Abstract: There is a long time gap between the formulation of the basic theory of low-dimensional (low-D) magnetism as advanced by Ising, Heisenberg and Bethe and its experimental verification. The latter started not long before the discovery of high-TC superconductivity in cuprates and has been boosted by this discovery result in an impressive succession of newly observed physical phenomena. Milestones on this road were the compounds which reached their quantum ground states upon lowering the temperature either gradually or through different instabilities. The gapless and gapped ground states for spin excitations in these compounds are inherent for isolated half-integer spin and integer spin chains, respectively. The same is true for the compounds hosting odd and even leg spin ladders. Some complex oxides of transition metals reach gapped ground state by means of spin-Peierls transition, charge ordering or orbital ordering mechanisms. However, the overwhelming majority of low-dimensional systems arrive to a long-range ordered magnetic state, albeit quite exotic realizations. Under a magnetic field some frustrated magnets stabilize multipolar order, e.g., showing a spin-nematic state in the simplest quadropolar case. Finally, numerous square, triangular, kagome and honeycomb layered lattices, along with Shastry–Sutherland and Nersesyan–Tsvelik patterns constitute the playground to check the basic concepts of two-dimensional magnetism, including resonating valence bond state, Berezinskii–Kosterlitz–Thouless transition and Kitaev model.

Abstract: Some $AB{X}_{3}$ perovskites exhibit different local environments (DLE) for the same $B$ atoms in the lattice, an effect referred to as disproportionation, distinguishing such compounds from common perovskites that have single local environments (SLE). The basic phenomenology associated with such disproportionation involves the absence of $B$-atom charge ordering, the creation of different B-X bond length (``bond alternation'') for different local environments, the appearance of metal (in SLE) to insulator (in DLE) transitions, and the formation of ligand holes. We point out that this phenomenology is common to a broad range of chemical bonding patterns in $AB{X}_{3}$ compounds, either with s-p electron $B$-metal cations (${\mathrm{BaBiO}}_{3}$, ${\mathrm{CsTlF}}_{3}$) or with noble-metal cations (${\mathrm{CsAuCl}}_{3}$), as well as with $d$-electron cations (${\mathrm{SmNiO}}_{3}$, ${\mathrm{CaFeO}}_{3}$). We show that underlying much of this phenomenology is the ``self-regulating response,'' whereby in strongly bonded metal-ligand systems with high-lying ligand orbitals, the system protects itself from creating highly charged cations by transferring ligand electrons to the metal, thus preserving a nearly constant metal charge in different local environments, while creating $B$-ligand bond alternation and ligand-like conduction band (``ligand hole'' states). We are asking what are the minimal theory ingredients needed to explain the main features of this SLE-to-DLE phenomenology, such as its energetic driving force, bond length changes, possible modifications in charge density, and density of state changes. Using as a guide the lowering of the total energy in DLE relative to SLE, we show that density functional calculations describe this phenomenology across the whole chemical bonding range without resort to special strong correlation effects, beyond what DFT naturally contains. In particular, lower total energy configurations (DLE) naturally develop bond alternation, gapping of the metallic SLE state, and absence of charge ordering with ligand hole formation.

Abstract: Anions have often been considered to act essentially as electron donors or acceptors in molecular conductors. However there is now growing evidence that they play an essential role in directing the structural and hence electronic properties of many of these systems. After reviewing the basic interactions and different ground states occurring in molecular conductors we consider in detail how anions influence the structure of donor stacks and often guide them toward different types of transitions. Consideration of the Bechgaard and Fabre salts illustrates how anions play a crucial role in directing these salts through complex phase diagrams where different conducting and localized states are in competition. We also emphasize the important role of hydrogen bonding and conformational flexibility of donors related to BEDT-TTF and we discuss how anions have frequently a strong control of the electronic landscape of these materials. Charge ordering, metal to metal and metal to insulator transitions occurring in these salts are considered.

Abstract: The semivalent oxyphosphate V2OPO4 is found to have long-range V2+/V3+ charge ordering up to 605 K where a monoclinic to tetragonal structural transition and a switch from positive to negative thermal expansion are observed. V–V bonding within orbital polymer chains is proposed as the key factor in the novel switch of thermal expansion behavior, as loss of V–V bonding enables transverse oxygen motions to dominate the thermal expansion at high temperatures. Ferrimagnetic order of V2+ spin up and V3+ spin down states is observed below a magnetic ordering transition at 164 K, and susceptibility measurements evidence local spin pairing correlations to higher temperatures.

Abstract: The degrees of freedom associated with orbital, spin, and charge ordering can strongly affect the properties of many crystalline solids, including battery materials, high-temperature superconductors, and naturally occurring minerals. This work reports on the development of a computational framework to systematically explore the ordering of electronic degrees of freedom and presents results on orbital ordering associated with Jahn–Teller distortions in four layered oxides relevant for Li- and Na-ion batteries: LiNiO2, NaNiO2, LiMnO2, and NaMnO2. Our calculations reveal a criterion for the stability of orbital orderings in these layered materials: each oxygen atom must participate in two short and one long transition-metal/oxygen bond. The only orderings that satisfy this stability criterion are row orderings, such as the “zigzag” ordering. The near degeneracy of such row-orderings in LiNiO2 suggests that boundaries between domains with distinct but symmetrically equivalent Jahn–Teller distortions will be r...

Abstract: In this paper, we have investigated the electrical and magnetic response of a La0.4Gd0.1Ca0.5MnO3 polycrystalline sample. This sample seems to exhibit fascinating phenomena like charge ordering, magnetic phase separation, training effects and kinetic arrest. It also shows colossal values of negative magnetoresistance (∼91.7% at 96 K under 1 T applied magnetic field), which raises the possibility of using this sample for technological applications. We have also proposed, in this work, a new empirical model to describe the evolution of resistivity and magnetoresistance as a function of magnetic field. This model was successfully tested on the La0.4Gd0.1Ca0.5MnO3 sample in spite of its complicated magnetic behavior, which suggests the use of this model for other magnetic samples in order to check its validity.

Abstract: A Verwey-type charge-ordering transition in magnetite at 120 K leads to the formation of linear units of three iron ions with one shared electron, called trimerons. The recently-discovered iron pentoxide (Fe4O5) comprising mixed-valent iron cations at octahedral chains, demonstrates another unusual charge-ordering transition at 150 K involving competing formation of iron trimerons and dimerons. Here, we experimentally show that applied pressure can tune the charge-ordering pattern in Fe4O5 and strongly affect the ordering temperature. We report two charge-ordered phases, the first of which may comprise both dimeron and trimeron units, whereas, the second exhibits an overall dimerization involving both the octahedral and trigonal-prismatic chains of iron in the crystal structure. We link the dramatic change in the charge-ordering pattern in the second phase to redistribution of electrons between the octahedral and prismatic iron chains, and propose that the average oxidation state of the iron cations can pre-determine a charge-ordering pattern.

Abstract: Materials in the form of thin films are getting worldwide attention because of their rapid development in the electronics industry. The demand is not only to prepare thin films using low-cost methods but also to induce tunable electronic properties (i.e., ferroelectricity, dielectric/impedance behavior, etc.) at room temperature. Keeping in view today’s demand for electronic materials, iron oxide thin films have been prepared using a low-cost sol–gel method with variation in the sol concentration in the range of 0.2–2.0 mM. Spin-coated films have been annealed at 300°C for 60 and 120 min in the presence of a magnetic field. The magnetite (Fe3O4) phase was observed at 1.4 mM, with preferred orientation along the (220) plane, under as-deposited and annealed conditions. The rest of the concentration range we studied results in the inclusion of small traces of maghemite (γ-Fe2O3) along with magnetite under all the preparation conditions. However, such inclusions result in the shift of preferred orientation from the (220) to the (400) plane of the magnetite (Fe3O4) phase. Formation of Fe3O4 phase has been confirmed using the Verwey transition at ∼ 124.8 K along with the appearance of a Raman A1g band at 667 cm−1. A high dielectric constant (∼ 80.23) and low tangent loss (∼ 0.00239) at log f = 5.0 were obtained at room temperature for 1.4 mM-based thin films. Such behavior may have been observed because of the high grain boundary resistance (5.5 × 104 Ω) and high grain boundary density (0.9939) at a sol concentration of 1.4 mM. An increase in dielectric constant and tangent loss was observed with the increase in temperature from 30 to 210°C. An activation energy of 2.007 eV was observed for the 1.4 mM-based thin films. The conductivity obeys Jonscher’s power law and has been associated with the overlapping large polaron tunneling model. Room-temperature ferroelectricity was observed for iron oxide thin films with maximum polarization (Pmax ∼ 14.74 μC/cm2) at 1.4 mM sol concentration.

Abstract: The metal-insulator phase transition in magnetite, known as the Verwey transition, is characterized by a charge-orbital ordering and a lattice transformation from a cubic to monoclinic structure. We use $x$-ray photon correlation spectroscopy to investigate the dynamics of this charge-orbitally ordered insulating phase undergoing the insulator-to-metal transition. By tuning to the Fe ${L}_{3}$ edge at the $(00\frac{1}{2})$ superlattice peak, we probe the evolution of the Fe ${t}_{2g}$ orbitally ordered domains present in the low temperature insulating phase and forbidden in the high temperature metallic phase. We observe two distinct regimes below the Verwey transition. In the first regime, magnetite follows an Arrhenius behavior and the characteristic timescale for orbital fluctuations decreases as the temperature increases. In the second regime, magnetite phase separates into metallic and insulating domains, and the kinetics of the phase transition is dictated by metallic-insulating interfacial boundary conditions.

Abstract: The Verwey transition in Fe 3 O 4 , a complex structural phase transition concomitant with a jump in electrical conductivity by two orders of magnitude, has been a benchmark for charge ordering (CO) phenomena in mixed-valence transition metal materials CO is of central importance, because it frequently competes with functional properties such as superconductivity or metallic ferromagnetism However, the CO state in Fe 3 O 4 turned out to be complex, and the mechanism of the Verwey transition remains controversial We demonstrate an archetypical Verwey-type transition in an open p -shell anionic mixed-valence compound using complementary diffraction and spectroscopic techniques In Cs 4 O 6 , a phase change from a cubic structure with a single crystallographic site for the molecular O 2 x − building units to a tetragonal structure with ordered superoxide O 2 − and peroxide O 2 2− entities is accompanied by a drastic drop in electronic conductivity and molecular charge fluctuation rates The simple CO pattern of molecular units and the lack of magnetic order suggest Cs 4 O 6 as a model system for disentangling the complex interplay of charge, lattice, orbital, and spin degrees of freedom in Verwey-type CO processes

Abstract: Fe3O4 with high Curie temperature and 100% spin polarization is a potential candidate for practical applications in flexible spintronics. In this work, combined with flexible muscovite substrates, the dynamic strain influenced Verwey transition of Fe3O4 has been studied. The Verwey transition temperature increases (decreases) in the inward (outward) bending heterostructures. From the analyses of Fe L2,3 edge X-ray absorption spectroscopy, the reversible modulation originates from the charge reconstruction effect with the valence variations of Fe ions on the tetrahedral site and octahedral site in different bending states. Meanwhile, the charge reconstruction effect enhances the net magnetic moments of the Fe3O4/muscovite heterostructures in bending states.

Abstract: We report a detailed study of magnetic properties in manganite (La0.5Pr0.5)0.67Ca0.33MnO3. In contrast to the usual beliefs, it shows an abnormal upturn deviation from the Curie–Weiss law on the inverse susceptibility curve. Such a non-Griffiths-like phase is further confirmed from the inverse double integrated intensities of electron paramagnetic resonance spectrum. Because La $$^{3+}$$ ions are substituted by Pr $$^{3+}$$ ions with 50% concentrations, the ratio of three ions (La $$^{3+}$$ , Pr $$^{3+}$$ , Ca $$^{2+}$$ ) is close to 1 on A-site sublattice. As a result, some short-range antiferromagnetic (CO AFM) phases come into being in the system due to the existence of localized charge ordering states. Therefore, the upturn deviation from Curie–Weiss law originates from the appearance of short-range CO AFM correlations above $$T_{\text{C}}$$ . Additionally, a magnetic field-driven-metamagnetic transition is found, which gives a main contribution for the large magnetic entropy change (MEC) observed in this sample. Both the Arrott plot and the renormalized MEC curves testify that this transition belongs to first-order magnetic transition. The insignificant hysteresis loop indicate that the inevitable thermal hysteresis can be ignored in the present first-order material implying that it is a potential candidate for the cryogenic temperature magnetic refrigeration.

Abstract: Some ABX3 perovskites exhibit different local environments (DLE) for the same B atoms in the lattice, an effect referred to as disproportionation, distinguishing such compounds from perovskites that have single local environments (SLE). The basic phenomenology of disproportionation involves the absence of B-atom charge ordering, the creation of different B-X bond length for different local environments, the appearance of metal (in SLE) to insulator (in DLE) transition, and the formation of ligand holes. We point out that this phenomenology is common to a broad range of chemical bonding patterns in ABX3 compounds, either with s-p electron B-metal cations (BaBiO3, CsTlF3), or noble metal cation (CsAuCl3), as well as d-electron cations (SmNiO3, CaFeO3). We show that underlying much of this phenomenology is the self-regulating response, whereby in strongly bonded metal-ligand systems with high lying ligand orbitals, the system protects itself from creating highly charged cations by transferring ligand electrons to the metal, thus preserving a nearly constant metal charge in DLE, while creating B-ligand bond alternation and ligand-like conduction band (ligand hole). We are asking what are the minimal theory ingredients needed to explain the main features of this SLE-to-DLE phenomenology, such as its energetic driving force, bond length changes, possible modifications in charge density and density of state changes. Using as a guide the lowering of the total energy in DLE relative to SLE, we show that density functional calculations describe this phenomenology across the whole chemical bonding range without resort to special strong correlation effects, beyond what DFT naturally contains. In particular, lower total energy configurations (DLE) naturally develop bond alternation, gaping of the metallic SLE state, and absence of charge ordering with ligand hole formation.

Abstract: The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions $2t\leq U\leq 10t$, temperatures $0.2t\lesssim T\lesssim t$ and electron concentrations $0.7\lesssim\bar{n}\leq1$ with $t$ the intersite hopping constant. For all considered $U$ the system exhibits a transition to the long-range antiferromagnetic order at $T_{\rm AF}\approx 0.2t$. At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the $U$-$T$ plane, the curve separating metallic solutions passes from $U\approx6t$ at the highest temperatures to $U=2t$ at $T\approx T_{\rm AF}$ for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low $T$, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for $U\gtrsim6t$ to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for $U\lesssim3t$. For $T\approx T_{\rm AF}$ and $U\gtrsim 7t$ doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband.

Abstract: Nd0.75Na0.25Mn1−xNixO3 (x = 0 − 0.07) were synthesized using a conventional solid-state synthesis method to investigate the effect of Ni substitution on their magnetic and electrical transport properties. XRD analysis using the Rietvield refinement method showed an increase in unit cell volume with increasing Ni content, indicating the possibility of substituting Ni for the Mn site. For x = 0, magnetization measurements showed paramagnetic (PM) to antiferromagnetic (AFM) transition at the transition temperature, TN ∼ 185 K, which may be related to the presence of charge-ordering (CO) state. For Ni-substituted samples, ferromagnetic (FM) to PM transition was induced with Curie temperature (TC), increasing from 91 K (x = 0.01) to 115 K (x = 0.03), followed by decreases in TC to 60 K (x = 0.07). Electrical resistivity measurements showed that samples for x ≤ 0.01 exhibited insulator behavior while both x = 0.03 and 0.05 samples exhibited metal-insulator transition suggesting that the CO state is weakened. For x = 0.07, the sample shows re-entrant of insulating characteristic. Inducement of FM metallic (FMM) state, as well as increased of TC for x = 0.03 is suggested to be related to FM SE between Ni2+ and Mn4+, which suppressed the CO state, hence inducing double-exchange (DE)-like mechanism. In addition, an increase in resistivity was observed as temperature decreased below the resistivity minimum (Rmin) at Tmin ∼ 40 K for x = 0.05 is possibly due to the Kondo-like effect mechanism. On one hand, the M(H) curve showed the presence of a hysteresis loop for x = 0 and 0.01 at T= 60 and 80 K, indicating the presence of an unstable phase, which may be related with the CO-AFM phase. For x = 0.03, no hysteresis loop was observed, indicating the suppression of the CO-AFM. Intriguingly, for x = 0.05 and 0.07, small hysteresis loop was observed, indicating the possible presence of a minor AFM component. Further, the observed MR behavior in present studies can be understood as a result of a decreased scattering mechanism in the presence of magnetic field.

Abstract: BaPb$_{1-x}$Bi$_x$O$_3$ is a superconductor, with transition temperature $T_c=11$ K, whose parent compound BaBiO$_3$ possess a charge ordering phase and perovskite crystal structure reminiscent of the cuprates. The lack of magnetism simplifies the BaPb$_{1-x}$Bi$_{x}$O$_3$ phase diagram, making this system an ideal platform for contrasting high-$T_c$ systems with isotropic superconductors. Here we use high-quality epitaxial thin films and magnetotransport to demonstrate superconducting fluctuations that extend well beyond $T_c$. For the thickest films (thickness above $\sim100$ nm) this region extends to $\sim27$ K, well above the bulk $T_c$ and remarkably close to the higher $T_c$ of Ba$_{1-x}$K$_x$BiO$_3$ ($T_c=31$ K). We drive the system through a superconductor-insulator transition by decreasing thickness and find the observed $T_c$ correlates strongly with disorder. This material manifests strong fluctuations across a wide range of thicknesses, temperatures, and disorder presenting new opportunities for understanding the precursor of superconductivity near the 2D-3D dimensionality crossover.

Abstract: The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions [Formula: see text], temperatures [Formula: see text] and electron concentrations [Formula: see text] with t the intersite hopping constant. For all considered U the system exhibits a transition to the long-range antiferromagnetic order at [Formula: see text]. At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the U-T plane, the curve separating metallic solutions passes from [Formula: see text] at the highest temperatures to U = 2t at [Formula: see text] for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low T, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for [Formula: see text] to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for [Formula: see text]. For [Formula: see text] and [Formula: see text] doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband. Obtained spectra feature waterfalls and Fermi arcs, which are similar to those observed in hole-doped cuprates.

Abstract: The recently-discovered high pressure material MnFe3O5 displays a rich variety of magnetically ordered states on cooling. Fe spins order antiferromagnetically below a Neel transition at 350 K. A second transition at 150 K marks Mn spin order that leads to spin canting of some of the Fe spins and ferrimagnetism. A further transition at 60 K is driven by charge ordering of Fe2+ and Fe3+ over two inequivalent Fe sites, with further canting of all spins. Electrical resistivity measurements reveal semiconducting behaviour in MnFe3O5 with a change in activation energy at 285 K.

Abstract: Most interesting phenomena of condensed matter physics originate from interactions among different degrees of freedom, making it a very intriguing yet challenging question how certain ground states emerge from only a limited number of atoms in assembly. This is especially the case for strongly correlated electron systems with overwhelming complexity. The Verwey transition of Fe3O4 is a classic example of this category, of which the origin is still elusive 80 years after the first report. Here we report, for the first time, that the Verwey transition of Fe3O4 nanoparticles exhibits size-dependent thermal hysteresis in magnetization, 57Fe NMR, and XRD measurements. The hysteresis width passes a maximum of 11 K when the size is 120 nm while dropping to only 1 K for the bulk sample. This behavior is very similar to that of magnetic coercivity and the critical sizes of the hysteresis and the magnetic single domain are identical. We interpret it as a manifestation of charge ordering and spin ordering correlation in a single domain. This work paves a new way of undertaking researches in the vibrant field of strongly correlated electron physics combined with nanoscience.

Abstract: La0.5Ca0.5MnO3 (LCMO) polycrystalline sample was synthesized by the solid-state reaction method. The result of X-ray diffraction shows that the LCMO is single phase. We have studied the magnetic response of charge-ordered (CO) state in the LCMO manganite. The magnetic hysteresis loop at 100 K displays an interesting butterfly-type structure, which indicates the existence of CO anti-ferromagnetic (AFM) structure in LCMO. The temperature-dependent magnetization measurements show a paramagnetic (PM) to ferromagnetic (FM) transition at Curie temperature (TC ≈ 130 K) and a FM to AFM transition at Neel temperature (TN ≈ 50 K), measured under different fields of 100, 500 and 5000 Oe. Moreover, there is an interesting intercross in zero-field cooling (ZFC) and filed-cooling (FC) measurements, i.e., an intercross of the ZFC/FC curves in the CO LCMO manganite. These present magnetism measurements are discussed and possible explanations are provided by the existence of CO AFM state.

Abstract: We report here the “incommensurate modulated” phase along with the ferromagnetic character in nanocrystalline Nd0.5Sr0.5MnO3 perovskite. The Rietveld analysis of powder X-ray diffraction data reveals that the structure of nanocrystalline Nd0.5Sr0.5MnO3 ceramic can be described as a modulated phase in the monoclinic structure with space group Pm and lattice parameters am ≈ 2ao, bm ≈ bo, and cm ≈ 3co, where ao, bo, and co correspond to the lattice parameters of the parent orthorhombic structure for the bulk sample at room temperature. Increasing the crystallite size converts the modulated monoclinic structure to an orthorhombic structure with the Imma space group for the bulk Nd0.5Sr0.5MnO3 sample. The magnetic measurements on nanocrystalline samples reveal ferromagnetic behaviour and the absence of charge ordering transition at low temperatures. The nanocrystalline samples also exhibit Griffith phase like behaviour near the paramagnetic to ferromagnetic phase transition. The Powder X-ray diffraction study of bulk Nd0.5Sr0.5MnO3 in the temperature range of 13 K–300 K reveals the transition from the orthorhombic to the monoclinic structure in the P21/m space group with the coexistence of the two phases in a wide temperature range below room temperature.

Abstract: Most interesting phenomena of condensed matter physics originate from interactions among different degrees of freedom, making it a very intriguing yet challenging question how certain ground states emerge from only a limited number of atoms in assembly. This is especially the case for strongly correlated electron systems with overwhelming complexity. The Verwey transition of Fe3O4 is a classic example of this category, of which the origin is still elusive 80 years after the first report. Here we report, for the first time, that the Verwey transition of Fe3O4 nanoparticles exhibits size-dependent thermal hysteresis in magnetization, 57Fe NMR, and XRD measurements. The hysteresis width passes a maximum of 11 K when the size is 120 nm while dropping to only 1 K for the bulk sample. This behavior is very similar to that of magnetic coercivity and the critical sizes of the hysteresis and the magnetic single domain are identical. We interpret it as a manifestation of charge ordering and spin ordering correlation in a single domain. This work paves a new way of undertaking researches in the vibrant field of strongly correlated electron physics combined with nanoscience.

Abstract: We report the tunability of the exchange bias effect by the first-order metal-insulator transition (known as the Verwey transition) of Fe3O4 in CoO (5 nm)/Fe3O4 (40 nm)/MgO (001) thin film. In the vicinity of the Verwey transition, the exchange bias field is substantially enhanced because of a sharp increase in magnetocrystalline anisotropy constant from high-temperature cubic to lowtemperature monoclinic structure. Moreover, with respect to the Fe3O4 (40 nm)/MgO (001) thin film, the coercivity field of the CoO (5 nm)/Fe3O4 (40 nm)/MgO (001) bilayer is greatly increased for all the temperature range, which would be due to the coupling between Co spins and Fe spins across the interface.

Abstract: We consider the extended half-filled Hubbard model on the honeycomb lattice for second nearest-neighbor interactions. Using a functional integral approach, we find that collective fluctuations suppress topological states and instead favor charge ordering, in agreement with previous numerical studies. However, we show that the critical point is not of the putative semimetal-Mott insulator variety. Due to the frustrated nature of the interactions, the ground state is described by a novel hidden metallic charge order with semi-Dirac excitations. We conjecture that this transition is not in the Gross-Neveu universality class.

Abstract: A comparative study of the dielectric properties and electric polarization of multiferroics GdMn2O5 and Gd0.8Ce0.2Mn2O5 has been carried out in the temperature range from 5 up to 300 K. The polarization properties in the ferroelectric state that forms due to a charge ordering and exchange striction have been studied at T less than 30 K. The properties of the restricted polar phase separation domains formed in the crystals containing ions Mn3+ and Mn4+ have been studied, too. These domains exhibit the electric polarization in the temperature range from 5 K to some temperatures Tf lager than TC. Such a high-temperature polarization is due to the frozen superparaelectric state of the restricted polar domains.

Abstract: The charge density wave (CDW) in solids is a collective ground state combining lattice distortions and charge ordering. It is defined by a complex order parameter with an amplitude and a phase. The amplitude and wavelength of the charge modulation are readily accessible to experiment. However, accurate measurements of the corresponding phase are significantly more challenging. Here we combine reciprocal and real space information to map the full complex order parameter based on topographic scanning tunneling microscopy (STM) images. Our technique overcomes limitations of earlier Fourier space based techniques to achieve distinct amplitude and phase images with high spatial resolution. Applying this analysis to transition metal dichalcogenides provides striking evidence that their CDWs consist of three individual charge modulations whose ordering vectors are connected by the fundamental rotational symmetry of the crystalline lattice. Spatial variations in the relative phases of these three modulations account for the different contrasts often observed in STM topographic images. Phase images further reveal topological defects and discommensurations, a singularity predicted by theory for a nearly commensurate CDW. Such precise real space mapping of the complex order parameter provides a powerful tool for a deeper understanding of the CDW ground state whose formation mechanisms remain largely unclear.