Topics%20in%20Magnetism%20III.%20Hysteresis%20and%20Domains

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Topics in MagnetismIII. Hysteresis and Domains
Anne Reilly Department of Physics College of
William and Mary
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After reviewing this lecture, you should be
familiar with
1. General features of ferromagnetic hysteresis
curves 2. Affects of anisotropy 3. Affects of
domains
Material from this lecture is taken from Physics
of Magnetism by Chikazumi, Chapters 15 - 18
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In ferromagnetic materials, exchange interaction
leads to an alignment of atomic spins. When a
magnetic field is applied, these spins are
reoriented, leading to hysteresis.
H
M
H
H
Mmagnetization along direction of H
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Features of Hysteresis Curve
M
Saturation magnetization (Ms)
Remnant magnetization (Mr)
H
Coercivity (Hc)
Mmagnetization along direction of H
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• What determines shape of hysteresis loop?
• Coherent rotation determined mainly by Anisotropy
• Domain formation and domain wall motion

Important principle
Magnetization will lie in direction which is an
energy minimum
Consider a simple example
M
f
H
q
easy axis
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(Stoner-Wohlfarth model)
Simple example
Zeeman energy
Uniaxial anisotropy
Find M (q) by condition
See http//www.student.uni-kl.de/mewes/magnet.e.
html
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Coherent rotation of magnetization considering
only uniaxial anisotropy
M
f00 (along easy axis)
f900 (along hard axis)
H
M
H
Hc2K1/Ms
For 00
Note Hysteresis shown above is the component of
M in the direction of H
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Magnetic Anisotropy

• Anisotropy preferred (easy axes) and
  unfavorable (hard axes) directions of
  magnetization
• Due to coupling of electronic spins to
  electronic charge density

For this rotation, as long as spins remain
parallel, exchange energy does not change, but
dipolar and LS coupling energy will change.
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Magnetic Anisotropy

• Anisotropy preferred (easy axes) and
  unfavorable (hard axes) directions of
  magnetization
• Due to coupling of electronic spins to
  electronic charge density

Example hcp Co
easy
M
c-axis (hard)
hard
(easy)
H (G)
8000
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Magnetic Anisotropy
Two major types of anisotropy, written in terms
of empirical anisotropy coefficients Uniaxial C
ubic
(e.g., Co)
(e.g., Fe, Ni)
Note cubic lattices can have several easy and
hard axes
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Domains
In ferromagnetic materials, exchange interaction
leads to an alignment of atomic spins
However, this leads to a large external and
dipolar magnetic fields which will tend to
demagnetize the material. Domains are formed to
minimize this effect.
Domain wall
From http//www.aacg.bham.ac.uk/magnetic_materials
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Domains
Domain size and wall size determined by energy
cost, dependent on material and geometry.
Ni thin film
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Domain Walls
Energy is minimized by having a wall of finite
width
N spins
Energy cost (exchange)
Energy cost (exchange anisotropy)
(per unit area)
K anisotropy constant a lattice constant
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Domain Walls
Energy is minimized by having a wall of finite
width
For iron, J2.16x10-21, S1, K4.2x104 and
a2.86x10-10
d42 nm (150 lattice constants)
domain size will depend on sample geometry (see
Chikazumi, Chp. 16)
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Domain Walls

• Domains have different shapes and orientations
• Two examples of thin film domain walls

Neel wall (rotation in plane)
Bloch wall (rotation out of plane)
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Domains and Hysteresis
Domain formation and domain wall motion affects
the shape of hysteresis loop
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Domains and Hysteresis
Barkhausen noise Tiny steps of domain walls
M
H
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Domains and Hysteresis
Domain walls move across energy landscape
(determined by film morphology)
Uw
irreversible motion
reversible motion
x
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Domains and Hysteresis
Coercivity can be increased over that for single
domain system because domain walls can become
pinned (hard to move).
Pinning on lattice defects (dislocations, voids,
etc.) , impurities. Walls move between pinning
points.
Defects and stress in thin film can increase
number of pinning sites and thus coercivity.