LiMnO[subscript 2] cathode stabilized by interfacial orbital ordering for sustainable lithium-ion ba
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Zhu, Xiaohui↗
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Results for “Orbital order”
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Orthorhombic distortion drives orbital ordering in the antiferromagnetic 3$d$ 1 Mott insulator PrTiO 3
The orbital, which represents the shape of the electron cloud, very often strongly influences the manifestation of various exotic phenomena, e.g., magnetism, metal-insulator transition, colossal magnetoresistance, unconventional superconductivity, etc. in solid-state systems. The observation of the antiferromagnetism in $RE$TiO 3 ($RE$ = rare-earth) series has been puzzling since the celebrated Kugel-Khomskii model of spin-orbital superexchange predicts ferromagnetism in an orbitally degenerate $d$ 1 system. Further, the existence of the orbitally ordered vs. orbital liquid phase in both antiferromagnetic and paramagnetic phase have been unsettled issues thus far. To address these longstanding questions, we investigate single crystalline film of PrTiO 3 . Our synchrotron x-ray diffraction measurements confirm the retention of bulklike orthorhombic ($D_{2h}$) symmetry in the thin film geometry. We observe similar x-ray linear dichroism signal in both paramagnetic and antiferromagnetic phase, which can be accounted by ferro-orbital ordering (FOO). While the presence of $D_{2h}$ crystal field does not guarantee lifting of orbital degeneracy always, we find it to be strong enough in these rare-earth titanates, leading to the FOO state. Thus, our work demonstrates the orthorhombic distortion is the driving force for the orbital ordering of antiferromagnetic $RE$TiO 3 .
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Interplay of hidden orbital order and superconductivity in CeCoIn5
Abstract Visualizing atomic-orbital degrees of freedom is a frontier challenge in scanned microscopy. Some types of orbital order are virtually imperceptible to normal scattering techniques because they do not reduce the overall crystal lattice symmetry. A good example is d xz / d yz (π,π) orbital order in tetragonal lattices. For enhanced detectability, here we consider the quasiparticle scattering interference (QPI) signature of such (π,π) orbital order in both normal and superconducting phases. The theory reveals that sublattice-specific QPI signatures generated by the orbital order should emerge strongly in the superconducting phase. Sublattice-resolved QPI visualization in superconducting CeCoIn 5 then reveals two orthogonal QPI patterns at lattice-substitutional impurity atoms. We analyze the energy dependence of these two orthogonal QPI patterns and find the intensity peaked near E = 0, as predicted when such (π,π) orbital order is intertwined with d -wave superconductivity. Sublattice-resolved superconductive QPI techniques thus represent a new approach for study of hidden orbital order.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Origin of the magnetic and orbital ordering in α-Sr 2 CrO 4
Motivated by recent experimental progress in transition metal oxides with the K 2 NiF 4 structure, in this study we investigate the magnetic and orbital ordering in α-Sr 2 CrO 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 α-Sr 2 CrO 4 , with the 3d 2 electronic configuration for the Cr 4+ oxidation state, opens up the possibility of orbital ordering in this material. Using real-space Hartree-Fock for multi-orbital systems, we constructed the ground state phase diagram for the two dimensional compound α-Sr 2 CrO 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 α-Sr 2 CrO 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 α-Sr 2 CrO 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.
36 MATERIALS SCIENCE↗
Ultrafast signatures of spin and orbital order in antiferromagnetic α-Sr2CrO4
Abstract The antiferromagnetic Mott insulator α -Sr 2 CrO 4 possesses multiple spin and orbital ordered phases, but their unique interplay is still relatively unexplored. Here, we used femtosecond optical spectroscopy to study ultrafast spin and orbital ordering dynamics in α -Sr 2 CrO 4 through their non-equilibrium response to photoexcitation. By varying the pump photon energy, we selectively drove inter-site spin hopping between neighboring Cr t 2 g orbitals and charge transfer-type transitions between oxygen 2 p and Cr e g orbitals. The resulting transient reflectivity dynamics revealed temperature-dependent anomalies across the Néel temperature for spin ordering as well as the transition temperatures linked to different types of orbital order. Our results reveal distinct relaxation timescales for spin and orbital orders in α -Sr 2 CrO 4 and provide experimental evidence for the phase transition at T O , possibly related to antiferro-type orbital ordering.
36 MATERIALS SCIENCE↗
Exploring the Links between Structural Distortions, Orbital Ordering, and Multipolar Magnetic Ordering in Double Perovskites Containing Re(VI) and Os(VII)
A combination of high-resolution powder diffraction techniques and solid-state NMR has been employed to explore the links between crystal structure, orbital ordering, and magnetism in three isostructural double perovskites containing transition metal ions with a 5d 1 configuration. In Ba 2 ZnReO 6 , both neutron and synchrotron X-ray powder diffraction data reveal a cubic-to-tetragonal transition at 23 K that breaks the degeneracy of the t 2g orbitals and leads to a pattern of orbital ordering that stabilizes magnetic ordering when the sample is cooled below 16 K. Similar behavior is observed in Ba 2 MgReO 6 , with an orbital ordering temperature of 33 K and a magnetic ordering temperature of 18 K. Prior theoretical works suggest that the pattern of orbital order seen in the P42/mnm space group is needed to stabilize the heavily canted antiferromagnetism of these compounds. Unfortunately, powder diffraction data is not sensitive enough to differentiate between the I4/mmm and P42/mnm structural models, as the distortions are too subtle to be unambiguously identified from either neutron or synchrotron X-ray powder diffraction methods. In contrast, both diffraction and 7 Li NMR data indicate that Ba 2 LiOsO 6 retains the cubic structure down to 1.7 K. The antiferromagnetic ground state and lack of any sign of orbital ordering in Ba 2 LiOsO 6 provide compelling evidence that the electronically driven tetragonal distortion seen in Ba2ZnReO6, and Ba2MgReO6 is intimately linked to the magnetic ordering seen in those compounds. The absence of magnetic reflections in high intensity neutron powder diffraction data collected on Ba 2 MgReO 6 strongly suggests ordering of multipolar moments on Re(VI), likely ferro-octupolar ordering.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Discovery of orbital ordering in Bi 2 Sr 2 CaCu 2 O 8+x
The primordial ingredient of cuprate superconductivity is the CuO 2 unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d 9 and 3d 10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p 6 orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p 6 and 3d 10 orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO 2 studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order bounded by dopant ions, and within whose domain walls low-energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q = 0 orbitally ordered state that splits the oxygen energy levels by ~50 meV, in underdoped CuO 2 .
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Stabilized Charge, Spin, and Orbital Ordering by the 6s 2 Lone Pair in Bi 0.5 Pb 0.5 MnO 3
Bi and Pb ions with charge degree of freedom depending on 6s 2 and 6s 0 electronic configurations were combined with the Mn ion in a perovskite oxide. Comprehensive theoretical and experimental investigations revealed the Bi 3+ 0.5 Pb 2+ 0.5 Mn 3+ 0.5 Mn 4+ 0.5 O 3 charge ordered state with CE-type spin and dz 2 orbital orderings as observed in La 0.5 Ca 0.5 MnO 3 , Nd 0.5 Sr 0.5 MnO 3 , and Bi 0.5 Sr 0.5 MnO 3 . Finally, the charge and orbital orderings were preserved above 500 K owing to the stereochemical activity of Bi 3+ and Pb 2+ ions which stabilized the structural distortion.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Orbital ordering in the layered perovskite material CsVF 4
In strongly correlated electronic systems, several novel physical properties are induced by the orbital degree of freedom. In particular, orbital degeneracy near the Fermi level leads to spontaneous symmetry breaking, such as the nematic state in FeSe and the orbital ordering in several perovskite systems. Here, the novel layered perovskite material CsVF 4 , with a 3 d 2 electronic configuration, was systematically studied using density-functional theory and a multiorbital Hubbard model within the Hatree-Fock approximation. Furthermore, our results show that CsVF 4 should be magnetic, with a G-type antiferromagnetic arrangement in the a b plane and weak antiferromagnetic exchange along the c axis, in agreement with experimental results. Driven by the Jahn-Teller distortion in the VF 6 octahedra that shorten the c axis, the system displays an interesting electron occupancy d x y 1 ( d x z d y z ) 1 corresponding to the lower nondegenerate d x y orbital being half-filled and the other two degenerate d y z and d x z orbitals sharing one electron per site. We show that this degeneracy is broken and a novel d y z / d x z staggered orbital pattern is here predicted by both the first-principles and Hubbard model calculations. This orbital ordering is driven by the electronic instability associated with degeneracy removal to lower the energy.
36 MATERIALS SCIENCE↗
Discerning element and site-specific fluctuations of the charge-orbital order in Fe 3 O 4 below the Verwey transition
Despite countless experimental probes into magnetite's electronic structure across the Verwey transition Fe 3 O 4 , the exact origin of this archetypical metal-insulator transition remains a puzzle. Advanced x-ray diffraction techniques have mostly resolved the monoclinic structure of the insulating phase, including interatomic bond lengths, but the complexity of the charge-orbitally ordered state is difficult to disentangle. Here we combined resonant elastic x-ray scattering and x-ray photon correlation spectroscopy to probe charge-orbital fluctuations in the insulating state of magnetite. By accessing the Bragg forbidden $(00\frac{1}{2})_{c}$ peak at the oxygen K-edge, we complement our previous study on the iron L 3 – edge to reveal the dynamics of the iron 3d and oxygen 2p orbital domains. Our new results reveal a decoupling of the orbital correlation lengths between the oxygen 2p states and site-specific iron 3d states, and we further show charge-orbital domain fluctuations at the iron t 2g orbital sites of trimeron chains. These results also demonstrate an experimental method capable of distinguishing electronic dynamics between the oxygen ligands and the transition metal that underpins emergent behaviors in complex oxides.
36 MATERIALS SCIENCE↗
Spin-orbital correlations from complex orbital order in MgV 2 O 4
MgV 2 O 4 is a spinel based on magnetic V 3+ ions, which host both spin (𝑆 = 1) and orbital (𝑙 eff = 1) moments. Owing to the underlying pyrochlore coordination of the magnetic sites, the spins in MgV 2 O 4 only antiferromagnetically order once the frustrating interactions imposed by the 𝐹𝑑$\overline{3}$𝑚 lattice are broken through an orbitally-driven structural distortion at T 𝑆 ≃ 60 K. Consequently, a Néel transition occurs at T 𝑁 ≃ 40 K. Low-temperature spatial ordering of the electronic orbitals is fundamental to both the structural and magnetic properties; however, considerable discussion on whether it can be described by complex or real orbital ordering is ambiguous. We apply neutron spectroscopy to resolve the nature of the orbital ground state and characterize hysteretic spin-orbital correlations using x-ray and neutron diffraction. Neutron spectroscopy finds multiple excitation bands and we parametrize these in terms of a multilevel (or excitonic) theory based on the orbitally degenerate ground state. Meaningful for the orbital ground state, we report an “optical-like” mode at high energies that we attribute to a crystal-field-like excitation from the spin-orbital 𝑗 eff = 2 ground-state manifold to an excited 𝑗 eff =1 energy level. We parametrize the magnetic excitations in terms of a Hamiltonian with spin-orbit coupling and local crystalline electric field distortions resulting from deviations from perfect octahedra surrounding the V 3+ ions. We suggest that this provides compelling evidence for complex orbital order in MgV 2 O 4 . We then apply the consequences of this model to understand hysteretic effects in the magnetic diffuse scattering where we propose that MgV 2 O 4 displays a high-temperature orbital memory of the low-temperature spin order.
Frustrated magnetism↗
Ferroaxial density wave from intertwined charge and orbital order in rare-earth tritellurides
The discovery of the axial amplitude mode—commonly referred to as the Higgs mode—in charge density wave systems, such as rare-earth tritellurides, indicates the presence of a hidden order. A theoretical study proposed that this axial Higgs mode arises from a hidden orbital texture of the charge density wave, which produces a ferroaxial charge order. However, experimental evidence for the specific hidden order has been lacking. Here, we demonstrate a ferroaxial order of electronic origin throughout the rare-earth tritellurides. In ErTe 3 and HoTe 3 , which exhibit two distinct charge density waves with different ordering temperatures, a detailed investigation shows that the high-temperature charge order phase breaks translational, rotational and all vertical as well as diagonal mirror symmetries. Furthermore, this phase produces an axial Higgs mode and an axial electronic gap. By contrast, the low-temperature phase breaks only translational symmetry and gives rise to a scalar Higgs mode. Notably, both phases preserve the space inversion and time-reversal symmetries. These findings are consistent with a ferroaxial phase driven by coupled orbital and charge orders, highlighting the role of Higgs modes in revealing hidden orders in systems with intertwined charge density waves.
36 MATERIALS SCIENCE↗
Spin-orbital order and excitons in magnetoresistive HoBi
The magnetism of the rocksalt fcc rare-earth monopnictide HoBi, a candidate topological material with extreme magnetoresistance, is investigated. From the Ho 3+ non-Kramers J=8 spin-orbital multiplet, the cubic crystal electric field yields six nearly degenerate low-energy levels. These constitute an anisotropic magnetic moment with a Jahn-Teller-like coupling to the lattice. In the cubic phase for T>T N =5.72(1)K, the paramagnetic neutron scattering is centered at k=($\frac{1}{2}$$\frac{1}{2}$$\frac{1}{2}$) and was fit to dominant antiferromagnetic interactions between Ho spins separated by {100} and ferromagnetic interactions between spins displaced by {$\frac{1}{2}$ $\frac{1}{2}$ 0}. For T < T N , a type-II AFM long-range order with k=($\frac{1}{2}$$\frac{1}{2}$$\frac{1}{2}$) develops along with a tetragonal lattice distortion. While neutron diffraction from a multidomain sample cannot unambiguously determine the spin orientation within a domain, the bulk magnetization, structural distortion, and our measurements of the magnetic excitations all show the easy axis coincides with the tetragonal axis. Finally, the weakly dispersive excitons for T < T N can be accounted for by a spin Hamiltonian that includes the crystal electric field and exchange interactions within the random phase approximation.
36 MATERIALS SCIENCE↗
Kinetics of orbital ordering in cooperative Jahn-Teller models: Machine-learning enabled large-scale simulations
Not Available
Ghosh, Supriyo (ORCID:0009000350877644)↗
Surface orbital order and chemical potential inhomogeneity of the iron-based superconductor Fe Te 0.55 Se 0.45 investigated with special STM tips
Not Available
Wang, Dongfei (ORCID:0000000346452881)↗
Transferring orbital angular momentum to an electron beam reveals toroidal and chiral order
Orbital angular momentum (OAM) and torque transfer play central roles in a wide range of magnetic textures and devices including skyrmions and spin-torque electronics. Analogous topological structures are now also being explored in ferroelectrics, including polarization vortex arrays in ferroelectric/dielectric superlattices. Unlike magnetic toroidal order, electric toroidal order does not couple directly to linear external fields. Instead, we find that the presence of an electric toroidal moment in a ferrorotational phase transfers measurable torque and OAM to a localized electron beam in the ballistic limit. We record these torque transfers from a high-energy electron beam using a momentum-resolved detector. This approach provides a high-sensitivity method to detect polarization fields and their more complex order parameters and topologies. In addition to toroidal order, we also demonstrate high-precision measurements of vorticity and chirality for polar vortexlike phases.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Orbital degree of freedom in high entropy oxides
The spin, charge, and lattice degrees of freedom and their interplay in high entropy oxides were intensively investigated in recent years. However, how the orbital degree of freedom is affected by the extreme disorder in high entropy oxides has not been studied. In this work, using perovskite structured RVO 3 as a materials playground, we report how the disorder arising from mixing different rare earth ions at the rare earth site affects the orbital ordering of V 3+ t 2g -electrons. Since each member of RVO 3 (R = rare earth and Y) crystallizes into the same orthorhombic Pbnm structure, the configurational entropy should not be critical for the stability of (R 1,..., Rn)VO 3 . The spin and orbital ordering was studied by measuring magnetic properties and specific heat of single crystals. Rather than the number and type of rare earth ions, the average and variance of ionic radius are the key factors determining the spin and orbital order in (R 1,..., Rn)VO 3 . When the size variance is small, the average ionic radius takes precedence in dictating spin and orbital order. Increasing size variance suppresses the G-type orbital order (G-OO) and C-type antiferromagnetic order (C-AF) but favors the C-OO/G-AF state and spin-orbital entanglement. In conclusion, these findings suggest that the extreme disorder introduced by mixing multiple rare earth ions in high entropy perovskites might be employed to preserve the orbital degree of freedom to near the magnetic order, which is necessary for the electronic driven orbital ordering in a Kugel-Khomskii compound.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗