Spin Density Wave Order Parameter Research Articles

Interplay of superconductivity and magnetism in the Fe1+yTe1‐xSex iron‐based superconductor: A theoretical study

AbstractThe competition between superconductivity and magnetism has been studied for the ongoing investigation of mechanisms in unconventional superconductors. Fe1+yTe1−xSex is distinct among iron‐based superconductors due to its structural simplicity, comprising solely FeTe/Se layers that are favorable for probing the superconductivity mechanism. The main goal of this article is to focus on the computational investigation of the interplay of magnetism and superconductivity in the Fe1+yTe1−xSex multiband superconductor. From the electronic structure of the Fe1+yTe1−xSex superconductor, a two‐band Hamiltonian model was considered to examine the interplay of magnetism and superconductivity in the Fe1+yTe1‐xSex superconductor. Using Green's function formalism with the Hamiltonian model, the mathematical statements for the superconducting (Sc) gap parameter, spin density wave (SDW) ordering parameter, Sc and magnetic transitional temperatures have been obtained. Using these mathematical expressions, the phase diagram of transition temperatures versus the gap parameters for the Fe1+yTe1‐xSex superconductor has been plotted. The intersection region in the phase diagram of transition temperatures as a function of the SDW order parameter has been plotted to show the possible interplay of superconductivity and magnetism in a Fe1+yTe1‐xSex iron‐based superconductor.

Theoretical study of the interplay of spin density wave and superconductivity in nickel substitution of the strontium–iron–arsenide (SrFe2−xNixAs2) superconductor in a two-band model

The main objective of this manuscript is to focus on the computational study of the interplay of spin density wave (SDW) and superconductivity using a two-band model for SrFe2−xNixAs2. We derived mathematical statements for the superconducting critical temperature, SDW critical temperature, superconductivity order parameter, and the SDW order parameter using the Hamiltonian model and Green’s function formalism for the SrFe2−xNixAs2 superconductor. A mathematical expression for the dependence of transition temperatures on the SDW order parameter was obtained for SrFe2−xNixAs2. Using these mathematical statements, transition temperatures versus the SDW order parameter phase diagrams were plotted to show the dependence of the SDW order parameter on transition temperatures. By merging these diagrams, we have depicted the intriguing possibility of the interplay of superconductivity and magnetism for the SrFe2−xNixAs2 superconductor. Phase diagrams of temperature versus superconducting order parameters and the SDW order parameter were also plotted to show the dependence of order parameters on temperature for the SrFe2−xNixAs2 superconductor.

Evidence for charge delocalization crossover in the quantum critical superconductor CeRhIn5.

The nature of charge degrees-of-freedom distinguishes scenarios for interpreting the character of a second order magnetic transition at zero temperature, that is, a magnetic quantum critical point (QCP). Heavy-fermion systems are prototypes of this paradigm, and in those, the relevant question is where, relative to a magnetic QCP, does the Kondo effect delocalize their f-electron degrees-of-freedom. Herein, we use pressure-dependent Hall measurements to identify a finite-temperature scale Eloc that signals a crossover from f-localized to f-delocalized character. As a function of pressure, Eloc(P) extrapolates smoothly to zero temperature at the antiferromagnetic QCP of CeRhIn5 where its Fermi surface reconstructs, hallmarks of Kondo-breakdown criticality that generates critical magnetic and charge fluctuations. In 4.4% Sn-doped CeRhIn5, however, Eloc(P) extrapolates into its magnetically ordered phase and is decoupled from the pressure-induced magnetic QCP, which implies a spin-density-wave (SDW) type of criticality that produces only critical fluctuations of the SDW order parameter. Our results demonstrate the importance of experimentally determining Eloc to characterize quantum criticality and the associated consequences for understanding the pairing mechanism of superconductivity that reaches a maximum Tc in both materials at their respective magnetic QCP.

Theoretical Investigation of the Interplay of Superconductivity and Magnetism in Ba1−xKxFe2As2 Superconductor in a Two-Band Model by Using the Bogoliubov Transformation Formalism

The main focus of this article is to investigate the theoretical interplay of magnetism and superconductivity in a two-band model for the iron-based superconductor Ba1−xKxFe2As2. On the basis of experimental results, the two-band model Hamiltonian was considered. We obtained mathematical statements for the superconductor Ba1−xKxFe2As2 superconducting (SC) transition temperature, spin-density-wave (SDW), transition temperature, superconductivity order parameter, and SDW order parameter from the Bogoliubov transformation formalism and the model Hamiltonian. Furthermore, an expression for the dependence of the SDW transition temperature on the SDW order parameter and the dependence of the SC transition temperature on the SDW order parameter was obtained for Ba1−xKxFe2As2. By substituting the experimental and theoretical values of the parameters in the derived statements, phase diagrams of the SC transition temperature versus the SDW order parameter and the SDW transition temperature versus the SDW order parameters have been plotted to demonstrate the dependence of the SDW order parameter on transition temperatures. By combining the two-phase diagrams, we depicted the possible coexistence of superconductivity and magnetism for the Ba1−xKxFe2As2 superconductor. The phase diagrams of temperature versus SC order parameter and temperature versus SDW order parameter were also plotted to show the dependence of order parameters on temperature for the Ba1−xKxFe2As2 superconductor.

Investigation of the Interplay Between Spin Density Wave and Superconductivity in High‐Temperature Iron‐Based Superconductor Ba1−xRbxFe2As2

The current research work deals with the theoretical investigation of the interplay between spin density wave (SDW) and superconductivity in a two‐band model high‐temperature iron‐based superconductor by using the double‐time temperature‐dependent Green's function formalism. The superconductivity transition temperature () versus the spin density wave order parameter () for the electron and hole intrabands as well as the interband for the iron‐based superconductor has been plotted. With an increase in of the material, the superconductivity transition temperature decreases. In both intra‐ and interband pairings, the temperature at which the spin density wave transition () rises with increasing . The interplay between superconductivity and spin density wave of the electron and hole intraband interactions for . Furthermore, the phase diagram of the spin density wave parameter () versus temperature has been plotted, and the spin density wave parameter () is observed to decrease as the temperature rises and vanishes at the spin density wave transition temperature ().

Femtosecond control of phonon dynamics near a magnetic order critical point

The spin-phonon interaction in spin density wave (SDW) systems often determines the free energy landscape that drives the evolution of the system. When a passing energy flux, such as photoexcitation, drives a crystalline system far from equilibrium, the resulting lattice displacement generates transient vibrational states. Manipulating intermediate vibrational states in the vicinity of the critical point, where the SDW order parameter changes dramatically, would then allow dynamical control over functional properties. Here we combine double photoexcitation with an X-ray free-electron laser (XFEL) probe to control and detect the lifetime and magnitude of the intermediate vibrational state near the critical point of the SDW in chromium. We apply Landau theory to identify the mechanism of control as a repeated partial quench and sub picosecond recovery of the SDW. Our results showcase the capabilities to influence and monitor quantum states by combining multiple optical photoexcitations with an XFEL probe. They open new avenues for manipulating and researching the behaviour of photoexcited states in charge and spin order systems near the critical point.

Thermal transport in superconductors with coexisting spin density wave order

We study thermal transport in a two-dimensional system with coexisting $s$- or $d$-wave Superconducting (SC) and Spin Density Wave (SDW) orders. We analyse the nature of coexistence phase in a tight-binding square lattice with $\mathbf{Q}=(\pi,\pi)$ SDW ordering. The electronic thermal conductivity is computed within the framework of the Boltzmann kinetic theory, using Born approximation for the impurity scattering collision integral. We describe the influence of the Fermi surface (FS) topology, the competition between the SC and SDW order parameters, the presence or absence of zero energy excitations in the coexistence phase, on the low temperature behavior of thermal conductivity of the various paring states. We present qualitative analytical, and fully numerical results that show that the heat transport signatures of various SC states emerging from collinear SDW order are quite distinct, and depend on the symmetry properties of the SC order parameter under translation by the SDW nesting vector $\mathbf{Q}$. {A combination of $(\pi,\pi)$-SDW and the $d_{x^2-y^2}$ pairing state results in fully gapped excitations, whereas $(\pi,\pi)$-SDW co-existing with either $d_{xy}$ or $s$-wave pairing states may always have gapless excitations. There appear special stable Dirac nodal points that are not gapped by the SC order in the coexistence phase, resulting in finite residual heat conductivity.

Theoretical investigation of the coexistence of superconductivity and spin density wave (SDW) in two-band model for the iron-based superconductor BaFe2(As1−xPx)2

This study focuses on the theoretical investigation of the coexistence of superconductivity and spin density wave (SDW) in a two-band model for the iron-based superconductor BaFe2(As1−xPx)2. By employing a system Hamiltonian in a two-band model for a given system and by using the double time temperature dependent Green’s function formalism at the Bardeen-Cooper-Schrieffer (BCS) mean field approximation (MFA) level, we obtained mathematical expressions for the dependence of superconducting transition temperature (TC) on SDW order parameter (ΔSDW) in the electron and hole intra-band interactions, and in the inter-band interactions for superconductor BaFe2(As1−xPx)2. Similarly, we have obtained an expression for the dependence of SDW transition temperature (TSDW) on the SDW order parameter (ΔSDW) for BaFe2(As1−xPx)2. By using experimental values and considering some plausible approximations of the parameters in the obtained expressions, phase diagrams of TC versus ΔSDW in the electron and hole intra-band interactions, and in the inter-band interactions are plotted for the BaFe2(As1−xPx)2 superconductor. Similarly, a phase diagram of TSDW versus ΔSDW is plotted for the same superconductor. By merging the two phase diagrams, we have demonstrated the possible coexistence of superconductivity and SDW in the electron and hole intra-band interactions, and in the inter-band interactions for BaFe2(As1−xPx)2. Furthermore, we have investigated the dependence of ΔSDW on temperature in pure SDW region and the phase diagram is plotted for the variation of ΔSDW with temperature for superconductor BaFe2(As1−xPx)2. Our findings are in agreement with previous experimental results.

Coexistence of superconductivity and magnetism in CaK(Fe1−xNix)4As4 as probed by 57Fe Mössbauer spectroscopy

Temperature dependent $^{57}$Fe M\"ossbauer spectroscopy and specific heat measurements for CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ with $x$ = 0, 0.017, 0.033, and 0.049 are presented. No magnetic hyperfine field (e.g. no static magnetic order) down to 5.5 K was detected for $x$ = 0 and 0.017 in agreement with the absence of any additional feature below superconducting transition temperature, $T_c$, in the specific heat data. The evolution of magnetic hyperfine field with temperature was studied for $x$ = 0.033 and 0.049. The long-range magnetic order in these two compounds coexists with superconductivity. The magnetic hyperfine field, $B_{hf}$, (ordered magnetic moment) below $T_c$ in CaK(Fe$_{0.967}$Ni$_{0.033}$)$_4$As$_4$ is continuously suppressed with the developing superconducting order parameter. The $B_{hf}(T)$ data for CaK(Fe$_{0.967}$Ni$_{0.033}$)$_4$As$_4$, and CaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$ can be described reasonably well by Machida's model for coexistence of itinerant spin density wave magnetism and superconductivity [K. Machida, J. Phys. Soc. Jpn. {\bf 50}, 2195 (1981)]. We demonstrate directly that superconductivity suppresses the spin density wave order parameter if the conditions are right, in agreement with the theoretical analysis.

Charge Density Wave and Spin Density Wave in Two-Orbital Model for Iron-Based Superconductors

We present a mean-field theoretical model study for the coexistence of the two strongly interacting charge density wave (CDW) and spin density wave (SDW) for iron-based superconductors in the under-doped region before the onset of the superconductivity in the system. The analytic expressions for the temperature dependence of the CDW and SDW order parameters are derived by using Zubarev’s technique of double-time single particle Green’s functions and solved self-consistently. Their interplay is studied by varying both the CDW and SDW coupling constants. Further, the electronic density of states (DOS) for the conduction electrons are studied in the pure CDW and SDW states and coexistence state for the cases, where the CDW transition temperature is greater than the SDW transition temperature and vice versa, which show two gap parameters.

Spin-density wave state in simple hexagonal graphite

Simple hexagonal graphite, also known as AA graphite, is a metastable configuration of graphite. Using tight-binding approximation it is easy to demonstrate that AA graphite is a metal with well-defined Fermi surface. The Fermi surface consists of two sheets, each shaped like a rugby ball. One sheet corresponds to electron states, another corresponds to hole states. The Fermi surface demonstrates good nesting: a suitable translation in the reciprocal space superposes one sheet onto another. In the presence of the electron-electron repulsion a nested Fermi surface is unstable with respect to spin-density wave ordering. This instability is studied using the mean-field theory at zero temperature, and the spin-density wave order parameter is evaluated.

Semiclassical dynamics of spin density waves

We present a theoretical framework for equilibrium and nonequilibrium dynamical simulation of quantum states with spin-density-wave (SDW) order. Within a semiclassical adiabatic approximation that retains electron degrees of freedom, we demonstrate that the SDW order parameter obeys a generalized Landau-Lifshitz equation. With the aid of an enhanced kernel polynomial method, our linear-scaling quantum Landau-Lifshitz dynamics (QLLD) method enables dynamical SDW simulations with $N \simeq 10^5$ lattice sites. Our real-space formulation can be used to compute dynamical responses, such as dynamical structure factor, of complex and even inhomogeneous SDW configurations at zero or finite temperatures. Applying the QLLD to study the relaxation of a noncoplanar topological SDW under the excitation of a short pulse, we further demonstrate the crucial role of spatial correlations and fluctuations in the SDW dynamics.

Nonlinear transport associated with spin density wave dynamics in Ca3Co4O9

We have carried out the transient nonlinear transport measurements on the layered cobalt oxide Ca$_3$Co$_{4}$O$_9$, in which a spin density wave (SDW) transition is proposed at $T_{\rm SDW} \simeq 30$ K. We find that, below $T_{\rm SDW}$, the electrical conductivity systematically varies with both the applied current and the time, indicating a close relationship between the observed nonlinear conduction and the SDW order in this material. The time dependence of the conductivity is well analyzed by considering the dynamics of SDW which involves a low-field deformation and a sliding motion above a threshold field. We also measure the transport properties of the isovalent Sr-substituted systems to examine an impurity effect on the nonlinear response, and discuss the obtained threshold fields in terms of thermal fluctuations of the SDW order parameter.

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.

Coexistence and competition of spin-density-wave and superconducting order parameters in iron-based superconductors

We theoretically study the coexistence of spin density wave (SDW) and superconductivity (SC) in ironpnictide superconductors based on a three-orbital model, focusing on the momentum-space and real-space distributions of SDW and SC order parameters in the coexistence region. We show that a SDW–SC coexisting state lies in the T–n phase diagram, in qualitative agreement with those of NaFe1−xCoxAs and Ba(Fe1−xCox)2As2. In the SC state the pairing wavefunction has s± symmetry with sx2y2 and sx2+y2 components. In the coexisting state, the SDW and SC order parameters display strong orbital-selective competitions in momentum space, which also result in real-space modulation and spin singlet–triplet mixing in the Cooper pairing amplitude. We expect that the obtained features may be observed in future experiments.

Quantitative determination of bond order and lattice distortions in nickel oxide heterostructures by resonant x-ray scattering

We present a combined study of Ni $K$-edge resonant x-ray scattering and density functional calculations to probe and distinguish electronically driven ordering and lattice distortions in nickelate heterostructures. We demonstrate that due to the low crystal symmetry, contributions from structural distortions can contribute significantly to the energy-dependent Bragg peak intensities of a bond-ordered NdNiO$_3$ reference film. For a LaNiO$_3$-LaAlO$_3$ superlattice that exhibits magnetic order, we establish a rigorous upper bound on the bond-order parameter. We thus conclusively confirm predictions of a dominant spin density wave order parameter in metallic nickelates with a quasi-two-dimensional electronic structure.

Coexistence of Superconductivity and Spin Density Wave (SDW) in Ferropnictide Ba1−x K x Fe2As2

This work focuses on the theoretical investigation of the coexistence of superconductivity and spin density wave (SDW) in ferropnictide Ba1−x K x Fe2As2. By developing a model Hamiltonian for the system and by using quantum field theory Green’s function formalism, we have obtained mathematical expressions for superconducting transition temperature (T C), spin density wave transition temperature (T sdw), superconductivity order parameter (ΔSc), and spin density wave order parameter (Δsdw). By employing the experimental and theoretical values of the parameters in the obtained expressions, phase diagrams of superconducting transition temperature (T C) versus superconducting order parameter (ΔSc) and spin density wave transition temperature (T sdw), versus spin density wave order parameter (Δsdw) have been plotted. By combining the two phase diagrams, we have demonstrated the possible coexistence of superconductivity and spin density wave (SDW) in ferropnictide Ba1−x K x Fe2As2.

Thermoelectric transport in the topological phase due to the coexistence of superconductivity and spin-density-wave

We study the thermoelectric transport in two dimensional topological system which has coexistence of superconductivity(SC) and spin-density wave(SDW). The SC is presumed to be of $d_{x^2-y^2}+(p_x + i p_y) $ type whereas the SDW order parameter is of $BCS$ symmetry. The Hamiltonian describing such a coexistence phase is shown to have topological phase in addition to the conventional one. The transport properties in such topological system have two distinct contributions: (i) the surface/edge and (ii) the bulk. The competition between the surface/edge versus the bulk transport is analyzed in different parameter regimes and the possibility of enhancing the figure of merit is discussed.

Novel topological phase due to coexistence of superconductivity and spin-density wave: Application to high Tc superconductors

We consider a model of a coexistence phase between superconductivity(SC) and spin-density wave(SDW) where the SC is assumed to be of dx2−y2+idxy(d1+id2) symmetry and the SDW order parameter is of s-wave as well as dxy symmetry. The Hamiltonian having such a symmetry is shown to yield a novel topological coexistence phase in addition to the conventional one. It is shown that the amplitudes of both the order parameters determine a new phase diagram characterizing different topological phases. A possible experimental realization of such topological phases in a recent ARPES data of high Tc superconductors in the extreme underdoped regime is analyzed by considering the effective order parameter to be a combination of dx2−y2 SC and dxy SDW.

The Coexistence of Super Conductivity and Spin Density Wave (SDW) in SmO<sub>1-x</sub>F<sub>x</sub>FeAs

The coexistence of superconductivity and spin density wave in SmO1-xFxFeAs is theoretically studied using the model Hamiltonian which contains BCS type superconductivity and spin density wave terms. Employing green function formalism, the expression for the spin density wave order parameter (M) and expression for spin density wave transition temperature TSDW is obtained. The interplay between the superconductivity and spin density wave is examined in these parameters and the coexistence of the two states is established in the order parameter range of 0.1≤MmeV≤0.13 which is seen to be in broad experimental agreement.