Ground state structure, domain walls, and external field response in random magnets

The ground state structure and domain walls in Ising-like magnets with quenched randomness are studied at zero temperature. The methods employed are exact ground state calculations using graph-theoretical optimization and extreme statistics arguments. The elastic manifolds, i.e., domain walls, with random-bond disorder are investigated with two different types of periodicity. The first type of periodicity is when the randomness is periodically repeated. It is shown to lead after a cross-over to the periodic elastic media universality class, whenever the period lambda is finite. The second periodicity is due to an additional modulating potential. There are two types of intermittence seen before the asymptotic random-bond roughness behavior is reached. The first type is when the manifolds jump between the minima of the periodic potential and the second type is when the interfaces roughen over pinning energy barriers. An external field is applied to the random manifolds. An energy minimization argument based on the glassy energy landscape indicates that in an equilibrium system the manifolds move by sharp jumps between nearly degenerate energy minima in analogy to a first-order transition. A mean field argument for the finite-size scaling of the first jump field is derived and numerically confirmed. Using extreme statistics and probabilistic arguments, the probability distribution of the first jump field and its finite size scaling are calculated. Based on these the susceptibility of the manifolds is derived. Random field magnets are studied in two dimensions. The break-up of long-range order is shown to have a first-order character. The domain wall behavior is studied, leading to an interface scaling with a roughness exponent greater than unity below the break-up length scale. The domain wall energy is demonstrated to vanish logarithmically confirming the destruction of the long-range order. The magnetization and susceptibility versus the external field are investigated, and they show continuous behaviors and are independent of the break-up length scale. However, another long-range order, percolation, is found in two-dimensional random field magnets. The percolation transition with respect to the external field belongs to the standard short-range correlated two-dimensional percolation universality class. The whole phase diagram for percolation as a function of the random field strength and the external field is predicted.reviewe

Ferromagnetic resonance in ϵ\epsilon-Co magnetic composites

We investigate the electromagnetic properties of assemblies of nanoscale $\epsilon$-cobalt crystals with size range between 5 nm to 35 nm, embedded in a polystyrene (PS) matrix, at microwave (1-12 GHz) frequencies. We investigate the samples by transmission electron microscopy (TEM) imaging, demonstrating that the particles aggregate and form chains and clusters. By using a broadband coaxial-line method, we extract the magnetic permeability in the frequency range from 1 to 12 GHz, and we study the shift of the ferromagnetic resonance with respect to an externally applied magnetic field. We find that the zero-magnetic field ferromagnetic resonant peak shifts towards higher frequencies at finite magnetic fields, and the magnitude of complex permeability is reduced. At fields larger than 2.5 kOe the resonant frequency changes linearly with the applied magnetic field, demonstrating the transition to a state in which the nanoparticles become dynamically decoupled. In this regime, the particles inside clusters can be treated as non-interacting, and the peak position can be predicted from Kittel's ferromagnetic resonance theory for non-interacting uniaxial spherical particles combined with the Landau-Lifshitz-Gilbert (LLG) equation. In contrast, at low magnetic fields this magnetic order breaks down and the resonant frequency in zero magnetic field reaches a saturation value reflecting the interparticle interactions as resulting from aggregation. Our results show that the electromagnetic properties of these composite materials can be tuned by external magnetic fields and by changes in the aggregation structure.Comment: 14 pages, 13 figure

Scaling of interfaces in brittle fracture and perfect plasticity

The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a linear size L=350 it is found that in the cases studied the fracture surfaces exhibit self-affine scaling with a roughness exponent close to 2/3, which is asymptotically exactly true for plasticity though finite-size effects are evident for both. The overlap of yield or minimum energy and fracture surfaces with exactly the same disorder configuration is shown to be a decreasing function of the system size and to be of a rather large magnitude for all cases studied. The typical ``overlap cluster'' length between pairs of such interfaces converges to a constant with $L$ increasing.Comment: Accepted for publication in Phys. Rev.

Results of genome-wide meta-analysis of sciatica

Raw result data of the genome-wide meta-analysis of sciatic

Manhattan plot for meta-analysis of adjusted genome-wide association results.

<p>Variants with p-values below the genome-wide significance level (p < 5x10^-8) are shown in red.</p

Sample demographics.

<p>Sample demographics.</p