Is Cobalt Magnetic?

Cobalt is a ferromagnetic metal, which means that it exhibits magnetic properties on its own due to the alignment of its electrons’ spins. The magnetic properties of cobalt can be quantified by several measurable values, including the saturation magnetization (Ms), the magnetic anisotropy energy (MAE), and the magnetic susceptibility (χ). These values can be influenced by the size, shape, and surface anisotropy of the cobalt particles, making cobalt a versatile magnetic material with a wide range of applications.

Saturation Magnetization (Ms) of Cobalt

The saturation magnetization (Ms) is the maximum magnetization that a magnetic material can achieve when it is fully magnetized. For cobalt, the bulk saturation magnetization is approximately 1.42 T. This value can be calculated using the following formula:

Ms = Nμ / V

Where:
– N is the number of magnetic moments per unit volume
– μ is the magnetic moment of each atom
– V is the volume of the material

The saturation magnetization can be affected by the size and shape of the cobalt particles. For example, a 1.5-nm-thick Co layer should present a saturation magnetization similar to the bulk one, as the size-dependent effects become negligible. However, as the particle size decreases, the surface-to-volume ratio increases, and the surface anisotropy can significantly impact the saturation magnetization.

Magnetic Anisotropy Energy (MAE) of Cobalt

The magnetic anisotropy energy (MAE) is the energy required to rotate the magnetization of a magnetic material from its easy axis to a hard axis. The MAE of cobalt is known to be strongly size-dependent, with values ranging from 0.1 kJ/m³ to 3000 kJ/m³.

The MAE can be influenced by the shape and surface anisotropy of the cobalt particles. The shape anisotropy arises from dipolar interactions within the nanoparticle and notably induces an easy axis along the long axis of an ellipsoid. The surface magneto-crystalline anisotropy is a much more subtle contribution due to the crystalline structure and its symmetry breaking at the surface. It only becomes important in systems with a high surface-to-volume ratio, such as thin films or small nanoparticles.

The MAE can be calculated using the following formula:

MAE = Ku * V

Where:
– Ku is the uniaxial anisotropy constant
– V is the volume of the material

The uniaxial anisotropy constant (Ku) for cobalt can vary depending on the size and shape of the particles, as well as the crystalline structure and surface effects.

Magnetic Susceptibility (χ) of Cobalt

The magnetic susceptibility (χ) is a measure of the degree of magnetization of a material in response to an applied magnetic field. The magnetic susceptibility can be used to determine the magnetic identity of a material, whether it be paramagnetic or diamagnetic, the presence or absence of a magnetic ordering or freezing transitions, anisotropy in single crystal measurements, low-dimensionality or frustration.

The magnetic susceptibility of cobalt can be described by the Curie-Weiss law, which relates the magnetic susceptibility to the temperature and the Curie constant:

χ = C / (T - Tc)

Where:
– χ is the magnetic susceptibility
– C is the Curie constant
– T is the absolute temperature
– Tc is the Curie temperature

The Curie constant for cobalt is approximately 1.7 × 10^-3 m³/kg, and the Curie temperature is around 1388 K. The magnetic susceptibility of cobalt is strongly dependent on temperature, with the material exhibiting ferromagnetic behavior below the Curie temperature and paramagnetic behavior above it.

Factors Affecting the Magnetic Properties of Cobalt

The magnetic properties of cobalt can be influenced by several factors, including:

1. Particle Size: As the particle size decreases, the surface-to-volume ratio increases, and the surface anisotropy can significantly impact the magnetic properties, such as the saturation magnetization and the magnetic anisotropy energy.

2. Particle Shape: The shape of the cobalt particles can also affect the magnetic properties, particularly the magnetic anisotropy energy. The shape anisotropy arises from dipolar interactions within the nanoparticle and can induce an easy axis along the long axis of an ellipsoid.

3. Crystalline Structure: The crystalline structure of cobalt can also influence its magnetic properties, particularly the magnetic anisotropy energy. The surface magneto-crystalline anisotropy is a subtle contribution due to the crystalline structure and its symmetry breaking at the surface.

4. Temperature: The magnetic susceptibility of cobalt is strongly dependent on temperature, with the material exhibiting ferromagnetic behavior below the Curie temperature and paramagnetic behavior above it.

5. Applied Magnetic Field: The application of an external magnetic field can also affect the magnetic properties of cobalt, such as the saturation magnetization and the magnetic anisotropy energy.

Examples and Numerical Problems

1. Example 1: Consider a 1.5-nm-thick cobalt thin film. Calculate the saturation magnetization (Ms) of the film, given that the bulk saturation magnetization of cobalt is 1.42 T.

Given:
– Bulk saturation magnetization of cobalt (Ms,bulk) = 1.42 T

Since the film thickness is 1.5 nm, the size-dependent effects are negligible, and the saturation magnetization should be similar to the bulk value.

Therefore, the saturation magnetization of the 1.5-nm-thick cobalt thin film is:
Ms = Ms,bulk = 1.42 T

1. Example 2: Calculate the magnetic anisotropy energy (MAE) of a cobalt nanoparticle with a volume of 1 × 10^-21 m³ and a uniaxial anisotropy constant (Ku) of 5 × 10^5 J/m³.

Given:
– Volume of the cobalt nanoparticle (V) = 1 × 10^-21 m³
– Uniaxial anisotropy constant (Ku) = 5 × 10^5 J/m³

Using the formula:
MAE = Ku * V
MAE = 5 × 10^5 J/m³ × 1 × 10^-21 m³
MAE = 5 × 10^-16 J

1. Numerical Problem: A cobalt thin film has a thickness of 10 nm and a surface area of 1 cm². Calculate the total magnetic moment of the thin film, given that the bulk saturation magnetization of cobalt is 1.42 T and the atomic volume of cobalt is 1.1 × 10^-29 m³.

Given:
– Thickness of the cobalt thin film = 10 nm
– Surface area of the thin film = 1 cm² = 1 × 10^-4 m²
– Bulk saturation magnetization of cobalt (Ms,bulk) = 1.42 T
– Atomic volume of cobalt = 1.1 × 10^-29 m³

Step 1: Calculate the volume of the cobalt thin film.
Volume of the thin film = Thickness × Surface area
Volume of the thin film = 10 × 10^-9 m × 1 × 10^-4 m²
Volume of the thin film = 1 × 10^-12 m³

Step 2: Calculate the number of cobalt atoms in the thin film.
Number of cobalt atoms = Volume of the thin film / Atomic volume of cobalt
Number of cobalt atoms = (1 × 10^-12 m³) / (1.1 × 10^-29 m³)
Number of cobalt atoms = 9.09 × 10^16 atoms

Step 3: Calculate the total magnetic moment of the thin film.
Total magnetic moment = Number of cobalt atoms × Magnetic moment per atom
Magnetic moment per atom = Ms,bulk × Atomic volume of cobalt
Magnetic moment per atom = 1.42 T × 1.1 × 10^-29 m³
Magnetic moment per atom = 1.562 × 10^-29 J/T

Total magnetic moment = 9.09 × 10^16 atoms × 1.562 × 10^-29 J/T
Total magnetic moment = 1.42 J/T

Conclusion

Cobalt is a ferromagnetic metal with unique magnetic properties that can be quantified by the saturation magnetization (Ms), the magnetic anisotropy energy (MAE), and the magnetic susceptibility (χ). These properties can be influenced by various factors, such as particle size, shape, crystalline structure, temperature, and applied magnetic field. Understanding and controlling the magnetic properties of cobalt is crucial for its wide range of applications, including permanent magnets, data storage, and spintronic devices.

References

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