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

We summarize and extend our study (using real-space response and correlation functions) of the properties of a continuous-symmetry ferromagnet with random anisotropy, distinguishing between the cases of weak and strong random anisotropy. For the weak-anisotropy case we find three different magnetic regimes, according to the strength of the external magnetic field H. In zero H, the net magnetization is zero, although the ferromagnetic correlation length (FCL) is large. We call a ferromagnet in this first regime a correlated spin glass (CSG). It has a very large magnetic susceptibility, and hence a relatively small coherent anisotropy converts it into a nearly typical ferromagnetic domain structure. Also, a relatively small magnetic field nearly aligns the CSG, producing the second regime, which we call a ferromagnet with wandering axis (FWA). The FWA is a slightly noncollinear structure in which the tipping of the magnetization with respect to the field varies over the system. The tipping angle is correlated over a (field-dependent) correlation length which is smaller than the FCL of the CSG. As the field increases the correlation length in the FWA decreases, until the third regime is reached, wherein the tipping angles (which are smaller than in the FWA) are completely uncorrelated from site to site. We obtain the magnetization or susceptibility (as appropriate) for each of these three regimes. We also show that the temperature dependence of the (single-ion) random anisotropy strength can provide a plausible explanation for certain classes of reentrant phenomena and susceptibility cusps observed in magnetization studies. Neutron scattering studies appear to be consistent with the predicted ${H}^{\mathrm{\ensuremath{-}}1/2}$ dependence of the FCL in the FWA regime, and display the expected rise of the FCL in the CSG regime as the random anisotropy strength decreases with increasing temperature.

Ordering in ferromagnets with random anisotropy.

The phenomenological model is proposed for amorphous magnets with ferromagnetic exchange and small random anisotropy. A new type of spin-glass state is described. Its behaviour in an external magnetic field is shown to deviate strongly from mean-field theory predictions. The effect of coherent anisotropy is discussed.

https://iopscience.iop.org/article/10.1088/0022-3719/16/21/019/pdf

Phenomenological theory of amorphous magnets with small random anisotropy

The spatial correlation between the directions of magnetization is calculated phenomenologically for an amorphous solid with a random distribution of easy axes. It is found that, for large exchange and small anisotropy, ferromagnetism can exist only in more than four dimensions. For all dimensions $dg2$, spin-glass states of different types are possible. The dependence of magnetic behavior on the intrinsic parameters of an amorphous solid is established.

Spin-glass and ferromagnetic states in amorphous solids

We analyze analytically the length dependence of the resistance \ensuremath{\rho} for the case of variable-range hopping in finite one-dimensional systems. The resistance shows large fluctuations with variations in the chemical potential of the system and the average value 〈ln\ensuremath{\rho}〉\ensuremath{\sim}(${T}_{0}$/T${)}^{1/2}$[ln(2\ensuremath{\alpha}L${)]}^{1/2}$, where \ensuremath{\alpha} is the inverse localization length and ${\mathrm{kT}}_{0}$=\ensuremath{\alpha}/N(0), N(0) being the density of states. This result is in good agreement with numerical simulations. Fluctuations of the log resistance, ${\ensuremath{\Delta}}^{2}$=〉(ln\ensuremath{\rho}-〈ln\ensuremath{\rho}〉${)}^{2}$ 〈, are conjectured to decrease with increasing length according to the relation \ensuremath{\Delta}\ensuremath{\sim}(${T}_{0}$/T${)}^{1/2}$[ln(2\ensuremath{\alpha}L${)\phantom{\rule{0ex}{0ex}}]}^{\mathrm{\ensuremath{-}}1/2}$. Numerical results show large fluctuations in \ensuremath{\Delta} for different ensembles of the same length which are characterized by the same set of parameters [T, \ensuremath{\alpha}, N(0), etc.]. Averaging over many such ensembles yields a good agreement with the above prediction for \ensuremath{\Delta}. Numerical simulations also confirm that the product \ensuremath{\Delta}〈ln\ensuremath{\rho}〉 does not change with the length of the wire. Our results can be useful for future experiments on ultranarrow-channel metal-oxide-semiconductor field-effect transistors.

New aspects of variable-range hopping in finite one-dimensional wires.

We address the problem of conductance fluctuations in real space. The nonlocal conductivity tensor and its correlation functions are calculated from the Kubo formula and are shown to exhibit long-ranged behavior. We offer a physical interpretation of our results. The results are used to calculate the long-range spatial correlations in the current density.

R. A. Serota

Papers

Ordering in ferromagnets with random anisotropy.

Phenomenological theory of amorphous magnets with small random anisotropy

Spin-glass and ferromagnetic states in amorphous solids

New aspects of variable-range hopping in finite one-dimensional wires.

Long-range correlations in disordered metals