Modeling Magnetic Properties of Materials

1. Modeling of the Magnetic Properties of Materialsby Kamel Idris-Bey

2. Presentation plan • 1 – Introduction • 2 - Magnetization and magnetic susceptibility • 3 - Maxwell's equations and relations between fields • 4 - The equations of magnetism • 5 - The macromagnetism • 6 - The micromagnetism • 6.1 - The diamagnetism • 6.2 - The paramagnetic • 6.2.1 - The ferromagnetism • 6.2.2 - The ferrimagnetism • 6.2.3 - The anti-ferromagnetism

3. 1 – Introduction • Some bodies are attracted to magnetic fields, others are repulsed. So there are two signs for the magnetic effect. One can easily put these two signs show with a strong electromagnet. Substances that are repelled by strong magnetic field are diamagnetic materials and substances that are attracted by strong magnetic field are paramagnetic materials. Strongmagneticfield H >> 1 Lowmagneticfield H << 1

4. To explain these two phenomena of magnetism a physical magnetization is defined, it is connected to the magnetic field by the following equation • 2 - Magnetization and magnetic susceptibility [ χ] is the susceptibility tensor. χ > 0 for paramagneticmaterials and χ< 0 for diamagneticmaterials. If χ = 0 the materialis no magnetic.

5. 3 - Maxwell's equations and relations between fields • 4 - The equations of magnetism • For the study of magnetism and magnetic properties and behaviors, it is essential to adopt the following basic assumptions: • and • With these two assumptions, the Maxwell equations are reduced to the following two equations

6. We express then the current density as The polarization current density can be written as a function of the polarization The magnetic current density is a function of the magnetization By replacing the current density one can obtain the relation

7. Put Thus Based on the assumptions of magnetism knowing that , the three equations of magnetism are IMPORTANT 5 - The macromagnetism The macroscopic magnetism studies the magnetic properties of the electromagnet. It provides access to the expressions of the magnetic field, the magnetization and the magnetic susceptibility prevailing between the two poles of the electromagnet in the absence of matter to explore.

8. The experimental conditions impose the direction and sense of orientation of the magnetic field. Let Oz to be the axis of orientation With the second equation of magnetism, the components of the current density vector are deduced as put the current density vector to be like

9. Now consider the successive plans of electrical current flow. Assuming that the intensity I of the current is constant, assumption is appropriate since it is known that there are two kinds of electric currents: either a constant current or alternating current depending only of time. Knowing that the current density J, is equal to the current I divided per the surface along which flows the electric current

10. It results the following differential equations • By integrating and using the magnetismequations, the equation of the macroscopic • magnetic field is foundlike • It is one expression of dimension 3 (3D).

11. The magnetisation is easilydeduced and the susceptibilityalso And the third component of the magnetic induction is It respect the first equation of magnetism

12. 6 - The micromagnetism • It studies the magnetic properties of the magnet which is between the two poles of the electromagnet, and undergoes the effect of the macroscopic magnetic field. • 6.1-The diamagnetism • The usual treatment of diamagnetism of atoms and ions uses the Larmor spin precession of trapped particles. The expression of the diamagnetic susceptibility is This is the classic result of Langevin, it pretty much describes the diamagnetic contribution in the dielectrics.

14. 6.2 - The paramagnetic It is the random distribution of spins and magnetic moments in all the space of the material.Paramagnetism appears almost usually at high temperature. The expression of the paramagnetic susceptibility is

15. 6.2.1-The ferromagnetism In ferromagnetic body the magnetic moments, induced by the applied magnetic field, are very important; this creates a very large magnetization. The spins of electrons and atoms are all aligned in the same direction, inside the material. The expression of the paramagnetic susceptibility is (Curie-Weiss law)

17. 6.2.2 -The ferrimagnetism B B A A A B A B A

19. 6.2.3 - The anti-ferromagnetism The anti-ferromagnetism results of anti-parallel alignment of the magnetic moments having the same module and the same intensity. The theory of ant-ferromagnetism is deduced from that of ferrimagnetism, with taking the same Curie constant for the two sub-networks B B A A A B A B A The expression of the ant-ferromagnetic susceptibility

21. 7 – Conclusion • An efficient method for the description of isotropic magnetic materials is studied in this article. It defines the different magnetic behaviorism which can appear in materials. The beginning of the article describes the experience of Feynman which identifies the diamagnetic with negative susceptibility and the paramagnetic with positive susceptibility. The next step shows the method which let’s to find the three equations of magnetism from the Maxwell equations. • The study of these three equations distinguishes the macromagnetism, which describes the electromagnet, and the micromagnetism, which describes the magnetic properties of the material submissive to the effect of the electromagnet.

22. Thank you for your attention