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Universality in magnetic phase transitions

Selected Article

Nat. Comm 7, 13611 (2016)
Critical exponents and scaling invariance in the absence of a critical point

Proc. R. Soc. A 472, 2195 (2016)
Thirty per cent contrast in secondary-electron imaging by scanning field-emission microscopy
Phys. Rev. B 89, 014429 (2014)
Domain-wall free energy in Heisenberg ferromagnets

Phys. Rev. B 87, 115436 (2013)
Scale invariance of a diodelike tunnel junction
Prof. Dr. Danilo Pescia
In the following, we summarize some of the results obtained in recent years.

1. Theoretical Background

When entering a new domain of Physics, one must develop suitable theoretical tools. In a work by D.Pescia and V. Pokrovsky of the Landau Institute in Russia, (Perpendicular versus In-Plane Magnetisation in a 2D Heisenberg Monolayer at finite temperatures, Phys. Rev. Lett. 65, 2599 (1990) and Phys. Rev. Lett. 70, 1185 (1993)) we suggest that thinning down a system until it looses one spatial dimension results in a very deep modification of its physical behavior, with wide implications for research and technology. The many implications of our original suggestion are still being tested experimentally.

2. Experimental confirmation of universality for a phase transition in two dimensions

C.H. Back, Ch. Würsch, A. Vaterlaus, U. Ramsperger, U. Maier and D. Pescia, Nature 378, 597 (1995)
When a system is poised at a critical point between two macroscopic phases, it exhibits dynamical structures on all available spatial scales, even though the underlying microscopic interactions tend to have a characteristic length scale. According to the universality hypothesis, diverse physical systems that share the same essential symmetry properties will exhibit the same physical behaviour close to their critical points; if this is so, even highly idealized models can be used to describe real systems accurately. Here we report experimental confirmation that the scaling behaviour of thermodynamic variables predicted by the universality hypothesis hold over 36 orders of magnitude. We show that the equation of state of a two-dimensional system (an atomic layer of ferromagnetic iron deposited on a non-magnetic substrate) closely follows the behaviour of the two-dimensional Ising model - the first and most elementary statistical model of a macroscopic system with short-range interactions.
The figure above reports the magnetization curves in constant magnetic field obtained in the vicinity of the Curie temperature as a function of the temperature t for a two-dimensional Fe film (t measures the deviation from the transition temperature t=0). The magnetic film undergoes a phase transition characterized by the complete, collective disordering of the individual Fe spins (M = 0) above t=0. Phase transitions are very common in nature, our own universe being the result of various phase transitions. Phase transitions are predicted to follow the same pattern, whether they involve stars or laboratory samples as in our experiment. Thus, by studying laboratory-scale phase transitions one reproduces accurately the phenomena occurring in completely different systems. The important feature about phase transitions reported in this figure is the shifting up of the magnetization curves when the magnetic field is increased.
One of the common features generally expected at a phase transition is scaling. This very important symmetry predicts that re-plotting the very same experimental data shown in previous figure using suitable variables results in all data collapsing onto one single curve. This remarkable symmetry is illustrated in the figure shown here. The variables, introduced by Griffiths, are y=H/M d versus x=t/M1/ b . d and b are very special numbers called critical exponents. The data with x>0 are represented in a log-log plot. The data points in the interval -1 < x < 10 are represented semi-logaritmically in the inset. The solid line through the experimental data is the theoretical scaling function for the 2d Ising model calculated by C.Domb. This coincidence between our experimental data and the calculations for the most famous mathematical model in Physics over so many decades (notice that the y-scale extends over 36 orders of magnitude) is the most impressive proof of a further symmetry of phase transitions, universality. Accordingly, all phase transitions should follow the same behaviour as few abstract models - a very remarkable property which put the behaviour of complex system into the domain of mathematics.

3. Quantum oscillations in a confined electron gas

Ch. Würsch, C. Stamm, S. Egger, D. Pescia, W. Baltensperger, and J.S. Helman, Nature 389, 937 (1997)
When metals are structures on nano-meter length scales, their electrons are subject to confinements effects: the response of a confined electron gas is governed by Friedel oscillations of the electron density and Rudermann-Kittel-Kasuya-Yosida oscillations of the spin density. Spatial oscillations of electron density have been observed directly at surfaces (in the vicinity of defects and steps) by scanning tunneling spectroscopy. But is has proved more difficult to probe such oscillations in bulk materials and over large distances. Here we report the detection of quantum oscillations in a three-dimensional electron gas confined to a half space by a surface. To facilitate the detection, we have inserted an atomically thin ferromagnetic cobalt film at a variable distance t from the surface of a copper single crystal. The cobalt film induces a total spin polarization P in the conduction electrons of the copper and, by virtue of the confining effects of the copper-vacuum interface, P varies as a function of t . Our measurements of P reveal both quantum oscillations (the wavelengths of which are governed by the extremal diameters of the copper Fermi surface) and a decay with t that are consistent with theoretical expectations. These observations show that a consequence of improving the quality of nano-structured materials is that long-range quantum interactions can emerge more effectively, so that even distant boundaries and defects can become pivotal in determining physical properties. The next figures displays schematically the composition of the multilayered structure used in the present experiment (left) and the essential experimental result (right), showing the observable which contains the long-ranged oscillation predicted by theory and observed for the first time in this experiment.
© 2017 ETH Zürich | Impressum | 2004-08-03 11:54:03