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PH752: Superconductivity and Magnetism

Lecture Notes

Dr. Jorge Quintanilla SEPnet and Hubbard Theory Consortium, University of Kent and STFC Rutherford Appleton Laboratory

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Lecture I. Jorge Quintanilla Magnetism and Superconductivity (PH752)1 About this course

We will have 28 lectures, roughly split as 14 on Magnetism and 14 on Superconductivity. I will make handouts available after each lecture. The handouts can be found at http://blogs.kent.ac.uk/strongcorrelations/teaching/superconductivity-and-magnetism/ Be sure to check that page regularly. Check also the reading list available online. familiar with by the end of this course: There are two recommended texts that you should be very

Stephen Blundell, Magnetism in Condensed Matter (OUP 2001). James F. Annett, Superconductivity, Superuids and Condensates (OUP 2004). An

References to these two books will be abbreviated SB and JFA, respectively, in these lecture notes. expanded reding list with additional references will be made available as the course progresses.

There will be 6 problem sheets, with a few practice problems each. The problem sheets will be handed out or made available online 2 weeks before they are due. Every problem sheet will have an assesed component. There will also be two class tests: one on Magnetism on week 14 (one week after the Winter break) and one on Superconductivity on week 19. Finally, in the third term we will have an exam. The assesment pattern can be found on the web. In addition to the lectures, we will have a number of workshops: two just before the rst class tests, two just before the second one, and a number of optional ones after the lectures and class tests are over. convenient for everyone nearer the date. My room is Ingram 230 however I do spend a lot of time doing research the ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Science Campus, Didcot, Oxfordshire, OX11 0QX. The best form of contact in any case is email: j.quintanilla@kent.ac.uk. You may also want to try Skype: j.quintanilla. In principle these have been scheduled in the latter part of the second term but we will agree whatever is most

2 2.1

What is special about magnetism and superconductivity? History

Magnetism and superconductivity are two of the most fascinating phenomena known to humankind.

Magnetism, as manifested in the ability of some materials to attract iron and each other and to sense thedirection of the magnetic North, has been known for millenia. The earliest known magnetic artifact dates from the 4th centruy BC. It is a magnetic compass from China:

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1

National High Magnetic Field Laboratory, Early Chinese Compass, http://www.magnet.fsu.edu/education/tutorials/museum/chinese

(accessed 29 July 2011).

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(This was not used to navigate, but to nd the spiritually most desirable alignment for new houses!) Even the word magnetism itself is very old. It comes from the Greek

magnes lithos,2

the Magnesian stone,

referring to a geographical region which was known to be rich in magnetite.

The magnetic compass uses ferromagnetism. Other magnetic phenomena include paramagnetism and antiferromagnetism. Some of them have been discovered recently - in fact new forms of magnetism are being discovered even nowadays. In contrast to magnetism,

Superconductivity is a much less ancient subject.

Kammerlingh Onnes found

superconductivity serendipitously in 1911 (this year is the 100th anniversary!) when he was studying the electrical properties of metals at very low temperatures. He found that the resistivity of Mercury (Hg) completely vanished when it was cooled below a critical value of about 4.2K. Here is an old photo of the gentleman alongside his historic plot of resistivity vs temperature:

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2.2

Applications

Both magnetism and superconductivity have important

applications.Computer hard disks store bits

Magnetism is ubiquitous in our technology. Sometimes the applications are quite humble, e.g. we use it to keep doors closed. More important is its application in

magnetic storage.

in the form of microscopic magnetisation domains on a ferromagnetic surface. The information is then read using a device that converts the magnetic eld into an electric signal (a magnetic read head). The read heads improved considerably with the discovery of giant magnetoresistance (GMR). In GMR, an electron current is passed through a stack of ultra-thin ferromagnetic layers. The magnetic elds created by dierent layers point in dierent directions. This scatters the electrons as they move from one layer to the next, increasing resistance. Under the inuence of an externally-applied magnetic eld, the dierent layers align their contributions, leading to a large drop in resistance:

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Douglas Harper, Magnet, in The Online Etymology Dictionary, http://www.etymonline.com/index.php?term=magnet Images from Rudolf de Bruyn Ouboter, Heike Kamerlingh Onnes's Discovery of Superconductivity, Scientic American The gure is from Giant Magnetoresistance, in Physics Central, American Physical Society,

(accessed 29 July 2011). (March 1997) and from Dirk van Delft and Peter Kes, The discovery of superconductivity, Physics Toda y (September 2010).

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http://www.physicscentral.com/explore/action/magnetoresistance-1.cfm (accessed 28 September 2011).

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These drops in resistence can be used to read the bits recorded on the magnetic disc underneath a read head. Thanks to GMR read heads, the density of magnetic storage kept increasing exponentially with time into the 21st century. This is what allowed, among other tings, the miniaturisation of the iPods. Fert and Grunberg, the discoverers of GMR, shared the Nobel prize in 2007. The increase in magnetic information storage density with time is even faster than the famous Moore's law for transistors in microchips. It is called Kryder's law. It is the great technological triumph of magnetism. Here is a graph:

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Superconductivity also has important applications, although it is not as ubiquitous as magnetism because, while many useful magnetic properties occur at room temperature, all known superconductors need to be kept at liquid nitrogen or lower temperatures in order to remain superocnducting. Nevertheless superconductivity is routinely used wherever it is important to generate large magnetic elds, such as in medical

Magnetic Resonance Imaging.

High-temperature superconductors are still poorly understood so most

applications employ low-temperature, or conventional superconductors. Finding a

perconductor remains one of the holy grails of physics.2.3 More is dierent

room-temperature su-

What is special, from a more fundamental point of view, about magnetism and superconductivity? First of all, they are both properties of matter whose understanding necessitatates they are both

emergent phenomena.is from Giant

quantum mechanics.American

Secondly,

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The

gure

Magnetoresistance:

Research,

in

Physics

Central,

Physical

Society,

http://www.physicscentral.com/explore/action/mr-research.cfm (accessed 28 September 2011).

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Let me explain what I mean by emergent.

The laws of physics that govern the behaviour of dierent Yet some materials are magnetic, others are

materials under dierent conditions are always the same.

superconducting, and many others do none of this. What is more, a superconducting or magnetic material will lose its properties if we change its thermodynamic conditions - for example, by raising the temperature. It is clear that just knowing the laws of physics is not enough to understand phenomena such as magnetism and superconductivity. We need to understand the principles of self-organisation whereby the prize-winning American physicist, Phil W. Anderson, summed this magic up with the motto

1023

particles

that make up the sample cooperate to allow new behaviour to emerge from the physical laws. The Nobel

More is dierent

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Magnetism: statement of the problem

We will do Magnetism rst because it is conceptually simpler and the theoretical tools required are less advanced, so by looking at the subjects in that order the learning curve will be less steep. (On the other hand as you will see superconductivity is a simpler subject in the sense that it deals with a single phenomenon. In contrast, in the rst part of the course we will be looking at paramagnetism, ferromagnetism, antiferromagnetism...)

3.1

The essential featue of magnetism: spontaneous magnetic induction

Our starting point are Maxwell's equations:

E = / B = 0 E =

0

(1) (2)

B t0 0

(3)

B = 0 J +These equations determine the electric eld current density

E t Bgiven the charge density

(4)

E

and magnetic induction

J

at each point in space

r

and moment in time

t.

The universal constants

0 and

and 0 are

the electric permitivity and magnetic permeability of free space, respectively. What the equations tell us, respectively, is the following:

Gauss' law for electric elds: electric elds ow out of electric charges. We prove this by integratin g both sides of the equation over a region of volume outside surface

V,

then using Gauss'

theorem to show that the integral on the LHS is the same as the ux of the vector eld

E

through the

S

of

V.

Thus the ux of