Magnetism: Feromagnetism

Amitava Moitra

Raidighi College

Electronic contribution

Magnetic properties of materials are totally determined by quantum mechanical nature of their molecular structure.

Electrons in atoms produce magnetic field

Electrons rotate around the nucleus in orbits

This is same as having a loop of current

Currents produce magnetic fields (Ampere)

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It is usually a small effect...

There are lots of electrons, orbits are randomly oriented:

What happens when we put the material in an external B? Lentz’s law: the orbits rearrange so that the magnetic field by the orbits opposes the external magnetic field

Net effect: the total magnetic field will be weaker

e

v

I

B

Mg. Moment Calculations

• Current due to electron in orbit of radius r: I=ev/2πr
• The magnetic moment μ of the loop is = IA/c
• = πr²I/c = evr/2cThe magnetic moment μ is related to the angular momentum L: rXp => μ = -eL/2m_ec

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• In addition to the standard angular momentum L electrons have intrinsic angular momentum (spin) intrinsic magnetic moment

B_ext

B_int

Intrinsic magnetic moment

• The intrinsic magnetic moment behaves very differently from the standard magnetic moment
• No Lentz’s law type behavior because this field is associated with the electron itself
• What happens when we put the material in an external B?
• A magnetic moment μ placed in an external filed B feels a torque τ
• τ=μ×B tends to line up the electron magnetic moments with external field
• Net effect: the total magnetic field will be stronger

B_ext

B_{intrinsic/spin}

Different naming

• Summary of the situation so far:
• Lentz’s law on the orbit of the electrons opposes B fields from entering material
• Magnetic torque acting on individual electrons augments the B field in the material
• Opposite behaviors! Who wins?
• It depends on the properties of the material (chemical structure, how free electrons are, etc)
• 3 categories: i) Diamagnetic materials ii) Paramagnetic materials iii) Ferromagnetic materials

Diamagnetism

• Diamagnetic materials defined as materials in which the magnetization opposes the external magnetic field
• When material is immersed in external B field, magnetic field inside the material is weaker than external B
• Lentz’s law wins out on effect of spin
• Diamagnetism is usually very weak and hard to see
• Lentz’s law plays a role in all materials. Spin effect (if present) are stronger if preset it usually covers completely diamagnetic behavior
• Examples of diamagnetic materials: Typically orbits filled with paired electron -> orbit has no net magnetic moment : Most substances: H₂0, Cu, NaCl, etc
• Consequence: diamagnetic substances will be expelled from B field

Paramagnetism

• Paramagnetic materials are defined as materials in which the magnetization augments the external magnetic field
• When material is immersed in B field, magnetic field inside the material is stronger than outside
• Effect of Spin wins out on Lentz’s law
• Examples of diamagnetic materials
• Typically have several electron orbits that contain unpaired electrons -> orbit has a net magnetic moment
• (Exception: Oxygen O2 is paramagnetic. To see this property need to cool it to a liquid state, or random motion will wipe out effect)
• Example: Na, Al, NiSO4, etc
• Consequence: Paramagnetic materials are pulled into magnetic fields
• If paramagnetic behavior is “extra strong”: Ferromagnetic material

Ferromagnetism

• “Ferromagnetism is paramagnetism on steroids” Prof. S. Hughes
• Nonlinearity distinguishes it from paramagnetism
• M and H do not have a simple linear relation
• Magnetization M is defined as the magnetic dipole moment of a substance per unit volume
• Magnetic moment of a material with volume V and magnetization M μ=MV
• B =H+4πM (B is the total magnetic field; H is the “normal field” due to currents, M is the magnetization, component of B due to material’s properties; In vacuum, B=H )
• Magnetization remains after external field is turned off
• This is how permanent magnets work!

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Ferromagnetism

• Ferromagnetism is conceptually similar to paramagnetism
• Difference: magnetic moments of many atoms are tend to be aligned in small regions (domains)
• Paramagnetic materials: moments are randomly arranged until external B aligns them
• Since domains are small (0.1 mm – few mm) and randomly oriented: overall M=0
• When material is put into externa B, domains re-align // to B
• When external B is removed they stay aligned: permanent magnets!

Ferromagnetism

• Sizes of domains range from a 0.1 mm to a few mm. When an external magnetic field is applied, the domains already aligned in the direction of this field grow at the expense of their neighbors. If all the spins were aligned in a piece of iron, the field would be about 2.1 Tesla. A magnetic field of about 1 T can be produced in annealed iron with an external field of about 0.0002 T, a multiplication of the external field by a factor of 5000!

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• Barkhausen effect: Domains are well modeled by the compass table, an array of about one hundred small compass needles used for showing fields of bar magnets, etc. When there is no strong external Bfield, sections of the array line up in different directions, each individual compass needle aligning itself with the local field. When the array is tapped sharply, it will be seen that the needles on the boundaries of the domains are the least stable (vibrate the most), and some of them realign causing one domain to grow at the expense of another. In the Barkhausen effect, a large coil of fine wire is connected through an amplifier to a speaker. When an iron rod is placed within the coil and stroked with a magnet, an audible roaring sound will be produced from the sudden realignments of the magnetic domains within the rod. A copper rod, on the other hand, produces no effect.

Experiment

Hysterisis Loop

• In ferromagnetic materials B and H have a nonlinear dependence
• Let’s find out experimentally what that is
• Apply external field H (x axis) and measure total field B (y axis) in the Start with value of H (H), decrease to 0, flip the direction and reach –H
• The curve describing relationship between H and B is called hysteresis curve
• When H=0, B.ne.0 What value will it take? +H? –H?
• It depends on the magnetization history

• Curie temperature is the temperature above which ferromagnetic materials stop acting as such NB: transition is very sudden!
• At T>TC the random motion of the magnetic moments becomes so strong that they cannot align anymore to form domains For Fe Tc=770 K

Curie

Curie Wiess La

The Curie–Weiss law describes the magnetic susceptibility of a ferromagnet in the paramagnetic region above the Curie Point: χ = C/(T − Tc) -->> where C is a material-specific Curie Constant is absolute temperature and TC is the Curie Temperature, both measured in K. The law predicts a singularity in the susceptibility at T = Tc. Below this temperature the ferromagnet has a spontaneous magnetization.

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