Charge density wave behavior and order-disorder in the antiferromagnetic metallic series Eu(Ga_1-xAl_x)_4
Macy Stavinoha, Joya A. Cooley, Stefan G. Minasian, Tyrel M. McQueen, Susan M. Kauzlarich, C.-L. Huang, E. Morosan
CCharge density wave behavior and order-disorder in the antiferromagnetic metallicseries Eu(Ga − x Al x ) Macy Stavinoha , Joya A. Cooley , Stefan G. Minasian , Tyrel M.McQueen , , , Susan M. Kauzlarich , C.-L. Huang , and E. Morosan , Department of Chemistry, Rice University, Houston, TX 77005 USA Department of Chemistry, University of California, Davis, CA 95616 USA Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA Institute for Quantum Matter and Department of Physics and Astronomy,The Johns Hopkins University, Baltimore, Maryland 21218 USA Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218 USA Department of Materials Science and Engineering,The Johns Hopkins University, Baltimore, Maryland 21218 USA Department of Physics and Astronomy, Rice University, Houston, TX 77005 USA (Dated: April 9, 2018)The solid solution Eu(Ga − x Al x ) was grown in single crystal form to reveal a rich variety of crys-tallographic, magnetic, and electronic properties that differ from the isostructural end compoundsEuGa and EuAl , despite the similar covalent radii and electronic configurations of Ga and Al.Here we report the onset of magnetic spin reorientation and metamagnetic transitions for x = 0 − T N changesnon-monotonously with x , and it reaches a maximum around 20 K for x = 0.50, where the a latticeparameter also shows an extreme (minimum) value. Anomalies in the temperature-dependent resis-tivity consistent with charge density wave behavior exist for x = 0.50 and 1 only. Density functionaltheory calculations show increased polarization between the Ga − Al covalent bonds in the x = 0.50structure compared to the end compounds, such that crystallographic order and chemical pressureare proposed as the causes of the charge density wave behavior. I. INTRODUCTION
The interplay of structural, magnetic, and electronicproperties of rare earth based intermetallics often resultsin emergent phenomena and competing ground states,such as unconventional superconductivity, heavy fermionbehavior, intermediate valence, and quantum criticality. Particularly, pressure, magnetic field, or chemical dopingin Ce and Yb compounds in their magnetic or nonmag-netic sublattices has been extensively used to tune thebalance between their versatile ground states.
Com-paratively less work has been done to explore the ef-fects of pressure or doping in Eu-based intermetallics,even though Eu presents similar opportunities to tunethe ground state through valence fluctuations betweenmagnetic Eu and nonmagnetic Eu ions. In thisstudy, we explored the effects of isovalent doping in theEu(Ga − x Al x ) series, motivated by the wide range ofapparently conflicting results observed when tuning theproperties of the end compounds EuGa and EuAl .Previous studies on single crystals of the stoichiomet-ric compounds EuGa and EuAl revealed that the twoshow similar magnetic behavior, with antiferromagnetic(AFM) ordering and very similar Ne´el temperatures T N = 15 K and 15.4 K, respectively. The compounds areisostructural, forming in a tetragonal crystal structureconsisting of two distinct transition metal sites, form-ing a covalently-bound anionic framework with divalentbody-centered cations. The structural and magnetic sim-ilarities between these two compounds may be easily un-derstood considering the chemical similarities of Ga and Al: they are isovalent, with very close covalent radii of1.22 ˚A and 1.21 ˚A, respectively. However, drastic dif-ferences have also been noted with either doping or ap-plied pressure, which cannot be readily explained. Whileno evidence for mass renormalization has been reportedin EuAl , electrical resistivity measurements have sug-gested heavy fermion behavior in EuGa . At ambientpressure, a plausible charge density wave (CDW) wasreported in the former compound below T ∗ = 140 K,and increasing pressure suppressed T ∗ to zero for p =2.5 GPa. However, in the latter compound, a plausi-ble CDW is observed only under applied pressure, with T ∗ = 105 K for p = 0.75 GPa, which subsequently in-creased to 160 K for p = 2.15 GPa. Doping Eu M ( M = Ga or Al) on either the magnetic (Eu) or nonmag-netic ( M ) sublattice has also shown notable changes inthe magnetic, electronic, and crystallographic properties.When Eu is substituted by Yb in (Eu . Yb . )Ga , T N is suppressed to 13 K. By comparison, doping EuGa in the nonmagnetic sublattice has shown that the AFMorder is suppressed down to T N = 9.6 K and 6.3 Kin polycrystalline Eu(Ga − x A x ) (A, x ) = (Mg,0.14) or(Li,0.18), respectively. In contrast, EuAl doped withSi resulted in ferromagnetic (FM) order below T C =17 Kin Eu(Al . Si . ) . The versatile interplay between spin, charge, and or-bital degrees of freedom in Eu M motivates the currentsystematic study of the solid solution between the Ga andAl end compounds in the series Eu(Ga − x Al x ) with x =0 to 1. Such a substitution should minimize the chemicaleffects brought about by doping, since replacing Ga with a r X i v : . [ c ond - m a t . s t r- e l ] A p r isoelectronic and similarly-sized Al does not change theelectron count or the volume of the unit cell (and hencethe chemical pressure). Thermodynamic and transportmeasurements on Eu(Ga − x Al x ) single crystals revealstrong correlations between the structural, magnetic, andelectronic properties. The compounds remain tetragonalwith space group I /mmm at room temperature for thewhole doping range, with Ga and Al preferentially occu-pying one or the other of the two transition metal ele-ment sites. Remarkably, for x = 0.50, the two transitionmetals fully separate into two sublattices and form anordered structure EuGa Al with a minimum unit cellvolume in the series. This, in turn, favors the occur-rence of a plausible CDW state at ambient pressure at T ∗ = 51 K, while T N is maximum in this composition at ∼
20 K. These results should be contrasted with thosefrom isoelectronic doping (Ca or Sr ) or hole doping(La ) in EuGa on the magnetic sublattice, where insome cases structural distortions preclude the occurrenceof a CDW transition down to 2 K. II. EXPERIMENTAL METHODS
Single crystals of Eu(Ga − x Al x ) were grown using aself-flux technique. Elemental metals were assembled inalumina crucibles with a 1:9 ratio of Eu:Ga/Al. In a typ-ical growth, the metals were melted and homogenized at900 ◦ C and cooled to 700 ◦ C at 3 ◦ C/hour in an inert argonatmosphere. Single crystals were separated from the fluxusing centrifugation through an alumina strainer placedbetween the crucibles. Powder x-ray diffraction was per-formed at ambient and low temperatures on a BrukerD8 Advance equipped with a Bruker MTC-LOWTEMPsample stage using Cu K α radiation. Rietveld refine-ments were done using the FullProf program suite. Sin-gle crystal x-ray diffraction was performed on a BrukerApex II diffractometer or a Rigaku SCX Mini diffrac-tometer using Mo K α radiation. Integration of raw framedata was done with Bruker Apex II software or Crystal-Clear 2.0. Refinement of the diffraction data was per-formed using XPREP and ShelXTL software packages.Electron microprobe analysis (EMPA) was performedusing a Cameca SX-100 electron probe microanalyzerwith a wavelength-dispersive spectrometer. An acceler-ating potential of 15 kV and a beam current of 20 nA ina 1 µ m fixed beam were used to collect elemental intensi-ties from 15 representative points on a polished surface ofeach crystal. The composition of each crystal was deter-mined using the averages and standard deviations of theelemental intensities of Eu, Ga, and Al. The elementalintensities of Eu and Ga were determined from a standardsample of EuGa , and the elemental intensity of Al wassimilarly determined from a standard sample of Al O .Chemical formulas for each crystal were calculated as-suming 5 atoms per formula unit and full occupancy ofthe Ga/Al site. The compositions obtained from EMPAand single crystal XRD free variable refinement were used to determine the doping fractions reported throughoutthis work with an error of ±
3% in the composition.Single energy images, elemental maps, and Eu M , -edge x-ray absorption spectra (XAS) were acquired usingthe scanning transmission x-ray microscope instrumentat the spectromicroscopy beamline 10ID-1 at the Cana-dian Light Source according to data acquisition method-ology described previously. Samples were preparedby grinding crystals of the analyte into a fine powder witha mortar and pestle and brushing the powder onto car-bon support films (3-4 nm carbon, Electron MicroscopySciences) with a fiber, which arranged a large number ofmicron-sized particles in a compact area suitable for EuM , -edge XAS.DC magnetic susceptibility measurements were per-formed on a Quantum Design Magnetic Properties Mea-surement System. Heat capacity measurements were per-formed using adiabatic thermal relaxation technique on aQuantum Design Physical Properties Measurement Sys-tem (PPMS). Temperature-dependent ac resistivity mea-surements were performed on a Quantum Design PPMSusing the current i = 2 mA and f = 462.02 Hz for aduration of 7 seconds with i || ab . III. RESULTSA. Crystallography
Single crystals of Eu(Ga − x Al x ) with dimensions ofapproximately 3 x 2 x 1 mm were grown with x = 0,0.18, 0.33, 0.50, 0.68, and 1. Powder x-ray diffractionindicates that all crystals in this series crystallize in thetetragonal I mmm space group at 300 K. A typical Ri-etveld analysis is shown for x = 0.50 in Fig. 1, indi-cating no significant flux inclusions or impurity phases.Temperature-dependent powder x-ray diffraction mea-surements (Appendix Fig. S1) on EuAl at T = 300 Kand 93 K confirm that the tetragonal crystal structure ispreserved down to low temperatures with no structuralphase transition, as was reported in some isostructuralBaAl -type structures. Single crystal x-ray refinementsconfirm the I mmm space group in all compounds re-ported herein and indicate full occupancy of all latticesites. In EuGa and EuAl , the Ga and Al atoms occupytwo inequivalent crystallographic sites corresponding tothe 4 d site, M (1), at (0, , ) and the 4 e site, M (2),at (0, 0, z ). Upon substituting Ga for Al, a clear sitepreference is shown: Al fully occupies the 4 d site beforeoccupying the 4 e site. Diffraction data for single crystalx-ray refinements can be found in the Appendix in TableS1. B. Physical Properties
Eu M , -edge x-ray spectromicroscopy was used toprobe electronic structure and bonding in selected sam-ples of Eu(Ga − x Al x ) with x = 0, 0.18, 0.50, and 1.In general, each of the Eu M - and M -edges exhibitscharacteristic multiplet splitting patterns with fine struc-ture that closely resembles expectations from earlier EuM , -edge studies of divalent Eu compounds. Pre-liminary calculations in the atomic limit for Eu thatdescribed transitions from 3 d f to 3 d f states alsoreproduced the salient features of the experimental spec-tra, including the high energy shoulders observed at ap-proximately 1132.5 eV as shown in Appendix Fig S2.Hence, the Eu M , -edge spectra support a ground stateEu valence formulation for each Eu(Ga − x Al x ) com-pound, and no evidence for mixed valence character wasdetected.Previous reports showed AFM order in EuGa andEuAl at T N = 15 K and 15.4 K, respectively, and theappearance of spin reorientation transitions in EuAl . However, in the doped series Eu(Ga − x Al x ) it appearsthat, as Al replaces Ga(1) at the 4 d site, multiple spinreorientation transitions occur, while T N changes non-monotonously with x . Magnetic susceptibility measure-ments with H (cid:107) ab and H (cid:107) c are shown in Fig. 2(a) and2(b). As many as three magnetic transitions occur downto 1.8 K in x = 0.50 and x = 1. The magnetic transi-tion temperatures were determined from magnetizationderivatives d ( M T ) /dT and C p ( T ) data. Even thoughthe end compounds order at virtually identical T N values,it appears that the ordering temperature is significantlyenhanced at intermediate compositions, and is maximum FIG. 1: Powder x-ray diffraction (black symbols) of a dopedsingle crystal of Eu(Ga − x Al x ) with x = 0.50 indicates thatthis crystal (and all crystals in this doped series) crystallizes inthe I /mmm space group with no significant flux inclusionor impurity phases. The red line is the diffraction patterncalculated from Rietveld refinement and the blue ticks are thecalculated peak positions. The orange line is the differencebetween the measured points and the calculated diffraction.The left inset is a picture of a crystal with each square = 1mm x 1 mm, and the right inset shows the tetragonal crystalstructure. at T N = 19.0 K near the ordered structure at x = 0.50(purple, Fig. 2). A summary of the magnetic transitiontemperatures for these compounds is given in AppendixTable S2. FIG. 2: Temperature-dependent magnetic susceptibilitymeasurements with (a) H (cid:107) ab and (b) left: H (cid:107) c . Right: Peaksdetermined from d ( MT ) /dT were used to indicated T N andspin reorientation transition temperatures. At high temper-atures, (c) left: ( M − M ) /H for x = 0.50 with closed sym-bols representing H (cid:107) ab and open symbols representing H (cid:107) c .Right: the inverse magnetic susceptibility of the polycrys-talline average indicates that these crystals show Curie-Weissbehavior and fully divalent Eu ions. High-temperature inverse magnetic susceptibility H/ ( M − M ) indicates Curie-Weiss behavior across theseries as H/ ( M − M ) are linear (Fig. 2c) above ∼
25 K.The linear fits are used to determine the effective mag-netic moment p eff and Weiss temperatures θ W , and theseare listed in Appendix Table S2. The p eff values arecomparable to the theoretical p theoryeff = 7.94 for Eu ,while the θ W values are positive and close to the T N tem-peratures for the whole series. Positive θ W values areindicative of FM correlations, which were also observedin an isostructural compound EuRh Si . No crystal electric field (CEF) effects are expected forEu ions, and this is indeed consistent with identical H (cid:107) ab and H (cid:107) c high temperature curves, with the x =0.50 data shown in Fig. 2c as an example. However,in the ordered state, slight differences in ( M − M ) /H are registered in the moment orientation relative to theapplied field below 50 K, as shown in Fig. 2a-b. This iseven better evidenced by the anisotropic M ( H ) isothermsmeasured at T = 1.8 K (Fig. 3a-b). The magnetiza-tion saturation for all measured compounds, except x =0, is 7 µ B /Eu , as expected for the J = 7 / (black squares, Fig.3a-b) appears to approach saturation slightly above the7 T maximum field for these measurements. As Al re-places Ga across the Eu(Ga − x Al x ) series, metamag-netic (MM) transitions are observed for x = 0.33, 0.50,0.68, and 1 with crystallographic anisotropy. Figure 3cshows an example of how the MM critical fields were de-termined from the peaks in dM/dH . As expected, thenumber of MM transitions at low T (Fig. 3, T = 1.8 K)coincides with the number of transitions in the low H magnetic susceptibility (Fig. 2).Specific heat measurements (Fig. 4) confirmed thepresence of multiple magnetic transitions in these com-pounds, with the transition temperatures consistent withthose derived from temperature-dependent magnetiza-tion measurements. Nakamura et al. argued for heavyfermion behavior in EuGa based on a Fermi liquid re-lation between the measured quadratic resistivity coeffi-cient A and the calculated electronic specific heat coef-ficient γ with a modest mass renormalization from γ =138 mJ / mol K . However, our low temperature C P /T data show no evidence for strong mass renormalizationin any of the Eu(Ga − x Al x ) compounds ( x = 0 − H = 0 elec-trical resistivity of Eu(Ga − x Al x ) (Fig. 5). For all x values, the high temperature resistivity decreases with T , until loss of spin disorder scattering at T N is markedby an abrupt drop. The residual resistivity ratios RRR= ρ (300K)/ ρ (listed in Appendix Table S2) with ρ = ρ (2K) are an order of magnitude larger for the endcompounds ( x = 0 and 1) compared to the doped sam-ples. Remarkably, we observed a sharp resistivity in-crease occurring for x = 0.50 and 1 around 51 and 140K, respectively. In the latter compound, Nakamura etal. associated the resistivity increase at 140 K with aCDW-like transition. Notably, such a transition appearsin Eu(Ga − x Al x ) only for x = 0.50, where (i) x-raydiffraction indicates an ordered structure, with Ga andAl fully occupying the two separate sublattices to form EuGa Al , and (ii) resistivity measurements reveal thelowest residual resistivity ρ and an enhanced RRR valuecompared to all other doped (disordered) samples. FIG. 3: Field-dependent magnetization measurements with(a) H (cid:107) ab and (b) H (cid:107) c show multiple metamagnetic tran-sitions that are anisotropic. An example of a metamag-netic transition in this series is shown in (c) with an exam-ple of how critical fields were determined using peaks from dM/dH vs. H . FIG. 4: Specific heat measurements confirm multiplemagnetic transitions and a first-order phase transition inEuAl .The inset shows no evidence of mass renormalizationin this system from C P /T vs. T . IV. DISCUSSIONS AND CONCLUSIONS
Given the chemical similarities between Ga and Al (iso-electronic, similar covalent radii of 1.22 ˚A and 1.21 ˚A,respectively ), no substantive differences in crystallo-graphic or physical properties are expected betweenthe isostructural EuGa and EuAl compounds. How-ever, as Al replaces Ga in Eu(Ga − x Al x ) , the mag-netic, electronic, and structural properties change non-monotonously: (i) As shown in Fig. 6a, a maximum T N occurs in x = 0.50. This is the result of the min-imum Eu − Eu ion spacing in this composition as evi-
FIG. 5: Temperature-dependent resistivity scaled by ρ .Anomalies in x = 0.50 and 1 are consistent with CDW-likebehavior. Inset: Absolute resistivity values at low tempera-ture. denced by the non-linear change in the a lattice param-eter and unit cell volume (squares and diamonds, re-spectively, Fig. 6b), which are minimum for x = 0.50,while c (triangles) increases linearly from x = 0 to 1.The ground state across the series is AFM (Fig. 2),even though the spin correlations appear FM ( θ W > θ W ∼ T N ). In the absence of frustration or CEF effect,magnetic order is likely a result of strong next-nearest-neighbor interactions (with exchange coupling J > J < J > | J | . This is consistent with the pro-posed magnetic structure of EuGa , where intra-planeEu magnetic moments are thought to couple ferromag-netically, while inter-plane Eu magnetic moments coupleantiferromagnetically. (ii) The observation of a possibleCDW transition in Eu(Ga − x Al x ) with x = 0.50 and 1may stem directly from the ordered structure, consider-ing the evidence for full site separation for Ga and Al inthe x = 0.50 compound. This, however, does not explainthe lack of a CDW in the x = 0 (also ordered) analogue,even though applied pressure appeared to induce such atransition. Additional qualitative differences exist evenin the pressure-dependence of the plausible CDW tran-sition in EuGa and EuAl . According to the change inlattice parameters shown in Fig. 6b, it seems that Alsubstituting for Ga acts as positive pressure, resulting inthe occurrence of a CDW at x = 0.50 in Eu(Ga − x Al x ) ,similar to the behavior in EuGa under applied pressure.(iii) Most notable of the non-monotonous trends in thisseries is the minimum in the in-plane lattice parameter a at x = 0.50 compared to the linear increase in c acrossthe entire series (Fig. 6b). In order to explain this non-linear structural trend, density functional theory (DFT)calculations with the local density approximation (LDA)were carried out in the linear muffin tin orbital tight bind-ing atomic spheres approximation (LMTO-TB-ASA) toprobe the bonding character between Al and Ga in thedoped compounds.DFT calculations were performed for x = 0, 0.50, and1. To avoid complications arising from the unpaired f electrons of Eu , Sr was substituted as an analog inthe calculations. In order to ensure that the non-linearchanges in a were associated solely with the Ga − Al bondsand not the Eu atoms, single crystals of SrGa , SrGa Al ,and SrAl were grown from self-flux, and their latticeparameters were measured from powder x-ray diffrac-tion (shown in Appendix Fig. S3). Trends in latticeparameters similar to those in the Eu analogues were ob-served, with a minimized in SrGa Al and c increasinglinearly from SrGa to SrAl . As expected given the iso-electronic nature of the series, all three band structuresare qualitatively very similar (Appendix Fig. S4). How-ever, analysis of the electron distribution extracted fromthe integrated density of states (DOS) up to E F revealssubstantive differences between the end compounds andthe x = 0.50 composition: there is charge transfer fromthe M (1) to the M (2) site as the composition approaches x = 0.50 from both end compounds, such that the M (1)[ M (2)] electron density is minimum [maximum] for x =0.50 (see Appendix Table S3). This maximum chargetransfer manifests when the two M sites are preferen-tially occupied by M (1) = Al and M (2) = Ga, implyingan enhanced polarization of the M (1) − M (2) covalentbond at x = 0.50 compared to both x = 0 and 1. Despitethe similar trends toward less polarization in the Al-richand Ga-rich compounds, the increased polarization from x = 0 to x = 0.50 prevents bond length expansion (as FIG. 6: (a) Left: Increasing x corresponds to a non-monotonic change in T N (orange circles) that could be as-sociated with changes in lattice parameters a and c . Right:RRR values (purple down triangles) calculated from resistiv-ity measurements show the low amount of disorder in the endcompounds and the decreased disorder in x = 0.50 comparedto other doped compounds in the series. (b) Left: Latticeparameters a (black squares) and c (red triangles) as a func-tion of doping fraction x indicating a linear change in c anda non-linear change in a with increasing x resulting in a lo-cal minimum. Right: Unit cell volume V (blue diamonds)as function of x . (c) Left: Bond distances between atoms lo-cated at the M (1) − M (2) (red left triangles) and M (2) − M (2)(black hexagons) crystallographic sites remain constant up to x = 0.50 but increase from x = 0.50 to 1. Right: The tetra-hedral bond angle between M (1) − M (2) − M (1) atoms (blueopen circles) decreases up to x = 0.50 and remains constantfrom x = 0.50 to 1. All dashed lines are guides to the eye. M (1) is replaced by Al but M (2) remains occupied byGa), but then polarization is reduced again from x =0.50 to x = 1 (as M (2) is also replaced by Al), resultingin a greater increase in bond lengths.This unexpected deviation from Vegard’s law canbe further explained by examining the trends in the M (1) − M (2) and M (2) − M (2) bond lengths and the M (1) − M (2) − M (1) bond angle, where M = Al or Ga.As shown in Fig. 6c, as Al occupies the M (1) site upto x = 0.50, the bond distance between M (1) and Ga(2)remains relatively unchanged. However, the bond angle M (1) − Ga(2) − M (1) in the Ga-centered tetrahedron de-creases linearly up to x = 0.50. These crystallographictrends acting together expand the c lattice parameterwhile simultaneously contracting the a lattice parameterto a minimum. As Al substitutes Ga in the M (2) siteup to x = 1, a different trend emerges. Here we observethat the tetrahedral bond angle remains constant whilethe bond lengths between Al(1) − M (2) and M (2) − M (2)increase, thus leading to both lattice parameters a and c increasing. These behaviors are likely caused by thegreater electronegativity of Ga, which renders the Ga-Ga bonds more polarized.In summary, we have observed that although Ga andAl are very similar in their valence and size, substitutingAl for Ga in the doped system Eu(Ga − x Al x ) producesstriking and unexpected magnetic, electronic, and struc-tural transitions. Substituting Ga with Al up to x =0.50 decreases a to a minimum and appears to increasethe ferromagnetic interactions in the system, resulting inhigher T N and multiple magnetic transitions. Addition-ally, temperature-dependent ρ ( T ) measurements showpronounced changes in electronic transport as manifestedby CDW formation in Eu(Ga − x Al x ) for x = 0.50 and 1.The CDW behavior is markedly different between EuAl and EuGa , and chemical and hydrostatic pressure canbe used as tools to elucidate the factors contributing tothe CDW formation in this series. Future studies willaim to distinguish between the effects of doping in themagnetic versus the nonmagnetic sublattice in EuGa and to explore the effects of hole-doping, positive chemi-cal pressure, and disorder on the magnetic and electronicproperties of EuGa . V. ACKNOWLEDGEMENTS
The authors would like to thank Wenhua Guo, Alan-nah Hallas, Manuel Brando, and Frank Steglich for fruit-ful discussions and Nicholas Botto for performing EMPAmeasurements. MS, CLH, and EM acknowledge supportfrom the Gordon and Betty Moore Foundation EPiQSinitiative through grant GBMF 4417. The work per-formed at University of California, Davis was supportedby NSF-DMR-1709382. SGM was supported by the Di-rector, Office of Science, Office of Basic Energy Sci-ences, Division of Chemical Sciences, Geosciences, andBiosciences Heavy Element Chemistry Program of theU.S. Department of Energy (DOE) at LBNL under Con-tract No. DE-AC02-05CH11231. Eu M , -edge spec-tra described in this paper were measured at the Cana-dian Light Source, which is supported by the CanadaFoundation for Innovation, Natural Sciences and Engi-neering Research Council of Canada, the University ofSaskatchewan, the Government of Saskatchewan, West- ern Economic Diversification Canada, the National Re-search Council Canada, and the Canadian Institutes ofHealth Research. TMM acknowledges support from theJohns Hopkins University Catalyst Award and a Davidand Lucile Packard Foundation Fellowship for Scienceand Engineering. M. Brian Maple,
J. Phys. Soc. Jpn. , , 222 (2005). M. Nicklas, M. E. Macovei, J. Ferstl, C. Krellner, C.Geibel, and F. Steglich,
Phys. Status Solidi B , , 727(2010). T. Takabatake, F. Iga, T. Yoshino, Y. Echizen, K. Ka-toh, K. Kobayashi, M. Higa, N. Shimizu, Y. Bando, G.Nakamoto, H. Fujii, K. Izawa, T. Suzuki, T. Fujita, M.Sera, M. Hiroi, K. Maezawa, S. Mock, H. v. L¨ohneysen,A. Br¨uckl, K. Neumaier, and K. Andres,
J. Magn. Magn.Mater. , , 277 (1998). T. N. Voloshok, N. V. Mushnikov, N. Tristan, R. Klingeler,B. B¨uchner, and A. N. Vasiliev,
Phys. Rev. B , , 172408(2007). Y. ¯Onuki, A. Nakamura, F. Honda, D. Aoki, T. Tekeuchi,M. Nakashima, Y. Amako, H. Harima, K. Matsubayashi,Y. Uwatoko, S. Kayama, T. Kagayama, K. Shimizu, S.Esakki Muthu, D. Braithwaite, B. Salce, H. Shiba, T. Yara,Y. Ashitomi, H. Akamine, K. Tomori, M. Hedo and T.Nakama,
Philos. Mag. , (2016). Svilen Bobev, Eric D. Bauer, J.D. Thompson, and John L.Sarrao,
J. Magn. Magn. Mater. , , 236 (2004). Ai Nakamura, Yuichi Hiranaka, Masato Hedo, TakaoNakama, Yasunao Miura, Hiroki Tsutsumi, Akinobu Mori,Kazuhiro Ishida, Katsuya Mitamura, Yusuke Hirose, Kiy-ohiro Sugiyama, Fuminori Honda, Rikio Settai, TetsuyaTakeuchi, Masayuki Hagiwara, Tatsuma D. Matsuda, Et-suji Yamamoto, Yoshinori Haga, Kazuyuki Matsubayashi,Yoshiya Uwatoko, Hisatomo Harima, and Yoshichika¯Onuki,
J. Phys. Soc. Jpn. , , 104703 (2013). Ai Nakamura, Taro Uejo, Fuminori Honda, TetsuyaTakeuchi, Hisatomo Harima, Etsuji Yamamoto, YoshinoriHaga, Kazuyuki Matsubayashi, Yoshiya Uwatoko, MasatoHedo, Takao Nakama, and Yoshichika ¯Onuki,
J. Phys. Soc.Jpn. , , 124711 (2015). Beatriz Cordero, Ver´onica G´omez, Ana E. Platero-Prats,Marc Rev´es, Jorge Echeverr´ıa, Eduard Cremades, FlaviaBarrag´an, and Santiago Alvarez,
Dalton Trans. , 2832(2008). G. D. Loula, R. D. dos Reis, D. Haskel, F. Garcia, N.M. Souza-Neto, and F. C. G. Gandra,
Phys. Rev. B , ,245128 (2012). Abishek K. Iyer, Lahari Balisetty, Sumanta Sarkar, andSebastian C. Peter,
J. Alloys Compd. , , 305 (2014). Paul H. Tobash and Svilen Bobev,
J. Alloys Compd. , ,58 (2006). M. Stavinoha, et al. , in preparation. Juan Rodr´ıguez-Carvajal,
Physica B , , 55 (1993). Stefan G. Minasian, Enrique R. Batista, Corwin H. Booth,David L. Clark, Jason M. Keith, Stosh A. Kozimor, WayneW. Lukens, Richard L. Martin, David K. Shuh, S. ChantalE. Stieber, Tolek Tylisczcak, and Xiao-dong Wen,
J. Am.Chem. Soc. , , 18052 (2017). Alison B. Altman, C. D. Pemmaraju, Selim Alayoglu, JohnArnold, Eric D. Bauer, Corwin H. Booth, Zachary Fisk,Joseph I. Pacold, David Prendergast, David K. Shuh, TolekTyliszczak, Jian Wang, and Stefan G. Minasian,
Phys. Rev.B , , 045110 (2018). Gordon J. Miller, Fan Li, and Hugo F. Franzenh,
J. Am.Chem. Soc. , , 3739 (1993). G. Kaindl, G. Kalkowski, W. D. Brewer, B. Perscheid, andF. Holtzberg,
J. Appl. Phys. , , 1910 (1984). B. T. Thole, G. van der Laan, J. C. Fuggle, G. A. Sawatzky,R. C. Karnatak, and J.-M. Esteva,
Phys. Rev. B , , 5107(1985). Michael E. Fisher,
Philos. Mag. , , 1731 (1962). Neeraj Kumar, S. K. Dhar, A. Thamizhavel, P. Bonville,and P. Manfrinetti,
Phys. Rev. B , , 144414 (2010). Z. Hossain, O. Trovarelli, C. Geibel, and F. Steglich,
J.Alloys Compd. , , 396 (2001). A.R. Denton and N.W. Ashcroft,
Phys. Rev. A , , 3161(1991). Appendix
Further details of the crystal structures in CIF formatfor Eu(Ga − x Al x ) with x = (0 −
1) may be obtained fromFIZ Karlsruhe, 76344 Eggenstein-Leopoldshafen, Ger-many (fax: (+49)7247-808-666; e-mail: crysdata(at)fiz-karlsruhe(dot)de, on quoting the deposition numbersCSD-(insert here upon receipt).
A. Summary of magnetic, transport, andcrystallographic data
FIG. S1: Powder x-ray diffraction of EuAl performed at300 K (red line) and 93 K (black line). This indicates thatthe tetragonal space group is preserved above and below theCDW-like transition, and the anomaly in resistivity is notcaused by a structural phase transition. Gray bars indicatelarge background peaks from the metal sample holder andstars indicate the presence of small amounts of Al flux. B. Lattice parameters and band structurecalculations for SrGa , SrAl Ga , and SrAl FIG. S2: Experimental Eu M , -edge spectra ofEu(Ga − x Al x ) and configuration interaction calculation inthe atomic limit for Eu . Ga L , -edge features emerge withdecreased values of x .TABLE S1: Crystallographic data for single crystals of Eu(Ga − x Al x ) (space group I /mmm ). Values for x determinedfrom EMPA.parameter x = 0 x = 0.18 x = 0.33 x = 0.50 x = 0.68 x = 1 x from free variable refinement 0 0.15 0.31 0.47 0.68 1 a (˚A) 4.3904(7) 4.381(3) 4.3551(9) 4.3301(7) 4.3429(13) 4.4113(9) c (˚A) 10.6720(18) 10.757(7) 10.833(2) 10.9253(17) 11.018(3) 11.204(3) V (˚A ) 205.71(7) 206.5(3) 205.47(9) 204.85(7) 207.80(14) 218.02(11)absorption coefficient (mm − ) 40.640 36.87 32.93 29.14 23.57 14.968measured reflections 1656 969 1734 1725 1769 1722independent reflections 137 92 138 139 139 140R int R ( F ) for F o > σ ( F o ) a wR ( F o ) b a R = (cid:80) || F o | − | F c || / (cid:80) | F o | b wR = [ (cid:80) [ w ( F o − F c ) ] / (cid:80) [ w ( F o ) ]] / TABLE S2: Summary of magnetic and transport properties in Eu(Ga − x Al x ) x T N (K) a T N (K) b T N (K) c p eff χ θ W H c (T) H c (T) RRR T ∗ T (K) a T (K) b T (K) c (emu/mol Eu ) (K) H c (T) H c (T) (K) T (K) a T (K) b T (K) c H (cid:107) ab H (cid:107) c > > a from d ( MT ) /dT with H (cid:107) ab b from d ( MT ) /dT with H (cid:107) c c from C p ( T )FIG. S3: Lattice parameters from powder x-ray diffractionof SrGa , SrAl Ga , and SrAl single crystals. Trends seenhere are consistent with trends observed in the Eu analogues,indicating that the non-linear change in a is associated withthe Ga − Al sublattice. FIG. S4: Band structure calculations for SrGa , SrAl Ga ,and SrAl . Sr is used as a substitute for Eu to avoidcomplications arising from unpaired 4 f electrons.TABLE S3: Analysis of the electron distribution extractedfrom the integrated density of states up to E F provides in-sight into the polarization of the Ga − Al bonds. In contrastto both end members, in SrAl Ga there is increased chargetransfer to the M (2) site. This charge transfer only manifestswhen M (1) = Al and M (2) = Ga, implying an enhanced po-larization in the M (1) − M (2) covalent bonds in SrAl Ga .compound e − / M (1) e − / M (2)SrGa Ga Ga structure parameters)SrAl Ga2