond-laser-excited nickel oxide (NiO) previously attributed to oscillatory reorientation dynamics of the magnetic structure induced by d-d excitations. Using time-resolved x-ray diffraction from the (3/2 3/2 3/2) magnetic planes, we show that changes in the magnitude of the magnetic structure factor following ultrafast optical excitation are limited to $\Delta/$ = 1.5% in the first 30 ps. An extended investigation of the ultrafast SHG response reveals a strong dependence on wavelength as well as characteristic echoes, both of which give evidence for an acoustic origin of the dynamics. We therefore propose an alternative mechanism for the SHG response based on perturbations of the nonlinear susceptibility via optically induced strain in a spatially confined medium. In this model, the two observed oscillation periods can be understood as the times required for an acoustic strain wave to traverse one coherence length of the SHG process in either the collinear or anti-collinear geometries., Comment: 26 pages, 7 figures

Electronic structure of the three-dimensional colossal magnetoresistive perovskite La1-xSrxMnO3 has been established using soft-X-ray ARPES with its intrinsically sharp definition of three-dimensional electron momentum. The experimental results show much weaker polaronic coupling compared to the bilayer manganites and are consistent with the GGA+U band structure. The experimental Fermi surface unveils the canonical topology of alternating three-dimensional electron spheres and hole cubes, with their shadow contours manifesting the rhombohedral lattice distortion. This picture has been confirmed by one-step photoemission calculations including displacement of the apical oxygen atoms. The rhombohedral distortion is neutral to the Jahn-Teller effect and thus polaronic coupling, but affects the double-exchange electron hopping and thus the colossal magnetoresistance effect.

A theory that fully describes previously observed neutron Bragg spots indicative of magnetic order in the pseudo-gap phase of YBa2Cu3O6 + x is presented. Magnetic diffraction intensities, unveiled by polarization analysis, are explained by parity-violating magnetic (magneto-electric) quadrupoles at in-plane Cu sites arranged in a simple ferro-type motif. An absence of conventional spin and orbital angular momentum dipoles in the theory is compatible with the occurrence of superconductivity and strongly suggests, moreover, that magneto-electric quadrupoles are the primary order-parameter in the pseudo-gap phase., Comment: arXiv admin note: text overlap with arXiv:1408.5562

Using femtosecond time-resolved x-ray diffraction we investigate the structural dynamics of the coherently excited A1g phonon mode in the Fe-pnictide parent compound BaFe2As2. The fluence dependent intensity oscillations of two specific Bragg reflections with distinctly different sensitivity to the pnictogen height in the compound allow us to quantify the coherent modifications of the Fe-As tetrahedra, indicating a transient increase of the Fe magnetic moments. By a comparison with time-resolved photoemission data we derive the electron-phonon deformation potential for this particular mode. The value of Delta mu/Delta z = -(1.0 - 1.5) eV/A is comparable with theoretical predictions and demonstrates the importance of this degree of freedom for the electron-phonon coupling in the Fe pnictides., Comment: 5 pages, 4 figures, Supplementary material

Understanding the pseudo-gap phase from which a superconducting state emerges is a central problem in the physics of cuprates. The phase exists below a temperature T* for less than optimal doping of holes, and no clear jump in the specific heat or change in lattice symmetry is observed on crossing T*. Here we show that, two sets of intriguing experimental results in the literature concerning magnetic properties of underdoped YBCO are united in a single theory based on Cu quadrupole moments. The quadrupole is a product of spin and the electric dipole, so there is no magnetic dipole moment, and standard crystallography describes the magnetic motif. One experiment employed the Kerr effect and the second Bragg diffraction of polarized neutrons, and both are shown to imply an order-parameter for the pseudo-gap phase composed of magneto-electric quadrupoles at in-plane Cu sites in a ferro-type order. The successful interpretation of neutron diffraction data for YBCO yields the first experimental evidence that neutrons are deflected by magneto-electric multipoles. Predicted in 2014, our verification of the effect validates a new application for the experimental technique of choice in studies of magnetic motifs and excitations.

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., Comment: 14 Pages, 4 figures

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 is different in the two harmonics. Our direct observation of melting is supported by a solid foundation of evidence, derived from extensive studies of the azimuthal-angle dependence of intensities with both linear and circular polarization.

Chiral properties of the two phases - collinear motif (below Morin transition temperature, TM=250 K) and canted motif (above TM) - of magnetically ordered hematite ({\alpha}-Fe2O3) have been identified in single crystal resonant x-ray Bragg diffraction, using circular polarized incident x-rays tuned near the iron K-edge. Magneto-electric multipoles, including an anapole, fully characterize the high-temperature canted phase, whereas the low-temperature collinear phase supports both parity-odd and parity-even multipoles that are time-odd. Orbital angular momentum accompanies the collinear motif, while it is conspicuously absent with the canted motif. Intensities have been successfully confronted with analytic expressions derived from an atomic model fully compliant with chemical and magnetic structures. Values of Fe atomic multipoles previously derived from independent experimental data, are shown to be completely trustworthy.

We have used soft x-ray magnetic diffraction at the Fe3+ L2,3 edges to examine to what extent the Dzyaloshinsky-Moriya interaction in Ba3NbFe3Si2O14 influences its low temperature magnetic structure. A modulated component of the moments along the c-axis is present, adding to the previously proposed helical magnetic configuration of co-planar moments in the a,b-plane. This leads to a helical-butterfly structure and suggests that both the multi-axial in-plane and the uniform out-of-plane Dzyaloshinsky-Moriya vectors are relevant. A non zero orbital magnetic signal is also observed at the oxygen K edge, which reflects the surprisingly strong hybridization between iron 3d and oxygen 2p states, given the nominal spherical symmetry of the Fe3+ half filled shell.

We apply grazing-incidence femtosecond x-ray diffraction to investigate the details of the atomic motion connected with a displacively excited coherent optical phonon. We concentrate on the low frequency phonon associated with the charge and orbital order in the mixed valence manganite La0.25Pr0.375Ca0.375MnO3 for T < 210 K. We measure the response of three superlattice reflections that feature different sensitivities to the motion of the unit cell constituents. The results support the assignment to a translational mode of the Mn4+ atoms together with the oxygen atoms connecting adjacent Mn4+ sites., Comment: 13 pages, 3 figures

We studied the charge-orbital ordering in the superlattice of charge-ordered insulating Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ and ferromagnetic metallic La$_{0.5}$Sr$_{0.5}$MnO$_3$ by resonant soft x-ray diffraction. A temperature-dependent incommensurability is found in the orbital order. In addition, a large hysteresis is observed that is caused by phase competition between insulating charge ordered and metallic ferromagnetic states. No magnetic phase transitions are observed in contrast to bulk, confirming the unique character of the superlattice. The deviation from the commensurate orbital order can be directly related to the decrease of ordered-layer thickness that leads to a decoupling of the orbital-ordered planes along the c axis., Comment: 4 pages, 5 figures

The effect of x-rays on an orbital and charge ordered epitaxial film of a Pr$_{0.5}$Ca$_{0.5}$MnO$_{3}$ 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 domains in the film and represents a novel way of manipulating magnetism., Comment: 5 pages, 5 figures

We present a detailed study of magnetism in LuFe2O4, combining magnetization measurements with neutron and soft x-ray diffraction. The magnetic phase diagram in the vicinity of T_N involves a metamagnetic transition separating an antiferro- and a ferrimagnetic phase. For both phases the spin structure is refined by neutron diffraction. Observed diffuse magnetic scattering far above T_N is explained in terms of near degeneracy of the magnetic phases., Comment: 5 pages, 5 figures + 6 pages of supplementary information

We investigated the magnetic structure of an orthorhombic YMnO3 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 YMnO3 thin film., Comment: 4 pages, 6 figures

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 re-orientation transition in CuO is limited by the long-wavelength magnetic excitation connecting the two phases., Comment: Accepted by Physical Review Letters (Dec. 2, 2011)

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 at being between 7 and 78 % of the quadrupolar moment., Comment: 11 pages, 2 figures

We present a systematic study of the electronic structure in A-site ordered manganites as function of doping and temperature. The energy dependencies observed with soft x-ray resonant diffraction (SXRD) at the Mn L_{2,3} edges are compared with structural investigations using neutron powder diffraction as well as with cluster calculations. The crystal structures obtained with neutron powder diffraction reflect the various orbital and charge ordered phases and show an increase of the Mn-O-Mn bond angle as function of doping and temperature. Cluster calculations show that the observed spectral changes in SXRD as a function of doping are more pronounced than expected from an increase in bandwitdh due to the increase in Mn-O-Mn bond angle, and are best described by holes that are distributed at the neighbouring oxygen ions. These holes are not directly added to the Mn 3d shell, but centered at the Mn site. In contrast, the spectral changes in SXRD as function of temperature are best described by an increase of magnetic correlations. This demonstrates the strong correlations between orbitals and magnetic moments of the 3d states.

Magnetic spiral structures can exhibit ferroelectric moments as recently demonstrated in various multiferroic materials. In such cases the helicity of the magnetic spiral is directly correlated with the direction of the ferroelectric moment and measurement of the helicity of magnetic structures is of current interest. Soft x-ray resonant diffraction is particularly advantageous because it combines element selectivity with a large magnetic cross-section. We calculate the polarization dependence of the resonant magnetic x-ray cross-section (electric dipole transition) for the basal plane magnetic spiral in hexaferrite Ba0.8Sr1.2Zn2Fe12O22 and deduce its domain population using circular polarized incident radiation. We demonstrate there is a direct correlation between the diffracted radiation and the helicity of the magnetic spiral., Comment: 4 pages, 4 figures

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+. Polarization and azimuthal angle dependence of the superlattice reflections demonstrates the absence of anisotropic scattering revealing random orientations of the Fe2+ orbitals characteristic of an orbital glass state., Comment: v2: refined analysis, added supplement, PRL, accepted for publication