LAUSR

Abstract In the reentrant (RE) state at low temperatures, the functional dependence of magnetization on temperature at fixed magnetic fields, M H ( T ) , in the Cr70Fe30 thin films deviates considerably from the well-known Bloch T 3 / 2 power law, predicted by the spin-wave (SW) theory for a conventional three-dimensional (3D) ferromagnet. Strong departures from the SW predictions are shown to be a manifestation of an anomalous softening of magnon modes in the RE regime. The model that invokes the Bose–Einstein condensation (BEC) of magnons provides a satisfactory explanation for this unusual behavior. The magnon BEC transition temperature, T c ( H ) , the volume, V ( H ) , over which the condensate wavefunction retains its phase coherence, the chemical potential, μ ( T , H ) , and the average number of magnon condensates in the ground state, 〈 n 0 ( T , H ) 〉 , are accurately determined from M H ( T ) using a self-consistent approach. Reduction in the film thickness from 978 nm to 21 nm enhances the BEC transition temperature at zero field, T c (H = 0), from 0.1 K to 0.33 K but drastically reduces the phase coherence length of the BE condensate wavefunction and the spin-wave stiffness at T = 0 and H = 0. The variation of T c with magnetic field has the form that is characteristic of the magnon BEC in a 3D spin system. Regardless of the film thickness, the BE condensate fraction at H = 0, 〈 n 0 ( H = 0 ) 〉 , turns out to be zero at T ≃ 2  K ≫ T c ( H = 0 ) , as expected. The ‘zero-field’ quantities M 0 ( H = 0 ) , D 0 ( H = 0 ) , V ( H = 0 ) and T c ( H = 0 ) are found to vary with the film thickness as M 0 ( H = 0 ) ∼ t 3 / 4 , D 0 ( H = 0 ) ∼ t - 3 / 4 , V ( H = 0 ) ∼ t 2 / 5 and T c ( H = 0 ) ∼ t - 1 / 3 . These power laws assert that the film thickness is the fundamental length scale so far as the magnon BEC phenomenon in the Cr70Fe30 thin films is concerned.