Synthesis, Crystal Structure, and Magnetic Properties of the Highly

Sep 21, 2017 - ABSTRACT: In an effort to understand the structure−property relationship in magnetically frustrated systems, an orthorhombic analog o...
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Synthesis, Crystal Structure, and Magnetic Properties of the Highly Frustrated Orthorhombic Li4MgReO6 JoAnna Milam-Guerrero,†,‡ Charles J. Bloed,† Phuong-Hieu T. Nguyen,† Gia T. Tran,† William P. Martin,∥ Demetrios V. Papakostas,∥ Jefferson Toro,∥ Murray N. Wilson,§ Jeremy P. Carlo,∥ Graeme M. Luke,§ Brent C. Melot,‡ Jiyeong Gu,⊥ and Shahab Derakhshan*,† †

Department of Chemistry and Biochemistry, California State University, Long Beach, 1250 Bellflower Boulevard, Long Beach, California 90840, United States ‡ Department of Chemistry, University of Southern California, 3620 McClintock Avenue, Los Angeles, California 90089-1062, United States § Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4M1, Canada ∥ Department of Physics, Villanova University, 800 Lancaster Avenue, Villanova, Pennsylvania 19085, United States ⊥ Department of Physics and Astronomy, California State University, Long Beach, 1250 Bellflower Boulevard, Long Beach, California 90840, United States ABSTRACT: In an effort to understand the structure−property relationship in magnetically frustrated systems, an orthorhombic analog of the S = 1/2 Re-based oxide Li4MgReO6 has been successfully synthesized and its physical properties were investigated. Li4MgReO6 had been previously synthesized in a monoclinic system in an ordered NaCl structure type. That system was shown to exhibit spin glass behavior below ∼12 K. The crystal structure of the latter phase was determined using powder X-ray diffraction data. A structural model was refined in the orthorhombic Fddd space group that resulted in cell dimensions of a = 5.84337 (7) Å, b = 8.33995 (9) Å, and c = 17.6237 (2) Å. The magnetic ions, Re6+ (S = 1/2), consist of various arrangements of interconnected triangles and trigonal prisms that offer potential for geometric magnetic frustration. Temperature dependent magnetic susceptibility reveals an AFM transition below ∼2 K along with a ZFC/FC divergence suggestive of spin freezing. The Curie−Weiss fitting parameters to the paramagnetic regime result in θ = −124 (1) K, which is indicative of predominant AFM interactions. A frustration index of ∼62 is in accordance with a highly frustrated magnetic ground state. Zero field (ZF) μSR data provides evidence for the onset of magnetic order below 4 K, along with the evidence for dynamical fluctuations up to 5 K. Moreover, longitudinal field (LF) μSR data reveals a complete decoupling in applied field at 2 K, which is indicative of static order in most or all of the volume fraction at ∼2 K, with partial ordered volumes coexisting with dynamical fluctuations up to 5 K. Estimates of the relative strengths of various magnetic exchange pathways at the level of spin-dimer analysis for this novel system are calculated and are compared to those of the previously reported values for the monoclinic analog.

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INTRODUCTION In materials composed of a triangular arrangement of paramagnetic ions when the nearest neighbor exchange interactions are antiferromagnetic (AFM), spin constraints cannot be satisfied simultaneously. This condition results in an unconventional magnetic ground state, which is known as geometric magnetic frustration (GMF).1 The degree of frustration is parametrized by the frustration index, f = |θW|/ TN,f, where θW is the Weiss constant and TN is the Neel temperature for long-range AFM order and Tf represents the spin freezing temperature.2 There are several families of transition metal oxides, which are composed of a face centered cubic (FCC) arrangement of cations. Such a structural pattern offers various triangular and tetrahedral cationic substructures, which may result in GMF. Among these families, ordered sodium chloride type systems © 2017 American Chemical Society

with the A5BO6 general formula have been the center of attention in our research program where A is a monovalent or divalent diamagnetic ion (such as Li+, Mg2+) and B is a highly oxidized paramagnetic 4d or 5d transition metal ion. A5BO6 systems are usually found in two space groups, namely C2/m and Fddd. We reported the first magnetic member of the family in Fddd symmetry, Li3Mg2RuO63 where Ru5+ (S = 3/2) ions form ribbons of edge-shared triangles. These ribbons are linked together by corner-sharing, which result in a three-dimensional arrangement of a magnetic ion sublattice. Li3Mg2RuO6 with relatively moderate frustration index (f = 6) is not highly frustrated. The temperature dependent magnetic susceptibility, heat capacity, and neutron diffraction data were all indicative of Received: June 20, 2017 Published: September 21, 2017 11633

DOI: 10.1021/acs.inorgchem.7b01537 Inorg. Chem. 2017, 56, 11633−11639

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Inorganic Chemistry a long range AFM order below 17 K for Li3Mg2RuO6.3 The isoelectronic and isostructural 5d analog, Li3Mg2OsO6,4 was shown to exhibit a very different magnetic ground state. A rather broad maximum in the DC susceptibility and heat capacity data at ∼8 K, along with the temperature dependent neutron diffraction study, indicated that a long-range order is not set, above 2 K. Other structurally related osmium-based systems such as Li4MgOsO65 and Li5OsO66 were synthesized and investigated. For the S = 1 case, Li4MgOsO6, specimens crystallizing in both monoclinic and orthorhombic systems (with C2/m and Fddd symmetries, respectively) were successfully synthesized. Both compounds exhibit predominant AFM exchange interactions, although neither of them undergoes an obvious transition down to 2 K.5 The S = 1/2 representative Li5OsO6, however, crystallizes only in the monoclinic crystal system and exhibits a long-range AFM transition with frustration index ∼1.6 The latter finding was a great surprise as its isoelectronic and isostructural Re-based compound (the monoclinic version of the title compound) had been previously shown to exhibit a highly frustrated spin glass magnetic ground state.7 The discrepancy was attributed to the local coordination environments of the two systems with socalled t2g1 electronic configurations. While the octahedral environment of the Os7+ system was extremely distorted, the Re6+ ions had relatively uniform distances from their six O2− neighbors, resulting in the almost equally probable occupation of the t2g states (dxy, dxz, and dyz orbitals) in the [ReO6]6− octahedra. This in turn results in effective competition between AFM interactions in the triangular lattice and is consistent with a highly frustrated magnetic ground state. However, the splitting within the so-called t2g levels in the [OsO6]6− octahedra is large and the most stable orbital has a significantly larger contribution of the unpaired electron and results in a dominant exchange interaction, which encourages low dimensional magnetic correlations, rather than GMF.6 Successful syntheses of Li4MgOsO65 in two crystal settings, namely in C2/ m and Fddd symmetries, motivated the search for the orthorhombic analogue of the previously reported Li4MgReO6. Here we report on the synthesis, crystal structure, and magnetic ground state of the novel orthorhombic modification of Li4MgReO6, which is the first S = 1/2 system in this crystal system.

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Phase analyses. To examine the formation and purity of the product, powder X-ray diffraction data were collected, employing a PANalytical X’Pert Pro MPD diffractometer, equipped with a linear X’Celerator detector, with Cu Kα1 radiation. Crystal structure determination using powder X-ray diffraction. The crystal structure was determined by Rietveld refinement of the powder X-ray data, using the General Structure Analysis System (GSAS) suite and the EXPGUI interface.8,9 The X-ray diffraction data were collected at room temperature in the range 17° ≤ 2θ ≤ 110° with ≈0.008° intervals. The crystal structure was obtained by refining the structural parameters from orthorhombic Li4MgOsO6, as an initial model. To improve the fitting quality, a second phase based on the monoclinic Li4MgReO67 was introduced. A pseudo-Voigt peak shape profile, which is a convolution of both Gaussian and Lorentzian functions, was chosen, and the parameters were refined to obtain the best fit to the experimental data. The residual factors are Rp = 0.069 and wRp = 0.092. The powder X-ray diffraction pattern along with the fit to the structural models is presented in Figure 1. The monoclinic/orthorhombic phase ratio was not significant and was calculated to be less than 5%.

Figure 1. Room temperature powder X-ray diffraction pattern of Li4MgReO6. The black crosses indicate the experimental data while the Rietveld refinement fit is shown as a solid green line. The thick black marks represent the peak positions of the orthorhombic phase, and the red ones represent those of the monoclinic phase. The bottom thin solid purple line represents the difference, and the peak positions are located by the vertical tick marks. Magnetic susceptibility measurement. The zero field cooled (ZFC) and field cooled (FC) temperature dependent DC magnetization data was collected on polycrystalline powders encased in a plastic capsule employing a Quantum Design PPMS equipped with a vibrating sample magnetometer (VSM). The temperature range was 2−360 K, and the applied magnetic field was 500 Oe. In addition, ZFC and FC low temperature susceptibility data were collected using a Quantum Design MPMS SQUID magnetometer equipped with an IQuantum He3 insert with a base temperature of 0.48 K, under the applied magnetic field of 1000 Oe. Muon spin relaxation spectroscopy. To further characterize the magnetic ground state, muon spin relaxation (μSR) measurements were undertaken. In a μSR experiment, a spin-polarized beam of muons is implanted into a sample, and the time dependence of the muon spin polarization is used to reconstruct the local magnetic field distribution. Measurements were conducted at TRIUMF (Vancouver, BC) using the M20 beamline with 4.2 MeV surface muons and the LAMPF spectrometer at temperatures from 2 to 125 K, in both zero field (ZF) and longitudinal field (LF) configurations. Theoretical calculations, spin dimer analyses. The relative values of the various spin exchange pathways were estimated by performing the extended Hückel, spin dimer analyses.10 The ReO66− units interact with each other by only supersuper exchange (SSE) mechanisms. For each designated pathway (Re2O1212− dimer) the

EXPERIMENTAL SECTION

Synthesis. Li4MgReO6 was synthesized via traditional solid state methods. Stoichiometric amounts of binary oxides (in accordance with the following equation, in desired oxidation states) were thoroughly mixed together using an agate mortar and pestle according to the following reaction in an argon-filled glovebox and pressed into a pellet. The pellet was placed in an alumina crucible and was sealed in an evacuated fused silica tube. 2Li 2O(s) + MgO(s) + ReO3(s) → Li4MgReO6(s) The sealed sample was subsequently heated at 725 °C in a muffle furnace for two cycles of 36 h each with an intermediate regrinding of the sample to ensure the homogeneity of the final product. The starting material ReO3 (99.9% Alfa Aesar) was used directly from the bottle; however, Li2O was prepared by heating lithium hydroxide monohydrate (Alfa Aesar, 98%) to 450 °C in a fused quartz tube under dynamic vacuum for 18 h and was then transferred into the glovebox. In addition, MgO was preheated by flame in a silica tube under dynamic vacuum to ensure the removal of trace amounts of moisture and also decomposition of carbonates before the mixing. 11634

DOI: 10.1021/acs.inorgchem.7b01537 Inorg. Chem. 2017, 56, 11633−11639

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Inorganic Chemistry intersite hopping energy, Δe, was estimated using the CAESAR package.11 For the oxygen s and p and rhenium d states double-ζ Slater type orbitals (STO’s) were employed whereas single-ζ STO’s were chosen for rhenium s and p states. The values of the ζi and ζ′i coefficients and valence shell ionization potentials, Hii, used for the calculations are presented in Table 1.

orthorhombic and monoclinic modifications are summarized in Table 2. There are four independent cationic sites in the unit cell. Re6+ ions with a significantly higher oxidation state and smaller ionic radius compared to those of the diamagnetic cations, Li+ = 0.76 Å, Mg2+ = 0.72 Å, and Re6+ = 0.55 Å,12 reside in an exclusive crystallographic site. The other three cationic positions are mixed occupied by diamagnetic monovalent and divalent ions. The chemical composition was refined to Li3.20(1)Mg1.80ReO6. This deviation from the nominal chemical composition is understood based on poor sensitivity of the powder X-ray diffraction method to the light elements such as lithium. A similar observation regarding the underestimated Li:Mg ratio in the empirical formula using X-ray diffraction analysis has previously been reported for Li3Mg2OsO6. The same reason applies for determination of thermal displacement parameters, so reasonably arbitrary fixed values of 0.01, 0.02, and 0.015 for Re, Li/Mg, and O sites, respectively, were used during the refinement. The overall residual factors of Rp = 0.067, wRp = 0.090 are indicative of a good quality refinement (Figure 1). The refinement parameters are summarized in Table 3. Re−O bond distances along with

Table 1. Values for the ζi Coefficients and Valence Shell Ionization Potentials Hii of the Atomic STO’s Employed for the Spin Dimer Calculations for Li4MgReO6 Atom

Orbital

Hii (eV)

ζi

C

ζ′i

C′

O O Re Re Re

2s 2p 6s 6p 5d

−32.300 −14.8000 −9.3600 −5.960 −12.660

2.688 3.694 2.346 1.730 4.339

0.7076 0.3322 1 1 0.5886

1.675 1.659

0.3745 0.7448

2.309

0.5627

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RESULTS AND DISCUSSION Crystal structure. The crystal structure of the orthorhombic Li4MgReO6 is shown in Figure 2. The novel

Table 3. Atomic Coordinates, Occupancy Factors, and Arbitrary Values of Equivalent Isotropic Displacement Parameters for Li4 MgReO6 Refined in Fddd Re M1 M2 M3 O1 O2

x

y

Z

0.125 0.125 0.125 0.125 0.125 0.1061(9)

0.125 0.125 0.625 0.625 0.3614(7) 0.3778(7)

0.125 0.2970(7) 0.2967(7) 0.125 0.125 0.2938(3)

Uiso (Å2)

Li/Mg Occ. 0.71(1)/0.29 0.36(1)/0.64 0.69(1)/0.31

0.01 0.02 0.02 0.02 0.015 0.015

the bond valence sums (BVS)13 for both structures are presented in Table 4. Since bond valence parameters are not Table 4. Coordination Sphere of Re6+ in Li4 MgReO6 Refined in Fddd and C2/m Space Groups 2×Re−O1 4×Re−O2 BVS for Re

Fddd

C2/m7

1.971(6) Å 1.968(4) Å 5.98

1.932 1.962 5.72

available in the literature for Re6+, those of Re7+ were employed for this purpose. Please note that of an essentially perfect octahedron in the coordination environment of Re, within the errors, is in place. Magnetic Susceptibilities. There is no indication of a magnetic transition in ZFC and FC magnetic susceptibility data for orthorhombic Li4MgReO6, between 5 and 360 K, which are presented in Figure 3a and Table 5. This is in contrast with what was previously shown for the monoclinic analog of the title compound where a divergence between ZFC and FC data was observed at ∼12 K. Inverse susceptibility data from 200 to 360 K are shown in Figure 3b. The data fit to the Curie−Weiss

Figure 2. Crystal structure of the new modification of Li4MgReO6. The blue octahedra represent [ReO6]6−, the yellow spheres represent Li/Mg sites, and the red spheres represent oxygen ions.

modification of Li4MgReO6 crystallizes in the orthorhombic crystal system with Fddd space group in an NaCl structure type with cell parameters a = 5.84337 (7) Å, b = 8.33995 (9) Å, and c = 17.6237 (2) Å and V = 858.86 (1) Å3, with eight formula units per unit cell. It should be noted that the cell volume is exactly four times larger than that of the previously discovered monoclinic analog, where the unit cell was occupied by two formula units of Li 4 MgReO 6 . Cell constants of both

Table 2. Unit Cell Constants and Refinement Parameters of Orthorhombic and Monoclinic Versions of Li4MgReO6

Fddd C2/m7

a (Å)

b (Å)

c (Å)

α, β, γ (deg)

V (Å 3)

Rp, wRp

5.84337 (7) 5.0979 (3)

8.33995 (9) 8.8163(5)

17.6237 (2) 5.0815(3)

90, 90, 90 90, 109.835(2), 90

858.86 (1) 214.83(2)

0.067, 0.090

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DOI: 10.1021/acs.inorgchem.7b01537 Inorg. Chem. 2017, 56, 11633−11639

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Figure 3. (a) Temperature dependent zero-field cooled/field cooled magnetic (ZFC, FC) susceptibility data for Li4MgReO6 between 5 and 360 K. The inset represents the Curie−Weiss fit in the paramagnetic regime, 200 K − 360 K. (b) Field dependence of the magnetic moment for Li4MgReO6 at 5 K and 300 K.

Table 5. Comparison between the Magnetic Properties of Orthorhombic Li4MgReO6 and Those of Monoclinic Modification Fddd C2/m7

TN (K)

θ (K)

μeff (B.M.)

f

∼2 12

−124 (1) −166 (3)

1.12 (1) 1.14 (1)

62 14

C

law, χ = T − θ . The resulting parameters from the fit are C = 0.157(1) emu·K/mol and θ = −124(1) K. The effective magnetic moment, μeff (derived from the C) is 1.12(1) μB, which is smaller than the expected spin only value of 1.74 μB for a 5d1, S = 1/2 ion. Such deviation is expected for a 5t2g1 electron configuration (with less than half-filled) where the spin−orbit coupling results in a smaller magnetic moment than that of a spin-only magnetic behavior. The observed negative Weiss temperature, θ, is indicative of predominantly AFM interactions in the system. There is not any observed anomaly down to ∼2 K, which is indicative of a highly frustrated magnetic ground state ( f > 62). While the μeff values for both systems are essentially identical, the previously reported Weiss constant of the monoclinic version is larger than that of the orthorhombic analog (−166 K vs −124 K). The field dependent magnetization curves at 5 K and 300 K are shown in Figure 3b. The lack of observed hysteresis behavior at both temperatures is in agreement with AFM predominant interactions. Low temperature SQUID ZFC and FC data are presented in Figure 4. The experiment reveals a magnetic transition at ∼2 K and the divergence between ZFC and FC data at ∼1.8 K is indicative of spin glass behavior. The spin glass magnetic ground state is also consistent with the structural disorder due to the mix occupancy between Li and Mg ions in three cationic positions. Such bond disorder results in various types of local environment for Re6+ cations and their orbital overlaps along the exchange pathways. Muon Spin Relaxation. The zero-field μSR data are shown in Figure 5a, from 2 K up to 125 K. Polarized muons undergo Larmor precession in the presence of local magnetic fields at the muon site. A fast relaxation due to rapid dephasing of muon

Figure 4. ZFC and FC SQUID data measured in a He-3 cryostat from 0.5−5 K under an applied magnetic field of 1000 Oe. The blue circles and red triangles represent ZFC and FC data, respectively.

spins coupled to internal magnetic fields is observed to set in below 5 K, increasing to the full volume fraction by 2−3 K, corresponding to ordering in the full sample volume. The Gaussian relaxation envelope at high temperature is due to nuclear dipolar moments, most likely large Li nuclear moments. At high temperatures, spins fluctuate so rapidly that the muons see only a very small time-averaged field, but as the fluctuations slow down, they couple to the muon spins, resulting in rapid dephasing and relaxation of the initial muon spin asymmetry. At the lowest temperatures, the frozen spins generate sizable random fields, which also rapidly dephase the initial muon spin asymmetry. As depicted in Figure 6, these data were fitted to the Uemura spin-glass function:14 Gz(t ) =

⎛ 1 2 exp( −Λdt ) + ⎜⎜1 − 3 3⎝

⎞ ⎟ ⎟ Λdt + as 2t 2 ⎠ as 2t 2

exp( − Λdt + as 2t 2 ) 11636

DOI: 10.1021/acs.inorgchem.7b01537 Inorg. Chem. 2017, 56, 11633−11639

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Inorganic Chemistry

Figure 5. (a) left: ZF-μSR data from 2 K to 125 K. These data were fitted to the Uemura spin-glass function as described in the text, multiplied by a Gaussian to account for nuclear dipolar fluctuations. (b) (right): Results of fits to ZF-μSR data as described in the text. The statically ordered moment as rapidly rises below 4 K, with a fully ordered volume achieved by 2.5 K. The dynamical relaxation Λd peaks at 4 K as fluctuating muon spins slow down through the muon time window. The Gaussian relaxation σg is fixed to the high-temperature value corresponding to nuclear dipolar fluctuations.

Figure 6. LF-μSR data collected at 2 K (left) and 5 K (right). At 2 K the muon spin asymmetry is fully decoupled from internal fields, corresponding to static order in the full sample volume. At 5 K only partial decoupling is observed.

in which as represents statically ordered moments and Λd represents dynamically fluctuating moments. The 1/3 and 2/3 coefficients, respectively, correspond to internal fields parallel to and perpendicular to the initial muon spin polarization; note that the parallel component is only affected by dynamically fluctuating fields whereas both static and fluctuating moments will relax the the orthogonal 2/3 component. Given the strong nuclear dipolar relaxation, this fit function was then multiplied by a Gaussian relaxation with relaxation rate fixed to the hightemperature value of 0.481(6) μs−1. Figure 5b shows the results of these fits. as is seen to exhibit a rapid rise around 3K, corresponding to a rapid onset of static ordering, with the full sample volume ordered by 2.5K. The dynamical relaxation Λd peaks at 4 K, as fluctuating spins slow down through the muon time window. To further probe the interplay between static and dynamic effects, measurements were conducted in applied longitudinal fields. Longitudinal applied fields add to static internal fields and make them more closely parallel to the initial muon spin polarization, effectively “decoupling” the static portion of the relaxation. Figure 6 depicts longitudinal fields at 2 K and 5 K, respectively. At 2 K, the full muon spin asymmetry is decoupled from internal spins by applied field, corresponding to a fully ordered volume fraction. At 5 K, only part of the asymmetry is decoupled, corresponding to partial volume ordering, with dynamical fluctuating spins in the remaining volume. Finally, Figure 7 depicts fits to the long-time behavior of relaxation in an applied longitudinal field of 200 G as a function of temperature. Data before 1 μs, corresponding to rapid static relaxation, were removed, and the long-time tail was fitted to an

Figure 7. Fits of the long-time relaxation of data collected in a field of 200 G, exhibiting a peak of dynamical relaxation around 3 K.

exponential envelope. Here we see a relaxation peak at 3 K, corresponding to a maximum of dynamical fluctuations. Collectively the μSR data point to a glassy ordered state with spin freezing occurring at 3 K, with gradual slowing down of fluctuations at ∼4−5 K giving rise to a fully frozen state by 2.5 K. Computational analysis; spin dimer calculations. The Re6+ sublattice in the Fddd space group is presented in Figure 8. The nearest neighbor magnetic exchange interaction pathways are designated by J1, J2, J3, and J4, for which the interionic distances are summarized in Table 6. 11637

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much smaller than the dominant interactions, J2 and J3 which result in corner-shared triangles in the ab crystallographic plane. These latter interactions with similar strengths are responsible for the highly frustrated magnetic ground state in this compound. To better understand the more frustrated nature of the title compound compared to the previously reported monoclinic analog, the molecular orbital energy diagram for the ReO66− octahedral motifs was calculated. The results of the energy states of 5d orbitals are presented in Table 7. It was Table 7. Energy States of 5d Orbitals in Octahedral Crystal Field in Both Orthorhombic and Monoclinic Versions of Li4MgReO6

Table 6. Re−Re Distances, Hopping Energies, and Relative Strengths of Magnetic Exchange Interactions (J values) for Orthorhombic Li4MgReO6 distance (Å)

⟨(e)2⟩ (meV)2

Relative Js

J1 J2 J3 J4

5.08855 5.09165 5.84336 6.56181

37.28 582.37 410.60 32.82

0.064 1 0.705 0.056

N

∑ (Δeμμ)2 μ=1

28 (/eV)

29 (/eV)

−10.547 −10.436

−2.844 −2.627

−2.811 −2.041

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1

For the 5d electronic configuration where only t2g states are occupied, three orbitals are involved, and therefore, it can be written as

ASSOCIATED CONTENT

Accession Codes

CCDC 1559862−1559863 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

1 (Δe)2 ≈ [(Δe11)2 + (Δe 22)2 + (Δe33)2 ] 9

On the other hand, the J values (spin exchange interactions constants) are given by J≅

27 (/eV)

−10.588 −10.465

CONCLUSION A novel modification of Li4MgReO6 was successfully prepared by a conventional high temperature solid-state method. The sample was characterized by a powder X-ray diffraction technique, and the crystal structure was determined by a Rietveld refinement method. The magnetic susceptibility data revealed a transition below 2 K and the divergence between ZFC and FC data at ∼1.8 K suggested spin glass behavior. The ZF μSR data are in agreement with the onset of magnetic order below 4 K, along with the evidence for dynamical fluctuations up to 5 K. In addition, ZF μSR data reveals a complete decoupling in applied field at 2 K, which is indicative of static order in almost all of the volume fraction at ∼2 K, with partial ordered volumes coexisting with dynamical fluctuations up to 5 K. Spin dimer analysis supports the higher degree of frustration of the Fddd structure, compared to that of C2/m. It was shown that this was due to the higher symmetry in the coordination environment of the orthorhombic variant.

The S = 1/2, Re6+ ions in octahedral crystal field follow the t2g electronic contribution. However, due to the nearly perfect coordination environment around the ions, splitting between these ideally degenerate states caused by the Jahn−Teller effect is insignificant, and therefore, with a good estimate one could assume that all three t2g orbitals equally contribute to the magnetic exchange interactions and therefore 1 N2

26 (/eV)

−10.621 −10.545

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1

(Δe)2 ≈

25 (/eV)

Fddd C2/m7

revealed that the energy states of the so-called t2g states in the orthorhombic phase are closer to each other and therefore the unpaired electron is almost equally hosted by all three orbitals, which in turn means that the magnetic exchange interactions can occur in different Cartesian coordinates and pathways of the same strengths are more likely to happen. Such competitive AFM interaction on the triangular pattern is the origin of the highly frustrated nature of the title compound.

Figure 8. Nearest neighbor Re−Re exchange pathways inside the unit cell. The blue spheres represent Re6+ ions. J1 is shown by the thin lines, J2 and J3 are represented by the white and black thick lines, respectively, and J4 is denoted by the hair lines.

Pathway

Re6+, 5d state number in octahedral field

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(Δe)2 U

AUTHOR INFORMATION

Corresponding Author

Since the U values, Coulomb forces, are the same for all the pathways, the relative magnitudes of the various J’s can be estimated, if ⟨(Δe)2⟩ values are known. The calculated ⟨(e)2⟩ values and the relative exchange interactions are summarized in Table 6. Although J1 occurs along the shortest pathway, it is

*E-mail: [email protected]. ORCID

Brent C. Melot: 0000-0002-7078-8206 Shahab Derakhshan: 0000-0002-3517-7514 11638

DOI: 10.1021/acs.inorgchem.7b01537 Inorg. Chem. 2017, 56, 11633−11639

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Inorganic Chemistry Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS SD is grateful for the financial support from NSF-DMR-RUI Award #1601811. SD also acknowledges the support from the W.M. Keck Foundation for establishment of the Keck Energy Materials Program at CSULB. We thank Z. Gong and the TRIUMF CMMS staff for assistance with μSR experiments. JPC acknowledges the support from the Research Corporation for Science Advancement (Cottrell College Science Award #23314). BCM acknowledges support from the Office of Naval Research under Grant #N00014-15-1-2411. G.M.L. acknowledges support from the Natural Sciences and Engineering Research Council (Canada) and the Canadian Institute for Advanced Research.

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REFERENCES

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DOI: 10.1021/acs.inorgchem.7b01537 Inorg. Chem. 2017, 56, 11633−11639