View by Category

The presentation will start after a short

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Condensed Matter Physics PowerPoint presentation | free to download

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Condensed Matter Physics

- Sharp 251
- 8115
- chui_at_udel.edu

- Text G. D. Mahan, Many Particle Physics
- Topics
- Magnetism Simple basics, advanced topics include

micromagnetics, spin polarized transport and

itinerant magnetism (Hubbard model) - Superconductivity BCS theory, advanced topics

include RVB (resonanting valence bond) - Linear Response theory advanced topics include

the quantized Hall effect and the Berry phase. - Bose-Einstein condensation, superfluidity and

atomic traps

Magnetism

- How to describe the physics
- Spin model
- In terms of electrons

Spin model Each site has a spin Si

- There is one spin at each site.
- The magnetization is proportional to the sum of

all the spins. - The total energy is the sum of the exchange

energy Eexch, the anisotropy energy Eaniso, the

dipolar energy Edipo and the interaction with the

external field Eext.

Exchange energy

- Eexch-J?i,d Si ? Si?
- The exchange constant J aligns the spins on

neighboring sites ?. - If Jgt0 (lt0), the energy of neighboring spins will

be lowered if they are parallel (antiparallel).

One has a ferromagnet (antiferromagnet)

Alternative form of exchange energy

- Eexch-J? (Si-Si?)2 2JSi2.
- Si2 is a constant, so the last term is just a

constant. - When Si is slowly changing Si-Si? ? ? ? r Si.
- Hence Eexch-J?2 /V ? dr r S2.

Magnitude of J

- kBTc/zJ¼ 0.3
- Sometimes the exchange term is written as A s d3

r r M(r)2. - A is in units of erg/cm. For example, for

permalloy, A 1.3 10-6 erg/cm

Interaction with the external field

- Eext-g?B H S-HM
- We have set M?B S.
- H is the external field, ?B e/2mc is the Bohr

magneton (9.27 10-21 erg/Gauss). - g is the g factor, it depends on the material.
- 1 A/m4? times 10-3Oe (B is in units of G) units

of H - 1 Wb/m(1/4?) 1010 G cm3 units of M (emu)

Dipolar interaction

- The dipolar interaction is the long range

magnetostatic interaction between the magnetic

moments (spins). - Edipo(1/4??0)?i,j MiaMjb?ia?jb(1/Ri-Rj).
- Edipo(1/4??0)?i,j MiaMjb?a,b/R3-3Rij,aRij,b/Rij5

- ?04? ? 10-7 henrys/m

Anisotropy energy

- The anisotropy energy favors the spins pointing

in some particular crystallographic direction.

The magnitude is usually determined by some

anisotropy constant K. - Simplest example uniaxial anisotropy
- Eaniso-K?i Siz2

Relationship between electrons and the spin

description

Local moments what is the connection between the

description in terms of the spins and that of the

wave function of electrons?

- Itinerant magnetism

Illustration in terms of two atomic sites

- There is a hopping Hamiltonian between the sites

on the left Lgt and that on the right Rgt

Htt(LgtltRRgtltL). - For non-interacting electrons, only Ht is

present, the eigenstates are gt (-gt) Lgt (-)

Rgt/20.5 with energies (-)t.

Non magnetic electrons

- For two electrons labelled by 1 and 2, the

eigenstate of the total system is

G0gt1,-upgt2,- downgt-1,-downgt2,-upgtby Paulis

exclusion principle. Note that ltG0SiG0gt0. - There are no local moments, the system is

non-magnetic.

Additional interaction Hunds rule energy

- In an atom, because of the Coulomb interaction,

the electrons repel each other. A simple rule

that captures this says that the energy of the

atom is lowered if the total angular momentum is

largest.

Some examples

- First single local moment

Single local moment

- H?k nk? Ed(ndnd-)Undnd-- ??k,?(ck?d?c.c.)

. - Mean field approximation Hd??k nk? Ed (nd

nd-)Und? ltnd-? gt ??k,?(ck?d?c.c.).

Nonmagnetic vs Magnetic case

Illustration of Hunds rule

- Consider two spin half electrons on two sites. If

the two electrons occupy the same site, the

states must be 1, upgt2,downgt-1,downgt2,upgt.

This corresponds to a total angular momentum 0

and thus is higher in energy. - This effect is summarized by the additional

Hamiltonian HUU?i ni,upni,down.

Formation of local moments

- The ground state is determined by the sum HUHt.

This sum is called the Hubbard model. - For the non-interacting state ltG0HUHtG0gtU-2t.
- Consider alternative ferromagnetic states

F,upgtL,upgtR,upgt etc and antiferromagnetic

states, AFgt(L,upgtR,downgt-L,downgtR,upgt)/20.5,

etc. Their average energy is zero. If Ugt2t, they

are lower in energy. These states have local

moments.

Moments are partly localized

- Neutron scattering results for Ni
- 3d spin 0.656
- 3d orbital0.055
- 4s-0.105

An example of the exchange interaction

- For our particular example, the interaction is

antiferromagnetic. There is a second order

correction in energy to the antiferromagnetic

state given by JltL,upL,downHtL,upR,

downgt2/? E. This energy correction is not

present for the state Fgt. In the limit of Ugtgtt,

J-t2/U. - In general, the exchange depends on the

concentarion of the electrons and the magnitude

of U and t.

Local Moment Details

- PWA, Phys. Rev. 124, 41 (61)

(No Transcript)

(No Transcript)

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2015 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2015 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Condensed Matter Physics" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Udel University and other schools with their online training by sharing educational presentations for free