Nature of e(g) electron order in La(1-x)Sr(1+x)MnO(4)

Incommensurate sinusoidal oxygen modulations in layered manganites La(1-x)Sr(1+x)MnO4 (x≥0.5)

We have studied the incommensurate-ordered phase in overdoped La0.4Sr1.6MnO4 by resonant x-ray diffraction at the Mn K edge. Weak resonant superlattice (h±0.2 h±0.2 0) and (h±0.4 h±0.4 0) reflections of the tetragonal structure were found below ~240 K. The energy, azimuth angle, and polarization dependencies of the resonant scattering have revealed sinusoidal modulations of the oxygen motions that are transverse and longitudinal to the tetragonal [110] direction. This result discards (Mn(3+),Mn(4+))-like stripe-type order but point to a charge-density-modulation picture.

Evidence for charge orbital and spin stripe order in an overdoped manganite

Overdoped La0.42Sr1.58MnO4 exhibits a complex ordering of charges, orbitals, and spins. Neutron diffraction experiments reveal three incommensurate and one commensurate order parameters to be tightly coupled. The position and the shape of the distinct superstructure scattering as well as higher-order signals are inconsistent with a harmonic charge and spin-density-wave picture but point to a stripe arrangement in which ferromagnetic zigzag chains are disrupted by excess Mn(4+).

KO2: realization of orbital ordering in a p-orbital system

KO2 is a molecular solid consisting of oxygen dimers. K present in the lattice donates an electron which goes on to occupy the O p levels. As the basic electronic structure is similar to that of an oxygen molecule, except for broadening due to solid state effects, KO2 represents the realization of the doping of oxygen molecules arranged in a lattice. These considerations alone result in magnetism with high ordering temperatures as our calculations reveal. However, we find that the high temperature structure is unstable to an orbital ordering (OO) transition. The microscopic considerations driving the OO transition, however, are electrostatic interactions instead of the often encountered superexchange driven ordering within the Kugel-Khomskii model often used to describe the OO. This OO transition is also found to preclude any possibility of high magnetic ordering temperatures, which otherwise seemed possible.

Charge ordering induced ferromagnetic insulator: K2Cr8O16

Usually metallicity accompanies ferromagnetism. K2Cr8O16 is one of the less common examples of magnetic materials, exhibiting ferromagnetism in the insulating state. Analyzing the electronic and magnetic properties within first principles electronic structure calculations, we find that the doped electrons due to K induce a charge-ordered and insulating ground state and interestingly also introduce a ferromagnetic coupling between the Cr ions. The primary considerations driving the charge ordering are found to be electrostatic ones with the charge being localized on two Cr atoms that minimize the electrostatic energy. The structural distortion that accompanies the ordering gives rise to a rare example of a charge-order driven ferromagnetic insulator.

Electronic self-organization in the single-layer manganite Pr1-xCa1+xMnO4

We use neutron scattering to investigate the doping evolution of the magnetic correlations in the single-layer manganite Pr1-xCa1+xMnO4, away from the x=0.5 composition where the CE-type commensurate antiferromagnetic (AF) structure is stable. We find that short-range incommensurate spin correlations develop as the system is electron doped (x<0.5), which coexist with the CE-type AF order. This suggests that electron doping in this system induces an inhomogeneous electronic self-organization, where commensurate AF patches with x=0.5 are separated by electron-rich domain walls with short-range magnetic correlations. This behavior is strikingly different than for the perovskite Pr1-xCaxMnO3, where the long-range CE-type commensurate AF structure is stable over a wide range of electron or hole doping around x=0.5.

Diffuse scattering in the layered perovskites

Single-crystal X-ray and neutron diffuse scattering techniques have been used to probe a variety of short-range displacive and magnetic orderings in the layered transition-metal perovskites which arise due to the intimate coupling of their structural, electronic and magnetic degrees of freedom. The present work reviews recent analyses that have successfully modeled short-range intralayer and/or interlayer correlations in these materials leading to useful physical insights, and describes the methods employed within a general formulation of the disordered structure function.

Spin-wave dispersion in orbitally ordered La1/2Sr3/2MnO4

The magnon dispersion in the charge, orbital, and spin ordered phase in La1/2Sr3/2MnO4 has been studied by means of inelastic neutron scattering. We find excellent agreement with a magnetic interaction model based on the CE-type superstructure. The magnetic excitations are dominated by ferromagnetic exchange parameters revealing a nearly one-dimensional character at high energies. The strong ferromagnetic interaction in the charge or orbital ordered phase appears to be essential for the capability of manganites to switch between metallic and insulating phases.

Solitonic phase in manganites

Orbital order present in several transition metal compounds could give rise to topological defects. Here we argue that the topological defects in orbital ordered half doped manganites are orbital solitons that carry a charge of +/-e/2. When extra charge is added to the system an array of solitons is formed and an incommensurate solitonic phase occurs. The striking experimental asymmetry in the phase diagram as electrons or holes are added to half doped manganites is explained by the energy difference between positive and negative charged solitons. The presence of nanoscale inhomogeneities in manganites is naturally explained by the existence of solitonic phases.

Weak charge-lattice coupling requires reinterpretation of stripes of charge order in La1-xCaxMnO3

Modulations in manganites attributed to stripes of charge/orbital/spin order are thought to result from strong electron-lattice interactions that lock the superlattice and parent lattice periodicities. Surprisingly in La1-xCaxMnO3 (x>0.5,90 K), convergent beam (3.6 nm spot) electron diffraction patterns rule out charge stacking faults and indicate a superlattice with uniform periodicity. Moreover, large area electron diffraction peaks are sharper than simulations with stacking faults. Since the electron-lattice coupling does not lock the two periodicities (to yield stripes) it may be too weak to strongly localize charge.

Electronically soft phases in manganites

The phenomenon of colossal magnetoresistance in manganites is generally agreed to be a result of competition between crystal phases with different electronic, magnetic and structural order; a competition which can be strong enough to cause phase separation between metallic ferromagnetic and insulating charge-modulated states. Nevertheless, closer inspection of phase diagrams in many manganites reveals complex phases where the two order parameters of magnetism and charge modulation unexpectedly coexist. Here we show that such experiments can be naturally explained within a phenomenological Ginzburg-Landau theory. In contrast to models where phase separation originates from disorder or as a strain-induced kinetic phenomenon, we argue that magnetic and charge modulation coexist in new thermodynamic phases. This leads to a rich diagram of equilibrium phases, qualitatively similar to those seen experimentally. The success of this model argues for a fundamental reinterpretation of the nature of charge modulation in these materials, from a localized to a more extended 'charge-density wave' picture. The same symmetry considerations that favour textured coexistence of charge and magnetic order may apply to many electronic systems with competing phases. The resulting 'electronically soft' phases of matter with incommensurate, inhomogeneous and mixed order may be general phenomena in correlated systems.

Two-dimensional charge order in layered 2-1-4 perovskite oxides

Monte Carlo simulations are performed on the three-dimensional (3D) Ising model with the 2-1-4 layered perovskite structure as a minimal model for checkerboard charge ordering phenomena in layered perovskite oxides. Because of the interlayer frustration, only 2D long-range order emerges with a finite correlation length along the c axis. Critical exponents of the transition change continuously as a function of the interlayer coupling constant. The interlayer long-range Coulomb interaction decays exponentially and is negligible even between the second-neighbor layers. Instead, monoclinic distortion of a tetragonal unit cell lifts the macroscopic degeneracy to induce a 3D charge ordering. The dimensionality of the charge order in La0.5Sr1.5MnO4 is discussed from this viewpoint.

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

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

Unraveling orbital ordering in La0.5Sr1.5MnO4

Orbital ordering (OO) in the layered perovskite La0.5Sr1.5MnO4 has been investigated using the enhanced sensitivity of soft x-ray resonant diffraction at the Mn L edges. The energy dependence of an OO diffraction peak over the L(2,3) edges is compared to ligand-field calculations allowing a distinction between the influences of Jahn-Teller distortions and spin correlations. The energy dependence of the diffraction peak at the Mn L1 edge is remarkably different from that observed at the Mn K edge.

Direct observation of orbital ordering in La0.5Sr1.5MnO4 using soft x-ray diffraction

We report the first direct resonant soft x-ray scattering observations of orbital ordering. We have studied the low temperature phase of La0.5Sr1.5MnO4, a compound that displays charge and orbital ordering. Previous claims of orbital ordering in such materials have relied on observations at the manganese K edge. These claims have been questioned in several theoretical studies. Instead we have employed resonant soft x-ray scattering at the manganese L(III) and L(II) edges which probes the orbital ordering directly. Energy scans at constant wave vector are compared to theoretical predictions and suggest that at all temperatures there are two separate contributions to the scattering: direct orbital ordering and strong cooperative Jahn-Teller distortions of the Mn3+ ions.