Spin-fermion Model Research Articles

Enhanced nematic and antiferromagnetic phases in the spin-fermion model for strained iron pnictides

The effects of anisotropic superexchange and Fe–Fe hoppings on phase transitions in the undoped three-orbital spin-fermion model are investigated to understand the experimentally reported strain effect in BaFe2As2. Monte Carlo simulated phase diagrams show that both the collinear antiferromagnetic and nematic transitions shift toward high temperature with the increasing magnitude of anisotropies, qualitatively consistent with experimental observation. Thus, both the anisotropic superexchange and Fe–Fe hoppings are suggested to be responsible for the variation of the transition temperatures of BaFe2As2 with uniaxial stress. In addition, we observed a 90 degree rotation of the collinear antiferromagnetic order, accompanied with a reversal of the orbital occupancy at the Fermi surface when the sign of the superexchange anisotropy changes, further supporting previous predictions by first principles calculation.

Odd- and Even-Frequency Superconductivities Mediated by Ferromagnetic Magnons

On the basis of a generalized Kondo-lattice model (i.e., spin-fermion model), we examine herein superconductivity mediated by magnetic excitations in ferromagnets. By applying the perturbation theory, we derive effective pairing interactions between conduction electrons. Pairing fluctuations are numerically calculated by fully accounting for the momentum and frequency dependences in quasi-one dimension. The results indicate that the normal state is unstable against even- and odd-frequency pairing fluctuations, depending on the temperature and model parameters. In a few cases, we obtain phase diagrams. The two-magnon exchange interaction is found to favor odd-frequency pairing at high temperatures (but below the ferromagnetic transition temperature); however, at low temperatures, triangle processes involving two magnons and one electron induce even- and odd-frequency pairings depending on the signs of the coupling constants of the Kondo interaction. Finally, we discuss the possibility of odd-frequency supe...

Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors

We address the timely issue of the presence of charge ordering at the hot-spots in the pseudo-gap phase of cuprate superconductors in the context of an emergent SU(2)-symmetry which relates the charge and pairing sectors. Performing the Hubbard-Stratonovich decoupling such that the free energy stays always real and physically meaningful we exhibit three solutions of the spin-fermion model at the hot spots. A careful examination of their stability and free energy shows that, at low temperature, the system tends towards a co-existence of charge density wave (CDW) and the composite order parameter made of diagonal quadrupolar density wave and pairing fluctuations of Ref. [Nat. Phys. $\bf{9}$, 1745 (2013)].The CDW is sensitive to the shape of the Fermi surface in contrast to the diagonal quadrupolar order, which is immune to it. SU(2) symmetry within the pseudo-gap phase also applies to the CDW state, which therefore admits a pairing density pave counterpart breaking time reversal symmetry.

D-Wave pairing in an ensemble of spin polaron quasiparticles in the spin-fermion model of the electronic structure of the CuO2 plane

Abstract It is demonstrated for the first time that the strong coupling between spin moments of copper ions and oxygen holes, which arises upon hybridization mixing of two hole subsystems in the Emery model, not only affects the formation of spin polaron quasiparticles but also ensures effective attraction between them via the exchange interaction. This results in the Cooper instability with d-wave pairing in a 2D ensemble of spin polaron quasiparticles. The T – x phase diagram obtained using this approach agrees well with the available experimental data.

Diverging nematic susceptibility, physical meaning ofT*scale, and pseudogap in the spin fermion model for the pnictides

Using Monte Carlo simulations with a tunable uniaxial strain, the nematic susceptibility of the spin fermion model for the pnictides is calculated. The results are in excellent agreement with the experiments by Chu et al. [Science 337, 710 (2012)]. Via a Ginzburg-Landau analysis, our study suggests a nematicity in the spin fermion model primarily originating in magnetism, but with the lattice/orbital also playing a key role by boosting up critical temperatures and separating the structural ${T}_{S}$ and N\'eel ${T}_{N}$ transitions. At $T>{T}_{S}$, Curie-Weiss behavior is observed with a characteristic temperature ${T}^{*}$ being the ${T}_{N}$ of the purely electronic system. In this temperature regime, short-range magnetic order with wave vectors $(\ensuremath{\pi},0)\text{\ensuremath{-}}(0,\ensuremath{\pi})$ induce local nematic fluctuations and a density-of-states pseudogap, compatible with several experiments. The present analysis relies on the study of a particular model for the iron superconductors; thus further studies are needed to conclusively establish the driver of nematicity in real materials.

Charge-density-wave order with momentum (2Q,0) and (0,2Q) within the spin-fermion model: Continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates

We analyze charge order within the the spin-fermion model. We show that magnetically-mediated interaction gives rise to charge order $\Delta_k^Q = \langle c^\dagger_{{\bf k}+{\bf Q}} c_{{\bf k}-{\bf Q}}\rangle$ with momenta ${\bf Q}=Q_x =(2Q,0)$ and ${\bf Q}=Q_y =(0,2Q)$, if the magnetic correlation length $\xi$ exceeds some critical value. We argue that $\Delta_k^Q$ and $\Delta_{-k}^Q$ are not equivalent, and their symmetric and antisymmetric combinations describe density modulations and bond current. We derive GL functional for four-component $U(1)$ order parameters $\Delta^Q_{\pm k}$ with ${\bf Q} = Q_x$ or $Q_y$. Within mean-field we find two types of CDW states, I and II, depending on system parameters. In state I density and current modulations emerge with the same ${\bf Q} = Q_x$ or $Q_y$, breaking $Z_2$ lattice rotational symmetry, and differ in phase by $\pm\pi/2$. The selection of $\pi/2$ or $-\pi/2$ additionally breaks $Z_2$ time-reversal symmetry, such that the total order parameter manifold is $U(1) \times Z_2 \times Z_2$. In state II density and current modulations emerge with different $\bf Q$ and the order parameter manifold is $U(1) \times U (1) \times Z_2$. We go beyond mean-field and show that discrete symmetries get broken before long-range charge order sets in. For state I, the system first breaks $Z_2$ lattice rotational symmetry ($C_4 \to C_2$) at $T= T_n$ and develops a nematic order, then breaks $Z_2$ time-reversal symmetry at $T_t < T_n$, and finally breaks $U(1)$ symmetry of a common phase of even and odd components of $\Delta^Q_{k}$ at $T= T_{\rm cdw} < T_t < T_n$ and develops a true charge order. We argue that the preemptive orders lift $T_{\rm cdw}$ and reduces $T_{\rm sc}$ such that at large $\xi$ charge order may develop prior to superconductivity. We obtain the phase diagram and present quantitative comparison with ARPES data for hole-doped cuprates.

Electron transport in nanoscale junctions with local anharmonic modes.

We study electron transport in nanojunctions in which an electron on a quantum dot or a molecule is interacting with an N-state local impurity, a harmonic ("Holstein") mode, or a two-state system ("spin"). These two models, the Anderson-Holstein model and the spin-fermion model, can be conveniently transformed by a shift transformation into a form suitable for a perturbative expansion in the tunneling matrix element. We explore the current-voltage characteristics of the two models in the limit of high temperature and weak electron-metal coupling using a kinetic rate equation formalism, considering both the case of an equilibrated impurity, and the unequilibrated case. Specifically, we show that the analog of the Franck-Condon blockade physics is missing in the spin-fermion model. We complement this study by considering the low-temperature quantum adiabatic limit of the dissipative spin-fermion model, with fast tunneling electrons and a slow impurity. While a mean-field analysis of the Anderson-Holstein model suggests that nonlinear functionalities, bistability and hysteresis may develop, such effects are missing in the spin-fermion model at the mean-field level.

Huge positive magnetoresistance in antiferromagnetic double perovskite metals

Metals with large positive magnetoresistance are rare. We demonstrate that antiferromagnetic metallic states, as have been predicted for the double perovskites, are excellent candidates for huge positive magnetoresistance. An applied field suppresses long range antiferromagnetic order leading to a state with short range antiferromagnetic correlations and strong electronic scattering. The field induced resistance ratio can be more than tenfold, at moderate field, in a structurally ordered system, and continues to be almost twofold even in systems with ∼25% antisite disorder. Although our explicit demonstration is in the context of a two- dimensional spin-fermion model of the double perovskites, the mechanism we uncover is far more general, complementary to the colossal negative magnetoresistance process, and would operate in other local moment metals that show a field driven suppression of non-ferromagnetic order.

Evidence of a short-range incommensurate [formula omitted]-wave charge order from a fermionic two-loop renormalization group calculation of a 2D model with hot spots

The two-loop renormalization group (RG) calculation is considerably extended here for the two-dimensional (2D) fermionic effective field theory model, which includes only the so-called “hot spots” that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t−t′ Hubbard model at low hole doping. We compute the Callan–Symanzik RG equation up to two loops describing the flow of the single-particle Green’s function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that–in addition to clearly dominant SDW correlations–an approximate (pseudospin) symmetry relating a short-range incommensurated-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates.

Magnetic orders in pnictide superconductors: the effect of biquadratic interaction

The undoped three-orbital spin-fermion model with the additional biquadratic interaction which arises from various factors, such as quantum or thermal fluctuation, is studied using the Monte Carlo method in order to investigate the spin orders in pnictide superconductors. The simulations show that the experimentally observed nematic state can be stabilized by the positive biquadratic interaction, suggesting that such interaction may be another origin for nematicity in pnictides in addition to the couplings to the lattice degrees of freedom. Furthermore, the so-called flux state at low temperatures is identified when a rather weak negative biquadratic interaction is introduced, which is the same as the phase predicted in earlier theoretical work.

Suppression of Decoherence by Periodic Forcing

We consider a finite-dimensional quantum system coupled to a thermal reservoir and subject to a time-periodic, energy conserving forcing. We show that, if a certain dynamical decoupling condition is fulfilled, then the periodic forcing counteracts the decoherence induced by the reservoir: for small system-reservoir coupling $\lambda$ and small forcing period $T$, the system dynamics is approximated by an energy conserving and non-dissipative dynamics, which preserves coherences. For times up to order $(\lambda T)^{-1}$, the difference between the true and approximated dynamics is of size $\lambda +T$. Our approach is rigorous and combines Floquet and spectral deformation theory. We illustrate our results on the spin-fermion model and recover previously known, heuristically obtained results.

Fermi surface evolution in the ensemble of spin-polarized quasiparticles in La2 − x Sr x CuO4

For the spin-fermion model, it has been shown that the concept of spin polarons makes it possible to reproduce fine details of the Fermi surface evolution in the nodal direction of La2 − x Sr x CuO4 occurring with changes in the doping level x. The physics here is determined by the spin-correlated hopping of charge carriers and by the doping dependence of the inverse magnetic correlation length.

Competing effective interactions of Dirac electrons in the Spin–Fermion system

Recently discovered advanced materials, such as heavy fermions, frequently exhibit a rich phase diagram suggesting the presence of different competing interactions. A unified description of the origin of these multiple interactions, albeit very important for the comprehension of such materials is, in general not available. It would be therefore very useful to have a simple model where the common source of different interactions could be possibly traced back. In this work we consider a system consisting in a set of localized spins on a square lattice with antiferromagnetic nearest neighbors interactions and itinerant electrons, which are assumed to be Dirac-like and interact with the localized spins through a Kondo magnetic interaction. This system is conveniently described by the Spin–Fermion model, which we use in order to determine the effective interactions among the itinerant electrons. By integrating out the localized degrees of freedom we obtain a set of different interactions, which includes: a BCS-like superconducting term, a Nambu–Jona-Lasinio-like, excitonic term and a spin–spin magnetic term. The resulting phase diagram is investigated by evaluation of the mean-field free-energy as a function of the relevant order parameters. This shows the competition of the above interactions, depending on the temperature, chemical potential and coupling constants.

Nuclear magnetic resonance studies of pseudospin fluctuations in URu2Si2

We report $^{29}$Si NMR measurements in single crystals and aligned powders of URu$_2$Si$_2$ in the hidden order and paramagnetic phases. The spin-lattice-relaxation data reveal evidence of pseudospin fluctuations of U moments in the paramagnetic phase. We find evidence for partial suppression of the density of states below 30 K, and analyze the data in terms of a two component spin-fermion model. We propose that this behavior is a realization of a pseudogap between the hidden order transition $T_{HO}$ and 30 K. This behavior is then compared to other materials that demonstrate precursor fluctuations in a pseudogap regime above a ground state with long-range order.

Effect of magnetic field on the competition between superconductivity and charge order below the pseudogap state

We theoretically investigate the $T$-$B$ phase diagram of cuprates building on the $\mathrm{SU}(2)$ pseudogap order recently obtained from the spin-fermion model. At low temperatures, our analysis reveals an almost temperature-independent critical magnetic field ${B}_{\mathrm{co}}$ at which $d$-wave superconductivity switches to a phase of charge order. For temperatures beyond a certain value of the order of the zero-field superconducting transition temperature ${T}_{c}$, the critical field ${B}_{\mathrm{co}}(T)$ sharply grows. We compare our results derived within the effective $\mathrm{SU}(2)$ nonlinear $\ensuremath{\sigma}$ model with the phase diagram recently obtained by sound velocity measurements by LeBoeuf et al. [Nat. Phys. 9, 79 (2013)].

Nematic State of Pnictides Stabilized by Interplay between Spin, Orbital, and Lattice Degrees of Freedom

The nematic state of the iron-based superconductors is studied in the undoped limit of the three-orbital (xz, yz, xy) spin-fermion model via the introduction of lattice degrees of freedom. MonteCarlo simulations show that in order to stabilize the experimentally observed lattice distortion and nematic order, and to reproduce photoemission experiments, both the spin-lattice and orbital-lattice couplings are needed. The interplay between their respective coupling strengths regulates the separation between the structural and Néel transition temperatures. Experimental results for the temperature dependence of the resistivity anisotropy and the angle-resolved photoemission orbital spectral weight are reproduced by the present numerical simulations.

Quantum criticality of reconstructing Fermi surfaces in antiferromagnetic metals

We present a functional renormalization group analysis of a quantum critical point in two-dimensional metals involving Fermi surface reconstruction due to the onset of spin-density wave order. Its critical theory is controlled by a fixed point in which the order parameter and fermionic quasiparticles are strongly coupled and acquire spectral functions with a common dynamic critical exponent. We obtain results for critical exponents and for the variation in the quasiparticle spectral weight around the Fermi surface. Our analysis is implemented on a two-band variant of the spin-fermion model which will allow comparison with sign-problem-free quantum Monte Carlo simulations.

Conductivity Close to Antiferromagnetic Criticality

We study the conductivity of a three-dimensional disordered metal close to antiferromagnetic instability within the framework of the spin-fermion model using the diagrammatic technique. We calculate the interaction correction δσ(ω,T) to the conductivity, assuming that the latter is dominated by the disorder scattering, and the interaction is weak. Although the fermionic scattering rate shows critical behavior on the entire Fermi surface, the interaction correction is dominated by the processes near the hot spots, narrow regions of the Fermi surface corresponding to the strongest spin-fermion scattering. Exactly at the critical point δσ is proportional to [max(ω,T)](3/2). At sufficiently large frequencies ω the conductivity is independent of the temperature, and δσ is proportional to (τ(-1)-iω)(-2), τ being the elastic scattering time. In a certain intermediate frequency range δσ(ω) is proportional to iω(τ(-1)-iω)(-2).

Insulating magnetism in vacancy-ordered K0.8Fe1.6Se2

We unveil the physical origin of the insulating block checkerboard antiferromagnetism in vacancy-ordered K${}_{0.8}$Fe${}_{1.6}$Se${}_{2}$. Our first-principles electronic structure analysis reveals its incompatibility with a simple Fermi-surface nesting or Mott insulator scenario, and suggests the picture of coexisting itinerant and localized electronic states. Consistently, we demonstrate that it can be unified with the metallic collinear or bicollinear antiferromagnetism of the vacancy-free parent compounds LaOFeAs, BaFe${}_{2}$As${}_{2}$, or FeTe in the spin-fermion model. These results indicate that the blocking effects of Hund's rule coupling and the resulting electron correlation are crucial to the electronic and magnetic structures of iron-based superconductors.

Anisotropy of Electrical Transport in Pnictide Superconductors Studied Using Monte Carlo Simulations of the Spin-Fermion Model

An undoped three-orbital spin-fermion model for the Fe-based superconductors is studied via Monte Carlo techniques in two-dimensional clusters. At low temperatures, the magnetic and one-particle spectral properties are in agreement with neutron and photoemission experiments. Our main results are the resistance versus temperature curves that display the same features observed in BaFe(2)As(2) detwinned single crystals (under uniaxial stress), including a low-temperature anisotropy between the two directions followed by a peak at the magnetic ordering temperature, that qualitatively appears related to short-range spin order and concomitant Fermi surface orbital order.