# Difference between revisions of "Electron Spin Resonance"

Electron Spin Resonance (ESR) is a phenomenon usefull for the investigation of materials which contain unpaired spins. Those are caused by various sources. One are not completely filled atomic shells, however, the more interesting ESR signals arise from different circumstances combined in the term defect. For instance, a important one is impurities of semiconductors or isolators which can trap electron or holes. Therefore this measuring technique is very powerfull evaluation of material properties and is used in lots of research fields in physics, chemistry and biology.

## Physical background

Precession of the two Quantum Vectors $\vec{S}$ and $\vec{\mu_S}$ around the magnetic field $\vec{B_Z}$

As the term Electron Spin Resonance already implies, the most essential part of the entire topic is the Spin, an intrinsic angular momentum of the electron. In an atom most of the electron are paired regarding spin. That is, each electron has a partner with an opposite spin, creating a zero net spin. Depending on the electron configuration of an atom or one step above in molecules and solids respectively, it is possible that there are a few or even many single electrons, being up to material.

Generally the magnetic moment of an electron is given by

$\vec{\mu}=-\mu_B\left(\vec{L}+g_e\vec{S}\right)$ ,

where $\mu_B$ is the Bohr's magneton and $g_e$ the magnetogyric ratio, for a free electron it is $g_e=2.0023\approx 2$. This formula includes the orbital angular momentum as well. With ESR it is only possible to detect and investigate the spin component of the total magnetic moment. Hence, in the further deviation we will look at the pure magnetic moment originating from the spin $\vec{S}$.

If the spin $\vec{S}$ and its magnetic moment $\vec{\mu_S}$ is placed in a externally applied magnetic field, the magnetic moment of the spin starts to precess around the axis of the magnetic field due to the torque

$\vec{M}=\vec{\mu_S}\times\vec{B_Z}$ .

As always in Quantum Physics the chosen axis of the magnetic field points in z direction.

The two allowed projections of $\vec{S}$ onto the z axis: $\pm m_S$

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