Critical exponents and scaling invariance in the absence of a critical point.

The paramagnetic-to-ferromagnetic phase transition is classified as a critical phenomenon due to the power-law behaviour shown by thermodynamic observables when the Curie point is approached. Here we report the observation of such a behaviour over extraordinarily many decades of suitable scaling variables in ultrathin Fe films, for certain ranges of temperature T and applied field B. This despite the fact that the underlying critical point is practically unreachable because protected by a phase with a modulated domain structure, induced by the dipole-dipole interaction. The modulated structure has a well-defined spatial period and is realized in a portion of the (T, B) plane that extends above the putative critical temperature, where thermodynamic quantities do not display any singularity. Our results imply that scaling behaviour of macroscopic observables is compatible with an avoided critical point.

Experimental phase diagram of perpendicularly magnetized ultrathin ferromagnetic films.

We image the domain patterns in perpendicularly magnetized ultrathin Fe films on Cu(100) as a function of the temperature T and the applied magnetic field H. Between the low-field stripe phase and the high-field uniform phase we find a bubble phase, consisting of reversed circular domains in a homogeneous background. The curvature of the transition lines in the H-T parameter space is in contrast to the general expectations. The pattern transformations show yet undetected scaling properties.