Dynamic cantilever magnetometry of individual ferromagnetic nanotubes

In this thesis, we focus on a particular aspect of nanotechnology, namely the understanding of magnetic states in nanometer-scale objects. Describing microscopic magnetization states and reversal is particularly important for the development of magnetic storage media. In order to further optimize information-bit density, innovative geometries involving magnetic nanowires have been suggested by Parkin et al. in 2008. The realization of both writing and reading in such magnetic nanowires depends on the reliable induction and control of domain wall movement. In this thesis we intend to shed light on basic dynamic effects in similar structures.
Ferromagnetic nanotubes are the focus of this work due to their unique magnetic properties and unusual geometry. The reduced dimensionality of these structures manifests itself in magnetic configurations not present in macroscopic magnets. The magnetic samples that we are interested in are in the shape of a hollow prism with hexagonal cross-section and a very high aspect ratio. These structures avoid magnetization point singularities as present in solid magnetic cylinders, but support core-free magnetization states as a prerequisite for fast and controllable magnetization reversal. For this thesis, two different sets of magnetic samples are probed. One set of samples is processed to be Ni nanotubes, the other to be CoFeB nanotubes.
Dynamic cantilever magnetometry (DCM) allows us to investigate the weak magnetic response of individual magnetic nanotubes without averaging over an inhomogeneous ensemble. With this sensitive method we are able to study the magnetization states, magnetization reversal mechanisms, and demagnetization factors of single nanotubes dependent on the applied field and the alignment of the sample. The study of demagnetizing factors has been a classical topic in magnetism since the development of modern electrodynamics by Maxwell in 1865.
The advantages of our technique are the high precision of the associated frequency measurement and the potential of investigating arbitrary geometries, even at the nanometer scale. At the same time, interfering electrostatic and magnetostatic fields are entirely avoided by a purely optical readout. DCM is sensitive to the volume magnetization of the sample, instead of probing the total magnetic field including the stray field for instance.
An individual nanotube is affixed to the end of an ultrasoft cantilever, which is a mechanical oscillator exhibiting beam-like shape, clamped at one end, free at the other, and capable of deflection in one direction only in the fundamental oscillation mode. To fabricate the sample-on-cantilever system, individual nanotubes are chosen from their substrate under an optical microscope, and glued to the cantilever using a hydraulic micro-manipulator setup, allowing the handling of nanometer-scale samples. The torque acting between the magnetic nanotube and the applied field shifts the resonant frequency of the cantilever. Changes in the magnetization state can be tracked in timescales in the order of a few cantilever oscillation cycles.
This thesis is divided into four parts. In chapter 2 we establish the basic concepts of magnetism and introduce the coordinate systems used throughout the thesis. To explain phenomena such as magnetic anisotropy, or magnetic domain formation we consider the total magnetostatic energy of a given sample. Minimization of the energy yields the optimal angle of the magnetization within a magnetic particle, as shown for an important model system, the prolate ellipsoid. We review deviant magnetization states for samples with different geometry.
Chapter 3 introduces our experimental method, DCM, after reviewing other means of magnetometry. To later explain our data, we derive the cantilever resonant frequency shift as a response to an applied magnetic field and discuss found solutions. We also derive demagnetization factors to describe the shape anisotropy of our samples.
In chapter 4 we mention the components necessary to perform DCM measurements, from the physical properties of the cantilever to the experimental methods. Following in Feynman's footsteps, we illustrate bottom-up nanotube sample growth and fabrication methods including micro-manipulation and focused ion beam microscopy.
Finally in chapter 5 we show and discuss the findings of our measurements. We measure the shift of the cantilever resonant frequency as a function of both the applied field and the alignment of the sample in three basic configurations to characterize the sample anisotropy.