Magnetics- Energy Terms and Hysteresis

Question 1

What are 4 main energy terms that behaviour of ferromagnetic materials depend on? MAZE

Answer 1

Magnetostatic energy (stray magnetic fields and internal demagnetising fields)
Magnetocrystalline anisotropy energy (alignment of magnetisation to particular crystallographic directions)
Zeeman energy (externally applied magnetic fields)
Exchange energy (quantum mechanical interaction creating ferromagnetic alignment)

Question 2

For a thin disk, when are magnetostatic energy, magnetocrystalline anisotropy energy, Zeeman energy and exchange energy 0/low?

Answer 2

Magnetostatic zero when there are no free poles (like in-plane vortex magnetisation. Magnetocrystalline anisotropy zero when magnetisation parallel to easy axis or there is no easy axis. Zeeman energy zero when no externally applied magnetic field or is perpendicular to magnetisation. Exchange energy low when there is aligned magnetisation.

Question 3

For a thin disk, when are magnetostatic energy, magnetocrystalline anisotropy energy, Zeeman energy and exchange energy high/very high/non-zero?

Answer 3

Magnetostatic high when not multiple domains in material and very high when opposite poles are close together making large demagnetising field (like uniform out-of-plane magnetisation). Magnetocrystalline anisotropy non-zero when magnetisation not in easy axis direction. Zeeman energy non-zero when applied magnet field not perpendicular to magnetisation. Exchange energy high when direction of magnetisation changes (like in-plane vortex magnetisation).

Question 4

What happens to domain walls when an external magnetic field is applied?

Answer 4

Domain parallel to magnetic field grows and domain opposite to magnetic field shrinks so the domain wall between them moves which reduces Zeeman energy to below zero.

Question 5

How do defects affect domain wall motion?

Answer 5

These could be grain boundaries, vacancies, impurities. Walls move smoothly under low magnetic fields until pinned by defects. Need higher field to move abruptly between defects. These are Barkhausen jumps and are irreversible. Magnetisation reversal is a stepped process called Barkhausen noise. Means graph of M vs H not smooth but has lots of small steps.

Question 6

Explain domain rotation

Answer 6

Domain wall motion often leaves magnetisation along crystallographic easy axes (for low MagX anisotropy energy) even if this isn’t applied field direction. Under higher applied fields, domain rotate into field direction so magnetisation is fully aligned with the magnetic field. Results in slight increase in MagX anisotropy energy but reduces Zeeman energy (due to Applied field).

Question 7

Describe M vs H graph for magnetisation reversal (hysteresis loop)

Answer 7

See lecture 5 page 19 for graph. From origin, goes up for reversible DW motion then bit steeper for irreversible DW motion then curves (DW rotation) to horizontal at saturation (no DWs). Goes back horizontal and curves down a bit (domain nucleation) but y intercept high. Then down steep then curve to saturation in reverse direction. Curves back up a bit (domain nucleation) but y intercept low. Then steep up and curve to saturation.

Question 8

What is hysteresis?

Answer 8

Where the magnetisation depends on both the value of the applied field and the history of the applied fields. Caused by irreversible DW motion and nucleation of ne domains.

Question 9

Saturation magnetisation, Ms, and where it is on hysteresis loop

Answer 9

Magnetisation of a material when all the atomic moments are aligned. Value of M at horizontal part in NE quadrant. Minus the value in the SW quadrant.

Question 10

Remanence, Mr, and where it is on hysteresis loop

Answer 10

The magnetisation of a sample when the applied magnetic field is zero (usually following saturation). The positive y intercept on graph and negative of negative y intercept.

Question 11

Coercivity, Hc, and where it is on hysteresis loop

Answer 11

The magnetic field required to reduce the magnetisation to zero. Positive x intercept and negative of negative x intercept.

Question 12

Difference between hysteresis loops for hard and soft ferromagnetic materials

Answer 12

Hard has large area inside of graph with high remanence and coercivity as magnetocrystalline anisotropy creates energy barrier to be overcome in magnetisation reversal. Soft has very small area inside graph with low remanence and coercivity (often materials with low magnetocrystalline anisotropy)

Question 13

How does hysteresis loop change if field applied along hard or easy axis?

Answer 13

For easy, square response with high remanence and coercivity where reversal is by domain wall nucleation and propagation. For hard, there is almost linear response until saturations so low remanence and coercivity and reversal is by domain wall rotation.

Question 14

How does increasing the number of defects in ferromagnetic material affect its magnetisation hysteresis loop?

Answer 14

Increases domain wall pinning likelihood and significance. Increases coercivity and remanence as DW motion is more restricted. Graph is bumpy and more sloped