We present the full analysis of the normal state of the spinfermion model near the antiferromagnetic instability in two dimensions. This model describes low-energy fermions interacting with their own collective spin fluctuations, which soften at the antiferromagnetic transition. We argue that in 2D, the system has two typical energies -an effective spin-fermion interactionḡ and an energy ω sf below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction λ 2 ∝ḡ/ω sf . We show that λ scales with the spin correlation length and diverges at criticality. This divergence implies that the conventional perturbative expansion breaks down. We developed a novel approach to the problem -the expansion in either the inverse number of hot spots in the Brillouin zone, or the inverse number of fermionic flavors -which allowed us to explicitly account for all terms which diverge as powers of λ, and treat the remaining, O(λ) terms in the RG formalism. We applied this technique to study the properties of the spinfermion model in various frequency and temperature regimes. We present the results for the fermionic spectral function, spin susceptibility, optical conductivity and other observables. We compare our results in detail with the normal state data for cuprates, and argue that the spin-fermion model is capable to explain the anomalous normal state properties of high Tc materials. We also discuss the non -applicability of the conventional φ 4 theory of the quantum-critical behavior in 2D.

Ultrathin ferromagnetic films with perpendicular spin anisotropy can possess an alternating up-down stripe-domain structure, with widths L 5. Considering the two inequivalent types of stripe domains to form a single unit, this structure may be thought of as a two-dimensional smectic crystal. It is subject to a weak stripe orientation energy. With increasing temperature the domain system changes from a smectic crystal phase to an "Ising nematic" phase, and then to a "tetragonal liquid" phase. We discuss its possible phase diagrams, in (H"H~~, T) space. This sequence of phases can occur whether or not the system ultimately undergoes a spin reorientation transition to a planar phase.

We argue that the resonant peak observed in neutron scattering experiments on superconducting cuprates and the peak/dip/hump features observed in ARPES measurements are byproducts of the same physical phenomenon. We argue that both are due to feedback effects on the damping of spin fluctuations in a d−wave superconductor. We consider the spin-fermion model at strong coupling, solve a set of coupled integral equations for fermionic and bosonic propagators and show that the dynamical spin susceptibility below Tc possesses the resonance peak at Ωres ∝ ξ −1 . The scattering of these magnetic excitations by electrons gives rise to a peak/dip/hump behavior of the electronic spectral function, the peak-dip separation is exactly Ωres.PACS numbers:71.10. Ca,74.20.Fg, One of the most intriguing recent developments in the physics of high T c materials is the realization that not only the normal but also the superconducting state of cuprates is not described by a weak coupling theory. In particular, ARPES experiments on Bi2212 have demonstrated [1,2] that even in slightly overdoped cuprates at T ≪ T c , the spectral function A(k, ω) near (0, π) does not possess a single quasiparticle peak at ω = ∆ 2 k + ǫ 2 k , where ∆ k is the superconducting gap and ǫ k is the fermionic dispersion. Instead, it displays a sharp peak which virtually does not disperse with k, a dip at frequencies right above the peak, and then a broad maximum (hump) which disperses with k and gradually recovers the normal state dispersion [1]. Simultaneously, the neutron scattering experiments on near optimally doped Y BCO [3] and Bi2212 [4] at T ≪ T c have detected a sharp resonance peak in the dynamical structure factor S(q, Ω) ∝ χ ′′ (q, Ω) centered at q = Q = (π, π) and at frequencies ∼ 40 meV.In this communication we show that the resonance peak in S(Q, Ω) and the peak/dip/hump features in A(k, ω) can be explained simultaneously by strong interaction between electrons and their collective spin degrees of freedom which near the antiferromagnetic instability are peaked at or near Q. Specifically, we demonstrate that a d-wave superconductor possesses propagating collective spin excitations at frequencies smaller than twice the maximum value of the d−wave gap. The propagating spin modes give rise to a sharp peak in S(Q, Ω) at Ω = Ω res ∝ ξ −1 where ξ is the spin correlation length. The interaction with collective spin excitations yields the fermionic self-energy Σ ω which at T = 0 has no imaginary part up to a frequency ω 0 which exceeds the measured superconducting gap by exactly Ω res .The point of departure for our analysis is the spinfermion model for cuprates which is argued [6] to be the low-energy theory for Hubbard-type lattice fermion models. The model is described byHere c † k,α is the fermionic creation operator for an electron with crystal momentum k and spin α, σ i are the Pauli matrices, and g is the coupling constant which measures the strength of the interaction between fermions and the collective bosonic spin degrees of freedom. The latter ...

We show that the Hertz phi(4) theory of quantum criticality is incomplete as it misses anomalous nonlocal contributions to the interaction vertices. For antiferromagnetic quantum transitions, we found that the theory is renormalizable only if the dynamical exponent z=2. The upper critical dimension is still d=4 - z=2; however, the number of marginal vertices at d=2 is infinite. As a result, the theory has a finite anomalous exponent already at the upper critical dimension. We show that for d<2 the Gaussian fixed point splits into two non-Gaussian fixed points. For both fixed points, the dynamical exponent remains z=2.

We consider spin and electronic properties of itinerant electron systems, described by the spin-fermion model, near the antiferromagnetic critical point. We expand in the inverse number of hot spots in the Brillouin zone, N, and present the results beyond the previously studied N = infinity limit. We found two new effects: (i) Fermi surface becomes nested at hot spots, and (ii) vertex corrections give rise to anomalous spin dynamics and change the dynamical critical exponent from z = 2 to z>2. To first order in 1/N we found z = 2N/(N-2) which for a physical N = 8 yields z approximately 2.67.

Near a quantum-critical point in a metal strong fermion-fermion interaction mediated by a soft collective boson gives rise to incoherent, non-Fermi liquid behavior. It also often gives rise to superconductivity which masks the non-Fermi liquid behavior. We analyze the interplay between the tendency to pairing and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions. We argue that superconducting Tc is non-zero even for strong incoherence and/or weak interaction due to the fact that the self-energy from dynamic critical fluctuations vanishes for the two lowest fermionic Matsubara frequencies ωm = ±πT . We obtain the analytic formula for Tc which reproduces well earlier numerical results for the electronphonon model at vanishing Debye frequency. Introduction.The interplay between superconductivity and non-Fermi liquid behavior in metals is one of most fascinating issues in the modern physics of correlated electron systems 1-18 A generic metallic system in D > 1 is a Fermi liquid with coherent quasiparticles at low energies. This coherence is destroyed if the system is brought to a quantum-critical point (QCP), beyond which it develops an electronic order in spin or charge channel. At a QCP fluctuations of the order parameter become massless. In D ≤ 3, the four-fermion interaction, mediated by these massless fluctuations, destroys fermionic coherence at T = 0, either at specific hot points on the Fermi surface 4,15,19,20 , if the order has a finite momentum, or everywhere on the Fermi surface, if the order develops with q = 0 (Ref. 21). The same massless fluctuations, however, also mediate the pairing interaction, and if this interaction has an attractive angular component the system can develop a superconducting instability at a finite T , before a QCP is reached. A dome of superconductivity above a QCP prevents a non-Fermi liquid, QC behavior from extending down to the lowest energies.The existence of superconductivity near a QCP is not guaranteed, however, because strong fermionic selfenergy acts against pairing. There are two effects from the self-energy. First, at T = 0 the self-energy from static (thermal) fluctuations acts as an impurity and may cause pair-breaking. This is crucial for spin-triplet superconductivity, for which thermal self-energy acts as a magnetic impurity 22 , but not for spin-singlet superconductivity, for which it acts as a non-magnetic impurity and its singular contribution cancels out by Anderson theorem 23 . In this paper we consider spin-singlet pairing and neglect the contribution from thermal fluctuations. Second, already at T = 0 the self-energy produces strong upturn mass renormalization and shrinks the range of a coherent fermionic behavior. Both these effects are detrimental to superconductivity.The pairing amplitude and the self-energy come from the same underlying interaction mediated by a soft boson, hence the two are generally of the same order. Zerotemperature studies of specific models in D = 2 and in ...

We study current induced magnetization dynamics in a long thin ferromagnetic wire with Dzyaloshinskii-Moriya interaction (DMI). We find a spiral domain wall configuration of the magnetization and obtain an analytical expression for the width of the domain wall as a function of the interaction strengths. Our findings show that above a certain value of DMI a domain wall configuration cannot exist in the wire. Below this value we determine the domain wall dynamics for small currents, and calculate the drift velocity of the domain wall along the wire. We show that the DMI suppresses the minimum value of current required to move the domain wall. Depending on its sign, the DMI increases or decreases the domain wall drift velocity.

The anomalous Hall effect in a magnetic two-dimensional electron gas with Rashba spin-orbit coupling is studied within the Kubo-Streda formalism in the presence of pointlike potential impurities. We find that all contributions to the anomalous Hall conductivity vanish to leading order in disorder strength when both chiral subbands are occupied. In the situation that only the majority subband is occupied, all terms are finite in the weak scattering limit and the total anomalous Hall conductivity is dominated by skew scattering. We compare our results to previous treatments and resolve some of the discrepancies present in the literature.