How does antiferromagnetism occur?

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In summary, the conversation is about the explanation of superexchange and the quantum mechanical origins of magnetism. The concept of spin up and spin down is used to explain why neighboring atoms anti-align instead of align in ferromagnetism. The notation used in the explanation involves substituting uA and uB with α and β, respectively, where α represents spin up and β represents spin down. The equation α(+1/2) = β(-1/2) = 1 means that the spins are antiparallel, resulting in antiferromagnetism in solids and diamagnetism in two-atomic molecules. The discussion also includes a link for further clarification on the topic.
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barnflakes
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Can someone explain this in simple terms to me? I know it's because the spins on neighbouring atoms anti-align - but WHY do they anti-align instead of align, as is the case in ferromagnetism?
 
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I found a good explanation, but there is one part I don't understand: http://en.wikipedia.org/wiki/Magnetism

about 1/2 - 2/3 of the way down under "quantum mechanical origins of magnetism"

I.e., not only uA and uB must be substituted by α and β, respectively (the first entity means "spin up", the second one "spin down"), but also the sign + by the − sign, and finally ri by the discrete values si (= ±½); thereby we have α( + 1 / 2) = β( − 1 / 2) = 1 and α( − 1 / 2) = β( + 1 / 2) = 0. The "singlet state", i.e. the - sign, means: the spins are antiparallel, i.e. for the solid we have antiferromagnetism, and for two-atomic molecules one has diamagnetism.

why does α( + 1 / 2) = β( − 1 / 2) = 1 ? and what does it mean by "(the first entity means "spin up", the second one "spin down")" - how is alpha representing spin up? In that notation alpha is a function?
 

Related to How does antiferromagnetism occur?

1. What is antiferromagnetism?

Antiferromagnetism is a phenomenon in which the magnetic moments of atoms or ions in a material align in opposite directions, resulting in a net magnetization of zero. This means that the material does not exhibit any overall magnetic properties.

2. How does antiferromagnetism occur?

Antiferromagnetism occurs when certain materials, such as transition metals, have neighboring atoms with opposite spins. The electrons in these atoms align themselves in opposite directions, resulting in a cancellation of their magnetic moments and a net magnetization of zero.

3. What are some examples of antiferromagnetic materials?

Some common examples of antiferromagnetic materials include chromium, manganese oxide, and nickel oxide. These materials are often used in magnetic storage devices, such as hard drives, due to their ability to maintain a stable magnetic state.

4. How does temperature affect antiferromagnetism?

At low temperatures, antiferromagnetic materials exhibit a highly ordered state in which all magnetic moments are aligned in opposite directions. As the temperature increases, thermal energy disrupts this alignment and the material becomes less antiferromagnetic. At a certain temperature, known as the Néel temperature, the material becomes paramagnetic, meaning it exhibits weak magnetic properties.

5. Can antiferromagnetism be used in any practical applications?

While antiferromagnetic materials do not exhibit strong magnetic properties, they can still be used in practical applications. For example, antiferromagnetic materials are used in spin-valve sensors, which are used in hard drives and magnetic field sensors. They are also being studied for use in spintronics, a technology that uses the spin of electrons to store and process information.

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