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An extremely well isolated 2D-antiferromagnetic layer
Inorganic Chemistry Communications 13 (2010) 1399–1401
Contents lists available at ScienceDirect
Inorganic Chemistry Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i n o c h e
An extremely well isolated 2D-antiferromagnetic layer Veli Selmani a, Christopher P. Landee b, Mark M. Turnbull a,⁎, Jan L. Wikaira c, Fan Xiao b a b c
Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, MA 01610, USA Department of Physics, Clark University, 950 Main Street, Worcester, MA 01610, USA Department of Chemistry, University of Canterbury, Private Bag 4800 Christchurch, New Zealand
a r t i c l e
i n f o
Article history: Received 6 April 2010 Accepted 31 July 2010 Available online 6 August 2010 Keywords: Cu(II) Pyrazine layers Isolated antiferromagnet
a b s t r a c t An exceptionally well isolated 2D-square quantum antiferromagnet has been prepared. Layers of Cu(II) ions bridged by pyrazine molecules form the layers which are separated by more than 12 Å due to ancillary organic ligands and counter ions. Magnetic data show that the interlayer coupling is less than 0.05% of the intralayer exchange strength (~8 K). © 2010 Elsevier B.V. All rights reserved.
Introduction
Experimental
Low dimensional magnetism has played an integral role in the study of phase transitions, critical behavior, and many other phenomena of quantum physics for decades [1]. The significant breakthroughs in the field in the neutron scattering studies of the excitation spectrum of the one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet [2] are the discovery of superconductivity in doped exchange-coupled layers of Cu(II) oxides [3] with the consequent flurry of theoretical [4] and experimental [5] research and the discovery of macroscopic quantum tunneling in high-spin nanomagnets [6]. Recent studies of [Cu(pz)2]2+ antiferromagnetic layers [7] have shown them to contain very well isolated 2D layers with exchange strengths J in the range of 5 to 15 K. Weak 3D interactions (J′) induce long-range order at low relative temperature (TN/J). If the layer separation could be substantially increased, it may be possible to observe intrinsic 2D behavior, including the never-observed Kosterlitz–Thouless transition [8]. Recent Monte Carlo simulations [9] have predicted that ideal 2D QHAF with weak planar anisotropy undergoes spontaneous Heisenberg-XY spin crossover, inducing a finite temperature phase transition [8]. However, the strong interlayer coupling in most compounds induces 3D long-range order in the 2D QHAF before such a feature can be seen. Better isolated compounds are needed in order to confirm the theoretical prediction. Here we describe the synthesis and preliminary characterization of such a complex.
Synthesis
⁎ Corresponding author. Tel.: + 1 508 882 3186; fax: +1 508 793 7167. E-mail address: [email protected] (M.M. Turnbull). 1387-7003/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.inoche.2010.07.045
Cu(ClO4)2∙6H2O (0.742 g, 2.00 mmol) was dissolved in 2 mL of 50% MeOH. 2-Hydroxypyridine (0.375 g, 4.00 mmol) was dissolved in 3 mL of 50% MeOH and added to the copper solution. Pyrazine (0.321 g, 4.00 mmol) was dissolved in 3 mL of 50% MeOH. The pyrazine solution was added resulting in immediate precipitate formation. An additional 10 mL of 50% MeOH was added, the mixture stirred and the precipitate removed by vacuum filtration. The filtrate was left to crystallize over three weeks at room temperature. Dark green crystals were recovered by vacuum filtration, washed with droplets of 50% MeOH, and allowed to air dry to give 0.260 g (18.1%). CHN calc. for C6H8N2CuBr2 (found): C, 21.7 (22.19); N, 8.45 (8.26); H, 2.43 (2.34). X-ray structure determination Data for 1 were collected on an Xcalibur, Ruby, Gemini diffractometer employing MoKα radiation (λ = 0.71073 Å) and a graphite monochromator. Data collection via ψ-scans, cell refinement and data reduction were performed using CrysAlisPro, Oxford Diffraction Ltd. software. Absorption corrections were made via face indexing. All nonhydrogen atoms were refined anisotropically. CCDC 760705 contains the supplemental crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via http://www.ccdc.cam.ac.uk/data_request/cif. Crystal data for 1: C18H18N6O10Cl2Cu Mr = 612.824 g mol− 1, T = 153(2), orthorhombic, space group Ibam, a = 20.5855(4), b = 24.3650(4), c = 13.7258(2) Å, V = 6884.4(3) Å3, Z = 12, ρcalcd= 1.774 Mg/m3, μ = 1.254, independent reflections 6269 [R(int) = 0.050], data 6269, parameters 294,
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V. Selmani et al. / Inorganic Chemistry Communications 13 (2010) 1399–1401
goodness-of-fit on F2 0.943, final R1= 0.0321 for 3564 reflections with I N 2sigma(I). Results and discussion Reaction of copper(II) perchlorate with two equivalents of pyrazine (pz) and two equivalents of 2-pyridone (2-pyone) yielded aqua green crystals of [Cu(pz)2(2-pyone)2](ClO4)2 (1) in 18% yield. Crystals suitable for X-ray diffraction formed in the solution overnight. The compound crystallizes in the orthorhombic space group Ibam with two independent Cu(II) ions in the asymmetric unit. Each Cu(II) is coordinated to four pyrazine molecules and two O-coordinated 2-pyone molecules which are trans to each other (Fig. 1). There are four independent pyrazine molecules in the structure. The N1-containing rings link Cu2 ions into chains, while N3-containing rings link Cu1 ions into chains, both parallel to the c-axis (Fig. 2). A third pyrazine ring, containing N2, links Cu1 chains into pairs (parallel to the a-axis) while the N5/N6 pyrazine ring links those pairs of Cu1 chains to the Cu2 chains (also parallel to a) giving an overall AABAAB pattern to the layer. Cu1 sits on a 2-fold axis while Cu2 sits on a 222 site. As a result, all angles about Cu2 are 90° as required by symmetry. The local symmetries about the Cu ions are classic Jahn–Teller distorted octahedral with short Cu–N bonds to pyrazine and longer Cu–O bonds to the 2-pyone oxygen atoms [10]. The layers are well separated by the 2-pyridone molecules which are interleaved between layers stacked parallel to the b-axis (Fig. 3). The perchlorate geganions are packed in the spaces between 2-pyone ligands partially filling that gap and causing a further separation of the layers. This results in an interlayer Cu…Cu distance of 12.65(1) Å and makes the layers exceptionally well isolated. Variable temperature magnetic susceptibility measurements over the range 1.8 to 300 K show the presence of dominant antiferromagnetic interactions [11]. A maximum is observed in the susceptibility near 7 K followed by a rapid decrease in χ at lower temperatures (see Fig. 4). Based upon the connectivity of the Cu(II) ions via pyrazine molecules, the data was initially fit to the uniform antiferromagnetic 2DHeisenberg model [12] where C = the Curie Constant, J = magnetic exchange constant and p = percent paramagnetic impurity. As can be
Fig. 1. Thermal ellipsoid plot of the coordination sphere about Cu1 in compound 1. Hydrogen atoms have been excluded for clarity.
Fig. 2. The layer structure of compound 1.
seen in Fig. 4 (top) this model fits the data well down to approximately 20 K, but measurably overestimates the susceptibility near the maximum, and then underestimates the data below the maximum until a distinct turn is seen arising from a paramagnetic impurity [C = 0.43(1) emu/mol, J = −7.9(1) K, p = 0.71(4), R2 = 0.99954]. However, the use of a rectangular 2D-Heisenberg model, [13] shows excellent correlation throughout the entire temperature range, especially in the critical region near the maximum in susceptibility. Various values of α (the ratio between the weaker and stronger exchange constants) were tried and a best fit resulted with α = 0.50 [C= 0.42(1) emu/mol, J = −10.1(1) K, p = 0.07(2), R2= 0.99997].
Fig. 3. Crystal structure of 1 showing the stacking of the layers parallel to the b-axis (vertical).
V. Selmani et al. / Inorganic Chemistry Communications 13 (2010) 1399–1401
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(most notably the work of Drillon, Rabu and co-workers)[16] including several at much larger distances, [17] these systems are predominately ferromagnetic layers which show interlayer interactions and 3D-ordering and thus are not suitable for study as well isolated 2D-QHAF systems. In summary, a new pyrazine-bridged two-dimensional Heisenberg antiferromagnetic lattice has been synthesized which exhibits excellent isolation of the layers. High-field magnetization measurements, along with neutron diffraction studies, are in progress to provide additional information toward eliciting the specific nature of the superexchange pathways. Acknowledgements The authors are grateful for grants from PCISynthesis, Inc. and the Kresge Foundation for the purchase of instrumentation. In addition, VS is grateful for a PCISynthesis Summer Undergraduate Research Fellowship (2009). Appendix A. Supplementary material Supplementary data to this article can be found online at doi:10.1016/j.inoche.2010.07.045. References
Fig. 4. a and b Magnetic susceptibility as a function of temperature for compound 1; (1.8 to 50, panel a, top; 1.8 to 16, panel b, bottom). Grey — fit to the uniform 2D-Heisenberg model. Black — fit to the rectangular-Heisenberg model. See text for fitted parameters.
The quite reasonable fit to the uniform 2D model suggests that although there are four distinct pyrazine-bridged superexchange pathways within the layers, the exchange constants for each pathway must be fairly similar. However, the significant improvement achieved using the rectangular model shows that the exchange pathways are indeed distinct, especially in light of the moderate value of α which achieved the best fit (0.50). Analysis of the geometry of the pyrazine rings with respect to the basal Cu-coordination planes shows distinct differences. The dihedral angles between the pyrazine rings and the coordination planes are moderate for the N1 ring (linking Cu2 ions into chains), N3 ring (linking Cu1 ions into chains) and N5/N6 rings (linking Cu1 chains to Cu2 chains) at 47.4(1), 56.0(3) and 64.4 (5)° respectively. However, the N2 rings (linking Cu1 chains to Cu1 chains) are nearly perpendicular to the Cu1 basal plane (89.9(1)°). Coupled with the small difference seen in the Cu1–N and Cu2–N bond lengths [10] the presence of more than one exchange constant is both reasonable and expected. It is interesting to note that the J value obtained from the uniform 2D fit (−7.9 K) is very close to the average of the two values obtained via the rectangular model (− 10.1 and −5.0 K). No ordering transition was observed in the susceptibility measurements above 1.8 K. Using the equation proposed by Yasuda et al. [14] and the values of J = −7.9 K, TN b 1.8 K, the interlayer/intralayer coupling ratio is estimated to be less than 4.7 × 10−4, better than any other compounds in the copper pyrazine family [15]. Although there are a number of other layered materials that have been well described
[1] H.A. Bethe, Z. Phys. 71 (1931) 205. [2] Y. Endoh, G. Shirane, R.J. Birgeneau, P.M. Richards, S.L. Holt, Phys. Rev. Lett. 32 (1974) 170; I.U. Heilmann, G. Shirane, Y. Endoh, R.J. Birgeneau, S.L. Holt, Phys. Rev. B 18 (1978) 3530. [3] J.G. Bednorz, K.A. Müller, Z. Phys. B: Condens. Matter 64 (1986) 189. [4] E. Manousakis, Rev. Mod. Phys. 63 (1991) 1. [5] M.A. Kastner, R.J. Birgeneau, G. Shirane, Y. Endoh, Rev. Mod. Phys. 70 (1998) 897. [6] J.R. Friedman, M.P. Sarachik, J. Tejada, R. Ziolo, Phys. Rev. Lett. 76 (1996) 3830; L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli, B. Barbara, Nature (London) 383 (1996) 145. [7] a) F. Xiao, F.M. Woodward, C.P. Landee, M.M. Turnbull, C. Mielke, N. Harrison, T. Lancaster, S.J. Blundell, P.J. Baker, P. Babkevich, F.L. Pratt, Phys. Rev. B 79 (2009) 134412; b) J.L. Manson, M.M. Conner, J.A. Schlueter, T. Lancaster, S.J. Blundell, M.J. Brooks, F.L. Pratt, T. Papageorgiou, A.D. Bianchi, J. Wosnitza, M.-H. Whangbo, Chem. Commun. (2006) 4894–4896. [8] a) V.L. Berezinskii, Sov. Phys. JETP 32 (1971) 493; b) J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6 (1973) 1181. [9] A. Cuccoli, T. Roscilde, R. Vaia, P. Verrucchi, Phys. Rev. Lett. 90 (2003) 167205. [10] Selected bond lengths (Å) and angles (°) for 1. Cu1–N2 2.0431(17), Cu1–N3 2.0412(12), Cu1–N6 2.0515(17), Cu1–O1 2.3019(11), Cu2–N1 2.0376(16), Cu2– N5 2.0388(18); Cu2–O2 2.3379(16) ; N3–Cu1–N2 89.46(3), N3–Cu1–N6 90.54 (3), N3–Cu1–O1 90.35(4), N2–Cu1–O1 90.65(3), N6–Cu1–O1 89.35(3). [11] All magnetic susceptibility data were collected on a powdered sample using a Quantum Design MPMS-XL superconducting quantum interference device magnetometer from 1.8 K to 310 K at 1 kOe field. Magnetization as a function of field was carried out at 1.8 K from 0–50, 000 Oe. A few data points were collected as the field was reduced to check for hysteresis; none was observed. The M vs. H data were linear from 0 to 4000 Oe. [12] F.M. Woodward, A.S. Albrecht, C.M. Wynn, C.P. Landee, M.M. Turnbull, Phys. Rev. B 65 (2002) 144412. [13] a) R.T. Butcher, C.P. Landee, M.M. Turnbull, F. Xiao, F. Inorg, Chim. Acta 361 (2008) 3654–3658; b) R.T. Butcher, M.M. Turnbull, C.P. Landee, B.M. Wells, J.J. Novoa, J. Ribas-Ariño, A.W. Sandvik, F.F. Awwadi, Chem. Commun. (2009) 1359–1361. [14] C. Yasuda, S. Todo, K. Hukushima, F. Alet, M. Keller, M. Troyer, H. Takayama, Phys. Rev. Lett. 94 (2005) 217201. [15] F.M. Woodward, P.J. Gibson, G.B. Jameson, C.P. Landee, M.M. Turnbull, R.D. Willett, Inorg. Chem. 46 (2007) 4256. [16] A) P. Rabu, S. Angelov, P. Legoll, M. Belaiche, M. Drillon, Inorg. Chem. 32 (1993) 2463; b) C. Hornick, P. Rabu, M. Drillon, Polyhedron 19 (2000) 259; c) M. Drillon, P. Panissod, P. Rabu, J. Souletie, V. Ksenofontov, P. Gutlich, Phys. Rev. B 65 (2002) 104404; d) K. Suzuki, J. Haines, P. Rabu, K. Inoue, M. Drillon, J. Phys. Chem. C 112 (2008) 19147. [17] A) P. Rabu, S.R. Valerie, C. Hornick, M. Drillon, Chem. Commun. (1996) 1107; b) V. Laget, P. Rabu, C. Hornick, F. Romero, R. Ziessel, P. Turek, M. Drillon, Mol. Cryst. Liq. Cryst. 305 (1997) 291.
Contents lists available at ScienceDirect
Inorganic Chemistry Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i n o c h e
An extremely well isolated 2D-antiferromagnetic layer Veli Selmani a, Christopher P. Landee b, Mark M. Turnbull a,⁎, Jan L. Wikaira c, Fan Xiao b a b c
Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, MA 01610, USA Department of Physics, Clark University, 950 Main Street, Worcester, MA 01610, USA Department of Chemistry, University of Canterbury, Private Bag 4800 Christchurch, New Zealand
a r t i c l e
i n f o
Article history: Received 6 April 2010 Accepted 31 July 2010 Available online 6 August 2010 Keywords: Cu(II) Pyrazine layers Isolated antiferromagnet
a b s t r a c t An exceptionally well isolated 2D-square quantum antiferromagnet has been prepared. Layers of Cu(II) ions bridged by pyrazine molecules form the layers which are separated by more than 12 Å due to ancillary organic ligands and counter ions. Magnetic data show that the interlayer coupling is less than 0.05% of the intralayer exchange strength (~8 K). © 2010 Elsevier B.V. All rights reserved.
Introduction
Experimental
Low dimensional magnetism has played an integral role in the study of phase transitions, critical behavior, and many other phenomena of quantum physics for decades [1]. The significant breakthroughs in the field in the neutron scattering studies of the excitation spectrum of the one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet [2] are the discovery of superconductivity in doped exchange-coupled layers of Cu(II) oxides [3] with the consequent flurry of theoretical [4] and experimental [5] research and the discovery of macroscopic quantum tunneling in high-spin nanomagnets [6]. Recent studies of [Cu(pz)2]2+ antiferromagnetic layers [7] have shown them to contain very well isolated 2D layers with exchange strengths J in the range of 5 to 15 K. Weak 3D interactions (J′) induce long-range order at low relative temperature (TN/J). If the layer separation could be substantially increased, it may be possible to observe intrinsic 2D behavior, including the never-observed Kosterlitz–Thouless transition [8]. Recent Monte Carlo simulations [9] have predicted that ideal 2D QHAF with weak planar anisotropy undergoes spontaneous Heisenberg-XY spin crossover, inducing a finite temperature phase transition [8]. However, the strong interlayer coupling in most compounds induces 3D long-range order in the 2D QHAF before such a feature can be seen. Better isolated compounds are needed in order to confirm the theoretical prediction. Here we describe the synthesis and preliminary characterization of such a complex.
Synthesis
⁎ Corresponding author. Tel.: + 1 508 882 3186; fax: +1 508 793 7167. E-mail address: [email protected] (M.M. Turnbull). 1387-7003/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.inoche.2010.07.045
Cu(ClO4)2∙6H2O (0.742 g, 2.00 mmol) was dissolved in 2 mL of 50% MeOH. 2-Hydroxypyridine (0.375 g, 4.00 mmol) was dissolved in 3 mL of 50% MeOH and added to the copper solution. Pyrazine (0.321 g, 4.00 mmol) was dissolved in 3 mL of 50% MeOH. The pyrazine solution was added resulting in immediate precipitate formation. An additional 10 mL of 50% MeOH was added, the mixture stirred and the precipitate removed by vacuum filtration. The filtrate was left to crystallize over three weeks at room temperature. Dark green crystals were recovered by vacuum filtration, washed with droplets of 50% MeOH, and allowed to air dry to give 0.260 g (18.1%). CHN calc. for C6H8N2CuBr2 (found): C, 21.7 (22.19); N, 8.45 (8.26); H, 2.43 (2.34). X-ray structure determination Data for 1 were collected on an Xcalibur, Ruby, Gemini diffractometer employing MoKα radiation (λ = 0.71073 Å) and a graphite monochromator. Data collection via ψ-scans, cell refinement and data reduction were performed using CrysAlisPro, Oxford Diffraction Ltd. software. Absorption corrections were made via face indexing. All nonhydrogen atoms were refined anisotropically. CCDC 760705 contains the supplemental crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via http://www.ccdc.cam.ac.uk/data_request/cif. Crystal data for 1: C18H18N6O10Cl2Cu Mr = 612.824 g mol− 1, T = 153(2), orthorhombic, space group Ibam, a = 20.5855(4), b = 24.3650(4), c = 13.7258(2) Å, V = 6884.4(3) Å3, Z = 12, ρcalcd= 1.774 Mg/m3, μ = 1.254, independent reflections 6269 [R(int) = 0.050], data 6269, parameters 294,
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V. Selmani et al. / Inorganic Chemistry Communications 13 (2010) 1399–1401
goodness-of-fit on F2 0.943, final R1= 0.0321 for 3564 reflections with I N 2sigma(I). Results and discussion Reaction of copper(II) perchlorate with two equivalents of pyrazine (pz) and two equivalents of 2-pyridone (2-pyone) yielded aqua green crystals of [Cu(pz)2(2-pyone)2](ClO4)2 (1) in 18% yield. Crystals suitable for X-ray diffraction formed in the solution overnight. The compound crystallizes in the orthorhombic space group Ibam with two independent Cu(II) ions in the asymmetric unit. Each Cu(II) is coordinated to four pyrazine molecules and two O-coordinated 2-pyone molecules which are trans to each other (Fig. 1). There are four independent pyrazine molecules in the structure. The N1-containing rings link Cu2 ions into chains, while N3-containing rings link Cu1 ions into chains, both parallel to the c-axis (Fig. 2). A third pyrazine ring, containing N2, links Cu1 chains into pairs (parallel to the a-axis) while the N5/N6 pyrazine ring links those pairs of Cu1 chains to the Cu2 chains (also parallel to a) giving an overall AABAAB pattern to the layer. Cu1 sits on a 2-fold axis while Cu2 sits on a 222 site. As a result, all angles about Cu2 are 90° as required by symmetry. The local symmetries about the Cu ions are classic Jahn–Teller distorted octahedral with short Cu–N bonds to pyrazine and longer Cu–O bonds to the 2-pyone oxygen atoms [10]. The layers are well separated by the 2-pyridone molecules which are interleaved between layers stacked parallel to the b-axis (Fig. 3). The perchlorate geganions are packed in the spaces between 2-pyone ligands partially filling that gap and causing a further separation of the layers. This results in an interlayer Cu…Cu distance of 12.65(1) Å and makes the layers exceptionally well isolated. Variable temperature magnetic susceptibility measurements over the range 1.8 to 300 K show the presence of dominant antiferromagnetic interactions [11]. A maximum is observed in the susceptibility near 7 K followed by a rapid decrease in χ at lower temperatures (see Fig. 4). Based upon the connectivity of the Cu(II) ions via pyrazine molecules, the data was initially fit to the uniform antiferromagnetic 2DHeisenberg model [12] where C = the Curie Constant, J = magnetic exchange constant and p = percent paramagnetic impurity. As can be
Fig. 1. Thermal ellipsoid plot of the coordination sphere about Cu1 in compound 1. Hydrogen atoms have been excluded for clarity.
Fig. 2. The layer structure of compound 1.
seen in Fig. 4 (top) this model fits the data well down to approximately 20 K, but measurably overestimates the susceptibility near the maximum, and then underestimates the data below the maximum until a distinct turn is seen arising from a paramagnetic impurity [C = 0.43(1) emu/mol, J = −7.9(1) K, p = 0.71(4), R2 = 0.99954]. However, the use of a rectangular 2D-Heisenberg model, [13] shows excellent correlation throughout the entire temperature range, especially in the critical region near the maximum in susceptibility. Various values of α (the ratio between the weaker and stronger exchange constants) were tried and a best fit resulted with α = 0.50 [C= 0.42(1) emu/mol, J = −10.1(1) K, p = 0.07(2), R2= 0.99997].
Fig. 3. Crystal structure of 1 showing the stacking of the layers parallel to the b-axis (vertical).
V. Selmani et al. / Inorganic Chemistry Communications 13 (2010) 1399–1401
1401
(most notably the work of Drillon, Rabu and co-workers)[16] including several at much larger distances, [17] these systems are predominately ferromagnetic layers which show interlayer interactions and 3D-ordering and thus are not suitable for study as well isolated 2D-QHAF systems. In summary, a new pyrazine-bridged two-dimensional Heisenberg antiferromagnetic lattice has been synthesized which exhibits excellent isolation of the layers. High-field magnetization measurements, along with neutron diffraction studies, are in progress to provide additional information toward eliciting the specific nature of the superexchange pathways. Acknowledgements The authors are grateful for grants from PCISynthesis, Inc. and the Kresge Foundation for the purchase of instrumentation. In addition, VS is grateful for a PCISynthesis Summer Undergraduate Research Fellowship (2009). Appendix A. Supplementary material Supplementary data to this article can be found online at doi:10.1016/j.inoche.2010.07.045. References
Fig. 4. a and b Magnetic susceptibility as a function of temperature for compound 1; (1.8 to 50, panel a, top; 1.8 to 16, panel b, bottom). Grey — fit to the uniform 2D-Heisenberg model. Black — fit to the rectangular-Heisenberg model. See text for fitted parameters.
The quite reasonable fit to the uniform 2D model suggests that although there are four distinct pyrazine-bridged superexchange pathways within the layers, the exchange constants for each pathway must be fairly similar. However, the significant improvement achieved using the rectangular model shows that the exchange pathways are indeed distinct, especially in light of the moderate value of α which achieved the best fit (0.50). Analysis of the geometry of the pyrazine rings with respect to the basal Cu-coordination planes shows distinct differences. The dihedral angles between the pyrazine rings and the coordination planes are moderate for the N1 ring (linking Cu2 ions into chains), N3 ring (linking Cu1 ions into chains) and N5/N6 rings (linking Cu1 chains to Cu2 chains) at 47.4(1), 56.0(3) and 64.4 (5)° respectively. However, the N2 rings (linking Cu1 chains to Cu1 chains) are nearly perpendicular to the Cu1 basal plane (89.9(1)°). Coupled with the small difference seen in the Cu1–N and Cu2–N bond lengths [10] the presence of more than one exchange constant is both reasonable and expected. It is interesting to note that the J value obtained from the uniform 2D fit (−7.9 K) is very close to the average of the two values obtained via the rectangular model (− 10.1 and −5.0 K). No ordering transition was observed in the susceptibility measurements above 1.8 K. Using the equation proposed by Yasuda et al. [14] and the values of J = −7.9 K, TN b 1.8 K, the interlayer/intralayer coupling ratio is estimated to be less than 4.7 × 10−4, better than any other compounds in the copper pyrazine family [15]. Although there are a number of other layered materials that have been well described
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