Tag Archives: S. Ishiwata

Japanese researchers note the emergence of the ‘Devil’s staircase’

I wanted to know why it’s called the ‘Devil’s staircase’ and this is what I found. According to Wikipedia there are several of them,

I gather the scientists are referring to the Cantor function (mathematics), Note: Links have been removed,

In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is also referred to as the Cantor ternary function, the Lebesgue function, Lebesgue’s singular function, the Cantor-Vitali function, the Devil’s staircase,[1] the Cantor staircase function,[2] and the Cantor-Lebesgue function.[3]

Here’s a diagram illustrating the Cantor function (from the Wikipedia entry),

CC BY-SA 3.0 File:CantorEscalier.svg Uploaded by Theon Created: January 24, 2009

CC BY-SA 3.0
File:CantorEscalier.svg
Uploaded by Theon
Created: January 24, 2009

As for this latest ‘Devil’s staircase’, a June 17, 2015 news item on Nanowerk announces the research (Note: A link has been removed),

Researchers at the University of Tokyo have revealed a novel magnetic structure named the “Devil’s staircase” in cobalt oxides using soft X-rays (“Observation of a Devil’s Staircase in the Novel Spin-Valve System SrCo6O11“). This is an important result since the researchers succeeded in determining the detailed magnetic structure of a very small single crystal invisible to the human eye.

A June 17, 2015 University of Tokyo press release, which originated the news item on Nanowerk, describes why this research is now possible and the impact it could have,

Recent remarkable progress in resonant soft x-ray diffraction performed in synchrotron facilities has made it possible to determine spin ordering (magnetic structure) in small-volume samples including thin films and nanostructures, and thus is expected to lead not only to advances in materials science but also application to spintronics, a technology which is expected to form the basis of future electronic devices. Cobalt oxide is known as one material that is suitable for spintronics applications, but its magnetic structure was not fully understood.

The research group of Associate Professor Hiroki Wada at the University of Tokyo Institute for Solid State Physics, together with the researchers at Kyoto University and in Germany, performed a resonant soft X-ray diffraction study of cobalt (Co) oxides in the synchrotron facility BESSY II in Germany. They observed all the spin orderings which are theoretically possible and determined how these orderings change with the application of magnetic fields. The plateau-like behavior of magnetic structure as a function of magnetic field is called the “Devil’s staircase,” and is the first such discovery in spin systems in 3D transition metal oxides including cobalt, iron, manganese.

By further resonant soft X-ray diffraction studies, one can expect to find similar “Devil’s staircase” behavior in other materials. By increasing the spatial resolution of microscopic observation of the “Devil’s staircase” may lead to the development of novel types of spintronics materials.

Here’s an example of the ‘cobalt’ Devil’s staircase,

The magnetic structure that gives rise to the Devil's Staircase Magnetization (vertical axis) of cobalt oxide shows plateau like behaviors as a function of the externally-applied magnetic field (horizontal axis). The researchers succeeded in determining the magnetic structures which create such plateaus. Red and blue arrows indicate spin direction. © 2015 Hiroki Wadati.

The magnetic structure that gives rise to the Devil’s Staircase
Magnetization (vertical axis) of cobalt oxide shows plateau like behaviors as a function of the externally-applied magnetic field (horizontal axis). The researchers succeeded in determining the magnetic structures which create such plateaus. Red and blue arrows indicate spin direction.
© 2015 Hiroki Wadati.

Here’s a link to and a citation for the paper,

Observation of a Devil’s Staircase in the Novel Spin-Valve System SrCo6O11 by T. Matsuda, S. Partzsch, T. Tsuyama, E. Schierle, E. Weschke, J. Geck, T. Saito, S. Ishiwata, Y. Tokura, and H. Wadati. Phys. Rev. Lett. 114, 236403 – Published 11 June 2015 (paper: Vol. 114, Iss. 23 — 12 June 2015)  DOI: 10.1103/PhysRevLett.114.236403

This paper is behind a paywall.