Superconductivity is among the most fascinating properties that a material can have. Below the transition temperature $T_c$, electrons condensate into a macroscopic quantum mechanical state and flow without dissipation. The quantum nature of the superconducting state also manifests in its magnetic properties. Superconductors fully expels magnetic field in a weak applied field, referred as Meissner effect. In an intermediate field, superconductors often contain microscopic whirlpools of electrons that carry quantized magnetic flux, called vortices. In this thesis, I present magnetic-force-microscopy (MFM) studies of unconventional superconductors both in the Meissner state and in the mix state. We extend the application of MFM beyond the conventional imaging mode and use it for quantitative analysis. In the mix state, we use MFM manipulating individual vortices with a high level of control and a known force to study the mechanics and dynamics of a single vortex in cuprate superconductors. In the Messiner state, we establish MFM as a novel local technique to measure the magnetic penetration depth $\lambda$ and implement it to study the pairing mechanism of iron-pnictide superconductors. Chapter 1 contains a brief introduction of MFM and its conventional application of imaging. We demonstrate high-spatial resolution images of isolated superconducting vortices. We show that by integrating images of isolated vortices at consecutive heights we are able to reconstruct the force between the MFM tip and vortices. We can also obtain the force by using a tip-vortex model. The two methods agree and both allow us to obtain the force used in vortex manipulation discussed in Chapter 2 and Chapter 3. Chapter 2 discusses the behavior of individual vortices in fully doped YBa$_2$Cu$_3$O$_{7-\delta}$ when subject to a local force. Because the anisotropy of fully doped YBa$_2$Cu$_3$O$_{7-\delta}$ is moderate, the vortex motion can be well described as an elastic string moving through a uniform three dimensional pinning landscape. We find an unexpected and marked enhancement of the response of a vortex to pulling when we wiggle it transversely. In addition, we find enhanced vortex pinning anisotropy that suggests clustering of oxygen vacancies in our sample. We demonstrate manipulation at the nanoscale with a level of control far beyond what has been reported before. We show that a dragged vortex can be used to probe deep into the bulk of the sample and to interact with microscopic structures much smaller than the tip size. Chapter 3 shows the vortex behavior in another limit. In an very underdoped YBa$_2$Cu$_3$O$_{6+x}$ single crystal, a cuprate superconductor with strong anisotropy, a vortex can be regarded as a stack of two-dimensional pancakes with weak interlayer Josephson coupling. We use the MFM tip to split the pancake stacks composing a single vortex and to produce a kinked structure. Our measurements highlight the discrete nature of stacks of pancake vortices in layered superconductors. We also measure the required force in the process, providing the first measurement of the interlayer coupling at the single vortex level. The discovery of iron-pnictide superconductors in 2008 motivates my efforts to locally measure the magnetic penetration depth $\lambda$, one of the two fundamental length scales in superconductors and known to be difficult to measure. Chapter 4 discusses the methodology of measuring $\lambda$ by MFM, which is based on the time-reversed mirror approximation an analytical model of the MFM tip-superconductor interaction in the Meissner state. A calibration run was performed on \YBCO\ single crystals with known $\lambda$. The same time-reversed mirror approximation can be applied to scanning SQUID sysceptometry (SSS) to measure the temperature variation of penetration depth $\Delta\lambda(T)\equiv\lambda(T)-\lambda(0)$. Chapter 5 includes brief introduction of the iron-pnictide superconductors. The multiple conduction bands and the vicinity of the superconducting phase to magnetic phase give additional challenges in $\lambda$ measurements. We demonstrated in this chapter on single crystals of Ba(Fe$_{0.95}$Co$_{0.05}$)$_2$As$_2$ that MFM can measure the absolute value of $\lambda$, as well as obtain its temperature dependence and spatial homogeneity. We observe that $\Delta\lambda(T)$ varies 20 times slower with temperature than previously reported by bulk techniques, and that $\rho_s(T)$ over the full temperature range is well described by a clean two-band fully gapped model, consistent with the proposed $s\pm$ pairing symmetry. Chapter 6 extends the measurements of $\rho_s(T)$ to the family Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ with Co doping level $x$ across the superconducting dome. We observe systematic evolution of $\rho_s(T)$ with $x$ that can be summarized as three main trends. First, $\rho_s(0)$ falls more quickly with $T_c$ on the underdoped side of the dome than on the overdoped. Second, the temperature variation of $\rho_s(T)$ at low temperature increases away from optimal doping. Third, $\rho_s(T)$ increases sharply with cooling through the superconducting transition temperature $T_c$ of both optimally doped and underdoped compounds. These observations hint an interplay between magnetism and superconductivity.

From the Introduction: Nanotechnology and its underpinning sciences are progressing with unprecedented rapidity. With technical advances in a variety of nanoscale fabrication and manipulation technologies, the whole topical area is maturing into a vibrant field that is generating new scientific research and a burgeoning range of commercial applications, with an annual market already at the trillion dollar threshold. The means of fabricating and controlling matter on the nanoscale afford striking and unprecedented opportunities to exploit a variety of exotic phenomena such as quantum, nanophotonic and nanoelectromechanical effects. Moreover, researchers are elucidating new perspectives on the electronic and optical properties of matter because of the way that nanoscale materials bridge the disparate theories describing molecules and bulk matter. Surface phenomena also gain a greatly increased significance; even the well-known link between chemical reactivity and surface-to-volume ratio becomes a major determinant of physical properties, when it operates over nanoscale dimensions. Against this background, this comprehensive work is designed to address the need for a dynamic, authoritative and readily accessible source of information, capturing the full breadth of the subject. Its six volumes, covering a broad spectrum of disciplines including material sciences, chemistry, physics and life sciences, have been written and edited by an outstanding team of international experts. Addressing an extensive, cross-disciplinary audience, each chapter aims to cover key developments in a scholarly, readable and critical style, providing an indispensible first point of entry to the literature for scientists and technologists from interdisciplinary fields. The work focuses on the major classes of nanomaterials in terms of their synthesis, structure and applications, reviewing nanomaterials and their respective technologies in well-structured and comprehensive articles with extensive cross-references. It has been a constant surprise and delight to have found, amongst the rapidly escalating number who work in nanoscience and technology, so many highly esteemed authors willing to contribute. Sharing our anticipation of a major addition to the literature, they have also captured the excitement of the field itself in each carefully crafted chapter. Along with our painstaking and meticulous volume editors, full credit for the success of this enterprise must go to these individuals, together with our thanks for (largely) adhering to the given deadlines. Lastly, we record our sincere thanks and appreciation for the skills and professionalism of the numerous Elsevier staff who have been involved in this project, notably Fiona Geraghty, Megan Palmer and Greg Harris, and especially Donna De Weerd-Wilson who has steered it through from its inception. We have greatly enjoyed working with them all, as we have with each other.

This book presents the important analytical technique of magnetic microscopy. This method is applied to analyze layered structures with high resolution. This book presents a number of layer-resolving magnetic imaging techniques that have evolved recently. Many exciting new developments in magnetism rely on the ability to independently control the magnetization in two or more magnetic layers in micro- or nanostructures. This in turn requires techniques with the appropriate spatial resolution and magnetic sensitivity. The book begins with an introductory overview, explains then the principles of the various techniques and gives guidance to their use. Selected examples demonstrate the specific strengths of each method. Thus the book is a valuable resource for all scientists and practitioners investigating and applying magnetic layered structures.

This book mainly focuses on the investigation of the electric-field control of magnetism and spin-dependent transportation based on a Co40Fe40B20(CoFeB)/Pb(Mg1/3Nb2/3)0.7Ti0.3O3(PMN-PT) multiferroic heterostructure. Methods of characterization and analysis of the multiferroic properties with in situ electric fields are induced to detect the direct magnetoelectric (ME) coupling. A switchable and non-volatile electric field control of magnetization in CoFeB/PMN-PT(001) structures is observed at room temperature, and the mechanism of direct coupling between the ferroelectric domain and ferromagnetic film due to the combined action of 109° ferroelastic domain switching in PMN-PT and the absence of magnetocrystalline anisotropy in CoFeB is demonstrated. Moreover, the electric-field control of giant magnetoresistance is achieved in a CoFeB-based spin valve deposited on top of (011) oriented PMN-PT, which offers an avenue for implementing electric-writing and magnetic-reading random access memory at room temperature. Readers will learn the basic properties of multiferroic materials, many useful techniques related to characterizing multiferroics and the interesting ME effect in CoFeB/PMN-PT structures, which is significant for applications.

Frontiers in Magnetic Materials focuses on the current achievements and state-of-the-art advancements in magnetic materials. Several lines of development- High-Tc Superconductivity, Nanotechnology and refined experimental techniques among them – raised knowledge and interest in magnetic materials remarkably. The book comprises 24 chapters on the most relevant topics written by renowned international experts in the field. It is of central interest to researchers and specialists in Physics and Materials Science, both in academic and industrial research, as well as advanced students.