Isotropic-Heisenberg to isotropic-dipolar crossover and finite-size scaling in Cr75−Fe25+ (x= 0, 5) thin films

Abstract ‘Zero-field’ linear ac magnetic susceptibility, χ 1 (T), of the Cr75−xFe25+x (x = 0, 5) thin films with thickness, t, ranging from 980 to 10 nm has been measured at temperatures close to T c , the temperature at which the ferromagnetic-paramagnetic phase transition occurs. An elaborate analysis of χ 1 ( T ⩾ T c ) for the films with t ⩾ 40 nm yields the temperature dependence of the effective critical exponent for susceptibility, γ eff ( T ) , that is characteristic of the three-dimensional (3D) isotropic Heisenberg-to-3D isotropic dipolar crossover. In the asymptotic critical region (ACR), these thin-film samples behave as a 3D isotropic dipolar (ID) ferromagnet. As the film thickness reduces from t ≃ 980 nm to 40 nm, ACR narrows down while the temperature, T dip , at which a dip in γ eff ( T ) occurs and the temperature, T IH ∗ , that marks the onset of the 3D isotropic Heisenberg (IH) behavior, shift to lower temperatures. For a given t, the width of ACR as well as the characteristic temperatures T dip and T IH ∗ increase with decreasing (increasing) Fe (Cr) concentration. Consistent with these observations, the ratios involving nonlinear ac magnetic susceptibilities obey the generalized magnetic equation of state with 3D ID critical exponents and the value of T c same as that determined from χ 1 (T). A quantitative comparison between theory and experiment highlights certain limitations of the existing theories. The films with t ≲ 20 nm do not exhibit 3D IH-to-3D ID crossover. Instead, the critical behavior of Cr70Fe30 thin films with t = 21 nm and t = 11 nm is that of a 3D IH and 3D Ising ferromagnet, respectively. By contrast, a 3D Ising (spin glass) critical behavior is observed in the Cr75Fe25 thin film with t = 19 nm (t = 12 nm). Curie temperature, T c , decreases with film thickness in accordance with the finite-size scaling.