Miniature antennas/coils like the ones used for MRI, implantable, detect electromagnetic signals
"MRI works by detecting radio waves emitted by the nuclei of hydrogen atoms in water".
"The sensor is initially tuned to the same frequency as the radio waves emitted by the hydrogen atoms. When the sensor picks up an electromagnetic signal from the tissue, its tuning changes and the sensor no longer matches the frequency of the hydrogen atoms. When this happens, a weaker image arises when the sensor is scanned by an external MRI machine.
The researchers demonstrated that the sensors can pick up electrical signals similar to those produced by action potentials (the electrical impulses fired by single neurons), or local field potentials (the sum of electrical currents produced by a group of neurons)".
Holder, DS; (1985) http://discovery.ucl.ac.uk/1436280/
Cited at above U.S. Patent 4719425 A (https://www.google.com/patents/US4719425) which refers to the detection and measurement of the electrical activity of the brain with Electron Spin Resonance (ESR)
D. S. Holder
"It is proposed that, for the rapid changes related to the action potential, electron spin resonance using a potential-sensitive spin, label, impedance imaging and NMR are suitable in principle but that only ESR and impedance methods may have sufficient sensitivity and these merit further assessment."
Remote detection of human electroencephalograms using ultrahigh input impedance electric potential sensors
"(...) for conventional clinical analysis, the EEG is recorded using electrodes that are in real charge current contact with the scalp tissue. In practice, this is provided by an Ag/AgCl electrode used in conjunction with an electrolytic paste. These act together to form an electrical transducer to convert the ionic current flow in the skin into an electron flow which can then be detected by an electronic amplifier ."
"This sensor operates using electric displacement, rather than real charge, current. It therefore does not require real electrical contact to the signal source (e.g., the human body) in order to function. This overcomes the disadvantages of conventional Ag/AgCl electrodes while still maintaining sufficient sensitivity ~70 nV/AHz at 1 Hz noise floor)  to detect body electrical signals off body."
"Furthermore, using similar techniques, we have been able to record the human heartbeat at distance up to 1 m off body with no electrical connection between the sensor and the body . In this letter, we demonstrate that we now have the sensitivity to detect EEGs through the scalp hair with no electrical contact to the scalp. We also show that it is now possible to detect brain electrical activity with an air gap between the scalp hair and the sensor."
"Given that there is still much scope for improvements in sensitivity, input impedance, and size of electric potential sensors, we anticipate rapid development and exploitation of these devices in the field of brain research and diagnostics in the near future."
Many thanks to Skizit Gesture's YouTube channel for mentioning the paper in one of her videos and to Neal Chevrier for sharing the video.
Remote control brain sensor - BBC News (2002) featuring above study
Excerpt: "From a distance" | "Instead of measuring electric current flow through a fixed-on electrode, the new method takes advantage of the latest developments in sensor technology to measure electric fields from the brain without actually having to make direct contact with the head."
Current-induced magnetic resonance phase imaging https://www.ncbi.nlm.nih.gov/pubmed/10053158
Introduction and experimentation
Magnetic resonance current-density imaging has been used to create images of electric current density in homogenous and heterogenous media (2,3).
Human brain mapping technology has made significant progress based on integrated anatomical and functional measurements. It would be ideal to directly detect neuronal electric firing. Ionic currents flow across the neuron cell membrane, the axon and the surrounding medium. These ionic currents produce a magnetic flux density Bc that if superimposed with the Bo field*, will alter the phase of the surrounding water protons.
*external magnetic flux (presumably from the ambient magnetic field cf. Earth magnetic field and other local events)
It is hypothesized that electric current-induced phase alterations could be imaged by fast magnetic resonance imaging (MRI) technology.
A thin copper wire (60 mm diameter) was formed into a 3-inch long and 2-inch wide rectangle (figure). A pulse electric current was applied.
A pulse generator was used to provide a 0-, 10-, 20-, 30-,50-, 70-, or 100-mA current with 2 s on and 2 s off cycle through the wire.
The induced magnetic field Bc, and specifically its Z component (parallel to Bo) was calculated.
The induced positive and negative phase changes occurred mainly in the left or right direction relative to the wire position corresponding to parallel and antiparallel components of the induced field (Bc) (figure).
Attached figured 2 shows the current-induced (70 mA) phase images (A) and time series of induced phase changes (B).
The induced change of magnetic field was calculated to be 1.7 +- 0.3 nT.
The magnetic field due to an action potential propagating down a crayfish axon was calculated to have a maximal strength of 1 nT for the distance of 0.12 mm from the axon (15, 16). That corresponds to ionic current flow of the order of microamperes.
The ionic current in a single neuron is of the order of picoamperes and results in a magnetic field strength of the order of 10^-15 T (16).
The field strength from magnetocardiogram is 10^-10 T and from the brain 10^-12 T for spontaneous (a wave) activity, and 10^-13 T for evoked response (17, 18). These magnetic field changes are far beyond MRI detection capabilities (note: paper published in 1999).
The magnetic field strength produced by a single neuron is too small to be measured by MRI; however, if, for example, 10^-6 parallel-oriented neurons act together then the resulting magnetic field could be detectable.
The authors believe that future work will result in the direct in vivo detection of electric neuronal activity.
"Magnetic resonance current density imaging (MRCDI) and MR electrical impedance tomography (MREIT) are two emerging modalities, which combine weak time-varying currents injected via surface electrodes with magnetic resonance imaging (MRI) to acquire information about the currentflow and ohmic conductivity distribution at high spatial resolution".
"The injected current flow creates a magnetic field in the head, and the component of the induced magnetic field ΔBz,c parallel to the main scanner field causes small shifts in the precession frequency of the magnetization. The measured MRI signal is modulated by these shifts, allowing to determine ΔBz,c for the reconstruction of the current flow and ohmic conductivity".
"Nanoscale Imaging of Current Density with a Single-Spin Magnetometer"
Do an Electron Paramagnetic Resonance (EPR) scan using microwaves from 2700 to 2800 MHz.
Based on fluorescence intensity determine the frequency of resonance, the ω for resonance (cf. attached image).
If you know the ω and the gyromagnetic ratio of the electron, you determine the B, the intensity of the magnetic field at a certain point.
You then create a 2D Fourier space and you determine the current density of a structure.
Electronic magnetic resonance techniques (EMRT) are used in material research and device characterization e.g. diodes, solar cells. The principle of these techniques is the detection of
changes in a specific observable e.g. conductivity when the condition for electron spin resonance is reached. The most common EMRT are:
a. Electron spin resonance (ESR)
b. Electrically detected magnetic resonance (EDMR)
c. Optically detected magnetic resonance (OMDR).
Consider a sample or device to be measured i.e. a device on DC current, represented by an RC circuit.
In an EDMR experiment, a magnetic field is modulated in order to create a small alternative current (AC) in the measuring circuit at the resonancecondtion. Note that this is much smaller than the sample DC current.
The magnetic field is swept linearly around a central magnetic field H0 close to the resonant condition. A modulation field with angular frequency ω=2πf, and amplitude Hm is used for phase sensitive detection (PSD).