[show abstract][hide abstract] ABSTRACT: The interface between the insulating oxides LaAlO3 and SrTiO3 exhibits a superconducting two-dimensional electron system that can be modulated by a gate voltage. While the conductivity has been probed extensively and gating of the superconducting critical temperature has been demonstrated, the question as to whether, and if so how, the gate tunes the superfluid density and superconducting order parameter needs to be answered. We present local magnetic susceptibility, related to the superfluid density, as a function of temperature, gate voltage, and location. We show that the temperature dependence of the superfluid density at different gate voltages collapses to a single curve that is characteristic of a full superconducting gap. Further, we show that the dipole moments observed in this system are not modulated by the gate voltage.
[show abstract][hide abstract] ABSTRACT: Manipulation of magnetism is a longstanding goal of research in exotic materials. In this work, we demonstrate that the small ferromagnetic patches in LaAlO(3)/SrTiO(3) heterostructures can be dramatically changed by in situ contact of a scanning probe. Our results provide a platform for manipulation of small magnets through either a strong magneto-elastic coupling or sensitivity to surface modification. The ability to locally control magnetism is particularly interesting due to the presence of superconductivity with strong spin-orbit coupling in LaAlO(3)/SrTiO(3).
[show abstract][hide abstract] ABSTRACT: The interface between the insulating oxides LaAlO3 and SrTiO3 exhibits a
superconducting two-dimensional electron system that can be modulated by a gate
voltage. While gating of the conductivity has been probed extensively and
gating of the superconducting critical temperature has been demonstrated, the
question whether, and if so how, the gate tunes the superfluid density and
superconducting order parameter is unanswered. We present local magnetic
susceptibility, related to the superfluid density, as a function of
temperature, gate voltage and location. We show that the temperature dependence
of the superfluid density at different gate voltages collapse to a single curve
characteristic of a full superconducting gap. Further, we show that the dipole
moments observed in this system are not modulated by the gate voltage.
[show abstract][hide abstract] ABSTRACT: Scanning SQUID susceptometry images the local magnetization and
susceptibility of a sample. By accurately modeling the SQUID signal we can
determine the physical properties such as the penetration depth and
permeability of superconducting samples. We calculate the scanning SQUID
susceptometry signal for a superconducting slab of arbitrary thickness with
isotropic London penetration depth, on a non-superconducting substrate, where
both slab and substrate can have a paramagnetic response that is linear in the
applied field. We derive analytical approximations to our general expression in
a number of limits. Using our results, we fit experimental susceptibility data
as a function of the sample-sensor spacing for three samples: 1) delta-doped
SrTiO3, which has a predominantly diamagnetic response, 2) a thin film of
LaNiO3, which has a predominantly paramagnetic response, and 3) a
two-dimensional electron layer (2-DEL) at a SrTiO3/AlAlO3 interface, which
exhibits both types of response. These formulas will allow the determination of
the concentrations of paramagnetic spins and superconducting carriers from fits
to scanning SQUID susceptibility measurements.
[show abstract][hide abstract] ABSTRACT: The interface of LaAlO3/SrTiO3 heterostructures
exhibits both conductivity and magnetism. Significant effort has been
invested researching the details and characteristics of the
conductivity, such as conductance only above a critical
LaAlO3 thickness. However, reports of ferromagnetism differ
in a variety of details requiring further investigation into the
material properties that control magnetism. In this study we use a
scanning SQUID microscope to locally image the landscape of
ferromagnetism as a function of several tuning parameters including the
LaAlO3 thickness, back gate voltage, local strain and surface
treatment. We find that the ferromagnetism is inhomogeneous within each
sample, varies considerably between samples, and appears only in samples
whose LaAlO3 layer is thicker than a threshold value, similar
to the conductance critical thickness. The ferromagnetism changes with
local strain, surface treatment with polar solvents and applied field.
However it is not affected by changing the gate voltage or cycling the
temperature up to 300K. These results provide experimental input for
determining and controlling the mechanisms of magnetism in engineered
complex oxide interfaces.
[show abstract][hide abstract] ABSTRACT: Point defects in two-dimensional superconductors produce significant
local variations in the superconducting properties. A model  of point
defects in a weak, two-dimensional superconductor, based on London's
equations, shows that defects appear as haloes of decreased diamagnetic
susceptibility as seen by the imaging kernel of a scanning SQUID
susceptometer. We report theoretical limits on the defect strength and
superconducting Pearl length λ required for defects to be
visible. We compare these models to our experimental data showing
similar haloes in the superconducting state of several types of
superconducting films as a function of magnetic field, gate voltage,
temperature, and height. Our ability to image these defects offers new
possibilities for studying the interplay between materials properties
and superconducting phenomena in thin film systems.[4pt]  V.G. Kogan
and J.R. Kirtley, Phys. Rev. B 83, 214521 (2011).
[show abstract][hide abstract] ABSTRACT: The interface between two insulating oxides, LaAlO3 and
SrTiO3, exhibits a two-dimensional electron system with high
mobility, magnetism, superconductivity at low temperatures, and an
electric-field-tuned superconductor-insulator transition. This interface
has been studied extensively using transport and magnetization, which do
not directly probe potential variation on a local length scale. We use a
scanning SQUID microscope to locally probe superconductivity and
magnetism in LAO/STO heterostructures. We measure the local diamagnetic
susceptibility and critical temperature of as a function of position and
gate voltage. Our local susceptibility measurement is related to the
density of superconducting carriers which gives us a map of superfluid
density. We find that the superfluid density is inhomogeneous, showing
regions of susceptibility that varies over a large fraction of the total
response while the critical temperature remains relatively uniform
across the sample. Tracking the evolution of both of these parameters as
a function of gate voltage and position enables investigation of the
local onset of the superconductor-insulator transitions on both sides of
[show abstract][hide abstract] ABSTRACT: In LaAlO(3)/SrTiO(3) heterointerfaces, charge carriers migrate from the LaAlO(3) to the interface in an electronic reconstruction. Magnetism has been observed in LaAlO(3)/SrTiO(3), but its relationship to the interface conductivity is unknown. Here we show that reconstruction is necessary, but not sufficient, for the formation of magnetism. Using scanning superconducting quantum interference device microscopy we find that magnetism appears only above a critical LaAlO(3) thickness, similar to the conductivity. We observe no change in ferromagnetism with gate voltage, and detect ferromagnetism in a non-conducting p-type sample. These observations indicate that the carriers at the interface do not need to be itinerant to generate magnetism. The ferromagnetism appears in isolated patches whose density varies greatly between samples. This inhomogeneity strongly suggests that disorder or local strain generates magnetism in a population of the interface carriers.
[show abstract][hide abstract] ABSTRACT: LaAlO3 and SrTiO3 are insulating, nonmagnetic oxides, yet the interface
between them exhibits a two-dimensional electron system with high electron
mobility,1 superconductivity at low temperatures,2-6 and electric-field-tuned
metal-insulator and superconductorinsulator phase transitions.3,6-8 Bulk
magnetization and magnetoresistance measurements also suggest some form of
magnetism depending on preparation conditions5,9-11 and suggest a tendency
towards nanoscale electronic phase separation.10 Here we use local imaging of
the magnetization and magnetic susceptibility to directly observe a landscape
of ferromagnetism, paramagnetism, and superconductivity. We find submicron
patches of ferromagnetism in a uniform background of paramagnetism, with a
nonuniform, weak diamagnetic superconducting susceptibility at low temperature.
These results demonstrate the existence of nanoscale phase separation as
suggested by theoretical predictions based on nearly degenerate interface
sub-bands associated with the Ti orbitals.12,13 The magnitude and temperature
dependence of the paramagnetic response suggests that the vast majority of the
electrons at the interface are localized, and do not contribute to transport
measurements.3,6,7 In addition to the implications for magnetism, the existence
of a 2D superconductor at an interface with highly broken inversion symmetry
and a ferromagnetic landscape in the background suggests the potential for
exotic superconducting phenomena.
[show abstract][hide abstract] ABSTRACT: The discovery of interface superconductivity in complex oxide heterostructures has generated significant excitement. We used scanning SQUID microscopy to investigate the magnetic properties of one such heterostructure, delta-doped structures in SrTiO3 thin films. We have observed a diamagnetic response and imaged vortices providing further evidence of a two-dimensional superconducting state. Finally we measured the magnetic susceptibility from which we observe spatial inhomogeneities in the superconducting response and can estimate the temperature dependence of the magnetic penetration depth.
[show abstract][hide abstract] ABSTRACT: We locally measure the superfluid density rhos(T) in Ba(Fe1-xCox)2As2 single crystals with magnetic force microscopy and scanning SQUID susceptometry. These high-precision, local-probe-based techniques enable us to measure both the zero temperature value of the superfluid density rhos(0) and the temperature variation, to distinguish homogeneous from spatially varying responses, and to report systematic behavior as a function of Co doping across the superconducting dome. We find that rhos(T) increases sharply with decreasing temperature below the superconducting transition temperature Tc of both optimally doped and underdoped compounds, and that rhos(0) falls more quickly with Tc on the underdoped side of the dome than on the overdoped. These observations, as well as the increasing temperature induced change of rhos(T) at low temperatures upon underdoping, are consistent with magnetic fluctuation mediated pairing and the coexistence of magnetism and superconductivity.
[show abstract][hide abstract] ABSTRACT: We measure the penetration depth λab(T) in Ba(Fe(1-x)Co(x))(2)As(2) using local techniques that do not average over the sample. The superfluid density ρs(T) ≡ 1/λab(T)2 has three main features. First, ρs (T = 0) falls sharply on the underdoped side of the dome. Second, λab(T) is flat at low T at optimal doping, indicating fully gapped superconductivity, but varies more strongly in underdoped and overdoped samples, consistent with either a power law or a small second gap. Third, ρs (T) varies steeply near Tc for optimal and underdoping. These observations are consistent with an interplay between magnetic and superconducting phases.
[show abstract][hide abstract] ABSTRACT: LaAlO3 and SrTiO3 are insulating, non-magnetic oxides, yet the interface between them exhibits a two-dimensional electron system with high electron mobility, superconductivity at low temperatures and electric-field-tuned metal-insulator and superconductor-insulator phase transitions. Bulk magnetization and magnetoresistance measurements also indicate some form of magnetism depending on preparation conditions and a tendency towards nanoscale electronic phase separation. Here we use local imaging of the magnetization and magnetic susceptibility to directly observe a landscape of ferromagnetism, paramagnetism and superconductivity. We find submicrometre patches of ferromagnetism in a uniform background of paramagnetism, with a non-uniform, weak diamagnetic superconducting susceptibility at low temperature. These results demonstrate the existence of nanoscale phase separation as indicated by theoretical predictions based on nearly degenerate interface sub-bands associated with the Ti orbitals. The magnitude and temperature dependence of the paramagnetic response indicate that the vast majority of the electrons at the interface are localized, and do not contribute to transport measurements. In addition to the implications for magnetism, the existence of a two-dimensional superconductor at an interface with highly broken inversion symmetry and a ferromagnetic landscape in the background indicates the potential for exotic superconducting phenomena.
[show abstract][hide abstract] ABSTRACT: Rings are a model system for studying phase coherence in one dimension.
Superconducting rings have states with uniform phase windings that are integer
multiples of 2$\pi$ called fluxoid states. When the energy difference between
these fluxoid states is of order the temperature so that phase slips are
energetically accessible, several states contribute to the ring's magnetic
response to a flux threading the ring in thermal equilibrium and cause a
suppression or downturn in the ring's magnetic susceptibility as a function of
temperature. We review the theoretical framework for superconducting
fluctuations in rings including a model developed by Koshnick$^1$ which
includes only fluctuations in the ring's phase winding number called fluxoid
fluctuations and a complete model by von Oppen and Riedel$^2$ that includes all
thermal fluctuations in the Ginzburg-Landau framework. We show that for
sufficiently narrow and dirty rings the two models predict a similar
susceptibility response with a slightly shifted Tc indicating that fluxoid
fluctuations are dominant. Finally we present magnetic susceptibility data for
rings with different physical parameters which demonstrate the applicability of
our models. The susceptibility data spans a region in temperature where the
ring transitions from a hysteretic to a non hysteretic response to a periodic
applied magnetic field. The magnetic susceptibility data, taken where
transitions between fluxoid states are slow compared to the measurement time
scale and the ring response was hysteretic, decreases linearly with increasing
temperature resembling a mean field response with no fluctuations. At higher
temperatures where fluctuations begin to play a larger role a crossover occurs
and the non-hysteretic data shows a fluxoid fluctuation induced suppression of
diamagnetism below the mean field response that agrees well with the models.
[show abstract][hide abstract] ABSTRACT: We use a scanning SQUID microscope to measure the suppression of the superconducting response of quasi-1D rings specifically designed to exhibit phase winding fluctuations below Tc. Extremely high flux sensitivity as well as a positionable sensor capable of measuring many individual rings and subtracting the background in situ make scanning SQUID ideal for this measurement. The physical ring parameters are carefully controlled during fabrication to reduce the ring's superconducting phase stiffness by tuning the energy spacing of states where a uniform phase winds an integer number of times around the ring. When the energy difference between adjacent phase winding states is approximately equal to the temperature, the superfluid density is suppressed by the contribution of multiple states to the response. We present susceptibility data and a theoretical framework that demonstrate how these fluxoid fluctuations suppress the ring's diamagnetism below Tc.
[show abstract][hide abstract] ABSTRACT: Susceptibility measurements of patterned thin films at sub-K temperatures were carried out using a scanning SQUID microscope that can resolve signals corresponding to a few hundred Bohr magnetons. Several metallic and insulating thin films, even oxide-free Au films, show a paramagnetic response with a temperature dependence that indicates unpaired spins as the origin. The observed response exhibits a measurable out-of-phase component, which implies that these spins will create 1/f-like magnetic noise. The measured spin density is consistent with recent explanations of low frequency flux noise in SQUIDs and superconducting qubits in terms of spin fluctuations, and suggests that such unexpected spins may be even more ubiquitous than already indicated by earlier measurements. Our measurements set several constraints on the nature of these spins.
[show abstract][hide abstract] ABSTRACT: The authors have measured the magnetic response of 33 individual cold mesoscopic gold rings, one ring at a time. The response of some sufficiently small rings has a component that is periodic in the flux through the ring and is attributed to a persistent current. Its period is close to h/e, and its sign and amplitude vary between rings. The amplitude distribution agrees well with predictions for the typical h/e current in diffusive rings. The temperature dependence of the amplitude, measured for four rings, is also consistent with theory. These results disagree with previous measurements of three individual metal rings that showed a much larger periodic response than expected. The use of a scanning SQUID microscope enabled in situ measurements of the sensor background. A paramagnetic linear susceptibility and a poorly understood anomaly around a zero field are attributed to defect spins.
[show abstract][hide abstract] ABSTRACT: Our recent scanning SQUID susceptometry measurements of individual mesoscopic normal metal rings found persistent currents consistent with theoretical predictions. In addition to the persistent current signal, all rings exhibited a step anomaly in the SQUID response vs flux around zero applied flux and a large paramagnetic linear susceptibility. We present the characteristics of the zero flux anomaly observed in multiple rings and thin films and explore possible explanations. Key features include a notable frequency dependence between 11 and 333 Hz and a strong spatial correlation with the large paramagnetic spin signal.
[show abstract][hide abstract] ABSTRACT: Superconducting quantum interference devices (SQUIDs) can have excellent spin sensitivity depending on their magnetic flux noise, pickup loop diameter, and distance from the sample. We report a family of scanning SQUID susceptometers with terraced tips that position the pickup loops 300 nm from the sample. The 600 nm –2 μ m pickup loops, defined by focused ion beam, are integrated into a 12-layer optical lithography process allowing flux-locked feedback, in situ background subtraction and optimized flux noise. These features enable a sensitivity of ∼70 electron spins per root hertz at 4 K .
[show abstract][hide abstract] ABSTRACT: Superconducting Quantum Interference Devices (SQUIDs) are well known as excellent magnetic field sensors. We present a scanning DC SQUID susceptometer that is designed to couple well to nanometer-sized objects. Its gradiometric design and local field coils allow for cancellation of the applied field so that dynamic range issues do not limit the SQUID's sensitivity. Integrated modulation coils linearize the signal and allow for optimal performance at all applied fields. Planar coaxial shielding, enabled by a multi-layer niobium process, results in a low inductance (100 pH) millimeter scale design where the pickup loops can be optimized independently from the junction and shunt resistor parameters. The sensor loop is on a terraced structure so that it can be scanned approximately 100 nm from the sample surface. Focused Ion Beam milling is used to fabricate pickup loops with inner diameters between 250 nm and 2 microns with line widths of approximately 200 nm. A white noise sensitivity of 0.8 muphi0/&surd;Hz gives an estimated spin sensitivity of 80 muB/&surd;Hz at 4 Kelvin. We will also report on on-going scanning susceptometry measurements, and on the spin sensitivity at low temperatures.