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I came across 'ODCR' in a preprint recently, and was intrigued! It's pretty old (<1980), as most things are in spin physics, but I don't think it's been seen in diamond. I think it might explain some of the CW-ODMR results we see with spin defects in hBN, so I was motivated to do some reading.
Introduction
Cyclotron resonance is a phenomenon where charged particles moving in a magnetic field absorb energy from an alternating electric field. This occurs at a specific frequency, known as the cyclotron frequency, which depends on the charge and mass of the particles as well as the strength of the magnetic field.
ω = q B / m*
Note that the spin-half resonance is at
ω = g q B / 2 mₑ
which matches for m* = mₑ.
In semiconductor physics
In semiconductor physics, cyclotron resonance is used to study the effective mass of charge carriers—electrons and holes—by observing how they move in a magnetic field. When a semiconductor with a magnetic field applied perpendicularly is subjected to an alternating electric field at the cyclotron frequency, charge carriers absorb energy efficiently. This allows researchers to measure this frequency and determine the effective mass (m*) of the carriers by using the above formula.
Optical detection of cyclotron resonance
First reported 1980, PRL.
ODCR via bandgap luminescence. The method is based on the measurement of resonant heating of the carriers by monitoring shapes and intensities of low-temperature photoluminescence lines.
Optical excitation of carriers by light exceeding the gap energy allows to detect CR on both types of carriers by the following mechanism: The absorption of microwave power occurring at the CR of either type of carrier increases the energy of both the electron and hole gases. The resulting carrier heating can be observed directly by measuring the effective temperature via the shape of optical emission lines or indirectly by monitoring luminescence line intensities.
Principle
Circular motion:
F = q(v x B)
Equate Lorentz force to centripetal force:
mv² / r = q v B
⇒
r = mv / qB
⇒
T = 2 π r / v
⇒
ω = q B / m
To measure, often consider the limit
ω τ >> 1
where τ is the mean scattering time. I.e. carrier must complete a full orbit to be observed. Bfield increases ω, low temperature improves τ.
ODCR:
- Hot carrier population changes recombination rates, changes pop. distribution.
- AND/OR cooling of hot carriers via interaction between the hot carriers and the defect excitation, e.g. bound exciton (BE).
- AND/OR cooling of hot carriers via interaction between the hot carriers and the lattice phonons (bolometric effect).
Note you usually monitor the recombination band itself.
- Can watch shape of recom. band (ODCR vs emission wavelength), or just intensity.
- Sweeping magnetic is equiv. to sweeping RF freq. in ODMR.
Example
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Magnetic field
Reproduced from Fig 2 of Romestain & Weisbuch2. Note the different locations of the electron and light hole on the D+-X recombination line in CdTe.
Why does CR increase free carrier lifetime?
Driving cyclotron resonance can increase carrier lifetime through several mechanisms:
-
Orbital Separation:
- CR puts carriers into higher Landau levels
- Spatially separates electrons and holes, reduces Ψ overlap
- Decreases recombination probability
-
Momentum Space Effects:
- CR gives carriers angular momentum, changes k-space distr.
- Can reduce the phase space available for recombination
- Particularly important for direct recombination processes
-
Energy! Hot carriers need to lose their energy somehow.
ODCR lineshape
Similar to ODMR with linewidth set by scattering time. Scattering time/carrier lifetime depends on temperature. Can measure different carrier masses separately (due to different resonance frequencies).
Defect measurement
CR increases free electron concentration => increase intensity of some emission (free-to-bound transition) & decrease others (donor-acceptor pair, bound exciton). Have to know your crystal/defect structure well though.
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Emission Wavelength
Reproduced from Fig 1 of Godlewski, Chen, & Monemar4. Sample is GaAs. The top curve is the PL spectrum, the lower curve the ODCR contrast. Note the annotated bound-exciton (BE), free-bound (FB) and donor-acceptor pair (DAP) transitions.
Delayed-ODMR & ODCR of nonradiative defects
ODCR reduces ODMR contrast, as ODCR is a broad resonance at e.g. room temperature that affects the ODMR 'baseline'. Noting that ODCR free carriers usually have a much shorter lifetime than the defect-related excitation (by orders of magnitude), simply introducing a delay after optical pumping (in a pulsed ODMR scheme) can mitigate the contrast drop.
On the other hand, the presence of free carriers mediates between nonradiative defects and radiative ones, due to competition for capture and recombination of free carriers. This makes optical detection of nonradiative defects possible via ODCR. A speed up in recombination of carriers via one channel can be detected as a reduced number of carriers recombining through the other channel, since the number of free carriers available is reduced.
Outstanding Questions
- How cold would we need to go to see ODCR in hBN?
- hBN has large effective masses (need a strong field to get to measurable fields) and strong electron-phonon coupling (short scattering times), does this preclude practical ODCR?
- The large bandgap in hBN implies recombination is likely defect dominated (with corresponding short lifetimes), but perhaps this makes investigation more intriguing.
See also
-
Optical spin readout of a silicon color center in the telecom L-band, Wen et al. arXiv:2502.07632 (2025) ↩
-
Optical Detection of Cyclotron Resonance in Semiconductors, Romestain & Weisbuch PRL 45 2067 (1980) ↩
-
Role of free carriers in the application of optically detected magnetic resonance for studies of defects in silicon, Chen & Monemar, Applied Physics A 53 130 (1991) ↩
-
Optically Detected Cyclotron Resonance for Defect Characterization, Godlewski, Chen, & Monemar Materials Science Forum 143 1353 (1993) ↩