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The Limits of Memory

August 27, 2018

One important concept in thermodynamics is the thermal reservoir, a thermodynamic system having an infinite capacity for heat. When such a reservoir is in thermal contact with another system, its temperature remains constant since its infinite heat capacity allows it to source or sink as much heat as is required for this thermal equilibrium.

Up until the modern age, human population was small, so man was free to take as much from the Earth as he needed, and to dump as much waste as needed, without damaging his local environment. There was always another ore deposit to mine, another fertile field to plow, and a place deep in the woods away from your house where you could dump your trash. The Earth was acting as a resource reservoir, remaining stable against these minor insults.

Today, such is not the case, since the world population is nearly eight billion. This problem was nicely explicated in 1972 in a Club of Rome report entitled, The Limits of Growth. This idea that population growth would be limited can be traced back to Thomas Malthus (1766-1834). In his 1798 publication, An Essay on the Principle of Population, Malthus realized that population increases geometrically, doubling in a certain time period, but food production grows arithmetically; that is, at a linear rate.

Figure caption

Thomas Malthus (1766-1834).

Malthus' publication of An Essay on the Principle of Population was done anonymously.

According to his simple model of population and food production, the world would inevitably reach what is now called a Malthusian catastrophe in which population is abruptly decreased by famine to a new equilibrium state.

I was quite impressed by Malthus when I read about him while I was in high school, since this was my first introduction to mathematical modeling.

(Detail of an 1833 portrait by John Linnell (1792–1882) in the collection of the Wellcome Trust, via Wikimedia Commons, modified for artistic effect.)

In their quest to provide us with better computing resources, computer scientists, electrical engineers, and physicists have wrestled with other limits of nature. They're now able to pack tens of billions of transistors onto a computer chip the size of a fingernail. Although Moore's law predicts a doubling of the number of transistors on such a chip size every two years,[1] we're close to the point at which such improvement will end. The problem, of course, is that we're getting too close to atomic dimension.[2-3] Echoing a Mathusian sentiment, Gordon Moore, who created his eponymous law in 1965, has said,
"It can't continue forever. The nature of exponentials is that you push them out and eventually disaster happens."[3]
While transistors are used for both computing and memory functions, there are other ways to create a data memory. I discussed optical and magnetic memory technology in two previous articles (Optical Memory, January 6, 2012 and Magnetic Memory, January 19, 2017). Now, scientists are investigating whether single atoms, or just a few atoms, can be used as data cells in optical and magnetic memories. Such a stretch in technology is important because of the present exponential growth of collected data.

A team of Australian scientists from the University of South Australia (Mawson Lakes, Australia), the University of Adelaide (Adelaide, Australia), and the University of New South Wales (Canberra, Australia) have investigated optical data storage in rare-earth doped inorganic insulators, and they've had good results using nanocrystalline BaFCl, an alkaline earth halide, doped with the rare earth element, samarium, as a multilevel re-writable data storage material.[4-5] Says Nick Riesen, a Research Fellow at the University of South Australia and the leader of this research project,
"With the use of data in society increasing dramatically due to the likes of social media, cloud computing and increased smart phone adoption, existing data storage technologies such as hard drive disks and solid-state storage are fast approaching their limits... We have entered an age where new technologies are required to meet the demands of 100s of terabyte (1000 gigabytes) or even petabyte (one million gigabytes) storage. One of the most promising techniques of achieving this is optical data storage."[5]

This optical memory functions by use of lasers to change the electronic state of the samarium atoms, and this changes their fluorescence.[5] Sm3+ is converted to Sm2+ upon exposure to ultraviolet light. The photoluminescence of the Sm2+ contains the data, and its intensity depends on the intensity of the ultraviolet light during the writing step. The intensity can code multiple bits of data, so each nanocrystal is a multilevel data storage cell.[4]

Since the optical reading and writing is done using confocal optics, the optical memory isn't limited to a two-dimensional array. It can be designed for three-dimensions, giving it a potential density of a petabyte/cm3.[4-5] It's estimated that a human brain can store about 2.5 petabytes.[5] Says Heike Ebendorff-Heidepriem, a professor at the University of Adelaide and a member of the research team,
"We think it's possible to extend this data storage platform to 3D technologies in which the nanocrystals would be embedded into a glass or polymer... This project shows the far-reaching applications that can be achieved through transdisciplinary research into new materials."[5]

Xuanzhao Pan and Nick Riesen

Xuanzhao Pan (left), and Nick Riesen (right) of the University of South Australia, demonstrate their optical data storage system.

University of South Australia photograph by Elizaveta Klantsataya

While this optical approach requires a bunch of atoms in its nanoscale memory cell, physicists at the École Polytechnique Fédérale de Lausanne (Lausanne, Switzerland), the Institute for Basic Science (Seoul, Republic of Korea), and Ewha Womans University (Seoul, Republic of Korea) have harnessed the magnetism of single atoms of another rare earth element, holmium, to make a magnetic memory.[6-7]

Using spin-polarized scanning tunneling microscopy, the research team found that individual holmium atoms on a magnesium oxide substrate will exhibit a stable magnetic bistability for many minutes.[6-7] The magnetized state of the holmium atoms were stable against an unusually large external magnetic field exceeding 8 tesla when the atoms were cooled to a temperature of 35 K.[6] When such atoms are densely packed on a surface, enormous data capacities are possible.[7]

STM imaging of holmium single-atom magnets.

Left, the scanning tunneling microscope used to image the holmium single-atom magnets. Right, magnetic atoms on a magnesium oxide substrate. (École Polytechnique Fédérale de Lausanne image by F. Natterer.)

Fabian Natterer, the paper's first author and a scientist at the Laboratory of Nanostructures at Surfaces of the École Polytechnique Fédérale de Lausanne, summarized this research as follows:
"Research in the miniaturization of magnetic bits has focused heavily on magnetic bistability... We have demonstrated that the smallest bits can indeed be extremely stable, but next we need to learn how to write information to those bits more effectively to overcome the magnetic trilemma of magnetic recording: stability, writability, and signal-to-noise ratio."[7]
This research was funded by the Swiss National Science Foundation.[7]


  1. G. E. Moore, "Cramming More Components Onto Integrated Circuits," Electronics, vol. 38, no. 8 (April 19, 1965), pp. 114-117. PDF reprint at University of Texas website.
  2. Suhas Kumar, "Fundamental Limits to Moore's Law," arXiv, November 18, 2015.
  3. Manek Dubash, "Moore's Law is dead, says Gordon Moore," Techworld, April 13, 2010.
  4. Nicolas Riesen, Xuanzhao Pan, Kate Badek, Yinlan Ruan, Tanya M. Monro, Jiangbo Zhao, Heike Ebendorff-Heidepriem, and Hans Riesen, "Towards rewritable multilevel optical data storage in single nanocrystals," Optics Express, vol. 26, no. 9 (2018), pp. 12266-12276, https://doi.org/10.1364/OE.26.012266.
  5. Using light for next generation data storage, University of South Australia Press Release, June 28 2018.
  6. Fabian Donat Natterer, Fabio Donati, François Patthey, and Harald Brune, "Thermal and Magnetic-Field Stability of Holmium Single-Atom Magnets," Phys. Rev. Lett., vol. 121, no. 2 (July 13, 2018), Article no. 027201, DOI:https://doi.org/10.1103/PhysRevLett.121.027201.
  7. A step closer to single-atom data storage, École Polytechnique Fédérale de Lausanne Press Release, July 10, 2018.

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