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The doping evolution behaviors of the normal state magnetic excitations (MEs) of the pressurized nickelate La3Ni2O7 are theoretically studied in this paper. It was found that the MEs of the parental compound have very strong dependence on the vertical momentum qz. For small qz, the low energy MEs exhibit a square-like pattern centered at (0, 0) which originates from the intrapocket particle-hole scatterings. With the increasing of qz, this square pattern diminishes gradually, and the MEs turn to be ruled by two new interpocket scattering modes with significantly larger intensity for qz around π. Hence, we have established the exotic qz evolution of the normal state MEs of the bilayer nickelates in the present study. Furthermore, we find that the main features of the MEs are very robust against doping. They persist in the wide hole- or electron-doping regime around the filling of n = 3.0. However, in the heavily electron-doped regime, the behaviors of the MEs change qualitatively due to the occurrence of a Lifshitz transition. With the absence of the hole γ pocket, for n = 4.0, there will exist nearly perfect nesting between the electron α and the hole β pockets guaranteed by the Luttinger theorem and the Fermi surface topology. As a result, a spin-density-wave phase was theoretically predicted to order around (π,π,π) near n = 4.0, in contrast with the parental compound which orders at (π/2,π/2,π) under ambient pressure. We expect that the doping-temperature phase diagram of the pressurized La3Ni2O7 will be explored in the near future which is helpful to unravel the intricate relation between the magnetic order and superconductivity.

The origin of unusual anisotropic electronic properties in the spin-density wave state of iron pnictides has conventionally been attributed to the breaking of four-fold rotational symmetry associated with the collinear magnetic order. By using a minimal two-orbital model, we show that a significant portion of the contribution to the anisotropy may come from the Dirac cones, which are not far away from the Fermi level. We demonstrate this phenomenon by examining optical conductivity and quasiparticle interference in the Dirac-semimetallic state with spin-density wave order, and the latter can be obtained by choosing appropriate interaction parameters and orbital splitting between the d xz and d yz orbitals. We further extend this study to investigate the low-energy spin-wave excitations in the Dirac-semimetallic state with spin-density wave order.

For more than a decade, the unusual distribution of electrons observed in ARPES (angle-resolved photoemission spectroscopy) data within the energy range of ~30 meV to ~300 meV below the Fermi level, known as the ARPES energy range, has remained a puzzle in the field of iron-based superconductivity. As the electron–phonon coupling of FeSe/SrTiO3 is very strong, our investigation is centered on exploring the synergistic interplay between spin-density waves (SDW) and charge-density waves (CDW) with differential phonons at the interface between antiferromagnetic maxima and minima under wave interference. Our analysis reveals that the synergistic energy is proportional to the ARPES energy range, as seen in the comparison between FeSe and FeSe/SrTiO3. This finding may suggest that the instantaneous interplay between these intricate phenomena may play a role in triggering the observed energy range in ARPES.

SrCu2(BO3)2 (Sr-122) has attracted considerable interest as a quasi-two-dimensional S = 1/2 Heisenberg antiferromagnetic spin system with a Shastry-Sutherland lattice (SSL) structure. It features a Cu2+ spin dimer ground state and exhibits intra-dimer Dzyaloshinskii–Moriya interactions, making Sr-122 a fascinating platform for studying quantum magnetic phenomena. In this study, we investigate the β-phase of SrCu2(BO3)2 (β-Sr-212), which retains the same spin structure as Sr-122, to explore how the carrier concentration affects the spin gap. Our results show that increasing the doping levels in SrCu2(BO3)2 modulates the magnetic properties and slightly suppresses the spin gap, offering new possibilities for tuning its quantum magnetic behavior.

Charge and spin density waves are typical symmetry broken states of quasi one-dimensional electronic systems. They demonstrate such common features of all incommensurate electronic crystals as a spectacular non-linear conduction by means of the collective sliding and susceptibility to the electric field. These phenomena ultimately require for emergence of static and transient topological defects: there are dislocations as space vortices and space-time vortices known as phase slip centers, i.e., a kind of instantons. Dislocations are statically built-in under a transverse electric field; their sweeping provides a conversion among the normal carriers and condensate which ensures the onset of the collective sliding. A special realization in a high magnetic field, when the density wave is driven by the Hall voltage, originated by quantized normal carriers, reveals the dynamic vorticity serving to annihilate compensating normal and collective currents. Spin density waves, with their rich multiplicative order parameter, bring to life complex objects with half-integer topologically bound vorticities in charge and spin degrees of freedom. We present the basic concepts and modelling results of the stationary states and their transient dynamics involving vorticity. The models take into account multiple fields in their mutual non-linear interactions: the complex order parameter, the self-consistent electric field, and the reaction of normal carriers. We explore the traditional time-dependent Ginzburg–Landau approach and introduce its generalization allowing the treatment of intrinsic normal carriers. The main insights and illustrations come from numerical solutions to partial differential equations for the dissipative dynamics of one and two space dimensions.

Most high-Tc superconductors are spatially inhomogeneous. Usually, this heterogeneity originates from the interplay of various types of electronic ordering. It affects various superconducting properties, such as the transition temperature, the magnetic upper critical field, the critical current, etc. In this paper, we analyze the parameters of spatial phase segregation during the first-order transition between superconductivity (SC) and a charge- or spin-density wave state in quasi-one-dimensional metals with imperfect nesting, typical of organic superconductors. An external pressure or another driving parameter increases the transfer integrals in electron dispersion, which only slightly affects SC but violates the Fermi surface nesting and suppresses the density wave (DW). At a critical pressure Pc, the transition from a DW to SC occurs. We estimate the characteristic size of superconducting islands during this phase transition in organic metals in two ways. Using the Ginzburg–Landau expansion, we analytically obtain a lower bound for the size of SC domains. To estimate a more specific interval of the possible size of the superconducting islands in (TMTSF)2PF6 samples, we perform numerical calculations of the percolation probability via SC domains and compare the results with experimental resistivity data. This helps to develop a consistent microscopic description of SC spatial heterogeneity in various organic superconductors.

We study an interacting electronic system exhibiting a spin nematic instability. Using a phenomenological form for the spin fluctuation spectrum near the spin-density-wave (SDW) phase, we compute the spin nematic susceptibility in energy and momentum space as a function of temperature and the magnetic correlation length . The spin nematic instability occurs when reaches a critical value , i.e., its transition temperature is always higher than the SDW critical temperature . In particular, decreases monotonically with increasing . Concomitantly, low-energy nematic fluctuations are present in a wider temperature region as becomes higher. Approaching the spin nematic instability, the nematic spectral function at zero momentum exhibits a central peak as a function of energy for a finite temperature and a soft mode at zero temperature. These properties originate from the general feature that the imaginary part of the spin-fluctuation bubble has a term linear in energy and its coefficient is proportional to the square of temperature. Furthermore we find that the nematic spectral function exhibits a diffusive peak around zero momentum and zero energy without clear dispersive features. A possible phase diagram for the spin nematic and SDW transitions is also discussed.

Advances in both non-resonant and resonant X-ray magnetic diffraction since the 1980s have provided researchers with a powerful tool for exploring the spin, orbital and ion degrees of freedom in magnetic solids, as well as parsing their interplay. Here, we discuss key issues for performing X-ray magnetic diffraction on single-crystal samples under high pressure (above 40 GPa) and at cryogenic temperatures (4 K). We present case studies of both non-resonant and resonant X-ray magnetic diffraction under pressure for a spin-flip transition in an incommensurate spin-density-wave material and a continuous quantum phase transition of a commensurate all-in–all-out antiferromagnet. Both cases use diamond-anvil-cell technologies at third-generation synchrotron radiation sources. In addition to the exploration of the athermal emergence and evolution of antiferromagnetism discussed here, these techniques can be applied to the study of the pressure evolution of weak charge order such as charge-density waves, antiferro-type orbital order, the charge anisotropic tensor susceptibility and charge superlattices associated with either primary spin order or softened phonons.

Solid solution compounds along the Li 1– x Na x FeGe 2 O 6 clinopyroxene series have been prepared by solid state ceramic sintering and investigated by bulk magnetic and calorimetric methods; the Na-rich samples with x (Na) > 0.7 were also investigated by low-temperature neutron diffraction experiments in a temperature range of 4–20 K. For samples with x (Na) > 0.76 the crystal structure adopts the C 2/ c symmetry at all measuring temperatures, while the samples display P 2 1 / c symmetry for smaller Na contents. Magnetic ordering is observed for all samples below 20 K with a slight decrease of T N with increasing Na content. The magnetic spin structures change distinctly as a function of chemical composition: up to x (Na) = 0.72 the magnetic structure can be described by a commensurate arrangement of magnetic spins with propagation vector k  = (½, 0 0), an antiferromagnetic (AFM) coupling within the Fe 3+ O 6 octahedra zig-zag chains and an alternating AFM and ferromagnetic (FM) interaction between the chains, depending on the nature of the tetrahedral GeO 4 chains. The magnetic structure can be described in magnetic space group P a 2 1 / c . Close to the structural phase transition for sample with x (Na) = 0.75, magnetic ordering is observed below 15 K; however, it becomes incommensurately modulated with k  = (0.344, 0, 0.063). At 4 K, the magnetic spin structure best can be described by a cycloidal arrangement within the M1 chains, the spins are within the a – c plane. Around 12 K the cycloidal structure transforms to a spin density wave (SDW) structure. For the C 2/ c structures, a coexistence of a simple collinear and an incommensurately modulated structure is observed down to lowest temperatures. For 0.78 ≤ x (Na) ≤ 0.82, a collinear magnetic structure with k  = (0 1 0), space group P C 2 1 / c and an AFM spin structure within the M1 chains and an FM one between the spins is dominating, while the incommensurately modulated structure becomes dominating the collinear one in the samples with x (Na) = 0.88. Here the magnetic propagation vector is k  = (0.28, 1, 0.07) and the spin structure corresponds again to a cycloidal structure within the M1 chains. As for the other samples, a transition from the cycloidal to a SDW structure is observed. Based on the neutron diffraction data, the appearance of two peaks in the heat capacity of Na-rich samples can now be interpreted as a transition from a cycloidal magnetic structure to a spin density wave structure of the magnetically ordered phase for the Na-rich part of the solid solution series.

The Hubbard model is widely believed to contain the essential ingredients of high-temperature superconductivity. However, proving definitively that the model supports superconductivity is challenging. Here, we report a large-scale density matrix renormalization group study of the lightly doped Hubbard model on four-leg cylinders at hole doping concentration δ = 12.5%. We reveal a delicate interplay between superconductivity and charge density wave and spin density wave orders tunable via next-nearest neighbor hopping t′. For finite t′, the ground state is consistent with a Luther-Emery liquid with power-law superconducting and charge density wave correlations associated with half-filled charge stripes. In contrast, for t′ = 0, superconducting correlations fall off exponentially, whereas charge density and spin density modulations are dominant. Our results indicate that a route to robust long-range superconductivity involves destabilizing insulating charge stripes in the doped Hubbard model.