Sign of canted ferromagnetism in the quasicrystal approximants Au-SM-R (SM = Si, Ge and Sn / R = Tb, Dy and Ho)

Magnetic dynamics and nonreciprocal excitation in uniform hedgehog order in icosahedral 1/1 approximant crystal

The hedgehog state in the icosahedral quasicrystal (QC) has attracted great interest as the theoretical discovery of topological magnetic texture in aperiodic systems. The revealed magnetic dynamics exhibits nonreciprocal excitation in the vast extent of the reciprocal lattice [Formula: see text]-energy [Formula: see text] space, whose emergence mechanism remains unresolved. Here, we analyze the dynamical as well as static structure of the hedgehog order in the 1/1 approximant crystal (AC) composed of the cubic lattice with spatial inversion symmetry. We find that the dispersion of the magnetic excitation energy exhibits nonreciprocal feature along the N-P-[Formula: see text] line in the [Formula: see text] space. The dynamical structure factor exhibits highly structured intensities where high intensities appear in the high-energy branches along the [Formula: see text]-H line and the P-[Formula: see text]-N line in the [Formula: see text] space. The nonreciprocity in the 1/1 AC and also in the QC is understood to be ascribed to inversion symmetry breaking by the hedgehog ordering. The sharp contrast on the emergence regime of nonreciprocal magnetic excitation between the QC and the 1/1 AC indicates that the emergence in the vast [Formula: see text]-[Formula: see text] regime in the QC is attributed to the QC lattice structure.

High Phase-Purity and Composition-Tunable Ferromagnetic Icosahedral Quasicrystal

We discovered a ferromagnetic Au-Ga-Dy icosahedral quasicrystal (i QC), not only with high phase purity but also with tunable composition. The isothermal magnetization of the polycrystalline ferromagnetic i QC was closely investigated and the mean-field-like nature of the ferromagnetic transition is elucidated. Moreover, the maximum Weiss temperature (θ_{p}) of the i QCs was found at the electrons-per-atom (e/a) ratio of 1.70 being well consistent with those of ACs, validating tunability of the magnetic properties of i QCs on the basis of θ_{p}-e/a scheme for the first time. Thus, the present work provided direct evidence that the magnetism of the i QCs depends on the e/a ratio or the Fermi energy, paving the way for future studies on various exotic magnetic textures formed on a quasiperiodic lattice through the e/a ratio.

Magnetic dynamics of ferromagnetic long range order in icosahedral quasicrystal

Quasicrystals lack translational symmetry and have unique lattice structures with rotational symmetry forbidden in periodic crystals. The electric state and physical property are far from complete understanding, which are the frontiers of modern matter physics. Recent discovery of the ferromagnetic long-range order in the rare-earth based icosahedral quasicrystal has made the breakthrough. Here, we first reveal the dynamical as well as static magnetic structure in the ferromagnetic long-range order in the terbium-based quasicrystal. The dynamical structure factor exhibits highly structured energy and wavenumber dependences beyond the crystalline-electric-field excitation. We find the presence of the magnetic excitation mode analog to magnon with unique hierarchical structure as well as the localized magnetic excitation with high degeneracy in the quasicrystal. Non-collinear and non-coplanar magnetic structure on the icosahedron is discovered to give rise to non-reciprocal magnetic excitation in the quasicrystal as well as non-reciprocal magnon in the periodic cubic 1/1 approximant. These findings afford illuminating insight into the magnetic dynamics in the broad range of the rare-earth-based quasicrystals and approximants.

Experimental Observation of Long-Range Magnetic Order in Icosahedral Quasicrystals

Quasicrystals (QCs), first discovered in 1984, generally do not exhibit long-range magnetic order. Here, we report on long-range magnetic order in the real icosahedral quasicrystals (i QCs) Au–Ga–Gd and Au–Ga–Tb. The Au₆₅Ga₂₀Gd₁₅i QC exhibits a ferromagnetic transition at T_C = 23 K, manifested as a sharp anomaly in both magnetic susceptibility and specific heat measurements, along with an appearance of magnetic Bragg peak below T_C. This is the first observation of long-range magnetic order in a real quasicrystal, in contrast to the spin-glass-like behaviors observed for the other magnetic quasicrystals found to date. Moreover, when Gd is replaced by Tb, i.e., for the Au₆₅Ga₂₀Tb₁₅i QC, a ferromagnetic behavior is still retained with T_C = 16 K. Although the sharp anomaly in the specific heat observed for the Au₆₅Ga₂₀Gd₁₅i QC becomes broadened upon Tb substitution, neutron diffraction experiments clearly show marked development of magnetic Bragg peaks just below T_C, indicating long-range magnetic order for the Au₆₅Ga₂₀Tb₁₅i QC also. Our findings can contribute to the further investigation of exotic magnetic orders formed on real quasiperiodic lattices with unprecedented highest global symmetry, i.e., icosahedral symmetry.

Topological magnetic textures and long-range orders in terbium-based quasicrystal and approximant

The quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in periodic crystals. The electric property is far from complete understanding. It has been a long-standing issue whether magnetic long-range order is realized in the QC. Here, we report our theoretical discovery of the ferromagnetic long-range order in the Tb-based QC. The difficulty in past theoretical studies on the QC was lack of the microscopic theory of the crystalline electric field (CEF), which is crucially important in the rare earth systems. By analyzing the CEF in the Tb-based QC, we clarify that magnetic anisotropy plays a key role in realizing unique magnetic textures in the Tb-based QC and approximant crystal (AC). By constructing the minimal model, we show that various magnetic textures on the icosahedron, at whose vertices Tb atoms are located, are realized. We find that the hedgehog state is characterized by the topological charge of one and the whirling-moment state is characterized by an unusually large topological charge of three. The hedgehog and whirling-moment states are shown to be realized as antiferromagnetic orders transcribed as the emergent monopole and antimonopole in the 1/1 AC. We find that these states exhibit the topological Hall effect under applied magnetic field accompanied by the topological as well as metamagnetic transition. Our model and the determined phase diagram are expected to be relevant to the broad range of the rare earth-based QCs and ACs with strong magnetic anisotropy, which are useful not only to understand magnetism but also, to explore topological properties.

Magnetism and topology in Tb-based icosahedral quasicrystal

Quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in conventional crystals. The electric property is far from complete understanding and it has been a long-standing issue whether the magnetic long-range order is realized in the QC. The main difficulty was lack of microscopic theory to analyze the effect of the crystalline electric field (CEF) at the rare-earth atom in QCs. Here we show the full microscopic analysis of the CEF in Tb-based QCs. We find that magnetic anisotropy arising from the CEF plays a key role in realizing unique magnetic textures on the icosahedron whose vertices Tb atoms are located at. Our analysis of the minimal model based on the magnetic anisotropy suggests that the long-range order of the hedgehog characterized by the topological charge of one is stabilized in the Tb-based QC. We also find that the whirling-moment state is characterized by unusually large topological charge of three. The magnetic textures as well as the topological states are shown to be switched by controlling compositions of the non-rare-earth elements in the ternary compounds. Our model is useful to understand the magnetism as well as the topological property in the rare-earth-based QCs and approximant crystals.

Structural-transition-driven antiferromagnetic to spin-glass transition in Cd-Mg-Tb 1/1 approximants

The magnetic susceptibility of the 1/1 approximants to icosahedral quasicrystals in a series of Cd85-xMgxTb15(x= 5, 10, 15, 20) alloys was investigated in detail. The occurrence of antiferromagnetic (AFM) to spin-glass (SG)-like transition was noticed by increasing Mg. Transmission electron microscopy analysis evidenced a correlation between the magnetic transition and suppression of the monoclinic superlattice ordering with respect to the orientation of the Cd4tetrahedron atT> 100 K. The possible origins of this phenomenon were discussed in detail. The occurrence of the AFM to SG-like magnetic transition is associated with the combination of chemical disorder due to a randomized substitution of Cd with Mg and the orientational disorder of the Cd4tetrahedra.

Noncoplanar ferrimagnetism and local crystalline-electric-field anisotropy in the quasicrystal approximant Au70Si17Tb13

Neutron scattering experiments have been performed to elucidate magnetic properties of the quasicrystal approximant Au70Si17Tb13, consisting of icosahedral spin clusters in a body-centered-cubic lattice. Bulk magnetic measurements performed on the single crystalline sample unambiguously confirm long-range ordering atTC= 11.6 ± 1 K. In contrast to the simple ferromagnetic response in the bulk measurements, single crystal neutron diffraction confirms a formation of intriguing non-collinear and non-coplanar magnetic order. The magnetic moment direction was found to be nearly tangential to the icosahedral cluster surface in the local mirror plane, which is quite similar to that recently found in the antiferromagnetic quasicrystal approximant Au72Al14Tb14. Inelastic neutron scattering on the powdered sample exhibits a very broad peak centered atℏω≃ 4 meV. The observed inelastic spectrum was explained by the crystalline-electric-field model taking account of the chemical disorder at the fractional Au/Si sites. The resulting averaged anisotropy axis for the crystalline-electric-field ground state is consistent with the ordered moment direction determined in the magnetic structure analysis, confirming that the non-coplanar magnetic order is stabilized by the local uniaxial anisotropy.

Magnetic properties of icosahedral quasicrystals and their cubic approximants in the Cd-Mg-RE (REGd, Tb, Dy, Ho, Er, and Tm) systems

A systematic investigation has been performed to elucidate effects of rare earth type and structural complexity on magnetic properties of icosahedral quasicrystal (iQC) and their cubic approximants (APs) in the ternary Cd-Mg-RE (RE = Gd, Tb, Dy, Ho, Er, and Tm) systems. At low temperatures, iQCs and 2/1 APs exhibit spin-glass-like freezing for RE = Gd, Tb, Dy, and Ho, while for Er and Tm they do not show freezing behavior down to the base temperature ∼2 K. The 1/1 APs exhibit either spin-glass-like freezing or antiferromagnetic (AFM) ordering depending on their constituent Mg content. TheTfvalues show increasing trend from iQC to 2/1 and 1/1 APs. In contrast, the absolute values of Weiss temperature for iQCs are larger than those in 2/1 and 1/1 APs, indicating that the total AFM interactions between the neighboring spins are larger in aperiodic, rather than periodic systems. Competing spin interactions originating from the long-range Ruderman-Kittel-Kasuya-Yoshida mechanism along with chemical disorder of Cd/Mg ions presumably account for the observed spin-glass-like behavior in Cd-Mg-RE iQCs and APs.

Atomic-Scale Tuning of Tsai-Type Clusters in RE-Au-Si Systems (RE = Gd, Tb, Ho)

Tsai-type quasicrystals and approximants are distinguished by a cluster unit made up of four concentric polyhedral shells that surround a tetrahedron at the center. Here we show that for Tsai-type 1/1 approximants in the RE–Au–Si systems (RE = Gd, Tb, Ho) the central tetrahedron of the Tsai clusters can be systematically replaced by a single RE atom. The modified cluster is herein termed a “pseudo-Tsai cluster” and represents, in contrast to the conventional Tsai cluster, a structural motif without internal symmetry breaking. For each system, single-phase samples of both pseudo-Tsai and Tsai-type 1/1 approximants were independently prepared as millimeter-sized, faceted, single crystals using the self-flux synthesis method. The full replacement of tetrahedral moieties by RE atoms in the pseudo-Tsai 1/1 approximants was ascertained by a combination of single-crystal and powder diffraction studies, as well as energy dispersive X-ray spectroscopy (EDX) analyses with a scanning electron microscope (SEM). Differential scanning calorimetry (DSC) studies revealed distinctly higher decomposition temperatures, by 5–35 K, for the pseudo-Tsai phases. Furthermore, the magnetic properties of pseudo-Tsai phases are profoundly and consistently different from the Tsai counterparts. The onset temperatures of magnetic ordering (T_mag) are lowered in the pseudo-Tsai phases by ∼30% from 24 to 17 K, 11.5 to 8 K, and 5 to 3.5 K in the Gd–Au–Si, Tb–Au–Si, and Ho–Au–Si systems, respectively. In addition, the Tb–Au–Si and Ho–Au–Si systems exhibit some qualitative changes in their magnetic ordering, indicating decisive changes in the magnetic state/structure by a moment-bearing atom at the cluster center.

Formation conditions of Tsai (IT) and pseudo-Tsai (CC) phases have been established, and their atomic structures and magnetic properties have been investigated for the RE−Au−Si systems (RE = Gd, Tb, Ho). Following a schematic pseudobinary (Au₇₉Si₂₁ versus RE) phase diagram, millimeter-sized single crystals were obtained for both structure types using the self-flux synthesis method. Variations in atomic structure, thermal behaviors, and magnetic properties were identified using SCXRD, DSC, and magnetic property measurements, respectively.

Long range ordered magnetic and atomic structures of the quasicrystal approximant in the Tb-Au-Si system

The atomic and magnetic structure of the 1/1 Tb(14)Au(70)Si(16) quasicrystal approximant has been solved by combining x-ray and neutron diffraction data. The atomic structure is classified as a Tsai-type 1/1 approximant with certain structural deviations from the prototype structures; there are additional atomic positions in the so-called cubic interstices as well as in the cluster centers. The magnetic property and neutron diffraction measurements indicate the magnetic structure to be ferrimagnetic-like below 9 K in contrast to the related Gd(14)Au(70)Si(16) structure that is reported to be purely ferromagnetic.