Antiferromagnetic Spin Density Wave Research Articles

Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo

A key component of the phase diagram of many iron-based superconductors and electron-doped cuprates is believed to be a quantum critical point (QCP), delineating the onset of antiferromagnetic spin-density wave order in a quasi-two-dimensional metal. The universality class of this QCP is believed to play a fundamental role in the description of the proximate non-Fermi liquid behavior and superconducting phase. A minimal model for this transition is the O(3) spin-fermion model. Despite many efforts, a definitive characterization of its universal properties is still lacking. Here, we numerically study the O(3) spin-fermion model and extract the scaling exponents and functional form of the static and zero-momentum dynamical spin susceptibility. We do this using a Hybrid Monte Carlo (HMC) algorithm with a novel auto-tuning procedure, which allows us to study unprecedentedly large systems of 80 × 80 sites. We find a strong violation of the Hertz-Millis form, contrary to all previous numerical results. Furthermore, the form that we do observe provides good evidence that the universal scaling is actually governed by the analytically tractable fixed point discovered near perfect “hot-spot’" nesting, even for a larger nesting window. Our predictions can be directly tested with neutron scattering. Additionally, the HMC method we introduce is generic and can be used to study other fermionic models of quantum criticality, where there is a strong need to simulate large systems.

Local pairs in high-temperature superconductors: The concept of pseudogap

The origin of the high-temperature superconductivity of cuprates remains a subject of debate after almost four decades of investigation. One of the main questions — what is the physics behind the mechanism of superconducting pairing, which makes it possible to obtain real Cooper pairs at temperatures much higher than 100 K, remains open. It is believed that the answer can be obtained by the studying the properties of cuprates in the normal state above Tc, where the pseudogap (PG) opens at T* >> Tc. The number of papers devoted to the study of PG is extraordinarily large, but its physics also remains in question. In cuprates, the question arises whether the pseudogap phase arises exclusively due to antiferromagnetic fluctuations, spin or charge density waves, or whether it can be explained by the formation below T* of specific paired fermions, the so-called local pairs. We review studies on both approaches to PG that should clarify this issue. In addition to theoretical considerations, we analyze and discuss various experimental results of fluctuation conductivity and PG measurements, as well as magnetic measurements, in an attempt to prove the decisive role of local pairs in the formation of the PG state. Accordingly, various types of supposed magnetic interactions can be considered as possible mechanisms of superconducting pairing in high-temperature 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.

Interplay of mass imbalance and frustration in correlated band insulators

We report the emergence or broadening of exotic magnetic metallic phases upon explicit breaking of $SU(2)$ symmetry by introduction of mass imbalance in a variant of Hubbard model, known as the ionic Hubbard model in the presence of frustration at half-filling on a square lattice. The ionic Hubbard model has in addition to hopping($\sim t$) and onsite coulomb repulsion ($\sim U$), a staggered ionic potential ($\sim \Delta$) which breaks translational symmetry of the underlying lattice. In the low to intermediate ranges of $U$ and $\Delta$, we use unrestricted Hartree-Fock theory to construct the phase diagram in the $U-\Delta$ plane for a fixed mass imbalance($\sim\eta$). Where as in the limit where both $U,\Delta$ are comparable and much larger than the first $(\sim t_{\sigma})$ and second $(\sim t_{\sigma}')$ neighbor hopping amplitudes , we employ the technique of generalized Gutzwiller approximation and subsequently use renormalized mean field theory to construct the phase diagram for varying values of hopping asymmetry. In both cases, starting from a correlated band insulator with weak antiferromagnetic spin density wave order, if we tune $U/\Delta$, we observe the opening of novel magnetically ordered metallic phases such as spin imbalanced ferromagnetic metal, ferrimagnetic metal and antiferromagnetic half metal. We also study singlet superconductivity in the d-wave and extended s-wave channels in the strong coupling limit of this model in the presence of mass imbalance.

Antiferromagnetic chiral spin density wave and strain-induced Chern insulator in the square lattice Hubbard model with frustration

We employ the Hartree-Fock approximation to identify the magnetic ground state of the Hubbard model on a frustrated square lattice. We investigate the phase diagram as a function of the Coulomb repulsion's strength $U$, and the ratio $t'/t$ between the nearest and next nearest neighbor hoppings $t$ and $t'$. At half-filling and for a sufficiently large $U$, an antiferromagnetic chiral spin density wave order with nonzero spin chirality emerges as the ground state in a wide regime of the phase diagram near $t'/t=1/\sqrt{2}$, where the Fermi surface is well-nested for both $(\pi,\pi)$ and $(\pi,0)/(0,\pi)$ wave vectors. This triple-${\bf Q}$ chiral phase is sandwiched by a single-${\bf Q}$ N\'{e}el phase and a double-${\bf Q}$ coplanar spin-vortex crystal phase, at smaller and larger $t'/t$, respectively. The energy spectrum in the chiral spin density wave phase consists of four pairs of degenerate bands. These give rise to two pairs of Dirac cones with the same chirality at the point $({\pi \over 2},{\pi\over 2})$ of the Brillouin zone. We demonstrate that the application of a diagonal strain induces a $d_{xy}$-wave next nearest neighbor hopping which, in turn, opens gaps in the two Dirac cones with opposite masses. As a result, four pairs of well-separated topologically-nontrivial bands emerge, and each pair of those contributes with a Chern number $\pm1$. At half-filling, this leads to a zero total Chern number and renders the topologically-notrivial properties observable only in the ac response regime. Instead, we show that at $3/4$ filling, the triple-${\bf Q}$ chiral phase yields a Chern insulator exhibiting the quantum anomalous Hall effect.

Longitudinal and anomalous Hall conductivity of a general two-band model

We derive and analyze the longitudinal and the anomalous Hall conductivity for a general momentum-block-diagonal two-band model. This model captures a broad spectrum of physically very different systems including N\'eel antiferromagnetic and spiral spin density waves as well as models that involve spin-orbit interaction and are known to show topological properties. We present a complete microscopic derivation for finite temperature and constant scattering rate $\Gamma$ that is diagonal and equal, but arbitrarily large for both bands. We identify two criteria that allow for a unique and physically motivated decomposition of the conductivities. On the one hand, we distinguish intraband and interband contributions that are defined by the involved quasiparticle spectral functions. On the other hand, we distinguish symmetric and antisymmetric contributions that are defined by the symmetry under the exchange of the current and the electric field directions. The (symmetric) intraband contributions generalize the formula of standard Boltzmann transport theory, which is valid only in the clean limit (small $\Gamma$), whereas the interband contributions capture interband coherence effects beyond independent quasiparticles. We show that the symmetric interband contribution is a correction only present for finite $\Gamma$ and is controlled by the quantum metric. The antisymmetric interband contributions generalize the formula of the anomalous Hall conductivity in terms of the Berry curvature to finite $\Gamma$. We study the clean (small $\Gamma$) and dirty (large $\Gamma$) limit analytically. The connection between the presented derivation and the Bastin and Streda formalism is given. We apply our results to a Chern insulator, a ferromagnetic multi-d-orbital, and a spiral spin density wave model.

Charge carrier drop at the onset of pseudogap behavior in the two-dimensional Hubbard model

We show that antiferromagnetic spin-density wave order in the two-dimensional Hubbard model yields a drop of the charge carrier density as observed in recent transport measurements for cuprate superconductors in high magnetic fields upon entering the pseudogap regime. The amplitude and the (generally incommensurate) wave vector of the spin-density wave is obtained from dynamical mean-field theory (DMFT). An extrapolation of the finite temperature results to zero temperature yields an approximately linear doping dependence of the magnetic gap $\Delta(p) \propto p^*-p$ in a broad doping range below the critical doping $p^*$. The magnetic order leads to a Fermi surface reconstruction with electron and hole pockets, where electron pockets exist only in a restricted doping range below $p^*$. DC charge transport properties are computed by combining the renormalized band structure as obtained from the DMFT with a doping-independent phenomenological scattering rate. A pronounced drop of the longitudinal conductivity and the Hall number in a narrow doping range below $p^*$ is obtained.

Iron-based superconductors: tales from the nuclei

High-temperature superconductivity in Fe-based pnictides and chalcogenides has been one of the most significant recent discoveries in condensed matter physics and has attracted remarkable attention in the last decade. These materials are characterized by a complex fermiology and, as a result, feature a wide range of electronic properties as a function of different tuning parameters such as chemical doping, temperature and pressure. Along the path towards the comprehension of the physical mechanisms underlying this rich phenomenology, NMR (nuclear magnetic resonance) and NQR (nuclear quadrupole resonance) have played a role of capital importance that we review in this work. In particular, we address how NMR has contributed to the current understanding of the main regions of the electronic phase diagram of Fe-based pnictides, that is, the -- sometimes coexisting -- antiferromagnetic spin-density wave and superconducting states. We evidence the unique capability of NMR as local-probe technique of investigating the effect of quenched disorder and chemical impurities. Then, we review the NMR signatures of low-frequency fluctuations associated with the development of electronic nematicity as well as with the motion of superconducting flux lines. Finally, we discuss recent contributions of NMR and NQR which evidence an intrinsically inhomogeneous electronic charge distribution as well as an orbitally-selective behaviour.

Correlation between the Hall Resistance and Magnetoresistance in the Mixed State of an Nd2 − xCe x CuO4 + δ Electronic Superconductor

The Hall resistance and the magnetoresistance in the mixed state of the Nd2 − xCe x CuO4 + δ quasi-two-dimensional system near the antiferromagnetic-superconductor (AF-SC) phase transition have been measured at doping levels x = 0.14 and 0.15, and a correlation has been established. This correlation can be analyzed using the following power relationship: ρ xy (B) ~ [ρ xx (B)]β. It was found that index β varied from 0.94 ± 0.03 in the region of AF and SC coexistence (x = 0.14) to 0.6 ± 0.1 in the SC region with the maximum critical temperature (x = 0.15) at low temperatures and weak magnetic fields. This reduction suggests that the symmetry of carrier pairing changes at the boundary of the transition from the phase of antiferromagnetic ordering and spin density waves to the superconducting phase in the presence of antiferromagnetic spin fluctuations.

Antiferromagnetism and competing charge instabilities of electrons in strained graphene from Coulomb interactions

We study the quantum many-body ground states of electrons on the half-filled honeycomb lattice with short- and long-ranged density-density interactions as a model for graphene. To this end, we employ the recently developed truncated-unity functional renormalization group (TU-fRG) approach which allows for a high resolution of the interaction vertex' wavevector dependence. We connect to previous lattice quantum Monte Carlo (QMC) results which predict a stabilization of the semimetallic phase for realistic \emph{ab initio} interaction parameters and confirm that the application of a finite biaxial strain can induce a quantum phase transition towards an ordered ground state. In contrast to lattice QMC simulations, the TU-fRG is not limited in the choice of tight-binding and interaction parameters to avoid the occurrence of a sign problem. Therefore, we also investigate a range of parameters relevant to the realistic graphene material which are not accessible by numerically exact methods. Although a plethora of charge density waves arise under medium-range interactions, we find the antiferromagnetic spin-density wave to be the prevailing instability for long-range interactions. We further explore the impact of an extended tight-binding Hamiltonian with second-nearest neighbor hopping and a finite chemical potential for a more accurate description of the band structure of graphene's $p_z$ electrons.

(Li1−xFex)OHFeSe Superconductors: Crystal Growth, Structure, and Electromagnetic Properties

This review focuses on the growth of high-quality (Li1−xFex)OHFeSe single crystals by a hydrothermal method using floating-zone-grown AxFe2−ySe2 (A = K, Rb, and Cs) as precursors. The structure, superconductivity, and magnetic behavior of the obtained crystals are highly influenced by the growth conditions, such as time, temperature, and composition. A phase diagram with temperature against the c-lattice constant is summarized including the antiferromagnetic spin density wave, superconducting, and paramagnetic phases.

Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional renormalization group calculation with high-wave-vector resolution

We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half-filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional Renormalization Group scheme which allows for highly resolved calculations of wavevector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure $n$-th nearest neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when non-local density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough non-local terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semi-metallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second nearest neighbor interactions is not realized in our results with high momentum resolution.

Electronic instabilities of the extended Hubbard model on the honeycomb lattice from functional renormalization

Interacting fermions on the half-filled honeycomb lattice with short-range repulsions have been suggested to host a variety of interesting many-body ground states, e.g., a topological Mott insulator. A number of recent studies of the spinless case in terms of exact diagonalization, the infinite density matrix renormalization group and the functional renormalization group, however, indicate a suppression of the topological Mott insulating phase in the whole range of interaction parameters. Here, we complement the previous studies by investigating the quantum many-body instabilities of the physically relevant case of spin-1/2 fermions with onsite, nearest-neighbor and second-nearest-neighbor repulsion. To this end, we employ the multi-patch functional renormalization group for correlated fermions with refined momentum resolution observing the emergence of an antiferromagnetic spin-density wave and a charge-density wave for dominating onsite and nearest-neighbor repulsions, respectively. For dominating second-nearest neighbor interaction our results favor an ordering tendency towards a charge-modulated ground state over the topological Mott insulating state. The latter evades a stabilization as the leading instability by the additional onsite interaction.

Ultrafast Spin Density Wave Transition in Chromium Governed by Thermalized Electron Gas.

The energy and momentum selectivity of time- and angle-resolved photoemission spectroscopy is exploited to address the ultrafast dynamics of the antiferromagnetic spin density wave (SDW) transition photoexcited in epitaxial thin films of chromium. We are able to quantitatively extract the evolution of the SDW order parameter Δ through the ultrafast phase transition and show that Δ is governed by the transient temperature of the thermalized electron gas, in a mean field description. The complete destruction of SDW order on a sub-100fs time scale is observed, much faster than for conventional charge density wave materials. Our results reveal that equilibrium concepts for phase transitions such as the order parameter may be utilized even in the strongly nonadiabatic regime of ultrafast photoexcitation.

Structure and superconductivity of (Li1−xFex)OHFeSe single crystals grown using AxFe2−ySe2 (A = K, Rb, and Cs) as precursors

We present results on the hydrothermal growth of ()OHFeSe single crystals using floating-zone-grown (A = K, Rb, and Cs) as precursors. The growth proceeds by the hydrothermal ion exchange of Li/Fe–O–H for K, Rb, and Cs, resulting in a stacking layer of ()OH sandwiched between the FeSe layers. Optimal growth parameters are achieved using high quality A0.80Fe1.81Se2 single crystals added to the mixtures of LiOH, H2O, Fe and C(NH2)2Se in an autoclave and subsequently heated to 120 °C for 2 d, to obtain highest quality single crystals. The obtained crystals have lateral dimensions up to centimeters, with the final size related to that of the precursor crystal used. All ()OHFeSe single crystals show a superconducting transition temperature Tc > 42 K, regardless of the phase of the precursor such as superconducting K0.80Fe1.81Se2 (Tc = 29.31 K) or non-superconducting Rb0.80Fe1.81Se2 or poor-superconducting Cs0.80Fe1.81Se2 (Tc = 28.67 K). The Tc and transition width ΔT vary in the obtained single crystals, due to the inhomogeneity of the ionic exchange. X-ray diffraction analysis demonstrates that the 245 insulating phase is absent in the ion-exchanged single crystals, while it is observed in the precursors. Comparative studies of the structure, magnetization, and superconductivity on the parent A0.80Fe1.81Se2 and the ion-exchanged ()OHFeSe crystals are discussed. A phase diagram including antiferromagnetic spin density wave and superconducting phases is also proposed.

Chiral spin density wave order on the frustrated honeycomb and bilayer triangle lattice hubbard model at half-filling.

We study the Hubbard model on the frustrated honeycomb lattice with nearest-neighbor hopping t_{1} and second nearest-neighbor hopping t_{2}, which is isomorphic to the bilayer triangle lattice, using the SU(2)-invariant slave boson theory. We show that the Coulomb interaction U induces antiferromagnetic (AF) chiral spin density wave (χSDW) order in a wide range of κ=t_{2}/t_{1} where both the two-sublattice AF order at small κ and the decoupled three-sublattice 120° order at large κ are strongly frustrated, leading to three distinct phases with different anomalous Hall responses. We find a continuous transition from a χSDW semimetal with the anomalous Hall effect to a topological chiral Chern insulator exhibiting the quantum anomalous Hall effect, followed by a discontinuous transition to a χSDW insulator with a zero total Chern number but an anomalous ac Hall effect. The χSDW is likely a generic phase of strongly correlated and highly frustrated hexagonal lattice electrons.

Euclidean action of Fermi-system with “hidden order”

Spontaneous break down of translational invariance of Fermi-system along Matsubara's time axis may lead to emergency of a new kind of “hidden order”. An exact solution is found that minimizes Landau–Ginzburg–Wilson (LGW) action of the fermionic system close to a usual spin density wave (SDW) instability. The solution has the form of SDW with amplitude that is analytic double-periodic function of the Matsubara and real time. This kind of order parameter behaves like a “hidden order”, since, e.g. in the limit of zero temperature, T=0K, the state is characterized by a bound state of two antiferromagnetic SDW's propagating in the opposite directions in real space and forming “standing wave” with zero expectation value for the magnetization. There is finite energy gap between this state and lowest excited states corresponding to SDW's propagating in the opposite directions with slightly different amplitudes. Green's function of the hidden order field (HOF) is finite and periodic along Matsubara's axis, but Wick-rotated to the axis of real frequencies, it reveals periodic “chain” of second order poles. Hence, the scattering cross section of the HOF is zero in the lowest order approximation and, therefore, HOF is indeed “invisible”. Despite this, HOF induces a gap in the fermionic quasiparticle spectrum at Fermi-level, and also possesses several “visible” spin-modes with discrete frequencies above a finite gap. Relevance of the picture to high-Tc “hidden order” and pseudo-gap state is briefly discussed.

Spin fluctuations and unconventional pairing on the Lieb lattice

Abstract The spin fluctuations and superconducting pairing symmetries in the dispersive band of Lieb lattice are studied by fluctuation exchange approximation. The antiferromagnetic spin density wave is found to exist on the A sublattice (the lattice sites with four nearest neighbors) at half filling. When slightly doped away from half filling, a balance between the combined effects of the ( π , π ) and ( 0.4 π , 0 ) spin fluctuations and the gaining of the condensation energy leads to the nearly degenerate d x 2 − y 2 - and g x y ( x 2 − y 2 ) -wave pairing states. After further doped, the d x y -wave state is favored via the intra-sublattice spin fluctuations with a wave vector ( π , 0 ). We emphasize that the sublattices' contribution and the renormalization of the spectral function play a crucial role on the spin fluctuations and the pairing symmetry. The effect of the imbalance of the on-site energy at different sublattices is also discussed.

Ultrafast above-transition-temperature resurrection of spin density wave driven by coherent phonon generation in BaFeAs

A model incorporating the time-dependent Ginzburg–Landau theory of ultrafast cooperative interplay among charge, spin, and lattice is presented for the pnictide superconductor BaFeAs. Under the ultrafast optical pumping, a pronounced spin–phonon coupling is found to drive the reconstruction of spin density wave (SDW) at (: SDW transition temperature) through the coherent phonon generation. First-principles electronic structure calculation confirms that the macroscopically coherent oscillation of As over a new equilibrium displacement offers a route to the antiferromagnetic SDW state. Our finding explains the recent experimental observation.

Triplet pair correlations and nonmonotonic supercurrent decay with Cr thickness in Nb/Cr/Fe/Nb Josephson devices

Supercurrents carry charge but not spin in the vast majority of superconductors. This is because the charge carriers are Cooper pairs which are formed of electrons with antiparallel spins (singlet pairs). It is now established that if singlet pairs propagate through a superconductor interface with an inhomogeneous ferromagnet, triplet pair correlations form so the supercurrents can acquire a net spin component. Although the spins at sputter-deposited Fe/Cr interfaces can be frustrated due to surface roughness and interdiffusion, an antiferromagnetic spin density wave (SDW) state can still form in Cr close to the interface. Here, we show evidence for triplet pair correlations in Josephson junctions with Cr/Fe and Cr/Fe/Cr barriers. Although the exact mechanism of pair conversion is unknown, we propose a simple model in which a SDW state in Cr and frustrated spins at the Cr/Fe interfaces serve as spin-mixers for generating triplet supercurrents and so provide a potential means to generating large superconducting spin current densities.