Magnetic Materials. 1. General Information About Magnetism. Numan Akdoğan.

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Magnetic Materials 1. General Information About Magnetism Numan Akdoğan akdogan@gyte.edu.

1 Magnetic Materials 1. General Information About Magnetism Numan Akdoğan Gebze Institute of Technology Department of Physics Nanomagnetism and Spintronic Research Center (NASAM)

2 Magnetic Materials 1. General Information About Magnetism References Soshin Chikazumi, Physics of Ferromagnetism B. D. Cullity, C. D. Graham. Introduction to Magnetic Materials Nicola Spaldin, Magnetic Materials Charles Kittel, Introduction to Solid State Physics

Spin light emitting diodes (Spin-LEDs) In medicine to

3 Why magnetism is important? Applications of magnetic materials: Read heads for magnetic hard disk drives Magnetic random access memories Spin field effect transistors (Spin-FETs) Spin light emitting diodes (Spin-LEDs) In medicine to image and destroy cancer cells From Agnes Barthelemy, Uni. Paris-Süd

4 History of magnetism Fe 3 O 4 -first magnetic material used by people William Gilbert ( )-first systematic work on magnetism On the magnet -first book on magnetism published by Gilbert in Hans Cristian Oersted ( ) discovered that an electric current produces a magnetic field 1825-first electromagnet 1988-dicovery of GMR (giant magneto-resistance)

5 Magnetic poles Iron filings have oriented in the magnetic field produced by a bar magnet Two poles where the field lines condensed are called as magnetic pole

6 Magnetic poles the forces of attraction and repulsion between poles was discovered independently in 1750 by John Michell ( ) and in 1785 by Charles Coulomb ( ).

7 Magnetic poles the forces of attraction and repulsion between poles was discovered independently in 1750 by John Michell ( ) and in 1785 by Charles Coulomb ( ). the force F between two poles is proportional to the product of their pole strengths p 1 and p 2 and inversely proportional to the square of the distance d between them F = p 1 d p 2 2 cgs (1) Dyne F = 1 4πµ 0 p 1 d p 2 2 SI Newton 1newton=10 5 dyne Permeability of free space (permeability of vacuum)=4π 10-7 henrys per meter (Hm -1 )

8 Earth s magnetic poles and compass (Southern polarity) (Northern polarity)

9 Magnetic field Generally a region of space in which a magnetic pole experiences an applied force is called a magnetic field. A magnetic field can be produced by other magnetic poles or by electric currents. A magnetic pole creates a magnetic field around it, and it is this field which produces a force on a second pole nearby. p F = d 1 p Hp = cgs (2)

10 Magnetic field p H = cgs (3) d 2 The unit of magnetic field is oersted (Oe) in cgs units 1 Oe=1 line of force/cm 2 In the SI system, the field from a pole is: H p = SI 4πµ d 0 The unit of magnetic field in the SI system is ampere per meter (Am -1 ). 1 Am -1 =4π 10-3 Oe 2

11 Magnetic field A magnetic field can also be produced by using a solenoid (Greek word for a tube or pipe). A uniform magnetic field exists inside a long, thin solenoid carrying an electric current. When a current of i flows in the winding of a solenoid having n turns per meter, the intensity of the field H at the center of the solenoid is defined by: ni H = Am -1 (SI) 1 Am -1 =4π 10-3 Oe l 4πni H 10 l = Oe (cgs) (4)

12 Magnetic field The magnetic field of the Earth is about 0.35 Oe The magnetic field of a bar magnet near one end is about 5000 Oe The magnetic field of a powerful electromagnet is about Oe (2 Tesla) The magnetic field of a superconducting magnet can be Oe (9 Tesla) or more. Relation between oersted (Oe), gauss (G) and tesla (T) 1 Oe=1 G (in vacuum) 1 T=10 4 G Tesla (T) is used in SI.

13 Magnetic moment F=pH l -p p θ F=pH H Consider a magnet with poles of strength p and lenght l is placed at an angle θ to a uniform field H. Then a torque acts on the magnet, tending to turn it parallel to the field. The moment of this torque is: phl/2sinθ+phl/2sinθ=phlsinθ When H=1 Oe and θ=90, the moment is given by µ = pl (5)

14 Magnetic moment F=pH l -p p θ F=pH H If no frictional forces act on the magnet, the work done by the torque is reversible, giving rise to a potential energy: E p = plh cosθ = µ H cosθ E p = µ H (6)

15 Magnetic moment = pl µ (5) weber meter (Wb m) in SI E p = µ H (6) µ: erg/oe or emu in cgs Because the energy E p is in ergs, the unit of magnetic moment µ is erg/oersted. This quantity is the electromagnetic unit of magnetic moment, generally but unofficially called simply the emu.

16 Magnetic moment A magnetic moment can also be produced by a closed loop carrying an electric current. i µ The magnetic moment produced by a current i which flows in a closed circuit or loop enclosing an area A is defined as A µ = ia (7) In SI units, magnetic moment is measured in A m 2.

17 Magnetic dipole A magnetic dipole is defined as either the magnetic moment, µ, of a bar magnet in the limit of small length but finite moment, or the magnetic moment µ of a current loop in the limit of small area but finite moment. Field lines around a magnetic dipole.

18 Magnetization The magnetization is defined to be the magnetic moment per unit volume, M = µ ν emu/cm 3 (8) It is sometimes convenient to refer the value of magnetization to unit mass rather than unit volume. The mass of a small sample can be measured more accurately than its volume, and the mass is independent of temperature whereas the volume changes with temperature due to thermal expansion. The specific magnetization is defined as µ µ M σ = = = emu/g (9) m ρν ρ When dealing with small volumes like the unit cell, the magnetic moment is often given in units called Bohr magnetons, µ B, where 1 µ B = erg/oe (or emu)

19 Magnetic flux density When a magnetic field, H, is applied to a material, the response of the material is called its magnetic flux density or magnetic induction, B. H 4πM B B cgs = H + 4πM (10) B: G, H: Oe, 4πM: G When M=0 (in free space or in air) and B=H, gauss is also used for H. B = µ ( H + M ) SI 0

20 Magnetic susceptibility The magnetic properties of a material are characterized not only by the magnitude and sign of M but also by the way in which M varies with H. The ratio of these two quantities is called the susceptibility χ. emu M χ = ν H 3 Oe cm Sometimes called as volume susceptiblity (χ v ) (11) χ m = χ ν ρ emu Oe g (12) The susceptibility indicates how responsive a material is to an applied magnetic field.

21 Magnetic permeability The ratio of B to H is called the permeability µ µ B p = G H Oe (12) Using B H + 4πM = we get the relationship between permeability and susceptibility: µ =1+ 4πχ p (13) The permeability indicates how permeable the material is to the magnetic field.

22 Types of magnetism Diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, ferrimagnetism

23 Types of magnetism M versus H (or B) graphs are called magnetization curves, and are characteristic of the type of material. Homework: How can we measure magnetization (magnetic moment)?

Magnetic Materials. 2. Diamagnetism. Numan Akdoğan.

Magnetic Materials. 2. Diamagnetism. Numan Akdoğan. Magnetic Materials. Diamagnetism Numan Akdoğan akdogan@gyte.edu.tr Gebze Institute of Technology Department of Physics Nanomagnetism and Spintronic Research Center (NASAM) Magnetic moments of electrons