Charge Order Parameters Research Articles

Quench dynamics in the one-dimensional mass-imbalanced ionic Hubbard model

Using the time-dependent Lanczos method, we study the nonequilibrium dynamics of the one-dimensional ionic-mass imbalanced Hubbard chain driven by a quantum quench of the on-site Coulomb interaction, where the system is prepared in the ground state of the Hamiltonian with a different Hubbard interaction. The exact diagonalization method (Lanczos algorithm) is adopted to study the zero temperature phase diagram in equilibrium, which is shown to be in good agreement with previous studies using density matrix renormalization group (DMRG). We then study the nonequilibrium quench dynamics of the spin and charge order parameters by fixing the initial and final Coulomb interactions while changing the quenching time protocols. Our study shows that the time evolution of the charge and spin order parameters strongly depend on the quenching time protocols. In particular, the effective temperature of the system will decrease monotonically as the quenching time is increased. By taking the final Coulomb interaction strength to be in the strong coupling regime, we find that the oscillation frequency of the charge order parameter increases monotonically with the Coulomb interaction. By contrast, the frequency of the spin order parameter decreases monotonically with increasing Coulomb interaction. We explain this result using an effective spin model and a two-site Hubbard model in the strong coupling limit. Finally, we take the final Coulomb interaction strength to be in the weak coupling regime and find that the oscillation frequency of both the charge and spin order parameters increases monotonically with decreasing Coulomb interaction. Our study suggests strategies to engineer the relaxation behavior of interacting quantum many-particle systems.

Charge order and emergent symmetries in cuprate superconductors

In this paper, we present our studies of the phase diagram of the cuprate superconductors performed in recent years. We describe how a few field-theoretical concepts can be used to account for the puzzling properties of these compounds. Starting with a short exposition of recent experimental developments, we then introduce the concept of an emergent SU(2) symmetry, which rotates between the superconducting and charge order parameters. We describe a solvable model for which this symmetry turns out to be exact and derive the corresponding effective field theory in terms of a non-linear σ model. We then turn to the experimental consequences of our model with the presence of skyrmions inside the vortex core and an elegant account of the B−T phase diagram. Next, we move on to the second concept, which is the one of an emergent U(1) gauge field in the theory. Within this more general framework, the pseudogap transition can be viewed as a confining/deconfining transition. Experimental consequences for a few spectroscopic probes like inelastic neutron scattering, Raman spectroscopy, phonon line in x-ray scattering and angle-resolved photoemission experiments are studied. This theory suggests the presence of incoherent bosons at moderate temperatures in the phase diagram of the cuprates, which would undergo a jamming transition at optimal doping (Urbani, 2022). Consequences of the presence of such bosons on the transport properties of these materials are examined.

Atomic insight into spin, charge and lattice modulations at SrFeO3-x/SrTiO3 interfaces.

Novel phenomena and functionalities at interfaces of oxide heterostructures are currently of great interest in a wide range of applications. At such interfaces, charge, spin, orbital and lattice ordering coexist and correlate closely, contributing to rich functional responses. By using atomically resolved imaging and spectroscopy techniques, we investigated magnetic behaviors and structural modulation at the SrFeO3-x/SrTiO3 interface. Fe/Ti element intermixing and oxygen vacancies occurred across a few unit cells at the interface. Furthermore, antiferromagnetic spin ordering of Fe with different valence states in the interface of SrFeO3-x/SrTiO3 induced uncompensated magnetic moments. Compared to the SrFeO3-x/La0.3Sr0.7Al0.65Ta0.35O3 heterojunction, the variations of charge and lattice order parameters at the SrFeO3-x/SrTiO3 interfaces were also determined by advanced electron microscopy, which provided a good understanding of the physical origin of disparate macroscopic magnetic properties, further investigated by magnetometer measurements and X-ray magnetic circular dichroism (XMCD) spectra. These studies provide comprehensive insight into the interfacial modulation of ferrite oxide, which may be useful for designing future devices in oxide electronics.

Spin Stripe Order in a Square Planar Trilayer Nickelate.

Trilayer nickelates, which exhibit a high degree of orbital polarization combined with an electron count (d^{8.67}) corresponding to overdoped cuprates, have been identified as a promising candidate platform for achieving high-T_{c} superconductivity. One such material, La_{4}Ni_{3}O_{8}, undergoes a semiconductor-insulator transition at ∼105 K, which was recently shown to arise from the formation of charge stripes. However, an outstanding issue has been the origin of an anomaly in the magnetic susceptibility at the transition and whether it signifies the formation of spin stripes akin to single layer nickelates. Here we report single crystal neutron diffraction measurements (both polarized and unpolarized) that establish that the ground state is indeed magnetic. The ordering is modeled as antiferromagnetic spin stripes that are commensurate with the charge stripes, the magnetic ordering occurring in individual trilayers that are essentially uncorrelated along the crystallographic c axis. A comparison of the charge and spin stripe order parameters reveals that, in contrast to single-layer nickelates such as La_{2-x}Sr_{x}NiO_{4} as well as related quasi-2D oxides including manganites, cobaltates, and cuprates, these orders uniquely appear simultaneously, thus demonstrating a stronger coupling between spin and charge than in these related low-dimensional correlated oxides.

Electro-optical and dielectric properties of TiO2 nanoparticles in nematic liquid crystals with high dielectric anisotropy

The electrical, optical and dielectric performance of high-dielectric-constant TiO2 nanoparticles (NPs) dispersed in nematic liquid crystals (NLCs) with high dielectric anisotropy is demonstrated. TiO2 doping decreases the pretilt angle of the NLC cell because of the increase in Van der Waals interaction between the NLC molecule and alignment layer. Moreover, TiO2 doping strengthens the electric field in the NLC bulk and suppresses the ionic screen effect on the substrate surface, thus decreasing the threshold and driving voltages of the NLC cell. The measured field-off response time and estimated conductivity initially increase and then decrease with increased TiO2 concentrations. This phenomenon is due to the antagonism between the entrained ion impurities during fabrication and the ion harvest effect of TiO2 NPs. Dielectric spectral measurements reveal that TiO2 doping changes the relative permittivity and dielectric anisotropy of NLCs because of the changed space–charge polarisation and order parameters in the NLC bulk. The physical mechanisms are discussed in detail accordingly.

Conditions for l=1 Pomeranchuk instability in a Fermi liquid

We perform a microscropic analysis of how the constraints imposed by conservation laws affect $q=0$ Pomeranchuk instabilities in a Fermi liquid. The conventional view is that these instabilities are determined by the static interaction between low-energy quasiparticles near the Fermi surface, in the limit of vanishing momentum transfer $q$. The condition for a Pomeranchuk instability is set by $F^{c(s)}_l =-1$, where $F^{c(s)}_l$ (a Landau parameter) is a properly normalized partial component of the anti-symmetrized static interaction $F(k,k+q; p,p-q)$ in a charge (c) or spin (s) sub-channel with angular momentum $l$. However, it is known that conservation laws for total spin and charge prevent Pomeranchuk instabilities for $l=1$ spin- and charge- current order parameters. Our study aims to understand whether this holds only for these special forms of $l=1$ order parameters, or is a more generic result. To this end we perform a diagrammatic analysis of spin and charge susceptibilities for charge and spin density order parameters, as well as perturbative calculations to second order in the Hubbard $U$. We argue that for $l=1$ spin-current and charge-current order parameters, certain vertex functions, which are determined by high-energy fermions, vanish at $F^{c(s)}_{l=1}=-1$, preventing a Pomeranchuk instability from taking place. For an order parameter with a generic $l=1$ form-factor, the vertex function is not expressed in terms of $F^{c(s)}_{l=1}$, and a Pomeranchuk instability does occur when $F^{c(s)}_1=-1$. We argue that for other values of $l$, a Pomeranchuk instability occurs at $F^{c(s)}_{l} =-1$ for an order parameter with any form-factor

Impurity Induced Phase Competition and Supersolidity

Several material families show competition between superconductivity and other orders. When such competition is driven by doping, it invariably involves spatial inhomogeneities which can seed competing orders. We study impurity-induced charge order in the attractive Hubbard model, a prototypical model for competition between superconductivity and charge density wave order. We show that a single impurity induces a charge-ordered texture over a length scale set by the energy cost of the competing phase. Our results are consistent with a strong-coupling field theory proposed earlier in which superconducting and charge order parameters form components of an $SO(3)$ vector field. To discuss the effects of multiple impurities, we focus on two cases: correlated and random distributions. In the correlated case, the CDW puddles around each impurity overlap coherently leading to a `supersolid' phase with coexisting pairing and charge order. In contrast, a random distribution of impurities does not lead to coherent CDW formation. We argue that the energy lowering from coherent ordering can have a feedback effect, driving correlations between impurities. This can be understood as arising from an RKKY-like interaction, mediated by impurity textures. We discuss implications for charge order in the cuprates and doped CDW materials such as NbSe$_2$.

Advances in Magnetics Epitaxial Multiferroic Heterostructures and Applications

The ever increasing demand for ultralow power electronics has propelled the exploration of novel multiferroics for realizing voltage control of magnetism in an energy efficient manner. Epitaxial multiferroic heterostructures, possessing a strong lattice-coupled mechanical interface and allowing an electric field (E-field) significantly modulating spin, charge, lattice, and orbital order parameters, have drawn much attention for creating novel magnetoelectric (ME) coupling effects. In this paper, we review the recent progress on control of ME properties in epitaxial multiferroic heterostructures, including their novel physical properties, various strong interfacial ME interactions, and potential applications. Meanwhile, the essential interfacial couplings, allowing cross-tuning of lattice and charge-coupled parameters, have been extensively reviewed. Electric tuning of magnetism in epitaxial multiferroic heterostructures provides a great platform to develop lightweight, compact, and energy-efficient spintronic or electronic devices.

Nonequilibrium lattice-driven dynamics of stripes in nickelates using time-resolved x-ray scattering

We investigate the lattice coupling to the spin and charge orders in the striped nickelate, ${\mathrm{La}}_{1.75}{\mathrm{Sr}}_{0.25}{\mathrm{NiO}}_{4}$, using time-resolved resonant x-ray scattering. Lattice-driven dynamics of both spin and charge orders are observed when the pump photon energy is tuned to that of an ${E}_{u}$ bond- stretching phonon. We present a likely scenario for the behavior of the spin and charge order parameters and its implications using a Ginzburg-Landau theory.

Charge and spin coupling in magnetoresistive oxygen-vacancy strontium ferrate SrFeO3–δ

Using magnetization, conductivity and x-ray scattering measurements, we demonstrate that the giant magnetoresistance of the oxygen-deficient ferrite SrFeO2.875±0.02 is a consequence of the coupling between the charge and spin order parameters and the tetragonal to monoclinic structural distortion. Upon cooling the sample at T ≃ 120 K we find a shoulder in both field-cool and zero field cool magnetization data and the simultaneous appearance of incommensurate structural satellites observed using x-ray diffraction. These satellites are shown to be due to incommensurate charge ordering with the high temperature delocalized Fe ions becoming localized with a charge disproportion forming an incommensurate charge-ordered phase. Strong resonant enhancement of these satellites at the Fe LIII absorption edge confirms that this charge ordering is occurring at the Fe(2) sites. Further cooling increases the charge order correlation until T ≃ 62 K where there is a full structural transition from the tetragonal phase to a mononclinic phase. This causes a jump in the charge order wavevector from an incommensurate value of 0.610 to a commensurate ground state position of 5/8. This first-order structural transition displays considerable hysteresis as well as dramatic reductions in the magnetization, resistivity and magnetoresistance. The transition also causes an antiferromagnetic spin-ordering with a doubled unit cell along the c-axis. Well as observing new commensurate magnetic reflections at the FeIII edge we also observed resonant enhancement at the oxygen K-edge showing considerable hybridization between the Fe 3d and oxygen 2p states at low temperatures. Our results show that the formation of a magnetic long-rage ordered ground state drives the charge ordering from an incommensurate ordering to a commensurate ground state. This is evidence of a strong coupling between the magnetic and charge order parameters which is the basis for the unusual magnetoresistive effects observed at the transition.

Photoinduced ultrafast charge-order melting: Charge-order inversion and nonthermal effects

The effect of photoexcitation is studied for a system with checkerboard charge order induced by displacements of ligands around a metal site. The motion of the ligands is treated classically and the electronic charges are simplified to two-level molecular bond charges. The calculations are done for a checkerboard charge-ordered system with about 100 000 ligand oscillators coupled to a fixed-temperature bath. The initial photoexcitation is followed by a rapid decrease in the charge-order parameter within 50–100 femtoseconds while leaving the correlation length almost unchanged. Depending on the fluence, a complete melting of the charge order occurs in less than a picosecond. While for low fluences, the system returns to its original state, for full melting, it recovers to its broken-symmetry state leading to an inversion of the charge order. Finally, for small long-range interactions, recovery can be slow due to domain formation.

Pure electronic metal-insulator transition at the interface of complex oxides.

In complex materials observed electronic phases and transitions between them often involve coupling between many degrees of freedom whose entanglement convolutes understanding of the instigating mechanism. Metal-insulator transitions are one such problem where coupling to the structural, orbital, charge, and magnetic order parameters frequently obscures the underlying physics. Here, we demonstrate a way to unravel this conundrum by heterostructuring a prototypical multi-ordered complex oxide NdNiO3 in ultra thin geometry, which preserves the metal-to-insulator transition and bulk-like magnetic order parameter, but entirely suppresses the symmetry lowering and long-range charge order parameter. These findings illustrate the utility of heterointerfaces as a powerful method for removing competing order parameters to gain greater insight into the nature of the transition, here revealing that the magnetic order generates the transition independently, leading to an exceptionally rare purely electronic metal-insulator transition with no symmetry change.

Charge Order Induced in an Orbital Density-Wave State

Motivated by the recent ARPES measurements (Evtushinsky et. al., PRL {\bf 105}, 147201 (2010)) and evidence for the density-wave state for the charge and orbital ordering (Garc\'{i}a et al., PRL {\bf 109}, 107202 (2012)) in La$_{0.5}$Sr$_{1.5}$MnO$_4$, the issue of charge and orbital ordering in a two orbital tight-binding model for layered manganite near half doping is revisited. We find that the charge order with an ordering wavevector 2${\bf Q}$ = $(\pi, \pi)$ is induced by the orbital order of $B_{1g}$ representation with a different ordering wavevector ${\bf Q}$, where the primary order parameter results from the strong Fermi-surface nesting. The orbital and charge order parameters develop according to $\sqrt{T_{CO}-T}$ and $T_{CO}-T$, respectively, by decreasing the temperature below the orbital ordering temperature $T_{CO}$. Moreover, the orbital order is found to stabilize the CE-type spin arrangement observed experimentally below $T_{CE} < T_{CO}$.

Metallic ferromagnetism-insulating charge order transition in doped manganites

We show that an interplay of double exchange and impurity randomness can explain the competition between metal-ferromagnetic and insulating charge ordered states in doped manganites. The double exchange is simplified in the Ising type, whereas the randomness is modeled by the Falicov-Kimball binary distribution. The combined model is considered in a framework of dynamical mean-field theory. Using the Kubo-Greenwood formalism, the transport coefficients are explicitly expressed in terms of single particle spectral functions. Dividing the system into two sublattices we have pointed out a direct calculation to the checkerboard charge order parameter and the magnetizations. Numerical results show us that the checkerboard charge order can settle inside the ferromagnetic state at low temperature. An insulator-metal transition is also found at the point of the checkerboard charge order-ferromagnetic transition.

Competition of Spin and Charge Orders in a Model Cuprate

We present results of the mean-field analysis of the competition between charge and spin orders in a model cuprate. Phase diagrams and temperature dependencies of the charge and magnetic order parameters are calculated for varying doping given different values of the on-site correlation parameter, inter-site density–density coupling, and spin exchange integral.

Competition of Spin and Charge Orders in a Model Cuprate

We present results of the mean-field analysis of the competition between charge and spin orders in a model cuprate. Phase diagrams and temperature dependencies of the charge and magnetic order parameters are calculated for different doping given different values of the on-site correlation parameter, inter-site density-density coupling, and Heisenberg spin exchange integral.

Symmetry‐Driven Atomic Rearrangement at a Brownmillerite–Perovskite Interface

Many of the recent advancements in oxide heterostructures have been attributed to modification of spin, charge, lattice, and orbital order parameters at atomically well-defined interfaces. However, the details on the structural, chemical, and electrostatic evolution of interfaces comprised of materials with different crystallographic symmetries remain to be understood. In this work, we have mapped out the interfacial connectivity of atoms of two dissimilar materials, the perovskite SrTiO3 and the brownmillerite SrCoO2.5, using high resolution scanning transmission electron microscopy and geometric phase analysis. We observed unique symmetry-mismatch driven atomic displacements restricted to only the first few atomic layers, which can critically modify the properties of the system. Provided that SrCoO2.5 is a promising energy material due to its open framework structure, the improved understanding of the interfacial structure on the atomic level can lead to the rational design of novel oxide heterostructures.

Fluctuating charge order in the cuprates: Spatial anisotropy and feedback from superconductivity

We analyze the form of static charge susceptibility $\chi(q)$ in underdoped cuprates near axial momenta $(Q,0)$ and $(0,Q)$ at which short-range static charge order has been observed. We show that the momentum dependence of $\chi (q)$ is anisotropic, and the correlation length in the longitudinal direction is larger than in the transverse direction. We show that correlation lengths in both directions decrease once the system evolves into a superconductor, as a result of the competition between superconductivity and charge order. These results are in agreement with resonant x-ray scattering data [R. Comin et al., Science 347, 1335 (2015)]. We also argue that density and current components of the charge order parameter are affected differently by superconductivity --- the charge-density component is reduced less than the current component and hence extends deeper into the superconducting state. This gives rise to two distinct charge order transitions at zero temperature.

Competition of Spin and Charge Orders in a Model Cuprate

We present results of the mean-field analysis of the competition between charge and spin orders in a model cuprate. Phase diagrams and temperature dependencies of the charge and magnetic order parameters are calculated for different doping given different values of the on-site correlation parameter, inter-site density-density coupling, and Heisenberg spin exchange integral.

Rotated stripe order and its competition with superconductivity inLa1.88Sr0.12CuO4

We report the observation of a bulk charge modulation in La$_{1.88}$Sr$_{0.12}$CuO$_4$ (LSCO) with a characteristic in-plane wave-vector of (0.236, $\pm \delta$), with $\delta$=0.011 r.l.u. The transverse shift of the ordering wave-vector indicates the presence of rotated charge-stripe ordering, demonstrating that the charge ordering is not pinned to the Cu-O bond direction. On cooling through the superconducting transition, we find an abrupt change in the growth of the charge correlations and a suppression of the charge order parameter indicating competition between the two orderings. Orthorhombic LSCO thus helps bridge the apparent disparities between the behavior previously observed in the tetragonal "214" cuprates and the orthorhombic yttrium and bismuth-based cuprates and thus lends strong support to the idea that there is a common motif to charge order in all cuprate families.