Ferromagnetic materials are ubiquitous in modern technology and are mainly used to store data in computers. They contain ordered magnetic moments that are aligned parallel to each other. Such ordering is a purely quantum phenomenon and is known as exchange interaction. More complicated types of magnetic ordering, such as that found in antiferromagnetism, for example, exists when half of the magnetic moments are directed in an up direction and the other half in a down direction.

Weak ferromagnets are an important class of magnetic materials that are basically antiferromagnetic but that contain a small canting of magnetic moments. This leads to ferromagnetism in the perpendicular direction. The most well known, weak ferromagnet is haematite, or iron oxide.

Perpendicular coupling of magnetic moments

Around 50 years ago, the two physicists Igor Dzyaloshinskii and Toru Moriya suggested a new type of quantum magnetic interaction in these materials that would be responsible for the canting and thus the weak ferromagnetism. Indeed, the Dzyaloshinskii–Moriya (DM) interaction, as it later came to be called, is part of the spin-orbital interaction, which couples electronic orbital and intrinsic spin magnetism. The DM interaction is the part of this interaction that favours perpendicular coupling of magnetic moments, rather than the normal parallel/antiparallel coupling.

The DM interaction causes a periodic (left, right, left, right) twisting in weak ferromagnets or a slow continuous rotation (left, left, left, left) in some materials such as bismuth ferrite (BiFeO3). It is also important because it is appears to be responsible for the magnetoelectric effect in multiferroics (materials with both magnetic and electric ordering) and in the newly discovered state of matter, the Skyrmion. However, the problem is that, important though it is, the DM interaction and, in particular, its sign, has proved notoriously difficult to measure – until now.

Enter the Diamond Synchrotron

Researchers in Russia, the UK, France, Germany and the Netherlands say that they have now overcome this problem by determining the phase of the X-ray scattering from the antiferromagnetic material iron borate (FeBO3). This was no easy task, explains team member Steven Collins of the Diamond Light Source, the UK's national synchrotron science facility: “Measuring the intensity of X-rays diffracted from the magnetic lattice structure (or its magnetic periodicity) – as opposed to just the normal atomic periodicity – was a challenge because the interaction is so weak that the signals produced are millions of times weaker than normal. In the past, we were only able to do this using neutron diffraction but thanks to the intense (1013 photons/second) beams at modern synchrotron facilities like Diamond, this has now become almost routine.

The main difficulty is that information concerning the sign of the DM interaction in this type of material is encoded in the phase of the X-ray scattering, which we do not normally observe, he adds. Traditional techniques for obtaining this phase information involve measuring two waves – a known wave (the reference) and an unknown one – in a process similar to holography.

Quadrupole resonant scattering

“In our case, the known wave comes from another, very weak and even more exotic scattering process called quadrupole resonant scattering. “The standard, so-called dipole-approximation theory, tells us that this type of scattering simply cannot happen,” Collins told nanotechweb.org. “What is more, the International Table for Crystallography (which is the crystallographer’s bible) also tells us that no diffraction can occur under such conditions. However, we now know that resonant quadrupole scattering can act as a reference wave and in our experiments we measured the scattered intensity of the combined effects of both magnetic and resonant quadrupole scattering. From these we can deduce the phase of the scattering and hence the sign of the DM interaction.”

According to the researchers, such information will help them better predict how magnetic moments twist in several important classes of weak ferromagnets. “Indeed, the interference technique we developed has already allowed us to unearth important information on the atomic magnetic patterns in several other materials and we have recently used it to image small domains that form naturally in the absence of a magnetic field,” said Collins.

The team, led by Mikhail Katsnelson of the Ural Federal University in Russia and Radboud University Nijmegen in The Netherlands, says that it has now begun to study other weak ferromagnets, such as the carbonates, using its technique to find out whether the DM twist direction here follows the same rules as in FeBO3. “We have also started to look at how magnetic domains form in these materials to discover, for example, whether the same patterns form when the magnetism is destroyed by heat and then recreated.”

The current work is detailed in Nature Physics doi:10.1038/nphys2859.

Further reading

Metallic nanowires grow on insulators (Mar 2009)
Multiferroic nanofibres spun out for nanoscale sensing and actuation (Jun 2011)
Ferromagnetic nanocrystals for room-temperature applications (Feb 2011)