Magnetic Materials

Magnetic Dipole Moment (Atomic)

• Each electron contributes to magnetism through orbital motion and spin;

• Both of which act like current loops and produce magnetic dipole moments

• The net atomic magnetic dipole moment is the vector sum of all electron dipoles.

μ

Symbol that represents Magnetic Dipole Moment

10^-23 A⋅m^2

Typical magnitude of a Magnetic Dipole Moment

Helium

Some atoms have zero net magnetic dipole moment because electron spins and orbital contributions cancel. Provide an example of one such atom.

randomly, net magnetic dipole moment

• Magnetic Dipoles in Matter (No External Field)

• In the absence of an external magnetic field, atomic magnetic dipoles are ________ oriented

• Producing zero ________________________ for the sample.

Effect of an Applied Magnetic Field

An external magnetic field tends to align magnetic dipoles, and the material’s response determines whether it is paramagnetic, diamagnetic, or ferromagnetic

Paramagnetic Material

• A material whose atoms have permanent magnetic dipole moments

• but only a small fraction align with an applied magnetic field.

Alignment torque from the magnetic field competes with thermal collisions, which randomizes the dipole orientations

Reason for Weak Alignment (Paramagnetism)

U_B = 2μB

• Magnetic Potential Energy of a Dipole

• Energy difference between aligned and anti-aligned states

U_T ≈ kT

Thermal Energy per Atom

U_T ≈ 4.1 × 10^-21 J

Thermal Energy per Atom at the Room temperature T ≈ 300K

Comparison of Energies (Paramagnetism)

Since U_T » U_B, thermal motion dominates, so only a small fraction of dipoles align.

B = B0 + Bm

Total Magnetic Field in a Material

B0

Symbol that represents the magnetic field from the solenoid current

Bm

Symbol that represents the magnetic field from the solenoid current

Magnetic Susceptibility (χ)

A dimensionless measurement of how strongly a material responds to an applied magnetic field.

Bm = χB0

Equation that shows the relationship between the magnetic field formed from the solenoid current and the magnetic field formed from the magnetized material

B = (1 + χ)B0

Formula of “Magnetic Field with Paramagnetic Material“

B = (1 + χ)μ0nI

Infinite Solenoid Filled with Paramagnetic Material

Magnetic Permeability (μ)

A measurement of how easily a magnetic field is established in a material.

μ = (1 + χ)μ0

Formula of Magnetic Permeability

B = μnI

Formula of a Field Inside a Filled Solenoid

Diamagnetic Material

• Material whose atoms have no permanent magnetic dipole moment

• But in an applied field they develop an induced dipole.

Direction of Induced Dipole (Diamagnetism)

The induced magnetic dipole moment points opposite to the applied magnetic field.

χ < 0

Magnetic Susceptibility of Diamagnetic Materials

Observable Effect of Diamagnetism

• Diamagnetic materials are repelled by magnetic fields

• Water (and thus living organisms) can be levitated in very strong magnetic field gradients.

Ferromagnetic Material

A material in which atomic magnetic dipoles are strongly coupled, producing large, permanent magnetization.

Magnetic Domains

Tiny regions within a ferromagnetic material where magnetic dipoles are rigidly aligned.

Volume and Atoms per domain

Typical magnetic domain properties

Unmagnetized Ferromagnet

Domains are randomly oriented, so the net magnetic dipole moment is zero.

10^-12 to 10^-8 m^3

Typical range of the Magnetic Domain’s volume

10^17 to 10^21

Typical range of the Atoms per Magnetic Domain

Magnetization of a Ferromagnet

When an external field is applied:

• Domains rotate to align with the field

• Aligned domains grow at the expense of others

• which results in the large net magnetization

Thermal Stability of Ferromagnets

Domain alignment is strong enough that thermal agitation cannot easily disrupt it, unlike in paramagnets.

χ ≈ 10^3 to 10^4

Magnetic Susceptibility of Ferromagnets

Hysteresis

The dependence of a ferromagnetic material’s magnetic field B on its previous magnetic history.

Hysteresis Loop

A plot of B versus applied field B0 showing that:

• The same B0 can produce different values of B

• Magnetization does not vanish when B0 = 0

Permanent Magnet

A ferromagnetic material that retains magnetization after the external field is removed.

Surface Current Model

Aligned magnetic domains are equivalent to a current flowing around the surface of the material.

Bar Magnet as a Solenoid

A bar magnet can be modeled as a tightly wound solenoid with a large circulating surface current

Magnetic Field Lines of a Bar Magnet

• Outside the magnet: field lines go from N to S

• Inside the magnet: field lines go from S to N

Yes, it is true!

Is it true, that Ferromagnetic Materials are used in hard disk drives and permanent data storage?

Spin Valve

A structure with alternating ferromagnetic and antiferromagnetic layers.

Spin Valve Principle

Electrical resistance changes significantly depending on whether an external magnetic field is applied, enabling data reading and writing.