Orbital Stripe Research Articles

Origin of the magnetic and orbital ordering in α−Sr2CrO4

Motivated by recent experimental progress in transition metal oxides with the ${\mathrm{K}}_{2}\mathrm{Ni}{\mathrm{F}}_{4}$ structure, we investigate the magnetic and orbital ordering in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Sr}}_{2}\mathrm{Cr}{\mathrm{O}}_{4}$. Using first-principles calculations, first we derive a three-orbital Hubbard model, which reproduces the ab initio band structure near the Fermi level. The unique reverse splitting of ${t}_{2g}$ orbitals in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Sr}}_{2}\mathrm{Cr}{\mathrm{O}}_{4}$, with the $3{d}^{2}$ electronic configuration for the ${\mathrm{Cr}}^{4+}$ oxidation state, opens up the possibility of orbital ordering in this material. Using real-space Hartree-Fock for multiorbital systems, we constructed the ground-state phase diagram for the two-dimensional compound $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Sr}}_{2}\mathrm{Cr}{\mathrm{O}}_{4}$. We found stable ferromagnetic, antiferromagnetic, antiferro-orbital, and staggered orbital stripe ordering in robust regions of the phase diagram. Furthermore, using the density matrix renormalization group method for two-leg ladders with the realistic hopping parameters of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Sr}}_{2}\mathrm{Cr}{\mathrm{O}}_{4}$, we explore magnetic and orbital ordering for experimentally relevant interaction parameters. Again, we find a clear signature of antiferromagnetic spin ordering along with antiferro-orbital ordering at moderate to large Hubbard interaction strength. We also explore the orbital-resolved density of states with Lanczos, predicting insulating behavior for the compound $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Sr}}_{2}\mathrm{Cr}{\mathrm{O}}_{4}$, in agreement with experiments. Finally, an intuitive understanding of the results is provided based on a hierarchy between orbitals, with ${d}_{xy}$ driving the spin order, while electronic repulsion and the effective one dimensionality of the movement within the ${d}_{xz}$ and ${d}_{yz}$ orbitals driving the orbital order.

Spin Nematicity and Large Low‐Field Positive Magnetoresistance in a Half‐Doped Manganite: An Approach Exploiting Cation Size Disorder

In principle, material disorder such as random dopants disfavors the long range electronic liquid crystal (ELC) order in quantum matters. It is reported that a minor A site cation size disorder (σ2 = 0.001 Å2) in half‐doped manganites (La1‐xYx)0.5(Ca1‐ySry)0.5MnO3 interestingly leads to spin nematicity which is accompanied by a large positive magnetoresistance (up to 40%) at fields (H ≤ 1 kOe at 60 K) much lower than that (Hcr ≈ 35 kOe) critical for melting the weakened antiferromagnetic charge‐orbital ordering (AFM‐COO). The spin nematicity, emerging with a suppressed orthorhombicity, is ascribed to the destabilization of the d3x2‐r2/d3y2‐r2 orbital stripe alternation and the consequent magnetic symmetry breaking. The non‐trivial low field magneto­resistance is found to be determined by the spin polarized hopping along the nematic filaments and across the perpendicular ferromagnetic zigzag Mn–O chains in the AFM‐COO host. While the present low‐field magneto­resistance holds great potential for future spintronic devices, the approach for spin nematic order based on cation size disorder opens up a new avenue for questing ELC and exotic properties in strongly correlated materials.

90° Rotation of orbital stripes in bilayer manganite PrCa2Mn2O7 studied by in situ transmission electron microscopy

Abstract We present an in situ transmission electron microscopy study on the half-doped bilayer manganite PrCa2Mn2O7 to reveal the rotation process of the orbital stripes. Between the reported initial and final ordering phases, we identified an intermediate state with two sets of satellite spots to bridge the 90° rotation of the orbital stripes. Furthermore, we determined that the rotation of the orbital stripes does not always occur. Some restricted conditions for the orbital rotation to occur were found and reasons are discussed.

The efficacy of using orbital periosteal stripe in the management of fixed esophoria

Objective To discuss the efficacy of using orbital periosteal stripe in the management of fixed esotropia.Methods Twenty-four eyes of 18 cases suffering fixed esophoria were treated with the operation including tenotomy of medial rectus muscle and resection of lateral rectus muscle and using orbital periosteal stripe to enhance the lateral rectus.Result Except for two eyes with residual esotropia of 5° ～10°,the other eyes were well corrected.All of the patients had improved in eye-position.The postoperative visual acuity improved in 12 eyes,which was 0.2 ～ 0.4.All patients were followed up for 1 to 5 years with no complication.Conclusion Using orbital periosteal stripe in the management of fixed esotropia is a safe and effective method for the treatment of fixed esophoria. Key words: Orbital rim; Periosteal stripe; Esophoria, fixed

Stripe, checkerboard, and liquid-crystal ordering from anisotropicp-orbital Fermi surfaces in optical lattices

We study instabilities of single-species fermionic atoms in the p-orbital bands in two-dimensional optical lattices at noninteger filling against interactions. Charge density wave and orbital density wave orders with stripe or checkerboard patterns are found for attractive and repulsive interactions, respectively. The superfluid phase, usually expected of attractively interacting fermions, is strongly suppressed. We also use field theory to analyze the possible phase-transitions from orbital stripe order to liquid-crystal phases and obtain the phase diagram. The condition of nearly-perfect Fermisurface nesting, which is key to the above results, is shown robustly independent of fermion fillings in such p-orbital systems, and the $(2k_F,\pm2k_F)$ momentum of density wave oscillation is highly tunable. Such remarkable features show the promise of making those exotic orbital phases, which are of broad interest in condensed-matter physics, experimentally realizable with optical lattice gases.

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+).

Real-space observation of a two-dimensional skyrmion crystal

Crystal order is not restricted to the periodic atomic array, but can also be found in electronic systems such as the Wigner crystal or in the form of orbital order, stripe order and magnetic order. In the case of magnetic order, spins align parallel to each other in ferromagnets and antiparallel in antiferromagnets. In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures. Among them is the unusual, topologically stable skyrmion spin texture, in which the spins point in all the directions wrapping a sphere. The skyrmion configuration in a magnetic solid is anticipated to produce unconventional spin-electronic phenomena such as the topological Hall effect. The crystallization of skyrmions as driven by thermal fluctuations has recently been confirmed in a narrow region of the temperature/magnetic field (T-B) phase diagram in neutron scattering studies of the three-dimensional helical magnets MnSi (ref. 17) and Fe(1-x)Co(x)Si (ref. 22). Here we report real-space imaging of a two-dimensional skyrmion lattice in a thin film of Fe(0.5)Co(0.5)Si using Lorentz transmission electron microscopy. With a magnetic field of 50-70 mT applied normal to the film, we observe skyrmions in the form of a hexagonal arrangement of swirling spin textures, with a lattice spacing of 90 nm. The related T-B phase diagram is found to be in good agreement with Monte Carlo simulations. In this two-dimensional case, the skyrmion crystal seems very stable and appears over a wide range of the phase diagram, including near zero temperature. Such a controlled nanometre-scale spin topology in a thin film may be useful in observing unconventional magneto-transport effects.

Soft x-ray diffraction from lattice constrained orbital order in Pr(Sr0.1Ca0.9)2Mn2O7

Controlling orbital occupancy is a fundamental prerequisite for orbitronics. It has been shown in the orthorhombic bilayer manganite Pr(Sr0.1Ca0.9)2Mn2O7 that the direction of orbital order stripes can be influenced by controlling temperature or through inducing strain in the material. In this paper we have used resonant soft x-ray diffraction at the Mn L-edge to confirm the rotation of the orbital direction TOO2 and furthermore prove that there is no change in the occupied orbital type, however the orbital rotation causes a switch from 3x2−r2 to 3y2−r2 on a single site. We find that unlike the tetragonal bilayer manganites, where an onset of A-type AFM quenches the orbital order, no such effect is found on the orbital order below TN.

Thermally induced rotation of3dorbital stripes inPr(Sr0.1Ca0.9)2Mn2O7

We have investigated orbital ordering in the bilayer manganite, $\text{Pr}{({\text{Sr}}_{0.1}{\text{Ca}}_{0.9})}_{2}{\text{Mn}}_{2}{\text{O}}_{7}$, using synchrotron x-ray diffraction techniques, in particular resonant soft x-ray diffraction. Diffraction signals are observed at $(0,\frac{1}{2},0)$ above 300 K and $(\frac{1}{2},0,0)$ below 300 K, corresponding to orbital stripes along the $a$ and $b$ axes, respectively. The previously observed transition at 300 K is evidence of a rotation of the orientation of the $3d$ orbital stripes. Large resonances of the orbital signals are observed at the $\text{Mn}\text{ }L$ edges, with a complex dependence on incident photon energy indicative of a weakly Jahn-Teller distorted system. A structural transition observed at 92 K is found not to involve a further change in the orbital order.

Effects of uniaxial stress on orbital stripe direction in half-doped layered manganites:Eu0.5Ca1.5MnO4andPr(Sr,Ca)2Mn2O7

We have studied the uniaxial-stress effects on the half-doped charge-orbital ordered (CO-OO) manganites ${\text{Eu}}_{0.5}{\text{Ca}}_{1.5}{\text{MnO}}_{4}$ and $\text{Pr}{({\text{Sr}}_{1\ensuremath{-}y}{\text{Ca}}_{y})}_{2}{\text{Mn}}_{2}{\text{O}}_{7}(y\ensuremath{\sim}0.9)$. ${\text{Eu}}_{0.5}{\text{Ca}}_{1.5}{\text{MnO}}_{4}$ with single Mn-O layer structure is ferroelastic and the application of weak uniaxial stress $(<8.5\text{ }\text{MPa})$ along the orbital stripe direction drives a rotation of the orbital stripes by $90\ifmmode^\circ\else\textdegree\fi{}$ through the lattice orthorhombicity channel. For $\text{Pr}{({\text{Sr}}_{1\ensuremath{-}y}{\text{Ca}}_{y})}_{2}{\text{Mn}}_{2}{\text{O}}_{7}(y\ensuremath{\sim}0.9)$ with double Mn-O layer structure, it is revealed that the phase stability of two CO-OO states with different orbital stripe direction can be controlled by the external uniaxial pressure. In addition, the application of higher uniaxial pressure also causes a rotation of the lattice orthorhombicity itself and hence rotates the orbital stripes as well as the electric polarization axis in the low-temperature CO-OO state.

Charge and Orbital-Ordering-Induced Charge-Polarized State in Bilayer Manganite

We have investigated a new type of electronic charge-polarized state in bilayer manganite, Pr(Sr0.1Ca0.9)2Mn2O7 (PSCMO). The PSCMO compound has two charge-orbital ordering (COOO) states with respect to the direction of the orbital stripe, which is clearly identified by addressing the optical anisotropy. Notably, a charge-polarized state is formed in the lower-temperature CO-OO state where the c-axis stacking patterns of the lattice and the charge modulations along the b-axis match with each other. We detail the correlation among the transport, the optical and the structural properties in the charge and orbital-ordering-induced charge-polarized states in bilayer manganite.

Optical detection of the rotation of orbital stripes in a charge–orbital ordered bilayer manganite at half-doping

The CE magnetic order of charge–orbital ordering pattern in half-doped manganites is characterized by the formation of orbital stripe as well as the checkerboard-type charge ordering. The quasi-one-dimensionality in the orbital arrangement results in the in-plane anisotropy of physical properties, e.g., optical spectra with light polarization along the orbital stripe exhibits the larger energy-gap state than those along the orbital chain. It has been recently reported that the spontaneous rotation of orbital stripe with variation of temperature ( T ) occurs in a bilayer manganite, Pr ( Sr 0.1 Ca 0.9 ) 2 Mn 2 O 7 . To confirm this peculiar behavior, we performed optical measurements of a single domain sample with polarization dependence. While the in-plane optical anisotropy is identified together with the initial formation of the charge–orbital ordering, it is reversed at a lower T , where the orbital stripe is rotated by 90 ∘ .

Change in optical anisotropy with rotation of orbital stripe in a half-doped bilayer manganite

We report an optical study of a half-doped bilayer manganite, $\mathrm{Pr}{({\mathrm{Sr}}_{0.1}{\mathrm{Ca}}_{0.9})}_{2}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$, which shows spontaneous rotation of the orbital stripe with variation of temperature $(T)$ in a charge-orbital ordered phase. While the in-plane optical anisotropy is identified together with the initial formation of the charge-orbital ordering, it is reversed at a lower $T$, where the orbital stripe is rotated by 90\ifmmode^\circ\else\textdegree\fi{}. The change in optical anisotropy leads to anomalous $T$ dependence of electrodynamic parameters while keeping the orthorhombic lattice axes intact.

Quantum Stripe Ordering in Optical Lattices

We predict the robust existence of a novel quantum orbital stripe order in the p-band Bose-Hubbard model of two-dimensional triangular optical lattices with cold bosonic atoms. An orbital angular momentum moment is formed on each site exhibiting a stripe order both in the superfluid and Mott-insulating phases. The stripe order spontaneously breaks time-reversal, lattice translation, and rotation symmetries. In addition, it induces staggered plaquette bond currents in the superfluid phase. Possible signatures of this stripe order in the time of flight experiment are discussed.

Rotation of orbital stripes and the consequent charge-polarized state in bilayer manganites

Nanoscale self-organization of electrons is ubiquitously observed in correlated electron systems such as complex oxides of transition metals. The phenomenon of charge ordering (CO) or the formation of charge stripes, as observed for layered-structure cuprates and nickelates, is one such example. Among them, CO in manganites is closely tied to the orbital degree of freedom of 3d electrons, leading to staggered orbital ordering or the formation of orbital stripes in the layered structure. Here, we describe the phenomena of thermally induced rotation of the orbital stripes by 90( composite function) for bilayered manganite crystals with half hole doping, that is, a 1:1 ratio of Mn3+/Mn4+. The rotation of orbital stripes and the consequent CO coupled with the underlying lattice distortion were found to produce the charge-polarized state, as also shown by its optical second-harmonic generation activity.

Orbital ordering, new phases, and stripe formation in doped layered nickelates.

Ground-state properties of layered nickelates are investigated based on the orbital-degenerate Hubbard model coupled with lattice distortions, by using numerical techniques. The Néel state composed of spin S=1 ions is confirmed in the undoped limit x = 0. At x = 1/2, novel antiferromagnetic states, called CE- and E-type phases, are found by increasing the Hund's coupling. (3x2-r2/3y2-r2)-type orbital ordering is predicted to occur in a checkerboard-type charge-ordered state. At x = 1/3, both Coulombic and phononic interactions are found to be important, since the former stabilizes the spin stripe, while the latter leads to the striped charge order.