Spin Density Wave State Research Articles

Superconductivity and spin density wave in AA stacked bilayer graphene

This work theoretically analyzes electronic ordering in AA-stacked bilayer graphene and the role of the Coulomb interaction in these many-body phenomena. Using the random phase approximation to account for screening, we find intra-layer effective interactions to be much stronger than inter-layer interactions; under certain circumstances, the latter may also become attractive. At zero doping, the Coulomb repulsion stabilizes the spin-density wave state, with a Néel temperature in the tens of Kelvin. While dominant in the undoped system, the spin-density wave is destroyed by sufficiently strong doping and a superconducting phase emerges. We find that the effective Coulomb inter-layer interaction can give rise to superconductivity. However, the corresponding critical temperature is negligibly small, and phonon-mediated attraction must be introduced to observe it. Strong intra-layer repulsion suppresses order parameters that couple two intra-layer electrons. We point out a possible superconducting state with finite Cooper pair momentum.

Stark Many-Body Localization in Interacting Infinite Dimensional Systems.

We study bulk particle transport in a Fermi-Hubbard model on an infinite-dimensional Bethe lattice, driven by a constant electric field. Previous numerical studies showed that one dimensional analogs of this system exhibit a breakdown of diffusion due to Stark many-body localization at least up to time that scales exponentially with the system size. Here, we consider systems initially in a spin density wave state using a combination of numerically exact and approximate techniques. We show that for sufficiently weak electric fields, the wave's momentum component decays exponentially with time in a way consistent with normal diffusion. By studying different wavelengths, we extract the dynamical exponent and the generalized diffusion coefficient at each field strength. Interestingly, we find a nonmonotonic dependence of the dynamical exponent on the electric field. As the field increases toward a critical value proportional to the Hubbard interaction strength, transport slows down, becoming subdiffusive. At large interaction strengths, however, transport speeds up again with increasing field, exhibiting superdiffusive characteristics when the electric field is comparable to the interaction strength. Eventually, at the large field limit, localization occurs and the current through the system is suppressed.

Incommensurate Spin Density Wave in Antiferromagnetic RuO_{2} Evinced by Abnormal Spin Splitting Torque.

Since the discovery of antiferromagnetism, metallic oxide RuO_{2} has exhibited numerous intriguing spintronics properties such as the anomalous Hall effect and anisotropic spin splitting effect. However, the microscopic origin of its antiferromagnetism remains unclear. By investigating the spin splitting torque in RuO_{2}/Py, we found that metallic RuO_{2} exhibits a spatially periodic spin structure which interacts with the spin waves in Py through interfacial exchange coupling. The wavelength of such structure is evaluated within 14-20nm depending on the temperature, which is evidence of an incommensurate spin density wave state in RuO_{2}. Our work not only provides a dynamics approach to characterize the antiferromagnetic ordering in RuO_{2}, but also offers fundamental insights into the spin current generation due to anisotropic spin splitting effect associated with spin density wave.

On the Size of Superconducting Islands on the Density-Wave Background in Organic Metals

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.

Multi- k magnetic structure and large anomalous Hall effect in candidate magnetic Weyl semimetal NdAlGe

The magnetic structure, magnetoresistance (MR), and Hall effect of the noncentrosymmetric magnetic semimetal NdAlGe are investigated, revealing an unusual magnetic state and anomalous transport properties that are associated with the electronic structure of this compound. The magnetization and MR measurements are both highly anisotropic and indicate an Ising-like magnetic system. The magnetic structure is complex in that it involves two magnetic ordering vectors, including an incommensurate spin density wave and commensurate ferrimagnetic state in zero field. We have discovered a large anomalous Hall conductivity that reaches $\ensuremath{\approx}430\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.28em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, implying that it originates from an intrinsic Berry curvature effect stemming from Weyl nodes found in the electronic structure. These electronic structure calculations indicate the presence of nested Fermi surface pockets with nesting wave vectors like the measured magnetic ordering wave vector and the presence of Weyl nodes in proximity to the Fermi surface. We associate the incommensurate magnetic structure with the large anomalous Hall response to be the result of the combination of Fermi surface nesting and the Berry curvature associated with Weyl nodes.

Semimetallic spin-density wave state in iron pnictides

We examine the existence of semimetallic spin-density wave (SDW) states in iron pnictides. In the experimentally observed metallic SDW state, the symmetry-protected Dirac cones are located away from the Fermi surface giving rise to tiny pockets and there are also additional Fermi pockets such as one around Γ. We find that the location of a pair of Dirac points with respect to the Fermi surface exhibits significant sensitivity to the orbital splitting between the d xz and d yz orbitals. Besides, in the presence of orbital splitting, the Fermi pockets not associated with the Dirac cones, can be suppressed so that a semimetallic SDW state can be realized. We explain these findings in terms of difference in the slopes and orbital contents of the bands which form the Dirac cone, and obtain the necessary conditions dependent on these two and other parameters for the coexisting Dirac semimetallic and SDW states. Additionally, the topologically protected edge states are studied in the ribbon geometry when the same are oriented either along x or y axes.

Magnetic field induced deformation of the spin density wave microphases in Ca3Co2O6

The frustrated triangular Ising magnet Ca$_3$Co$_2$O$_6$ has long been known for an intriguing combination of extremely slow spin dynamics and peculiar magnetic orders, such as the evenly-spaced non-equilibrium metamagnetic magnetization steps and the long-wavelength spin density wave (SDW) order, the latter of which is essentially an emergent crystal of solitons. Recently, an elaborate field-cooling protocol to bypass the low-field SDW phase was proposed to overcome the extraordinarily long timescale of spin relaxation that impeded previous experimental studies in equilibrium, which may point to a deep connection between the low-temperature slow relaxation and the cooling process passing through the low-field SDW phase. As the first step to elucidate the conjectured connection, we investigate the magnetic field-induced deformation of the SDW state and incommensurate-commensurate transitions, thereby mapping out the equilibrium in-field phase diagram for a realistic three-dimensional lattice spin model by using Monte Carlo simulations. We also discuss Ginzburg-Landau theory that includes several Umklapp terms as well as an effective sine-Gordon model, which can qualitatively explain the observed magnetic field-induced deformation of the SDW microphases.

Enhanced charge density wave with mobile superconducting vortices in La1.885Sr0.115CuO4

Superconductivity in the cuprates is found to be intertwined with charge and spin density waves. Determining the interactions between the different types of order is crucial for understanding these important materials. Here, we elucidate the role of the charge density wave (CDW) in the prototypical cuprate La1.885Sr0.115CuO4, by studying the effects of large magnetic fields (H) up to 24 Tesla. At low temperatures (T), the observed CDW peaks reveal two distinct regions in the material: a majority phase with short-range CDW coexisting with superconductivity, and a minority phase with longer-range CDW coexisting with static spin density wave (SDW). With increasing magnetic field, the CDW first grows smoothly in a manner similar to the SDW. However, at high fields we discover a sudden increase in the CDW amplitude upon entering the vortex-liquid state. Our results signify strong coupling of the CDW to mobile superconducting vortices and link enhanced CDW amplitude with local superconducting pairing across the H − T phase diagram.

Functional renormalization group study of the two-dimensional Su-Schrieffer-Heeger-Hubbard model

We study the Hubbard model on the square lattice coupled in addition to the optical Su-Schrieffer-Heeger (SSH) phonons, using the singular-mode functional renormalization group method. At half-filling and in the absence of the Hubbard interaction $U$, we find the degenerate spin-density-wave (SDW)/charge-density-wave (CDW)/s-wave superconductivity (sSC) state at smaller electron-phonon coupling strength $\lambda$ and higher phonon frequency $\omega$, and the valence bond solid (VBS) state at larger $\lambda$ and lower $\omega$. After switching on a positive $U$, the VBS state is suppressed, while the SDW state is enhanced. At finite doping, the SSH phonon is found to favor sSC at $U=0$. With increasing positive $U$, we find d-wave superconductivity (dSC) and incommensurate SDW states. In a narrow window of moderate $U$ and $\lambda$, we also find the incommensurate VBS state. The sSC and dSC here can be naturally related to the CDW and SDW fluctuations, both of which can be triggered by the SSH phonons. In contrast, the repulsive interaction $U$ enhances SDW but suppresses CDW fluctuations. Our results at half filling are consistent with quantum Monte Carlo (QMC), and provide insights at finite doping where QMC may suffer from the minus sign problem.

Spin-density-wave order controlled by uniaxial stress in CeAuSb2

The tetragonal heavy fermion compound CeAuSb$_2$ (space group $P4/nmm$) exhibits incommensurate spin density wave (SDW) order below $T_{N}\approx6.5~K$ with the propagation vector $\mathbf{q}_A = (\delta_A,\delta_A,1/2)$. The application uniaxial stress along the [010] direction induces a sudden change in the resistivity ratio $\rho_a/\rho_b$ at a compressive strain of $\epsilon \approx -0.5$\%. Here we use neutron scattering to show that the uniaxial stress induces a first-order transition to a SDW state with a different propagation vector $(0,\delta_B,1/2)$ with $\delta_B=0.25$. The magnetic structure of the new (B) phase consists of Ce layers with ordered moments alternating with layers with zero moment stacked along the $c$-axis. The ordered layers have an up-up-down-down configuration along the $b$-axis. This is an unusual situation in which the loss of spatial inversion is driven by itinerant magnetic order. We argue that the change in SDW wavevector leads to a concomitant Fermi surface reconstruction, similar to other materials where a SDW can be controlled by uniaxial stress or magnetic field such as Sr$_3$Ru$_2$O$_7$.

Antiferromagnetic chromium thin films as piezoresistive sensor materials

Sputter-deposited thin films of pure chromium and of chromium with small amounts of nitrogen are characterized regarding their electrical resistivity and strain dependence, i.e., piezoresistivity. They show a temperature dependent piezoresistive effect with gauge factors ranging approximately from 10 to 20. Related to this effect, they exhibit signs of a paramagnetic–antiferromagnetic transition at temperatures of 420 K and higher. For characterization, resistivity is measured at different strain levels: in a bending setup with a fixed radius and in a four-point bending system with reference strain gauges. Several parameter series of the sputter deposition of pure Cr films show that the higher gauge factor is correlated to a higher temperature coefficient of resistivity (TCR). The addition of nitrogen extends the range of TCR toward negative values, with gauge factors still in the same range as pure Cr. A Cr–N strain gauge is characterized and shows a linear, low-hysteresis strain–resistivity effect as well as a relatively large transverse sensitivity. Resistivity and gauge factor of one Cr and one Cr–N sample are measured from room temperature up to 600 K. These films have a resistivity anomaly indicating an antiferromagnetic ordering temperature TN that is much higher than in bulk Cr. The gauge factor has a maximum near TN and falls to small values at higher temperatures. The results indicate that the piezoresistivity of Cr and Cr-rich films is coupled to their spin-density wave (SDW) antiferromagnetism. Since the SDW state is known to be tunable through alloying, internal stress, and crystallinity, it appears that piezoresistivity can be influenced by these parameters as well.

Incommensurate spin density wave and magnetocaloric effect in the metallic triangular lattice HoAl2Ge2

We report the magnetic structure and the magnetocaloric effect (MCE) of the ternary compound $\mathrm{Ho}{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ with a trigonal ${\mathrm{CaAl}}_{2}{\mathrm{Si}}_{2}$-type crystal structure. A neutron powder diffraction experiment reveals that $\mathrm{Ho}{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ exhibits an incommensurate spin density wave (SDW) with a propagation vector $\mathbit{k}=(0.23,\phantom{\rule{0.28em}{0ex}}0,\phantom{\rule{0.28em}{0ex}}0.06)$. The special arrangement of magnetic moments in $\mathrm{Ho}{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ induces interesting physical phenomena and large magnetocaloric effects. The rise in resistivity at low temperatures indicates the effect of the SDW state in the electronic transport. The maximum magnetic-entropy change is $\ensuremath{-}16.1\phantom{\rule{0.16em}{0ex}}\mathrm{J}/\mathrm{kg}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ under a magnetic field change of 0--70 kOe for an isotropic $\mathrm{Ho}{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ powder and it increases to $\ensuremath{-}17.9\phantom{\rule{0.16em}{0ex}}\mathrm{J}/\mathrm{kg}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for a single crystal when the magnetic field ($H$) is applied parallel to the $ab$ plane. A large rotating magnetic-entropy change of $\ensuremath{-}5.1\phantom{\rule{0.16em}{0ex}}\mathrm{J}/\mathrm{kg}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for $H=20\phantom{\rule{0.16em}{0ex}}\mathrm{kOe}$ in a $\mathrm{Ho}{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ single crystal is obtained, which is closely associated to the magnetic anisotropy of the SDW order and its response to the external magnetic field. We discuss the large MCE in terms of the field-induced metamagnetic transition from the incommensurate SDW order to the ferromagnetic order. Our study establishes the triangular lattice $R{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ ($R$ = rare-earth elements) as a unique family of compounds to explore the existence of the incommensurate spin density waves and the correlated physical properties.

Evaluating Second-Order Phase Transitions with Diagrammatic Monte Carlo: Néel Transition in the Doped Three-Dimensional Hubbard Model

Diagrammatic MonteCarlo-the technique for the numerically exact summation of all Feynman diagrams to high orders-offers a unique unbiased probe of continuous phase transitions. Being formulated directly in the thermodynamic limit, the diagrammatic series is bound to diverge and is not resummable at the transition due to the nonanalyticity of physical observables. This enables the detection of the transition with controlled error bars from an analysis of the series coefficients alone, avoiding the challenge of evaluating physical observables near the transition. We demonstrate this technique by the example of the Néel transition in the 3D Hubbard model. At half filling and higher temperatures, the method matches the accuracy of state-of-the-art finite-size techniques, but surpasses it at low temperatures and allows us to map the phase diagram in the doped regime, where finite-size techniques struggle from the fermion sign problem. At low temperatures and sufficient doping, the transition to an incommensurate spin density wave state is observed.

Spin Density Wave versus Fractional Magnetization Plateau in a Triangular Antiferromagnet.

We report an excellent realization of the highly nonclassical incommensurate spin-density wave (SDW) state in the quantum frustrated antiferromagnetic insulator Cs_{2}CoBr_{4}. In contrast to the well-known Ising spin chain case, here the SDW is stabilized by virtue of competing planar in-chain anisotropies and frustrated interchain exchange. Adjacent to the SDW phase is a broad m=1/3 magnetization plateau that can be seen as a commensurate locking of the SDW state into the up-up-down (UUD) spin structure. This represents the first example of the long-sought SDW-UUD transition in triangular-type quantum magnets.

Topological Phases in AB-Stacked MoTe_{2}/WSe_{2}: Z_{2} Topological Insulators, Chern Insulators, and Topological Charge Density Waves.

We present a theory on the quantum phase diagram of AB-stacked MoTe_{2}/WSe_{2} using a self-consistent Hartree-Fock calculation performed in the plane-wave basis, motivated by the observation of topological states in this system. At filling factor ν=2 (two holes per moiré unit cell), Coulomb interaction can stabilize a Z_{2} topological insulator by opening a charge gap. At ν=1, the interaction induces three classes of competing states, spin density wave states, an in-plane ferromagnetic state, and a valley polarized state, which undergo first-order phase transitions tuned by an out-of-plane displacement field. The valley polarized state becomes a Chern insulator for certain displacement fields. Moreover, we predict a topological charge density wave forming a honeycomb lattice with ferromagnetism at ν=2/3. Future directions on this versatile system hosting a rich set of quantum phases are discussed.

Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle twisted bilayer graphene

Starting from a realistic extended Hubbard model for a ${p}_{x,y}$-orbital tight-binding model on the Honeycomb lattice, we perform a thorough investigation of the possible electron instabilities in magic-angle twisted bilayer graphene near the van Hove (VH) dopings. Here we focus on the interplay between the two symmetries of the system. One is the approximate $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry which leads to the degeneracy between the intervalley spin density wave (SDW) and valley density wave (VDW) as well as that between the intervalley singlet and triplet superconductivities (SCs). The other is the ${D}_{3}$ symmetry which leads to the degeneracy among the three symmetry-related wave vectors of the density-wave (DW) orders, originating from the Fermi-surface nesting. The interplay between these two degeneracies leads to intriguing quantum states relevant to recent experiments, as revealed by our systematic random-phase-approximation based calculations followed by a succeeding mean-field energy minimization for the groundstate energy. At the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetric point, the degenerate intervalley SDW and VDW are mixed into a new state of matter dubbed as the chiral SO(4) spin-valley DW. This state simultaneously hosts three four-component vectorial spin-valley DW orders with each adopting one wave vector, and the polarization directions of the three DW orders are mutually perpendicular to one another. In the presence of a tiny intervalley exchange interaction with coefficient ${J}_{H}\ensuremath{\rightarrow}{0}^{\ensuremath{-}}$ which breaks the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry, a pure chiral SDW state is obtained. In the case of ${J}_{H}\ensuremath{\rightarrow}{0}^{+}$, although a nematic VDW order is favored, the two SDW orders with equal amplitudes are accompanied simultaneously. This nematic $\mathrm{VDW}+\mathrm{SDW}$ state possesses a stripy distribution of the charge density, consistent with the recent STM observations. On the aspect of SC, while the triplet $p+ip$ and singlet $d+id$ topological SCs are degenerate at ${J}_{H}=0$ near the VH dopings, the former (latter) is favored for ${J}_{H}\ensuremath{\rightarrow}{0}^{\ensuremath{-}}$ (${J}_{H}\ensuremath{\rightarrow}{0}^{+}$). In addition, the two asymmetric doping-dependent behaviors of the obtained pairing phase diagram are well consistent with experiments.

Hund’s coupling and electronic anisotropy in the spin-density wave state of iron pnictides

In the multiband systems, Hund’s coupling (J) plays a significant role in the spin and charge excitations. We study the dependence of electronic anisotropy on J in terms of Drude weight along different directions as well as the orbital order in the four-fold symmetry broken spin-density wave state of iron pnictides. A robust behavior of the Drude-weight anisotropy within a small window around J∼0.25U with U as intraorbital Coulomb interaction is described in terms of orbital-weight distribution along the reconstructed Fermi surfaces. We also find that the ferro-orbital order increases with J in the widely accepted regime for the latter, which is explained as a consequence of rising exchange field with an increase in magnetization.

Pressure-induced superconductivity in lightly doped RFeAsO1-xFx (R=Sm and Nd)

We performed the measurements of electrical resistivity (ρ) and dc magnetization (M) as a function of temperature (T) under pressure to investigate whether or not the superconductivity is induced by the application of pressure in lightly doped RFeAsO1-xFx (R=Sm and Nd) using pulse current sintered (PCS) high density polycrystalline specimens. We have successfully observed pressure induced superconductivity with T c of ∼6 K (∼8 K) above ∼4 GPa (∼1 GPa) for R=Sm (R=Nd). An anomaly corresponding to a magnetic phase transition into spin density wave (SDW) state was observed in the ρ(T) curves in the entire pressure range, indicating that the superconducting and SDW states coexist in the T-P phase diagram. Volume fraction of the superconductivity is found to be very small. This is consistent with the coexistence of the superconducting and SDW phases.

High-Harmonic Generation Approaching the Quantum Critical Point of Strongly Correlated Systems.

By employing the exact diagonalization method, we investigate the high-harmonic generation (HHG) of the correlated systems under the strong laser irradiation. For the extended Hubbard model on a periodic chain, HHG close to the quantum critical point (QCP) is more significant compared to two neighboring gapped phases (i.e., charge-density-wave and spin-density wave states), especially in low frequencies. We confirm that the systems in the vicinity of the QCP are supersensitive to the external field and more optical-transition channels via excited states are responsible for HHG. This feature holds the potential of obtaining high-efficiency harmonics by making use of materials approaching QCP. Based on the two-dimensional Haldane model, we further propose that the even- or odd-order components of generated harmonics can be promisingly regarded as spectral signals to distinguish the topologically ordered phases from locally ordered ones. Our findings in this Letter pave the way to achieve ultrafast light source from HHG in strongly correlated materials and to study quantum phase transition by nonlinear optics in strong laser fields.

Real-space observation of incommensurate spin density wave and coexisting charge density wave on Cr (001) surface

In itinerant magnetic systems, a spin density wave (SDW) state can be induced by Fermi surface nesting and electron-electron interaction. It may intertwine with other orders such as charge density wave (CDW), while their relation is still yet to be understood. Here via spin-polarized scanning tunneling microscopy, we directly observed long-range spin modulation on Cr(001) surface, which corresponds to the well-known incommensurate SDW of bulk Cr. It displays 6.0 nm in-plane period and anti-phase behavior between adjacent (001) planes. Meanwhile, we simultaneously observed the coexisting CDW with half the period of SDW. Such SDW/CDW have highly correlated domain structures and are in-phase. Surprisingly, the CDW displays a contrast inversion around a density-of-states dip at −22 meV, indicating an anomalous CDW gap opened below EF. These observations support that the CDW is a secondary order driven by SDW. Our work is not only a real-space characterization of incommensurate SDW, but also provides insights on how SDW and CDW coexist.