Neutrons: an essential tool for a spin-based future
Though continuous down-scaling in microelectronics has enabled the industry to achieve phenomenal success, the trend is now approaching fundamental limits. Promising alternative technologies for next generation devices exploit not only the charge of the electron – as used in conventional microelectronics – but also the electron spin (spintronics) or spin waves (magnonics) in order to transmit, store and process information with improved energy efficiency, processing speed and memory storage density. Neutrons are a uniquely powerful probe for the advancement of these technologies due to the intrinsic spin of neutrons that provides them with a magnetic moment and thus the capability to reveal not only the atomic-level structure of materials but also the microscopic magnetic structure and dynamics. The Institut Laue-Langevin (ILL) is at the forefront of research in this area, contributing to and benefiting from the world-class magnetism expertise in Grenoble that can be traced back to Louis Néel, whose contributions to magnetism were acknowledged by a Nobel Prize.
For several decades, yttrium iron garnet (YIG) has been the prototypical material used to study and advance research in a variety of spintronic and magnonic domains. This essential material was discovered and its magnetic structure elucidated by Bertaut, Forrat and Néel, working in Grenoble in the 1950s. Neutron diffraction was subsequently used to verify the proposed models and provide a detailed description of YIG’s complex ferrimagnetic structure. “In common ferromagnetic materials, such as iron, the magnetic moments are aligned in the same direction creating a north and south pole,” explains Timothy Ziman, CNRS research director and member of the ILL Theory Group. “YIG, however, is composed of charged iron atoms caged within two structurally different types of interlocking crystal subunits. Overall net magnetisation is created by the 3:2 ratio of these subunits, with the iron ions collectively aligned but in opposite directions.”
Theory had long predicted that magnons propagating in a structurally complex ferrimagnet like YIG split into two branches with opposite polarisations and different energies. This magnon polarisation was explicitly demonstrated in YIG for the first time by an experiment successfully carried out on the polarised neutron inelastic scattering instrument – IN20 – at the ILL, with the results published in Physical Review Letters in 2020.  “IN20 is the uncontested best instrument worldwide to study the polarisation of magnons in the thermal energy range,” explains Mechthild Enderle, ILL scientist and first responsible for IN20. “The most original aspect of the experiment,” continues Ziman, “is that the chirality was visible not only near absolute zero temperature, as was expected, but even at room temperature, which could be hugely significant for potential future applications such as spintronics.”
The unique properties of YIG have ensured that it is a well-known and widely used material. In comparison, the other members of the rare-earth iron garnet series have currently very limited use. “It’s an incredibly flexible family of compounds, all chemically very similar and with essentially the same fairly open structure, where yttrium can be replaced by other rare-earths such as terbium, gadolinium, thulium or samarium,” explains Ziman. YIG, though complicated, is the simplest member of the rare-earth iron garnet series due to the fact that the yttrium ion has no magnetic moment, as opposed to the other rare-earth ions which each bear their own magnetic moments. Though the substitution of non-magnetic yttrium ions with magnetic rare-earth ions introduces an additional level of complexity, it is also responsible for interesting properties with strong potential applications. There has thus been a significant renewal of interest in the study of the spin structures and spin wave dynamics of the entire rare-earth iron garnet series.
Terbium iron garnet is one such example for which exploratory experimental data has been acquired at the ILL using IN20. “In terbium iron garnet, the terbium ions are pointing in one direction and the iron ions in the other direction but the overall net moment is dominated by terbium due to their much greater magnetisation, meaning that you’re starting with a ferrimagnet like YIG,” explains Ziman. “As the temperature increases though, terbium starts fluctuating up and down and its average moment gets smaller. At a certain point, referred to as the compensation temperature, the magnetisation moment of the terbium ions and iron ions are exactly balanced and essentially you have, at this one temperature, an antiferromagnet.”
Antiferromagnetism – where the magnetic moments in a material are of equal magnitude but aligned in opposite directions – was first proposed by Néel and later proved using neutrons. Today, antiferromagnets attract significant interest due to their promising applications in the field of spintronics-based magnetic memory. “Uniformly magnetised regions in magnetic materials are called domains and domain walls are the finite regions separating domains and over which the magnetisation rotates from one domain orientation to another,” explains Ziman. “A major challenge in magnetic memory is the speed at which domain walls can be moved and ultrafast domain wall motion has been observed in ferrimagnetic materials near a second compensation temperature at which the net angular momenta of the sublattices cancel.” The spin dynamics at and around the compensation temperatures is thus an active area of research.
It is expected that future polarised neutron inelastic scattering experiments on IN20 at the ILL will cover the entire series of rare-earth iron garnets in order to attain a full quantitative understanding of their spin-wave dynamics. In parallel, theoretical and experimental neutron diffraction studies continue to advance our understanding of the structures of these compounds, first elucidated in Grenoble in the 1950s. A recently published study has investigated the complicated umbrella-like spin structure of rare-earth iron garnets and how it changes with temperature.  “At low temperature, terbium iron garnet has three terbium ions which each point in different directions and together form a three-ribbed open umbrella structure. The ribs of the umbrella close, however, as the temperature is raised,” explains Ziman. The detailed information provided by such studies contributes to the interpretation of experimental observations, in addition to the guidance of future experimental work.
FIG. 1. Illustration of polarization for (a) a ferromagnet, (b) an antiferromagnet, and (c) two magnon modes in a ferrimagnet. The “positive” polarization acoustic mode is a coherent right-handed circular precession of the sublattice moments, whereas the “negative” polarization optical mode is a left-handed precession dominated by the exchange interaction between Feoct and Fetet sites. (d) Crystallographic unit cell of Y3Fe5O12 with arrows marking the tetrahedral and octahedral sites. The magnetic moment direction is either parallel or antiparallel to the applied magnetic field direction (). (e) Sketch of the IN20 instrument with bold black arrows denoting the neutron path.
ILL instrument used: IN20, the thermal neutron three-axis spectrometer with polarization analysis
 Nambu, Y., Barker, J., Okino, Y., Kikkawa, T., Shiomi, Y., Enderle, M., Weber, T., Winn, B., Graves-Brook, M., Tranquada, J.M. and Ziman, T., 2020. Observation of magnon polarization. Physical review letters, 125(2), p.027201.
 Tomasello, B., Mannix, D., Geprägs, S. and Ziman, T., 2022. Origin and dynamics of umbrella states in rare-earth iron garnets. Annals of Physics, 447, p.169117.