Magnetoresistance

Key takeaways

Magnetoresistance belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Magnetoresistance to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Magnetoresistance from memory before moving on to harder problems.

Reference excerpt

Magnetoresistance is the tendency of a material (often ferromagnetic) to change the value of its electrical resistance in an externally-applied magnetic field. There are a variety of effects that can be called magnetoresistance. Some occur in bulk non-magnetic metals and semiconductors, such as geometrical magnetoresistance, Shubnikov–de Haas oscillations, or the common positive magnetoresistance in metals. Other effects occur in magnetic metals, such as negative magnetoresistance in ferromagnets or anisotropic magnetoresistance (AMR). Finally, in multicomponent or multilayer systems (e.g. magnetic tunnel junctions), giant magnetoresistance (GMR), tunnel magnetoresistance (TMR), colossal magnetoresistance (CMR), and extraordinary magnetoresistance (EMR) can be observed. The first magnetoresistive effect was discovered in 1856 by William Thomson, better known as Lord Kelvin, but he was unable to lower the electrical resistance of anything by more than 5%. Today, systems including semimetals and concentric ring EMR structures are known. In these, a magnetic field can adjust the resistance by orders of magnitude. Since different mechanisms can alter the resistance, it is useful to separately consider situations where it depends on a magnetic field directly (e.g. geometric magnetoresistance and multiband magnetoresistance) and those where it does so indirectly through magnetization (e.g. AMR and TMR).

Discovery William Thomson (Lord Kelvin) first discovered ordinary magnetoresistance in 1856. He experimented with pieces of iron and discovered that the resistance increases when the current is in the same direction as the magnetic force and decreases when the current is at 90° to the magnetic force. He then did the same experiment with nickel and found that it was affected in the same way but the magnitude of the effect was greater. This effect is referred to as anisotropic magnetoresistance (AMR).

In 2007, Albert Fert and Peter Grünberg were jointly awarded the Nobel Prize for the discovery of giant magnetoresistance.

Geometrical magnetoresistance An example of magnetoresistance due to direct action of magnetic field on electric current can be studied on a Corbino disc (see Figure). It consists of a conducting annulus with perfectly conducting rims. Without a magnetic field, the battery drives a radial current between the rims. When a magnetic field perpendicular to the plane of the annulus is applied, (either into or out of the page) a circular component of current flows as well, due to Lorentz force. Initial interest in this problem began with Boltzmann in 1886, and independently was re-examined by Corbino in 1911. In a simple model, supposing the response to the Lorentz force is the same as for an electric field, the carrier velocity v is given by:

v = μ ( E + v × B ) , {\displaystyle \mathbf {v} =\mu \left(\mathbf {E} +\mathbf {v\times B} \right),}

where μ is the carrier mobility. Solving for the velocity, we find:

v = μ 1 + ( μ B ) 2 ( E + μ E × B + μ 2 ( B ⋅ E ) B ) = μ 1 + ( μ B ) 2 ( E ⊥ + μ E × B ) + μ E ∥ {\displaystyle {\begin{aligned}\mathbf {v} &={\frac {\mu }{1+(\mu B)^{2}}}\left(\mathbf {E} +\mu \mathbf {E\times B} +\mu ^{2}(\mathbf {B\cdot E} )\mathbf {B} \right)\\&={\frac {\mu }{1+(\mu B)^{2}}}\left(\mathbf {E} _{\perp }+\mu \mathbf {E\times B} \right)+\mu \mathbf {E} _{\parallel }\,\end{aligned}}}

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Magnetoresistance

Start with the simplest possible case. Write down what Magnetoresistance claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Magnetoresistance before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Magnetoresistance ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Magnetoresistance

In research: Magnetoresistance appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Magnetoresistance in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Magnetoresistance is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1856 in science, 1856 introductions, Magnetic ordering, so understanding it makes those chapters shorter.
In everyday life: Look for Magnetoresistance outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Magnetoresistance in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Magnetoresistance means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Magnetoresistance out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Magnetoresistance in simple terms?

Magnetoresistance is the tendency of a material (often ferromagnetic) to change the value of its electrical resistance in an externally-applied magnetic field. There are a variety of effects that can be called magnetoresistance.

Why does Magnetoresistance matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Magnetoresistance?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Magnetoresistance.