6 research outputs found
Critical exponents and scaling invariance in the absence of a critical point
The paramagnetic-to-ferromagnetic phase transition is believed to proceed
through a critical point, at which power laws and scaling invariance,
associated with the existence of one diverging characteristic length scale --
the so called correlation length -- appear. We indeed observe power laws and
scaling behavior over extraordinarily many decades of the suitable scaling
variables at the paramagnetic-to-ferromagnetic phase transition in ultrathin Fe
films. However, we find that, when the putative critical point is approached,
the singular behavior of thermodynamic quantities transforms into an analytic
one: the critical point does not exist, it is replaced by a more complex phase
involving domains of opposite magnetization, below as well as the
putative critical temperature. All essential experimental results are
reproduced by Monte-Carlo simulations in which, alongside the familiar exchange
coupling, the competing dipole-dipole interaction is taken into account. Our
results imply that a scaling behavior of macroscopic thermodynamic quantities
is not necessarily a signature for an underlying second-order phase transition
and that the paramagnetic-to-ferromagnetic phase transition proceeds, very
likely, in the presence of at least two long spatial scales: the correlation
length and the size of magnetic domains.Comment: 10 pages, added figure 1, rearranged section
Froth-like minimizers of a non local free energy functional with competing interactions
We investigate the ground and low energy states of a one dimensional non
local free energy functional describing at a mean field level a spin system
with both ferromagnetic and antiferromagnetic interactions. In particular, the
antiferromagnetic interaction is assumed to have a range much larger than the
ferromagnetic one. The competition between these two effects is expected to
lead to the spontaneous emergence of a regular alternation of long intervals on
which the spin profile is magnetized either up or down, with an oscillation
scale intermediate between the range of the ferromagnetic and that of the
antiferromagnetic interaction. In this sense, the optimal or quasi-optimal
profiles are "froth-like": if seen on the scale of the antiferromagnetic
potential they look neutral, but if seen at the microscope they actually
consist of big bubbles of two different phases alternating among each other. In
this paper we prove the validity of this picture, we compute the oscillation
scale of the quasi-optimal profiles and we quantify their distance in norm from
a reference periodic profile. The proof consists of two main steps: we first
coarse grain the system on a scale intermediate between the range of the
ferromagnetic potential and the expected optimal oscillation scale; in this way
we reduce the original functional to an effective "sharp interface" one. Next,
we study the latter by reflection positivity methods, which require as a key
ingredient the exact locality of the short range term. Our proof has the
conceptual interest of combining coarse graining with reflection positivity
methods, an idea that is presumably useful in much more general contexts than
the one studied here.Comment: 38 pages, 2 figure
A Scaling Hypothesis for Modulated Systems
We propose a scaling hypothesis for pattern-forming systems in which
modulation of the order parameter results from the competition between a
short-ranged interaction and a long-ranged interaction decaying with some power
of the inverse distance. With L being a spatial length characterizing
the modulated phase, all thermodynamic quantities are predicted to scale like
some power of L. The scaling dimensions with respect to L only depend on the
dimensionality of the system d and the exponent \alpha. Scaling predictions are
in agreement with experiments on ultra-thin ferromagnetic films and
computational results. Finally, our scaling hypothesis implies that, for some
range of values \alpha>d, Inverse-Symmetry-Breaking transitions may appear
systematically in the considered class of frustrated systems.Comment: 13 pages, 6 figures, expanded versio
Straight motion of half-integer topological defects in thin Fe-N magnetic films with stripe domains
Dipolar-energy-activated magnetic domain pattern transformation driven by thermal fluctuations
Two-dimensional ferromagnetic layers can serve as a playground for the study of basic physical properties of various pattern forming systems by virtue of their tuneable magnetic properties. Here we use threshold photoemission magnetic circular dichroism in combination with photoemission electron microscopy to investigate ultra-thin ferromagnetic Fe/Ni/Cu(001) films in the stripe domain phase near the spin reorientation transition as a function of film thickness, temperature and effective anisotropy. Here we report a metastable domain state with domain width larger than the thermodynamically stable one as a result of a rapid reduction of the anisotropy. The transformation into the equilibrium state takes place via the propagation of a transition front, which originates from defined steps in the film thickness