Magnetic force microscopy studies of unconventional superconductors [electronic resource] : single vortex manipulation and magnetic penetration depth measurements
Keywords: Physics

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 \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