Magnetic Susceptibility

Definition: What is Magnetic Susceptibility?

Magnetic susceptibility is used to examine the behaviour of substances in magnetic fields, including diamagnetism, paramagnetism and ferromagnetism. These terms refer to:

• Diamagnetism: negative susceptibility, weakly repelled by a magnetic field.
• Paramagnetism: positive susceptibility, weakly attracted by a magnetic field.
• Ferromagnetism: very positive susceptibility, strongly attracted by a magnetic field, and can be permanently magnetised even in the absence of an external magnetic field.

Anisotropy of Magnetic Susceptibility: A Special Case

Measuring the anisotropy helps geologists determine the past states of stress and deformation in a rock. This is because as rocks form and deform, their minerals can align in particular ways leading to an anisotropic response to the magnetic field.

Commercial instruments used to measure AMS do so by subjecting a sample to magnetic fields of different orientations and recording the resulting induced magnetisation. This enables us to calculate not only the magnitude of magnetic susceptibility but also its direction.

The Mathematics behind Magnetic Susceptibility

The world of quantum physics holds the key to the mathematics behind magnetic susceptibility. The susceptibility of a magnetic material is intricately tied to the behaviour of its electrons in the presence of a magnetic field. The mathematical framework of quantum physics, along with statistical mechanics, allows us to quantify this phenomenon. Now, let's delve deeper into the formula for magnetic susceptibility and further explore volume magnetic susceptibility.

The Magnetic Susceptibility Formula Explained

Magnetic susceptibility, denoted by \( \chi \), is calculated using the formula \( \chi = \frac{M}{H} \), where \( M \) is the magnetisation - a measure of how strongly a region of a material is magnetised, and \( H \) is the magnetic field strength. The strength of a magnetic field, measured in amperes per meter (A/m), characterises how large an influence the magnetic field has on objects in the vicinity.

Depending on the orbital and spin configurations of a material's electrons, different types of magnetic behaviour can be expected, associated with different values of susceptibility. Let's look into some common configurations:

• Diamagnetic substances: These materials have electrons paired in such a way that their spin and orbital motions cancel each other out, resulting in an overall magnetic moment of zero. When a magnetic field is applied, these substances induce a weak magnetic field in opposition to the applied field, resulting in a small negative susceptibility.
• Paramagnetic substances: These materials consist of atoms or ions with unpaired electrons, hence a net magnetic moment. When a magnetic field is applied, these atomic magnetic moments tend to align with the field, resulting in a small positive susceptibility.
• Ferromagnetic substances: In these materials, the atomic moments interact with each other in such a way that they end up aligned even in the absence of an external field. When a magnetic field is applied, the susceptibility can be very high and positive.

Volume Magnetic Susceptibility: Delving Deeper

Volume magnetic susceptibility denotes how a material responds to a magnetic field per unit volume. Often, this is the main parameter referred to when discussing magnetic susceptibility. The volume magnetic susceptibility \( \chi_{v} \) is related to mass susceptibility and density \( \rho \) of a material by the following equation:

Knowledge of volume magnetic susceptibility provides valuable insights into various fields, such as geology, materials science, and medicine. For example, in medicine, by measuring the volume magnetic susceptibility of various tissue types, doctors can enhance MRI images, providing a clearer differentiation of tissues and aiding in accurate diagnosis.

In materials science and engineering, understanding volume magnetic susceptibility can aid in the design of devices that use magnetic materials. For instance, transformer cores need materials with high magnetic susceptibility for efficient operation, while shielding materials for sensitive electronics require materials with low susceptibility.

Interpreting Magnetic Susceptibility

Understanding classical and quantum mechanisms is crucial to interpreting magnetic susceptibility effectively. Additionally, familiarity with the effects of temperature on a material's magnetic properties enhances your ability to draw insights from the numerical value of a substance's magnetic susceptibility. Two critical aspects to consider are the unit of magnetic susceptibility and how susceptibility varies with temperature.

Relevance of the Magnetic Susceptibility Unit

When it comes to magnetic susceptibility, the unit used plays a highly significant role in the interpretation of results. The SI unit of magnetic susceptibility is \( \text{m}^3/\text{kg} \), but other units like emu/g, pure numbers, or volume susceptibilities (\( \text{cm}^3/\text{g} \)) are also widely used in literature.

However, because magnetic susceptibility varies over several orders of magnitude among different types of materials, its numerical value alone, without proper units, can be misleading. Here's a simple example to illustrate:

• A substance with a susceptibility of \(10^{-5}\) might be said to have a 'low' susceptibility. But if we change the units from \( \text{m}^3/\text{kg} \) (SI units) to \( \text{cm}^3/\text{g} \) (cgs units) without adjusting the numerical value, that result becomes \(10^{-5} \, \text{cm}^3/\text{g}\) or \(0.1 \, \text{m}^3/\text{kg}\).

Thus, the units are a key part of understanding the nature of the material's response to a magnetic field. It’s crucial to always specify them when reporting or comparing magnetic susceptibility values.

Magnetic Susceptibility with Temperature: How it Varies

Understanding how magnetic susceptibility varies with temperature is pivotal to the behaviour of magnetic materials. The relationship between magnetic susceptibility and temperature depends on the type of magnetic material being considered: paramagnetic, diamagnetic, or ferromagnetic.

For paramagnetic substances, the susceptibility typically increases with increasing temperature. This is due to the Curie-Weiss Law, which can be expressed as:

According to this law, the susceptibility of a paramagnetic substance should decrease as temperature increases, but in reality, there can be deviations, especially at high temperatures.

Diamagnetic substances, on the other hand, have a susceptibility that is typically independent of temperature. Their negative susceptibility arises due to the motion of electrons, which is generally not affected by temperature.

Finally, ferromagnetic substances have a susceptibility that decreases with increasing temperature and typically becomes paramagnetic above a certain critical temperature known as the Curie temperature.

As such, understanding how magnetic susceptibility varies with temperature is crucial for interpreting measurements, as it provides insights into the underlying magnetic mechanisms at play in a material.

Practical Applications of Magnetic Susceptibility

The realm of magnetic susceptibility extends far beyond academic exploration, finding its way into an array of practical applications. It threads into your everyday life in unassuming ways, from geological analysis to household devices and medical technologies.

Everyday Uses of Magnetic Susceptibility

The everyday practicality of magnetic susceptibility may get overlooked, as it's quietly making crucial contributions. At this moment, it could be influencing the workings of an appliance in your home, the encoding of your favourite song, or the diagnostics of a critical health condition.

• In Home Appliances: Magnetic susceptibility plays an important role in household appliances that use electromagnetic fields. An obvious example of this is the humble microwave oven. The magnetron, a critical component, generates microwaves by negatively charged electrons circling a central magnetic field. The alternating electric field heats food moreso than the microwave itself, and this is influenced by the magnetic susceptibility of the material inside the oven.
• In Data Storage: The storage of data on hard drives of computers and related storage devices is premised on the principles of magnetic susceptibility. Hard drives store data as bits, tiny areas of magnetic material that can represent a 0 or 1 depending on their magnetic state. The magnetic susceptibility of these areas helps determine their contribution to the overall magnetic state of the system.
• In Health Care: MRI, a non-invasive imaging technique, extensively employs the principles of magnetic susceptibility to produce detailed images of the human anatomy. This technique capitalises on the magnetic property of hydrogen atoms in the body. The machine uses a strong magnetic field to align these atoms, then pulsates radio waves at them, which changes their spin. Based on the spin recovery time and the magnetic susceptibility of different tissues, an image is created.

Unique Applications of Magnetic Susceptibility

In addition to the everyday applications, magnetic susceptibility takes centre stage in many unique scenarios too, bringing its unique contributions to the fields of geology, archaeology, material science, and more.

• Material Science: Magnetic susceptibility is an essential consideration in material engineering applications where materials are exposed to magnetic fields. The magnetic properties of elements and compounds, defined largely by their magnetic susceptibility, become profoundly significant when fabricating components for machines, devices, or detecting magnetic anomalies in materials.
• In Geological and Archaeological Exploration: Magnetic susceptibility has been extensively used in archaeological explorations to locate buried remains. Certain types of soils, due to their higher magnetic susceptibility (often resulting from human activity like pottery making), allow archaeologists to identify regions of archaeological interest. Similarly, geologists use susceptibility measurements for lithological characterisation and stratigraphic correlation.
• In Space Exploration: The field of space exploration is not untouched by magnetic susceptibility. It plays a considerable role in many space-related projects. For instance, magnetic susceptibility measurements of meteorites provide valuable information about their composition and history, aiding in the understanding of solar system evolution.

In short, whether you realise it or not, magnetic susceptibility plays a critical role in shaping the world around you. From the household gadgets you use every day to the technological marvels that explore the mysteries of outer space, it's involved in myriad aspects of life and science, showcasing the remarkable applications of this physical property.