Ph272- General Physics II (Electricity and Magnetsism)

Lecture 16: Ch. 29 - Magnetism in Matter

Key Topics

Overview

• This lecture will give a qualitative description of magnetic materials.
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• There are three classification of magnetic materials:

Ferromagnetic materials: Materials which can produce magnetic field (e.g. a bar magnet made of iron)

Paramagnetic materials: Materials which can be magnetized by a magnetic field and the magnetization is in the same direction of the magnetic field. When you place a magnet near a paramagnetic material, the material will attract to the magnet.

Diamagnetic materials: Materials which can be magnetized by a magnetic field but the magnetization is in the opposite direction of the magnetic field. When you place a magnet near a paramagnetic material, the material will repel away from the magnet.

(All materials can be magnetized to some extent. Some materials (eq. wood, plastic, etc.) require extremely large magetic field to magnetize them)

• We will discuss qualitatively the microscopic theory of paramagnetic, diamagnetic, and ferromagnetic effects.
• The three effects can occur simulataneously in a material, but usually one effect dominates the other two. We classify that material according to its dominant effect.
• We will describe the microscopic picture which accounts for "why" certain materials are paramagnetic, diamagnetic, or ferromagentic.

Atomic magnetic moment vs. Magnetization.

• Conceptual picture: A big magnetic is composed of many tiny magnets line up in the same direction.

Each tiny magnet is an atom which has a net mangetic dipole moment.

Some atoms possess magnetic dipole moment and some don't.

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• Origin of magnetic moment of an atom:

Three origins:

(1) Orbital motion of the electrons (The direction of the magetic moment depends on direction of orbital motion)

(2) Spin of the electrons (The direction of the magetic moment depends on direction of spin)

(3) Spin of the protons (This is the weakest because the mass of proton is big)

Note: We really should use quantum mechanics to describe these motions correctly. You need to understand , at least, electronic shell structure of an atom (from chemistry for example).

• Net magnetic moment of an atom: Some atoms have non-zero net mangetic moment while others have zero net magnetic moment.

General Rule:

Net magnetic moment is zero: Atoms with "closed electronic shell" has zero net magnetic moment. (There are as many electrons ortibing or spinning in one direction as the opposite direction, we say all the electrons are paired)

Net magnetic moment is non-zero: Atoms with "partially filled electronic shell" has non-zero net magnetic moment. (There are more electrons ortibing or spinning in one direction than the opposite direction, we say there are unpaired electrons). (The "Rare-earth" atoms have largest atomic magnetic moment because they have many unpaired electrons; partially filled "f"-shell.)

• Magnetization (M): Just because the atoms in a materials possess magnetic dipole moment does not mean that the material is a magnet. The magnetic dipoles have to line up in the same direction. We define a macroscopic measurement called magnetization as the magentic moment per volume. It is used to quantify how "magnetized" is a material.
• M =0 => the material is not magnetized.

There are two ways M can be zero.

(1) The atomic magnetic moments are zero. (This is what happens in diamagnetic materials, see later discussion)

(2) The atomic moments are oriented randomly (This is what happens in paramagnetic materials. We can line up the atomic moments by putting the paramagnetic materials in an external magnetic field, see later discussion on paramagnetic effect.)

In a ferromagnetic material (such as iron), M is non-zero. The atomic moments line up in the same direction even without an external magnetic field (see discussion on magnetic domains for further clarification.)

Paramagnetic, Diamagnetic, and Ferromagnetic Effects (Microscopic Picture).

• Paramangetic effect: A magnetic dipole moment likes to line up with the (external) mangetic field (energetically favorable. Think of the magnetic dipole as a tiny magnet).

The atomic magnetic moments do not line up exactly with the (external) mangetic field because there are thermal flutuations.)

• Diamagnetic effect: A magnetic field can effect the orbital currents of the electrons by inducing a current. The direction of the induced current is given by Lenz's Law. This induced current produces a magnetic moment in the opposite direction of the magnetic field. (There is no diamangetic effect on the spin because the spin has a fixed value)
• Ferromagnetic effect: There is an interaction between neighboring atomic moments (origin is quantum mechanical). If the atoms are close enough, this interaction cause the neighboring atomic moments to line up in the same direction. At "low" temperature, all the moments line up in the same direction without an external magnetic field. This is what happen in a piece of iron magnet. At high temperature, the alignment is destroy by thermal motion. The transition temperature is called the Curie temeprature. The Curie temperature is typically a several hundred degree Celsius.
• Domain structure: A piece of iron is casted by melting the ore and cool down slowly. If the cooling process was too rapid, then there are magnetic domains where within each domain, the moements line up but the magnetization of different domains points at different directions. This is why an ordinary piece of nail is not magnetized. However, you can magnetized a nail by placing it near magnet. The magnetic field lines up the domains. After you remove the magnet, the domains remain align for sometime but eventually become randomized again.
• Note:

Paramagnetic and diamagnetic effects only occur in the presence of an applied magnetic field.

Ferromagnetic effect occurs even when there is zero applied field

Paramagnetic, Diamagnetic, and Ferromagnetic Materials

More than one of the above effect can occur in the same material, but usually one effect dominants and categorize the materials according to its dominant effect.

For example diamagnetic effect occurs in all materials but this effect is usually the weakest, so it dominats only when the other two effects are essentially zero.

	Ferromagnetic matreial	Paramagnetic materials	Diamagnetic materials
Net atomic moment	non-zero	non-zero	zero
Interaction between neighboring moments	strong (atomic moments are correlated)	very weak (atomic moments are nearly indepedent of each otehr)	none
Zero applied B-field at room temperature	Ferro effect >> thermal fluctuation. M =/=0	(very weak) ferro effecy << thermal fluctuation. M=0	ferro effect is non-existence M =0
Non-zero applied B-field	Strong ferro and para effects, weak dia effect	Para > dia effect Feroo effect ~ 0.	diamagnetic effect dominants Para effect ~ 0. Ferro effect = 0.
elements	Atoms with partially filled shell and nearest-neighbor distance is not too big, e.g. iron, cobalt, nickel.	Most "simple" metals (like aluminium). Rare-earths, where the atomic moments are too far apart to interact.	Some metals like copper. Mostly noble gas, close shell atoms or molecules.

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