A signal that outpaced absorption
Co-doped cerium oxide thin films showed a much stronger magneto-optical signal in one of the study's comparisons without a matching rise in optical absorption, according to an arXiv preprint. Near 3.5 electronvolts (eV), the Co10 film had around five times the Faraday rotation of Co5, while the absorption increase between the two films was only a few percent. The Faraday-rotation-to-optical-loss figure of merit, a measure of rotation relative to optical loss, was more than four times higher for Co10.
The work examined three reported composition conditions: Co5, with x = 0.05, and Co10, with x = 0.10, both on MgO, plus Co20, with x = 0.20, on oxidized silicon. X-ray diffraction described the films as polycrystalline. The researchers extracted both diagonal and off-diagonal elements of the permittivity tensor, a way of describing how the material responds to light and magnetism, and provided full spectra for prospective modeling.
The films also differed in thickness: 753 nanometres for Co5, 262 nanometres for Co10 and 391 nanometres for Co20. Wavelength-dispersive spectroscopy measured actual cobalt concentrations of 2% in Co5 and 6% in Co10. An actual concentration for Co20 was not reported.
Optical changes without a shifting gap
To map the optical response, ellipsometry was performed at incidence angles of 65, 70 and 75 degrees over 1 to 5 eV, with reflectivity and transmission measured as well. The optical fit assumed an MgO substrate, a homogeneous doped layer and a rough surface layer. Least-squares fitting adjusted the optical parameters, thickness and roughness.
The fitted diagonal response showed two features around 3.9 and 8.1 eV. The authors assumed these reflected O 2p-to-Ce 4f and O 2p-to-Ce 5d charge-transfer transitions. Estimated optical bandgaps were 3.25 eV for Co5 and 3.21 eV for Co10. Despite earlier reported doping-related narrowing as large as 300 millielectronvolts, these films showed no significant bandgap narrowing as cobalt concentration increased.
The optical response did change in another respect. The imaginary diagonal permittivity, the absorptive part of the response, had a noticeably larger amplitude than in undoped films and generally increased with cobalt content through almost the investigated range up to around 4 eV. But the undoped films were used as contextual comparisons rather than as a matched control, and the analysis did not directly test whether cobalt states or oxygen vacancies accounted for the increase.
Magnetic signals varied with composition
At room temperature and 3.3 eV, magnetic circular dichroism (MCD) loops, a light-based magnetic measurement, showed ferromagnetic behavior. In the reported comparison, saturation magnetization, coercivity and remanence all increased with cobalt content. Co5 had almost zero coercivity, while Co10 had an estimated coercivity of around 0.06 tesla. With the field applied in plane, the magnetization was still not saturated at 1 tesla.
Faraday rotation, the change in light's polarization as it passes through a magnetized film, showed two main room-temperature features near 1.1 and 3.5 eV. Their amplitudes depended on cobalt content. Faraday rotation and MCD were measured across 0.6 to 3.8 eV. A low-temperature check used approximately 80 K and 0.6 T, while room-temperature polar Kerr measurements used 1 T.
The mechanism is still a model
To represent the off-diagonal response, the part of the tensor used for the magneto-optical signal, the authors fitted two paramagnetic oscillators. One was assigned to a Co2+ crystal-field transition and the other to a Co 3d-to-Ce 4f charge-transfer transition. The fitted resonant energies for the crystal-field component were 0.90 eV for Co5 and 0.87 eV for Co10; for the charge-transfer component they were 3.77 and 3.63 eV. The reported amplitudes were 0.0026 and 0.0109 for the charge-transfer component, compared with -0.0009 and -0.0036 for the crystal-field component.
The model also reported broadenings of 0.5031 and 0.6133 eV for the crystal-field component in Co5 and Co10, and 0.4182 and 0.5177 eV for the charge-transfer component. These transition labels are model interpretations rather than direct spectroscopic identifications, so the fit supports a description of the response without settling the microscopic assignments.
Under the measured conditions, the two-transition model reproduced the reported Faraday and Kerr behavior. The Faraday spectrum at 80 K was essentially identical to the room-temperature spectrum, and experimental polar Kerr rotation agreed excellently with the theoretical model. That agreement supports the tensor model, but it does not resolve whether cobalt-related transitions are the dominant microscopic source of room-temperature ferromagnetism.
The authors concluded that ferromagnetic properties were enhanced as cobalt concentration rose up to x = 0.20, while optical data showed little evidence for oxygen vacancies. They proposed that cobalt-related crystal-field and charge-transfer transitions might be the major influence on magneto-optical behavior. The reported result is therefore an association between cobalt content and measured signals, not a demonstrated causal mechanism.
The report did not include formal uncertainty estimates, replicate counts or inferential statistical testing for these comparisons and fits, so the size of the differences should be read as results from the reported films. Device operation was not tested, and the evidence does not generalize beyond the listed compositions, substrates and measurement settings. The document is an arXiv version 1 preprint dated 26 August 2026.
Paper data and sources
Original title: Optical and magneto-optical interactions in Co-doped CeO$_2$ thin films prepared by pulsed laser deposition
Authors: Martin Zahradník, Miroslav Kučera, Roman Antoš et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text