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İçerik
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| 1. hafta: |
Introduction in FMR
1. What is FMR and what is the radiospectroscopy?
2. What kind of energy levels does FMR (radiospectroscopy) measure? Zeeman effect.
3. Resonance condition, g-factor and the ? parameter. Typical frequency range for the resonance absorption.
4. Two methods to register the resonance. Which one is usually used and why?
5. What does it mean the "qausiclassical approach"?
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| 2. hafta: |
Basics of ferromagnetism - I
1. Exchange energy. Various types of exchange interactions.
2. Main groups of the magnetic elements (atoms).
3. Exchange field. Mean field approximation. Curie temperature.
4. Curie-Weiss law for susceptibility in paramagnetic phase.
5. Estimation of the mean (exchange) field and comparison with dipole-dipole magnetic field in a typical ferromagnet (i.e. Fe).
6. Heisenberg model.
7. Temperature dependence of magnetization given by mean field theory. Graphical solution for M. Comparison with experimental results.
8. Features of ferromagnetic substances. Effect of the exchange and magnetostatic (dipolar) interactions on FMR. What does it mean the "effective" (internal) magnetic field? |
| 3. hafta: |
Basics of ferromagnetism - II
9. Spin wave excitations (magnons). Dispersion relation and its approximation for long wavelengths (ka<<1).
10. Ferrimagnetic order. The mean exchange fields for various sublattices. Ferrimagnetic Curie temperature. Susceptibility of ferrimagnet in the paramagnetic phase.
11. Antiferromagnetic order. Neel temperature. Susceptibility in the paramagnetic region.
12. Ferromagnetic domains. Typical magnetization loop. Magnetization rotation and domain wall movement.
13. Anisotropy energy. Uniaxial and cubic anisotropies.
14. Bloch and Neel type of domain walls. Origin of domains (which kinds of energies are involved?). |
| 4. hafta: |
Magnetization dynamics: Equations of motion.
1. Gyromagnetic (i.e. magnetogyric) ratio. Basic equation of motion for M. What kind of the M movement does this equation explain (there is only static magnetic field)?
2. Motion equation for M due to the radiofrequency field. Form of the solutions to be searched. Dynamic susceptibility and gyration vector. |
| 5. hafta: |
Magnetostatic phenomena. Magnetization of ferromagnets and demagnetizing field (shape anisotropy).
1. Force between magnetic poles. Magnetic field definition. Magnetic field of a solenoid.
2. The torque due to magnetic field. Magnetic moment. Energy of a magnetic moment. Magnetic moment due to closed loop of electrical current.
3. Energy of the (magnetic) dipole-dipole interaction. Estimation of the energy for typical distance and magnetic moments (1A and 1 ?B).
4. Magnetization concepts. Relations to magnetic poles (density).
5. Demagnetizing field. Demagnetizing factors. Microscopic origin of the demagnetizing field (shape anisotropy).
6. Easy and hard axes of an ellipsoid. Relations for the demagnetizing factors. Demagnetizing factors for sphere, a long cylinder, semi-infinite plate. |
| 6. hafta: |
Effective internal field in a ferromagnet. General expression for resonance field.
1. Equation of motion with Heff. Apparent g-factor shift. Smit-Suhl method to calculate Heff.
2. Two conditions for free energy: equilibrium and resonance. Their form in the spherical coordinates.
3. Possible contributions to the free energy density. |
| 7. hafta: |
The effect of the shape anisotropy.
1. Free energy of an ellipsoid. Condition on demagnetizing factors. Resonance condition for ellipsoid in the large magnetic field along the principal axis.
2. Resonance frequency for a) spherical shape, parallel and perpendicular to b) long cylinder and c) thin plate. Typical resonance fields for a) and c) cases for iron. |
| 8. hafta: |
The effect of uniaxial magneto-crystalline anisotropy.
1. Free energy of cubic and uniaxial crystals. Anisotropy constants. Anisotropy field.
2. The simplest case of the rotation ellipsoid: the effect of the magneto-crystalline anisotropy on resonance conditions along and perpendicular to the rotational axis of the ellipsoid.
3. Along which directions will be the maximal, intermediate and minimal resonance magnetic field for a cubic (spherical) crystal with a) K_1> 0 and b) K_1< 0 |
| 9. hafta: |
FMR in the case of cubic magneto-crystalline anisotropy.
1. General discussion of the effect of cubic anisotropy in FMR of spherical sample (without shape anisotropy term)
2. Artman`s monogrammes and resonance conditions for vaious crystal axes.
3. Approximate solution in the case of small cubic anisotropy: derivation and discussion.
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| 10. hafta: |
Domain structure in FMR.
1. Polder`s model to treat the effect of domain structure on FMR. Figures of magnetization precession for hrf parallel and perpendicular to domain boundaries.
2. "Minimal" and "maximal" resonance frequencies in the domain FMR and their relations with the magnetization precession for hrf parallel and perpendicular to domain walls. |
| 11. hafta: |
Damping in FMR.
1. Explain why we need to take into account the damping. General form of motion equation with damping term.
2. Two forms of Landau – Lifshitz damped equation.
3. Form of the solutions for the M components with damping. Figure for the damped precession.
4. Gilbert equation and its advantages.
5. Bloch – Bloembergen equation.
6. FMR linewidth – definition. An approximate equation for linewidth (?, M, and second derivatives of F).
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| 12. hafta: |
Spin wave resonance.
1. Heisenberg form of exchange energy. Form of the motion equation with exchange term for non-uniform magnetization.
2. Resonance condition for standing spin waves the perpendicular orientation of H to thin film.
3. Dependence of the resonance field on mode number of the spin wave.
4. Dependence of amplitude of dynamic magnetization versus thickness for spin wave modes in a thin film (H is perpendicular to the film). |
| 13. hafta: |
Öğrenci sunuları |
| 14. hafta: |
Genel tekrar |
| 15. hafta*: |
Genel tekrar |
| 16. hafta*: |
Final sınavı |
| Ders kitapları ve materyaller: |
1. A.G.Gurevich, G.A.Melkov. Magnetization Oscillations and Waves, CRC Press, Boca Raton - NY - London - Tokyo, 1996.
2. Kittel C. Introduction to Solid State Physics, 7th edition, Wiley, 1996.
3. G.V. Skrotski and V. L. Kurbatov. Ferromagnetic Resonance, edited by S. V. Vonsovskii, Pergamon Press, London, 1966.
4. Soshin Chikazumi, Physics of ferromagnetism, Clarendon Press, 1997. |
| Önerilen kaynaklar: |
Landau & Lifshitz, Shlomann, Kittel classical articles on FMR |
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* 15. ve 16. haftalar arası final sınavına hazırlık haftası bulunmaktadır.
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