Annals of physics

Understanding the correlation between magnetic properties and nanostructure involves collaborative efforts between chemists, physicists, and materials scientists to study both fundamental properties and potential applications. This article introduces a classification of nanostructure morphology according to the mechanism responsible for the magnetic properties. The fundamental magnetic properties of interest and the theoretical frameworks developed to model these properties are summarized. Common chemical and physical techniques for the fabrication of magnetic nanostructures are surveyed, followed by some examples of recent investigations of magnetic systems with structure on the nanometer scale. The article concludes with a brief discussion of some promising experimental techniques in synthesis and measurements.

Magnetic Properties of Nanostructured Materials

The transport properties of disordered solids have been the subject of much work since at least the 1950s, but with a new burst of activity during the 1980s which has survived up to the present day. There have been numerous reviews of a more or less specialized nature. The present review aims to fill the niche for a non-specialized review of this very active area of research. The basic concepts behind the theory are introduced with more detailed sections covering experimental results, one-dimensional localization, scaling theory, weak localization, magnetic field effects and fluctuations.

https://iopscience.iop.org/article/10.1088/0034-4885/56/12/001/pdf

Localization: theory and experiment

We review some electron transport experiments on few-electron, vertical quantum dot devices. The measurement of current versus source–drain voltage and gate voltage is used as a spectroscopic tool to investigate the energy characteristics of interacting electrons confined to a small region in a semiconducting material. Three energy scales are distinguished: the single-particle states, which are discrete due to the confinement involved; the direct Coulomb interaction between electron charges on the dot; and the exchange interaction between electrons with parallel spins. To disentangle these energies, a magnetic field is used to reorganize the occupation of electrons over the single-particle states and to induce changes in the spin states. We discuss the interactions between small numbers of electrons (between 1 and 20) using the simplest possible models. Nevertheless, these models consistently describe a large set of experiments. Some of the observations resemble similar phenomena in atomic physics, such as shell structure and periodic table characteristics, Hund’s rule, and spin singlet and triplet states. The experimental control, however, is much larger than for atoms: with one device all the artificial elements can be studied by adding electrons to the quantum dot when changing the gate voltage.

https://iopscience.iop.org/article/10.1088/0034-4885/64/6/201/pdf

Few-electron quantum dots

TOPICAL REVIEW: Nanomagnetics

Spin-wave localization in ferromagnets with weak random-axes anisotropy

We demonstrate that distributions of human response times have power-law tails and, among closed-form distributions, are best fit by the generalized inverse gamma distribution. We speculate that the task difficulty tracks the half-width of the distribution and show that it is related to the exponent of the power-law tail.

Distribution of Human Response Times

On donne une formulation de la reponse lineaire de ce diamagnetisme qui caracterise le tenseur de susceptibilite diamagnetique a desordre non moyenne La susceptibilite moyenne d'un metal desordonne est identique a un metal propre

Theory of Landau diamagnetism of dirty metals.

We study a stochastic process defined by the interaction strength for the return to the mean and a stochastic term proportional to the magnitude of the variable. Its steady-state distribution is the Inverse Gamma distribution, whose power-law tail exponent is determined by the ratio of the interaction strength to stochasticity. Its time-dependence is characterized by a set of discrete times describing relaxation of respective cumulants to their steady-state values. We show that as the progressively lower cumulants diverge with the increase of stochasticity, so do their relaxation times. We analytically evaluate the correlation function and show that it is determined by the longest of these times, namely the inverse interaction strength, which is also the relaxation time of the mean. We also investigate relaxation of the entire distribution to the steady state and the distribution of relaxation times, which we argue to be Inverse Gaussian.

Correlation and relaxation times for a stochastic process with a fat-tailed steady-state distribution

The variance of the number of levels in an energy interval around a level with large quantum numbers (semiclassical quantization) is studied for a particle in a rectangular box. Sampling involves changing the ratio of the rectangle's sides while keeping the area constant. For sufficiently narrow intervals, one finds the usual linear growth with the width of the interval. For wider intervals, the variance undergoes large, nondecaying oscillations around what is expected to be the saturation value. These oscillations can be explained as a superposition of just a few harmonics that correspond to the shortest periodic orbits in the rectangle. The analytical and numerical results are in excellent agreement.

R. A. Serota

Papers

Spin-wave localization in ferromagnets with weak random-axes anisotropy

Distribution of Human Response Times

Theory of Landau diamagnetism of dirty metals.

Correlation and relaxation times for a stochastic process with a fat-tailed steady-state distribution

Persistence of strong correlations in the energy spectrum of a separable Hamiltonian system: the rectangular box.