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Spin structure of the nanoscale molecular magnet V15 cluster revealed by V-NMR51
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 310 (2007) 1429–1431 www.elsevier.com/locate/jmmm
Spin structure of the nanoscale molecular magnet V15 cluster revealed by 51VNMR Y. Furukawaa,, Y. Nishisakaa, K. Kumagaia, P. Ko¨gerlerb a
Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan Department of Physics and Astronomy, Ames Laboratory, Iowa State University, IA 50011, USA
b
Available online 15 November 2006
Abstract 51
V nuclear magnetic resonance (NMR) measurements below 100 mK using a 3 He–4 He dilution refrigerator have been carried out to investigate the magnetic states of V ions in the V15 cluster. We report a direct evidence for spin structure of the V15 cluster where the V4þ ðs ¼ 12Þ spins on the outer hexagons are in a singlet state and V ions on the inner triangle have s ¼ 12 spin moments at low temperature. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.Xx; 76.60.k Keywords: Magnetic molecule; V15 cluster; Nuclear magnetic resonance
The nanoscale molecular magnet K6 ½V15 As6 O42 ðH2 OÞ8H2 O (abbreviated as V15) has recently attracted a great deal of interest, because the cluster is considered to be a typical s ¼ 12 Heisenberg triangular system [1]. The V15 cluster contains 15 V4þ ions with s ¼ 12 [1,2], which are arranged in a layered structure with a triangle sandwiched between two hexagons. Fig. 1(a) shows the configuration of V4þ ðs ¼ 12Þ ions and exchange coupling scheme in the V15 cluster where all exchange interactions between V4þ spins are antiferromagnetic (AF) [1,2]. Each hexagon of the cluster consists of three pairs of strongly coupled spins with J 1 800 K. Each spin of the V4þ ions in the central triangle is coupled with the spins in both hexagons with J 2 ¼ 150 K and J 3 ¼ 300 K [2]. The exchange interaction between the spins within the triangle is very weak with J 0 ¼ 2:44 K [3]. The energy scheme is given by the nearly degenerate two S ¼ 12 ground state and the excited state of S ¼ 32 which lies 3:8 K above [3]. By the application of an external magnetic field, the ground state can be changed from two S ¼ 12 states to a S ¼ 32 state around H2:7 T, as shown in Fig. 1(b). Corresponding author.
E-mail address: [email protected] (Y. Furukawa). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.734
The magnetic properties of the V15 cluster at low temperatures are considered to be determined only by the three V4þ spins on the triangle because the V4þ spins on the hexagons are assumed to be a spin singlet state due to the strong AF interaction of J 1 800 K. In fact, magnetic properties such as the magnetization curve [3] at low temperature were well explained by an s ¼ 12 triangular Heisenberg model. However, there is no direct experimental confirmation for spin structure of the V15 cluster at low temperatures. In this paper, we have carried out 51 V nuclear magnetic resonance (NMR) measurements in order to elucidate the spin state of each V ion in the V15 cluster. Our results provide a direct evidence for the singlet state of the V4þ spins on the hexagons and s ¼ 12 spin of V ions on the triangle in the V15 cluster. Polycrystalline samples of the V15 cluster used in this study is same as in our previous study [4]. NMR measurements were carried out using a phase-coherent spin echo pulse spectrometer below 1 K using a 3 He–4 He dilution refrigerator. Fig. 2(b) shows the 51 VNMR spectrum measured at T ¼ 50 mK and f ¼ 50:78 MHz. Two peaks labeled as P2 and P3 in the figure are observed with almost equal intensity around H4 T where the ground state of the
ARTICLE IN PRESS Y. Furukawa et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1429–1431
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a
b J1 6 V2
V1
3 T (K)
J3 J0 V3 J2
0
-3 HC
V1 V2
-6
0
1
2
3
4
5
H (T) Fig. 1. (a) Schematic view of V4þ ðs ¼ 12Þ ions (solid circles) and exchange coupling scheme in V15 cluster. The two non-equivalent V ions on the hexagons are labeled as V1 and V2, respectively. The three equivalent V ions on the triangle are labeled as V3. (b) Level scheme of V15 cluster as a function of the external magnetic field. Solid and broken lines show nearly
a
b
c
Fig. 2. (a) 51 VNMR spectrum measured at T ¼ 100 mK and f ¼ 21:03 MHz. (b) 51 VNMR spectrum measured at T ¼ 50 mK and f ¼ 50:78 MHz. (c) External magnetic field dependence of resonance frequency for each 51 VNMR peak measured below 100 mK.
cluster is S ¼ 32. Another 51 VNMR signal labeled as P1 shown in Fig. 2(a) is also observed at different resonance frequency in the S ¼ 32 ground state. Fig. 2(c) shows the external field dependence of the resonance frequencies for the three 51 VNMR signals. On increasing the magnetic field, the P2 and P3 shift to a higher frequency, while P1 shifts to a lower frequency. The slope of the magnetic field dependence of the resonance frequency is j11:3j MHz=T for each peak, which coincides with the gyromagnetic ratio gN ð¼ 11:293 MHz=TÞ of the 51 V nucleus. As the resonance frequency is proportional to the vector sum of the internal field ðH int Þ and external field ðH ext Þ as f ¼ gN ðH int þ H ext Þ, internal field is estimated to be 76:5 kOe for P1, 8 kOe for P2 and 4 kOe for P3. The internal magnetic field of V4þ ions with a net spin moment of s ¼ 12 is considered to be dominated by inner-core polarization mechanism which induces a large negative internal field of the order of 100 kOe=mB at the nuclear site. Since the value of 76:5 kOe for P1 is close to a reported value of 85 kOe for 1 mB by the inner-core polarization mechanism of V4þ ions in VO2 [5], 51 VNMR signal labeled as P1 is assigned to V4þ ions with s ¼ 12. Using a relation H int ¼ AhMiwith A ¼ 85 kOe=mB , the spin moment hMi for the V site is estimated to be 0:89 mB whose direction is parallel to the external field. On the other hand, P2 and P3 with small and positive internal fields cannot be explained in terms of inner-core polarization mechanism, indicative of no spin moments on the V4þ ions. In our previous paper [6], the internal field for P2 and P3 was interpreted to be transferred hyperfine fields (THF) from the V4þ spins with net spin moments. The THF would depend on the distance between the two V ions because it originates from the strength of V–O–V covalent bond. The distance between the V3 and V2 ions is 3:73 A˚ which is longer than the 3:02 A˚ distance between the V3 and V1 sites [1]. The shortest distance is 2:87 A˚ between the V1 and V2 sites. Taking the almost equal signal intensity for P2 and P3 into consideration, the two V ions observed in the spectrum shown in Fig. 2(b) can be considered as the two V ions in the hexagon, while P1 can be assigned to the V3 site in the triangle. The peaks P2 and P3 can then be assigned to the V1 and V2 sites, respectively, because the distance between the V3 and V1 ions is shorter than the distance between the V3 and V2 ions. Thus, we conclude that both V ions on the hexagon have no net spin moments at low temperature. These results are direct evidences for the magnetic state for each V ions in the V15 cluster in which V4þ ions in the triangle have almost full moments of s ¼ 12 and the V4þ spins on the hexagon are in singlet state. This is a direct confirmation of the spin structure of the V15 cluster in its S ¼ 32 ground state from a microscopic point of view. The present work was in part supported by Grant-in-Aid for Scientific Research (C) and 21 Century COE Programs ‘‘Topological Science and Technology’’ at Hokkaido
ARTICLE IN PRESS Y. Furukawa et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1429–1431
University from the Ministry of Education, Culture, Sports, Science and Technology of Japan. One of the authors (Y.F.) thanks the Sumitomo Foundation for financial supports. References [1] A.L. Barra, et al., J. Am. Chem. Soc. 114 (1992) 8509. [2] D. Gatteschi, et al., Mol. Eng. 3 (1993) 157.
[3] [4] [5] [6]
1431
I. Chiorescu, et al., J. Magn. Magn. Mater. 221 (2000) 103. Y. Furukawa, et al., Polyhedron 24 (2005) 2737. K. Takanashi, et al., J. Phys. Soc. Japan 52 (1983) 3953. Y. Nishisaka, et al., AIP Conference Proceedings 80 (2006) 1143.
Journal of Magnetism and Magnetic Materials 310 (2007) 1429–1431 www.elsevier.com/locate/jmmm
Spin structure of the nanoscale molecular magnet V15 cluster revealed by 51VNMR Y. Furukawaa,, Y. Nishisakaa, K. Kumagaia, P. Ko¨gerlerb a
Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan Department of Physics and Astronomy, Ames Laboratory, Iowa State University, IA 50011, USA
b
Available online 15 November 2006
Abstract 51
V nuclear magnetic resonance (NMR) measurements below 100 mK using a 3 He–4 He dilution refrigerator have been carried out to investigate the magnetic states of V ions in the V15 cluster. We report a direct evidence for spin structure of the V15 cluster where the V4þ ðs ¼ 12Þ spins on the outer hexagons are in a singlet state and V ions on the inner triangle have s ¼ 12 spin moments at low temperature. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.Xx; 76.60.k Keywords: Magnetic molecule; V15 cluster; Nuclear magnetic resonance
The nanoscale molecular magnet K6 ½V15 As6 O42 ðH2 OÞ8H2 O (abbreviated as V15) has recently attracted a great deal of interest, because the cluster is considered to be a typical s ¼ 12 Heisenberg triangular system [1]. The V15 cluster contains 15 V4þ ions with s ¼ 12 [1,2], which are arranged in a layered structure with a triangle sandwiched between two hexagons. Fig. 1(a) shows the configuration of V4þ ðs ¼ 12Þ ions and exchange coupling scheme in the V15 cluster where all exchange interactions between V4þ spins are antiferromagnetic (AF) [1,2]. Each hexagon of the cluster consists of three pairs of strongly coupled spins with J 1 800 K. Each spin of the V4þ ions in the central triangle is coupled with the spins in both hexagons with J 2 ¼ 150 K and J 3 ¼ 300 K [2]. The exchange interaction between the spins within the triangle is very weak with J 0 ¼ 2:44 K [3]. The energy scheme is given by the nearly degenerate two S ¼ 12 ground state and the excited state of S ¼ 32 which lies 3:8 K above [3]. By the application of an external magnetic field, the ground state can be changed from two S ¼ 12 states to a S ¼ 32 state around H2:7 T, as shown in Fig. 1(b). Corresponding author.
E-mail address: [email protected] (Y. Furukawa). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.734
The magnetic properties of the V15 cluster at low temperatures are considered to be determined only by the three V4þ spins on the triangle because the V4þ spins on the hexagons are assumed to be a spin singlet state due to the strong AF interaction of J 1 800 K. In fact, magnetic properties such as the magnetization curve [3] at low temperature were well explained by an s ¼ 12 triangular Heisenberg model. However, there is no direct experimental confirmation for spin structure of the V15 cluster at low temperatures. In this paper, we have carried out 51 V nuclear magnetic resonance (NMR) measurements in order to elucidate the spin state of each V ion in the V15 cluster. Our results provide a direct evidence for the singlet state of the V4þ spins on the hexagons and s ¼ 12 spin of V ions on the triangle in the V15 cluster. Polycrystalline samples of the V15 cluster used in this study is same as in our previous study [4]. NMR measurements were carried out using a phase-coherent spin echo pulse spectrometer below 1 K using a 3 He–4 He dilution refrigerator. Fig. 2(b) shows the 51 VNMR spectrum measured at T ¼ 50 mK and f ¼ 50:78 MHz. Two peaks labeled as P2 and P3 in the figure are observed with almost equal intensity around H4 T where the ground state of the
ARTICLE IN PRESS Y. Furukawa et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1429–1431
1430
a
b J1 6 V2
V1
3 T (K)
J3 J0 V3 J2
0
-3 HC
V1 V2
-6
0
1
2
3
4
5
H (T) Fig. 1. (a) Schematic view of V4þ ðs ¼ 12Þ ions (solid circles) and exchange coupling scheme in V15 cluster. The two non-equivalent V ions on the hexagons are labeled as V1 and V2, respectively. The three equivalent V ions on the triangle are labeled as V3. (b) Level scheme of V15 cluster as a function of the external magnetic field. Solid and broken lines show nearly
a
b
c
Fig. 2. (a) 51 VNMR spectrum measured at T ¼ 100 mK and f ¼ 21:03 MHz. (b) 51 VNMR spectrum measured at T ¼ 50 mK and f ¼ 50:78 MHz. (c) External magnetic field dependence of resonance frequency for each 51 VNMR peak measured below 100 mK.
cluster is S ¼ 32. Another 51 VNMR signal labeled as P1 shown in Fig. 2(a) is also observed at different resonance frequency in the S ¼ 32 ground state. Fig. 2(c) shows the external field dependence of the resonance frequencies for the three 51 VNMR signals. On increasing the magnetic field, the P2 and P3 shift to a higher frequency, while P1 shifts to a lower frequency. The slope of the magnetic field dependence of the resonance frequency is j11:3j MHz=T for each peak, which coincides with the gyromagnetic ratio gN ð¼ 11:293 MHz=TÞ of the 51 V nucleus. As the resonance frequency is proportional to the vector sum of the internal field ðH int Þ and external field ðH ext Þ as f ¼ gN ðH int þ H ext Þ, internal field is estimated to be 76:5 kOe for P1, 8 kOe for P2 and 4 kOe for P3. The internal magnetic field of V4þ ions with a net spin moment of s ¼ 12 is considered to be dominated by inner-core polarization mechanism which induces a large negative internal field of the order of 100 kOe=mB at the nuclear site. Since the value of 76:5 kOe for P1 is close to a reported value of 85 kOe for 1 mB by the inner-core polarization mechanism of V4þ ions in VO2 [5], 51 VNMR signal labeled as P1 is assigned to V4þ ions with s ¼ 12. Using a relation H int ¼ AhMiwith A ¼ 85 kOe=mB , the spin moment hMi for the V site is estimated to be 0:89 mB whose direction is parallel to the external field. On the other hand, P2 and P3 with small and positive internal fields cannot be explained in terms of inner-core polarization mechanism, indicative of no spin moments on the V4þ ions. In our previous paper [6], the internal field for P2 and P3 was interpreted to be transferred hyperfine fields (THF) from the V4þ spins with net spin moments. The THF would depend on the distance between the two V ions because it originates from the strength of V–O–V covalent bond. The distance between the V3 and V2 ions is 3:73 A˚ which is longer than the 3:02 A˚ distance between the V3 and V1 sites [1]. The shortest distance is 2:87 A˚ between the V1 and V2 sites. Taking the almost equal signal intensity for P2 and P3 into consideration, the two V ions observed in the spectrum shown in Fig. 2(b) can be considered as the two V ions in the hexagon, while P1 can be assigned to the V3 site in the triangle. The peaks P2 and P3 can then be assigned to the V1 and V2 sites, respectively, because the distance between the V3 and V1 ions is shorter than the distance between the V3 and V2 ions. Thus, we conclude that both V ions on the hexagon have no net spin moments at low temperature. These results are direct evidences for the magnetic state for each V ions in the V15 cluster in which V4þ ions in the triangle have almost full moments of s ¼ 12 and the V4þ spins on the hexagon are in singlet state. This is a direct confirmation of the spin structure of the V15 cluster in its S ¼ 32 ground state from a microscopic point of view. The present work was in part supported by Grant-in-Aid for Scientific Research (C) and 21 Century COE Programs ‘‘Topological Science and Technology’’ at Hokkaido
ARTICLE IN PRESS Y. Furukawa et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1429–1431
University from the Ministry of Education, Culture, Sports, Science and Technology of Japan. One of the authors (Y.F.) thanks the Sumitomo Foundation for financial supports. References [1] A.L. Barra, et al., J. Am. Chem. Soc. 114 (1992) 8509. [2] D. Gatteschi, et al., Mol. Eng. 3 (1993) 157.
[3] [4] [5] [6]
1431
I. Chiorescu, et al., J. Magn. Magn. Mater. 221 (2000) 103. Y. Furukawa, et al., Polyhedron 24 (2005) 2737. K. Takanashi, et al., J. Phys. Soc. Japan 52 (1983) 3953. Y. Nishisaka, et al., AIP Conference Proceedings 80 (2006) 1143.