Spin Density Wave Research Articles

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.

Origin of the Efficient Nonlinear Optical Response of Two-Dimensional Layered CuFeTe2 Nanosheets.

Two-dimensional ternary transition metal chalcogenides (TMCs) have aroused great research interest owing to outstanding semiconducting properties and diverse magnetic response. CuFeTe2, as a typical TMC, exhibits ambiguous magnetic behavior and ground state of spin density waves nature. Herein, we first report efficient nonlinear absorption and superior nonlinear refraction of CuFeTe2 nanosheets. The nonlinear absorption and refraction coefficients reach -0.22 cm/GW and -1.66 × 10-12 cm2/W, respectively. Semiempirical theory for direct bandgap semiconductors was applied to estimate the nonlinearities of CuFeTe2 nanosheets. The calculation results indicate that the efficient nonlinearities stem from the free carrier induced band filling effect.

Magnetotransport of thin film topological insulators in proximity with helical spin density wave

The magnetoconductivity of an ultrathin film of topological insulator in proximity with helical spin density wave is calculated. Pronounced Weiss oscillations periodic in the inverse magnetic field appear for upper and bottom surfaces. With finite Zeeman coupling and hybridization across the surfaces Weiss oscillations for the top surface are more pronounced than the bottom surface. However in the absence of Zeeman coupling both the surfaces show same magnitude of oscillations.

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.

Latent superconductivity at parallel interfaces in a superlattice dominated by another collective quantum phase

We theoretically examine behavior of superconductivity at parallel interfaces separating the domains of another dominant collective excitation, such as charge density waves or spin density waves. Due to their competitive coupling in a two-component Ginzburg-Landau model, suppression of the dominant order parameter at the interfacial planes allows for nucleation of the (hidden) superconducting order parameter at those planes. In such a case, we demonstrate how the number of the parallel interfacial planes and the distance between them are linked to the number and the size of the emerging superconducting gaps in the system, as well as the versatility and temperature evolution of the possible superconducting phases. These findings bear relevance to a broad selection of known layered superconducting materials, as well as to further design of artificial (e.g., oxide) superlattices, where the interplay between competing order parameters paves the way towards otherwise unattainable superconducting states, some with enhanced superconducting critical temperature.

Ising and XY paramagnons in two-dimensional 2H−NbSe2

Paramagnons are the collective modes that govern the spin response of nearly magnetic conductors. In some cases they mediate electron pairing leading to superconductivity. This scenario may occur in 2H-NbSe$_2$ monolayers, that feature spin-valley coupling on account of spin-orbit interactions and their lack of inversion symmetry. Here we explore spin anisotropy of paramagnons both for non-centrosymmetric Kane-Mele-Hubbard models for 2H-NbSe$_2$ monolayers described with a DFT-derived tight-binding model. In the infinite wavelength limit we find spatially uniform paramagnons with energies around $1$~meV that feature a colossal off-plane uniaxial magnetic anisotropy, with quenched transversal spin response. At finite wave vectors, longitudinal and transverse channels reverse roles: XY fluctuations dominate within a significant portion of the Brillouin zone. Our results show that 2H-NbSe$_2$ is close to a Coulomb-driven in-plane (XY) spin density wave instability.

A brief review of the physical properties of charge density wave superconductor LaPt2Si2

The study of materials with multiple phases, such as superconductivity (SC) coexisting with charge density wave (CDW) or spin density wave (SDW) instability, attracts considerable interest from the condensed matter research community. The CDW superconductors started drawing in heaps of attention soon after the discovery of CDW instability in high-T c cuprates, where understanding the underlying superconducting mechanism of the latter may turn out to be path-breaking for the discovery of room temperature SC. Understanding the pairing mechanism of high-T c superconductors necessitates less complex systems and this makes searching for CDW superconductors all the more important. Such systems avoid the additional complexity in contrast to the well-sought after Fe-based superconductors, which show more competing orders like SDW, nematicity and SC. RPt2Si2 (R = La, Pr, Eu) is a recently discovered series of materials, members of which crystallizes in CaBe2Ge2 type structure which has a close resemblance to the ThCr2Si2 type structure commonly found in pnictide-122 superconductors. This review is focused on LaPt2Si2, which undergoes a structural transition from high-temperature tetragonal to low-temperature orthorhombic structure, accompanied by a CDW transition around 112 K, which is then followed by a superconducting transition below 1.8 K. We discuss the physical properties of single crystal and polycrystalline LaPt2Si2 samples. Additionally, we present the results of transport and ac susceptibility measurements under external hydrostatic pressure to map out the temperature-pressure phase diagram of LaPt2Si2.

Multiple magnetic orders in LaFeAs1-xPxO uncover universality of iron-pnictide superconductors

The iron-pnictide superconductors have generated tremendous excitement as the competition between magnetism and superconductivity has allowed unique in-roads towards elucidating a microscopic theory of unconventional high-temperature superconductivity. In addition to the stripe spin density wave ({C}_{2M}^{a}) phase observed in the parent compounds of all iron-pnictide superconductors, two novel magnetic orders have recently been discovered in different parent structures: an out-of-plane collinear double-Q ({C}_{4M}^{c}) structure in the hole-doped (Ca, Sr, Ba)1-x(Na)xFe2As2 and Ba1-xKxFe2As2 families, and a spin vortex crystal “hedgehog” ({C}_{4M}^{{ab}}) structure in the CaKFe4As4 family. Using neutron diffraction, we demonstrate that LaFeAs1-xPxO contains all three magnetic orders within a single-phase diagram as a function of substitution, all of which compete strongly with superconductivity. Our experimental observations combined with theoretical modeling demonstrate how the reduction in electronic correlations by chemical substitution results in larger Fermi surfaces and the sequential stabilization of multiple magnetic anisotropies. Our work presents a unified narrative for the competing magnetic and superconducting phases observed in various iron-pnictide systems with different crystal structures and chemistry.

Phase degree of freedom and topology in multiple- Q spin textures

A periodic array of topological spin textures, such as skyrmions and hedgehogs, is called the multiple-$Q$ spin texture, as it is represented by a superposition of multiple spin density waves. Depending on the way of superposition, not only the magnetic but also the topological properties are modified, leading to a variety of quantum transport and optical phenomena caused by the emergent electromagnetic fields through the Berry phase. Among others, the phase degree of freedom of the superposed waves is potentially important for such modifications, but its effect has not been fully elucidated thus far. Here we perform systematic theoretical analyses of magnetic and topological properties of the multiple-$Q$ spin textures with the phase degree of freedom. By introducing a hyperspace with an additional dimension corresponding to the phase degree of freedom, we establish a generic framework to deal with the phase shift in the multiple-$Q$ spin textures. Applying the framework to the two-dimensional 3$Q$ spin textures, we clarify the complete topological phase diagram while changing the phase and magnetization, which depends on the types of the superposed waves. We also study the three-dimensional 4$Q$ spin textures and clarify even richer topological phase diagrams. In particular, we find novel topological phase transitions associated with the previously unidentified Dirac strings on which the hedgehogs and antihedgehogs cause pair creation and fusion. Moreover, we demonstrate that phase shifts are caused by an external magnetic field in both 3$Q$ and 4$Q$ cases by analyzing the numerical data in the previous studies. Our results illuminate the topological aspects of the skyrmion and hedgehog lattices with the phase degree of freedom, which would be extended to other multiple-$Q$ textures and useful for the exploration of topologically nontrivial magnetic phases and exotic quantum phenomena.

Impurity bands in magnetic superconductors with spin density wave

Magnetic superconductors define a broad class of strongly correlated materials in which superconductivity may coexist with either localized or itinerant long-range magnetic order. In this work we consider a multiband model of a disordered magnetic superconductor which realizes coexistence of unconventional superconductivity and a spin-density-wave. We derive an exact T-matrix and compute a single particle density of states in this system. In a purely superconducting state the interband scattering potential leads to an appearance of the localized Yu–Shiba–Rusinov bound states. Our main finding is that in the fairly broad swath of the coexistence region superconductivity remains fully gapped despite the presence of the impurity bands. We also discuss the effects of spatial inhomogeneities on the density of states in strongly contaminated superconductors.

Theoretical Model Study of Low-Energy Spin Excitations in Iron Chalcogenide AxFe2−xSe2: One Band Approach

In this paper, we propose a one band tight binding model Hamiltonian for the newly discovered 122-type Selenide family of the iron-based system incorporated with the nearest-neighbor (NN) and the next-nearest-neighbor (NNN) hopping integrals [Formula: see text] and [Formula: see text], respectively. The spin–spin interactions of the electrons leading to the antiferromagnetic spin density wave (SDW) order have been studied at wave vector [Formula: see text]. The electron Green’s functions are calculated from the Hamiltonian model using Green’s function technique and finally the SDW gap equation is derived and studied using their NN and NNN spin coupling [Formula: see text] and [Formula: see text], respectively.

Field-induced quantum critical point in the itinerant antiferromagnet Ti3Cu4

New phases of matter emerge at the edge of magnetic instabilities, which can occur in materials with moments that are localized, itinerant or intermediate between these extremes. In local moment systems, such as heavy fermions, the magnetism can be tuned towards a zero-temperature transition at a quantum critical point (QCP) via pressure, chemical doping, and, rarely, magnetic field. By contrast, in itinerant moment systems, QCPs are more rare, and they are induced by pressure or doping; there are no known examples of field induced transitions. This means that no universal behaviour has been established across the whole itinerant-to-local moment range—a substantial gap in our knowledge of quantum criticality. Here we report an itinerant antiferromagnet, Ti3Cu4, that can be tuned to a QCP by a small magnetic field. We see signatures of quantum criticality and the associated non-Fermi liquid behaviour in thermodynamic and transport measurements, while band structure calculations point to an orbital-selective, spin density wave ground state, a consequence of the square net structural motif in Ti3Cu4. Ti3Cu4 thus provides a platform for the comparison and generalisation of quantum critical behaviour across the whole spectrum of magnetism.

Phonon-assisted formation of an itinerant electronic density wave

Electronic instabilities drive ordering transitions in condensed matter. Despite many advances in the microscopic understanding of the ordered states, a more nuanced and profound question often remains unanswered: how do the collective excitations influence the electronic order formation? Here, we experimentally show that a phonon affects the spin density wave (SDW) formation after an SDW-quench by femtosecond laser pulses. In a thin film, the temperature-dependent SDW period is quantized, allowing us to track the out-of-equilibrium formation path of the SDW precisely. By exploiting its persistent coupling to the lattice, we probe the SDW through the transient lattice distortion, measured by femtosecond X-ray diffraction. We find that within 500 femtoseconds after a complete quench, the SDW forms with the low-temperature period, directly bypassing a thermal state with the high-temperature period. We argue that a wavevector-matched phonon launched by the quench changes the formation path of the SDW through the dynamic pinning of the order parameter.

Emergent Multifunctional Magnetic Proximity in van der Waals Layered Heterostructures.

Proximity effect, which is the coupling between distinct order parameters across interfaces of heterostructures, has attracted immense interest owing to the customizable multifunctionalities of diverse 3D materials. This facilitates various physical phenomena, such as spin order, charge transfer, spin torque, spin density wave, spin current, skyrmions, and Majorana fermions. These exotic physics play important roles for future spintronic applications. Nevertheless, several fundamental challenges remain for effective applications: unavoidable disorder and lattice mismatch limits in the growth process, short characteristic length of proximity, magnetic fluctuation in ultrathin films, and relatively weak spin–orbit coupling (SOC). Meanwhile, the extensive library of atomically thin, 2D van der Waals (vdW) layered materials, with unique characteristics such as strong SOC, magnetic anisotropy, and ultraclean surfaces, offers many opportunities to tailor versatile and more effective functionalities through proximity effects. Here, this paper focuses on magnetic proximity, i.e., proximitized magnetism and reviews the engineering of magnetism‐related functionalities in 2D vdW layered heterostructures for next‐generation electronic and spintronic devices. The essential factors of magnetism and interfacial engineering induced by magnetic layers are studied. The current limitations and future challenges associated with magnetic proximity‐related physics phenomena in 2D heterostructures are further discussed.

Magnetic field–temperature phase diagrams for multiple- Q magnetic ordering: Exact steepest descent approach to long-range interacting spin systems

Multiple-$Q$ magnetic orderings represent magnetic textures composed of superpositions of multiple spin density waves or spin spirals, as represented by skyrmion crystals and hedgehog lattices. Such magnetic orderings have been observed in various magnetic materials in recent years, and attracted enormous attention, especially from the viewpoint of topology and emergent electromagnetic fields originating from noncoplanar magnetic structures. Although they often exhibit successive phase transitions among different multiple-$Q$ states while changing temperature and an external magnetic field, it is not straightforward to elucidate the phase diagrams, mainly due to the lack of concise theoretical tools as well as appropriate microscopic models. Here, we provide a theoretical framework for a class of effective spin models with long-range magnetic interactions mediated by conduction electrons in magnetic metals. Our framework is based on the steepest descent method with a set of self-consistent equations that leads to exact solutions in the thermodynamic limit, and has many advantages over existing methods such as biased variational calculations and numerical Monte Carlo simulations. Applying the framework to the models with instabilities toward triple- and hextuple-$Q$ magnetic orderings, we find that interesting reentrant phase transitions where the multiple-$Q$ phases appear only at finite temperature and/or nonzero magnetic field. Furthermore, we show that the multiple-$Q$ states can be topologically-nontrivial stacked skyrmion crystals or hedgehog lattices, which exhibit large net spin scalar chirality associated with nonzero skyrmion number. The results demonstrate that our framework could be a versatile tool for studying magnetic and topological phase transitions and related quantum phenomena in actual magnetic metals hosting multiple-$Q$ magnetic orderings.

Evolution of interorbital superconductor to intraorbital spin-density wave in layered ruthenates

The ruthenate family of layered perovskites has been a topic of intense interest, with much work dedicated to the superconducting state of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. Another long-standing puzzle is the lack of superconductivity in its sister compound, ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$, which constrains the possible mechanisms of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. Here we address a microscopic mechanism that unifies the orders in these materials. Beginning from a model of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ featuring interorbital spin-triplet pairing via Hund's and spin-orbit couplings, we find that bilayer coupling alone enhances, while staggered rotations destroy interorbital superconductivity. A magnetic field then shifts van Hove singularities, allowing intraorbital spin-density wave order to form in ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$. Our theory predicts that ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ without staggered rotations exhibits interorbital superconductivity with a possibly higher transition temperature.

Phase driven topological states in correlated Haldane model on a honeycomb lattice

Using mean field method and random phase approximation, we studied the phase driven topological exotic states in correlated Haldane model on a honeycomb lattice. It is found that topological spin density waves emerge with the phase change of next-nearest-neighbor hopping. We also investigated the topological properties of these spin density waves, including Chern number, edge state and Hall conductivity. Our work provides a new insight for topological phase transitions in correlated quantum anomalous Hall insulators.

Quantum Phases of Transition Metal Dichalcogenide Moiré Systems.

Moiré systems provide a rich platform for studies of strong correlation physics. Recent experiments on heterobilayer transition metal dichalcogenide Moiré systems are exciting in that they manifest a relatively simple model system of an extended Hubbard model on a triangular lattice. Inspired by the prospect of the hetero-transition metal dichalcogenide Moiré system's potential as a solid-state-based quantum simulator, we explore the extended Hubbard model on the triangular lattice using the density matrix renormalization group. Specifically, we explore the two-dimensional phase space spanned by the key tuning parameters in the extended Hubbard model, namely, the kinetic energy strength and the further-range Coulomb interaction strengths. We find competition between Fermi fluid, chiral spin liquid, spin density wave, and charge order. In particular, our finding of the optimal further-range interaction for the chiral correlation presents a tantalizing possibility.