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What's that ?

ODMR is an abbreviation for: Optically Detected Magnetic Resonance. It's a means to investigate the structure of the solid state, i. e. crystals such as ruby and semiconductors.

"Aha. And what does this tell me ?"

"Optically" already suggests, that we're working with light.
"Magnetic" suggests some magnetic fields. The ones I use in the Lab are some 3.5 Tesla strong. Just to give you a rough idea: this is sufficient to move screwdrivers through the air. When you move a chair with metal parts you'll feel that you're not the only one who pulls on it ! Now we need some Resonance. For that purpose we use microwaves ("...we've got to install microwave ovens...") and exhibit the material under inverstigation cold temperatures ("we've got move these refrigerators..."). When I say "cold" I really mean "cold": some minus 270 degree Centigrade !!!

The physics behind that

Electrons have a so-called "Spin".
This spin causes a magnetic moment which can couple to an external magnetic field. Maybe you can imagine that as a ship with a sail and winds. The latter one is the external magnetic field, the former one the Spin. We're dealing here with quantum physics, so this picture is of course dangerous: first, spins can't be freely oriented to that field. Second: the electron is not blown through the crystal by the magnetic field. So the boat should use an anchor :-)
Okay, let's proceed. The orientation of the sail to the wind influences the pull on the boat. Now you can imagine that as an energetic state; depending on the orientation we find different energetic states.
In the case of the electron it's quite similar: the orientation of the magnetic moment which is due to the spin in respect to the magnetic field puts the electron in a certain energetic state and these are different for different orientations.
What happens now, if there's a sudden blast of wind from another direction ?
The sail can be pushed and hence the boat enters a different state.
Microwaves are electromagnetic radiation; the name already says it: there are magnetic fields caused by the radiation. This fields can push the electron from one energetic state into a different one.

"That's fine, but how does it help?"

The gag behind this is: we can observe this !
These energetic sublevels, which are caused by the external magnetic field, are still part of energetic levels which can participate on optical transitions. For those readers who are more familiar with this stuff: "light" has an energy of 1.8 through 3.2 electron volts (eV). I don't want to go too much in the details, just to roughly explain "eV": if one has LED of different colour, these have different voltages on which they start to emitt. This is a quite direct measure.
The energetic levels caused by the magnetic fields are of the order milli-eV. That's why we have to use low temperatures: in room temperature all of these levels are populated, because the electrons obtain energy from lattice vibrations of the crystal.
Another thing helps us: different orientation of the electronic spin results in different kind of polarisations of the emitted light.

What we do now

We either observe the light which a crystal emitts (PL) or watch, which part is absorbed (Abs). To select different energetic sublevels we use a polarizer for analysation (PL) or excitation (Abs).

"May I humbly ask, what the sense of that ?"

Good question :-)
All which has been said up this point is just a rough idea, what ODMR is about. It's far from being a complete story ! There are thick books written about it ... But with this method we can:
  • investigate the structure and nature of so-called defects in crystals
  • learn about the amount of defects
In that way we help those guys, who prepare crystals and semiconductors. For the use in everyday applications, material scientists and manufacturers have to have a clue, what is going on in the material they use. Otherwise you're computer, cellphones, CD-Player, Laserpointer, ... will refuse to work.
ODMR is one step to a better understanding.