Mean-field theories for disordered electrons: Diffusion pole and Anderson localization

We discuss conditions to be put on mean-field-like theories to be able to describe fundamental physical phenomena in disordered electron systems. In particular, we investigate options for a consistent mean-field theory of electron localization and for a reliable description of transport properties. We argue that a mean-field theory for the Anderson localization transition must be electron-hole symmetric and self-consistent at the two-particle (vertex) level. We show that such a theory with local equations can be derived from the asymptotic limit to high spatial dimensions. The weight of the diffusion pole, i. e., the number of diffusive states at the Fermi energy, in this mean-field theory decreases with the increasing disorder strength and vanishes in the localized phase. Consequences of the disclosed behavior for our understanding of vanishing of electron diffusion are discussed.Comment: REVTeX4, 11 pages, no figure

Spin-wave interactions in quantum antiferromagnets

We study spin-wave interactions in quantum antiferromagnets by expressing the usual magnon annihilation and creation operators in terms of Hermitian field operators representing transverse staggered and ferromagnetic spin fluctuations. In this parameterization, which was anticipated by Anderson in 1952, the two-body interaction vertex between staggered spin fluctuations vanishes at long wavelengths. We derive a new effective action for the staggered fluctuations only by tracing out the ferromagnetic fluctuations. To one loop order, the renormalization group flow agrees with the nonlinear-$\sigma$-model approach.Comment: 7 pages, no figures; new references added; extended discussion on vertex structure. To appear in Europhysics Letter

Low-frequency noise in tunneling through a single spin

We propose measurements of low-frequency noise in the tunneling current through a single molecule with a spin as an experimental probe for identifying a mechanism of the spin-dependent tunneling. A specific tail near the zero frequency in the noise spectrum is predicted; the amplitude and the width of being of the same order of magnitude as the recently reported peak in the noise spectrum at the spin Larmor frequency. The ratio of the spectrum amplitudes at zero- and Larmor frequencies is shown to be a convenient tool for testing theoretical predictions.Comment: 4 pages, 3 figures. In the replaced version some mistakes are fixe

Magnetic properties of a metal-organic antiferromagnet on a distorted honeycomb lattice

For temperatures T well above the ordering temperature T*=3.0+-0.2K the magnetic properties of the metal-organic material Mn[C10H6(OH)(COO)]2x2H20 built from Mn^2+ ions and 3-hydroxy-2-naphthoic anions can be described by a S=5/2 quantum antiferromagnet on a distorted honeycomb lattice with two different nearest neighbor exchange couplings J2 \approx 2J1 \approx 1.8K. Measurements of the magnetization M(H,T) as a function of a uniform external field H and of the uniform zero field susceptibility \chi(T) are explained within the framework of a modified spin-wave approach which takes into account the absence of a spontaneous staggered magnetization at finite temperatures.Comment: 11 pages, 11 figures; more thorough discussion of the dependence of the correlation length on the uniform magnetic field adde

Symplectic N and time reversal in frustrated magnetism

Identifying the time reversal symmetry of spins as a symplectic symmetry, we develop a large N approximation for quantum magnetism that embraces both antiferromagnetism and ferromagnetism. In SU(N), N>2, not all spins invert under time reversal, so we have introduced a new large N treatment which builds interactions exclusively out of the symplectic subgroup [SP(N)] of time reversing spins, a more stringent condition than the symplectic symmetry of previous SP(N) large N treatments. As a result, we obtain a mean field theory that incorporates the energy cost of frustrated bonds. When applied to the frustrated square lattice, the ferromagnetic bonds restore the frustration dependence of the critical spin in the Neel phase, and recover the correct frustration dependence of the finite temperature Ising transition.Comment: added reference

Quantum criticality of dipolar spin chains

We show that a chain of Heisenberg spins interacting with long-range dipolar forces in a magnetic field h perpendicular to the chain exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave theory the magnon dispersion for small momenta k is [Delta^2 + v_k^2 k^2]^{1/2}, where Delta^2 \propto |h - h_c| and v_k^2 \propto |ln k|. For fields close to h_c linear spin-wave theory breaks down and we investigate the system using density-matrix and functional renormalization group methods. The Ginzburg regime where non-Gaussian fluctuations are important is found to be rather narrow on the ordered side of the transition, and very broad on the disordered side.Comment: 6 pages, 5 figure

Nonequilibrium orbital magnetization of strongly localized electrons

The magnetic response of strongly localized electrons to a time-dependent vector potential is considered. The orbital magnetic moment of the system, away from steady-state conditions, is obtained. The expression involves the tunneling and phonon-assisted hopping currents between localized states. The frequency and temperature dependence of the orbital magnetization is analyzed as function of the admittances connecting localized levels. It is shown that quantum interference of the localized wave functions contributes to the moment a term which follows adiabatically the time-dependent perturbation.Comment: RevTeX 3.

Two-dimensional quantum spin-1/2 Heisenberg model with competing interactions

We study the quantum spin-1/2 Heisenberg model in two dimensions, interacting through a nearest-neighbor antiferromagnetic exchange ($J$) and a ferromagnetic dipolar-like interaction ($J_d$), using double-time Green's function, decoupled within the random phase approximation (RPA). We obtain the dependence of $k_B T_c/J_d$ as a function of frustration parameter $\delta$, where $T_c$ is the ferromagnetic (F) transition temperature and $\delta$ is the ratio between the strengths of the exchange and dipolar interaction (i.e., $\delta = J/J_d$). The transition temperature between the F and paramagnetic phases decreases with $\delta$, as expected, but goes to zero at a finite value of this parameter, namely $\delta = \delta_c = \pi /8$. At T=0 (quantum phase transition), we analyze the critical parameter $\delta_c(p)$ for the general case of an exchange interaction in the form $J_{ij}=J_d/r_{ij}^{p}$, where ferromagnetic and antiferromagnetic phases are present.Comment: 4 pages, 1 figur

Dipolar ground state of planar spins on triangular lattices

An infinite triangular lattice of classical dipolar spins is usually considered to have a ferromagnetic ground state. We examine the validity of this statement for finite lattices and in the limit of large lattices. We find that the ground state of rectangular arrays is strongly dependent on size and aspect ratio. Three results emerge that are significant for understanding the ground state properties: i) formation of domain walls is energetically favored for aspect ratios below a critical valu e; ii) the vortex state is always energetically favored in the thermodynamic limit of an infinite number of spins, but nevertheless such a configuration may not be observed even in very large lattices if the aspect ratio is large; iii) finite range approximations to actual dipole sums may not provide the correct ground sta te configuration because the ferromagnetic state is linearly unstable and the domain wall energy is negative for any finite range cutoff.Comment: Several short parts have been rewritten. Accepted for publication as a Rapid Communication in Phys. Rev.