▪ There is no such thing as a “nonmagnetic” material. ▪ All materials respond to magnetic fields. When a magnetic field is applied to a material, several types of behavior are observed.

▪ The magnetic moment opposes the magnetic field in diamagnetic materials.

▪ Progressively stronger moments are present in paramagnetic, ferrimagnetic, and ferromagnetic materials for thesame applied field.

Diamagnetic, Paramagnetic, Ferromagnetic, Ferrimagnetic, andSuperparamagnetic Materials

▪ Diamagnetic materials are weakly magnetised in a direction opposite to that of the magnetising field when placed in a magnetic field. This behavior is called diamagnetism, gives a relative permeability of about 0.99995 (or a negative susceptibility approximately -10-6)

▪ Diamagnetic materials do not retain their magnetic properties when the external magnetic field is removed.

▪ They have negative susceptibility. The magnetisation opposes the external field.

Diamagnetic materials are composed of atoms/molecules which have no net magneticmoment, with completely filled electronic shells. This is due to the completely filled shell there are equal number of electrons with positive and negative spins, so that the total magnetic moment is zero. Materials such as copper, silver, silicon, gold are diamagnetic at room temperature.

▪ Superconductors are perfect diamagnets (m=-1); they lose their superconductivity at higher temperatures or in the presence of a magnetic field.

▪ In a diamagnetic material, the magnetization (M) direction is opposite to the direction of applied field (H).

▪ The behavior of a Diamagnetic substance is independent of temperature.

Diamagnetism

▪ When materials have unpaired electrons, a net magnetic moment due to electron spin is associated with each atom.

▪ After a magnetic field is applied, the dipoles align with the field, causing a positive magnetization. Because the dipoles do not interact, extremely large magnetic fields are required to align all of the dipoles.

▪ Additionally, the effect is lost as soon as the magnetic field is removed. This effect is called paramagnetism, and is found in metals such as aluminum, titanium, and alloys of copper. The magnetic susceptibility (m) of paramagnetic materials is positive and lies between 10-4 and 10-5.

▪ Ferromagnetic and ferrimagnetic materials above the Curie temperature also exhibit paramagnetic behavior.

Paramagnetism

Ferromagnetism

▪ Ferromagnetic behavior is caused by the unfilled energy levels in the 3d level of iron, nickel, and cobalt.

▪ In ferromagnetic materials, the permanent unpaired dipoles easily line up with the imposed magnetic field due to the exchange interaction, or mutual reinforcement of the dipoles.

▪ Large magnetizations are obtained even for small magnetic fields, giving large susceptibilities approaching 106. The susceptibility of ferromagnetic materials depends upon the intensity of the applied magnetic field.

▪ Above the Curie temperature, ferromagnetic materials behave as paramagnetic materials and their susceptibility is given by the following equation, known as the Curie-Weiss law:

C: constant that depends upon the material, Tc : Curie temperature,T : The temperature above Tc.

Anti-Ferromagnetism

▪ In some materials (such as manganese, chromium, MnO, and NiO) the magnetic moments produced in neighboring dipoles line up in opposition to one another in the magnetic field, even though the strength of each dipole is very high.

▪ These materials are antiferromagnetic and have zero magnetization. The magnetic susceptibility is positive and small.

▪ CoO and MnCl2 are examples of antiferromagnetic materials.

The crystal structure of MnO consists of alternating layers of {111} type planes of oxygen and manganese ions. The magnetic moments of the manganese ions in every other (111) plane are oppositely aligned. Consequently, MnO is antiferromagnetic.

Ferrimagnetism

▪ In materials like ceramics, different ions have different magnetic moments.

▪ When set in a magnetic field, the dipoles of cation A may line up with the field, while dipoles of cation B oppose the field. And due to the unequal strength or number of dipoles, a net magnetization results.

▪ The ferrimagnetic materials can provide good amplification of the imposed field.

▪ Ferrimagnetics show a large, magnetic-field dependent magnetic susceptibility like in ferromagnetic materials.

▪ They also show Curie-Weiss behavior (similar to ferromagnetic materials) at temperatures above the Curie temperature.

▪ Most ferrimagnetic materials are ceramics and are good insulators of electricity.

Superparamagnetism

▪ When the grain size of ferromagnetic and ferrimagnetic materials falls below a specific critical size, they behave as a paramagnetic material.

▪ The magnetic dipole energy of each particle becomes comparable to the thermal energy. As a result of thermal energy, this small magnetic moment changes its direction randomly. Thus, the material behaves as if it has no net magnetic moment. This is known as superparamagnetism.

▪ For instance, if iron oxide (Fe3O4) particles are produced in a 3 to 5 nm size, they behave as superparamagnetic materials.

▪ Such iron-oxide superparamagnetic particles are used to form dispersions in aqueous or organic carrier phases or to form “liquid magnets” or ferrofluids.

Type m

(typical

values)

m

vs. T Comment and examples

Negative and

small (–10

-6)

T independent Atoms of the material have closed shells. Organic

materials, e.g. many polymers; covalent solids, e.g. Si, Ge, diamond; some ionic solids, e.g.

alkalihalides, some metals e.g. Cu, Ag, Au.

Diamagnetic

Negative and large (–1)

Below a criticaltemperature

Superconductors

Positive and

small,(10

-5– 10

-4)

Independent of T Due to the alignment of spins of conduction

electrons. Alkali and transition metals.Paramagnetic

Positive and

small

(10-5)

Curie or Curie-Weiss

law

m

= C / (T–TC)

Materials in which the constituent atoms have a

permanent magnetic moment, e.g. gaseous and

liquid oxygen, ferromagnets (Fe),

antiferromagnets (Cr) and ferrimagnets at high temperatures.

Ferromagnetic Positive and

very large

Ferromagnetic below

and paramagnetic above the Curie

temperature

May possess a large permanent magnetization

even in the absence of an applied field.Some transition and rare earth metals, Fe, Co, Ni

Antiferromagnetic Positive and

small

Antiferromagnetic

below and

paramagnetic above the Neel temperature

Mainly salts and oxides of trans ition metals e.g.

MnO, NiO, MnF2, and some transition metals, a–

Cr, Mn.

Ferrimagnetic Positive and

very large

Ferrimagnetic below

and paramagnetic

above the Curie

temperature

May possess a large permanent magnetization

even in the absence of an applied fi eld.

Ferrites.

Types of Magnetic Materials

❑ Regions in a material where all of the dipoles are aligned in a certain direction arecalled domains. ❑ The individual domains in a material have a random orientation if not exposed to a magnetic field. Because of this, the net magnetization in the pure ferromagnetic or ferrimagnetic material as a whole is zero.

Domain Structure and the Hysteresis Loop

❑ Boundaries which separate the individual magnetic domains are called Bloch walls. The Bloch walls are narrow zones in which the direction of the magnetic moment gradually and continuously changes from that of one domain to that of the next.

(a) A qualitative sketch of magnetic domains in a polycrystalline material. Thedashed lines show demarcation between different magnetic domains; the dark curves show the grain boundaries. (b) The magnetic moments change direction continuously across the boundarybetween domains

❑ A hysteresis loop shows the relationship between the induced magnetic flux density, B (or magnetization, M) and the magnetic field strength, H.❑ Hysteresis loop can be observed by measuring the magnetic flux density of a ferromagnetic material while changing the magnetic field strength.

source:nde-ed.org

source:chalmers.se

Domain Structure and the Hysteresis Loop

❑A non-magnetized ferromagnetic material would follow the dashed line when increasingthe magnetic field.After reaching at a point "a" almost all of the magnetic domains are aligned. If the magnetic field is still increased it can neglicably increase magnetic flux. This point is called, saturation level.❑ When H is decreased to zero, B does not retrieve its original path and will follow point "a" to point "b“. (It retains a considerable degree of magnetization)❑ The value of B when H is zero is called retentivity. This point of retentivity on the graph indicates the level of residual magnetism in the material.(In this point some of the magnetic domains remain aligned and some have lost their alignment)❑ When the magnetic field is reversed, curve reaches the point “c“ where B is zero andthis is the point of coercivity. (The reversed magnetic field has changed the direction ofdomains enough so that the net flux within the material is zero)❑ As the magnetic field is increased in the negative direction, the material will again become to the saturation in the opposite direction at point "d“. Decreasing the H to zeroreaches the point “e“. A residual magnetism equal to that of the level achieved in the other direction can be observed. ❑ Increasing H back in the positive direction will return B to zero at point "f" and back to the saturation point where complete the loop.

Domain Structure and the Hysteresis Loop

❑ Hard ferromagnetic materials have large coercivity and are characterized by a broad hysteresis loop. These materials are used to make permanent magnets.Generally, if the coercivity value is about>104 A.m-1, the material can be considered as magnetically hard.

❑ Soft ferromagnetic materials have small coercivity and are characterized by narrow hysteresis loop. They dissipate less energy when they are cycled through a hysteresis loop. They are used in electrical applications. If the coercivityvalues are

The magnetic force obtainable using a permanent magnet is given by:

A: cross-sectional area of the magnetM: magnetizationm0: magnetic permeability of free space.

Hard and Soft Ferromangetics

❑ The lifting power of the magnet is related to the size of the hysteresis loop, or the maximumproduct of B and H.

REFER TO THE LECTURE NOTES FOR THIS PART

Sources

Materials Science and Engineering An Introduction, William D. Callister Jr., John Wiley&Sons Inc.

The Science and Engineering of Materials, Donald R. Askeland, Springer Science Business Media

Properties of Materials for Electrical Engineers, K. J. Pascoe

Physics of Semiconductor Devices, J. P. Collinge, C. A. Collinge