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Magnetic domains play a fundamental role in physics of magnetism and its technological applications. Dynamics of antiferromagnetic domains is poorly understood, although antiferromagnets are expected to be extensively used in future electronic devices wherein it determines the stability and operational speed. Dynamics of antiferromagnets also features prominently in the studies of topological quantum matter. Real-space imaging of fluctuating antiferromagnetic domains is therefore highly desired but has never been demonstrated. We use coherent x-ray diffraction to obtain videos of fluctuating micrometer-scale antiferromagnetic domains in Ni 2 MnTeO 6 on time scales from 10 −1 to 10 3 s. In the collinear phase, thermally activated domain wall motion is observed in the vicinity of the Néel temperature. Unexpectedly, the fluctuations persist through the full range of the higher-temperature helical phase. These observations illustrate the high potential significance of the dynamic domain imaging in phase transition studies and in magnetic device research.

Controlling electric polarization with a magnetic field is of technological and fundamental significance. This can be achieved in magnetoelectric materials. ${A}_{4}$${B}_{2}$${O}_{9}$ ($A$=Fe, Co; $B$=Nb, Ta) are promising magnetoelectrics because they combine magnetic ions possessing large orbital moments with heavy elements exhibiting strong spin-orbit coupling. Magnetic symmetry is key for the magnetoelectric properties. Neutron diffraction and anisotropic magnetic susceptibility measurements reported in this paper revise the magnetic structure of Co${}_{4}$Ta${}_{2}$O${}_{9}$ and explain its previously puzzling magnetoelectric tensor.

Optical spectroscopy, x-ray diffraction measurements, density functional theory (DFT), density functional theory + embedded dynamical mean-field theory ($\mathrm{DFT}+eDMFT$), and crystal-field calculations have been used to characterize structural and electronic properties of hexagonal ${M}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ $(M=\mathrm{Fe},\mathrm{Mn})$ polar magnets. Our experimental data are consistent with the room-temperature structure belonging to the space group $P{6}_{3}mc$ for both compounds. The experimental structural and electronic properties at room temperature are well reproduced within $\mathrm{DFT}+eDMFT$ method, thus establishing its predictive power in the paramagnetic phase. With decreasing temperature, both compounds undergo a magnetic phase transition, and we argue that this transition is concurrent with a structural phase transition (symmetry change from $P{6}_{3}mc$ to $P{6}_{3}$) in the Fe compound and an isostructural transition (no symmetry change from $P{6}_{3}mc$) in the Mn compound.

Strongly correlated materials with multiple order parameters provide unique insights into the fundamental interactions in condensed matter systems and present opportunities for innovative technological applications. A class of antiferromagnetic honeycomb lattices compounds, A4B2O9 (A = Co, Fe, Mn; B = Nb, Ta), have been explored owing to the occurrence of linear magnetoelectricity. From our investigation of magnetoelectricity on single crystalline Co4Ta2O9, we discovered strongly nonlinear and antisymmetric magnetoelectric behavior above the spin-flop transition for magnetic fields applied along two orthogonal in-plane directions. This observation suggests that two types of inequivalent Co2+ sublattices generate magnetic-field-dependent ferroelectric polarization with opposite signs. The results motivate fundamental and applied research on the intriguing magnetoelectric characteristics of these buckled-honeycomb lattice materials.

The interplay of space and time symmetries, ferroic properties, chirality and notions of reciprocity determines many of the technologically important properties of materials such as optical diode effect, e.g., in polar ferromagnet FeZnMo3O8. We illustrate these concepts, including the non-reciprocal directional dichroism, through a number of practical examples. In particular, the conditions for non-reciprocity of ferro-rotational order are discussed and the possible use of linear optical gyration is suggested as a way to detect ferro-rotational domains. In addition, we provide the means to achieve high-temperature optical diode effect and elucidate multiferroic behaviors as a result of helical vs. cycloidal spins. Finally, we identify different entities behaving similarly under all symmetry operations, which are useful to understand non-reciprocity and multiferroicity in various materials intuitively.

Understanding and utilizing novel antiferromagnetic (AFM) materials has been recently one of the central issues in condensed matter physics, as well as in materials science and engineering. The relevant contemporary topics include multiferroicity, topological magnetism and AFM spintronics. The ability to image magnetic domains in AFM materials is of key importance for the success of these exciting fields. While imaging techniques of magnetic domains on the surfaces of ferro-(ferri)magnetic materials with, for example, magneto-optical Kerr microscopy and magnetic force microscopy have been available for a number of decades, AFM domain imaging is a relatively new development. We review various experimental techniques utilizing scanning, optical, and synchrotron X-ray probes to visualize AFM domains and domain walls, and to unveil their physical properties. We also discuss the existing challenges and opportunities in these techniques, especially with further increase of spatial and temporal resolution., npj Quantum Materials, 5 (1), ISSN:2397-4648

Circularly polarized light with spin angular momentum is one of the most valuable probes of magnetism. We demonstrate that light beams with orbital angular momentum (OAM), or vortex beams, can also couple to magnetism exhibiting dichroisms in a magnetized medium. Resonant optical absorption in a ferrimagnetic crystal depends strongly on both the handedness of the vortex and the direction of the beam propagation with respect to the sample magnetization. This effect exceeds the conventional dichroism for circularly polarized light. Our results demonstrate the high potential of the vortex beams with OAM as a new spectroscopic probe of magnetism in matter.

Manipulating magnetic domains is essential for many technological applications. Recent breakthroughs in Antiferromagnetic Spintronics brought up novel concepts for electronic device development. Imaging antiferromagnetic domains is of key importance to this field. Unfortunately, some of the basic domain types, such as antiphase domains, cannot be imaged by conventional techniques. Herein, we present a new domain projection imaging technique based on the localization of domain boundaries by resonant magnetic diffraction of coherent X rays. Contrast arises from reduction of the scattered intensity at the domain boundaries due to destructive interference effects. We demonstrate this approach by imaging antiphase domains in a collinear antiferromagnet Fe2Mo3O8, and observe evidence of domain wall interaction with a structural defect. This technique does not involve any numerical algorithms. It is fast, sensitive, produces large-scale images in a single-exposure measurement, and is applicable to a variety of magnetic domain types., Imaging the antiferromagnetic (AFM) domains facilitates the understanding and design of AFM spintronics but is still challenging. Here the authors show an imaging approach for antiphase domains in AFM Fe2Mo3O8 by resonantly scattered coherent soft X-rays, which is also applicable to collinear antiferromagnets.

Inelastic neutron scattering studies in single crystals of ${\mathrm{TbInO}}_{3}$ and ${\mathrm{TbIn}}_{0.95}{\mathrm{Mn}}_{0.05}{\mathrm{O}}_{3}$ with nearly triangular antiferromagnetic lattice are reported. At low energies, a broad and apparently gapless continuum of magnetic excitations, located at the triangular lattice (TL) Brillouin zone boundary, is observed. The data are well described by the uncorrelated nearest-neighbor valence bonds model. At higher energies, a broad excitation branch dispersing from the TL zone boundary is observed. No signs of static magnetic order are found down to the temperatures two orders of magnitude smaller than the effective interaction energy. The fluctuating magnetic moment exceeds two-thirds of the ${\mathrm{Tb}}^{3+}$ free-ion value and is confined to the TL plane. These observations are consistent with a TL-based spin liquid state in ${\mathrm{TbInO}}_{3}$.

We report the observation of the de Haas-van Alphen effect in IrTe2 measured using torque magnetometry at low temperatures down to 0.4 K and in high magnetic fields up to 33T. IrTe2 undergoes a major structural transition around 283 K due to the formation of planes of Ir and Te dimers that cut diagonally through the lattice planes, with its electronic structure predicted to change significantly from a layered system with predominantly three-dimensional character to a tilted quasi-two dimensional Fermi surface. Quantum oscillations provide direct confirmation of this unusual tilted Fermi surface and also reveal very light quasiparticle masses (less than 1 me), with no significant enhancement due to electronic correlations. We find good agreement between the angular dependence of the observed and calculated de Haas-van Alphen frequencies, taking into account the contribution of different structural domains that form while cooling IrTe2., Latex, 4 pages, 3 figures

Multiferroics are materials that evince both ferroelectric and magnetic order parameters. These order parameters when coupled can lead to both exciting new physics as well as new device applications. Potential device applications include memory, magnetic field sensors, small antennas and so on. Since Kimura’s discovery of multiferroicity in TbMnO3, there has been a renaissance in the study of these materials. Great progress has been made in both materials discovery and in the theoretical understanding of these materials. In type-II systems the magnetic order breaks the inversion symmetry of the material, driving a secondary ferroelectric phase transition in which the ferroelectric polarisation is exquisitely coupled to the magnetic structure and thus to magnetic field. In type-I systems, the magnetic and ferroelectric orders are established on different sublattices of the material and typically are weakly coupled, but electric field can still drive changes in the magnetisation. Besides single-phase multiferroics, there has been exciting progress in composite heterostructures of multiferroics. Here, we review neutron measurements of prototypical examples of these different approaches to achieving multiferrocity.

We present a scanning tunneling microscopy (STM) study of the domain evolution across two first-order phase transitions of stripe modulations in ${\mathrm{IrTe}}_{2}$ that occur at ${T}_{\mathrm{C}}\ensuremath{\approx}275$ K and ${T}_{\mathrm{S}}\ensuremath{\approx}180$ K, respectively. Phase coexistence of the hexagonal $(1\ifmmode\times\else\texttimes\fi{}1)$ structure and the $(5\ifmmode\times\else\texttimes\fi{}1)$ stripe modulation is observed at ${T}_{\mathrm{C}}$, while various $(p\ifmmode\times\else\texttimes\fi{}1)$ modulations ($p=3n+2$ with $2\ensuremath{\le}n\ensuremath{\in}\mathbb{N}$) are observed below ${T}_{\mathrm{S}}$. Using STM atomic resolution, we observe anisotropic propagation of domain boundaries along different directions, indicating significantly different kinetic energy barriers. These results are consistently explained by a theoretical analysis of the energy barrier for domain wall propagation as obtained by density functional theory. Individual switching processes observed by STM indicate that the wide temperature range of the transition from the $(5\ifmmode\times\else\texttimes\fi{}1)$ stripes to the $(6\ifmmode\times\else\texttimes\fi{}1)$-ordered ground state is probably caused by the numerically limited subset of switching processes that are allowed between a given initial and the final state. The observations on ${\mathrm{IrTe}}_{2}$ are discussed in terms of a ``harmless staircase'' with a finite number of first-order transitions between commensurate phases and within a ``dynamical freezing'' scenario.

Magnetoelectric (ME) effect is recognized for its utility for low-power electronic devices. Largest ME coefficients are often associated with phase transitions in which ferroelectricity is induced by magnetic order. Unfortunately, in these systems, large ME response is revealed only upon elaborate poling procedures. These procedures may become unnecessary in single-polar-domain crystals of polar magnets. Here we report giant ME effects in a polar magnet Fe2Mo3O8 at temperatures as high as 60 K. Polarization jumps of 0.3 μC/cm2 and repeated mutual control of ferroelectric and magnetic moments with differential ME coefficients on the order of 104 ps/m are achieved. Importantly, no electric or magnetic poling is needed, as necessary for applications. The sign of the ME coefficients can be switched by changing the applied “bias” magnetic field. The observed effects are associated with a hidden ferrimagnetic order unveiled by application of a magnetic field.

We study magnetic and multiferroic behavior in Ca${}_{3}$Co${}_{2\ensuremath{-}x}$Mn${}_{x}$O${}_{6}$ ($x\ensuremath{\sim}$ 0.97) by high-field measurements of magnetization ($M$), magnetostriction [$L$($H$)/$L$], electric polarization ($P$), and magnetocaloric effect. This study also gives insight into the zero- and low-magnetic-field magnetic structure and magnetoelectric coupling mechanisms. We measured $M$ and $\ensuremath{\Delta}$$L$/$L$ up to pulsed magnetic fields of 92 T, and determined the saturation moment and field. On the controversial topic of the spin states of Co${}^{2+}$ and Mn${}^{4+}$ ions, we find evidence for $S=\frac{3}{2}$ spins for both ions with no magnetic-field-induced spin-state crossovers. Our data also indicate that Mn${}^{4+}$ spins are quasi-isotropic and develop components in the $ab$ plane in applied magnetic fields of 10 T. These spins cant until saturation at 85 T, whereas the Ising Co${}^{2+}$ spins saturate by 25 T. Furthermore, our results imply that the mechanism for suppression of electric polarization with magnetic fields near 10 T is flopping of the Mn${}^{4+}$ spins into the $ab$ plane, indicating that appropriate models must include the coexistence of Ising and quasi-isotropic spins.

We review our recent x-ray scattering studies of charge and orbital order in doped manganites, with specific emphasis on the role of orbital correlations in Pr_1-xCa_xMnO_3. For x=0.25, we find an orbital structure indistinguishable from the undoped structure with long range orbital order at low temperatures. For dopings 0.3, Comment: 22 pagegs, 7 figures

We have performed detailed magnetic susceptibility measurements as well as synchrotron x-ray diffraction studies to determine the temperature vs concentration ($T$ - $x$) phase diagram of Cu${}_{1-x}$Mg${}_x$GeO${}_3$. We observe clear double peaks in the magnetic susceptibility implying two antiferromagnetic (AF) transition temperatures in samples with Mg concentrations in the range 0.0237 $\le x \le$ 0.0271. We also observe a drastic change in the inverse correlation length in this concentration range by x-ray diffraction. The drastic change of the AF transition temperature as well as the disappearance of the spin-Peierls (SP) phase have been clarified; these results are consistent with a first-order phase transition between dimerized AF (D-AF) and uniform AF (U-AF) phases as reported by T. Masuda {\it et al.} \lbrack Phys. Rev. Lett. {\bf 80}, 4566 (1998)\rbrack. The $T$ - $x$ phase diagram of Cu${}_{1-x}$Zn${}_x$GeO${}_3$ is similar to that of Cu${}_{1-x}$Mg${}_x$GeO${}_3$, which suggests that the present phase transition is universal for Cu${}_{1-x}M_{x}$GeO${}_3$.

Charge-ordered manganites of composition Pr1 x(Ca1 ySry)xMnO3 exhibit persistent photo-conductivity when illuminated by X-rays. We review transport and X-ray diffraction data as functions of X-ray exposure, magnetic field, and temperature which shed light on the origin of this unusual behavior. The experimental evidence suggests that the mechanism primarily involves a ferromagnetic polarization of local spins by hot electrons generated by the X-rays. © 1999 Elsevier Science S.A. All rights reserved.

How the magnetoelectric coupling actually occurs on a microscopic level in multiferroic BiFeO3 is not well known. By using the high-resolution single crystal neutron diffraction techniques, we have determined the electric polarization of each individual elements of BiFeO3, and concluded that the magnetostrictive coupling suppresses the electric polarization at the Fe site below TN. This negative magnetoelectric coupling appears to outweigh the spin current contributions arising from the cycloid spin structure, which should produce a positive magnetoelectric coupling., Comment: 10 pages, 4 figures, Accepted in Phys. Rev. B(Rapid Communications)

Macroscopic ensembles of weakly interacting argon nanoclusters are studied using x-ray diffraction in low vacuum. As the clusters grow by fusion with increasing temperature, their structure transforms from essentially face-centered cubic (fcc) to hexagonal close packed as the cluster size approaches $\ensuremath{\sim}{10}^{5}$ atoms. The transformation involves intermediate orthorhombic phases. These data confirm extant theoretical predictions. They also indicate that growth kinetics and spatial constraints might play an important role in the formation of the fcc structure of bulk rare-gas solids, which still remains puzzling.

Using inelastic neutron scattering technique, we measured the spin wave dispersion over the entire Brillouin zone of room temperature multiferroic BiFeO3 single crystals with magnetic excitations extending to as high as 72.5 meV. The full spin waves can be explained by a simple Heisenberg Hamiltonian with a nearest neighbor exchange interaction (J=4.38 meV), a next nearest neighbor exchange interaction (J'=0.15 meV), and a Dzyaloshinskii-Moriya-like term (D=0.107 meV). This simple Hamiltonian determined, for the first time, for BiFeO3 provides a fundamental ingredient for understanding of the novel magnetic properties of BiFeO3., Comment: 10 pages, 3 figures

Neutron diffraction is used to show that small (∼7 MPa, or 70 bar) uniaxial pressure produces significant changes in the populations of magnetic domains in a single crystal of 2% Nd-doped bismuth ferrite. The magnetic easy plane of the domains converted by the pressure is rotated 60° relative to its original position. These results demonstrate extreme sensitivity of the magnetic properties of multiferroic bismuth ferrite to tiny (less than 10(-4)) elastic strain, as well as weakness of the forces pinning the domain walls between the cycloidal magnetic domains in this material.

$E$-type perovskite magnet HoMnO${}_{3}$ is considered to be a prototype Mn-Mn exchange-striction driven multiferroic. We have grown orthorhombic HoMnO${}_{3}$ single crystals and studied the directional dependence of their electric polarization P. The direction of P is not along the crystallographic $a$ axis, as predicted, but along the $c$ axis. The magnetic state is incommensurate. The direction P along the $c$ axis is primarily induced by Ho-Mn exchange striction, and Mn-Mn striction in the incommensurate spin state leads to an antiferroelectric order along the $a$ axis. We predict the rotation of P with temperature in commensurate $E$-type $R$MnO${}_{3}$ ($R$ denotes magnetic rare earth).

We report neutron diffraction and magnetization studies of the magnetic order in multiferroic BiFeO3. In ferroelectric monodomain single crystals, there are three magnetic cycloidal domains with propagation vectors equivalent by crystallographic symmetry. The cycloid period slowly grows with increasing temperature. The magnetic domain populations do not change with temperature except in the close vicinity of the N{\P}eel temperature, at which, in addition, a small jump in magneti- zation is observed. No evidence for the spin-reorientation transitions proposed in previous Raman and dielectric studies is found. The magnetic cycloid is slightly anharmonic for T=5 K. The an- harmonicity is much smaller than previously reported in NMR studies. At room temperature, a circular cycloid is observed, within errors. We argue that the observed anharmonicity provides important clues for understanding electromagnons in BiFeO3., Comment: In Press at PRB

Polarized small-angle neutron scattering studies of single-crystalline multiferroic ${\mathrm{BiFeO}}_{3}$ reveal a long-wavelength spin density wave generated by $\ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{}$ spin canting of the spins out of the rotation plane of the antiferromagnetic cycloidal order. This signifies weak ferromagnetism within mesoscopic regions of dimension 0.03 microns along $[1\overline{1}0]$, to several microns along [111], confirming a long-standing theoretical prediction. The average local magnetization is $0.06\text{ }\text{ }{\ensuremath{\mu}}_{B}/\mathrm{Fe}$. Our results provide an indication of the intrinsic macroscopic magnetization to be expected in ferroelectric ${\mathrm{BiFeO}}_{3}$ thin films under strain, where the magnetic cycloid is suppressed.

Unidirectional electric current flow, such as that found in a diode, is essential for modern electronics. It usually occurs at asymmetric interfaces such as p-n junctions or metal/semiconductor interfaces with Schottky barriers. We report on a diode effect associated with the direction of bulk electric polarization in BiFeO 3 : a ferroelectric with a small optical gap edge of ∼2.2 electron volts. We found that bulk electric conduction in ferroelectric monodomain BiFeO 3 crystals is highly nonlinear and unidirectional. This diode effect switches its direction when the electric polarization is flipped by an external voltage. A substantial visible-light photovoltaic effect is observed in BiFeO 3 diode structures. These results should improve understanding of charge conduction mechanisms in leaky ferroelectrics and advance the design of switchable devices combining ferroelectric, electronic, and optical functionalities.

Ferroelectric Ising chain magnet Ca$_3$Co$_{2-x}$Mn$_x$O$_6$ ($x\simeq$0.96) was studied in magnetic fields up to 33 T. Magnetization and neutron scattering measurements reveal successive metamagnetic transitions from the zero-field $\uparrow \uparrow \downarrow \downarrow$ spin configuration to the $\uparrow \uparrow \uparrow \downarrow$ state with a broad magnetization plateau, and then to the $\uparrow \uparrow \uparrow \uparrow$ state. The absence of hysteresis in these plateaus reveals an intriguing coupling between the intra-chain state and the three-dimensional geometrically frustrated magnetic system. Inversion symmetry, broken in the $\uparrow \uparrow \downarrow \downarrow$ state, is restored in the $\uparrow \uparrow \uparrow \downarrow$ state, leading to the complete suppression of the electric polarization driven by symmetric superexchange., accepted for publication as a Brief Report in Physical Review B

We have studied quasi-two-dimensional multiferroic ${\mathrm{LuFe}}_{2}{\mathrm{O}}_{4}$ with strong charge-spin-lattice coupling, in which low-temperature coercivity approaches an extraordinary value of 9 T in single crystals. The enhancement of the coercivity is connected to the collective freezing of nanoscale pancakelike ferrimagnetic domains with large uniaxial magnetic anisotropy (``Ising pancakes''). Our results suggest that collective freezing in low-dimensional magnets with large uniaxial anisotropy provides an effective mechanism to achieve enhanced coercivity. This observation may help identify novel approaches for synthesis of magnets with enhanced properties.

We report on polarized neutron-scattering and piezoresponse force microscopy studies of millimeter-sized single crystals of multiferroic ${\text{BiFeO}}_{3}$. The crystals, grown below the Curie temperature, consist of a single ferroelectric domain. Two unique electric polarization directions, as well as the populations of equivalent spiral magnetic domains, can be switched reversibly by an electric field. A ferroelectric monodomain with a single-$q$ single-helicity spin spiral can be obtained. This level of control, so far unachievable in thin films, makes single-crystal ${\text{BiFeO}}_{3}$ a promising object for multiferroics research.

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. We determine the nature of the orderings and discuss our picture with respect to novel theoretical models. In the stripe order system Bi0.31 Ca0.69 MnO3, hole-doped O states are found to be orbitally ordered, at the same propagation vector as the Mn orbital ordering, but no evidence is found to support a picture of oxygen charge stripes at this periodicity. In La 7/8 Sr 1/8 MnO3, we observe a 2p charge ordering described by alternating hole-poor and hole-rich MnO planes that is consistent with recent predictions., 5 pages

Recent state-of-the-art crystallographic investigations of transition metal spinel compounds have revealed that the d- orbital charge carriers undergo ordering transitions with the formation of local "molecular bonding" units such as dimers in MgTi2O4, octomers in CuIr2S4, and heptamers in AlV2O4. Herein, we provide a unifying scheme involving one- dimensional orbital wave ordering applicable to all of these spinels. The relative phase of the orbitals in the chains is shown to be crucial to the formation of different local units, and thus both the amplitude and phase of the orbital wave play important roles. Examination of Horibe et al.'s [1] structure for AlV2O4 serves as the vehicle for developing the general behavior for such orbital wave ordering. Ordered AlV2O4 will be seen to organize into three equivalent chains in 2D Kagome planes coupled so as to form units of three dimer bonds. Three additional equivalent chains manifest a more complex tetramerization with three different charge states and two different bonding schemes. The orbital wave ordering scheme developed is extended to other spinel and related compounds with local triangular transition metal coordination and partial filling of the t2g-d orbitals.

Manganese oxides of the general formula A1–xBxMnO3 (where A and B are trivalent and divalent cations, respectively) have recently attracted considerable attention by virtue of their unusual magnetic and electronic properties1–9. For example, in some of these materials magnetic fields can drive insulator-to-metal transitions where both the conductivity and magnetization change dramatically—an effect termed 'colossal magneto-resistance'1–3—raising hopes for application of these materials in the magnetic recording industry1–9. Here we show that in one such compound, Pr0.7Ca0.3MnO3, a transition from the insulating antiferromagnetic state to the metallic ferromagnetic state can be driven by illumination with X-rays at low temperatures (

We report neutron-diffraction measurements of the magnetic phase diagram of the colossal magnetoelectric $\mathrm{Dy}{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$. Our measurements reveal the magnetic origin of the complex dielectric anomalies in this material. Frustrated magnetic interactions result in a large density of low-energy magnetic states which can be selected by the application of relatively small magnetic fields. The unusual combination of magnetic frustration and strong magnetoelastic coupling is responsible for the remarkable changes of the dielectric properties of $\mathrm{Dy}{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$ in small applied magnetic fields.

We report a study of electronic excitations in manganites exhibiting a range of ground states, using resonant inelastic x-ray scattering (RIXS) at the Mn K edge. Excitations with temperature dependent changes correlated with the magnetism were observed as high as 10 eV. By calculating Wannier functions, and finite-q response functions, we associate this dependence with intersite d-d excitations. The calculated dynamical structure factor is found to be similar to the RIXS spectra.

Neutron scattering measurements on a magnetoresistive manganite La$_{0.75}$(Ca$_{0.45}$Sr$_{0.55}$)$_{0.25}$MnO$_3$ show that uncorrelated dynamic polaronic lattice distortions are present in both the orthorhombic (O) and rhombohedral (R) paramagnetic phases. The uncorrelated distortions do not exhibit any significant anomaly at the O-to-R transition. Thus, both the paramagnetic phases are inhomogeneous on the nanometer scale, as confirmed further by strong damping of the acoustic phonons and by the anomalous Debye-Waller factors in these phases. In contrast, recent x-ray measurements and our neutron data show that polaronic correlations are present only in the O phase. In optimally doped manganites, the R phase is metallic, while the O paramagnetic state is insulating (or semiconducting). These measurements therefore strongly suggest that the {\it correlated} lattice distortions are primarily responsible for the insulating character of the paramagnetic state in magnetoresistive manganites., 10 pages, 8 figures embedded

We report a resonant x-ray-diffraction study of the magnetoresistant perovskite Pr 0 . 6 Ca 0 . 4 MnO 3 . We discuss the spectra measured above and below the semiconductor-insulator transition temperature with the aid of a detailed formal analysis of the energy and polarization dependences of the structure factors and ab initio calculations of the spectra. In the low-temperature insulating phase, we find that inequivalent Mn atoms order in a CE-type pattern and that the crystallographic structure of La 0 . 5 Ca 0 . 5 MnO 3 [Radaelli et al., Phys. Rev. B 55, 3015 (1997)] can also describe this system in detail. Instead, the alternative structure proposed for the so-called Zener-polaron model [Daoud-Aladine et al., Phys. Rev. Lett. 89, 097205 (2002)] is ruled out by crystallographic and spectroscopic evidence. Our analysis supports a model involving orbital ordering. However, we confirm that there is no direct evidence of charge disproportionation in the Mn K-edge resonant spectra. Therefore, we consider a CE-type model in which there are two Mn sublattices, each with partial e g occupancy. One sublattice consists of Mn atoms with the 3x 2 -r 2 or 3y 2 -r 2 orbitals partially occupied in an alternating pattern, the other sublattice with the x 2 -y 2 orbital partially occupied.

Extensive experimental results are presented on the multi-scale phase modulation phenomena observed in colossal magnetoresistance manganites. Two key types of phase inhomogeneities directly relevant to the colossal magnetoresistance (CMR) are discussed. The first type involves micrometer-scale coexistence of structurally and electronically different phases. We present extensive experimental data for a prototypical system exhibiting such a phase coexistence, (La,Pr)5/8Ca3/8MnO3. These data reveal that percolative transport phenomena play the key role in the metal-insulator transition in this system, and are largely responsible for the significant magnitude of the magnetoresistance. The phase composition of the multiphase states is governed by both the electron correlations and the effects of martensitic accommodation strain. The second type of an inhomogeneous state is realized in the paramagnetic state commonly found in manganites at high-temperatures. In this state, nanometer-scale structural correlations associated with nanoscale charge/orbital ordered regions are observed. Experimental investigation of numerous manganite systems indicates that these correlations are generic in orthorhombic mixed-valent manganites, and that the correlated regions play an essential role in the CMR effect. This chapter is organized as follows. An introduction to the subject is given in Section 1. In Section 2, the phase diagram of (La,Ca)MnO3 is presented. Electronic and structural properties of both the high- and low-temperature phases are discussed. Section 3 is devoted to the studies of the micrometer-scale multiphase states in (La,Pr)5/8Ca3/8MnO3. In Section 4, high temperature nanoscale correlations are discussed. Extensive studies of electronic and thermal transport, and optical spectroscopy are presented. Section 5 focuses on x-ray scattering studies of the nanoscale correlations. Finally, Section 6 concludes this Chapter.

We report x-ray scattering studies of nanoscale structural correlations in the paramagnetic phases of the perovskite manganites La$_{0.75}$(Ca$_{0.45}$Sr$_{0.55}$)$_{0.25}$MnO$_3$, La$_{0.625}$Sr$_{0.375}$MnO$_3$, and Nd$_{0.45}$Sr$_{0.55}$MnO$_3$. We find that these correlations are present in the orthorhombic $O$ phase in La$_{0.75}$(Ca$_{0.45}$Sr$_{0.55}$)$_{0.25}$MnO$_3$, but they disappear abruptly at the orthorhombic-to-rhombohedral transition in this compound. The orthorhombic phase exhibits increased electrical resistivity and reduced ferromagnetic coupling, in agreement with the association of the nanoscale correlations with insulating regions. In contrast, the correlations were not detected in the two other compounds, which exhibit rhombohedral and tetragonal phases. Based on these results, as well as on previously published work, we propose that the local structure of the paramagnetic phase correlates strongly with the average lattice symmetry, and that the nanoscale correlations are an important factor distinguishing the insulating and the metallic phases in these compounds., Comment: a note on recent experimental work, and a new reference added

At low temperatures, spinel ${\mathrm{CuIr}}_{2}{\mathrm{S}}_{4}$ is a charge-ordered spin-dimerized insulator with triclinic lattice symmetry. We find that x rays induce a structural transition in which the local triclinic structure is preserved, but the average lattice symmetry becomes tetragonal. These structural changes are accompanied by a thousandfold reduction in the electrical resistivity. The transition is persistent, but the original state can be restored by thermal annealing. We argue that x-ray irradiation disorders the lattice dimerization pattern, producing a state in which the orientation of the dimers is preserved, but the translational long-range order is destroyed.

The intrinsic linewidth Γ T A of the transverse acoustic phonon observed in the relaxor ferroelectric compound Pb(Mg 1 / 3 Nb 2 / 3 ) 0 . 8 Ti 0 . 2 O 3 (PMN-20%PT) begins to broaden with decreasing temperature around 650 K, nearly 300 K above the ferroelectric transition temperature T c (∼360 K). We speculate that this anomalous behavior is directly related to the condensation of polarized, nanometer-sized, regions (PNR) at the Burns temperature T d . We also observe the "waterfall" anomaly previously seen in pure PMN, in which the transverse optic branch appears to drop precipitously into the TA branch at a finite momentum transfer q w f ∼0.15 A - 1 . The waterfall feature is seen even at temperatures above T d . This latter result suggests that the PNR exist as dynamic entities above T d .

Inorganic compounds with the AB2X4 spinel structure have been studied for many years, because of their unusual physical properties. The spinel crystallographic structure, first solved by Bragg in 1915, has cations occupying both tetrahedral (A) and octahedral (B) sites. Interesting physics arises when the B-site cations become mixed in valence. Magnetite (Fe3O4) is a classic and still unresolved example, where the tendency to form ordered arrays of Fe2+ and Fe3+ ions competes with the topological frustration of the B-site network. The CuIr2S4 thiospinel is another example, well known for the presence of a metal-insulator transition at 230 K with an abrupt decrease of the electrical conductivity on cooling accompanied by the loss of localized magnetic moments. Here, we report the determination of the crystallographic structure of CuIr2S4 below the metal-insulator transition. Our results indicate that CuIr2S4 undergoes a simultaneous charge-ordering and spin-dimerization transition-a rare phenomenon in three-dimensional compounds. Remarkably, the charge-ordering pattern consists of isomorphic octamers of Ir83+S24 and Ir84+S24 (as isovalent bi-capped hexagonal rings). This extraordinary arrangement leads to an elegant description of the spinel structure, but represents an increase in complexity with respect to all the known charge-ordered structures, which are typically based on stripes, slabs or chequerboard patterns.

We report x-ray scattering studies of nanoscale structural correlations in Nd$_{1-x}$Sr$_x$MnO$_3$ and La$_{1-x}$(Ca,Sr)$_x$MnO$_3$, $x$=0.2--0.5. We find that the correlated regions possess a temperature-independent correlation length of 2-3 lattice constants which is the same in all samples. The period of the lattice modulation of the correlated regions is proportional to the Ca/Sr doping concentration $x$. Remarkably, the lattice modulation periods of these and several other manganites with a ferromagnetic ground state fall on the same curve when plotted as a function of $x$. Thus, the structure of the correlated regions in these materials appears to be determined by a single parameter, $x$. We argue that these observations provide important clues for understanding the Colossal Magnetoresistance phenomenon in manganites., 6 pages, 5 embedded eps figures

We report synchrotron x-ray scattering studies of charge/orbitally ordered (COO) nanoclusters in Nd$_{0.7}$Sr$_{0.3}$MnO$_3$. We find that the COO nanoclusters are strongly suppressed in an applied magnetic field, and that their decreasing concentration follows the field-induced decrease of the sample electrical resistivity. The COO nanoclusters, however, do not completely disappear in the conducting state, suggesting that this state is inhomogeneous and contains an admixture of an insulating phase. Similar results were also obtained for the zero-field insulator-metal transition that occurs as temperature is reduced. These observations suggest that these correlated lattice distortions play a key role in the Colossal Magnetoresistance effect in this prototypical manganite.

We report x-ray scattering studies of broad peaks located at a (0.5 0 0)/(0 0.5 0)-type wavevector in the paramagnetic insulating phases of La_{0.7}Ca_{0.3}MnO_{3} and Pr_{0.7}Ca_{0.3}MnO_{3}. We interpret the scattering in terms of correlated polarons and measure isotropic correlation lengths of 1-2 lattice constants in both samples. Based on the wavevector and correlation lengths, the correlated polarons are found to be consistent with CE-type bipolarons. Differences in behavior between the samples arise as they are cooled through their respective transition temperatures and become ferromagnetic metallic (La_{0.7}Ca_{0.3}MnO_{3}) or charge and orbitally ordered insulating (Pr_{0.7}Ca_{0.3}MnO_{3}). Since the primary difference between the two samples is the trivalent cation size, these results illustrate the robust nature of the correlated polarons to variations in the relative strength of the electron-phonon coupling, and the sensitivity of the low-temperature ground state to such variations., Comment: 13 pages, 6 figures

In this paper, we report polarized optical microscopy and electrical transport studies of manganese oxides that reveal that the charge ordering transition in these compounds exhibits typical signatures of a martensitic transformation. We demonstrate that specific electronic properties of charge-ordered manganites stem from a combination of martensitic accommodation strain and effects of strong electron correlations. This intrinsic strain is strongly affected by the grain boundaries in ceramic samples. Consistently, our studies show a remarkable enhancement of low field magnetoresistance and the grain size effect on the resistivity in polycrystalline samples and suggest that the transport properties of this class of manganites are governed by the charge-disordered insulating phase stabilized at low temperature by virtue of martensitic accommodation strain. High sensitivity of this phase to strains and magnetic field leads to a variety of striking phenomena, such as unusually high magnetoresistance (10^10 %) in low magnetic fields., Comment: Short paper, 4 figures, to appear in Rapid Communication

We report x-ray scattering studies of short-range structural correlations and diffuse scattering in ${\mathrm{Nd}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_{3}.$ On cooling, this material undergoes a series of transitions, first from a paramagnetic insulating (PI) to a ferromagnetic metallic (FM) phase, and then to a charge-ordered (CO) insulating state. Highly anisotropic structural correlations were found in both the PI and FM states of this compound. The correlations increase with decreasing temperature, reaching a maximum at the CO transition temperature. Below this temperature, they abruptly collapsed. Single-polaron diffuse scattering was also observed in both the PI and FM states suggesting that substantial local lattice distortions are present in these phases. We argue that our measurements indicate that nanoscale regions exhibiting layered orbital order exist in the paramagnetic and ferromagnetic phases of ${\mathrm{Nd}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_{3}.$

We report x-ray scattering studies of diffuse peaks in the paramagnetic insulating phase of La0.7Ca0.3MnO3. The peaks occur at a (0.5 0 0)/(0 0.5 0)-type wavevector, and are found to disappear abruptly upon cooling through the transition into the ferromagnetic metallic phase. Based on the wavevector and measured correlation length of 1–2 lattice constants, the peaks are found to be consistent with the formation of CE-type bipolarons, and their collapse at Tc is attributed to the energy gain associated with itineracy in the ferromagnetic state.

The insulator-metal transition in single crystal ${\mathrm{La}}_{5/8\ensuremath{-}y}{\mathrm{Pr}}_{y}{\mathrm{Ca}}_{3/8}{\mathrm{MnO}}_{3}$ with $y\ensuremath{\approx}0.35$ was studied using synchrotron x-ray diffraction, electric resistivity, magnetic susceptibility, and specific heat measurements. Despite the dramatic drop in the resistivity at the insulator-metal transition temperature ${T}_{\mathrm{MI}},$ the charge-ordering (CO) peaks exhibit no anomaly at this temperature and continue to grow below ${T}_{\mathrm{MI}}.$ Our data suggest then, that in addition to the CO phase, another insulating phase is present below ${T}_{\mathrm{CO}}.$ In this picture, the insulator-metal transition is due to the changes that occur within this latter phase. The CO phase does not appear to play a major role in this transition. We propose that a percolationlike insulator-metal transition occurs via the growth of ferromagnetic metallic domains within the parts of the sample that do not exhibit charge ordering. Finally, we find that the low-temperature phase-separated state is unstable against x-ray irradiation, which destroys the CO phase at low temperatures.