The study was led by Assistant Professor Farid Labib of the Research Institute for Science and Technology at Tokyo University of Science, together with Associate Professor Kazuhiro Nawa of the Institute of Multidisciplinary Research for Advanced Materials at Tohoku University and Professor Ryuji Tamura of Tokyo University of Science. The team focused on Tsai-type compounds, a class of multi-shell cluster-based structures in which moment-bearing rare-earth atoms occupy an icosahedral site. In these materials, nested atomic shells, including the rhombic triacontahedron, icosidodecahedron, icosahedron, dodecahedron, and an inner tetrahedron, build up a cluster architecture whose rare-earth icosahedral shell carries the magnetic moments responsible for the compounds’ magnetic response.

Historically, materials chemists have relied on chemically tunable parameters to organize the magnetic properties of complex intermetallics. The most influential of these is the valence-electron concentration, commonly expressed as the electron-per-atom, or e/a, ratio. In metallic systems such as Heusler alloys and approximant crystals, the e/a ratio has been widely used to classify magnetic ground states. In gold-based Tsai-type approximant crystals specifically, the e/a ratio was found to control whether the compounds developed long-range antiferromagnetic order, long-range ferromagnetic order, or a spin-glass state in which the magnetic moments freeze in random orientations. But the predictive power of e/a has a serious limitation: it does not transfer cleanly across different alloy families and constituent elements.

That limitation matters because quasicrystal-based intermetallics are considered promising platforms for exploring emergent magnetic phenomena and quantum states not found in ordinary periodic crystals. Without a reliable, experimentally accessible parameter to guide the search, researchers have lacked a systematic way to identify which compositions are worth synthesizing. As Dr. Labib explained, quasicrystals are among the most uniquely structured materials discovered to date and are expected to exhibit novel magnetic states and quantum phenomena not found in ordinary crystals, yet until now there has been no unified guideline for systematically exploring these phenomena in quasicrystals and their approximant crystals.

To close that gap, the team synthesized a family of gold-based 1/1 approximant crystals containing aluminum or gallium and the rare-earth elements terbium, dysprosium, and holmium, and then systematically measured their structural and magnetic properties. Approximant crystals are periodic structures whose local atomic environments closely mimic those of true quasicrystals, making them experimentally tractable stand-ins for the quasiperiodic originals. The measurements revealed a nearly monotonic inverse correlation between the e/a ratio and the lattice parameter, meaning that as the electron concentration per atom rises, the physical size of the cubic unit cell shrinks in a regular, predictable way.

The researchers then extended their experiments to non-Heisenberg Tsai-type compounds containing terbium, dysprosium, and holmium. These compounds are called non-Heisenberg because their magnetic moments do not behave as simple, freely rotating spins; instead, the crystal electric field generated by the surrounding lattice imposes strong uniaxial magnetic anisotropy that favors specific orientations of the moments. Under these conditions, the team observed characteristic whirling antiferromagnetic and ferromagnetic orders, in which the constrained moments arrange themselves in swirling patterns dictated by the interplay of anisotropy and the conduction-electron-mediated interactions between rare-earth moments on the icosahedral shell.

When the researchers plotted the magnetic ground states against the lattice parameter, the result was striking. The compounds organized with high accuracy according to the size of the unit cell, whereas the conventional e/a classification showed systematic shifts depending on which rare-earth element was present and what the alloy composition was. The phase boundaries were sharply defined. Compounds with lattice parameters above approximately 14.72 angstroms adopted the whirling antiferromagnetic state. Those with lattice parameters between 14.62 and 14.72 angstroms became whirling ferromagnets. And those with lattice parameters below approximately 14.62 angstroms froze into spin-glass states. These well-defined thresholds establish the lattice parameter as a unified and experimentally accessible structural descriptor for predicting magnetic ground states in the Tsai-type family.

The physical interpretation is that structural length scales, alongside electron concentration, must be explicitly considered when understanding the conduction-electron-mediated magnetic interactions in these complex alloys. In rare-earth intermetallics, the magnetic moments communicate with one another indirectly through the conduction electrons, and the strength and sign of that communication depend sensitively on the distances between the moment-bearing atoms. A change in the lattice parameter therefore directly reshapes the geometry of the magnetic interaction network on the icosahedral shell, which in turn determines whether the system settles into antiferromagnetic whirling, ferromagnetic whirling, or glassy freezing. The e/a ratio captures part of this physics but conflates it with element-specific electronic effects, which is why it fails to produce a single, element-independent classification.

The practical implications extend well beyond classification. Because the lattice parameter can be tuned through alloy composition and measured with routine structural characterization, it offers materials designers a direct control knob for targeting a desired magnetic ground state. Dr. Nawa noted that the unified magnetic phase diagram constructed in the study can serve as a practical roadmap for the systematic exploration of new magnetic quasicrystals and approximant crystals exhibiting novel magnetic orders and quantum phenomena, and that it can provide a guideline for designing new magnetic materials with targeted magnetic ground states, opening new opportunities for discovering unconventional magnetism in quasiperiodic and complex intermetallic systems.

The study was supported by the Japan Society for the Promotion of Science through multiple Grants-in-Aid for Scientific Research, by the Murata Science and Education Foundation, and by the Japan Science and Technology Agency through its CREST program. The authors declared no competing interests. For a field that has spent decades cataloguing the exotic magnetism of quasiperiodic materials one compound at a time, the message of this work is unusually clean: in the Tsai-type family, the size of the atomic cage appears to decide the fate of the spins inside it. If the lattice-parameter thresholds hold across further alloy families, the search for new magnetic quasicrystals may become far less of a treasure hunt and far more of an engineering exercise, with the next generation of unconventional magnets designed first on paper, in angstroms.

Subject of Research: Lattice-parameter control of magnetic ground states in Tsai-type quasicrystals and approximant crystals

Article Title: Lattice parameter as a unified parameter governing magnetic ground states in Tsai-type compounds

Article References: Lattice parameter as a unified parameter governing magnetic ground states in Tsai-type compounds. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: quasicrystals, Tsai-type clusters, lattice parameter, magnetic ground states, antiferromagnetism, ferromagnetism, spin glass, rare-earth intermetallics, electron-per-atom ratio, magnetic anisotropy, approximant crystals, Tokyo University of Science

The material at the heart of the study belongs to the perovskite manganite family, chemical compounds with the general formula La0.77Sr0.23Mn1-yFeyO3, in which the researchers systematically replaced a small fraction of manganese with iron, up to ten percent. Lanthanum-strontium manganites are famous for their colossal magnetoresistance and their delicate balance of electronic interactions, and they have attracted sustained interest for applications ranging from spintronics to magnetic refrigeration and biomedical hyperthermia. In the parent compound, double-exchange interactions between neighboring manganese ions, mediated by oxygen, align magnetic moments and produce ferromagnetic order. Introducing iron into the manganese sublattice disturbs this delicate choreography, and the new study quantifies exactly how deeply that disturbance runs.

Using high-field magnetization measurements across a temperature range from 100 to 340 kelvin, the researchers tracked two key indicators of magnetic health: the saturation magnetization, which measures the maximum alignment of magnetic moments, and the Curie temperature, the point at which ferromagnetic order collapses. Both quantities decreased steadily as iron content increased. The interpretation is physically intuitive. Iron ions at manganese sites break the double-exchange pathways that bind neighboring moments together, weakening the collective ferromagnetic state and raising the energetic cost of full alignment. At the same time, the substitution enhances magnetic inhomogeneity, creating a landscape in which different regions of the sample experience slightly different local magnetic environments rather than behaving as a uniform ferromagnet.

The most striking result, however, emerged when the team compared nanoparticles with ceramics made of the same chemistry. In ceramic samples, where each grain is large enough to break up into multiple magnetic domains, the magnetization mechanism is dominated by the motion and growth of domain walls. In nanoparticles, by contrast, the grains are small enough to exist in a nearly single-domain state, meaning the entire particle behaves as one giant magnetic moment that must rotate as a whole to align with an applied field. This difference is not a subtle detail; it completely changes how the material responds to magnetic fields and, crucially, how its intrinsic anisotropy can be extracted from experimental data.

To quantify anisotropy, the researchers turned to a venerable technique known as the law of approach to saturation, or LAS. The idea is elegant: as a magnetic field grows very strong, the magnetization of a ferromagnet approaches its saturation value along a characteristic curve whose shape encodes the anisotropy energy that resists full alignment. In its classical form, the high-field magnetization deficit follows an inverse-square dependence on the applied field, a term proportional to H to the power of minus two, from which the effective anisotropy field and anisotropy constants can be computed. The method has underpinned decades of anisotropy measurements, but it rests on assumptions about the magnetic microstructure that are easy to overlook.

For the nanoparticles, the classical picture held up beautifully. The high-field asymptote of the magnetization was well described by the H to the power of minus two term, and the anisotropy-related parameters extracted from the fits remained stable and physically meaningful across the measured temperature range. In other words, when a magnetic particle is essentially a single domain, the law of approach to saturation delivers what it promises: a clean, model-independent window into the intrinsic anisotropy of the material. This is a reassuring result for anyone designing nanoparticle-based magnetic systems, because it means the anisotropy values measured on such particles can be trusted as genuine material properties rather than artifacts of the fitting procedure.

The ceramics told a very different story. When the researchers applied the same LAS analysis to the multidomain ceramic samples, the fitting results proved highly sensitive both to the choice of fitting model and to the range of magnetic fields included in the analysis. Change the field window or the functional form, and the extracted anisotropy parameters shifted appreciably. The reason lies in the physics of domains: in a multidomain magnet, the approach to saturation is contaminated by contributions from domain wall motion and domain rotation, processes that have nothing to do with magnetocrystalline anisotropy but that masquerade as anisotropy signals in a naive fit. Structural inhomogeneity in polycrystalline samples compounds the problem further.

The practical lesson the authors draw is a caution for the entire field: reliable anisotropy evaluation requires taking the magnetic microstructure into account. LAS-derived parameters extracted from multidomain or structurally inhomogeneous systems should be interpreted with care, and ideally cross-checked against complementary techniques. This warning carries real weight because the law of approach to saturation remains one of the most widely used methods for estimating anisotropy in oxides, ferrites, and nanocomposites, and uncritical application of it to ceramics could propagate questionable anisotropy values through the literature and into device design calculations.

The findings also feed directly into a promising biomedical application. Previous work by members of the same collaboration identified iron-doped lanthanum-strontium manganites as promising mediators of self-controlled magnetic nanohyperthermia, a cancer therapy in which magnetic nanoparticles injected into a tumor generate heat under an alternating magnetic field, with the material’s Curie temperature acting as a built-in thermostat that prevents overheating. Because iron substitution tunes both the Curie temperature and the anisotropy, and because anisotropy governs how efficiently nanoparticles convert magnetic energy into heat, the ability to measure anisotropy reliably in single-domain particles is a genuine enabler for optimizing such therapeutic agents.

Beyond the immediate material system, the study offers a broader conceptual takeaway that resonates across magnetism research: there is no such thing as a structure-independent magnetic property. The same chemical formula, whether sintered into a dense ceramic or dispersed as nanoscale grains, harbors two distinct magnetic objects governed by different physics. As nanotechnology continues to push magnetic materials into ever smaller dimensions, distinguishing single-domain from multidomain behavior is not an academic nicety but a prerequisite for meaningful measurement. The Ukrainian team’s systematic comparison, supported by the National Research Foundation of Ukraine, provides both a practical protocol and a conceptual warning, reminding researchers that before trusting an anisotropy number, they should first ask what kind of magnetic animal they are actually measuring.

Subject of Research: Magnetic anisotropy in iron-substituted lanthanum-strontium manganite nanoparticles and ceramics

Article Title: Magnetic anisotropy evolution in Fe-substituted La0.77Sr0.23Mn1-yFeyO3: from multidomain ceramics to single-domain nanoparticles

Article References: Magnetic anisotropy evolution in Fe-substituted La0.77Sr0.23Mn1-yFeyO3: from multidomain ceramics to single-domain nanoparticles. (n.d.). https://doi.org/10.1007/s11051-026-06771-2

Image Credits: AI Generated

DOI: 10.1007/s11051-026-06771-2

Keywords: perovskite manganites, magnetic anisotropy, law of approach to saturation, nanoparticles, single-domain magnetism, multidomain ceramics, iron substitution, double-exchange interaction, Curie temperature, magnetic nanohyperthermia, spintronics, La0.77Sr0.23MnO3