Aims. We used solar observations of a plage-enhanced network with the Atacama Large Millimeter/sub-millimeter Array (ALMA) in Band 3 and Band 6, together with synthetic continuum maps from numerical simulations with Bifrost in the same bands, to carry out a detailed study of bright small-scale magnetic features.

Methods. We made use of an algorithm to automatically identify and trace bright features within the field of view (FoV) of the ALMA observations and the simulation. In particular, the algorithm recovers information of the time evolution of the shape, motion of the centre of gravity, temperature, and size for each feature. These quantities are used to determine the oscillatory properties of each feature utilising wavelets analysis.

Results. We found 193 and 293 features in the Bands 3 and 6 observations, respectively. In the degraded simulation, the total number of features were 24 for Band 3 and 204 for Band 6. In the original simulation, the total number of features were 36 for Band 3 and 392 for Band 6. Based on the simulation, we confirm the magnetic nature of the features. We have obtained average oscillation periods of 30–99 s for the temperature, 37–92 s for size, and 37–78 s for horizontal velocity. There are indications for the possible presence of transverse (kink) waves with average amplitude velocities of 2.1–5.0 km s⁻¹. We find a predominant anti-phase behaviour between temperature and size oscillations suggesting that the variations of the bright features are caused by compressible fast-sausage magnetohydrodynamics (MHD) modes. For the first time to our knowledge, we estimated the flux of energy of the fast-sausage waves at the chromospheric heights sampled by ALMA as 453–1838 W m⁻² for Band 3 and 3640–5485 W m⁻² for Band 6.

Conclusions. We have identified MHD waves, both transverse (kink) and compressible sausage modes, in small-scale (magnetic) structures, independently, in both ALMA Band 3 and Band 6 observations, along with their corresponding synthetic images from simulations. The decrease of wave energy-flux with height (from Band 6 to Band 3) could possibly suggest energy dissipation at chromospheric heights, namely, wave heating, with the assumptions that the identified small-scale waves are typical at each band and they propagate upward through the chromosphere.