Detection of electric/magnetic activity with magnetic resonance

Last update: 2024-02-07

Use of magnetic resonance for electric/magnetic field detection

A less known application of magnetic resonance is the possibility to detect electric and magnetic fields. We may consider that the spin, which resembles a bar magnet, performs a 360° rotation around the magnetic field lines (Figure 1, where B is symbolizing the magnetic field). This is actually a special rotation, called precession, as the spin is tilted and draws a cone, similarly to a top toy. We may also compare a spin to a clock with one hand running 360 degrees.

In general, in science, if an object performs a circle motion and we want to describe the position of the object on the circle, we may use an angle measure called "phase" (reference "unit circle"). We may say for instance that the object is found at 30° or has a phase of 30°.

Let us consider the example of an electric current running on a wire as in the study by Bodurka J. et al. entitled “Current-Induced Magnetic Resonance Phase Imaging.” [Journal of Magnetic Resonance, vol. 137, no. 1, 1 Mar. 1999, pp. 265–271, https://doi.org/10.1006/jmre.1998.1680 (PDF)]. We use an electric current which has a specific waveform, known as a "square waveform", shown in Figure 2 on the top. This signal is generated by having the current ON for two seconds and OFF for two seconds.

While a spin rotates, the magnetic field at a given time point may exert a magnetic force on the spin and change its phase i.e. its position on the circle. For example, from a 20° phase, the spin may acquire a 90° phase (Figure 1). The phase change in this case is 70°. It is possible to measure the phase change (or phase shift) and determine the strength of the magnetic field which caused it at a certain time point. By measuring the phase shift at different time points, we can determine the magnetic field at these time points and thereby obtain the changing magnetic field for a certain interval. It can be said that the magnetic field modulates the phase change of the spins.

Figure 1: Principle of measuring the magnetic activity based on spin phase change.  The magnetic field exerts a magnetic influence on the spin and changes its phase i.e. its position on the circle: from a 20° phase, the spin acquires a 90° phase. The phase change in this case is 70°. It is possible to measure the phase change (or phase shift) and determine the strength of the magnetic field which caused it.

Figure 1: Principle of measuring magnetic activity based on spin phase change. The magnetic field influences how fast the spin precesses. A small additional magnetic field slightly changes the precession frequency, causing the spin to rotate a bit faster or slower. Over time, this difference in rotation rate leads to an accumulated phase shift — for example, from 20° to 90° (a 70° shift). By measuring this accumulated phase shift, which reflects the underlying frequency change, the strength of the magnetic field can be determined. 

In Figure 2, at the bottom, we can appreciate how the phase of the spins changes by following the strength of the electric field. When the electric field increases, the phase increases and vice versa. The changing electric field creates a magnetic field which exerts a force on the spins, changing their phase φ.

The amount of phase change (Δφ) is obtained from magnetic resonance phase images. The magnetic flux density change (ΔΒ) which induced the phase change is calculated by multiplying the latter with a time quantity, the time of echo (TE): 

ΔΒ=(Δφ)/(γTE)

Figure 2: Excerpt from Figure 2 of the publication by Bodurka J., et al. “Current-Induced Magnetic Resonance Phase Imaging.” Journal of Magnetic Resonance, vol. 137, no. 1, 1 Mar. 1999, pp. 265–271, https://doi.org/10.1006/jmre.1998.1680 (https://bit.ly/2JhxtXj). On the top, an electric current waveform (square waveform implemented with a  boxcar function) . On the bottom, the phase measured with MRI.

Theoretically, if we applied this technique to the brain, we could obtain the magnetic field of the brain over a time interval. That would correspond to an magnetoencephalogram. 

In accordance with what is mentioned in the above publication, neuronal activity consists of "the flow of ionic current across the neuron cell membrane, along the interior of the axon, and in the surrounding medium. This ionic current will produce" a magnetic flux density (Bc), that, superimposed with the B0 field, will alter the phase of the magnetic resonance signal (cf. precession) of surrounding water protons.

(Please note that this is applicable to environmental water protons as well.)

It must be noted that the most pronounced phase changes are expected only parallelly/antiparallely to the static magnetic field Bo, which in this case is the Earth's magnetic field. Practically, if we analyze the induced magnetic flux in two components, one parallel and one perpendicular to the static (external) magnetic flux, the perpendicular component would be below the threshold of measurement; conversely, the parallel could be measured by adding it or subtracting it from the Bo, which itself is measurable.

How do spins respond to electromagnetic waves?

It is noted that spins couple to the magnetic field through the Zeeman interaction: 

H= -μ * B (t)

Let us consider a composite wave consisting of low-frequency components either matching the Larmor frequency or being near that frequency and of very igh frequency components

A spin responds to each frequency component of the magnetic field independently — resonantly to the Larmor-frequency matching one, adiabatically to proximal-frequency ones, and negligibly to far‑off ones.

(adiabatically: without proceeding/crossing-over to a different (quantum) state

⭐ A spin responds independently to each frequency component of the magnetic field.

1) If one frequency matches the Larmor frequency → resonance

If one of the components satisfies:

𝜔𝑘 = 𝜔𝐿

then the spin will:

• precess coherently

• undergo Rabi oscillations

• flip or align depending on geometry

• absorb energy from that component

2) If multiple components are near the Larmor frequency → multi‑photon or multi‑tone effects

If you have:

• one component at ωL

• another at ωL+δ

• another at ωL−δ

the spin can experience:

✔️ multi‑photon transitions

✔️ sideband absorption

✔️ dressed‑state formation

✔️ Autler–Townes splitting

✔️ Rabi frequency modulation

This is the physics behind: atomic clocks, double‑resonance spectroscopy, coherent population trapping

The spin “feels” a richer landscape of driving fields.

3) If the frequencies are far from resonance → the spin barely reacts

A spin is extremely selective.

This is why high‑frequency carriers do not affect spins unless they contain a real component at the Larmor frequency.

4) If the field contains a real LF/ULF component → the spin follows it adiabatically

This is the regime you’ve been exploring.

If the field contains:

BLFcos⁡(ωLFt)

with ωLF≪ωL, then:

• the spin slowly follows the field direction

• the motion is adiabatic

• the spin aligns and realigns periodically

• no resonance is needed

5) If the field contains both HF and LF components → the spin responds to both

Suppose:

B(t)=BHFcos⁡(ωHFt)+BLFcos⁡(ωLFt)

Then:

✔️ The HF part drives fast precession (if near resonance)

✔️ The LF part slowly tilts the quantization axis

✔️ The spin’s trajectory becomes a superposition of fast and slow motions

This produces:

• nutation

• amplitude modulation of Rabi oscillations

• frequency pulling

• Bloch–Siegert shifts

This is the physics behind:

• NMR with modulated fields

• double‑modulation spectroscopy

• spin‑locking techniques

6) If the field is strongly multi‑frequency → the spin enters a “dressed” regime

When the driving field is strong and contains many frequencies, the spin no longer behaves like a simple magnetic moment.

It becomes a dressed spin, meaning:

• the spin + field form a combined quantum system

• energy levels split

• new resonances appear

• the effective Larmor frequency shifts

This is the physics behind:

• Floquet engineering

• quantum control

• spin‑based qubits

• coherent manipulation in atomic clocks