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Can electromagnetic waves be used to magnetize matter if in strong enough and coherent enough? How?

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Electromagnetic waves consist of oscillating electric and magnetic fields. Magnetic materials consist of many small magnetic dipoles. Magnetic dipoles tend to align themselves, if possible, along magnetic field lines (following the field in paramagnets, opposing the field in diamagnets). Therefore, a coherent set of EM waves can cause a large number of dipoles in the plane perpendicular to the wave propagation to oscillate in phase with each other, producing an oscillating magnetization in that plane.

At this point, part or all of the EM wave is absorbed, and a weaker version is re-emitted from the oscillating dipoles. This weaker secondary signal makes the dipoles in the next plane oscillate, but with a phase that is determined by the lattice spacing, the wavelength of the wave, and a quarter-wave phase delay from the absorption-reradiation process that just went on. Unless these parameters are very carefully tuned, the phase of this second set of dipole oscillations might be significantly different than the phase of the first set. This process continues until the EM waves propagate only negligibly through the material.

The bottom line: Unless your material and the coherent EM radiation are very precisely tuned to each other (in other words, unless the EM radiation "resonates" with your material), it will produce lots of oscillating magnetizations of different phases, which most likely destructively interfere and produce little to no net magnetization.

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