This doctoral dissertation examines some magnetic properties of nanoscale conductors. It comprises two classes of problems, namely, the response of closed nanoscopic systems to an external magnetic field, and the magnetization dependent transport of nanomagnets. In the first class of closed nanoscopic structures like quantum dots or metal grains, the system has discrete energy levels which can be modeled by Random Matrix Theory. The addition of a magnetic field is analyzed using a crossover random matrix model. In Chapter 2, we show that in the crossover there exist correlations between elements of the same eigenvector and between different eigenvectors. We show that these correlations between different eigenvectors lead to enhanced fluctuations of the electron-electron interaction matrix elements which are absent in the pure ensembles. In Chapter 3, we generalize these results to analyze the magnetic field response of energy levels in ultrasmall metal grains. We present a theory of mesoscopic fluctuations of g-tensors and avoided crossing energies in a small metal grain that contains both orbital and spin contributions to the g-tensor.

In the second class of problems we study two effects in small ferromagnets where the charge transport is coupled to the magnetization. In Chapter 4, we show that a sufficiently large unpolarized current can cause a spin-wave instability in a nanomagnet with asymmetric contacts. The dynamics beyond the instability is calculated analytically in the perturbative regime of small spinwave amplitudes, and numerically for larger currents. In Chapter 5, we study "anisotropic magnetoresistance fluctuations" which is the ferromagnetic analog of the well-known Universal Conductance Fluctuations in metals. The conductance of a ferromagnetic particle depends on the relative orientation of the magnetization with respect to the direction of current flow. This phenomenon is known as "anisotropic magnetoresistance" and has no counterpart in normal-metal conductors. We show that quantum interference leads to an additional, random yet (statistically) universal dependence of the conductance of a ferromagnet on the magnetization direction. The mechanism for these anisotropic magnetoresistance fluctuations is the interplay of spin-orbit scattering, random impurity scattering, and the ferromagnet's exchange field.