# Neutron scattering - determing the magnetic moment for MnO

• peripatein
In summary, to determine the magnetic moment of an ion at the position Rj in MnO, you need to first calculate the position vector Rj and then use the reciprocal lattice vectors to find the vector K for MnO.
peripatein
I'm told that the MnO crystal resembles in structure that of NaCl (FCC) with lattice constant a, and am first asked to write a general expression for the position vector Rj of the ion j in the unit cell of MnO. I am then asked to find the vector K for MnO in order to use the relation μj0e(iK⋅Rj) to determine the magnetic moment of an ion at the position Rj.

I initially wrote down the unit cell vectors for one of the two atoms, and added to these a basis (due to the second atom): a1=a/2(x^+y^),a2=a/2(x^+z^),a3=a/2(y^+z^), with basis: d1=0,d2=a/2(x^+y^+z^).
How am I to formulate the expression for the general position vector Rj? Would it simply be a linear combination of all these vectors? Next, for determining the value of the vector K, need I to first find the reciprocal lattice?
I'd appreciate some explicit assistance/guidance.

For the position vector Rj of the ion j in the unit cell of MnO, it can be expressed as:Rj = n1a1 + n2a2 + n3a3 + d1d1 + d2d2 where n1, n2 and n3 are integers representing the number of unit cells along each of the lattice vectors (a1, a2 and a3). To find the vector K for MnO, you need to first calculate the reciprocal lattice vectors. The reciprocal lattice is defined as a set of vectors that are perpendicular to the lattice vectors and have a length such that the dot product between two reciprocal lattice vectors is equal to 2π. The reciprocal lattice vectors for MnO are then given by:K1 = 2π/a (y^-z^)K2 = 2π/a (z^-x^)K3 = 2π/a (x^-y^)Using these reciprocal lattice vectors, you can then calculate the vector K for MnO using the relation μj=μ0e(iK⋅Rj).

## 1. What is neutron scattering?

Neutron scattering is a technique used in physics and materials science to study the structure and properties of materials at the atomic and molecular level. It involves directing a beam of neutrons at a sample and analyzing the scattered neutrons to gather information about the sample's composition, structure, and dynamics.

## 2. How is neutron scattering used to determine the magnetic moment for MnO?

Neutron scattering can be used to determine the magnetic moment for MnO by measuring the neutron diffraction pattern of the sample. The magnetic moment of MnO affects the direction and intensity of the scattered neutrons, providing information about the magnetic properties of the material. By comparing the scattering pattern to theoretical models, the magnetic moment of MnO can be calculated.

## 3. What is the significance of determining the magnetic moment for MnO?

Determining the magnetic moment for MnO is important for understanding the magnetic properties of the material. MnO is a ferromagnetic material, meaning it has a permanent magnetic moment, and it is also used in various technologies such as magnetic storage and spintronics. Knowing the magnetic moment can help in the development of new materials and technologies.

## 4. What are the advantages of using neutron scattering over other techniques for determining the magnetic moment?

Neutron scattering has several advantages over other techniques for determining the magnetic moment for MnO. It is a non-destructive technique, meaning the sample remains intact after the experiment. Neutrons also have a high sensitivity to magnetic moments, making it a precise technique. Additionally, neutron scattering can provide information about the magnetic moment in different environments, such as under different temperatures or pressures.

## 5. Can neutron scattering be used to determine the magnetic moment for other materials?

Yes, neutron scattering can be used to determine the magnetic moment for a wide range of materials, not just MnO. It is a versatile technique that can be applied to different types of materials, including metals, ceramics, and biological samples. Neutron scattering is particularly useful for studying magnetic materials, as it provides detailed information about their magnetic properties at the atomic level.

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