Communication pubs.acs.org/JACS
Octa-Kagomé Lattice Compounds Showing Quantum Critical Behaviors: Spin Gap Ground State versus Antiferromagnetic Ordering Yingying Tang,† Cheng Peng,# Wenbin Guo,† Jun-feng Wang,‡ Gang Su,# and Zhangzhen He*,† †
State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, People’s Republic of China # Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China ‡ Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People’s Republic of China S Supporting Information *
ABSTRACT: Search for a new geometrically frustrated lattice is a great challenge. Herein, we report on a successful synthesis of two new layered compounds BiOCu2(XO3)(SO4)(OH)·H2O [X = Te (1) and Se (2)] with a new type of geometrically frustrated lattice (i.e., the octa-kagomé lattice) between kagomé and star motifs. Magnetic measurements confirmed that 1 exhibits a spin gap ground state, while 2 possesses a typical antiferromagnetic ordering at low-temperature. Such different magnetic behaviors between two isostructural compounds are suggested to originate from a slightly structural modification induced by nonmagnetic XO3 anionic groups. Theoretical simulations suggest that the origin of gapped ground state in 1 may be due to the dimerization of Cu2+ ions, while 2 may break the limiting of such dimerization, leading to an antiferromagnetic ordering.
Figure 1. Structural evolution from (a) the kagomé lattice to (b) the octa-kagomé lattice and (c) star lattice with exchange interactions J pathways.
investigations are quite rare. One of the most representative examples is ZnCu3(OH)6Cl2, which is found to exhibit a prefect kagomé lattice,12 showing no any magnetic orderings or spin freezings down to 50 mK.13 Several of the key characteristics of a QSL ground state have been observed using a single crystal sample of ZnCu3(OH)6Cl2.14 The nature of QSL, however, remains still an open question, regarding that the spinon excitation spectrum is gapped or gapless. A NMR experiment has confirmed a gapped QSL in ZnCu3(OH)6Cl2.15 Recently, a new 2D frustrated lattice, dubbed as the octakagomé lattice (OKL) has been suggested by theoretical study to observe QSL and quantum phase transition (QPT) behaviors.16 In fact, the OKL (Figure 1b) can be regarded as a variant of the standard kagomé lattice by inserting a bridge between triangles along one direction, which is also related to the star lattice (T9) with three bridges between triangles (Figure 1c). From the viewpoint of exchange interactions between neighboring magnetic ions, kagomé lattice (Figure 1a) shows only one equivalent exchange interaction (J) while the OKL (Figure 1b) and star lattice (Figure 1c) have two different J (Jt and Jd), in which Jt is inside the triangles and Jd is between the triangles via a bridge. Owing to strong geometric frustration and low coordination numbers in the OKL, it has been suggested that a spin-1/2 OKL compound may be a promising and intriguing candidate for the realization of a QSL ground state. According to the theoretical prediction,16 the nature of
T
he investigation of quantum spin liquid (QSL) in twodimensional (2D) geometrically frustrated magnets has attracted great scientific interest because QSL has been proposed to play a prominent role in high-temperature superconductors.1 Geometrical frustration often happens in a spin-triangle when the competing antiferromagnetic interactions cannot be satisfied simultaneously, giving rise to a large degeneracy of ground states.2 Among the 2D Archimedean motifs, the kagomé lattice (T8) is composed of triangles with corner-sharing (Figure 1a), which is considered as one of the most geometrically frustrated lattices. The theoretical studies have shown that spin-1/2 kagomé compounds are promising candidates for the realization of a QSL ground state,3−7 since a strong spin quantum fluctuation and geometrical frustration can suppress classical long-range magnetic ordering at low temperature. There are many compounds including [NH4]2[C7H14N][V 7 O 6 F 1 8 ] family, 8 , 9 Cu 3 V 2 O 7 (OH) 2 ·2H 2 O, 1 0 BaCu3V2O8(OH)2,11 and ZnCu3(OH)6Cl2,12 which have been found to exhibit a typical spin-1/2 kagomé structure in the past decades. However, candidate spin-1/2 kagomé compounds that can really realize a QSL ground state through experimental © 2017 American Chemical Society
Received: August 31, 2017 Published: September 27, 2017 14057
DOI: 10.1021/jacs.7b09246 J. Am. Chem. Soc. 2017, 139, 14057−14060
Communication
Journal of the American Chemical Society
(3,82)(3, 8, 3, 8) based on the Grünbaum and Shephard manner.17 There are three nodes, in which two of them are four-bonded with two triangles and two octagons, and the third one is surrounded by one triangle and two octagons. It is wellknown that the kagomé and star lattices are described as the notation of (3, 6, 3, 6) and (3, 122),17 respectively. Compared with these notations, it is clear that three topological lattices (Figure 1) are closely correlated. It must be noted that the OKL of 1 is slightly distorted with four different distances between neighboring Cu2+ ions (d1 = 3.52(3) Å, d2 = 3.17(9) Å, d3 = 3.07(1) Å and d4 = 2.94(9) Å), which correspond to four different exchange interactions of J1, J2, J3 and J4 (Figure 2d). As shown in Figure 3a, the magnetic susceptibility of 1 increases with decreasing temperature, while a broad maximum
ground state of a OKL compound is determined by the coupling ratio of Jd/Jt, while a QPT can occur at the critical point of Jd/Jt = 0.6. The system shows a gapped excitation at 0 < Jd/Jt < 0.6 and a gapless excitation at Jd/Jt > 0.6, while the system shows a Fermionic algebraic QSL ground state at Jd/Jt = 1. In this Communication, we report on a successful synthesis of new isostructural compounds BiOCu2(XO3)(SO4)(OH)· H2O [X = Te (1), Se (2)] with a distorted OKL. Magnetic measurements indicate that 1 exhibits a gapped ground state, while 2 possesses a typical antiferromagnetic ordering at lowtemperature. Such different magnetic behaviors between two isostructural compounds are suggested to originate from a slightly structural modification induced by nonmagnetic XO3 anionic groups. Further the theoretical simulations suggest that the origin of gapped ground state in 1 may be due to the dimerization of Cu2+ ions, while 2 may break the limiting of such dimerization, leading to an antiferromagnetic ordering. Figure 2a shows a two-dimensional layered structure of 1 built by the CuO5 tetragonal pyramids and TeO3 trigonal
Figure 2. Features of 1 and 2 for (a) layered structure along b-axis and (b) a layer constructed by CuO5, in which (c) the linkages of TeO3 and CuO5 with bond angles and (d) the corresponding J pathways are seen. The circles show a pair of spin-dimer.
Figure 3. (a) Temperature dependence of magnetic susceptibility for 1, in which the solid curve is Curie−Weiss Law χCW = C′/(T−θ′); the circles the susceptibility subtracted from impurity component χSpin = χ − χCW; the red dashed line the fitting by theoretical simulation. The inset shows the heat capacity data of 1 obtained at H = 0 T. (b) Magnetization (M) vs applied field (H) at 1.5 K for 1.
pyramids, in which the layers are separated by dangling SO4 groups and Bi3+ ions along the a-axis. It is noted that the shortest distance of Cu··Cu between layers is 7.04(1) and 6.80(6) Å for 1 and 2, respectively. Figure 2b shows the layers composed of CuO5 tetragonal pyramids. There are two different crystallographic Cu sites (Cu1 and Cu2), in which Cu1 sites form [Cu12O8] dimers with edge-sharing O3 atoms while Cu2 sites form linear chains running along the b-axis via corner-sharing O2 atoms. Further, the [Cu12O8] dimers are located between linear Cu2-chains via corner-sharing O2 atoms, forming a unique network. Since H2O, Bi3+, TeO32− and SO42− groups are nonmagnetic, the spin−lattice of 1 is determined by the topological arrangement of magnetic Cu2+ ions. Removing H2O, Bi3+, TeO32−, and SO42− groups from the structure, magnetic Cu2+ ions of the layers are found to form a new spin−lattice as seen in Figure 1b. This new spin−lattice, dubbed as OKL, is likely between the so-called regular kagomé and star lattices, which can be represented as the notation of
is observed around 45 K, indicating the onset of a short-range ordering. Further, a sudden upturn is observed below 12 K, considering as a Curie tail originating from the isolated Cu2+ ions due to lattice defect.18 No signature of a long-range order is seen down to 0.3 K. This can be confirmed by the lowtemperature heat capacity data without any λ-like peaks (the inset of Figure 3a), ruling out the appearance of a long-range ordering. Also, a typical Curie−Weiss behavior is observed above 100 K, giving the Curie constant C = 0.842(5) emu· mol−1·K and Weiss temperature θ = −6.6(3) K. The effective magnetic moment is calculated to be 1.83(5) μB, which is close to the theoretical value of 1.732 μB for Cu2+ (S = 1/2, g = 2). The negative Weiss temperature shows the dominative antiferromagnetic (AF) interactions between Cu2+ ions in the system. It is noted that the upturn below 12 K can also be fitted 14058
DOI: 10.1021/jacs.7b09246 J. Am. Chem. Soc. 2017, 139, 14057−14060
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simulation is performed by the OKL model using the network contractor dynamics (NCD) method.16 The fitting of the OKL model (Figure 3a) gives J1 ≈ −78 K, J2 ≈ −15.6 K, J3 ≈ −15.6 K and J4 ≈ −7.8 K, showing the ratio of J1:J2:J3:J4 ≈ 1:0.2:0.2:0.1. The theoretical results support a gapped ground state of 1 with J4/J1 = 0.1, agreeing with the critical condition at 0 < Jd/Jt < 0.6. Since the J1 is quite larger than the other three exchange pathways, the results also suggest that the origin of a gapped ground state of 1 may be due to the dimerization of Cu2+ ions along the J1 pathways as seen in Figure 2d. In fact, the magnitude and the sign of the exchange constant J are determined by the bonding geometry according to the Goodenough rules.24 To further clarify the nature of such different magnetic behaviors between 1 and 2, we investigate the structural modification related to nonmagnetic TeO3 or SeO3 groups. As shown in Figure 2c, TeO3 or SeO3 trigonal pyramids are connected to [Cu12O8] dimers via corner-sharing O3 atoms and Cu2-chains via corner-sharing O1 and O4 atoms, which may directly affect the exchange distances or coupling angles between the [Cu12O8] dimers and Cu2-chains. A comparison of structural parameters between 1 and 2 is shown in Table 1. It is noted that the coupling angle ∠1 = 129.3(4)°
well by the Curie−Weiss law and the remaining susceptibility subtracted from paramagnetic components χCW approaches zero as the temperature is lowered to 0 K, indicating that magnetic ground state of 1 is a spin-gap state. To further confirm a gapped state of 1, a high field magnetization measurement is performed at 1.5 K (Figure 3b). The magnetization increases initially with increasing field, corresponding to paramagnetic impurity or the Van-Vleck paramagnetic contribution of Cu2+ ions,19 while a rapid upturn is seen at the critical field of ∼25 T (Hc). Such rapid upturn in magnetization is due to the increase of magnons that the Zeeman energy gμBH overcomes the spin gap between the singlet ground state (S = 0) and the excited triplet states (S = 1). Similar behaviors have also been observed in many quantum spin systems with a singlet ground state such as PbNi2V2O8,20 Ba3Mn2O821 and SrCu2(PO4)2.22 The spin gap of 1 can be estimated as Δ = 34 K using the equation, Δ = gμBHc.23 As shown in Figure 4a, the magnetic susceptibility of 2 shows a sharp peak at ∼24 K, indicating the onset of antiferromagnetic
Table 1. Cu−Cu Lengths (Å) and Corresponding Cu−O− Cu Bond Angles (deg) in 1 and 2 d1 d2 d3 d4
1
2
3.52(3) 3.17(9) 3.07(1) 2.94(9)
3.46(6) 3.17(3) 3.04(1) 3.02(1)
1 ∠1 ∠2 ∠3 ∠4
129.3(4) 103.0(1) 107.2(8) 1 97.3(3)
2 126.0(2) 102.0(1) 107.5(3) 98.6(3)
of the J1 pathway in 1 is the largest and that of the J4 pathway [∠4 = 97.3(3)°] is smallest, supporting J1 > J4. This is because when the Cu−O−Cu bond angle is close to 180°, the 3d orbitals of Cu2+ ions overlap in the maximum extent, whereas the bond angle reaches 90°, the 3d orbitals hardly overlap.25 Such behaviors can also be illustrated in edge-shared chains Li2CuO226 with a small J and corner-sharing chains Sr2CuO3 and SrCuO2 with a large J,27 showing the strong antiferromagnetic interactions due to the overlap of orbitals, while antiferromagnetic interaction is reduced by the orthogonality. Moreover, we note a slight change on the coupling angle ∠1 = 126.0(4)° of the J1 pathway and ∠4 = 98.6(3)°] of J4 pathway in 2, when the Se atoms substitute for Te atoms of 1. This change may be due to the different radii of Se4+ and Te4+ ions. However, such changes of coupling angles in 2 may induce a relatively weaker J1 and a stronger J4 with a large ratio of J4/J1, further breaking the limiting of dimerization of Cu2+ ions. The disorder-to-order transition induced by a slight change on the bonding geometry can also be seen in Si-substituted CuGeO3.28 In summary, two isostructural compounds 1 and 2 with a unique spin−lattice (i.e., OKL) have been synthesized by a hydrothermal technique. Magnetic results confirmed that 1 exhibits a gapped ground state, while 2 possesses an antiferromagnetic ordering at ∼24 K. We suggest that their different magnetic behaviors are due to a slight change on the bonding geometry induced by nonmagnetic Se4+/Te4+ ions. Also, theoretical simulation suggests that 1 is a spin-1/2 highly anisotropic Heisenberg antiferromagnetic OKL system with J1:J2:J3:J4 = 1:0.2:0.2:0.1, satisfying the critical condition at 0 < Jd/Jt < 0.6. The results also suggest that the origin of gapped ground state in 1 may be due to the dimerization of Cu2+ ions,
Figure 4. (a) Temperature dependence of magnetic susceptibility for 2. The inset shows the heat capacity data of 2 obtained at H = 0 T. (b) Magnetization (M) vs applied field (H) at 2 K for 2.
ordering. This is also confirmed by a λ-like peak in the lowtemperature heat capacity data (the inset of Figure 4a), supporting a long-range magnetic ordering. A typical Curie− Weiss behavior is observed above 50 K, giving the Curie constant C = 1.23(2) emu·mol−1·K and θ = −4.2(3) K. The effective magnetic moment is calculated to be 2.22(3) μB, which is slightly larger than that of 1. The isothermal magnetization (Figure 4b) increases linearly with increasing field and does not saturate at 8 T, agreeing with an antiferromagnetic ground state. The above results combined from magnetic and heat capacity measurements have confirmed that 1 exhibits spin-singlet ground state with a spin gap, while 2 possesses an antiferromagnetic ordering at ∼24 K. To understand the nature of magnetic properties of 1 and 2, a theoretical 14059
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(18) Lu, H. C.; Yamamoto, T.; Yoshimune, W.; Hayashi, N.; Kobayashi, Y.; Ajiro, Y.; Kageyama, H. J. Am. Chem. Soc. 2015, 137, 9804. (19) Tanaka, H.; Kurita, N.; Okada, M.; Kunihiro, E.; Shirata, Y.; Fujii, K.; Uekusa, H.; Matsuo, A.; Kindo, K.; Nojiri, H. J. Phys. Soc. Jpn. 2014, 83, 103701. (20) Tsujii, N.; Suzuki, O.; Suzuki, H.; Kitazawa, H.; Kido, G. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 104402. (21) Uchida, M.; Tanaka, H.; Mitamura, H.; Ishikawa, F.; Goto, T. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 054429. (22) Belik, A. A.; Azuma, M.; Matsuo, A.; Whangbo, M. H.; Koo, H. J.; Kikuchi, J.; Kaji, T.; Okubo, S.; Ohta, H.; Kindo, K.; Takano, M. Inorg. Chem. 2005, 44, 6632. (23) Yamauchi, T.; Narumi, Y.; Kikuchi, J.; Ueda, Y.; Tatani, K.; Kobayashi, T. C.; Kindo, K.; Motoya, K. Phys. Rev. Lett. 1999, 83, 3729. (24) Goodenough, J. B. Magnetism and the Chemical Bond; John Wiley and Sons: New York, 1963. (25) Cheng, J. G.; Tian, W.; Zhou, J. S.; Lynch, V. M.; Steinfink, H.; Manthiram, A.; May, A. F.; Garlea, V. O.; Neuefeind, J. C.; Yan, J. Q. J. Am. Chem. Soc. 2013, 135, 2776. (26) Mizuno, Y.; Tohyama, T.; Maekawa, S.; Osafune, T.; Motoyama, N.; Eisaki, H.; Uchida, S. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 5326. (27) (a) Motoyama, N.; Eisaki, H.; Uchida, S. Phys. Rev. Lett. 1996, 76, 3212. (b) Suzuura, H.; Yasuhara, H.; Furusaki, A.; Nagaosa, N.; Tokura, Y. Phys. Rev. Lett. 1996, 76, 2579. (28) Schoeffel, J. P.; Pouget, J. P.; Dhalenne, G.; Revcolevschi, A. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 53, 14971.
while 2 may break the limiting of such dimerization, leading to an antiferromagnetic ordering.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b09246. The detailed experiments including the synthesis process, crystallography data, magnetic measurements, and theoretical simulation; magnetic data; XRD pattern (PDF) Data for BiCu2O10SSe (CIF) Data for BiCu2H3O10STe (CIF)
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AUTHOR INFORMATION
Corresponding Author
*
[email protected] or
[email protected] ORCID
Wenbin Guo: 0000-0002-2467-0952 Zhangzhen He: 0000-0002-8496-1532 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (NSFC) (No. 21573235, 21403234, 11474279), the Joint Fund of Research Utilizing Large-scale Scientific Facilities under cooperative agreement between NSFC and CAS (No. 1632159) and the Chinese Academy of Sciences (ACS) under Grant No. KJZD-EW-M05.
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REFERENCES
(1) Anderson, P. W. Science 1987, 235, 1196. (2) Balents, L. Nature 2010, 464, 199. (3) Elser, V. Phys. Rev. Lett. 1989, 62, 2405. (4) Jiang, H. C.; Weng, Z. Y.; Sheng, D. N. Phys. Rev. Lett. 2008, 101, 117203. (5) Yan, S.; Huse, D.; White, S. R. Science 2011, 332, 1173. (6) Depenbrock, S.; McCulloch, I. P.; Schollwock, U. Phys. Rev. Lett. 2012, 109, 067201. (7) Jiang, H. C.; Wang, Z. H.; Balents, L. Nat. Phys. 2012, 8, 902. (8) Aidoudi, F. H.; Aldous, D. W.; Goff, R. J.; Slawin, A. M. Z.; Attfield, J. P.; Morris, R. E.; Lightfoot, P. Nat. Chem. 2011, 3, 801. (9) Clark, L.; Aidoudi, F. H.; Black, C.; Arachchige, K. S. A.; Slawin, A. M. Z.; Morris, R. E.; Lightfoot, P. Angew. Chem., Int. Ed. 2015, 54, 15457. (10) Yoshida, H.; Yamaura, J. I.; Isobe, M.; Okamoto, Y.; Nilsen, G. J.; Hiroi, Z. Nat. Commun. 2012, 3, 860. (11) Okamoto, Y.; Yoshida, H.; Hiroi, Z. J. Phys. Soc. Jpn. 2009, 78, 033701. (12) Shores, M. P.; Nytko, E. A.; Bartlett, B. M.; Nocera, D. G. J. Am. Chem. Soc. 2005, 127, 13462. (13) Helton, J. S.; Matan, K.; Shores, M. P.; Nytko, E. A.; Bartlett, B. M.; Yoshida, Y.; Takano, Y.; Suslov, A.; Qiu, Y.; Chung, J.-H.; Nocera, D. G.; Lee, Y. S. Phys. Rev. Lett. 2007, 98, 107204. (14) Han, T. H.; Helton, J. S.; Chu, S. Y.; Nocera, D. G.; RodriguezRivera, J. A.; Broholm, C.; Lee, Y. S. Nature 2012, 492, 406. (15) Fu, M. X.; Imai, T.; Han, T. H.; Lee, Y. S. Science 2015, 350, 655. (16) Peng, C.; Ran, S.-J.; Liu, t.; Chen, X.; Su, G. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 95, 075140. (17) Grünbaum, B.; Shephard, G. C. Tilings and Patterns; W. H. Freeman: New York, 1987. 14060
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