Magnetoresistance of Two-Dimensional Fermions in a Random Magnetic Field

We perform a semiclassical calculation of the magnetoresistance of spinless two-dimensional fermions in a long-range correlated random magnetic field. In the regime relevant for the problem of the half filled Landau level the perturbative Born approximation fails and we develop a new method of solving the Boltzmann equation beyond the relaxation time approximation. In absence of interactions, electron density modulations, in-plane fields, and Fermi surface anisotropy we obtain a quadratic negative magnetoresistance in the weak field limit.Comment: 12 pages, Latex, no figures, Nordita repor

Semiclassical theory of transport in a random magnetic field

We study the semiclassical kinetics of 2D fermions in a smoothly varying magnetic field $B({\bf r})$. The nature of the transport depends crucially on both the strength $B_0$ of the random component of $B({\bf r})$ and its mean value $\bar{B}$. For $\bar{B}=0$, the governing parameter is $\alpha=d/R_0$, where $d$ is the correlation length of disorder and $R_0$ is the Larmor radius in the field $B_0$. While for $\alpha\ll 1$ the Drude theory applies, at $\alpha\gg 1$ most particles drift adiabatically along closed contours and are localized in the adiabatic approximation. The conductivity is then determined by a special class of trajectories, the "snake states", which percolate by scattering at the saddle points of $B({\bf r})$ where the adiabaticity of their motion breaks down. The external field also suppresses the diffusion by creating a percolation network of drifting cyclotron orbits. This kind of percolation is due only to a weak violation of the adiabaticity of the cyclotron rotation, yielding an exponential drop of the conductivity at large $\bar{B}$. In the regime $\alpha\gg 1$ the crossover between the snake-state percolation and the percolation of the drift orbits with increasing $\bar{B}$ has the character of a phase transition (localization of snake states) smeared exponentially weakly by non-adiabatic effects. The ac conductivity also reflects the dynamical properties of particles moving on the fractal percolation network. In particular, it has a sharp kink at zero frequency and falls off exponentially at higher frequencies. We also discuss the nature of the quantum magnetooscillations. Detailed numerical studies confirm the analytical findings. The shape of the magnetoresistivity at $\alpha\sim 1$ is in good agreement with experimental data in the FQHE regime near $\nu=1/2$.Comment: 22 pages REVTEX, 14 figure

Field-induced magnetic phases in the normal and superconducting states of ErNi2B2C

We present a comprehensive neutron-diffraction study of the magnetic structures of ErNi2B2C in the presence of a magnetic field applied along [010], [110], or [001]. In zero field, the antiferromagnetic structure is transversely polarized with Qapproximate to0.55a* and the moments along the b direction. At the lowest temperatures, the modulation is close to a square wave, and transitions of Q between different commensurable values are observed when varying the field. The commensurable structures are analyzed in terms of a detailed mean-field model. Experimentally, the minority domain shows no hysteresis and stays stable up to a field close to the upper critical field of superconductivity, when the field is applied along [010]. Except for this possible effect, the influences of the superconducting electrons on the magnetic structures are not directly visible. Another peculiarity is that Q rotates by a small, but clearly detectable, angle of about 0.5degrees away from the [100] and the field direction, when the field is applied along [110] and is approximately equal to or larger than the upper critical field.This article is published as Jensen, A., K. Nørgaard Toft, A. B. Abrahamsen, D. F. McMorrow, M. R. Eskildsen, N. H. Andersen, J. Jensen et al. "Field-induced magnetic phases in the normal and superconducting states of ErNi 2 B 2 C." Physical Review B 69, no. 10 (2004): 104527. DOI: 10.1103/PhysRevB.69.104527. Copyright 2004 American Physical Society. Posted with permission