ac (“zero-field”) susceptibility of the amorphous ferromagnetic alloys $({\mathrm{Fe}}_p{\mathrm{Ni}}_{1-p}{)}_{80}{\mathrm{B}}_{16}{\mathrm{Si}}_4$ $(0.0540\mathrm{}<~p<~0.1375)$ and $({\mathrm{Co}}_{p^{\prime }}{\mathrm{Ni}}_{1-p^{\prime }}{)}_{80}{\mathrm{B}}_{16}{\mathrm{Si}}_4$ $(0.1125\mathrm{}<~p^{\prime }<~0.2375)$ with Fe or Co concentration above the critical concentration $p_c$ or $p_c^{\prime }$ for the onset of long-range ferromagnetic order has been measured to very high precision in the absence and presence of dc (static) magnetic field over a wide temperature range embracing the critical region near the ferromagnetic-paramagnetic phase transition. Elaborate data analyses permit the accurate determination of the asymptotic critical exponents ${\beta }_D,$ ${\gamma }_D,$ and ${\delta }_D$ for spontaneous magnetization, susceptibility and the critical isotherm as well as the leading “correction-to-scaling” exponent for susceptibility (these exponents characterize the isotropic dipolar fixed point) and hence assert that the asymptotic critical behavior of amorphous ferromagnets with $p_c\lesssim p<\mathrm{}0.1\mathrm{}$ or $p_c^{\prime }\lesssim p^{\prime }<0.2\mathrm{}$ (that exhibit reentrant behavior at low temperatures) is that of a $d=3\mathrm{}$ isotropic dipolar ferromagnet. The presently determined values for the exponents ${\beta }_D,$ ${\gamma }_D,$ and ${\delta }_D$ do satisfy the Widom scaling relation $\beta +\gamma =\beta \delta$ accurately. In addition, the temperature dependence of the effective critical exponent for susceptibility observed in the amorphous ferromagnetic alloys with $p<\mathrm{}0.1\mathrm{}$ or $p^{\prime }<0.2\mathrm{}$ for temperatures above the Curie point displays features characteristic of the isotropic dipolar-to-isotropic Heisenberg crossover. A quantitative comparison between theory and experiment exposes certain limitations of the existing theories. By contrast, such a crossover is not observed even at reduced temperatures as close to Curie point $T_C$ as $\epsilon =(T-T_C{)/T}_C\simeq {10}^{-5}$ in the alloys with $p>\mathrm{}0.1\mathrm{}$ or $p^{\prime }>0.2,$ which behave as normal ferromagnets down to 3.8 K. A sharp contrast in the critical behavior of ferromagnets that either do or do not exhibit reentrant behavior at low temperatures is shown to reflect the decisive role played by the isotropic dipolar long-range interactions in establishing long-range ferromagnetic order in dilute magnetic systems exhibiting reentrant behavior.

• Received 6 March 2000

DOI:https://doi.org/10.1103/PhysRevB.62.11649