From Theory to Reality: X-rays Reveal the Unexplored Magnetic Domains

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Theoretical interpretation often steps into the spotlight first once breakthrough experiments have been finished. A much more exciting situation, especially in the realm of spectral properties of magnetic materials, is when a theoretical prediction persuades researchers to undertake a specific measurement approach, and subsequently, the collected data align precisely with the prediction. Research that resulted in a paper published last week in Physical Review Letters, where an international team reported that the way light is absorbed by a magnetic substance varies according to its state of polarization, followed just this less common line of development.

The underlying discovery allows to establish a new method for local detection of the magnetic state in a specific type of materials where previously available techniques lacked the appropriate spatial resolution. It could be used in the development of memory devices made of manganese telluride (MnTe) or other altermagnetic materials and, in the future, to determine whether the size of magnetic domains on the order of tens of nanometres corresponds to the desired dimensions of the memory bit. The prospect of microscopic imaging of magnetic textures (such as domain walls or vortices) is also very appealing both from the vantage point of applications and fundamental research in magnetism.

As already mentioned, the theoretical prediction was the starting point: x-ray magnetic circular dichroism (XMCD) had commonly been considered to be absent in materials with zero net magnetisation and even if this assumption was in the end proven wrong in general, materials with magnetic moments parallel to each other (collinear magnets such as MnTe) were exempt.  "The existence of circular dichroism in manganese telluride is related to symmetries, which have recently been used by colleagues at FZU to classify this material as an altermagnet," Jan Kuneš at Masaryk University (MUNI), the corresponding author of the paper, told FZU. "Experiments carried out at Diamond Light Source confirmed our theoretical prediction, and they constitute the first observation of this effect used commonly to study ferromagnets."

A related effect, linear dichroism (XMLD), has been studied in MnTe by scientists at FZU since 2017. Karel Výborný and Dominik Kriegner were attempting to obtain information about the orientation of magnetic moments with respect to crystallographic directions in this material at that time. Models relying on density functional theory (DFT), however, yielded only modest agreement with measured data. Moreover, the magnetic order in the measured sample was not homogeneous - it breaks up into domains - and this further hampered understanding of magnetic order in measured samples.

Theoretical prediction for MnTe
Theoretical prediction for MnTe and experimental confirmation of x-ray absorption (top), circular dichroism at zero (middle) and non-zero magnetic field (bottom). Panel (b) shows experimental data confirming the sensitivity of XMCD in MnTe to direction of magnetic moments. | Source: Hariki et al., Phys. Rev. Lett. 132, 176701 (2024) | photo: Copyright: American Physical Society

Circular dichroism turned out to be the missing piece in the puzzle but modelling approach still had to be improved. "The theoretical prediction of XMCD demands high-precision modelling of the interaction between high-energy x-rays (approximately 650 electron volts) and a multitude of electrons carrying spin within the solid," explains Atsushi Hariki of Osaka Metropolitan University while making the connection to magnetism. "This has been made possible by a quantum embedded approach based on the DFT combined with dynamical mean-field theory." The spectral character of circular dichroism (the dependence of XMCD on wavelength, or equivalently, on energy) turns out to be a fingerprint of magnetic order.

At that point, the research paper describing theoretical prediction had been peer-reviewed and while the validity of results was not put in question, the referees asked for experimental confirmation, citing high standards of publications in Physical Review Letters. In fact, such an effort has already been underway so that in the meantime, while the referees were preparing their reports, our British colleagues were collecting data to prepare a stronger reply.

Diamond Light Source,  britské národní synchrotronové rentgenového zařízení
Tenké vrstvy materiálu připravili již dříve vědci z Nottinghamské univerzity a převezli je v ultravysokém vakuu do Diamondu, britského národního synchrotronového rentgenového zařízení. | photo: Diamond Light Source Ltd.

Thin films of this material were prepared at the University of Nottingham and transported under ultra-high vacuum to Diamond, the UK's national synchrotron x-ray facility. "We were looking for changes in the x-ray absorption under a specific set of experimental conditions which made it hard to measure,” says one of the lead experimentalists involved in this work, Kevin Edmonds. “However, when the signal emerged from the background noise, it agreed remarkably well with the theory prediction.” Such agreement finally convinced the referees and the manuscript was accepted for publication in Physical Review Letters.

Scientists are now in a position to exploit circular dichroism in MnTe to detect its magnetic state and its texture. In combination with linear dichroism, we can use it to visualise magnetic domains. If a MnTe-related material (or some other altermagnet) is chosen for the production of memory devices, photoemission microscopy based on XMCD together with XMLD at suitable energy of x-ray photons can be used to monitor the domain structure. This way, we can make sure, for example, that the domain size (which is under some circumstances at the scale of tens of nanometres) matches the dimensions of the device. This approach is not limited only to MnTe. "We now have a completely new way of studying magnetic materials with vanishing net magnetisation, which are much more abundant in nature than ferromagnets," Tomáš Jungwirth of FZU explains. Visualisation of sub-micrometre magnetic domains and nano-textures in MnTe has in fact already been achieved recently and a manuscript has already appeared on the preprint server.