Magnetic Properties of Solids and Their Applications

Magnetic Properties of Solids

Materials can be classified based on their response to externally applied magnetic fields into three categories: diamagnetic, paramagnetic, and ferromagnetic.
- These classifications differ significantly in their magnetic responses' strength.

All materials exhibit diamagnetism, which is a property that opposes applied magnetic fields.
It is characterized as a very weak effect and is present in all materials.
When a magnetic field is applied, diamagnetic materials develop an induced magnetic moment that opposes the field, thereby weakening it.
The absolute value of the magnetic susceptibility χ is typically in the range of ext{|χ| ext{~} 10^{-6} ext{ to } 10^{-4}}.
Common examples include:
- Inert gases,
- Bismuth,
- Silver,
- Water,
- Hydrogen,
- Carbon,
- Copper,
- Germanium,
- Silicon.
Diamagnetism was discovered by Michael Faraday, who named the phenomenon.
Importantly, the magnetic susceptibility χ of diamagnetic materials does not depend on temperature or the intensity of the external magnetic field.

Paramagnetic materials are characterized by a magnetic susceptibility χ > 0, where they exhibit a weak amplification of the resultant magnetic field when placed in an applied magnetic field, following the relationship χ ext{~} 10^{-4} ext{ to } 10^{-3}.
Common paramagnetic materials include:
- Aluminum,
- Platinum,
- Liquid oxygen,
- Electron gas in metals,
- Rare earth elements,
- Alkaline and alkaline earth metals.
In such materials, the atomic magnetic moments align partially in the direction of the applied field, although thermal motion limits the degree of alignment.
Curie's Law applies to paramagnetic materials: the susceptibility follows the equation χ = rac{C}{T}, where C is Curie’s constant and T is the temperature. This law holds true for weak external fields and at moderate temperatures.
Paramagnetic materials can be magnetized to saturation at high external field values.

Ferromagnetic materials demonstrate a very high magnetic susceptibility χ >> 0, and possess own magnetic fields significantly exceeding the external applied field (by hundreds or thousands of times).
Examples of ferromagnetic materials include:
- Iron,
- Nickel,
- Cobalt,
- Gadolinium,
- Special alloys.
Specific characteristics include:
- Magnetic hysteresis, where the magnetization depends on the historical value of the magnetic field.
- The magnetic permeability C{ 8{B} = C{0} ext{H}} exhibits nonlinear behavior with respect to H_0.
The magnetic susceptibility of ferromagnets changes with temperature:
- Each ferromagnetic material has a notable Curie Temperature (TC); for example, iron has TC = 768 °C, nickel has TC = 358 °C, and cobalt has TC = 1120 °C.
Magnetostriction: changes in dimensions occur during magnetization and demagnetization of ferromagnetic materials, useful for applications in ultrasonic devices.

Ferrites are materials with ferromagnetic properties characterized by semiconductor properties, having a specific resistance ρ ext{~} 10^7 ext{ } ext{Ωm}.
Typical examples include magnetite (Fe₃O₄) and compounds like MeO ext{.Fe₂O₃}, where Me represents divalent metals (e.g., Mg, Ni, Co, Cr).
Ferrites are advantageous for high-frequency applications due to their low eddy current losses and relatively low Curie temperatures (30 to 700 °C).

Antiferromagnetic materials exhibit slightly greater magnetic susceptibility than paramagnets but become paramagnetic above a critical temperature (the Néel temperature).
Common examples include manganese, chromium, various oxides, sulfides, and halides.
Antiferromagnets exhibit antiparallel arrangements of identical spin magnetic moments in their structure.
Typical compounds include manganese oxide (MnO) and cobalt oxide (CoO).

Atoms and molecules can possess or acquire magnetic moments in an external magnetic field:
- The total magnetic moment of an atom is the vector sum of the orbital (p{ml}) and spin magnetic moments (p{ms}) of electrons, as well as that of the nucleus (p{mn}).
- The equations governing these properties include:
  oldsymbol{p}{ma} = oldsymbol{p}{ml} + oldsymbol{p}{ms} + oldsymbol{p}{mn}
  oldsymbol{p}_{ml} = rac{e v r}{2 l}, where l denotes the orbital angular momentum.

MCG technique records the magnetic fields generated by the heart's electrical activity.
It offers spatially and temporally accurate measurements of weak heart magnetic fields.
MCG provides diagnostic information surpassing traditional electrocardiogram (ECG) readings in some cases.

A therapeutic modality employing magnets (often made from ferrites) for health applications.
Magnets used may include static and electromagnetic types, with various application approaches.
Treatment options include permanent magnets or specialized devices integrating electromagnetic fields (e.g. jewelry, mattresses).

EPR studies the behavior of unpaired electrons in a magnetic field.
It involves the resonance condition h
u_{res} = oldsymbol{oldsymbol{ ext{C{B}}}} ext{ and } ext{energy }
u, where oldsymbol{oldsymbol{B}} represents the magnetic field.
EPR methods are pivotal in biological research, aiding in understanding free radical impact.
- EPR's foundation lies in the magnetic moment leading to the splitting of spectral lines (Zeeman effect).

NMR refers to the absorption and reemission of energy by atomic nuclei when subjected to magnetic fields.
Characterized by resonance frequency dependent on magnetic field strength and nucleus type, focusing on isotopes like ^{1}H and ^{13}C.
MRI employs hydrogen nuclei as a primary imaging method, enhancing the visualization of tissues due to their high mobility and concentration in human bodies.
Image resolution in MRI hinges on magnetic field strength, slice thickness, and tissue properties.
Contrast manipulations vary with T1 and T2 weighting, aiding in the differentiation of normal and pathological tissues.

MRI is particularly effective in visualizing soft tissues, aiding diagnoses in multiple medical fields including neurology, orthopedics, and vascular studies.
High-field MRI systems surpass low-field counterparts in image quality, making them optimal for specialized investigations.
The advent of advanced computers and imaging techniques continues to evolve MRI applications.