Electron Spin Resonance: Difference between revisions
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As always in Quantum Physics the chosen axis of the magnetic field points in z direction. | As always in Quantum Physics the chosen axis of the magnetic field points in z direction. | ||
[[File:Spin_projection_onto_z_axis.JPG|thumb|left|200px|alt=A| The two allowed projections of <math> \vec{S} </math> onto the z axis: <math> \pm m_S </math>|The two allowed projections of <math> \vec{S} </math> onto the z axis: <math> \pm m_S </math>]] | [[File:Spin_projection_onto_z_axis.JPG|thumb|left|200px|alt=A| The two allowed projections of <math> \vec{S} </math> onto the z-axis: <math> \pm m_S </math>|The two allowed projections of <math> \vec{S} </math> onto the z axis: <math> \pm m_S </math>]] | ||
In generell, the energy <math> E </math> of a magnetic moment <math> \vec{\mu} </math> given by | |||
<math> E=-\vec{\mu}\cdot\vec{B_Z} </math> . | |||
The magnetic moment <math> \vec{\mu} </math> is related to the spin <math> \vec{S} </math>, which is a so called Quantum Vector with special properties: | |||
#Absolute value: <math> |S|=\sqrt{s\left(s+1\right)} </math> | |||
#Projection onto the z-axis: <math> m_S=\pm\frac{\hbar}{2} </math> | |||
'''''TO BE CONTINUED''''' | '''''TO BE CONTINUED''''' | ||
Revision as of 03:47, 10 November 2014
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
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
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{\mu}=-\mu_B\left(\vec{L}+g_e\vec{S}\right) } ,
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_B } is the Bohr's magneton and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g_e } the magnetogyric ratio, for a free electron it is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{S} } .
If the spin Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{S} } and its magnetic moment Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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.
In generell, the energy Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E } of a magnetic moment Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{\mu} } given by
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E=-\vec{\mu}\cdot\vec{B_Z} } .
The magnetic moment Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{\mu} } is related to the spin Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{S} } , which is a so called Quantum Vector with special properties:
- Absolute value: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |S|=\sqrt{s\left(s+1\right)} }
- Projection onto the z-axis: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_S=\pm\frac{\hbar}{2} }
TO BE CONTINUED