Magnetic Materials

Energy Terms

Exchange Energy

Minimize exchange energy when all spins are parallel

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<math>E = -2J \sum_

Unknown macro: {i=j}

S_i S_j</math>

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Domain walls are the interfaces between domains. There is a significant angle among the magnetic moments of the atoms at the border. The higher the exchange constant <math>A_

Unknown macro: {ex}

</math>, the higher the exchange energy.

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Reduce the exchange energy by spreading the angular transition over a very large number of atoms. The angle between two adjacent moments is very small, but there is a cost in anisotropy energy. Almost all the moments that are in the transition deviate from the easy magnetization direction, and there is a cost in magnetocrystalline energy. This grows with the anisotropy constant, <math>K</math>.

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The width of the domain wall is defined by a compromise. The compromise depends on the relative values of the constants <math>A_

</math> and <math>K</math>. The higher the <math>A_

Unknown macro: {ex}

/ K</math> ratio, the wider the domain walls.

Magnetostatic Energy

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<math>E = -M \cdot H</math>

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Demagnetization factor

Anisotropy Energy

Easy and hard direction. The angle, <math>\theta</math>, is the angle from the easy angle. Extra energy to magnetize along a particular angle. Squared due to symmetry. Energy required to rotate spins from favored direction.

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<math>K = K_1 \sin^2 \theta + K_2 \sin^4 \theta + K_3 \sin^6 \theta</math>

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Magnetostrictive Energy

The magnetization of a ferromagnetic material is in nearly all cases accompanied by changes in dimensions. The resulting strain is called the magnetostriction <math>\lambda</math>. From a phenomenological viewpoint there are really two main types of magnetostriction to consider: spontaneous magnetostriction arising from the ordering of magnetic moments into domains at the Curie temperature, and field-induced magnetostriction.

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Spontaneous magnetostriction within domains arises from the creation of domains as the temperature of the ferromagnet passes through the Currie (or ordering) temperature. Field-induced magnetostriction arises when domains that show spontaneous magnetostriction are reoriented under action of a magnetic field.

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The field-induced bulk-magnetostriction is the variation of <math>\lambda</math> with <math>\vec H</math> or <math>\vec B</math> and is often the most interesting feature of the magnetostrictive properties to the materials scientist. However, the variations <math>\lambda (\vec H)</math> or <math>\lambda (\vec B)</math> are very structure sensitive so that it is not possible to give any general formula for the relation of magnetostrictino to field.

Demagnetizing fields

In view of the fact that the magnetization <math>\vec M</math> and the magnetic field <math>\vec H</math> point in opposite directions inside a magnetized material of finite dimensions, due to the presence of the magnetic dipole moment, it is possible to define a demagnetizing field <math>\vec H_d</math> which is present whenever magnetic poles are created in a material

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The demagnetizing field depends on two factors only. These are the magnetization in the material (i.e. the pole strength) and the shape of the specimen (i.e the pole separation which is determined by sample geometry). The demagnetizing field is proportional to the magnetization.

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When dealing with samples of finite dimensions in an applied magnetic field <math>\vec H_

Unknown macro: {app}

</math> it is necessary to make some demagnetizing field correction to determine the exact internal field in the solid, <math>\vec H_

Unknown macro: {in}

</math>.

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<math>\vec H_

= \vec H_

- N_d \vec M</math>

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Examples involving energy terms

  • Spins in sphere
  • Small, long rods to store energy

References:

  • David Jiles Introduction to Magnetism and Magnetic Materials

Spintronics

In order to make a spintronic device, the primary requirement is to have a system that can generate a current of spin polarised electrons, and a system that is sensitive to the spin polarization of the electrons. Most devices also have a unit in between that changes the current of electrons depending on the spin states.

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The simplest method of generating a spin polarised current is to inject the current through a ferromagnetic material. The most common application of this effect is a giant magnetoresistance (GMR) device. A typical GMR device consists of at least two layers of ferromagnetic materials separated by a spacer layer. When the two magnetization vectors of the ferromagnetic layers are aligned, then an electrical current will flow freely, whereas if the magnetization vectors are antiparrallel then the resistance of the system is higher. Two variants of GMR have been applied in devices, current-in-plane where the electric current flows parallel to the layers and current-perpendicular-to-the-plane where the electric current flows in a direction perpendicular to the layers.

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The most successful spintronic device to date is the spin valve. This device utilizes a layered structure of thin films of magnetic materials, which changes electrical resistance depending on applied magnetic field direction. In a spin valve, one of the ferromagnetic layers is "pinned" so its magnetization direction remains fixed and the other ferromagnetic layer is "free" to rotate with the application of a magnetic field. When the magnetic field aligns the free layer and the pinned layer magnetization vectors, the electrical resistance of the device is at its minimum. When the magnetic field causes the free layer magnetization vector to rotate in a direction antiparallel to the pinned layer magnetization vector, the electrical resistance of the device increases due to spin dependent scattering. The magnitude of the change, (Antiparallel Resistance - Parallel Resistance) / Parallel Resistance x 100% is called the GMR ratio. Devices have been demostrated with GMR ratios as high as 200% with typical values greater than 10%. This is a vast improvement over the anisotropic magnetoresistance effect in single layer materials which is usually less than 3%. Spin valves can be designed with magnetically soft free layers which have a sensitive response to very weak fields (such as those originating from tiny magnetic bits on a computer disk), and have replaced anisotropic magnetoresistance sensors in computer hard disk drive heads since the late 1990s.

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Future applications may include a spin-based transistor which requires the development of magnetic semiconductors exhibiting room temperature ferromagnetism. The operation of MRAM or magnetic random access memory is also based on spintronic principles.

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Reference

GMR

The development of devices that sense and store information is driven by the demand for more capable computers. The utilization of the phenomenon of giant magneto-resistance (GMR) has led to the creation of more sensitive sensors that read bits coded on magnetized regions of disks. An understanding of GMR has led to a large increase in information storage capacity. The phenomenon of GMR has also been of interest to physicists.

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The magneto-resistance effect (MR effect) describes the change in the electrical resistance of a material due to the application of a magnetic field. Research advances related to electron spin, tunneling effects, and production of ultra-thin layers have made possible the design of electrical devices based on quantum mechanical effects of the electron. The giant magneto-resistance effect is dependent on spin properties of electrons. Several other magneto-resistive effects have been discovered, and they are classified under XMR effects or XMR technology.

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An example of a structure where the giant magneto-resistive effect is observed consists of a layer of copper, a normal metal, between layers of cobalt, a ferromagnetic material. When the magnetic moments of the ferromagnetic layers are parallel, there is less resistance to the flow of current. In current devices, the direction of magnetization of one layer is typically fixed in one direction, while the other is determined by an external field. The difference of resistance between parallel and anti-parallel configurations is 10-15% in current devices.

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The effect of GMR is similar to phenomenon of polarization. In a polarization experiment, light cannot pass through if two polarizers are perpendicular to one another. Similarly, one magnetic layer may allow electrons of one type of spin to pass, and, if the second structure is aligned in the same direction, current can easily pass through. If the second layer is misaligned, neither spin channel can pass through the structure easily, and the electrical resistance is high.

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Early studies in which GMR was first observed may have been published in 1987. The patent of the effect is owned by Peter Grunberg, who led a team at the Julich Research Centre and observed the effect in trilayers of Fe/Cr/Fe. The effect was simultaneously and independently observed in multilayers of Fe/Cr.

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Three types of GMR are multilayer, granular, and spin-valve GMR. The effect was first observed in multilayer configurations and the effect in granular GMR is not as large as multilayer GMR. Spin-valve GMR is the most useful industrially, and the magnetic recording industry is researching structures that are very sensitive to magnetic fields. IBM and Seagate develop high density disk and tape playback heads. Additional applications include avionic compasses, swipe-card readers, wheel rotation sensors in ABS brakes, and current sensors for use in safety powerbreakers and electricity meters.

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References:

TMR

In physics, the tunnel magnetoresistance effect, commonly abbreviated as TMR, occurs when two ferromagnets are separated by a thin (about 1 nm) insulator. Then the resistance of the tunneling current changes with the relative orientation of the two magnetic layers. The resistance is normally higher in the anti-parallel case.

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It was discovered in 1975 by M. Julliere, using iron as the ferromagnet and germanium as the insulator.

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Room temperature TMR was discovered in 1995 by Moodera et. al. following renewed interest in this field fueled by the discovery of the giant magnetoresistive effect. It is now the base for the magnetic random access memory (MRAM) and read sensors in hard disk drives. For more technical information see [Moodera and Mathon 1999].

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References:
*Tunnel Magnetoresistance http://en.wikipedia.org/wiki/TMR

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