Magnetic Properties of Materials

Magnetic Properties Of Materials

When a material is placed in an external magnetic field ($\vec{B}_0$), the material itself becomes magnetised, and the resulting magnetic field inside the material ($\vec{B}$) is generally different from the applied field. This response of materials to magnetic fields is categorised into different types of magnetic behaviour. The magnetic properties of materials arise from the magnetic dipole moments of the electrons within the atoms (due to their orbital motion and intrinsic spin) and, in some cases, the magnetic moments of the nuclei.

The total magnetic field inside the material ($\vec{B}$) is the sum of the applied external field ($\vec{B}_0$) and the magnetic field produced by the magnetisation of the material ($\vec{B}_m$). Using the concept of magnetic intensity $\vec{H}$ (which represents the external magnetising field, $\vec{H} = \vec{B}_0/\mu_0$ in vacuum), the total magnetic field is given by:

$ \vec{B} = \mu_0 (\vec{H} + \vec{M}) $

where $\vec{M}$ is the magnetisation vector of the material. As we learned, the magnetisation is related to the magnetic intensity by $\vec{M} = \chi_m \vec{H}$, and the total field is also related to the magnetic intensity by $\vec{B} = \mu \vec{H} = \mu_0 (1 + \chi_m) \vec{H} = \mu_0 \mu_r \vec{H}$. The behaviour of a material in a magnetic field is classified based on the value and sign of its magnetic susceptibility ($\chi_m$) or relative permeability ($\mu_r$).

Based on their response to external magnetic fields, materials are broadly classified into three main types: diamagnetic, paramagnetic, and ferromagnetic. Other, less common types exist but these three are the principal classifications.

Diamagnetism

Diamagnetic materials are those which, when placed in an external magnetic field, become weakly magnetised in a direction opposite to the applied field. They tend to move from a stronger part of the magnetic field to a weaker part.

Diagram showing a diamagnetic material repelled by a magnet

Diamagnetic material is weakly repelled by a magnet.

Mechanism: Diamagnetism is a property present in all materials, but it is the *only* magnetic behaviour observed in purely diamagnetic substances (where paramagnetism and ferromagnetism effects are absent). It arises from the changes in the orbital motion of electrons induced by the external magnetic field. According to Lenz's Law of electromagnetic induction, the change in magnetic flux through the electron's orbit induces a tiny current loop in the atom. This induced current loop creates a magnetic dipole moment that opposes the applied magnetic field.

In atoms of diamagnetic materials, all electron shells are filled, and there are no permanent magnetic dipole moments from electron spin or orbital motion. The induced dipole moment is the sole magnetic effect, and it always opposes the external field.

Properties of Diamagnetic Materials:

They are weakly repelled by magnets.
Magnetic field lines prefer to avoid passing through a diamagnetic material. If placed in a uniform magnetic field, a diamagnetic rod aligns itself perpendicular to the field.
Their magnetic susceptibility ($\chi_m$) is small and negative (typically $-10^{-5}$ to $-10^{-6}$).
Their relative permeability ($\mu_r = 1 + \chi_m$) is slightly less than 1 ($\mu_r < 1$). Consequently, their permeability ($\mu$) is slightly less than $\mu_0$.
Diamagnetism is largely independent of temperature. The induced dipole moments are not affected by thermal agitation.

Examples: Copper, Gold, Silver, Zinc, Bismuth, Lead, Water, Diamond, Nitrogen gas, Hydrogen gas, Vacuum (although vacuum isn't a material, it's the baseline with $\chi_m = 0$). Superconductors are perfect diamagnets ($\chi_m = -1, \mu_r = 0$), exhibiting the Meissner effect where they completely expel magnetic field lines.

Paramagnetism

Paramagnetic materials are those which, when placed in an external magnetic field, become weakly magnetised in a direction parallel to the applied field. They are weakly attracted to magnets and tend to move from a weaker part of the magnetic field to a stronger part.

Diagram showing a paramagnetic material weakly attracted by a magnet

Paramagnetic material is weakly attracted by a magnet.

Mechanism: Paramagnetism arises in materials where the atoms or molecules have permanent magnetic dipole moments, even in the absence of an external field. These permanent moments are typically due to unpaired electrons in the atoms or ions (e.g., in atoms with incomplete inner electron shells). In the absence of an external field, these permanent dipoles are randomly oriented due to thermal agitation, so the net magnetic moment of the material is zero.

When an external magnetic field is applied, these permanent dipoles experience a torque ($\vec{\tau} = \vec{M}_{atomic} \times \vec{B}$) that attempts to align them parallel to the field. Thermal motion opposes this alignment. The degree of alignment, and hence the magnetisation $\vec{M}$, depends on the strength of the applied field and the temperature. A stronger field encourages alignment, while higher temperature increases random thermal motion, disrupting alignment.

Properties of Paramagnetic Materials:

They are weakly attracted by magnets.
Magnetic field lines are slightly concentrated within a paramagnetic material. If placed in a uniform magnetic field, a paramagnetic rod aligns itself parallel to the field.
Their magnetic susceptibility ($\chi_m$) is small and positive (typically $10^{-5}$ to $10^{-3}$).
Their relative permeability ($\mu_r = 1 + \chi_m$) is slightly greater than 1 ($\mu_r > 1$). Consequently, their permeability ($\mu$) is slightly greater than $\mu_0$.
Paramagnetism is temperature-dependent. The susceptibility decreases with increasing temperature, following Curie's Law: $\chi_m \propto \frac{1}{T}$ or $\chi_m = \frac{C}{T}$, where $C$ is the Curie constant and $T$ is the absolute temperature. This is because increased thermal motion at higher temperatures makes it harder for the dipoles to align with the field.

Examples: Aluminium, Sodium, Platinum, Copper Chloride ($CuCl_2$), Oxygen gas, Magnesium, Lithium.

Ferromagnetism (Hysteresis)

Ferromagnetic materials are those which are strongly magnetised in a direction parallel to the applied field. They are strongly attracted to magnets and can retain their magnetism even after the external field is removed (making them suitable for permanent magnets). They tend to move from a weaker part of the magnetic field to a much stronger part.

Diagram showing a ferromagnetic material strongly attracted by a magnet

Ferromagnetic material is strongly attracted by a magnet.

Mechanism: Ferromagnetism is a quantum mechanical effect related to the strong interaction between the permanent magnetic dipole moments of neighbouring atoms. In ferromagnetic materials (like iron, cobalt, nickel, and their alloys), there is a strong tendency for the atomic dipole moments to align parallel to each other in certain regions, even in the absence of an external field. These regions of spontaneous alignment are called magnetic domains. Each domain is spontaneously magnetised to saturation, but in the absence of an external field, the magnetisation directions of different domains are random, so the net magnetisation of the bulk material is zero.

Diagram showing magnetic domains in a ferromagnetic material

Magnetic domains in a ferromagnetic material. (a) Randomly oriented domains in the absence of a field. (b) Domains aligned with the field, resulting in net magnetisation.

When an external magnetic field is applied, two things happen:

Domains that are already oriented favourably with respect to the field grow in size at the expense of unfavourably oriented domains.
The magnetisation direction within domains may rotate to align more closely with the applied field.

Both processes lead to a large net magnetisation parallel to the applied field. The magnetisation can become very strong, many thousands of times greater than in paramagnetic materials.

Properties of Ferromagnetic Materials:

They are strongly attracted by magnets.
Magnetic field lines are greatly concentrated within a ferromagnetic material.
Their magnetic susceptibility ($\chi_m$) is large and positive (typically hundreds or thousands). It is not constant but varies with the applied field.
Their relative permeability ($\mu_r = 1 + \chi_m$) is much greater than 1 ($\mu_r \gg 1$). Consequently, their permeability ($\mu$) is much greater than $\mu_0$. Like susceptibility, permeability is also not constant.
Ferromagnetism is strongly temperature-dependent. Above a certain critical temperature, called the Curie temperature ($T_C$), the strong domain interactions break down due to thermal agitation, and the material loses its ferromagnetic properties, becoming paramagnetic. Each ferromagnetic material has a specific Curie temperature (e.g., about 770°C for iron, 358°C for nickel, 1130°C for cobalt).

Examples: Iron (Fe), Cobalt (Co), Nickel (Ni), Gadolinium (Gd), and their alloys (like steel, Alnico).

Ferromagnetism (Hysteresis)

A unique characteristic of ferromagnetic materials is hysteresis. Hysteresis refers to the phenomenon where the value of the magnetic field inside a ferromagnetic material ($\vec{B}$) or its magnetisation ($\vec{M}$) depends not only on the current value of the applied magnetic intensity ($\vec{H}$) but also on the history of the magnetising field. This means that the magnetic state of the material lags behind the applied field.

The Hysteresis Loop (B-H Curve)

The relationship between the magnetic field inside a ferromagnetic material ($B$) and the applied magnetic intensity ($H$) is typically represented by a graph called the hysteresis loop or B-H curve.

Diagram of a typical Hysteresis Loop (B-H curve) for a ferromagnetic material

Typical B-H hysteresis loop for a ferromagnetic material.

Let's trace a typical hysteresis loop for a ferromagnetic material initially in an unmagnetised state ($B=0, H=0$).

O to a: As the external magnetic intensity $H$ is increased from zero, the magnetic field $B$ inside the material increases rapidly but not linearly. This is due to the growth of favourably oriented domains.
a to b (Saturation): As $H$ is further increased, the magnetisation $M$ approaches a maximum value called saturation magnetisation ($M_s$), where all domains are essentially aligned. Beyond this point, increasing $H$ only slightly increases $B$ (linearly, with slope $\mu_0$), as $B \approx \mu_0 H + \mu_0 M_s$. The state is called magnetic saturation.
b to c (Remanence/Retentivity): If the applied field $H$ is now decreased from saturation back to zero, the magnetic field $B$ does not return to zero. When $H=0$, there is a residual magnetic field $B_r$ remaining in the material. This value $B_r$ is called the remanence or retentivity. This residual magnetism is what makes permanent magnets possible.
c to d (Coercivity): To reduce the magnetic field $B$ to zero, a magnetic intensity must be applied in the opposite direction. The value of the reversed magnetic intensity ($H_c$) required to bring $B$ to zero is called the coercive force or coercivity.
d to e (Reverse Saturation): As the reversed field $H$ is further increased, the material becomes saturated in the opposite direction.
e to f to b (Completing the Loop): When the reversed field is decreased to zero (e to f), the material again retains a residual magnetism ($B_r$ in the opposite direction). Increasing $H$ in the original direction from f to b completes the loop.

The entire closed loop cdefb is the hysteresis loop. The area of the hysteresis loop represents the energy lost per unit volume of the material during one cycle of magnetisation and demagnetisation. This energy loss occurs due to the work done against the friction-like forces involved in domain wall motion and rotation.

Hard vs. Soft Ferromagnetic Materials

The shape and size of the hysteresis loop vary for different ferromagnetic materials, providing insight into their suitability for different applications.

Hard Ferromagnetic Materials: These have a broad hysteresis loop with high retentivity and high coercivity. They are difficult to magnetise and demagnetise. These materials are suitable for making permanent magnets (e.g., steel, Alnico).
Soft Ferromagnetic Materials: These have a narrow hysteresis loop with low retentivity and low coercivity. They are easily magnetised and demagnetised. These materials are suitable for applications involving frequent magnetisation and demagnetisation cycles, such as cores of electromagnets, transformers, and inductors (e.g., soft iron, Mu-metal). The small area of the loop means low energy loss during AC operation.

Comparison of Magnetic Properties

Property	Diamagnetic	Paramagnetic	Ferromagnetic
Behaviour in Field	Weakly repelled	Weakly attracted	Strongly attracted
Direction of Magnetisation	Opposite to $\vec{B}_0$	Parallel to $\vec{B}_0$	Parallel to $\vec{B}_0$
Origin	Induced orbital dipole moments	Permanent atomic dipole moments (randomly oriented)	Permanent atomic dipole moments (aligned in domains)
Magnetic Susceptibility ($\chi_m$)	Small, negative (e.g., $-10^{-5}$)	Small, positive (e.g., $10^{-5}$ to $10^{-3}$)	Large, positive (e.g., hundreds to thousands)
Relative Permeability ($\mu_r$)	Slightly less than 1 ($\mu_r < 1$)	Slightly greater than 1 ($\mu_r > 1$)	Much greater than 1 ($\mu_r \gg 1$)
Temperature Dependence	Independent of temperature	Decreases with temperature (Curie's Law)	Strongly decreases with temperature; becomes paramagnetic above Curie temperature ($T_C$).
Field Lines	Avoid the material	Slightly concentrated	Greatly concentrated

Understanding these magnetic properties is essential for the design and application of various magnetic devices and materials used in technology and industry.