Single-crystal neutron diffraction study on the Ho 13.6 Au 61.1 Al 25.3 quasicrystal approximant

A single-crystal neutron diffraction study was conducted on a Ho 13


Introduction
The atomic structure of quasicrystals (QCs) and its consequences on magnetic ordering has been a long-standing topic of interest due to the unusual aperiodic structure, where a spin glass state is most often found at low temperature [1] in RE-Cd samples (RE = Gd-Tm).However, recent studies of quenched QCs in the RE-Au-Ga systems (RE = Gd and Tb) have exhibited long-range order [2,3].Approximant crystals (ACs) that form with a composition close to their related quasicrystals have similar building units but are arranged in a periodic manner.Amidst the family of quasicrystals and approximants, categorised by their polyhedral clusters, we focus on Tsai-type icosahedral quasicrystals (i-QC) and their approximants, which are more widely available and have been subject to extensive study compared to the other two types of QCs, namely Bergman [4,5] and Mackay [6,7].Tsai-type QCs and ACs consist of four concentric atomic shells possessing icosahedral symmetry, surrounding either a tetrahedron or a rare earth atom at the cluster centre [8,9].They have garnered significant interest as they have exhibited phenomena such as quantum criticality [10], superconductivity [11,12], magnetocaloric effect [13,14], and their non-coplanar spin configuration could make them of interest to investigate spin chirality phenomena [15].A long-range magnetic ordering was first reported in an i-QC RE-Au-Ga (RE = Gd and Tb) system by R. Tamura et al. [2] through bulk magnetic measurements.However, the quenched samples have small grain sizes and are metastable, preventing macroscopic grains suitable from being synthesized.The presence of a secondary AC phase mixed with them further complicates any investigation of their magnetic structure by neutrons.Very recently a phase pure ferromagnetic Dy-Au-Ga i-QC with a tunable Au/Ga ratio was also reported [3].On one hand, it is worth noting that advancements in the analysis methods are essential to determine the complex magnetic structure of quasicrystals through neutron diffraction and may become successful.On the other hand, Tsai-type 1/1 approximants have also captured significant attention owing to their experimentally observed non-trivial magnetic ground states [16][17][18].The first long-range magnetic ordering in a Tsai-type 1/1 approximant was observed in a binary Cd 6 Tb system in 2010 [19].The magnetic structure of Cd 6 Tb could not be elucidated due to the low-temperature structural phase transition in the system [20].The studies were then extended to ternary 1/1 approximants of Au and rare-earth containing Tsai-type systems resulting in the observation of long-range magnetic ordering in RE-Au-Al (RE = Gd and Tb) [21,22], RE-Au-Si (RE = Gd, Tb, Dy and Ho) [23,24], and RE-Au-Ga (RE = Eu and Tb) [25,26] systems.However, magnetic structure determination has been performed only for a handful of approximant systems; RE-Au-Si (RE = Tb and Ho) [18], Tb-Au-Ga [26,27] and Tb-Au-Al [17,28].All these systems exhibit a non-collinear non-coplanar whirling spin order around the 3-fold symmetry direction in the icosahedral cluster with the ferrimagnetically and antiferromagnetically ordered ones having R3 [18]and I p mʹ3ʹ [28] magnetic space groups respectively.A non-coplanar ferrimagnetic ordering is observed for the studied compositions of RE-Au-Si (RE = Tb and Ho) whilst both ferrimagnetic and antiferromagnetic ordering was observed for the Tb-Au-Ga system.In the RE-Au-Al system, the only two compositions studied for the Tb-Au-Al system exhibit non-coplanar antiferromagnetic ordering.It should be noted that the term ferrimagnetic ordering in the approximant systems, means that they exhibit non-zero magnetisation in the magnetic field-dependent magnetisation data and the magnetic structure has spins arranged in the icosahedral cluster that do not cancel exactly each other.To the best of our knowledge, there is no reported study of a ferrimagnetic 1/1 approximant in the RE-Au-Al system so far.Hence it is significant to study a system in the region of ferrimagnetic ordering in the recently established magnetic phase diagram of a RE-Au-Al system (RE = Gd) [21].This study will help to gain a better understanding of the general magnetic behaviour of 1/1 approximants and how it varies with different chemical compositions.Studies on Gd-Au-Al by Ishikawa et al. [21] demonstrated that the RE-Au-Al system is intriguing due to its composition-dependent magnetic ordering.They observed that with an increase of z in the Au z Al 1-z nonmagnetic elements ratio, the system changes from spin glass, to ferromagnetic, then to antiferromagnetic ordering.The dependence of the Curie-Weiss temperature θ CW on the Au/Al ratio is explained by the dependence of Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, the dominant type of magnetic interaction present in the approximants intermetallics, whose intensity depends on the Fermi wave number k F and the distance r between magnetic ions.A very recent study on the Gd-Au-Al system by Huang et al. [29] has shown that it is not only the valence electron concentration (number of valence electrons per atome/a) that is responsible for the change in magnetic ordering but also the non-random mixing of non-magnetic Au and Al atoms surrounding the magnetic RE atoms which distorts the magnetic icosahedra.Hence this study will also help in a better understanding of how the structural changes affect the magnetism in approximants since this particular composition of Ho-Au-Al AC has not been studied before in any other approximant system.
In this study, we report the magnetic properties of the Ho 13.6 Au 61.1 Al 25.3 (HAA) Tsai-type 1/1 approximant.DC magnetization measurements reveal a ferrimagnetic-like ordering with a transition temperature T c ~6 K. Single-crystal neutron diffraction measurements confirm the presence of long-range order, giving rise to a non-coplanar whirling spin configuration around the crystallographic [1 1 1] direction in the icosahedral cluster.The magnetic structure of the present Ho 13.6 Au 61.1 Al 25.3 approximant is compared to the previously published magnetic structures in the RE-Au-SM (RE = Tb and Ho; SM = Al, Si and Ga) systems.

Synthesis and characterisation
Approximant crystal of starting composition Ho 8 (Au 60 Al 30 ) 92 was prepared using self-flux synthesis method, with conditions similar to previous reports [30], to synthesise large single crystal grains of quasicrystal approximants.Granules of Ho (99.99 %), Au (99.99 %) and Al (99.9999 %) purchased from ChemPur were used as raw materials.The synthesis reaction involves a pseudo-binary alloy using RE and Au x- Al 100-x (x = 67) as reactants.To obtain the Au x Al 100-x alloy, Au and Al were melted three times in an arc-melting chamber to ensure a homogeneous melt.The rare earth element, Ho, was weighed in an Argon-filled glove box and transferred to an Alumina crucible containing the weighed precursor alloy, Au x Al 100-x .The Alumina crucible was sealed inside a stainless-steel ampoule using arc welding in an Ar atmosphere and annealed in a multi-step programmable furnace.A temperature program tuned based on DSC measurement of a similar sample (Gd-Au-Al) [29] was employed to get the desired phase of the Ho-Au-Al approximant.After the heat treatment, the AC was centrifuged to separate the single crystal from the melt flux.A single crystal large enough for neutron diffraction measurements was obtained by this method, see the inset of Fig. 1(b).The chemical composition of the single crystals was confirmed by energy dispersive X-ray spectroscopy (EDX) measurements [31].Powder X-ray diffraction (PXRD) measurements were performed on a D8 Bruker diffractometer with Cu-Kα radiation (Kα1 = 1.540598Å and Kα2 = 1.544390Å) and the single-crystal X-ray diffraction (SCXRD) measurements were carried out on a D8 venture single-crystal diffractometer with Mo-Kα radiation (Mo-Kα = 0.71073 Å), both, at room temperature.The phase purity was confirmed through PXRD measurements.SCXRD measurements further confirmed the space group to be Im3, and the compound was classified as a 1/1 Tsai-type quasicrystal approximant [31].In this structure, the icosahedral cluster is exclusively occupied by Ho atoms, while the remaining clusters and the inner disordered tetrahedron are occupied by Au/Al atoms or their mixed sites.
The magnetic susceptibility measurements were performed in a MPMS XL SQUID magnetometer from Quantum Design Inc. on single crystal of Ho 13.6 Au 61.1 Al 25.3 .The Zero-field cooled (ZFC) and field cooled (FC) dc magnetic susceptibility was acquired between 2 and 20 K at a fixed field of 1 mT, and between 2 and 300 K in 500 mT for the Curie-Weiss analyses.
Single crystal neutron diffraction was performed on HAA at the D9 beamline in Institute Laue Langevin (ILL).D9 diffractometer was operated in the four-circle configuration equipped with the self-dedicated low-temperature displex.A Cu monochromator using the (220) planes provides hot neutrons of a wavelength of 0.83 Å, and the λ/2 contribution was filtered out with a Er filter.The crystal was aligned in the hk0 plane using Orient Express, a Laue neutron diffractometer at ILL.Two datasets were collected for the sample, one above the magnetic transition temperature, at 20 K and the other below, at 2 K.The data was collected in the reciprocal lattice in the index range 0 < h < 20, 0 < k < 20, and − 20 < l < 0. Nuclear and magnetic structure refinements were performed using the software package JANA2006 [32].Only the reflections with intensity, I > 3 σ(I) were used for the nuclear and magnetic structure refinements.

Magnetisation
Fig. 1(a) shows the temperature dependence of DC magnetisation of HAA.The zero field-cooled and field-cooled curves measured under a magnetic field of 1 mT are reminiscent of those observed in the Tb-Au-Si systems [8] and suggest a ferrimagnetic transition below 6 K.The inverse magnetic susceptibility data collected in a larger field obeys the Curie-Weiss law at high temperatures and can be fitted with a straight line (Inset of Fig. 1(a)) to extract the effective magnetic moments per Ho atom.We obtained a value of p eff = 10.75 μ B , which is close to the theoretical magnetic moment of Ho 3+ ions (g calculated from Hund's rule of maximum multiplicity, indicating that the Ho ions are well localized on the icosahedral vertices.The Curie-Weiss temperature (θ CW ) obtained from the fit is +3.75 K.A positive value of Weiss temperature indicates that the dominant interaction is ferromagnetic.The transition temperature being close to the Curie-Weiss temperature indicates that the system has little to no magnetic frustration.The magnetic field dependence of magnetisation measured at 2 K (Fig. 1(b)) shows a ferrimagnetic-like behavior for HAA, with a step increase for magnetic fields ~500 mT followed by a milder slope in higher fields.The magnetisation at 5 T corresponds to only about 7μ B /Ho, lower than the expected theoretical value of gJ = 10 μ B K.K. Thilakan et al.
per Ho.The absence of saturation may be related to the complex magnetic structure of HAA.

Single crystal neutron diffraction
The nuclear structure of Ho 13.6 Au 61.1 Al 25.3 was determined from the Bragg intensities collected at 20 K in the paramagnetic phase using the charge-flipping method in JANA2006.The obtained structure is similar to the structure of 1/1 Tsai-type approximants previously reported in the RE-Au-SM (RE = Gd, Tb and Ho, SM = Si and Al) systems [8,29].To avoid redundancy, only a short description is presented here.The nuclear structure has the Im3 space group and can be represented as interpenetrating Tsai cluster building units arranged in a bcc cubic structure.Tsai clusters comprise a tetrahedron at the centre surrounded by four polyhedral cluster shells: a pentagonal dodecahedron, an icosahedron, an icosidodecahedron, and a rhombic triacontahedron, see Fig. 2. The inner tetrahedron is disordered at 20 K, therefore the average structure obtained from neutron diffraction reveals each site of the tetrahedron is divided into three distinct sites, with each showing an occupancy of one-third [33].The Ho atoms are only present at the vertices of the icosahedral shell.There was no sign of rare-earth substitution at the cluster centre (0 0 0) in the current HAA sample from the observed electron density map.Such substitution at the cluster centre has so far been observed only in the RE-Au-SM (RE = Ho, Tb, Yb and Gd; SM = Si and Ge) systems [18,30,34].The nuclear structure observed for the current HAA compound agrees with the atomic structure obtained from single crystal X-ray diffraction measurement.The detailed results from the X-ray diffraction measurements will be presented elsewhere [31].
When cooling below 5 K, an intensity increase was observed for some nuclear reflections, indicating long-range magnetic order in the sample.The Bragg intensities collected at 2 K were used to obtain the magnetic structure of HAA.During the cooling process, the intensities of three reflections were measured between 7 K and 2 K at intervals of approximately 0.25 K to determine the magnetic transition temperature, T c .Fig. 3 displays the temperature dependence of the intensity for three reflections: (2 0− 2), (0 6− 10), and (0 8 0).The intensities of these reflections begin to increase at around 5.5 K, which is in agreement with the magnetization data indicating a magnetic transition below 6 K.The three reflections that have been selected exhibit a substantial magnetic contribution and a minor nuclear contribution to the Bragg intensities.Due to the relatively short wavelengths used, strong magnetic reflections such as (2 1 0) and (1 2 0) are too close to the direct beam and could not be collected.These reflections are usually observed in other RE-Au-SM (SM = Si and Al) systems as the signature reflections of whirling spin order [16,28].
The intensity increase was observed at the nuclear Bragg peak positions below 5.5 K and no additional magnetic reflections were observed.This suggests that the magnetic unit cell and the nuclear unit  cell are the same and the magnetic propagation vector, k = (0, 0, 0).The observed reflections obey the reflection condition, h + k + l = 2 n (n = integer).No reflections with the condition h + k + l = 2 n + 1 were observed.This suggests that the body centring symmetry of the nuclear structure is retained for the magnetic structure.
The nuclear structure model (Im3 space group) refined from the 20 K Bragg intensities was used as the magnetic parent structure.Based on the magnetic space group analysis incorporated in JANA2006 [32], the space group R3 was selected for refining the magnetic structure.The refinement resulted in the lowest R factors and a good agreement between calculated and observed structure factors was obtained, see Fig. 4. Table 1 summarizes the results of the refinement of data collected at 20 K and 2 K.The unique reflections at 20 K in Table 1 represent the number of reflections obtained after applying symmetry averaging for the Im3 space group in JANA2006.However, for the 2 K data, the symmetry restriction was not applied when generating the reflection file for refinement, resulting in a difference in the number of reflections for the 20 K and 2 K refinements in Table 1.In the refinement of the magnetic structure, cubic constraints were imposed on the atomic positions, while the magnetic moments were refined independently for the two distinct sites resulting from rhombohedral symmetry.The refinement at 2 K involved fewer parameters compared to that at 20 K, as the atomic displacement parameters were fixed for the former.The 1/1 Tsai-type approximants in the RE-Au-SM (RE = Tb and Ho; SM = Si and Ga) have been observed to have R3 magnetic space groups in the previously published results [18,27] below their magnetic transition temperatures.The magnetic structure of HAA contains two independent Ho sites, Ho_1 and Ho_2 with slightly different magnetic moments.The magnitude of refined magnetic moments and their uncertainties for each site are given in Table 2.The value of refined magnetic moments is close to the theoretical magnetic moment of Ho 3+ (gJ µ B = 10 µ B ).Note that magnetic domains are formed due to the magnetic structure having a space group with lower symmetry than the nuclear structure with the number of domains equivalent to the number of symmetry operations lost during the transformation.The symmetry operators that define the relative orientations of the magnetic domains are presented in a previously published result [18].The refined volumes of magnetic domains are listed in Table 3.
The magnetic structure revealed from the neutron diffraction measurements shows a typical bcc arrangement of RE icosahedral clusters of a Tsai-type 1/1 approximant, see Fig. 5(a).The arrangement of spins in a single icosahedral cluster and the whirling spin order around the crystallographic [1 1 1] direction are depicted in Fig. 5(b) and (c) respectively.The two independent moments of Ho are represented in dark green (Ho_1) and red (Ho_2) colour (Fig. 5).The orientation of the magnetic moments slightly deviates from a magnetic structure having the spins pointing along the cubic axes [18] (a, b or c) depending on the RE site.The sublattice of the Ho_1 moment points along the crystallographic axis while the sublattice of the Ho_2 moment has a small angular shift.The Ho moments are observed to have a non-collinear non-coplanar whirling spin order around the crystallographic [1 1 1] direction in the icosahedral cluster with a ferrimagnetic spin arrangement.The magnetic structure of HAA agrees with the structure first proposed by Hiroto et al. for the Tb-Au-Si approximant with a non-collinear non-coplanar ferrimagnetic ordering of magnetic moments [16].
Non-coplanar ferrimagnetic ordering has been observed for several compositions of Tsai-type 1/1 approximants in the RE-Au-SM system (RE = Tb and Ho and SM = Si and Ga) [16,18,26,27].Among the RE-Au-based approximant systems, the RE-Au-Si (RE = Tb and Ho) system is particularly interesting since the cluster centre tetrahedron can be partially/fully replaced with a single moment-bearing RE atom [8,9].The incorporation of a magnetic atom at the cluster centre is found to affect the orientation of magnetic moments at the icosahedral vertices in the Tb-Au-Si compounds [18], as well as adding magnetic frustration in the system, leading to glassy dynamics [15].The magnetic spin arrangement of the present compound Ho 13.6 Au 61.1 Al 25.3 is similar to that observed in the Ho 14.7 Au 68.7 Si 16.6 referred to as HAS(52) with the value inside the parenthesis representing the percentage of RE at the  cluster centre replacing the inner tetrahedron atoms.For the present Ho 13.6 Au 61.1 Al 25.3 , the magnetic moments at the icosahedral vertices are pointing almost along the crystallographic axes in each mirror plane similar to that observed in HAS(52) but slightly different for Tb 13.6 Au 65.6 Si 20.8 referred to as TAS(0) and Tb 13.9 Au 69.9 Si 16.2 referred to as TAS (14).There is a clear angular shift for the Tb moments at the icosahedral vertices of TAS( 14) when compared to the Ho-based compounds.It can be also noted that for the Tb-compounds TAS(0) and TAS (14), the moments tend to be perpendicular to the pseudo five-fold (5 f) axis (all axes passing from the centre of the icosahedral cluster to the icosahedral vertices [16]) while in Ho compounds-HAS(52) and HAA, even though the moments are tilted away from the pseudo 5 f-axis, they are not perpendicular to this direction.Here, we can see that the easy-axis anisotropy of Ho moments is the same for HAA and HAS(52), pointing slightly away from the pseudo 5 f-axis in the icosahedron.The main difference between the HAS(52) approximant and the Ho 13.6 Au 61.1 Al 25.3 approximant is in the magnitude of magnetic moments at the icosahedral vertices.The observed magnetic moments for the HAA are between 9.1 and 9.2 µ B at 2 K while for HAS(52) it was between 7.71 and 7.74 µ B at 2 K.The magnetic moment at the cluster centre of HAS( 52) is rather quenched with a value close to zero.The magnitude of magnetic moments for HAA is much closer to the theoretical value of a free Ho 3+ magnetic moment.The decrease in magnetic moment for the HAS(52) sample is attributed to the measurement temperature (2 K) being close to the transition temperature (T c = 3 K), since the moments would not be completely aligned at this temperature.
Previously studied magnetic structures in the RE-Au-Al system of Tb 14 Au 72 Al 14 and Tb 14 Au 70 Al 16 AC compounds exhibit complex AFM ordering, different from the unidirectional AFM ordering observed in conventional crystals [17,28].The Tb moments are antiparallelly arranged on opposite vertices within a single icosahedral cluster, resulting in a net zero moment, but otherwise appear to align along loops.The ferrimagnetically ordered Ho 13.6 Au 61.1 Al 25.3 approximant and the antiferromagnetically ordered Tb 14 Au 72 Al 14 approximant possess a non-coplanar whirling spin ordering around the [1 1 1] direction in the icosahedral shell.We get an antiferromagnetic arrangement of spins in the icosahedral cluster if half of the spins of the ferrimagnetically ordered cluster are inverted.The comparison of magnetic moment arrangement in the icosahedral clusters of FM Ho 13.6 Au 61.1 Al 25.3 and AFM Tb 14 Au 72 Al 14 is shown in Fig. 6.
A whirling spin arrangement of magnetic moments around the 3-fold direction in the icosahedral shell was also observed for the recently determined magnetic structures of the Tb-Au-Ga 1/1 approximants [26,27].The ordered moment direction for the antiferromagnetic Tb 14 Au 72 Al 14 and Tb 14 Au 65 Ga 21 and the ferrimagnetic Tb 14 Au 60 Ga 26 is almost perpendicular to the pseudo 5 f-axis.The e/a ratio of the present HAA sample and the Tb 14 Au 60 Ga 26 sample have the same value of 1.8.This is also true for the case of HAS(52) as the e/a value is 1.79.Even though the e/a value is similar and these three compounds exhibit non-coplanar ferrimagnetic ordering, the orientation of magnetic moments in the icosahedral cluster is different for Ho-based compounds from the Tb-based ones.This can be attributed to the difference in the chemical composition and potentially magnetic anisotropy induced by crystal electric field effects [35].

Conclusion
Single crystal neutron investigation on the Tsai-type 1/1 quasicrystal approximant Ho 13.6 Au 61.1 Al 25.3 , revealed a non-coplanar whirling spin order around the crystallographic [1 1 1] direction with a ferrimagnetic arrangement of spins in the icosahedral cluster.The magnetisation measurements show a ferrimagnetic behaviour in the temperature and field-dependent data.The magnetic moments obtained from the singlecrystal neutron diffraction measurements and the magnetization data closely agree with each other.The nuclear structure crystallizes in the space group Im3 similar to the Tsai type 1/1 approximants.The magnetic structure has a space group of R3 similar to the ferrimagnetically ordered approximants in the RE-Au-SM (RE = Tb and Ho; SM = Si and Ga) system.The orientation of magnetic moments in the Ho 13.6 Au 61.1 Al 25.3 approximant is similar to a previously reported Ho 14.7 Au 68.7 Si 16.6 (HAS(52)) approximant which has a non-coplanar ferrimagnetic ordering with ordered moments pointing slightly away from the pseudo 5 f-axis.whirling AFM of the Tb 14 Au 72 Al 14 [17] with the magnetic space group I p mʹ3ʹ.

Fig. 1 .
Fig. 1.(a) ZFC and FC magnetisation as a function of temperature in an applied magnetic field of 1 mT.The inset shows the inverse magnetic susceptibility (1/χ) with a diamagnetic constant (χ 0 = − 7.66 × 10 − 9 ) subtracted as a function of temperature.The blue line is the fit to the Curie-Weiss law.(b) Magnetisation as a function of the applied magnetic field measured at 2 K.The insets show the single crystal of HAA (left) and close-up view of the low field region (right).

Fig. 5 .
Fig. 5. (a) Body-centered arrangement of RE (Ho) icosahedra in the structure.(b) The arrangement of refined magnetic moments in a single icosahedral cluster and (c) an icosahedral cluster with Ho magnetic moments viewed from the [1 1 1] direction.The orange line represents the 3-fold symmetry axis.

Fig. 6 .
Fig. 6.Icosahedral shell at the body centre and one of the vertices showing (a) whirling FM order of the Ho 13.6 Au 61.1 Al 25.3 with the magnetic space group R3 and (b)whirling AFM of the Tb 14 Au 72 Al 14[17] with the magnetic space group I p mʹ3ʹ.

Table 1
Results of nuclear and magnetic structure refinement of Ho 13.6 Au 61.1 Al 25.3 .

Table 2
Refined magnetic moments of HAA in Bohr magnetons (µ B ) from the refinement.

Table 3
Refined magnetic domain volumes of HAA.