III–5 Magnetic Properties of Materials

Main Topics Introduction to Magnetic Properties Magnetism on the Microscopic Scale. Diamagnetism. Paramagnetism. Ferromagnetism.

Introduction Into Magnetic Properties I Magnetic properties of materials are generally more complicated than the electric ones even on the macroscopic scale. We had conductors in which the electric field was zero and dielectrics (either polar or non-polar), in which the field was always weakened. Other behaviour is rare. More subtle differences can be revealed only by studying thermal or frequency properties.

Introduction Into Magnetic Properties II If a material is exposed to an external magnetic field is gets magnetized and an internal magnetic field appears in. It can be described as the density of magnetic dipole moments: The volume V is small on macroscopic but large on the atomic scale.

Introduction Into Magnetic Properties III The total field in the magnetized material can be then written as a superposition of the original field and internal field : Here, we can shall deal only with linear behavior: The parameter  m is the magnetic susceptibility which can now be greater or less than zero.

Introduction Into Magnetic Properties IV We can combine these equations: and define the relative permeability K m, usually also written as  r. The absolute permeability is defined as:  =  0  r =  0 K m The internal field of a long solenoid with a core can then be written as: B =  nI.

Introduction Into Magnetic Properties V Three common types of magnetic behavior exist. The external field in materials can be weakened (  m < 0 or K m < 1) this is called diamagnetism slightly intensified, (  m > 0 or K m >1) this is called paramagnetism considerably intensified, (  m >> 0 or K m >> 1) this is called ferromagnetism.

Introduction Into Magnetic Properties VI If a material can be ferromagnetic is is a dominant behavior which masks other behavior (diamagnetism) that is also always present but is much weaker. But the dominant behavior may disappear with high temperature. Ferromagnetism changes to paramagnetisms above Courie’s temperature.

Magnetism on Microscopic Scale I Magnetic behavior of materials is an open field of research. But the main types of behavior can be illustrated by means of relatively simple models. All must start from the microscopic picture. We know that if we cut a piece of any size and shape from a permanent magnet, we get again a permanent magnet with both poles.

Magnetism on Microscopic Scale II If we continue to cut a permanent magnet we would once get to the atomic scale. The question is: which elementary particles are responsible for magnetic behavior? We shall show that elementary magnetic dipole moment is proportional to the specific charge so electrons are responsible for the dominant magnetic properties. Experiments exist, however, which are sensitive to nucleus magnetic moment (NMR, Neutron Diff.).

Magnetism on Microscopic Scale III Electrons can generate magnetism in three ways: As moving charges as current. Due to their spin. Due to their orbital rotation around a core. The later two mechanisms add together and the way it is done is responsible for magnetic behavior in particular material.

Magnetism on Microscopic Scale IV Electrons can be viewed as a tiny spinning negative charged particles. The quantum theory predicts spin angular momentum s: s = h/4  = Js Here h = Js is the Planck constant Since electron is charged it also has a magnetic dipole moment due to the spin: 1 m s = eh/4  m e = J/T

Magnetism on Microscopic Scale V m s = m b is called Bohr magneton and it is the smallest magnetic dipole moment which can exist in Nature. So it serves as a microscopic unit for dipole moments. We see that magnetic dipole is quantised. Spin is a quantum effect not a simple classical rotation. Electron would irradiate energy and slow down and fall on the core.

Magnetism on Microscopic Scale VI When electrons are bound in atoms they also have orbital angular momentum. It also is a quantum effect. It is illustrative to look at a classical planetary model of electron, even if it is not realistic, to see where the dependence on the specific charge comes from.classical

Magnetism on Microscopic Scale VII Even in a very small but macroscopic piece of material there is enormous number of electrons, each having some spin and some angular momentum. The total internal magnetic field is a superposition of all electron dipole moments. The magnetic behavior generally depends on whether all the magnetic moments are compensated or if some residual magnetic moment remains.

Diamagnetism I Materials, in which all magnetic moments are exactly compensated are diamagnetic. Their internal induced magnetic field weakens the external magnetic field. We can explain this behavior on (non- realistic but sometimes useful) planetary model of one electron orbiting around an atom.

Diamagnetism II Due to an external magnetic field a radial force acts on the electron. It points toward or out of the center depending on the direction of the field. The force can’t change the radius but if it points toward the center it speeds the electron and if out it slows it. This leads to a change in the magnetic moment which is always opposite to the field. So the field is weakened.

Paramagnetism I Every electron is primarily diamagnetic but if atoms have internal rest magnetic dipole moment diamagnetism is masked by much stronger effects. If the spin and orbital moments in matter are not fully compensated, the atoms as a whole have magnetic moments and they behave like magnetic dipoles. They tend to line up with the external field and thereby reinforce it.

Paramagnetism II The measure of organizing of dipoles due to the external field depends on its strength and it is disturbed by temperature movement. For fields and temperatures of reasonable values Curie’s law is valid: B m = CB/T where C is a material parameter.

Ferromagnetism I If we think of magnetism, we usually have in mind the strongest effect ferromagnetism. In some materials (Fe, Ni, Co, Ga and many special alloys) a quantum effect, called exchanged coupling leads to rigid parallel organizing of atomic magnetic moments in spite of the randomizing tendency of thermal motions.

Ferromagnetism II Atomic magnetic moments are rigidly organized in domains which are microscopic but at the same time large on the atomic scale. Their typical volumes are – m 3, yet they still contain – atoms. If the matter is not magnetized the moments of domains are random and compensated.

Ferromagnetism III In external magnetic field the domains whose moments were originally in the direction of the field grow and the magnetic moment of some other can collectively switch its direction to that of the field. This leads to macroscopic magnetization.

Ferromagnetism IV Ferromagnetic magnetization: Is a strong effect  r  1000! Depends on the external field. Ends in saturation. Has hysteresis and thereby it can be permanent. Disappears if T > T C, Curie’s temperature.

Ferromagnetism V The internal magnetization is saturated at some point. That means it can’t be further increased by increasing of the external field. The alignment at saturation can be of the order of 75%. The Curie’s temperature for Fe is 1043 K.

Ferromagnetism VI The hysteresis is due the fact that domains can’t return at low temperatures and in reasonable times to their original random configuration. Due to this, so called memory effect, some permanent magnetization remains. This effect is widely used e.g. to store information on floppy and hard-drives.

Homework Homework from yesterday is due tomorrow!

Things to read This Lecture Covers Chapter 28 – 7, 8, 9, 10 Advance Reading Chapter 29 – 1, 2, 3, 5

Planetary model of a charge I Let’s have a charge q with speed v on orbit of the radius r and calculate its magnetic dipole moment m 0 = IA. The area is simply A =  r 2. To get the current we first have to find the period of rotation: T = 2  r/v. Then if we realize that every T one charge of q passes, the current is: I = q/T = qv/2  r.

Planetary model of a charge II Now the magnetic moment m 0 = IA =rqv/2. On the other hand the angular momentum is: b = mvr. If we put this together, we finally get: m 0 = b q/2m. This can be generalized into a vector form: If the charge is an electron q = -e so the vectors of the magnetic moment and orbital momentum have opposite directions. ^