1. J. R. Kirtley et al., Phys. Rev. Lett. 76 (1996), 1336-1339
Scanning
SQUID
Microscopy
Scanning SQUID Microscopy
Introduction
SQUID
SSM
Applications
Prospects
J. R. Kirtley et al., Phys. Rev. Lett. 76 (1996),
New techniques to probe local properties
Superconducting QUantum Interference
Scanning SQUID Microscopy
Nowadays, many new techniques are developed, which have as main goal to probe the local physical properties of a material. Examples of very successful scanning techniques are STM (Scanning Tunneling Microscopy) and AFM (Atomic Force Microscopy). During this talk I will discuss a less familiar scanning technique that is based on the Superconducting Quantum Interference Device (SQUID).
The SQUID is a very sensitive magnetometer that is used quite frequently for the characterization of magnetically ordered structures and superconductors. It detects magnetic flux.This flux can be produced by a current, a magnetic gradient or a magnetic field.
In this talk I will explain the working of the SQUID in general and the Scanning SQUID Microscope in particular. I will give an overview of the achievements of this technique and I will compare them to other devices that determine the magnetic topology. Moreover, I will give some examples of applications of this technique in recent research and in the industry. Finally I will discuss the possibilities for improving the Scanning SQUID Microscope in the near future.
Device
Anne Arkenbout

2. Flux in a superconducting ring
Scanning
SQUID
Microscopy
Flux in a superconducting ring
Introduction
SQUID
SSM
Applications
Prospects
No resistance below critical temperature
The magnetic flux is quantized
Adjustment of supercurrent to maintain the quantisation
The basis of a superconducting quantum interference device is a ring made of superconducting material. A superconductor is characterised by the complete lack of electrical resistance beneeth a certain critical temperature. In a superconductor there is an effective elextron electron interaction due to which electron pairs are formed which are called cooper pairs.
The cooperpairs that are formed in the superconducting phase are all derscribed by one wave functionwhich. All the cooperpairs move in phase in the superconducting ring. This leads to a quantization in magnetic flux, which is shown in the figure.
The figure shows an experiment in which the flux trapped in the ring is plotted as a function of the applied magnetic field. It is clear that the trapped flux in the ring can only take discrete values which are denoted by the horizontal terraces in the picture. When the magnetic field becomes so high that a higher level can be reached, the flux jumps from one to the other quantum level with almost infinite slope. The size of the flux quantum is h/2e.
The total flux through such a superconducting ring consists of two components; The first is the internal flux, which is caused by the electrical current through the ring. The other contribution to the total flux is the flux applied by an external source. The total flux in the superconducting ring is quanized. So, when the external flux is changed a little, the internal flux has to change to remain in the same quantum state. The internal flux can be changed by ajusting the current in the superconducting ring.
Anne Arkenbout

3. Josephson junction Dc josephson effect Ac josephson effect
Scanning
SQUID
Microscopy
Josephson junction
Introduction
SQUID
SSM
Applications
Prospects
Dc josephson effect
Ac josephson effect
J=J0sin (0+ 2e/h Vt )
superconductor
Weak link
The superconducting ring in the SQUID is interrupted by one or more josephson junctions. A Josephson junction is a piece of material in which the superconductivity is weakened. If two superconductors are separated by a very thin (in the order of the correlation length) weak link, quantum mechanical tunneling of Cooper pairs can occur without breaking up the pairs.
In the absence of an applied field a current will be present which will be proportional to the phase difference between the wave functions of the cooperpairs on both sides of the junction. This spotaneous creation of a current in absence of a field is called the DC (direct current) Josephson effect.
When a constant voltage is generated around the weak link, the phase difference becomes linear function in time. Due to the quantisation this linear increasing phase difference leads to an oscillation in the current .The period of the oscillating current is proportional to the applied voltage. This is called the Ac (alternating current) josephson effect
Both effects are summarized in the formula for the current density.
Anne Arkenbout V

4. Dc SQUID. I I/2-J I/2+J Scanning SQUID Microscopy Introduction SQUID
SSM
Applications
Prospects I
In the ssm a direct current squid is used.
The dc SQUID consists of two parallel josephson junctions. The SQUID is connected to the electrical circuit, which applies a dc current. This current does not create a flux in the ring, because the current has the same direction in both parts of the ring.
When a magnetic field is applied another current will be created.This is shown in the figure. This current is zero, whenever the applied magnetic field has a value which in an integer times the flux quantum.
The induced circulating current creates an difference in current between the two halves of the superconducting ring. Due to the presence of the josephson juntions, these two currents can interfere which produces an oscillation in the critical current. This critical current is the maximum current that can flow through a weak link without the creation of a voltage drop.
The oscillation in the critical current finally results in an oscillation in the voltage over the SQUID as a function of the applied field. The SQUID can thus convert a magnetic flux in a change in a voltage.
When we are in the steep areas of this curve the magnetization can be determined very accurately. A lock-in feedback cirquit is created to Maintain the SQUID in this area.
I/2-J
I/2+J
Anne Arkenbout

5. Scanning SQUID Microscope
Microscopy
Scanning SQUID Microscope
Introduction
SQUID
SSM
Applications
Prospects
SQUID on a tip
Local magnetic properties
Refrigeration
In the Scanning SQUID Microscope, a very small dc SQUID is placed on top of a tip which can be moved with respect to the substrate. In this way, it can measure locally the magnetic properties.For the SQUId to work it needs to be at a temperature below Tc. There are two different refrigeration techniques used in Scanning SQUID Microscopes.
In the first method the SSM and the sample are placed in the same system. They are both cooled down, below the critical temperature. This is a very time consuming method, because everytime you want to measure a new sample, you need to cool down the system. Moreover, not every sample survives the cooling down to very low temperatures.
In the second technique however, the sample can be kept at room temperature.In this technique the SQUID is cooled down in a small cabin , separated from the sample. The cabin wall in front of the SQUID consists of a sapphire window.This window is transparent for magnetic flux but it isolates the SQUID from the external temperature.
Anne Arkenbout

6. Spatial resolution SQUID – sample separation
Scanning
SQUID
Microscopy
Spatial resolution
Introduction
SQUID
SSM
Applications
Prospects
SQUID – sample separation
The smaller the loop the higher the spatial resolution
Maximal resolution ~ m
The separation between the sample and the SQUID has a great influence on the spatial resolution of the SSM. When the distance from the SQUID to the material is big, the exact location of the measured flux is less apparent.
The low temperature technique has a small sample squid separation, and thus the spatial resolution is high(about 4 m). The techniques which probe a sample at room temperature have a large squid sample sparation, therefore this technique has a low spatial resolution (about 40 m).
The invention of high tc superconductors has improved the spatial resolution. Due to the higher working temperature of the high Tc superconductor, the system needs less isolation and so the SQUID to sample distance can be reduced.
Also the size and shape of the squid loop influence the spatial resolution. The smaller the SQUID the bigger will be the spatial resolution. The spatial resolution can never be higher than the size of the SQUID.
Nowadays the smallest SQUIDs that can be created are 3 micro meter in diagonal.
Anne Arkenbout

7. Sensitivity Larger loop is higher sensitivity
Scanning
SQUID
Microscopy
Sensitivity
Introduction
SQUID
SSM
Applications
Prospects
Larger loop is higher sensitivity
Up to 2x10-15 Tm2 ~ 1x10-10 T/(Hz)1/2 for a 7m2 SQUID
However, when one miniaturizes the SQUID to obtain a higher spatial resolution, there is a loss of sensitivity. When the loop becomes smaller, it picks up less fluxlines and so the sensitivity is lower. As a rule of thumb, the best combination of spatial resolution and field sensitivity is observed when the size of the loop is approximately the same as the spacing between the loop and the sample
Sensitivity can be specified in terms of the system noice, this can be expressed in flux, energy or field. For squids with a diameter of half a mm, the sensitivity is higher than 0.1 nT. For comparison, the earth magnetic field is 30 micro Tesla, which is one milion times stronger than the sensitivity of the SQUID.
For smaller SQUIDs the sensitivity is lower; a SQUID which has a 7 micrometer squared area has a resoluotion of 1x10-10 T/(Hz)1/2 per hz is reached.
Anne Arkenbout

8. SSM versus other techniques
Scanning
SQUID
Microscopy
SSM versus other techniques
Introduction
SQUID
SSM
Applications
Prospects
MFM
Spatial resolution: 10 – 100 nm
Sensitivity: pN ~ 10-6 T/(Hz)1/2
Scanning Hall microscope
Spatial resolution: 0.8 m
Sensitivity: 3x10-8 T/(Hz)1/2
Another technique that is often used to probe the magnetic properties is magnetic force microscopy. MFM is a technique in which an oscillating ferromagnetic tip is scanned over the surface. When the tip approaches a magnetic area it is attracted or repulsed and the oscillation is disturbed, which results in a signal.. The MFM technique has a spatial resolution of 10 to 100 nm, which is much higher that the resolution of the SSM. The sensitivity depends on the magnetization of the tip, it has a resolution of a few pico Newton in the force. This corresponds to a field sensitivity of micro teslas thousand times less sensitive than the SSM.
The scanning hall microscope makes use of a hall probe which is put on top of an STM scanning device. The magnetic field is locally probed , making use of the hall effect. The spatial resolution of this technique is higher than that of the SQUID but the sensitivity is hundred times less.
Anne Arkenbout

9. J. Kirtley et al. Annu. Rev. Mater. Sci. (1999)29, 717
Scanning
SQUID
Microscopy
Non destructive testing
Introduction
SQUID
SSM
Applications
Prospects
Current detection
Corrosion
Chip industry
One of the applications of the SQUID is the detection of currents in materials. Around a current a flux in generated, which can be detected by the SQUID. The SQUID is sensitive to currents as low as nano amperes
The scanning SQUID is used to detect hidden corrosion in aircraft components. The high sensitivity allows to detect corrosion through a thick layer of paint even at low applied currents. And so corrosion can be detected without damaging the material.
The Scanning SQUID microscope can locate shorts in electronics. The smallest details in common electronics are in the micrometer range, which is in the scope of the Scanning SQUID. Because the SQUID is very sensitive, only a small current needs to be applied to the system. And so the material is not damaged during this examination.
Anne Arkenbout
J. Kirtley et al. Annu. Rev. Mater. Sci. (1999)29, 717

10. High Tc superconductors
Scanning
SQUID
Microscopy
High Tc superconductors
The pairing symmetry of the Cooper pair
Low Tc: spherical s-wave
High Tc: d-wave
Introduction
SQUID
SSM
Applications
Prospects
The SSM has been very important in the research on d-wave symmetry in high tc superconductors. As I already mentioned, electrons form pairs in a superconductor These two electrons are described by one single wave function. In normal superconductors the shape of this wavefunction in real space in (the pairing symmetry of the cooperpair) is spherical.
This group of normal superconductors consists of materials like lead and niobium, their critical temperature is generally below 30K and their behaviour can be described by the BCS theory
For another group of superconductors, the high Tc superconductors the critical temperature can become as high as 150K These materials are mostly complex mixtures of several elements containing layers of copper oxide. No complete theory has been found yet which can describe this group of superconductors.
With the SSM it was showed that this last group of superconductors has a different pairing symmetry of the cooper pair. It does have d-wave symmetry, as is shown in the picture.
Anne Arkenbout

11. J. R. Kirtley et al., Europhys. Lett., 36 (1996), 707-712
Scanning
SQUID
Microscopy
Half integer flux quanta
Introduction
SQUID
SSM
Applications
Prospects
Detection set up
Spontaneous flux formation
Half integer flux quanta
The presence of d-wave pairing symmetry can be experimentally proved with the following set up. High Tc superconductor films of three different lattice orientations were brought togheter in a way that is shown in the picture. The interfaces between the different films behave as josephson junctions, due to the lattice mismatch at the boundary. Due to the interference of the Cooper pairs in these three areas, the system gets energetically frustrated, whenever the pairing symmetry of the cooper pairs is d-wave. The system relaxes by creating a vortex at the tricrystal point. A vortex is a circulating current. This spontaneous creation of a vortex only occurs when the d-wave symmetry is present.
When a magnetic field is applied vortices are created in d-wave symmetry materials but also in s-wave symmetry materials. So, how can we make sure that this vortex is due to d-wave pairing symmetry.
First the vortex is created without an applied magnetic field exactly at the tricrystal point.
Second the flux produces by the vortex is exactly half a flux quantum, while the flux produced by the normal vortices is an integer times this flux quantum, just as for the superconducting ring.
The Scanning SQUID microscope is up till now the only technique that can locate this vortices and measure their flux accurate enough to be able to distinguish the normal vortex from the half integer flux quantum vortex.
Anne Arkenbout
J. R. Kirtley et al., Europhys. Lett., 36 (1996),

12. T. Kondo et al., Physica C 392-396 (2003), 1401-1405
Scanning
SQUID
Microscopy
Prospects
Introduction
SQUID
SSM
Applications
Prospects
Flux guide
A lot of effort is done nowadays to improve the spatial resolution of the squid. One of the attemptsis the use of a flux guide. This flux guide is a small tip that is placed on top of the SQUID pointing to the sample. The flux guide can be made such that the point is much smaller that the SQUID. The idea is then that the flux guide will transfer the local magnetic ordering to the SQUID, improving the spatial resolution.
For the high temperature technique, where the sample is placed in air, this flux guide has improved the spatial resolution from 40 to only a few micrometers.
For the low temperature measurements, in wich the sample and the squid are both cooled down, no improvements have been reported yet.
T. Kondo et al., Physica C (2003),
Anne Arkenbout

13. T. Kondo et al., Physica C 412-414 (2004),1501-1805
Scanning
SQUID
Microscopy
Prospects
Sample vibration technique
Introduction
SQUID
SSM
Applications
Prospects
A technique to improve the sensitivity of the SQUID is the sample vibration technique The sampling vibration technique makes use of a vibrating sample to reduce the noise in the squid measurement. The sample makes a sinusoidal movement during the scan which induces a modulation in the magnetic field detected by the SQUID. The data of the SQUID and the piezo device are combined by lock in detection system. Now, the differential magnetic field can be calculated, for which the noise much lower.
Anne Arkenbout
T. Kondo et al., Physica C (2004),

14. Conclusion Poor spatial resolution Promissing recent developments
Scanning
SQUID
Microscopy
Conclusion
Poor spatial resolution
Promissing recent developments
Very good sensitivity
Introduction
SQUID
SSM
Applications
Prospects
To conclude my talk, the highest spatial resolution that can be achieved with the Scanning SQUID microscope is in the order of micro meters, which is enough for the mentioned applications. However, it is rather poor in comparison with other techniques as MFM and the scanning hall technique. However, the recent development improving the spatial resolution by making use of the flux guide is very promising.
Nevertheless, the SQUID is, by far, the most sensitive magnetometer available. And the sensitivity might even be improved by making use of the sample vibration technique. The application of this detector in a scanning system has been proven to be very useful in industrial applications. And moreover, the Scanning SQUID Microscope is a crucial tool in the fundamental experiments on high Tc superconductors, as it is the only technique that can visualize vortices with such great accuracy.
Anne Arkenbout

15. Scanning
SQUID
Microscopy
Acknowledgement
Introduction
SQUID
SSM
Applications
Prospects
I would like to thank prof. T. T. M. Palstra for supervising me during this project.
Anne Arkenbout

16. Thank you for listening!
Scanning
SQUID
Microscopy
Introduction
SQUID
SSM
Applications
Prospects
Thank you for listening!
Anne Arkenbout