A neutron diffraction demonstration of long-range magnetic order in the quasicrystal approximant DyCd6

We have used neutron powder diffraction to demonstrate the existence of long-range antiferromagnetic order of Ising-like Dy moments in the DyCd6 quasicrystal approximant phase. This cubic compound undergoes a slight distortion to a monoclinic cell at low temperatures. The Néel temperature is 18.0(2) K and the magnetic order of the Dy sublattice may be described in the parent cubic Im3 structure using a combination of two propagation vectors, k1 = [0 0 0] and k2 = [ 2 0 1 2 ], yielding ‘anti-I’ order. Alternatively, when referred to the monoclinic C2/c cell, the magnetic structure may be described by a single propagation vector: k = [1 0 0]. © 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5079991


I. INTRODUCTION
The cadmium-rich side of most rare-earth (R) cadmium alloy phase diagrams contains RCd 6 , a 1/1 cubic approximant based on a bcc packing of interpenetrating Tsai-type icosahedral clusters. 1 These clusters are the building blocks of two remarkable families of thermodynamically stable binary quasicrystalline rare-earth containing phases: YbCd5.7 2 and RCd7.5 (R = Gd -Tm, Y) 3 that lie either side of the cubic RCd 6 phase. Together, these three systems provide an invaluable window onto the properties of quasicrystalline materials. As stable binary compounds they greatly simplify preparation and structural analysis. The presence of large, local-moment rare-earths opens the possibility of studying magnetic ordering in a quasiperiodic environment -is long-ranged magnetic order compatible with such structures? 4 The existence of periodic approximant phases that are close both in structure and composition means that almost-direct comparisons can be made between the behaviour of a periodic and a quasiperiodic compound.
Perhaps surprisingly, the properties of the RCd 6 compounds are quite complex, with most undergoing a structural change from cubic to monoclinic near 170 K 5 and many exhibiting multiple features in heat capacity (Cp) and susceptibility (χ) at much lower temperatures that likely reflect magnetic ordering. 5 Indeed, the sharp nature of the features in Cp and χ 1,5,6 have been interpreted as evidence for long-ranged magnetic order rather than the spin-glasslike behaviour observed in most other quasicrystalline systems. 4 The rather large neutron absorption cross-section of natural cadmium has discouraged direct searches for long-ranged magnetic order in the RCd 6 system by neutron diffraction, however x-ray resonant magnetic scattering (XRMS) has been used to demonstrate that both TbCd 6 7 and HoCd 6 8 adopt long-ranged antiferromagnetic structures below their respective Néel temperatures of 24 K and 8.5 K.
Here we present a neutron powder diffraction study of a DyCd 6 sample prepared using natural cadmium and employing a largearea flat-plate technique 9 to reduce the impact of absorption by ARTICLE scitation.org/journal/adv cadmium. We find that below TN=18 K, DyCd 6 is antiferromagnetically ordered in a structure that breaks the body centering symmetry of the underlying bcc crystal structure such that dysprosium moments associated with the cube-corner clusters are coupled antiparallel to those associated with the cube-centre clusters. The magnetic diffraction peaks show no additional broadening relative to the nuclear Bragg peaks, indicating that the magnetic correlations are at least long-ranged. These results are fully consistent with the earlier XRMS data on TbCd 6 7 and HoCd 6 . 8

II. EXPERIMENTAL METHODS
The DyCd 6 sample was prepared at Ames Laboratory using the method outlined by Das et al. 10 CuKα x-ray diffraction confirmed the single-phase nature of the sample with the body-centred cubic Im3 (#204) space group. Magnetic characterization was carried out on a Quantum Design Magnetic Properties Measurement System (MPMS) equipped with a 9 T magnet and operated down to 1.8 K.
The crystal structure of RCd 6 is cubic Im3 (#204) at ambient temperatures. Dy occupies the 24g site while Cd occupies several sites (12d, 12e, 16f, 24g (×3) and 48h). 5 It is known that this structure undergoes a slight distortion to a low temperatures monoclinic C2/c (#15) cell with unit cell sides of The monoclinic angle is far too close to 90 ○ for us to be able to resolve it in our neutron powder diffraction experiments, so the material was treated as effectively cubic for most of our analysis.
Neutron diffraction experiments were carried out on the C2 800-wire powder diffractometer (DUALSPEC) at the NRU reactor, Canadian Neutron Beam Centre, Chalk River, Ontario. Temperatures down to 3 K were obtained using a closed-cycle refrigerator. The neutron wavelength was 2.3722(17) Å. The sample consisted of 1.78 grams of fine powder (obtained by hand grinding single crystals under hexane, to protect from oxidation) spread on a singlecrystal silicon plate. 9 All refinements of the neutron diffraction patterns employed the FullProf/WinPlotr package. 11,12 Both elements, Dy and Cd, are strongly neutron-absorbing and this fact, coupled with the effectively cubic symmetry of our powder samples, placed severe limitations on the amount of useful information that could be extracted from a simple neutron powder diffraction experiment. For these reasons, we concentrate herein on our Le Bail 13 ("profile matching") fits to the diffraction patterns since our aim is to present irrefutable evidence for the existence of long-range magnetic order in the DyCd 6 quasicrystal approximant. Figure 1 shows the complete diffraction patterns obtained at 25 K (well above TN) and at 3K (well below TN) for DyCd 6 . The two very strong peaks at 50 ○ ≤ 2θ ≤ 60 ○ are due to the sample mount. Comparison of the two patterns shows that the magnetic scattering is stronger than the nuclear scattering over a wide angle range. The difference patterns at the bottom of Figure 1 show how extensive the magnetic signal is. Many of the magnetic peaks are clearly at nuclearforbidden positions suggesting that the magnetic structure breaks the I-centering symmetry of the Im3 nuclear structure.

FIG. 1.
Neutron diffraction patterns of DyCd 6 measured in the magnetically ordered state at 3 K (top, blue) and above the magnetic transition at 25 K (middle, green). Several strong magnetic peaks are evident in the 3 K pattern. The extensive array of magnetic Bragg peaks is emphasised in the difference patterns (bottom, red and magenta) where it is clear that significant magnetic scattering extends past 2θ=60 ○ . The two very strong peaks at 50 ○ ≤ 2θ ≤ 60 ○ are due to the sample mount.
Tracking the intensity of the first three (and best isolated) magnetic peaks in Figure 1 at 2θ ∼ 6 ○ , 9 ○ and 11 ○ allows us to determine TN and also to look for anomalies that might signal the presence of additional transitions. Figure 2 shows that a simple J= 1 2 squared Brillouin function fits the temperature dependence of the three peaks very well, yielding an average TN of 18.0(2) K, consistent with the 17.8 K reported by Mori et al. 5 The fact that a J= 1 2 function works best indicates that the local anisotropy at the Dy sites is strong enough to render the moments essentially Ising-like in DyCd 6 . Finally, we see no evidence for significant breaks in the behaviour that would indicate additional transitions, in agreement with earlier conclusions based on Cp and χ data. 5 Given the weakness of the monoclinic distortion, we evaluated our diffraction patterns in terms of the cubic Im3 structure. At 3 K, we observed strong magnetic contributions at 2θ = 6.25 ○ and 8.85 ○ , indexed as the purely magnetic ( 1 2 0 1 2 ) and (100). To account for these, and other peaks in the magnetic diffraction pattern, within the Im3 space group, we require two propagation vectors to describe the antiferromagnetic order: k1 = [0 0 0] and k2 = [ 1 2 0 1 2 ], yielding 'anti-I' order. We can also describe this same magnetic order in terms of the low-temperature monoclinic group C2/c (#15) and in this case only a single propagation vector, k1 = [1 0 0], is required.
In Figure 3 we show Le Bail fits to the 25 K and 3 K neutron powder diffraction patterns of DyCd 6 . As mentioned above, the effect of the magnetic ordering of the Dy is immediately apparent in the 3 K pattern, especially with the intense, purely magnetic AIP Advances  peaks at 2θ ∼ 6 ○ , 9 ○ , 11 ○ . At 25 K, the lattice parameter (referred to the cubic cell) is 15.380(1) Å, decreasing slightly to 15.343(1) Å at 3 K. In our analysis, the magnetic and nuclear Bragg peaks shared a common profile function, indicating that the magnetic peaks are resolution limited and that the magnetic order observed here is long-ranged. The deduced antiferromagnetic structure of DyCd 6 is fully consistent with those reported for TbCd 6 7 and HoCd 6 8 based on XRMS.

IV. CONCLUSIONS
We have used neutron powder diffraction to show unequivocally that the quasicrystal approximant phase DyCd 6 exhibits longrange antiferromagnetic order below a Néel temperature of 18.0(2) K. The magnetic structure is described by the propagation vectors k1 = [0 0 0] and k2 = [ 1 2 0 1 2 ], when referred to the parent cubic Im3 structure, or k1 = [1 0 0] when referred to the lowtemperature monoclinic C2/c structure. Local anisotropy at the Dy sites is strong enough to render the moments essentially Ising-like in DyCd 6 .