Exchange Interaction and their Consequences.pptx

Hello, I am Subhajit Pramanick. I and my classmate, Anannya Sahaw, both presented this ppt in seminar of our Institute, Indian Institute of Technology, Kharagpur. The topic of this presentation is on exchange interaction and their consequences. It includes the basic of exchange interaction, the origin of it, classification of it and their discussions etc. We hope you will all enjoy by reading this presentation. Thank you.

1. Topic: - Exchange Interactions and Their Consequences Presented by :- Name – Subhajit Pramanick Roll No – 22PH91R16 Department of Physics IIT Kharagpur Name – Anannya Sahaw Roll No – 22CY91R01 Department of Chemistry IIT Kharagpur

2. Contents What is Exchange Interaction? Origin of Exchange Interaction Classification of Exchange Interaction Direct Exchange Indirect Exchange Super Exchange RKKY Exchange Double Exchange Anisotropic Exchange Interaction

3. What is Exchange Interaction? Purely QM effect, occurs only between identical particles. Boson and fermion both can experience it. For fermions, it is Pauli repulsion, related to Pauli exclusion principle whereas for bosons, it is one type of effective attraction which makes them close to each other, as in Bose-Einstein Condensation. In case of two fermions, if they are parallel, they remain far apart (Pauli Exclusion Principle) whereas if they are antiparallel, they may come closer together such that their wave functions may overlap (see figure). Charges of same sign cost energy when they are close together and save energy when they are far apart.

4. Origin of Exchange Interaction f Consider a simple model with just two electrons ( = = ) . So, total spin, S =  , ( = 0 (singlet),1 (triplet) Singlet State : S = 0. So, = only one state Total wave function,    = symmetric, antisymmetric (since antisymmetric). Here, = [ ( ) ( ) + ( ) ( ) ] and = [ - ] Energy: = d d and . = -   Triplet States : S = 1. So, = -1, 0,+1 total three states Total wave function,    = antisymmetric, symmetric (since antisymmetric). Here, = [ ( ) ( ) - ( ) ( ) ] and = , , [ + ] Energy: = d d and . =  

5. Origin of Exchange Interaction So, - = 2 ) ) d d Now, Hamiltonian can be written as : = ( + 3 ) – ( - ) . Define , Exchange Integral: J = = ) ) d d So, the spin-dependent term in the Hamiltonian becomes: = - 2J . This term in the Hamiltonian is the origin of exchange interaction between two identical particles. If J>0, > then triplet state S=1 is favoured (Ferromagnetism). If J<0, < then singlet state S=0 is favoured (Anti-ferromagnetism). In many electron system for ferromagnetism or anti-ferromagnetism, considering exchange interaction Heisenberg gave the simplest model in which, = - . or = - 2 . sometimes, = - . more simply, = - J  

6. Classification of Exchange Interaction There are mainly two types of exchange interactions: Besides this, there are many other exchange interactions like: Double Exchange interaction, Anisotropic Exchange Interaction etc.

7. Direct Exchange Electrons of neighbouring magnetic atoms interact via an exchange interaction. It don’t need any intermediary. Direct interaction between neighbouring atoms is due to the spatial overlap of orbitals. The simplest model for this kind of interactions is the Heisenberg model: = - J Depending on J values some of the metals are FM and some are AFM (see, Bethe-Slater Curve). Very often direct exchange cannot be an important mechanism in controlling the magnetic properties because there is insufficient direct overlap between neighbouring magnetic orbitals as in case of rare earths and transition metals. Then it becomes necessary to consider indirect exchange.   Bethe-Slater Curve

8. Indirect Exchange It is the coupling between magnetic moments over long distance and requires a mediator. It can be of two types (a) Super Exchange (b) RKKY Exchange Indirect Exchange in Ionic Solid: Super Exchange In systems in which direct exchange cannot be realized due to insufficient overlap of magnetic orbitals, magnetic coupling may be mediated by orbitals of a nonmagnetic ligand in between them. It is the super exchange interaction, which is responsible for the magnetic properties of the most of magnetic materials, especially nonmetallic compounds, for example, oxides or fluorides. Generally found in metal oxides where the magnetic atoms are separated by non magnetic ions ( O 2- ).

9. Superexchange depends on the electron configuration of magnetic ions and –O– bond angle. The rules given by Goodenough, Kanamori, and Anderson help us to predict the resulting coupling:   Indirect Exchange Goodenough-Kanamori rules Strong negative coupling when –O– angle is equal to 180 o : There is a strong antiferromagnetic exchange interaction if the half-filled orbitals of two cations overlap with the same empty or filled orbital of the intervening anion. Weak positive coupling when –O– angle is equal 90 o : There is a weaker ferromagnetic exchange interaction if the half-filled orbitals of two cations overlap with orthogonal orbitals of the same intervening anion.  

10. Indirect Exchange Indirect Exchange in Metal: RKKY or Itinerant Exchange Another type of indirect exchange is active in metals, where conduction electrons may mediate the interaction between localized magnetic moments of metal ions known as (Ruderman, Kittel, Kasuya, and Yosida interaction) or RKKY exchange. This type of coupling applies mainly to lanthanides based materials, in which the 4f shells are localized close to the nucleus. The 4f moments polarize spins of the 5d or 6s electrons and this polarization is transferred to the moment of the adjacent metal ion. The RKKY mechanism depends on a density of states of conduction electrons and works on a long range. Exchange integral , J RKKY Depending upon the distance between the localized moments of two magnetic ions, it may be either FM or AFM.  

11. Double Exchange In compounds in which magnetic ion occurs in two oxidation states (mixed valency), for example Fe 2+ and Fe 3+ or Mn 3+ and Mn 4+ , magnetic coupling may be realized by means of a real electron delocalization to the empty orbital of the neighbour. The hopping of an extra electron of Fe 2+ or of Mn 3+ via the 2p orbital of oxygen proceeds without the spin-flip of the hopping electron and results in the ferromagnetic coupling of the two centers. The double exchange operates in Fe 3 O 4 , La 1−x Sr x MnO 3 .

12. Anisotropic Exchange Interaction This is also known as Dzyaloshinsky-Moriya (D-M) interaction. Here spin-orbit interaction plays the role as the oxygen atoms act in super exchange. The excited state is produced by the spin-orbit interaction in one of the magnetic ions and an exchange interaction occurs between excited state of one ion and ground state of other ion. This interaction includes a term in the Hamiltonian, = . will lie parallel or perpendicular to the line connecting two spins, depending on the symmetry. This interaction is such that it tries to force and to be at right angles in a plane perpendicular to in such an orientation as to ensure that energy is negative. Its effect is therefore very often cant the spins by small angle. For this spin canting, antiferromagnetic materials show some non-zero magnetic moment near absolute zero (Weak Ferrimagnetism).