Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
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Frustrated Magnetism in a 2-D Ytterbium Fluoride Ningxin Jiang† and Henry S. La Pierre*,†,‡ †
School of Chemistry and Biochemistry and the ‡Nuclear and Radiological Engineering Program, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States
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S Supporting Information *
ABSTRACT: Geometric frustration of magnetic ions combines with spin−orbit coupling and structural disorder to give rise to potentially, highly entangled magnetic states such as quantum spin liquids. While fluoride-based frustrated magnets are common in the d-block, in the f-block, fluoride-based frustrated magnets are extremely rare. Herein, we report the synthesis of KYb2F5SO4, a fluoride-based distorted triangular lattice antiferromagnet with no structural disorder but significant geometric distortion from an ideal triangular lattice. In KYb2F5SO4, no long-range ordering can be observed down to 0.10 K, and the low-temperature Curie−Weiss temperature θcw = −0.46(2) K yields a frustration parameter of greater than 4.6. The magnetic entropy released at low temperature indicates an effective spin-1/2 Kramer’s doublet ground state. However, the low saturation field and incomplete recovery of magnetic entropy down to 0.10 K under zero-field imply weak quantum entanglement.
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lanthanide fluoride compounds,20 no 2-D frustrated magnet has been characterized and only a few 1-D lanthanide magnets with fluoride-bridges have been characterized.21 The lack of low-dimensional f-element frustrated magnets is not surprising since lanthanide fluorides are poorly soluble and, thus, have a limited chemical space that can be employed for their synthesis.14 Herein, the synthesis and the magnetic and structural characterization of a fluoride-bridged, 2-D TLAF, KYb2F5SO4, 1-Yb, are described. No spin ordering is observed down to 0.10 K, and a fit of the magnetic susceptibility data from 1.8 to 10 K yields a Curie−Weiss temperature of −0.46 K. The magnetic entropy released from 4 to 0.10 K under 0.5 and 1 T are both close to R ln 2, which indicates that the magnetic ground state of the Yb3+ ion is an effective spin-1/2 Kramer’s doublet. However, the low saturation magnetic field at 1.7 K and incomplete recovery of magnetic entropy under 0 T implies that the magnetic interaction between spins is relatively weak. This weak interaction is in contrast to the disorder- and fielddependent QSL and valence-bond glass behavior observed in the recently reported ytterbium-based, layered rare-earth hydroxide, Yb3(OH)7SO4·H2O.22
INTRODUCTION Geometrically frustrated magnetism can lead to several unusual magnetic states, especially the long-sought quantum spin liquid (QSL) state.1−3 The study of such phases derived from felement frustrated magnets is central to understanding how frustration, magnetic ordering, and spin-orbit coupling (SOC) interplay to stabilize unusual magnetic, electronic, or superconducting phases in f-element materials. Two ytterbiumbased triangular lattice antiferromagnets (TLAFs), YbMgGaO4 and NaYbO2, with perfect triangular lattices were demonstrated to be potential QSLs.4−7 Some ytterbium-based TLAFs with other bridging ligands such as BO33− and S2− have also been synthesized recently.8−12 However, several drawbacks have been found in these systems including structural disorder,6,8 weak magnetic interaction,10 or instability of QSL ground states.13 To address these issues and to understand the role of the bridging ligand in determining bulk properties derived from magnetic superexchange, a fluoride-bridged TLAF was sought since fluoride ions possess a smaller ionic radius and lead to a unique local chemical environment for lanthanides. Fluoride materials and complexes have rich coordination chemistry, and the contracted valence orbitals of fluoride (in contrast to its heavier cogners) which have led to a resurgence in interest in the development of fluoride-based magnetic materials.14−16 While fluoride is more electronegative than other bridging ligands (which may reduce the degree of electron delocalization), several transition-metal fluorides have demonstrated strongly frustrated magnetic behavior, including the 1-D spin chains such as KCuF3,17 2-D kagome materials such as [NH4]2[C7H14N][V7O6F18],18 and 3-D pyrochlores including NaCaNi2F7.19 However, among the abundant © XXXX American Chemical Society
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EXPERIMENTAL SECTION
The general methods, experimental techniques, and data analysis are similar to those reported recently in the literature.22 Further details are provided in the Supporting Information. Synthesis of 1-Yb, KYb2F5SO4. Single crystals of KYb2F5SO4 were synthesized by a hydrothermal method. A mixture of 898 mg of Received: May 21, 2019
A
DOI: 10.1021/acs.inorgchem.9b01489 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry Yb(NO3)3·5H2O (2.0 mmol), 291 mg of KF (5.0 mmol), 853 μL of 98% H2SO4 (15.7 mmol), and 4.0 mL of deionized water were sealed in a stainless-steel Parr vessel equipped with a 23 mL Teflon liner. The Parr vessel was placed in a preheated gravity convection oven at 230 °C for 18 h under autogenous pressure and then cooled to room temperature at a rate of 0.5 °C/min. Colorless ,elongated, and hexagonal plate-like crystals were separated from the liner by vacuum filtration, washed with deionized water and ethanol sequentially, and dried in air to afford 382 mg of the title compound (yield: 66%). The bulk phase purity was established by powder X-ray diffraction (PXRD) analysis (Figure S4). The concentration of H2SO4 is important to the formation of the desired phase. Varying the amount of H2SO4 leads to the formation of KYb3F10 or YbF3 in the reaction products based on the PXRD results. Details of the control experiments are listed in Table S1.
coordinated to six fluoride anions with Yb−F bond lengths in the range of 2.2200(19) to 2.392(3) Å, while the Yb2 is coordinated to seven fluoride anions with Yb−F bond lengths in the range of 2.213(2) to 2.452(3) Å. The Yb1 polyhedra share vertices to form chain 1, while Yb2 polyhedra share edges to form chain 2, as shown in the right corner of Figure 1a. These two types of chains align alternatively along the a-axis with the adjacent Yb1 and Yb2 polyhedra from different chains sharing vertices to form the ytterbium-based triangular lattice layers (Figure 1a). The 2-D ytterbium layers are not flat but have a wave-like feature (Figure 1b). Chain 1, composed of Yb1 polyhedra, is a zigzag with half of the Yb1 atoms above the (010) lattice plane and the other half below the plane (for the nearest three Yb1 atoms, ∠Yb1−Yb1−Yb1 = 146.590(19)°). Chain 2, composed of only Yb2 polyhedra, is straight, with the Yb ions located on the (010) lattice plane. Since adjacent ytterbium ions are bridged only by the fluoride ligands within the layer, the dominant magnetic exchange between nearest-neighboring ytterbium ions are through fluorides. The fluorides within layers have two different bridging modes, i.e., μ2 and μ3 (Figure S2). This Yb-based triangular lattice has four different types of isosceles triangles (Figure S3). The distance between ytterbium ions spans the range of 3.7218(7) to 4.0776(9) Å. The distance between two adjacent layers is 6.646(2) Å, which is larger than the average distance dYb−Yb, avg = 3.878(2) Å between near-neighboring ytterbium ions. The layers are connected by sulfate anions along the b-axis (Figure 1c). The potassium cations are located between the layers and balance the charge. The four oxygen atoms from one sulfate anion are coordinated to three ytterbium (two Yb2 atoms and one Yb1 atom) from one layer and one ytterbium ion (one Yb1 atom) from the neighboring layer (Figure 1d). This asymmetric coordination environment of sulfate atoms can be further seen by the splitting of IR vibrational peaks (Figure S5).23 It is noteworthy that the crystal structure of 1-Yb is similar to previously reported layered rare-earth hydroxides (LRHs), Ln2(OH)6−m(Ax−)m/x·nH2O (m = 1, 4/3 and 2), which have lanthanide ions in the hydroxide host layers.24,25 The material 1-Yb, with ytterbium centers in the fluoride host layers, can therefore be regarded as the first layered rare-earth fluoride. At low temperature, 1-Yb displays magnetic frustration. The magnetic susceptibility measured under zero-field and field cooling shows no obvious difference, and no long-range magnetic ordering is observed down to 1.8 K (Figure 2a). Fitting the inverse susceptibility data from 150 to 300 K yields a Curie−Weiss temperature (θcw) of −54.6(4) K and an effective magnetic moment 4.955(5) μB/Yb3+, which is close to the expected value for free Yb3+ ions (4.54 μB/Yb3+). In the high temperature regime, the magnetic susceptibility is effected by the crystal electric-field excitations of Yb3+.5 The Curie− Weiss fit from 1.8 to 10 K yields a negative Curie−Weiss temperature of θcw = −0.46(2) K, which confirms the antiferromagnetic interactions between Yb3+ magnetic moments. No sharp λ-like peak can be observed under zero-field in the heat capacity measurements (Figure 2c) which suggests no long-range ordering down to 0.10 K. Values of the frustration parameter, f = |θcw|/Tc, larger than 5−10 are typically taken as empirical evidence of a highly frustrated magnet.26 The 1-Yb material presents an f > 4.6, demonstrating significant frustration. The low-temperature magnetic behavior of 1-Yb is dominated by a ground state Kramer’s doublet and can be
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RESULTS AND DISCUSSION The 1-Yb material was synthesized by a conventional hydrothermal reaction with Yb(NO3)3·5H2O, KF, concentrated H2SO4, and deionized water. The reaction product, 1Yb, is produced as colorless plate-like crystals (Figure S1) in 66% yield. It is notable that the isolation of the layered material, 1-Yb, is dependent on the quantity and concentration of H2SO4 in solution; no well-crystallized solid can be isolated if the concentration of H2SO4 is changed, and YbF3 or KYb3F10 can be identified as co-products via PXRD under nonideal reaction conditions (results of control experiments are shown in Table S1). The as-synthesized 1-Yb crystallizes in the orthorhombic space group, Pbcm. Unlike some of the previously reported ytterbium-based TLAFs, no structural disorder was found in this compound.6,8 There are two crystallographically distinct ytterbium sites in 1-Yb. The two types of polyhedra formed by the ytterbium ions and their surrounding ligands are shown in Figure 1a. Both ytterbium sites coordinate to two oxygen atoms from two different sulfate groups. The Yb1 is
Figure 1. (a) Yb1 and Yb2 polyhedra (top left), chain 1 and chain 2 assembled by Yb1 and Yb2 polyhedron, respectively (top right), and the 2D ytterbium layer (bottom). (b) The demonstration of the triangular lattice and the wave-like feature of the layer with the (010) lattice plane (marked in pale yellow) as a reference. (c) View of the layered structure in the ab-plane and (d) the coordination environment of sulfate group in 1-Yb. In all parts, Yb1 atoms are cyan, Yb2 atoms are dark green, oxygen atoms are red, fluorine atoms are green, potassium atoms are purple, and sulfur atoms are yellow. B
DOI: 10.1021/acs.inorgchem.9b01489 Inorg. Chem. XXXX, XXX, XXX−XXX
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Figure 2. (a) Temperature dependence of magnetic susceptibility (left axis) and temperature dependence of inverse magnetic susceptibility (right axis) of 1-Yb at 0.1 T. The red solid line and green solid line indicate a Curie−Weiss fit to the inverse magnetic susceptibility in the range of 150 to 300 K and 1.8 to 10 K, respectively. (b) Isothermal magnetization curve measured at 1.7 K up to 5.5 T in 1-Yb (left axis). The red dashed line marks the Van Vleck contribution. The thin dashed line is the first derivative of isothermal magnetization curve (right axis). (c) The temperature dependence of specific heat under different magnetic fields in 1-Yb. (d) The temperature dependence of entropy under different magnetic fields in 1-Yb.
Table 1. Comparison of Structural and Magnetic Features of Ytterbium-Based TLAFs compound
bridging ligand
average distance between nearestneighboring ytterbium (Å)
average distance between ytterbium layers (Å)
description of distortion to the triangular lattice
low temperature Curie− Weiss temperature (K)
ref
KYb2F5SO4
F−
3.88
6.65
corrugated layer
−0.46
YbMgGaO4
O2−
3.40
8.38
−4.11
2−
3.34 3.89 3.73 5.41
5.82 6.61 4.37 5.95
Yb slightly displaced along c-axis perfect triangular lattice perfect triangular lattice slightly distorted flat layers slightly distorted flat layers
this work 6
−5.64 ⊥ = −13.5; // = −4.5 −0.28 −0.08
4 12 10 9
NaYbO2 NaYbS2 YbBO3 RbBaYb(BO3)2
O S2− B3O99− BO33−
small slope which can be attributed to the Van Vleck contribution (Xvv = 0.0363(1) μB/Yb3+/T) when the field reaches 4.5 T. This saturation field is much lower than the 8 T in YbMgGaO4 and 16 T in NaYbO2, which have stronger coupling between ytterbium ions.4,6 While 1-Yb is a strongly distorted triangular antiferromagnet, the above value of θcw yields an average antiferromagnetic value of |J1| ≈ 0.31 K which is also smaller than 2.7 K in YbMgGaO4 and 3.8 K in NaYbO2.4 Heat capacity measurements were carried out to probe the low-temperature thermodynamics in the 1-Yb (Figures 2c and S6). As the temperature decreases to around 4 K, the heat capacity of 1-Yb exhibits a broad peak centered at 0.15 K (Figure 2c). The peak shifts to a higher temperature with
assigned as an effective spin-1/2 ground state. The smaller effective magnetic moment μeff = 3.137(5) μB/Yb3+ derived from the Curie−Weiss fit at low temperature is close to the value reported in several effective spin-1/2 systems and indicates the settling of Yb3+ ions into a Kramer’s doublet ground state.12,13 This assignment is further supported by the magnetic entropy for 1-Yb under 0.5 and 1 T which recovers entropies close to the expected R ln 2 value from the lowest measured temperature to 4 K (Figure 2d). The nearest-neighboring magnetic interaction is weaker in 1Yb compared to several ytterbium-based triangular lattice compounds. The isothermal magnetization up to 5.5 T at 1.7 K is shown in Figure 2b. The magnetization increases rapidly below 3 T and becomes linearly dependent on the field with a C
DOI: 10.1021/acs.inorgchem.9b01489 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry increasing field, indicating that the specific heat measured from 0.10 to 4 K is field dependent and predominately magnetic. An obvious upturn of this peak can be observed in the temperature dependence of specific heat divided by temperature under 0.5 and 1 T at around 0.15 K (Figure S6). A similar upturn in specific heat has been observed in other lanthanide-based systems and can be attributed to the nuclear contribution which accounts for the slightly higher entropy under 0.5 and 1 T.27,28 The broad peak under 0 T is not complete and results in a much lower recovered magnetic entropy than the expected value, R ln 2, which is further indication of the weak magnetic interaction between the Yb3+ ions. Therefore, despite the effective spin-1/2 ground state and the antiferromagnetic interaction, 1-Yb does not present signatures consistent with QSL behavior in the probed temperature region. In related ytterbium-based TLAFs systems, the observed magnetic behavior is dependent on chemical composition and the resultant changes in the observed structural features, i.e., identity of the bridging ligands, the average nearestneighboring ytterbium ions distance, the average distance between ytterbium layers, and the type of distortion (Table 1). The Curie−Weiss temperature in the low temperature regime can be used to semiquantitatively determine the strength of magnetic coupling.4 The systems with O2− or S2−, such as NaYbO2, NaYbS2, and the YbMgGaO4, have a dramatically more negative Curie−Weiss temperature. Nonetheless, compared to nonmonoatomic bridged systems, YbBO3, and RbBaYb(BO3)2, the fluoride-bridged 1-Yb exhibits stronger magnetic coupling. However, the effect of structural distortion on the collective magnetic behaviors in these systems cannot be ignored. It should also be noted that the interlayer interaction between spins that are bridged by sulfate groups cannot be entirely neglected in 1-Yb.
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CONCLUSION
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ASSOCIATED CONTENT
Accession Codes
CCDC 1916942 contains 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.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Ningxin Jiang: 0000-0001-7055-9334 Henry S. La Pierre: 0000-0002-0895-0655 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This study was supported by the Beckman Foundation as part of a Beckman Young Investigator Award to H.S.L. Singlecrystal diffraction experiments were performed at the Georgia Institute of Technology SCXRD facility directed by John Bacsa and established with funding from the Georgia Institute of Technology. We thank Martin Mourigal for providing access to a PPMS. This work was performed in part at the Georgia Tech Institute for Electronics and Nanotechnology, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation (ECCS-1542174).
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REFERENCES
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In summary, a distorted, layered triangular lattice antiferromagnet 1-Yb has been synthesized. No structural disorder was found, and the nearest-neighboring Yb3+ are all bridged by fluoride anions. The material 1-Yb presents a frustration parameter greater than 4.6, indicating a high degree of frustration. The magnetic ground state of Yb3+ ions is an effective spin-1/2 Kramer’s doublet based on the magnetic susceptibility and the specific heat measurements. The Curie− Weiss temperature θcw = −0.46(2) K derived between 1.8 to 10 K, the low saturation field, and the incomplete recovery of magnetic entropies down to 0.10 K under zero-field suggest a weak magnetic interaction between the neighboring Yb3+ ions. Therefore, 1-Yb does not display QSL behaviors in the probed temperature region. However, this unique fluoride-bridged, felement frustrated magnet still sheds light on the ligand constraints (orbital energy, electronegativity, and connectivity) and lattice constraints driving the emergence of quantum magnetic properties.
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.9b01489. Experimental details; IR spectroscopy; magnetism data; heat capacity data; and crystallographic data (PDF) D
DOI: 10.1021/acs.inorgchem.9b01489 Inorg. Chem. XXXX, XXX, XXX−XXX
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Er, Yb). Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92 (14), 140407.
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