Matrix Isolation Spectroscopy of atoms or molecules has recently been proposed also for investigating new physics beyond the Standard Model with atoms and molecules, such as search for time-reversal or CP symmetry violations, electric dipole moment of standard-model particles, as well as DM [4][5][6][7].Cosmological axions are supposed to be one of the possible constituents of the DM of the Universe, whose composition is still unknown [8]. Axions were initially introduced by Peccei and Quinn in order to solve the strong CP problem in quantum chromodynamics [9][10][11][12], and are assumed to interact very weakly with ordinary matter. Successively, it was proposed that they could be one of the possible constituents of DM [13], and Sikivie proposed that they could induce magnetic-type transitions between atomic Zeeman sub-levels, yielding possibility of their indirect detection [14]. It is thus of fundamental importance to envisage possible mechanisms, and relative experiments, to detect these particles. Several possibilities have been recently proposed; for a review, see for example [13,[15][16][17][18][19].Recently, possible detection schemes for cosmological axions in the meV energy range, based on electron transitions between Zeeman-shifted levels of dilute alkali or oxygen atoms [20], or their ionization [21], embedded in