- Email: [email protected]
Direct estimation of zero-field energy gap in the nano-scale single molecular magnet V15
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 310 (2007) 1203–1205 www.elsevier.com/locate/jmmm
Direct estimation of zero-field energy gap in the nano-scale single molecular magnet V15 K. Kajiyoshia,, T. Kambea, M. Minoa, H. Nojirib, P. Ko¨gerlerc, M. Lubanc a
Graduate school of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan b Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan c Ames Laboratory & Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA Available online 3 November 2006
Abstract The electron spin resonance (ESR) at low frequency (0.6–3 GHz) and at low temperature (0.5 K) was performed for the single molecular magnet V15 . Non-linear field dependence of resonance at the lowest temperature implies the existence of the zero-field gap. The angle dependence of resonance field has strong anisotropy. We directly estimate the zero-field energy gap of 30 mK and analyze the energy levels using the model with Dzyaloshinskii–Moriya interaction. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.Xx; 76.30.v; 75.30.Gw; 75.10.Jm Keywords: Single molecular magnet (SMM); Quantum tunneling; Dzyaloshinskii–Moriya interaction (DMI); V15 ; Electron spin resonance (ESR)
1. Introduction Single molecular magnet has attractive attention such as quantum tunneling. Among many single molecular magnets, K6 ½As6 V15 O42 ðH2 OÞ8H2 O cluster (being V15 ) has a typical quasi-spherical structure, which is constructed by three layers made by V4þ ions ðS ¼ 12Þ [1]. One triangular spin ring is put between two hexagons. The spins within the hexagons are strongly coupled by AFM exchange interactions. At low temperatures, this molecule is regarded as the triangular spin system due to the spin singlet formation of the spins in the two hexagons. It should be expected that the ground state of V15 is degenerated Kramers doublets of the residual S ¼ 12 spin of the triangle. On the contrary, the magnetization measurements suggest that the degeneracy of doublets should be removed and the doublets have zerofield energy gap (20 m–80 mK). It is an important problem to determine what kind of perturbation dominates the energy levels. Recently, it is suggested that Dzyaloshinskii– Moriya interaction (DMI) as well as hyper fine interaction Corresponding author. Tel.: +81 86 251 8619.
E-mail address: [email protected] (K. Kajiyoshi). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.313
(HFI) would contribute to the energy gap [2,3]. The gap under the magnetic field definitely depends on the perturbation term: DMI should induce the strong anisotropy in the energy levels under the magnetic field while HFI did not. ESR is a powerful tool to determine such lowenergy excitations with high accuracy. In this paper, we measured low-frequency cm-wave region ESR which is comparable with the expected zero-field energy gap.
2. Experimental We use the single crystal sample which dimension is 3:0 3:0 3:0 mm3 . The direction of the c-axis ðC 3 axisÞ was determined by X-ray diffraction and X-band ESR measurement. In low-frequency region, we use a bridged loop-gapped (LG) type resonator [4]. The resonance frequency varies quasi-continuously from 600 MHz to 3 GHz. ESR absorption signals are directly obtained by monitoring the reflection intensity from the resonator using a scalar network analyzer (Agilent Technology, 8719ET). The DPPH absorption is used as a marker of magnetic field.
ARTICLE IN PRESS K. Kajiyoshi et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1203–1205
1204
3. Results and discussion Fig. 1(a) shows the temperature dependence of ESR intensity. The spin susceptibility deviates from simple Curie law around 2 K, which is due to the variation of effective number of spins from N ¼ 3 to 1 [5]. Below this temperature, the resonance fields show remarkable angle dependence. The anisotropy of resonance field develops with decreasing temperature, as shown in Fig. 1(b), where the shift from DPPH marker are shown. The shift of resonance field is remarkable along the c-axis. Fig. 2 (a) and (b) show the frequency dependence of the resonance fields for H ? c and Hkc at 0.5 K, respectively. For H ? c, the resonance condition is represented by following equation: o=g ¼ ½H 2 þ D2 1=2 . D is defined as a zero-field energy gap. The solid line indicates the calculation with D of 232 Oe (30 mK). This is a direct evidence of
b
1.4K 0.5K
0
~2K
100
-100 H⊥c
θ = 45° 1.9GHz
1
HV15-HDPPH (Oe)
ESRIntensity (a.u.)
a
-200
H//c 1.56GHz
1 10 Temperature (K)
-50
0 50 100 θ (degree)
Fig. 1. (a) Temperature dependence the ESR intensity at 1.9 GHz. (b) Angle dependence of resonance field at 1.56 GHz, where the shifts from DPPH marker are shown.
b
0
1000
H⊥c
0 2000
400 800 Magnetic Field (Oe)
~30 mK
1000 0 1000 Magnetic Field (Oe)
1000
ω/γg=1.98 (Oe)
H // c 0.94GHz
2000 ( (1→ 1→4 ) (2→ 3),(2 → 3) 4)
2000
Signal Intensity (a.u.)
ω/γg=1.95 (Oe)
a
H // c
0 2000
Fig. 2. Frequency ðo=gÞ-field (H) diagram for (a) H ? c and (b) Hkc. The inset of figure (a) shows the typical ESR spectrum and the fitted result by three Gaussian curves for Hkc. The open circles are experimental results at 0.5 K. The solid line for H ? c is represented in the text and the dot-dashed lines show the resonance conditions determined by the energy level diagram. i ! j stands for the transition form jii state to jji state in Fig. 3.
Fig. 3. Calculated energy level diagrams for (a) H ? c and (b) Hkc, respectively.
the zero-field energy gap. The inset of Fig. 2 (a) shows the typical ESR spectrum for Hkc. In the case of Hkc, however, the spectrum splits into several peaks at low–temperatures and can be decomposed by a couple of Gaussian curves. Note that the splitting of spectra is observed in the Hkc configuration and becomes definitely at lower frequency region. These angle dependence implies that the anisotropic DM interaction mainly contributes to the energy gap. We assume the spin Hamiltonian with DMI in Eq. (1) of Ref. [2] and obtained the symmetric exchange coupling of J ¼ 1:223 K [6] and the DM interaction of Dx ¼ Dz ¼ 30 mK, Dy ¼ 0 mK. Fig. 3 shows the energy level diagrams for two field directions. The dot-dashed lines in Fig. 2(b) indicate the transitions in the energy level diagrams. The resonance fields are roughly represented by the calculations. The weak deviation for 2 ! 3 transition at low-field may be due to an anti-crossing between 2–3 levels, which may be caused by the slight tilt of sample. Moreover, we found another resonance peaks above 1 kOe for Hkc, as shown by a dotted line in Fig. 2(b). At present, these peaks could not be assigned by the energy diagram. The absorption strength for the 1 ! 4 and 2 ! 3 transitions are comparable with each other, but that for the 1 ! 3 and 2 ! 4 transitions are too weak to be separable. The weak intensity of 1 ! 3 and 2 ! 4 transitions may be led by the DM interaction. 4. Conclusion We have performed the low-frequency ESR in the 0.6–3 GHz range on the single molecular magnet V15 at low temperatures. We directly observed non-linear ESR relations associated with the zero-field gap between Kramers doublets for the first time and estimated the zero-field energy gap using the model which include the DM interactions. References [1] D. Gatteschi, L. Pardi, A.L. Barra, A. Muller, J. Doring, Nature 354 (1991) 463.
ARTICLE IN PRESS K. Kajiyoshi et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1203–1205 [2] H. De Raedt, S. Miyashita, K. Michielsen, M. Machida, Phys. Rev. B 70 (2004) 64401. [3] S. Miyashita, H. De Raedt, K. Michielsen, Prog. Theor. Phys. 110 (2003) 889. [4] K. Kajiyoshi, T. Kambe, M. Tamura, K. Oshima, J. Phys. Soc. Japan 75 (2006) 74702.
1205
[5] Y. Ajiro, Y. Inagaki, H. Itoh, T. Asano, Y. Narumi, K. Kindo, T. Sakon, H. Nojiri, M. Motokawa, A. Cornia, D. Gatteschi, A. Muller, B. Barbara, Physica B 329–333 (2003) 1138. [6] I. Chiorescu, W. Wernsdorfer, A. Muller, H. Bogge, B. Barbara, J. Magn. Magn. Mater. 221 (2000) 103.
Journal of Magnetism and Magnetic Materials 310 (2007) 1203–1205 www.elsevier.com/locate/jmmm
Direct estimation of zero-field energy gap in the nano-scale single molecular magnet V15 K. Kajiyoshia,, T. Kambea, M. Minoa, H. Nojirib, P. Ko¨gerlerc, M. Lubanc a
Graduate school of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan b Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan c Ames Laboratory & Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA Available online 3 November 2006
Abstract The electron spin resonance (ESR) at low frequency (0.6–3 GHz) and at low temperature (0.5 K) was performed for the single molecular magnet V15 . Non-linear field dependence of resonance at the lowest temperature implies the existence of the zero-field gap. The angle dependence of resonance field has strong anisotropy. We directly estimate the zero-field energy gap of 30 mK and analyze the energy levels using the model with Dzyaloshinskii–Moriya interaction. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.Xx; 76.30.v; 75.30.Gw; 75.10.Jm Keywords: Single molecular magnet (SMM); Quantum tunneling; Dzyaloshinskii–Moriya interaction (DMI); V15 ; Electron spin resonance (ESR)
1. Introduction Single molecular magnet has attractive attention such as quantum tunneling. Among many single molecular magnets, K6 ½As6 V15 O42 ðH2 OÞ8H2 O cluster (being V15 ) has a typical quasi-spherical structure, which is constructed by three layers made by V4þ ions ðS ¼ 12Þ [1]. One triangular spin ring is put between two hexagons. The spins within the hexagons are strongly coupled by AFM exchange interactions. At low temperatures, this molecule is regarded as the triangular spin system due to the spin singlet formation of the spins in the two hexagons. It should be expected that the ground state of V15 is degenerated Kramers doublets of the residual S ¼ 12 spin of the triangle. On the contrary, the magnetization measurements suggest that the degeneracy of doublets should be removed and the doublets have zerofield energy gap (20 m–80 mK). It is an important problem to determine what kind of perturbation dominates the energy levels. Recently, it is suggested that Dzyaloshinskii– Moriya interaction (DMI) as well as hyper fine interaction Corresponding author. Tel.: +81 86 251 8619.
E-mail address: [email protected] (K. Kajiyoshi). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.313
(HFI) would contribute to the energy gap [2,3]. The gap under the magnetic field definitely depends on the perturbation term: DMI should induce the strong anisotropy in the energy levels under the magnetic field while HFI did not. ESR is a powerful tool to determine such lowenergy excitations with high accuracy. In this paper, we measured low-frequency cm-wave region ESR which is comparable with the expected zero-field energy gap.
2. Experimental We use the single crystal sample which dimension is 3:0 3:0 3:0 mm3 . The direction of the c-axis ðC 3 axisÞ was determined by X-ray diffraction and X-band ESR measurement. In low-frequency region, we use a bridged loop-gapped (LG) type resonator [4]. The resonance frequency varies quasi-continuously from 600 MHz to 3 GHz. ESR absorption signals are directly obtained by monitoring the reflection intensity from the resonator using a scalar network analyzer (Agilent Technology, 8719ET). The DPPH absorption is used as a marker of magnetic field.
ARTICLE IN PRESS K. Kajiyoshi et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1203–1205
1204
3. Results and discussion Fig. 1(a) shows the temperature dependence of ESR intensity. The spin susceptibility deviates from simple Curie law around 2 K, which is due to the variation of effective number of spins from N ¼ 3 to 1 [5]. Below this temperature, the resonance fields show remarkable angle dependence. The anisotropy of resonance field develops with decreasing temperature, as shown in Fig. 1(b), where the shift from DPPH marker are shown. The shift of resonance field is remarkable along the c-axis. Fig. 2 (a) and (b) show the frequency dependence of the resonance fields for H ? c and Hkc at 0.5 K, respectively. For H ? c, the resonance condition is represented by following equation: o=g ¼ ½H 2 þ D2 1=2 . D is defined as a zero-field energy gap. The solid line indicates the calculation with D of 232 Oe (30 mK). This is a direct evidence of
b
1.4K 0.5K
0
~2K
100
-100 H⊥c
θ = 45° 1.9GHz
1
HV15-HDPPH (Oe)
ESRIntensity (a.u.)
a
-200
H//c 1.56GHz
1 10 Temperature (K)
-50
0 50 100 θ (degree)
Fig. 1. (a) Temperature dependence the ESR intensity at 1.9 GHz. (b) Angle dependence of resonance field at 1.56 GHz, where the shifts from DPPH marker are shown.
b
0
1000
H⊥c
0 2000
400 800 Magnetic Field (Oe)
~30 mK
1000 0 1000 Magnetic Field (Oe)
1000
ω/γg=1.98 (Oe)
H // c 0.94GHz
2000 ( (1→ 1→4 ) (2→ 3),(2 → 3) 4)
2000
Signal Intensity (a.u.)
ω/γg=1.95 (Oe)
a
H // c
0 2000
Fig. 2. Frequency ðo=gÞ-field (H) diagram for (a) H ? c and (b) Hkc. The inset of figure (a) shows the typical ESR spectrum and the fitted result by three Gaussian curves for Hkc. The open circles are experimental results at 0.5 K. The solid line for H ? c is represented in the text and the dot-dashed lines show the resonance conditions determined by the energy level diagram. i ! j stands for the transition form jii state to jji state in Fig. 3.
Fig. 3. Calculated energy level diagrams for (a) H ? c and (b) Hkc, respectively.
the zero-field energy gap. The inset of Fig. 2 (a) shows the typical ESR spectrum for Hkc. In the case of Hkc, however, the spectrum splits into several peaks at low–temperatures and can be decomposed by a couple of Gaussian curves. Note that the splitting of spectra is observed in the Hkc configuration and becomes definitely at lower frequency region. These angle dependence implies that the anisotropic DM interaction mainly contributes to the energy gap. We assume the spin Hamiltonian with DMI in Eq. (1) of Ref. [2] and obtained the symmetric exchange coupling of J ¼ 1:223 K [6] and the DM interaction of Dx ¼ Dz ¼ 30 mK, Dy ¼ 0 mK. Fig. 3 shows the energy level diagrams for two field directions. The dot-dashed lines in Fig. 2(b) indicate the transitions in the energy level diagrams. The resonance fields are roughly represented by the calculations. The weak deviation for 2 ! 3 transition at low-field may be due to an anti-crossing between 2–3 levels, which may be caused by the slight tilt of sample. Moreover, we found another resonance peaks above 1 kOe for Hkc, as shown by a dotted line in Fig. 2(b). At present, these peaks could not be assigned by the energy diagram. The absorption strength for the 1 ! 4 and 2 ! 3 transitions are comparable with each other, but that for the 1 ! 3 and 2 ! 4 transitions are too weak to be separable. The weak intensity of 1 ! 3 and 2 ! 4 transitions may be led by the DM interaction. 4. Conclusion We have performed the low-frequency ESR in the 0.6–3 GHz range on the single molecular magnet V15 at low temperatures. We directly observed non-linear ESR relations associated with the zero-field gap between Kramers doublets for the first time and estimated the zero-field energy gap using the model which include the DM interactions. References [1] D. Gatteschi, L. Pardi, A.L. Barra, A. Muller, J. Doring, Nature 354 (1991) 463.
ARTICLE IN PRESS K. Kajiyoshi et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1203–1205 [2] H. De Raedt, S. Miyashita, K. Michielsen, M. Machida, Phys. Rev. B 70 (2004) 64401. [3] S. Miyashita, H. De Raedt, K. Michielsen, Prog. Theor. Phys. 110 (2003) 889. [4] K. Kajiyoshi, T. Kambe, M. Tamura, K. Oshima, J. Phys. Soc. Japan 75 (2006) 74702.
1205
[5] Y. Ajiro, Y. Inagaki, H. Itoh, T. Asano, Y. Narumi, K. Kindo, T. Sakon, H. Nojiri, M. Motokawa, A. Cornia, D. Gatteschi, A. Muller, B. Barbara, Physica B 329–333 (2003) 1138. [6] I. Chiorescu, W. Wernsdorfer, A. Muller, H. Bogge, B. Barbara, J. Magn. Magn. Mater. 221 (2000) 103.