Long-range magnetic order in real icosahedral quasicrystals Ryuji Tamura  (  tamura@rs.tus.ac.jp ) Tokyo University of Science https://orcid.org/0000-0001-8589-4311 Asuka Ishikawa  Tokyo University of Science Shintaro Suzuki  Tokyo University of Science Akihiro Kotajima  Tokyo University of Science Yujiro Tanaka  Tokyo University of Science Takehito Seki  University of Tokyo Naoya Shibata  University of Tokyo https://orcid.org/0000-0003-3548-5952 Tsunetomo Yamada  Tokyo University of Science https://orcid.org/0000-0003-0138-9778 Takenori Fujii  The University of Tokyo Chin-Wei Wang  National Synchrotron Radiation Research Center https://orcid.org/0000-0001-9012-2420 Maxim Avdeev  Australian Nuclear Science and Technology Organisation, Australia Taku Sato  Tohoku University Article Keywords: Quasicrystals (QCs), long-range magnetic order, icosahedral symmetry Posted Date: March 23rd, 2021 DOI: https://doi.org/10.21203/rs.3.rs-215127/v1 License:   This work is licensed under a Creative Commons Attribution 4.0 International License.   Read Full License 1 Long-range magnetic order in real icosahedral quasicrystals 2 3 Ryuji Tamura1*, Asuka Ishikawa2, Shintaro Suzuki1, Akihiro Kotajima1, Yujiro Tanaka1, 4 Takehito Seki3, Naoya Shibata3, Tsunetomo Yamada4, Takenori Fujii5, Chin-Wei Wang6, 5 Maxim Avdeev7,8 and Taku J. Sato9* 6 7 1Department of Materials Science and Technology, Tokyo University of Science, 8 Katsushika, Tokyo 125-8585, Japan, 9 2Research Institute for Science and Technology, Tokyo University of Science, Katsushika, 10 Tokyo 125-8585, Japan, 11 3Institute of Engineering Innovation, School of Engineering, The University of Tokyo, 12 Bunkyo, Tokyo 113-8656, Japan, 13 4Department of Applied Physics, Tokyo University of Science, Katsushika, Tokyo 125- 14 8585, Japan, 15 5Cryogenic Research Center, The University of Tokyo, Bunkyo, Tokyo 113-0032, Japan, 16 6National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan, 17 7Australian Nuclear Science and Technology Organisation, New Illawarra Road, Lucas 18 Heights, NSW 2234, Australia, 19 8 School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia, 20 9Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1- 21 1 Katahira, Aoba, Sendai 980-8577, Japan 22 *e-mail: tamura@rs.tus.ac.jp; taku@tohoku.ac.jp 23 Abstract 24 Quasicrystals (QCs), first discovered in 19841, generally do not exhibit long-range 25 magnetic order. Here, we report on long-range magnetic order in the real 26 icosahedral quasicrystals (i QCs) Au–Ga–Gd and Au–Ga–Tb. The Au65Ga20Gd15 i 27 QC exhibits a ferromagnetic transition at TC = 23 K, manifested as a sharp anomaly 28 in both magnetic-susceptibility and specific-heat measurements. Quick magnetic 29 saturation to almost the full moment (7B/Gd3+) is observed under 100 Oe at 2 K. 30 This is the first observation of long-range magnetic order in a real quasicrystal, in 31 contrast to the spin-glass-like behaviours observed for the other magnetic 32 quasicrystals found to date. Moreover, when Gd is replaced by Tb, i.e. for the 33 Au65Ga20Tb15 i QC, a ferromagnetic behaviour is still retained with TC = 16 K. 34 Although the sharp anomaly in the specific heat observed for the Au65Ga20Gd15 i QC 35 is significantly broadened upon Tb substitution, neutron-diffraction experiments 36 clearly show the marked development of magnetic Bragg peaks below TC, indicating 37 long-range magnetic order for the Au65Ga20Tb15 i QC also. Our findings can 38 contribute to the further investigation of exotic magnetic orders formed on real 39 quasiperiodic lattices with unprecedented highest global symmetry, i.e. icosahedral 40 symmetry. 41 Main 42 Quasicrystals (QCs) are solids that possess long-range positional order with 43 crystallographically forbidden symmetries such as 5-fold, 10-fold, and 12-fold rotational 44 symmetries (Fig. 1). Since the discovery of Al86Mn14 icosahedral quasicrystal (i QC) in 45 19841, researchers have evinced tremendous interest in the physical properties of this new 46 class of ordered solids. However, no physical property directly reflecting the long-range 47 quasiperiodic order has been reported to date; in particular, no long-range magnetic order 48 has been observed thus far. Meanwhile, all magnetic-moment-bearing QCs exhibit a spin- 49 glass-like freezing behaviour without exception6-21. In the search for long-range magnetic 50 order in i QCs, researchers have particularly focused on rare-earth (R)-containing i QCs 51 with well-localised magnetic moments, such as Zn–Mg–R9-16, Cd–Mg–R17-19, and Cd–R 52 i QCs20,21, However, their magnetic susceptibilities commonly display spin-freezing 53 phenomena characterised by bifurcation in the zero-field-cooled (ZFC) and field-cooled 54 (FC) susceptibilities without any accompanying sharp anomaly in the specific heat. Here, 55 it is noteworthy that both antiferromagnetism and other long-range magnetic orders such 56 as ferro- and ferrimagnetism have not been observed in real QCs. 57 58 This situation is similar to that of approximant crystals (ACs), whose atomic 59 configurations closely approximate the local atomic structures in QCs, until a decade ago 60 when antiferromagnetic transitions were discovered in Cd6Tb 1/1 AC22 and a family of 61 Cd6R 1/1 ACs23. The observations of antiferromagnetic transitions and the subsequent 62 finding of ferromagnetic transitions in Au–Si–R (R = Gd, Tb, Dy, Ho) 1/1 ACs24,25 have 63 motivated us to search for magnetically ordered i QCs that are likely to exist in the vicinity 64 of the magnetic ACs. Here, to the best of our knowledge, we report on the first long-range 65 magnetic order in QCs, obtained by finely tuning the average electron-per-atom ratio (e/a 66 = 1.70) near which the strongest ferromagnetism (highest TC) was recently observed for 67 Au–Al–Gd 1/1 AC26. 68 69 Search for first ferromagnetic quasicrystals 70 In this study, Au–Ga–R alloys with various compositions in the vicinity of 1/1 71 Au–Ga–R ACs with e/a ~ 1.70 were rapidly quenched to search for new ferromagnetic i 72 QCs. Figure 2 presents the powder X-ray diffraction (XRD) patterns of the Au65Ga20R15 73 (R = Gd, Tb) samples with e/a = 1.70; most of the peaks can be identified as i QC peaks 74 for both compounds. For both systems, some peaks are assigned to those of the 1/1 Au– 75 Ga–R AC (solid triangles). The inset displays the selected-area electron diffraction 76 patterns of i Au65Ga20Gd15 with incidence along the 2-fold, 3-fold, and 5-fold rotational- 77 symmetry axes; the images clearly exhibit icosahedral symmetry features unique to i QCs. 78 We note here that the -scaling property observed in the 2-fold pattern indicates that the 79 obtained i QC is a primitive i QC, identical to the prototype i Cd5.7Yb. Thus, we 80 successfully obtained new i QCs with e/a = 1.70, which can be regarded as candidates of 81 strong ferromagnetic i QCs based on the magnetic phase diagram recently obtained for 82 Au–Al–Gd 1/1 ACs26 (see Fig. 5). 83 84 Observation of ferromagnetic transitions in real quasicrystals 85 Figures 3a and 3b show the magnetic susceptibility χ = M/H as a function of 86 the temperature below 60 K for Au65Ga20R15 (R = Gd, Tb) i QCs, respectively, together 87 with specific heat Cp in the temperature range of 2–50 K (insets). The magnetic 88 susceptibility clearly obeys the Curie–Weiss law χ = 𝑁A𝜇eff2⁄3𝑘B(𝑇 − 𝛩) for both i 89 QCs, where 𝑁A denotes the Avogadro number, 𝑘B the Boltzmann constant, and 𝛩 the 90 Weiss temperature (see Supplementary Information). The effective magnetic moments 91 𝜇eff obtained from the fitting are 7.90B for i Au65Ga20Gd15 and 9.64B for i 92 Au65Ga 3+20Tb15, which are in good agreement with the theoretical values of R (R = Gd, 93 Tb) free ions, 7.94B and 9.72B, respectively. Thus, the magnetic moments are strongly 94 localised on the R3+ ions, as in the cases of the other R-containing i QCs. A distinct 95 difference from the previously reported R-containing i QCs lies in the sign of 𝛩 as a 96 consequence of fine-tuning the e/a ratio to 1.70, for which we obtained a strongly 97 ferromagnetic 1/1 AC; the 𝛩 values are 27.9 K for i Au65Ga20Gd15 and 12.9 K for i 98 Au65Ga20Tb15, which clearly demonstrate that the inter-spin interactions are expectedly 99 strongly ferromagnetic for these i QCs; this result is in contrast with the negative 𝛩 100 values exclusively observed for all the other i QCs reported to date (see Fig.5). 101 102 From Figs. 3a and 3b, we note that χ increases sharply at 23.4 K and 16.0 K for 103 the Au65Ga20R15 (R = Gd, Tb) i QCs, respectively, suggesting the occurrence of a 104 ferromagnetic transition for both i QCs. For i Au65Ga20Tb15, a deviation of χ between 105 the FC and ZFC susceptibilities is observed below 16.0 K; this behaviour is similar to 106 that observed for Tb-containing ACs25,27. The M–H curves for Au65Ga20R15 (R = Gd, Tb) 107 i QCs under fields up to 7 T at 2 K are provided in the Supplementary Information. For i 108 Au65Ga20Gd15, M quickly saturates to ~7 /Gd3+B , nearly the full moment of a free Gd3+ 109 ion (7B/Gd3+), at a low field of 100 Oe. On the other hand, for i Au65Ga20Tb15, the M 110 magnitude is suppressed to ~6 /Tb3+B at 7 T, about two-thirds of the full moment of a 111 Tb3+ ion (9B/Tb3+). This behaviour is closely consistent with those of Tb-containing 112 ACs25-27, which was attributed to the existence of the strong uniaxial anisotropy of the 113 Tb3+ spins. The M suppression is ascribed to the formation of non-coplanar spin 114 configuration due to this strong uniaxial anisotropy of Tb3+ spins in Au–Si–Tb 1/1 AC28. 115 The insets of Figs. 3a and 3b show the variation in specific heat Cp of the Au65Ga20R15 (R 116 = Gd, Tb) i QCs, respectively. For i Au65Ga20Gd15, Cp clearly displays a -shaped 117 anomaly at 23.1 K, which corresponds to the sharp increase in χ at 23.4 K; this result 118 validates the magnetic-transition occurrence at TC = 23 K. In contrast, for i Au65Ga20Tb15, 119 Cp exhibits a broad anomaly around 16 K, close to the temperature corresponding to the 120 sharp rise in χ. 121 122 Verification of the ferromagnetism in i Au65Ga20Tb15 by neutron-diffraction 123 experiments 124 To unambiguously prove the occurrence of long-range magnetic order in i 125 Au65Ga20Tb15, we next performed neutron-diffraction experiments. Figure 4a shows 126 powder-neutron-diffraction patterns of i Au65Ga20Tb15 measured at T = 3.5 K and 20 K, 127 which are below and above the anomaly temperature of 16 K observed in the χ–T and 128 Cp–T curves. Diffraction patterns measured at various temperatures are provided in the 129 Supplementary Information. We clearly observe magnetic Bragg reflections at the base 130 temperature of 3.5 K. Some magnetic reflections newly appear at the base temperature, 131 while many others are observed as an enhancement of the nuclear reflections (211111, 132 221001, and 332002, to note a few), confirming the ferromagnetic nature of the magnetic 133 order. We note that several magnetic peaks at low angles are due to the contaminating 1/1 134 Au-Ga-Tb AC, inclusion of which is detected in the XRD pattern (as denoted by the 135 triangles in Fig. 2). Details of the appearance of the magnetic Bragg peaks from the 1/1 136 AC phase are given in the Supplementary Information, where the powder-neutron- 137 diffraction pattern of the Au–Ga–Tb 1/1 AC of the same nominal composition prepared 138 by additional annealing at 923 K for 50 h is provided. Here, it is noted that the magnetic 139 reflections from the 1/1 Au–Ga–Tb AC can be consistently indexed with the cubic 140 commensurate indices (see Fig. S4). In addition, due to the loss of the bcc symmetry by 141 the magnetic order, similar to the whirling magnetic order discovered in the 1/1 Au-Al- 142 Tb AC29, the magnetic reflections from the 1/1 Au-Ga-Tb AC appear separately from its 143 nuclear reflections. In the i Au65Ga20Tb15 QC shown in Fig. 4a, we clearly observe 144 reflections that cannot be assigned to those of the 1/1 AC and that are located exactly at 145 the positions of the nuclear Bragg reflections of the i QC, such as the 111000 and 111100 146 reflections (as newly appearing magnetic reflections), and 211111, 221001 and 332002 147 reflections (as reflections appearing on the nuclear-reflection positions). Figure 4b 148 magnifies the low-2 region between 30° – 33°, wherein we observe the development of 149 the strongest 111000 magnetic Bragg reflection with decreasing temperature below TC = 150 16 K, which indicates ferromagnetic order formation in i Au65Ga20Tb15. Figure 4c shows 151 the temperature evolution of the 111000 magnetic Bragg reflection intensity, wherein TC 152 is estimated using the critical exponent fit as TC = 16.1(3) K, which is in excellent 153 agreement with the Curie temperature of TC = 16 K observed in the bulk magnetic 154 measurements. Here, we note that this is the first direct microscopic observation of long- 155 range magnetic order in a QC via neutron-diffraction experiments. The next epoch- 156 making issue is to determine the complex magnetic structure of Au–Ga–Tb i QC. This 157 requires the development of analysis methods and algorithms for the magnetic-structure 158 determination of ferromagnetic i QCs via higher-dimensional crystallography. 159 160 Discussion and conclusion 161 Next, we discuss the reason for the formation of the ferromagnetic QCs in the 162 present Au65Ga20R15 (R = Gd, Tb) compounds. According to the theory underlying the 163 Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction30, which is the major magnetic 164 interaction between R3+ spins for R-containing QCs, the RKKY interaction magnitude 2 165 scales with the de-Gennes factor (dG) [(𝑔𝐽 − 1) 𝐽(𝐽 + 1)], where 𝑔𝐽 denotes the Landé 166 g-factor and 𝐽 the total angular momentum. Figure 5 shows the normalised Weiss 167 temperature, 𝛩/dG, as a function of the e/a ratio over a wide e/a range from 1.5 to 2.2 168 for all the R-containing Tsai-type i QCs reported to date17,20,31, together with the 𝛩/dG 169 values for the Au–Al–Gd 1/1 ACs (orange circles) for comparison26. The figure also 170 shows the magnetic-ground-state regime of the Au–Al–Gd 1/1 AC in terms of the e/a 171 ratio, wherein we note that the magnetic order changes from antiferromagnetic to 172 ferromagnetic and then to spin glass (SG) with increasing e/a ratio. From Fig. 5, we 173 clearly observe that the magnitude of the 𝛩/dG value and its sign are sensitively and 174 systematically dependent on the e/a ratio for the AC. Consequently, it is clear that the 175 negative 𝛩 values exclusively observed for previously reported i QCs are attributed to 176 their relatively large e/a values of 2.10 - 2.15, around which spin-glass-like behaviours 177 are predominantly observed for both QCs and ACs. In contrast, the large positive 𝛩 178 values for the present Au–Ga–R i QCs suggest that their e/a ratios (=1.70) correspond to 179 the middle of the ferromagnetic regime of the Au–Al–Gd 1/1 AC. Thus, our successful 180 synthesis of ferromagnetic QCs justifies that the magnetic phase diagram obtained for 181 ACs also holds for i QCs. This result means that we have also obtained the long-sought 182 conditions for realising various magnetic orders including antiferromagnetic i QCs. 183 Moreover, our findings have shown that the Weiss temperature (or net magnetic 184 interaction) is also tuneable for i QCs via the tuning of the e/a ratio. Consequently, the 185 quest for the first antiferromagnetic i QCs can now progress along this research line. 186 187 Ferromagnetic Au65Ga20R15 (R = Gd, Tb) i QCs are ordered solids with the 188 highest possible symmetry, i.e. icosahedral symmetry; these QCs have not been 189 synthesised previously. Hence, Au–Ga–R i QCs are the most isotropically ordered 190 magnets among all materials discovered to date. For the icosahedral point groups (I and 191 Ih), there exist six 5-fold, ten 3-fold, and fifteen 2-fold axes, and accordingly, there can 192 be 6, 10, and 15 easy axes, respectively, depending on the easy magnetisation direction. 193 The existence of such a large number of equivalent easy axes can result in significantly 194 low energy barriers between the neighbouring easy axes (as observed in cubic soft 195 magnets), which can lead to the more pronounced easy rotation of magnetic moments. 196 From the technological viewpoint, isotropic materials should exhibit zero 197 magnetocrystalline anisotropy energy, which results in low coercivity, low hysteresis loss, 198 and high permeability. For icosahedral symmetry, the magnetic anisotropy energy is only 199 associated with the higher-order terms (sixth-order and higher). In contrast, conventional 200 crystals of the highest symmetry, i.e. cubic symmetry, where the fourth-order terms are 201 nonzero, exhibit crystal anisotropy as the lower-order terms mostly contribute to the 202 magnetic anisotropy. Thus, it would be a challenging issue to eliminate the sixth-order 203 terms in the ferromagnetic i QC by tuning structural parameters via tweaking the e/a ratio 204 and/or by isovalent substitution. 205 206 Finally, our successful synthesis of ferromagnetic i QCs shows that e/a tuning is 207 effective in controlling the QC magnetism and that various exotic magnetic orders 208 reflecting quasiperiodicity and/or high global/local symmetry can now be achieved by 209 simply varying the e/a ratio. Moreover, our study opens pathways for the fundamental 210 and technological exploration of the intrinsic nature of magnetic i QCs across various 211 disciplines. 212 References 213 1. Shechtman, D., Blech, D., Gratias, D. & Chan, J. W. 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M., Al-Qadi, K., & Wang, P. Magnetic properties and 155Gd Mössbauer 282 spectroscopy of the icosahedral quasicrystal Ag50In36Gd14. J. Phys.: Condens. Matter. 283 19, 326208 (2007). 284 32. Avdeev, M., & Hester, J. R. ECHIDNA: a decade of high‐resolution neutron powder 285 diffraction at OPAL. J. Appl. Crystallogr. 51, 1597-1604 (2018). 286 Figure legends 287 Figure 1 | Atomic structure of the Tsai-type icosahedral quasicrystal. 288 a, Arrangement of the rare-earth (R) atoms viewed along a 5-fold axis. The R atoms in 289 blue (84.57% of the total R atoms) are located at the vertices of the icosahedra whereas 290 those in silver (15.43%) are situated inside the acute rhombohedra (shown at the bottom 291 of b). b, Five successive concentric clusters that form the rhombic triacontahedral 292 (RTH) cluster (top) and acute rhombohedron (bottom). The atoms in blue and silver 293 represent the same R atoms shown in a whereas those in gold and red denote Au and Ga 294 atoms, respectively. The cluster structure is illustrated based on the structure model of 295 the Cd–Yb QC2 and Au–Ga–Yb 1/1 approximant3, and the acute rhombohedron is 296 drawn based on the structure model of the Cd–Ca 2/1 approximant4. This image was 297 obtained by using the VESTA 3 program package5. 298 299 Figure 2 | Powder X-ray diffraction patterns for Au65Ga20Gd15 and Au65Ga20Tb15 300 samples. Mother alloys of various compositions near e/a = 1.70, prepared by arc- 301 melting, were subjected to rapid quenching onto a Cu wheel rotating at 4000 rpm. As 302 shown in the patterns, icosahedral quasicrystals (i QCs) are formed for Au65Ga20R15 (R 303 = Gd, Tb) compositions with e/a = 1.70. Most of the peaks are indexed as those of a 304 primitive i QC, indicating that a nearly single-phase i QC is formed for both samples. 305 The peaks denoted by the triangles are from the 1/1 Au–Ga–R approximant. The inset 306 displays selected-area electron diffraction patterns of Au65Ga20Gd15 along the (a) 2-fold, 307 (b) 3-fold, and (c) 5-fold axes, depicting the formation of an i QC. 308 309 Figure 3 | Temperature dependences of the FC and ZFC magnetic susceptibilities, 𝛘 310 = M/H, for (a) the Au65Ga20Gd15 and (b) Au65Ga20Tb15 i QCs. FC and ZFC magnetic 311 susceptibilities measured under 10 Oe are shown in the temperature range of 2–60 K. The 312 insets show temperature dependences of specific heat, Cp, for Au65Ga20R15 (R = Gd, Tb) 313 i QCs, respectively. For the Au65Ga20Gd15 i QC, a -shaped anomaly is observed at 23.1 314 K, clearly indicating a magnetic-transition occurrence, whereas a broad anomaly is 315 observed around 16 K for the Au65Ga20Tb15 i QC, suggesting the occurrence of a magnetic 316 transition. In the inset of b, the Curie temperature TC is estimated from the peak position 317 of the dCp/dT curve. 318 319 Figure 4 | (a,b,c) Powder-neutron-diffraction patterns of the Au65Ga20Tb15 i QC. 320 In a, neutron-diffraction patterns measured at the base temperature (3.5 K) and the 321 paramagnetic temperature (20 K), which are below and above TC = 16 K inferred from 322 the bulk measurements, are shown, together with the nuclear peak positions and their 323 6D indices for the i QC calculated with the 6D lattice constant a6D = 5.2966 Å. The low- 324 2 region, which contains the strongest magnetic peak from the i QC, is magnified in b. 325 Magnetic 111000 peak is clearly observed at 2 = 31.8 below TC and disappears above 326 TC, evidencing the formation of long-range magnetic order in the Au65Ga20Tb15 i QC. 327 The temperature dependence of the integrated intensity of the 111000 reflection is 328 plotted in c, in which the critical exponent fit [I ∝ (1– T/T )2C ] gives an estimate of the 329 transition temperature as TC = 16.1(3) K. 330 331 Figure 5 | Normalised Weiss temperature, 𝜣/dG, and the magnetic ground state as 332 a function of the e/a ratio. The 𝛩/dG values are plotted over a wide e/a range between 333 1.5 and 2.2 for all the R-containing Tsai-type i QCs reported to date, together with the 334 𝛩/dG values reported for the Au–Al–Gd 1/1 AC (orange circles) for comparison. The 335 magnetic ground state of the Au–Al–Gd 1/1 AC is also shown. The 𝛩/dG values of the 336 present Au–Ga–R (R = Gd, Tb) i QCs are large positive values, whereas those for the 337 previously reported i QCs are large negative values without exception. This dependence 338 of the 𝛩/dG value on the e/a ratio is in good agreement with the behaviour observed in 339 the Au–Al–Gd 1/1 AC. 340 Methods 341 Sample preparation and macroscopic measurements. Ternary (Au,Ga)85R15 (R = Gd, 342 Tb) alloys with various Au/Ga ratios were prepared by arc-melting high-purity Au 343 (99.99 wt%), Ga (99.9999 wt%), Gd (99.9 wt%), and Tb (99.9 wt%) raw elements. 344 Nominal compositions were selected to ensure that electron-per-atom ratio (e/a) was 345 close to 1.70, which corresponds to the near-centre of the ferromagnetic regime recently 346 obtained for Au–Al–Gd 1/1 ACs13. The alloys were then rapidly quenched onto a Cu 347 wheel rotating at 4000 rpm. The phase purity of the samples was examined via powder 348 X-ray diffraction (Rigaku MiniFlex 600) with Cu K radiation. Electron diffraction 349 patterns were acquired by using a JEM-2010HC (JEOL Ltd.) microscope. The magnetic 350 properties were measured by using a magnetic property measurement system (MPMS; 351 Quantum Design) in the temperature range of 2–300 K under magnetic fields up to 7 T. 352 Specific-heat measurements were performed by using a physical property measurement 353 system (PPMS; Quantum Design) via the relaxation method between 2 and 50 K. 354 355 Neutron-diffraction experiments. Neutron-powder-diffraction experiments were 356 performed by using the high-resolution powder diffractometer ECHIDNA installed at 357 the OPAL reactor28, Australian Nuclear Science and Technology Organization. Neutrons 358 with  = 2.4395 Å were selected by using the Ge 331 reflections. The powder sample 359 was loaded in a 6 mm vanadium can and then set in a closed-cycle 4He refrigerator 360 with the base temperature of 3.5 K. 361 362 Acknowledgements 363 We acknowledge and thank S. Yoshida for assistance with the neutron-diffraction 364 experiments. This work was supported by JSPS KAKENHI Grant Numbers 365 JP19H05817 and JP19H05818. 366 367 Author contributions 368 R.T. and T.J.S. designed and conducted the experiments; A.I., A.K. and S.S. synthesized 369 the samples, and performed the magnetization measurements; T.Y., T.S. and N.S. 370 performed characterization of the samples; T.F. performed specific heat measurements; 371 C.W.W., M.A., T.J.S. and A.I. performed neutron-diffraction experiments; R.T. drafted 372 the manuscript and all authors participated in the writing and review of the final draft. 373 374 Additional information 375 Correspondence and requests for materials should be addressed to R.T. or T.J.S. 376 Competing financial interests 377 The authors declare no competing financial interests. 378 379 380 Figure 1 | Atomic structure of the Tsai-type icosahedral quasicrystal. 381 a, Arrangement of the rare-earth (R) atoms viewed along a 5-fold axis. The R atoms in 382 blue (84.57% of the total R atoms) are located at the vertices of the icosahedra whereas 383 those in silver (15.43%) are situated inside the acute rhombohedra (shown at the bottom 384 of b). b, Five successive concentric clusters that form the rhombic triacontahedral 385 (RTH) cluster (top) and acute rhombohedron (bottom). The atoms in blue and silver 386 represent the same R atoms shown in a whereas those in gold and red denote Au and Ga 387 atoms, respectively. The cluster structure is illustrated based on the structure model of 388 the Cd–Yb QC2 and Au–Ga–Yb 1/1 approximant3, and the acute rhombohedron is 389 drawn based on the structure model of the Cd–Ca 2/1 approximant4. This image was 390 obtained by using the VESTA 3 program package5. 391 392 393 394 Figure 2 | Powder X-ray diffraction patterns for Au65Ga20Gd15 and Au65Ga20Tb15 395 samples. Mother alloys of various compositions near e/a = 1.70, prepared by arc- 396 melting, were subjected to rapid quenching onto a Cu wheel rotating at 4000 rpm. As 397 shown in the patterns, icosahedral quasicrystals (i QCs) are formed for Au65Ga20R15 (R 398 = Gd, Tb) compositions with e/a = 1.70. Most of the peaks are indexed as those of a 399 primitive i QC, indicating that a nearly single-phase i QC is formed for both samples. 400 The peaks denoted by the triangles are from the 1/1 Au–Ga–R approximant. The inset 401 displays selected-area electron diffraction patterns of Au65Ga20Gd15 along the (a) 2-fold, 402 (b) 3-fold, and (c) 5-fold axes, depicting the formation of an i QC. 403 30 (a) Au–Ga–Gd 2.5 23.1 K 2 23.4 K 1.5 20 1 0.5 0 0 10 20 30 40 50 10 T (K) ZFC H = 10 Oe FC 0 0 10 20 30 40 50 60 Temperature (K) 100 (b) Au–Ga–Tb 2.5 2 80 1.5 1 16 K 60 0.5 0 0 10 20 30 40 50 40 T (K) 16.0 K 20 ZFC H = 10 Oe FC 0 0 10 20 30 40 50 60 Temperature (K) 404 405 406 Figure 3 | Temperature dependences of the FC and ZFC magnetic susceptibilities, 𝛘 407 = M/H, for (a) the Au65Ga20Gd15 and (b) Au65Ga20Tb15 i QCs. FC and ZFC magnetic 408 susceptibilities measured under 10 Oe are shown in the temperature range of 2–60 K. The 409 insets show temperature dependences of specific heat, Cp. In both insets, the Curie 410 temperature TC was estimated from the peak position of the dCp/dT curve. 411  (emu/mol-Tb)  (emu/mol-Gd) 2 2 Cp/T (J/mol(Tb)K ) Cp/T (J/mol(Gd)K ) 412 (a) 413 414 415 416 417 (b) (c) 418 419 420 421 422 423 Figure 4 | (a,b,c) Powder-neutron-diffraction patterns of the Au65Ga20Tb15 i QC. 424 In a, neutron-diffraction patterns measured at the base temperature (3.5 K) and the 425 paramagnetic temperature (20 K), which are below and above TC = 16 K inferred from 426 the bulk measurements, are shown, together with the nuclear peak positions and their 427 6D indices for the i QC calculated with the 6D lattice constant a6D = 5.2966 Å. The low- 428 2 region, which contains the strongest magnetic peak from the i QC, is magnified in b. 429 Magnetic 111000 peak is clearly observed at 2 = 31.8 below TC and disappears above 430 TC, evidencing the formation of long-range magnetic order in the Au65Ga20Tb15 i QC. 431 The temperature dependence of the integrated intensity of the 111000 reflection is 432 plotted in c, in which the critical exponent fit [I ∝ (1– T/TC)2] gives an estimate of the 433 transition temperature as TC = 16.1(3) K. 434 435 436 437 Figure 5 | Normalised Weiss temperature, 𝜣/dG, and the magnetic-ground-state 438 regime as a function of the e/a ratio. The 𝛩/dG values are plotted over a wide e/a 439 range between 1.5 and 2.2 for all the R-containing Tsai-type i QCs reported to date, 440 together with the 𝛩/dG values reported for the Au–Al–Gd 1/1 AC (orange circles) for 441 comparison. The magnetic-ground-state regime of the Au–Al–Gd 1/1 AC is also shown. 442 The 𝛩/dG values of the present Au–Ga–R (R = Gd, Tb) i QCs are large positive values, 443 whereas those for the previously reported i QCs are large negative values without 444 exception. This dependence of the 𝛩/dG value on the e/a ratio is in good agreement 445 with the behaviour observed in the Au–Al–Gd 1/1 AC. Figures Figure 1 Atomic structure of the Tsai-type icosahedral quasicrystal. a, Arrangement of the rare-earth (R) atoms viewed along a 5-fold axis. The R atoms in blue (84.57% of the total R atoms) are located at the vertices of the icosahedra whereas those in silver (15.43%) are situated inside the acute rhombohedra (shown at the bottom of b). b, Five successive concentric clusters that form the rhombic triacontahedral (RTH) cluster (top) and acute rhombohedron (bottom). The atoms in blue and silver represent the same R atoms shown in a whereas those in gold and red denote Au and Gaatoms, respectively. The cluster structure is illustrated based on the structure model of the Cd–Yb QC2 and Au–Ga–Yb 1/1 approximant3, and the acute rhombohedron is drawn based on the structure model of the Cd–Ca 2/1 approximant4. This image was obtained by using the VESTA 3 program package5. Figure 2 Powder X-ray diffraction patterns for Au65Ga20Gd15 and Au65Ga20Tb15 samples. Mother alloys of various compositions near e/a = 1.70, prepared by arc-melting, were subjected to rapid quenching onto a Cu wheel rotating at 4000 rpm. As shown in the patterns, icosahedral quasicrystals (i QCs) are formed for Au65Ga20R15 (R = Gd, Tb) compositions with e/a = 1.70. Most of the peaks are indexed as those of a primitive i QC, indicating that a nearly single-phase i QC is formed for both samples. The peaks denoted by the triangles are from the 1/1 Au–Ga–R approximant. The inset displays selected-area electron diffraction patterns of Au65Ga20Gd15 along the (a) 2-fold, (b) 3-fold, and (c) 5-fold axes, depicting the formation of an i QC. Figure 3 Temperature dependences of the FC and ZFC magnetic susceptibilities, ฀ = M/H, for (a) the Au65Ga20Gd15 and (b) Au65Ga20Tb15 i QCs. FC and ZFC magnetic susceptibilities measured under 10 Oe are shown in the temperature range of 2–60 K. The insets show temperature dependences of specic heat, Cp, for Au65Ga20R15 (R = Gd, Tb) i QCs, respectively. For the Au65Ga20Gd15 i QC, a λ-shaped anomaly is observed at 23.1 K, clearly indicating a magnetic-transition occurrence, whereas a broad anomaly is observed around 16 K for the Au65Ga20Tb15 i QC, suggesting the occurrence of a magnetic transition. In the inset of b, the Curie temperature TC is estimated from the peak position of the dCp/dT curve. Figure 4 (a,b,c) Powder-neutron-diffraction patterns of the Au65Ga20Tb15 i QC. In a, neutron-diffraction patterns measured at the base temperature (3.5 K) and the paramagnetic temperature (20 K), which are below and above TC = 16 K inferred from the bulk measurements, are shown, together with the nuclear peak positions and their 6D indices for the i QC calculated with the 6D lattice constant a6D = 5.2966 Å. The low- 2θ region, which contains the strongest magnetic peak from the i QC, is magnied in b. Magnetic 111000 peak is clearly observed at 2θ = 31.8 below TC and disappears above TC, evidencing the formation of long-range magnetic order in the Au65Ga20Tb15 i QC. The temperature dependence of the integrated intensity of the 111000 reection is plotted in c, in which the critical exponent t [I ∞(1– T/TC)2β ] gives an estimate of the transition temperature as TC = 16.1(3) K. Figure 5 Normalised Weiss temperature, ฀/dG, and the magnetic ground state as a function of the e/a ratio. The ฀/dG values are plotted over a wide e/a range between 1.5 and 2.2 for all the R-containing Tsai-type i QCs reported to date, together with the ฀/dG values reported for the Au–Al–Gd 1/1 AC (orange circles) for comparison. The magnetic ground state of the Au–Al–Gd 1/1 AC is also shown. The ฀/dG values of thepresent Au–Ga–R (R = Gd, Tb) i QCs are large positive values, whereas those for the previously reported i QCs are large negative values without exception. This dependence of the ฀/dG value on the e/a ratio is in good agreement with the behaviour observed in the Au–Al–Gd 1/1 AC. Supplementary Files This is a list of supplementary les associated with this preprint. Click to download. SupplementaryInformationtamuranature.pdf