Cubic Re6+ (5d1) Double Perovskites, Ba2MgReO6, Ba2ZnReO6

Oct 4, 2016 - In Muon Science: Muons in Physics, Chemistry and Materials; Lee , S. L. ; Kilocoyne , S. H. ; Cywinski , R., Eds.; The Scottish Universi...
0 downloads 0 Views 3MB Size
Download PDF
Article pubs.acs.org/IC

Cubic Re6+ (5d1) Double Perovskites, Ba2MgReO6, Ba2ZnReO6, and Ba2Y2/3ReO6: Magnetism, Heat Capacity, μSR, and Neutron Scattering Studies and Comparison with Theory Casey A. Marjerrison,† Corey M. Thompson,‡ Gabrielle Sala,† Dalini D. Maharaj,† Edwin Kermarrec,† Yipeng Cai,† Alannah M. Hallas,† Murray N. Wilson,† Timothy J. S. Munsie,† Garrett E. Granroth,§ Roxana Flacau,∥ John E. Greedan,*,‡,⊥ Bruce D. Gaulin,†,⊥,# and Graeme M. Luke†,⊥,# †

Department of Physics and Astronomy and ‡Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada § Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ∥ Canadian Neutron Beam Centre, Canadian Nuclear Laboratories, Chalk River, Ontario K0J 1J0, Canada ⊥ Brockhouse Institute for Materials Research, Hamilton, Ontario L8S 4M1, Canada # Canadian Institute for Advanced Research, 180 Dundas Street W, Toronto, Ontario M5G 1Z8, Canada S Supporting Information *

ABSTRACT: Double perovskites (DP) of the general formula Ba2MReO6, where M = Mg, Zn, and Y2/3, all based on Re6+ (5d1, t2g1), were synthesized and studied using magnetization, heat capacity, muon spin relaxation, and neutron-scattering techniques. All are cubic, Fm3̅m, at ambient temperature to within the resolution of the X-ray and neutron diffraction data, although the muon data suggest the possibility of a local distortion for M = Mg. The M = Mg DP is a ferromagnet, Tc = 18 K, with a saturation moment ∼0.3 bohr magnetons at 3 K. There are two anomalies in the heat capacity: a sharp feature at 18 K and a broad maximum centered near 33 K. The total entropy loss below 45 K is 9.68 e.u., which approaches R ln 4 (11.52 e.u.) supporting a j = 3/2 ground state. The unit cell constants of Ba2MgReO6 and the isostructural, isoelectronic analogue, Ba2LiOsO6, differ by only 0.1%, yet the latter is an anti-ferromagnet. The M = Zn DP also appears to be a ferromagnet, Tc = 11 K, μsat(Re) = 0.1 μB. In this case the heat capacity shows a somewhat broad peak near 10 K and a broader maximum at ∼33 K, behavior that can be traced to a smaller particle size, ∼30 nm, for this sample. For both M = Mg and Zn, the low-temperature magnetic heat capacity follows a T3/2 behavior, consistent with a ferromagnetic spin wave. An attempt to attribute the broad 33 K heat capacity anomalies to a splitting of the j = 3/2 state by a crystal distortion is not supported by inelastic neutron scattering, which shows no transition at the expected energy of ∼7 meV nor any transition up to 100 meV. However, the results for the two ferromagnets are compared to the theory of Chen, Pereira, and Balents, and the computed heat capacity predicts the two maxima observed experimentally. The M = Y2/3 DP, with a significantly larger cell constant (3%) than the ferromagnets, shows predominantly anti-ferromagnetic correlations, and the ground state is complex with a spin frozen component Tg = 16 K from both direct current and alternating current susceptibility and μSR data but with a persistent dynamic component. The lowtemperature heat capacity shows a T1 power law. The unit cell constant of B = Y2/3 is less than 1% larger than that of the ferromagnetic Os7+ (5d1) DP, Ba2NaOsO6.

■

INTRODUCTION Interest in the B-site ordered double perovskites (DP), of composition A2BB′O6, has increased recently. When both the B and B′ ions are magnetic, such as in Sr2FeMoO6 or Sr2FeReO6, one finds, often but not always, ferrimagnetism with Tc > 400 K and spin-polarized bands giving rise to potential application in spintronic technologies.1,2 If only the B′ site is magnetic an opportunity for geometric magnetic frustration is present, as the B′ sublattice has a face-centered cubic topology, consisting of edge-sharing tetrahedra.3 In many cases the B′ ion is from © XXXX American Chemical Society

the 4d or 5d transition metal series, and phenomena that are minor concerns with 3d elements, such as spin−orbit coupling (SOC), acquire greater importance. There are three series of these DP materials with B′ electronic configurations nd1(t2g1), nd2(t2g2), and nd3(t2g3). Each series presents different issues. For example, nd3 ions are orbital singlets, while the orbital moment is not fully quenched in the other two cases. As well, Received: August 11, 2016

A

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry Table 1. A Summary of the Structure and Magnetic Properties of Double Perovskite Materials with a t2g1 B′ Ion DP

SG

Vcell a (Å3)

t** b

θc (K), Tord (K), f*** c,d

grd state

ref

Ba2YMoO6 Ba2MgReO6 Ba2LiOsO6 Ba2NaOsO6 Ba2CaReO6 Sr2MgReO6 Sr2CaReO6 La2LiMoO6 Sr2YMoO6

Fm3m ̅ Fm3̅m Fm3̅m Fm3̅m [I4/m] Fm3̅m [I4/m] I4/m P21/n P21/n P21/n

591.01 521.1 532.4 569.1 586.6 [582.2] 491.6 549.6 502.0 554.0

0.990 1.049 1.045 0.989 0.982 0.989 0.925 0.938 0.933

−219, −, − NR, ∼20, NR −40, 8, 5 −32, 6.8, 5 −40, 15, 3 −443, 14, 32 −460, 50, 9 −45, 5, 9 −50, NR, NR

gapped singlet F AF F AF? spin glass spin glass AF SRO gapped singlet, F?

7−10 11 12 12 13 14 15 8 16

a

The cell volumes of all DP are normalized to that for Fm3̅m symmetry to facilitate comparisons. That is, for Fm3̅m materials V = a03, while for I4/m or P21/n V = Vcell (for the indicated symmetry) × 2. bt**is the “tolerance factor”, t = [r(A) + r(O)]/21/2[⟨r(B,B′)⟩ + r(O)], where r(A) is the XIIfold radius for the A-cation, ⟨r(B,B′)⟩ is the average VI-fold radius of the B and B′ cations, and r(O) is the IV-fold radius for the O2− anion. Radii taken from ref 17. cf *** is the “frustration index”, f = |θc|/Tord, where θc is the Curie−Weiss temperature and Tord is either a critical temperature or a spin-freezing temperature.3 dNRnot reported

t2g1 and t2g2 ions are potentially subject to Jahn−Teller induced crystallographic distortions, while t2g3 ions are not. Recent publications summarize in tabular form what is known about the t2g2 and t2g3 cases.4−6 In this study the focus is on three DP materials based on the t2g1 ion Re6+. Table 1 lists the structure and magnetic properties of several t2g1 DP materials. Dealing first with crystal structure, note that three space group symmetries are listed: Fm3̅m, I4/m, and P21/n. While group theoretical considerations for DP allow 12 possible symmetries, these three are the most common.18 Note also that the descent in symmetry Fm3̅m → I4/m → P21/n tracks, roughly, the decrease in the tolerance factor t, first introduced by Goldschmidt and defined in the footnote to Table 1.19 Two DP are reported to undergo Fm3̅m → I4/m transitions as the temperature is lowered, namely, Ba 2 CaReO 6 and Ba2NaOsO6.13,20 In the latter case the distortion is reported to occur above ambient temperature in spite of a single-crystal X-ray study in which the symmetry is determined as Fm3̅m.12 The magnetic properties vary widely within this series. There is no obvious correlation between the magnetic ground state and crystal symmetry. Three magnetic t2g1 ions are involved, Mo5+, Re6+, and Os7+. Two of the Mo-based DP show a very unusual and unpredicted gapped spin-singlet ground state, Ba2YMoO6 and Sr2YMoO6, although characterization of the latter is not as convincing, and a weak ferromagnetic (F) signal is detected. The third DP, La2LiMoO6 with the same P21/n symmetry as Sr2YMoO6, shows at least short-range antiferromagnetic (AF) order below 20 K, possible long-range AF order below 5 K, and no apparent gap. The Os7+ materials are the most conventional, showing long-range AF and F order with relatively small frustration indices f, but Ba2NaOsO6 is F with a negative θ suggesting a competition between F and AF exchange pathways. The Re6+ compounds tend to show high f values, at least for Sr2MgReO6 and Sr2CaReO6, and long-range magnetic order has not been demonstrated convincingly for Ba2CaReO6. In fact both Sr2MgReO6 and Sr2CaReO6 have a spin-frozen ground state, but a significant level of BB′ site disorder has not been detected in either material.21 Recent theoretical efforts to understand both cubic and distorted t2g1 DP magnetic materials has predicted both F and AF ground states and some other less ordered variants at the level of mean field theory, but a framework by which to predict magnetic properties of previously unknown materials or even to

rationalize the properties of known DP materials is still at an early but promising stage of development.20,22,23 In this study three Re6+ DP oxides, namely, Ba2MgReO6, Ba2ZnReO6, and Ba2Y2/3ReO6, were synthesized and characterized using a variety of techniques including X-ray and neutron diffraction, magnetization (susceptibility), heat capacity, μSR, and inelastic neutron scattering. The first two materials had been reported before, although characterization details are very limited, while the latter is reported for the first time.11,24,25 For example, only Ba2MgReO6 has been studied in much detail.11 The crystal structure had been refined at ambient temperature from CoKa1 powder X-ray data over a range to Qmax ≈ 6 Å−1. No attempt was made to look for peak splittings at high Q, which might disclose a subtle distortion, as this work was performed well before the case of Ba2NaOsO6 was known. Neither X-ray or neutron diffraction data are reported at low temperatures. Only magnetization data exist, which show a F transition near 20 K with a saturation moment at 10 K of ∼0.1 μB. No data from the paramagnetic regime were reported, and the samples are possibly contaminated by a F impurity. No heat capacity data are known. Ba2MgReO6 is also of great interest in comparison with isostructural and isoelectronic Ba2LiOsO6, as these two differ by only 0.1% in cell constant, and the latter is an antiferromagnet with TN = 8 K.12 Thus, a more detailed study of Ba2MgReO6 is clearly warranted. For Ba2ZnReO6 only a low-precision cell constant is reported.24,25 As this is only 0.2% larger than that of F Ba2MgReO6 and 0.1% larger than that of AF Ba2LiOsO6, it is of considerable interest to determine the magnetic ground state. BaY2/3ReO6 is reported here for the first time. As the radius of Y3+(coordination number six) = 0.90 Å compared with Mg2+ (0.72 Å) and Zn2+(0.74 Å),17 the unit cell constant is expected to be significantly larger, which affords the opportunity to study the effect of increasing interionic distances on the net magnetic exchange correlations. For example, Ba2CaReO6 shows strong AF correlations, although the symmetry is I4/m. The radius of Ca2+ (1.00 Å) is similar to Y3+ as is that of Na+ (1.02 Å). As mentioned, Ba2NaOsO6 is a ferromagnet, and thus it is of great interest to determine the ground state for Ba2Y2/3ReO6. Finally, comparisons are made with the mean-field theory results of Chen, Pereira, and Balents for the cubic t2g1 DP case, particulary observables, such as the heat capacity and magnetization.22 B

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry Table 2. Summary of X-ray and Neutron Powder Refinements for Ba2MReO6 a0 (Å)

x (O)

B (Å2) [Ba]

B (Å2) [Mg]

B (Å2) [Re]

B (Å2) [O]

Rwp (%)

2.33(45) 0.54(12)

0.61(6) 0.10

0.99(28) 0.61(5)

17.3 4.90

0.20(11)

0.10

0.40(4)

5.65

1.2(2) 0.33(8)

0.33(6) 0.120

0.90(28) 0.50(3)

24.9 7.73

0.20

0.33(2) Y (occ)

8.71 Rwp (%)

M = Mg 290 K X-ray neutron

8.0849(2) 8.0857(3)

0.239(2) 0.2384(4)

0.80(6) 0.36(6)

neutron

8.0702(3)

0.2386(4)

0.30

3.5 K M = Zn 290 K X-ray neutron

8.1148(1) 8.1143(2)

0.236(1) 0.2369(2)

neutron

8.1010(2) a0 (Å)

0.2375(2) x (O)

0.79(8) 0.22(4) 3.5 K 0.20 B (Å2) [Ba]

X-ray neutron

8.3602(2) 8.3599(4)

0.233(2) 0.2309(2)

1.17(7) 1.12(5)

neutron

8.3460(4)

0.2311(2)

0.68(5)

0.30 B (Å2) [Y] M = Y2/3 290 K 0.1 0.92(14) 3.5 K 0.52(4)

B (Å2) [Re]

B (Å2) [O]

0.32(6) 0.15(5)

1.6(4) 1.28(4)

0.65(3) 0.70(3)

27.2 5.30

0.12(6)

0.77(4)

0.70(3)

6.11

Figure 1. (a) Rietveld refinement of X-ray diffraction data at 290 K for Ba2MgReO6. The resolution is estimated as Δd/d = 5 × 10−4 for the range of 100° < 2θ < 120°. The red circles are the data, the black line is the fit to the Fm3̅m model, the blue line is the difference plot, and the green tic marks locate the Bragg peaks. (b) Comparison of the refined profile of the (822)/(660) reflection for Ba2MgReO6 in Fm3m ̅ (top) with a simulated profile for a weak tetragonal distortion (c/a = 1.001) in I4/m (bottom).

C

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 2. (a) Rietveld refinement of neutron powder data at 290 K for Ba2MgReO6 in Fm3m ̅ . Only the λ = 1.33 Å data are shown. (inset) High angle data. (b) Rietveld refinement of neutron powder data at 3.5 K for Ba2MgReO6 in Fm3̅m. Only the λ = 1.33 Å data shown. (inset) High angle data.

■

Neutron Diffraction. Elastic neutron powder diffraction data for Ba2MReO6 (M = Mg, Zn, Y2/3) were collected at the Canadian Neutron Beam Centre, Chalk River Nuclear Laboratories, on the C2 diffractometer. The ∼2 g sample was loaded into a vanadium can. Two incident wavelengths of neutrons were used, 1.33 and 2.37 Å. The wavelengths were calibrated against a standard sample of Al2O3. Measurements were performed at 3 and 290 K for each neutron wavelength. Temperature was controlled using a top-loading closed cycle refrigerator. Magnetization. For Ba2MReO6 (where M = Mg, Zn, Y2/3), zerofield-cooled (ZFC) and field-cooled (FC) magnetic susceptibility measurements were performed using a SQUID magnetometer with an applied field of 0.05 T. Magnetization measurements were taken at 2 K

EXPERIMENTAL SECTION

Synthesis and Structural Characterization. The Ba2MReO6 (M = Mg, Zn, Y2/3) compounds were prepared by conventional solid-state reactions. Stoichiometric amounts of BaCO3, MgO, ZnO, Y2O3, and ReO3 were ground together and heated in argon for 2 d in a Pt crucible at 1200 °C for M = Mg and Y2/3 and at 1000 °C for M = Zn. The prepared samples were characterized as single-phase using X-ray diffraction. X-ray Diffraction. X-ray powder diffraction data were collected using a PANAlytical X-pert diffractometer using Cu Kα1 radiation (λ = 1.540 56 Å) at ambient temperature for all samples over the range of 10°−120° in 2θ. D

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 3. (a) FC susceptibility, (b) inverse susceptibility, (c) Fisher’s heat capacity, (d) isothermal magnetization at 2 K. M = Mg (red), Zn (blue). over an applied field range from −5 to 5 T. The susceptibility data were corrected for a diamagnetic contribution using literature values.26 Heat Capacity. Heat capacity measurements were performed using an Oxford Instruments Maglab system using the quasi-static equilibrium relaxation method. For these measurements ∼10 mg of sintered pellets were fixed on a sapphire plate with ∼100 mg of apezion grease and heat pulses were applied. The contribution from the apezion grease was subtracted from the final results. Muon Spin Relaxation. Muon spin relaxation (μSR) spectra on Ba2Y2/3ReO6 and Ba2MgReO6 were collected using the LAMPF lowbackground helium flow cryostat on the M20 surface-muon beamline at TRIUMF laboratory in Vancouver, Canada. This instrument gives access to temperatures between 1.6 and 300 K, fields up to 0.4 T using an electromagnet, and a time resolution of 0.4 ns. Only muons that stop in the sample contribute to the experimental spectra, as those that miss or pass through the sample are excluded. Inelastic Neutron Scattering. Neutron scattering measurements were performed at the Spallation Neutron Source (SNS; Oak Ridge National Laboratory), on the SEQUOIA Fine Resolution Fermi Chopper Spectrometer.27 Incident neutron energies of 12, 25, 60, and 120 meV were used with a temperature range of 6−70 K. The samples were enclosed in annular aluminum cells with a He exchange gas atmosphere and loaded into an orange 4He-flow cryostat. An identical empty can was measured under the same experimental conditions and used for background subtraction.

Data for M = Zn and Y2/3 are presented in the Supporting Information, Figures 1−4. A central issue for all three is whether there is evidence for a distortion to lower symmetry as has been reported for Ba2CaReO6 and Ba2NaOsO6 within the resolution of the data presented here. Recall that the t2g1 configuration is potentially subject to a Jahn−Teller induced distortion. Ba2MgReO6. Refinement of the X-ray diffraction data (Cu Kα1) at 290 K is shown in Figure 1a. There is no discernible deviation from cubic symmetry at 290 K, as is clear from Figure 1b, in which the profile of the (822)/(660) reflection is compared with a simulated profile in I4/m with c/a = 1.001. This is 4 times smaller than the distortion reported for Ba2CaReO6, c/a = 1.004.13 The estimated resolution of the diffractometer in this angular range is Δd/d = 5 × 10−4. Note that the refined cell constant from the ambient temperature Xray data is in excellent agreement with the literature, a0 = 8.0847(1) Å.11 The fits to the neutron data, Figure 2a,b, in Fm3̅m are excellent at both temperatures, and there is no discernible distortion upon cooling to 3.5 K at this resolution even at high angles (insets). In the refinements of the neutron data it was necessary to fix the displacement factor B of Re at 290 K and of Ba and Re at 3.5 K to avoid negative values. Attempts to refine the site occupations of the Mg and Re sites did not lead to any improvement in this situation, and one can conclude that there is no firm evidence from these refinements of significant levels of site mixing. Ba2ZnReO6. As already mentioned only a low-precision unit cell constant had been reported in work from the 1960s.24,25 Again, it was necessary to fix the values of certain displacement parameters in the refinements. For the M = Zn DP the neutron data were taken at higher resolution, Δd/d = 2 × 10−3, than for the M = Mg case. The refinements are shown in Figures 1 and 2 in the Supporting Information. While there is no evidence in the X-ray data for a distortion to I4/m symmetry, see inset

■

RESULTS AND DISCUSSION Crystal Structure. The results of the structural analysis of all three DP using both X-ray and neutron powder data at ambient temperature (290 K) and 3.5 K are summarized in Table 2. In all cases refinements were done with Ba in 8c (1/4 1/4 1/4), M in 4b (1/2 1/2 1/2), Re in 4a (0 0 0), and O in 24e (x 0 0) of space group Fm3̅m (No. 225). Selected interatomic distances are given in Table 1 of the Supporting Information. For all three DP materials the structure is well-described by the Fm3̅m model at both 290 and 3.5 K. Each sample will be discussed briefly, and selected data will be shown for M = Mg. E

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 4. Heat capacity results for Ba2MReO6 M = Mg and Zn. (a) M = Mg, comparison with the lattice match material, Ba2MgWO6. (b) M = Zn, comparison with the lattice match material, Ba2ZnWO6. (c) The magnetic components for both M = Mg and Zn. Note sharp λ peak for M = Mg at 18 K and the much broader peak at 11 K for M = Zn. In both cases a second broad anomaly appears near 33 K. (d) The total magnetic entropy loss for M = Mg showing the approach to R ln 4. (e, f) Evidence for an F spin wave, T1.5 power law, in the low-temperature magnetic heat capacity for both M = Mg and Zn.

anticipated, the unit cell constant is larger by ∼3% than those for either M = Mg or Zn but very close to that for Ba2NaOsO6, being larger by only 0.9%. Physical Properties. M = Mg and Zn. It is convenient to discuss the cases of M = Mg and Zn together, as the results are similar. As already mentioned, the M = Mg phase had been reported before, but here the characterization is significantly more thorough. As discussed above, the structure is examined in greater detail both at ambient and lower temperatures by Xray and neutron diffraction to search for evidence of a distortion as has been reported for Ba 2 CaReO 6 and Ba2NaOsO6. Magnetization measurements were done to confirm the F state and to investigate the paramagnetic regime. Heat capacity data are reported for the first time to determine Tc with better accuracy and to examine the entropy losses. Are these consistent with a j = 3/2 ground state or with j = 1/2 claimed for Ba2NaOsO6?29 Muon spin relaxation data are used to determine the order parameter. No data for the M = Zn DP had been reported before. Magnetic Susceptibility. In Figure 3a−d are shown magnetic susceptibility, isothermal magnetization, and Fisher heat capacity data for Ba2MReO6, M = Mg and Zn. Note,

Supporting Information Figure 1, it was noticed that the peak widths were approximately twice those for Ba2MgReO6 for the same reflections. This was interpreted as evidence of a finite particle size for this sample of Ba2ZnReO6. The particle size was estimated by fitting several peaks for both materials to a Lorenztian line shape (after conversion from 2θ to Q = 4π sin θ/λ). The line widths for Ba2MgReO6 were taken as the resolution limit, and the resulting particle size estimate was 320(20) Å or ∼32 nm, which corresponds to ∼40 DP unit cells. The neutron data, Figure 2 (Supporting Information), were refined in Fm3̅m. Simulations of a distortion to I4/m symmetry were performed, and it was estimated that deviations from Fm3̅m symmetry would have been detected for c/a = 1.002. Ba2Y2/3ReO6. Results of the Rietveld refinements are shown in Figures 3 and 4 in the Supporting Information. The peak widths for the X-ray data were comparable to those for M = Mg with no evidence for systematic broadening, unlike the case for M = Zn, and no evidence for distortion to I4/m symmetry at ambient temperature. As well, the neutron data showed no clear evidence for a crystallographic distortion at either 290 K or 3.5 K at the stated resolution. The occupation of the Y site refines to 2/3 to within one standard deviation in all cases. As F

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

the λ anomaly at 18 K approaches that of R ln 2, ∼5 J/mol·K. The total entropy loss for M = Zn (not shown) is only 4.99 J/ mol·K. Again this is likely traceable to the nanoparticle size of this sample. Finally, the low-temperature magnetic component for both M = Mg and Zn follows a T3/2 power law expected for an F spin wave, Figure 4e,f.28 The results for M = Re should be compared with those reported for Ba2NaOsO6, also a ferromagnet with Tc = 6.8 K and a saturation moment/Os7+ ≈ 0.2 μB.29 For this material the heat capacity data extended to only 15 K, and a lattice match material was not measured. A λ-anomaly was indeed observed at 6.8 K, and the entropy loss was just below 5 J/mol·K2, consistent with a doublet ground state. This was taken as evidence of a crystallographic distortion, possibly Jahn−Teller (JT) in origin, which splits the j = 3/2 ground state into two doublets as indicated in Figure 5. The detection of such a

Figure 3a, typically F behavior with Tc near 18 K (Mg) and 11 K (Zn). In both cases the ZFC and FC susceptibilities are indistinguishable above the respective Curie temperatures. The inverse susceptibility data, Figure 3b, do not show an obvious Curie−Weiss regime over the studied temperature range. Attempts to fit the high-temperature regions for both materials (∼200−300 K) yield rather large, negative θ = −373 K (Mg) and −66(2) K (Zn), which seem inconsistent with the observed F behavior. Effective moments derived from these fits μeff = 1.51 μB (Mg) and 0.940 μB are both below the spin-only value of 1.73 μB, but these values should be interpreted with caution. For M = Mg there does exist a very narrow temperature range, ∼22−40 K, for which a linear χ−1 versus T behavior obtains, and the C−W parameters are θ = 20.8(2) K and μeff = 0.496 μB, which are more consistent with the observed F behavior. The Fisher heat capacity, Figure 3c, shows peaks centered at 18 K (Mg) and 11 K (Zn) agreeing nicely with Figure 3a.30 Saturation moments/Re6+ ion at 2 K, Figure 3d, approach 0.3 μB (Mg) with an appreciable coercivity of ∼0.2 T and 0.13 μB with a smaller coercivity, ∼0.08 T (Zn). As the D−M interaction is not allowed in Fm3m ̅ symmetry and as the moment is too large in any event, a canted AF origin for these moments can be ruled out. The overall conclusion from the analysis of bulk susceptibility and magnetization data is that both Ba2MgReO6 and Ba2ZnReO6 are F with Tc = 18 K (Mg) and 11 K (Zn). These results for M = Mg are in reasonable agreement with those of Bramnik et al.,11 although this group did not report C−W parameters and measured μsat = 0.13 μB/ Re6+ at 10 K, less than half of the value reported here. It is important to compare these results with those for two related, isoelectronic DP materials, namely, Ba2LiOsO6 and Ba2NaOsO6. The former, which has a unit cell constant of 8.1049 Å, which is bracketed by the M = Mg phase (0.25% smaller) and the M = Zn phase (0.12% larger), is AF with TN = 8 K. Ba2NaOsO6, however, is F with Tc = 6.8 K, ∼3 times smaller than Tc = 18 K found for Ba2MgReO6 and slightly smaller than Tc = 11 K for Ba2ZnReO6. The saturation moment, 0.2 μB, is intermediate between the M = Mg and Zn Re6+-based DP. The cell constant for Ba2NaOsO6 is 2.5% and 2.1% larger than those for M = Mg and Zn, respectively. These results, especially for the pairs Ba 2 LiOsO 6 / Ba2MgReO6 and Ba2LiOsO6/Ba2ZnReO6, which might be called structural, compositional and electronic doppelgängers, are difficult to understand. While the phase diagram of Chen, Pereira, and Balents, developed for cubic t2g1 DP systems with strong SOC, does indeed contain both F and AF ground states, the parameters involved, J′ the relative magnitude of competing nearest neighbor F and AF exchange and V, an electric quadrupole moment, are difficult to quantify, experimentally.22 Heat Capacity. These results are displayed in Figure 4a−f. The total heat capacity of M = Mg and Zn is shown along with those for the lattice match materials Ba2MgWO6 and Ba 2 ZnWO 6 in Figure 4a,b. Subtraction of the lattice components yields the magnetic contribution for both materials, Figure 4c. Note the sharp lambda maximum for M = Mg at 18 K, consistent with the Fisher heat capacity, Figure 3c. The maximum for M = Zn near 11 K is much broader. This is likely due to the nanosize particles of this sample. Remarkably, both show a second broad maximum near 33 K, a feature not reported before for any nd1 DP. For M = Mg the entropy loss over the entire temperature range, Figure 4c, is 9.68 J/mol·K, which approaches that for a j = 3/2 ground state, 11.52 J/mol·K. Interestingly, the entropy loss associated with

Figure 5. Possible energy level scheme for a t2g1 ion subject to SOC and a JT splitting. The numbers in parentheses indicate the state degeneracy.

distortion has been reported anecdotally, but, to our knowledge, a detailed study has not been published.20 It is important to determine if a JT distortion also occurs for Ba2MgReO6, One possible interpretation of the broad anomaly near 33 K for both DP is that it is a Schottky-type feature that arises from the splitting of the j = 3/2 state into two doublets separated by the energy Δ as in Figure 5. Δ can be estimated from the standard theory for Schottky anomalies, that is, Δ = T(Cpmax)/ 0.417 = 80 K or ∼7 meV.28 This energy lies within the range that is easily detected by spectroscopic methods, particulary, inelastic neutron scattering (INS). Inelastic Neutron Scattering. Data were collected for all three samples M = Mg, Zn, and Y2/3 using incident energies, Ei = 25, 60, and 120 meV. The data set for 25 meV has energy resolution sufficient to explore the low-energy excitation spectrum to locate any excitation at Δ ≈ 7 meV. These data are shown in Figure 5 of the Supporting Information for 6 K with the empty can subtracted. Note the absence of any Qindependent excitation near 7 meV, nor is there is any evidence for a Q-independent excitation up to 100 meV. Thus, there is no spectroscopic evidence for any electronic transition within the measured range, and it is difficult to explain the 33 K heat capacity anomaly in the context of a structural distortion that splits the j = 3/2 ground state. Muon Spin Relaxation. Given the very small ordered moment on Re6+ inferred from Figure 3c of ∼0.3 μB, detection with unpolarized neutrons is highly unlikely. μSR can detect order due even to such small moments and affords an opportunity to determine the behavior of the order parameter. Figure 6a,b shows the temperature development of the G

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 6. (a) Temperature development of the asymmetry parameter for Ba2MgReO6 in ZF mode. Note the onset of strong relaxation below 20 K and the appearance of weak oscillations below 15 K. The dashed line is a fit to the function described in the preceding text. (b) Temperature dependence of the weighted internal field seen by the muon. The data are consistent with Tc = 18 K, as found from both magnetization and heat capacity studies, Figures 3 and 4.

Figure 7. Calculated heat capacity (a), magnetization (b), and inverse susceptibility (c) for the FM110 phase, J = 1, J′ = 0.05, and V = 0.5. See Supporting Information for details.

asymmetry and that of the derived internal field. The spectra were fitted to a sum of three signals, two of which were damped cosines, while the third was an exponential as follows: t

t

A1·cos(ω1t + φ)·e−λ1 + A 2 ·cos(ω2t + φ)·e−λ 2 + A3 ·e−λ 3

close to the value of 1/3 expected for a polycrystalline sample. The presence of two oscillating signals suggests that there are two distinct muon sites in Ba2MgReO6, although there is one crystallographic oxygen site in Fm3̅m. This suggests the possibility of a local distortion, as the diffraction data point to Fm3̅m symmetry at all temperatures. However, there is no spectroscopic (INS) evidence for a distortion, which would be observable even for a local effect. The precession signals are highly damped, indicating that there is a broad distribution of

t

The relative amplitudes of the three signals were fit globally as a function of temperature as was the ratio between the frequencies of the two cosine signals. The amplitude of the slow exponential refined to a value of 0.27 of the total asymmetry, H

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 8. Calculated heat capacity (a), magnetization (b), and inverse susceptibility (c) for the FM100 phase. J = 1, J′ = 0.19, and V = 0.24. See Supporting Information for details.

Figure 9. Magnetic susceptibility results for Ba2Y2/3ReO6. (a) The inverse susceptibility, which does not follow the C−W law to 300 K. (b) Evidence for a spin glass transition at 16 K. (inset) The Fisher heat capacity with a sharp maximum near 14 K. (c) A hysteresis loop at 2 K. (d) Alternating current data showing clear frequency dependence within the Mydosh limits for a classic spin glass.33

internal fields at the muon sites. This behavior is consistent with F ordering in a polycrystalline sample, where it is expected that a range of grain and magnetic domain sizes would result in a highly inhomogeneous internal field distribution. The temperature dependence of the average internal field, obtained from the fitted precession frequencies and their relative amplitudes, is plotted in Figure 8, indicating a transition temperature of ∼18 K, consistent with the bulk measurements. The average internal field at low temperatures is ∼190 G.

In summary, both Ba2MgReO6 and Ba2ZnReO6 are welldescribed by Fm3̅m symmetry at room temperature within the resolution limits stated and likely remain cubic to 3.5 K although the resolution at that temperature is lower. Both are ferromagnets with Tc = 18 K (Mg) and 11 K (Zn), respectively, from magnetization and heat capacity studies. A remarkable feature is the appearance of a second broad maximum in the heat capacity near 33 K for both, which could be taken as evidence for an electronic excitation due to a crystallographic I

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 10. Heat capacity results for Ba2Y2/3ReO6. (a) Comparison with the lattice match material, Ba2Y2/3WO6. (b) The magnetic contribution showing a broad maximum at ∼27 K, not Tg = 16 K. (c) A linear dependence at low temperatures, typical for the spin glass state.

Thus, it is tempting to characterize the magnetic structure as FM110 for both DP. Ba2Y2/3ReO6. Having discussed the two F materials, attention is now paid to the M = Y2/3 phase, which shows very different behavior. This material has not been reported before, but the closely related DP material, Ba2Y2/3WO6 is known.31 As mentioned earlier, the main goal here is to examine the effect of the anticipated larger cell constant on the net magnetic exchange correlations and, in particular, to compare with F Ba2NaOsO6, which has nearly the same unit cell constant. Magnetic Susceptibility. These data are shown in Figure 9. From 9a, the inverse susceptibility, it is clear that the C−W law is not obeyed up to 300 K. Attempts to fit the data in the range from 200 to 300 K result in μeff = 2.34 μB and θ = −714(12) K. Clearly, the μeff value is impossible, and while the large negative θ suggests strong AF exchange, this should be regarded with great caution. Figure 9b shows a clear ZFC/FC divergence at 16 K, typical of a spin-glass-type transition, and from the inset the Fisher heat capacity indicates a peak near 14 K. A weak divergence is seen below 4 K. This may be due to an undetected impurity phase, as there is no signature of this effect in the heat capacity. The hysteresis loop, Figure 9c, shows no saturation and moments ∼40 times smaller than for either Ba2MgReO6 or Ba2ZnReO6. Finally, the alternating current susceptibility, Figure 9d, is consistent with a classic spin glass, satisfying the Mydosh criterion, ΔTf/[TfΔ(log ν)] = 0.022, where Tf is the spin freezing temperature, and ν is the frequency.32 Heat Capacity. From Figure 10, there are some surprises. In 10a, the heat capacity is compared with that for the lattice match Ba2Y2/3WO6. The data for the latter were fit to the polynomial Cp = 0.01T + 1.0 × 10−3T3 − 2.27 × 10−7T5 to an agreement index of 0.999 and are shown as a red line. Note the absence of any obvious anomaly near Tg = 16 K. The magnetic component, Figure 10b, shows a broad maximum near 25 K,

distortion, local or otherwise, as reported for Ba2NaOsO6. There is, however, no evidence from inelastic neutron scattering for an excitation arising from the splitting of the j = 3/2 ground state up to 100 meV for either Ba2MgReO6 or Ba2ZnReO6.

■

COMPARISON WITH THEORY At this stage it is important to compare the results for the two F 5d1 DP with the mean-field theory of Chen, Pereira, and Balents for nd1 cubic DP subject to strong SOC.22 They predict three ordered phases, one AFM and two F, FM110 and FM100, although the existence range of the latter is severely limited. FM110 and FM100 are simple ferromagnets with the easy axes along [110] and [100], and the AFM state is described by an ordering wave vector Q = (001), which is that for a Type I facecentered cubic AFM. From the formalism of the heat capacity,22 susceptibility, and magnetization for both F phases have been calculated, as described in the Supporting Information and shown in Figures 7 and 8. Note first that the calculated heat capacity for both the FM110 and FM100 phases shows two peaks, one narrow at lower T and one broader at higher T, in agreement with the experimental results for both Ba2MgReO6 and Ba2ZnReO6. Thus, the double peak heat capacity behavior appears to follow naturally from the Chen/Pereira/Balents mean field theory and provides a plausible explanation for the 33 K peak seen for both samples. The magnetization for FM110 is consistent with a continuous phase transition, while that for FM100 signals a first-order or discontinuous transition. Magnetization and μSR results for Ba2MgReO6 indicate a continuous transition. Furthermore, the calculated inverse susceptibility for FM110, Figure 7c, does not appear to follow the Curie−Weiss (C−W) law over a wide temperature range, which is consistent with the results for both M = Mg and Zn. As well, any force fitting to a C−W law would result in a negative temperature intercept. J

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 11. μSR spectra of Ba2Y2/3ReO6 measured in zero applied field for temperatures of (a) 14−37 K and (b) 2−12 K. The solid lines show fits to the data using two dynamic Kubo−Toyabe functions as described by the text. Panel (c) shows the temperature dependence of the relaxation rates extracted from the fits, and panel (d) shows the temperature dependence of the hopping parameters.

two components contain one-third (for λ1, Γ1) and two-thirds (for λ2, Γ2) of the total asymmetry. We attribute these two components to inequivalent muon sites caused by relative proximity to yttrium on the partially occupied B-site. The temperature dependence of the relaxation rates shown in Figure 11c shows an order−parameter-like behavior below 20 K, with a small rate slowly decreasing to ∼30 K that may indicate some disorder broadening the transition. This may explain the very broad heat capacity anomaly seen near 25 K. The hopping rates of Figure 11d show a large fluctuation rate near the apparent glass transition at ∼16 K and persistent fluctuations that decrease with decreasing temperature. The picture of the ground state of Ba2Y2/3ReO6 that emerges from these μSR results is rather more complex than that of a ideal spin glass, with both spin frozen components along with persistent spin dynamics even below 2 K. It is worth contrasting these results with those for Sr2MgReO6, another DP Re6+-based spin glass, where the spectra were fit to a single Kubo−Toyabe function with no residual relaxation.14 Sr2MgReO6 also shows no obvious positional disorder, unlike Ba2Y2/3ReO6.(22)

not Tg. The total entropy loss below 45 K is only 2.99 J/mol·K far less than that for even a doublet ground state, which suggests a high level of frustration. In Figure 10c the lowtemperature data follow a linear power law in temperature, classic spin glass behavior.32 In summary, Ba2Y2/3ReO6, with a unit cell constant more than 3% greater than either of the ferromagnets Ba2MgReO6 or Ba2ZnReO6, but only 0.9% greater than F Ba2NaOsO6, shows strong AF spin correlations. Instead of forming a Neél ground state, both magnetic susceptibility and heat capacity data support a classical spin glass picture for Ba2Y2/3ReO6 with Tg ≈ 16 K. This is almost certainly due to the high concentration (33%) of Y vacancies on the B site. Thus, the correlation between cell constant and net exchange for the Re6+-based DP appears to be opposite to that for the Os7+-based DP. That is, for the Os7+ phases, smaller cell constants are associated with AF order (Ba 2LiOsO6 ), which gives way to F order (Ba2NaOsO6) as the cell constant increases. Muon Spin Relaxation. Insight into the spin dynamics of this material can be obtained from μSR studies. Figure 11a,b shows the μSR asymmetry spectra for BaY2/3ReO6. These data show relaxation continuously developing below 30 K, with a distinct minimum at early times appearing below ∼12 K. Asymmetry spectra with such a minimum are characteristic of systems with frozen, randomly oriented, spins. However, systems with fully frozen spins will exhibit a recovery of the asymmetry to 1/3 of the initial asymmetry after this minimum, while our data only show a partial recovery followed by further relaxation. This indicates that the spins are not fully frozen, and some dynamic fluctuations remain even down to 2 K. The data were fit to a sum of two dynamic Lorentzian Kubo−Toyabe functions, with relaxation rates λ1 and λ2 representing the static field distributions and hopping parameters Γ1 and Γ2 representing the fluctuations.33 The

■

SUMMARY AND CONCLUSIONS Comparing the three Re6+ DP phases studied here, two are F with a true phase transition for Ba2MgReO6 and at least fairly long-range F correlations for 30 nm particles of Ba2ZnReO6. However, Ba2Y2/3ReO6 shows dominant AF exchange and a rather complex ground state with both static spin frozen and dynamic components. The stabilization of such a ground state is due both to the high concentration of vacancies on the Y site and the dominant AF exchange. While the cell constants of the two F phases differ by only 0.37%, that for Ba2Y2/3ReO6 is larger by 3.4%, nearly an order of magnitude, suggesting that a transition to dominant AF spin correlations occurs at large cell constants. This is exactly opposite to the behavior of the K

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry isostructural and isoelectronic Os7+ DP. A remarkable feature of the F phases is the occurrence of two heat capacity peaks, one sharp at Tc and one broad at higher temperatures. One explanation, that the broad peak is a Schottky anomaly associated with a crystallographic distortion, suffers from a lack of evidence, as diffraction data are consistent with Fm3̅m symmetry for both DP, unlike the cases of Ba2CaReO6 and Ba2NaOsO6, which show a distortion to I4/m symmetry. Also, a predicted excitation at ∼7 meV is absent in the INS spectra of either material; nor is there any observable excitation up to 100 meV. However, the heat capacity computed from the Chen/ Pereira/Balents mean field theory is in semiquantitative agreement with the experimental results, predicting a sharp peak at low temperature (Tc) and a broad peak at higher temperature.

■

(5) Thompson, C. M.; Marjerrison, C. A.; Sharma, A. Z.; Wiebe, C. R.; Maharaj, D. D.; Sala, G.; Flacau, R.; Hallas, A. M.; Cai, Y.; Gaulin, B. D.; Luke, G. M.; Greedan, J. E. Frustrated magnetism in the double perovskite La2LiOsO6: A Comparison with La2LiRuO6. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 01443. (6) Yuan, Y.; Feng, H. L.; Ghimire, M. P.; Matsushita, Y.; Tsujimoto, Y.; He, J.; Tanaka, Y.; Katsuya, M.; Yamaura, K. High-Pressure Synthesis, Crystal Structures and Magnetic Properties of the 5d Double Perovskite Oxides Ca2MgOsO6 and Sr2MgOsO6. Inorg. Chem. 2015, 54, 3422−3431. (7) Cussen, E. J.; Lynham, C. R.; Rogers, J. Magnetic Order Arising from Structural Distortion: Structure and Magnetic Properties of Ba2LnMoO6. Chem. Mater. 2006, 18, 2855−2866. (8) Aharen, T.; Greedan, J. E.; Bridges, C. A.; Aczel, A. A.; Rodriguez, J.; MacDougall, G.; Luke, G. M.; Imai, T.; Michaelis, V.; Kroeker, S.; Zhou, H.; Wiebe, C. R.; Cranswick, L. M. D. Magnetic properties of the geometrically frustrated S = 1/2 antiferromagnets, La2LiMoO6 and Ba2YMoO6 with the B-site ordered double perovskite structure: Evidence for a collective spin singlet ground state. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 224409. (9) de Vries, M. A.; Mclaughlin, A. C.; Bos, J.-W. Valence Bond Glass on a fcc Lattice in the Double Perovskite Ba2YMoO6. Phys. Rev. Lett. 2010, 104, 177202. (10) Carlo, J. P.; Clancy, J. P.; Aharen, T.; Yamani, Z.; Ruff, J. P. C.; Wagman, J. J.; van Gastel, G. J.; Noad, H. M. L.; Granroth, G. E.; Greedan, J. E.; Dabkowska, H. A.; Gaulin, B. D. Singlet − Triplet excitations out of the singlet ground state in the quantum fcc antiferromagnet, Ba2YMoO6. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 100404 (R).. (11) Bramnik, K. G.; Ehrenberg, H.; Dehn, J. K.; Fuess, H. Preparation, crystal structure and magnetic properties of double perovskites M2MgReO6(M = Ca,Sr,Ba). Solid State Sci. 2003, 5, 235− 241. (12) Stitzer, K. E.; Smith, M. D.; zur Loye, H.-C. Crystal growth of Ba2MOsO6 (M = Li,Na) from reactive hydroxide fluxes. Solid State Sci. 2002, 4, 311−316. (13) Yamamura, K.; Wakeshima, M.; Hinatsu, Y. Structural phase transition and magnetic properties of double perovskites Ba2CaMO6(M = W,ReOs). J. Solid State Chem. 2006, 179, 605−612. (14) Wiebe, C. R.; Greedan, J. E.; Kyriakou, P. P.; Luke, G. M.; Gardner, J. S.; Fukaya, A.; Gat-Malureanu, I. M.; Russo, P. L.; Savici, A. T.; Uemura, Y. J. Frustration-driven spin freezing in the S = 1/2 fcc perovskite Sr2MgReO6. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 134410. (15) Wiebe, C. R.; Greedan, J. E.; Luke, G. M.; Gardner, J. S. Spinglass behavior in the S = 1/2 fcc ordered double perovskite, Sr2CaReO6. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65, 144413. (16) Mclaughlin, A. C.; de Vries, M. A.; Bos, J.-W. Persistence of the valence bond glass state in the double perovskites Ba2‑xSrxYMoO6. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 094424. (17) Shannon, R. D. Revised Efective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides. Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 1976, 32, 751−767. (18) Howard, C. J.; Kennedy, B. J.; Woodward, P. M. Ordered double perovskites − a group theoretical analysis. Acta Crystallogr., Sect. B: Struct. Sci. 2003, 59, 463−471. (19) Goldschmidt, V. M. Die Gesetze der Krystallochemie. Naturwissenschaften 1926, 14, 477−485. (20) Ishizuka, H.; Balents, L. Magnetism in S= 1/2 double perovskites with strong spin orbit coupling. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 184422. (21) Greedan, J. E.; Derakhshan, S.; Ramezanipour, F.; Siewenie, J.; Proffen, Th. Search for disorder in the spin-glass double perovskites Sr2CaReO6 and Sr2MgReO6 using neutron diffraction and neutron pair distribution function analysis. J. Phys.: Condens. Matter 2011, 23, 164213.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b01933. Refinements of X-ray and neutron powder diffraction data for Ba2ZnReO6 and Ba2Y2/3ReO6; a table of selected interatomic distances; neutron inelastic scattering data for Ba2MReO6, where M = Mg, Zn, and Y2/3; details for the calculation of the heat capacity, magnetization, and susceptibility based on the mean field theory of Chen, Pereira, and Balents. (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS J.E.G., G.M.L., and B.D.G. thank the Natural Sciences and Engineering Research Council of Canada for support via the Discovery Grant Program. P. Dube assisted with collection of magnetization and heat capacity data. We thank the TRIUMF CMMS staff for invaluable assistance with the μSR experiments. Research at Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy.

■

REFERENCES

(1) Tokura, Y.; Kimura, T.; Sawada, H.; Terakura, K.; Kobayashi, K.I. Room temperature magnetoresistance in an oxide material with an ordered double perovskite structure. Nature 1998, 395, 677−680. (2) Kobayashi, K.-I.; Kimura, T.; Tomioka, Y.; Sawada, H.; Terakura, K.; Tokura, Y. Intergrain tunneling magnetoresistance in polycrystals of the ordered double perovskite Sr2FeReO6. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 11159−11161. (3) Ramirez, A. P. Strongly Geometrically Frustrated Magnets. Annu. Rev. Mater. Sci. 1994, 24, 453−480. (4) Thompson, C. M.; Carlo, J. P.; Flacau, R.; Aharen, T.; Leahy, I. A.; Pollichemi, J. R.; Munsie, T. J. S.; Medina, T.; Luke, G. M.; Munevar, J.; Cheung, S.; Goko, T.; Uemura, Y. J.; Greedan, J. E. Long range order in the 5d2 double perovskite Ba2CaOsO6: Comparison with spin-disordered Ba2YReO6. J. Phys.: Condens. Matter 2014, 26, 306003. L

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry (22) Chen, G.; Pereira, R.; Balents, L. Exotic phases induced by spin orbit coupling in ordered double perovskites. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 174440. (23) Dodds, T.; Choy, T.-P.; Kim, Y. B. Interplay between lattice distortion and spin orbit coupling in double perovskites. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 104439. (24) Longo, J.; Ward, R. Magnetic Compounds of Hexavalent Rhenium with the Perovskite-type Structure. J. Am. Chem. Soc. 1961, 83, 2816−2818. (25) Sleight, A. W.; Longo, J.; Ward, R. Compounds of Osmium and Rhenium with the Ordered Perovskite Structure. Inorg. Chem. 1962, 1, 245−250. (26) Selwood, P.W. Magnetochemistry; Interscience Publishers: New York, 1956. (27) Granroth, G. E.; Kolesnikov, A. I.; Sherline, T. E.; Clancy, J. P.; Ross, K. A.; Ruff, J. P. C.; Gaulin, B. D.; Nagler, S. E. SEQUOIA: A Newly Operating Chopper Spectrometer at the SNS. J. of Phys. Conf. Ser. 2010, 251, 012058. (28) Gopal, E. S. R. Specific Heats at Low Temperatures; Plenum Press: New York, 1966; pp 90, 104. (29) Erickson, A. S.; Misra, S.; Miller, G. J.; Gupta, R. R.; Schlesinger, Z.; Harrison, W. A.; Kim, J. M.; Fisher, I. R. Ferromagnetism in the Mott Insulator Ba2NaOsO6. Phys. Rev. Lett. 2007, 99, 106404. (30) Fisher, M. E. Relation between the specific heat and susceptibility of an antiferromagnet. Philos. Mag. 1962, 7, 1731−1743. (31) Schittenhelm, H.-J.; Kemmler-Sack, S. Uber die Polymorphie der Wolframperowskite Ba2SE0.67WO6. Z. Anorg. Allg. Chem. 1976, 425, 175−179. Rauser, G.; Kemmler-Sack, S. Strukturbestimmungen an geordneten Perowskiten des Typs Ba2BIII0.67MVIO6. Z. Anorg. Allg. Chem. 1977, 429, 181−184. (32) Mydosh, J. A. Spin Glasses. An Experimental Introduction; Taylor and Francis Ltd: London, 1993; pp 67, 98. (33) Uemura, Y. J. μSR relaxation functions in magnetic materials. In Muon Science: Muons in Physics, Chemistry and Materials; Lee, S. L., Kilocoyne, S. H., Cywinski, R., Eds.; The Scottish Universities Summer School in Physics, Institute of Physics Publishing: London, 1998; pp 85−112.

M

DOI: 10.1021/acs.inorgchem.6b01933 Inorg. Chem. XXXX, XXX, XXX−XXX