- Email: [email protected]
ESR experiments of molecular magnet V15 at ultra-low temperatures
ARTICLE IN PRESS
Physica B 346–347 (2004) 206–210
ESR experiments of molecular magnet V15 at ultra-low temperatures Takuo Sakona,*, Keiichi Koyamab, Mitsuhiro Motokawab, Yoshitami Ajiroc, Achim Muller . d, Bernard Barbarae a b
Department of Mechanical Engineering, Faculty of Engineering and Resource Science, Akita University, Akita City 010-8502, Japan High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan c Department of Physics, Faculty of Science, Kyushu University, Fukuoka 812-8581, Japan d Facultat fur . Chemie, Universitat Bielefeld, D-33501 Bielefeld, Germany e Laboratorie de Magnetisme Louis N’eel, CRNS, BP 166, F-38042 Grenoble Cedex 9, France
Abstract The low-temperature magnetism of fascinating molecular magnet V15 is studied using by ESR technique. A new ESR apparatus for use a Helium-3 cryostat and a Vector Network Analyzer has been developed. Using this system, ESR investigations were performed at low temperatures down to 0:5 K: At 4:2 K; a resonant peak was observed clearly. Both the width and height increase with lowering temperature, which indicates the intensity of the absorption signal increases steadily. Nevertheless, from the analysis of temperature dependence of the signal intensity, we found that the magnetic moments of V15 clusters drastically decrease with lowering temperature. This result indicates the ground state of spins of V15 ions is doublet with S ¼ 12: r 2004 Elsevier B.V. All rights reserved. PACS: 75.10.Jm; 75.50.Xx; 76.30.v Keywords: Electron spin resonance; Ultra-low temperature; Quantum molecular magnet; V15
1. Introduction Low-dimensional quantum spin systems, such as one-dimensional spin chains and magnetic molecular clusters, have attracted much attention because of their interesting quantum phenomena, for example, quantum fluctuation and quantum tunneling [1]. Among many molecular magnets, V15-polyoxyvanadate molecules, K6 ½V15 As6 O42 ðH2 OÞ8H2 O is characterized by a remarkable layer structure in an each quasi-spherical cluster, *Corresponding author. E-mail address: [email protected] (T. Sakon).
which has an overall trigonal symmetry with C3 axis along the c-axis [2]. A cluster containing 15 vanadium ions V4þ (S ¼ 12 in each V ion), consists of three distinct layers. Two hexagons (6 ions and 2 layers, total 12 ions) separate by a triangle (three ions). Interesting phenomenon in an interacting finite spin system is a quantum effect which manifests in well-defined discrete energy levels [3]. Some low-energy states are concerned with the low-temperature behavior. Ajiro et al. [4] carried out the experimental ESR and magnetic susceptibility study. The ESR spectrum shows a quite distinct behavior in the three temperature regions: a temperature between 300 and 100 K (region I),
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.01.051
ARTICLE IN PRESS T. Sakon et al. / Physica B 346–347 (2004) 206–210
an intermediate temperature region between 100 and 20 K (region II), and a low-temperature region below 20 K (region III). At region I, the effective magnetic moment meff X3 and gradually decreases with lowering temperature. At region II, meff is about 3 and almost constant at this temperature. At region III, meff decreases with lowering temperature. They also analyzed of angular-dependent behaviors and they provided that the triangle unit is well decoupled from the hexagon units. In this paper, we extended the measurement to lower temperature and investigate the magnetic properties by the ESR measurements between 4.2 and 0:5 K at region III, which is much lower than the energy gap. We also measured ESR above 3 T at ultra-low temperature and the magnetic field dependence of this spin system is discussed.
207
A clear peak was observed at 4:2 K for the external magnetic field m0 H ¼ 2:1 T: With lowered temperature, the peak becomes broader, which means that the amount of the microwave absorption W becomes larger. In V15, the most closed hexagonal V atoms are coupled antiferromagnetically by an exceeding large exchange interaction Jhex =kB B1000 K: This is obtained from the first principle density-functional calculation by Kortus et al. [6] Therefore, the number of total spins Shex of low-energy states of two hexagons in the ground state is zero. The higher total spin states are irrelevant to the magnetization at low temperature below 4:2 K: Therefore we consider only about three spins in a triangle. The energy levels of a triangle unit are two Kramers doublets with Stri ¼ 1 2 as the ground state and a low lying excited quartet state with Stri ¼ 32; which is separated from the ground state by an energy gap D ¼ Jtri : The
2. Experimental apparatus 4.2 K
3. Results and discussion The temperature dependence of the transmission spectra of the microwave for Hjjc is shown in Fig. 1. The microwave frequency is 57:831 GHz:
3.1 K
2.8 K 2.3 K
Transmission (arb. unit)
This experimental study has been performed at High Field Laboratory for Superconducting materials, Institute for Materials Research, Tohoku University. We have developed an ESR measurement system at ultra-low temperatures using a vector network analyzer (AB millime! ter Co. Ltd.) that makes low power microwaves and an ultrahigh sensitive analyzer and 3 He cryostat [5]. The microwave frequency was between 45 and 110 GHz and the transmission method using a cavity was used. In this system, the power of the microwave supplied to the sample is few mW: Rectangular pipes are used for the wave guide. In order to avoid heat leaks through wave guide, thermal anchors and filters are installed at the best positions. The size of the sample is 0:5 0:5 0:5 mm3 : Superconducting magnet was used in this study. The homogeneity of this magnet is 105 T=cm:
2.0 K
1.7 K
1.4 K 1.2 K 0.8 K
0.5 K
V15 f = 57.831 GHz
1.5
2.0
2.5
3.0
Magnetic Field (T) Fig. 1. ESR transmission spectra of the microwave for Hjjc and the microwave frequency is 57:831 GHz:
ARTICLE IN PRESS T. Sakon et al. / Physica B 346–347 (2004) 206–210
208
total magnetic susceptibility wtot is expressed by this formula.
properly by the Boltzmann factors, and the absorption power P is given more accurately by [8]
wtot ¼ wtri þ 2whex :
Ppðe2b 1Þð2eb þ ed ð3eb þ eb þ 3e3b ÞÞ=
ð1Þ
At low temperature ðT5Jhex =kB B1000 KÞ; whex ¼ 0; because the ground state of the spins of the hexagonals is singlet. The susceptibility of the triangle wtri is expressed as wtri ¼ ðg2 m2B =4kB TÞð1 þ 5 expðD=kB TÞÞ= ð1 þ expðD=kB TÞÞ:
ð3Þ
where b ¼ hn=kB T; and d ¼ D=kB T: The temperature dependence of ESR absorption power P at about 60 GHz (Fig. 4) and 110 GHz (Fig. 5) is shown. Filled circles and filled triangles are data
ð2Þ
Fig. 3. Schematic drowning of the energy level in a triangle unit.
H //c-axis 57.8310 GHz H //ab-plane 55.2888 GHz calculation (∆ = 3.7 K)
1.0
P ( arb. unit)
Based on this model, Ajiro et al. [4] analyzed their X-band ESR and magnetic susceptibility results and they obtained that the gap D between the ground state and a low-lying excited state in the triangle unit is 3:7 K: In ordinary case where kB Tbhn; the ESR absorption power P is proportional to the magnetic susceptibility wtri : Therefore, the effective magnetic moment meff per cluster is pffiffiffiffiffiffiffi given by the relation meff p PT ; using the definition wtri ¼ m2eff =3kB T: Fig. 2 shows the temperature dependence of meff thus obtained. Closed circles and crosses are experimental values for Hjjc and Hjjab-plane respectively. Solid line is a calculated value from Eq. (2). Overall qualitative behavior is well reproduced with D ¼ 3:7 K: This result indicates the ground state of V15 ions of the triangle is doublet with Stri ¼ 12: However, in the case where kB Tphn; the populations of the energy levels illustrated in Fig. 3, have to be weighted
3.0
eff
Effective Magnetic Moment M (µΒ)
ð2ðeb þ eb Þ þ ed ðe3b þ eb þ eb þ e3b ÞÞ;
2.5
2.0
1.5
V15 (∆ = 3.7 K) ESR (H //c-axis 57.8310 GHz) ESR (H //ab-plane 55.2888 GHz) calculation (Eq.(2) )
0.5
1.0 0
1
2
3
4
5
T (K)
Fig. 2. Temperature dependence of the effective magnetic moment meff per cluster.
0
1
2
3
4
5
T (K) Fig. 4. Temperature dependence of an absorption power P at 60 GHz:
ARTICLE IN PRESS T. Sakon et al. / Physica B 346–347 (2004) 206–210
obtained by ESR measurements for Hjjc-axis and Hjjab-plane, respectively. Solid lines are results of the calculation by Eq. (3). D is 3:7 K: The experimental data are normalized at 4:2 K: At low temperature, experimental data are smaller than the calculated values, but the characteristic features of the experimental results are well reproduced by Eq. (3). As shown in Fig. 4, there is a peak around 1 K at 60 GHz: On the other hand, at 110 GHz in Fig. 5, the power P gradually increases with lowering temperature. The temperature and frequency dependence of P is well explained by this model. Now, we confirm again that the ground state of V15 ions of the triangle is doublet with Stri ¼ 12: The magnetization measurement at ultra-low temperature below 1 K shows meta-magnetic transition around 3 T; which is due to a crossover between Stri ¼ 12 and Stri ¼ 32 [7]. The energy gap, which was obtained from their study, is as same as the value of our study. At 0:5 K; the ESR spectra are measured at some frequencies. The resonant frequency of the ESR is
209
proportional to the magnetic fields. The obtained g-value is about 1.97. This is as same as g-value obtained from X-band ESR measurements studied by Ajiro et al. [4]. The characteristic of V15 is that the ESR spectra are much broader than the spectra of other molecular magnets. The ESR line width increases nearly in proportion to the resonance frequency. Temperature dependence of the line width DH for Hjjc-axis is shown in Fig. 6. The frequency is 57:831 GHz (filled triangles) and 107:956 GHz (filled circles). At each frequency, line width goes broader with lowering temperature. It should be noted that these behaviors are quite different from those in the usual paramagnetic crystal for which the line width goes to zero for T-0 and H-N as the spin system is aligned at low temperature and in a strong magnetic field since DH is proportional to 2 ð/Hloc S /Hloc S2 Þ1=2 ¼ /dðHloc Þ2 S1=2 ;
ð4Þ
where Hloc represents the local field [9]. The present result suggests that the local field increases
3.0 0.4
ESR (H //c-axis 107.9562 GHz) ESR (H //ab-plane 109.6344 GHz) calculation (∆ = 3.7 K)
V15 H // c-axis
2.5
Line Width (T)
P (arb. unit)
0.3
2.0
0.2 107.9562 GHz
1.5 0.1
57.831 GHz
1.0 0 0
0
1
2
3
4
5
T (K) Fig. 5. Temperature dependence of an absorption power P at 110 GHz:
1
2
3
4
T (K) Fig. 6. Temperature dependence of the ESR line width. The frequency is 57:831 GHz (filled triangles) and 107:956 GHz (filled circles).
ARTICLE IN PRESS 210
T. Sakon et al. / Physica B 346–347 (2004) 206–210
with lowering temperature and increasing field in highly contrast with the usual case. One problem is the splitting of the ground state two doublets due to DM interaction. The splitting is about 100 mK [10]. Therefore the effect of the splitting should be considered when we analyze the line width of the ESR spectrum. Theoretical investigation is needed for clarify this problem. In conclusion, ESR investigations were performed at low temperatures down to 0:5 K using a Vector Network Analyzer. A resonant peak was observed clearly. Both the width and height increase with lowering temperature, which indicates the intensity of the ESR absorption signal increases steadily. From the analysis of temperature dependence of the signal intensity, we found that the magnetic moments of V15 drastically decrease with lowering temperature. This result indicates the ground state of spins of V15 ions is doublet with S ¼ 12:
References [1] B. Barbara, L. Thomas, F. Lionti, I. Chiorescu, A. Sulpice, J. Magn. Magn. Mater. 200 (1999) 167. [2] D. Gatteschi, L. Pardi, A.L. Barra, A. Muller, J. Doring, Nature 354 (1991) 463. [3] I. Chirescu, W. Wernsdorfer, A. Muller, H. Bogge, B. Barbara, Phys. Rev. Lett. 84 (2000) 3454. [4] Y. Ajiro, Y. Inagaki, H. Itoh, T. Asano, T. Sakon, M. Motokawa, B. Barbara, Quantum Properties of LowDimensional Antiferromagnets Vol. 80, Kyushu Univ. Press, Fukuoka, Japan, 2002. [5] T. Sakon, K. Koyama, M. Motokawa, Rev. Sci. Instrum. 73 (2002) 1242. [6] J. Kortus, C.S. Helberg, M.R. Pederson, Phys. Rev. Lett. 86 (2001) 3400. [7] I. Chirescu, W. Wernsdorfer, A. Muller, H. Bogge, B. Barbara, J. Magn. Magn. Mater. 221 (2000) 103. [8] C.P. Slichter, Principles of Magnetic Resonance, Springer, Berlin, Heidelberg, 1978. [9] I. Svare, G. Seidel, Phys. Rev. 134 (1964) A172. [10] S. Miyashita, N. Nagaosa, Prog. Theor. Phys. 106 (2001) 533.
Physica B 346–347 (2004) 206–210
ESR experiments of molecular magnet V15 at ultra-low temperatures Takuo Sakona,*, Keiichi Koyamab, Mitsuhiro Motokawab, Yoshitami Ajiroc, Achim Muller . d, Bernard Barbarae a b
Department of Mechanical Engineering, Faculty of Engineering and Resource Science, Akita University, Akita City 010-8502, Japan High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan c Department of Physics, Faculty of Science, Kyushu University, Fukuoka 812-8581, Japan d Facultat fur . Chemie, Universitat Bielefeld, D-33501 Bielefeld, Germany e Laboratorie de Magnetisme Louis N’eel, CRNS, BP 166, F-38042 Grenoble Cedex 9, France
Abstract The low-temperature magnetism of fascinating molecular magnet V15 is studied using by ESR technique. A new ESR apparatus for use a Helium-3 cryostat and a Vector Network Analyzer has been developed. Using this system, ESR investigations were performed at low temperatures down to 0:5 K: At 4:2 K; a resonant peak was observed clearly. Both the width and height increase with lowering temperature, which indicates the intensity of the absorption signal increases steadily. Nevertheless, from the analysis of temperature dependence of the signal intensity, we found that the magnetic moments of V15 clusters drastically decrease with lowering temperature. This result indicates the ground state of spins of V15 ions is doublet with S ¼ 12: r 2004 Elsevier B.V. All rights reserved. PACS: 75.10.Jm; 75.50.Xx; 76.30.v Keywords: Electron spin resonance; Ultra-low temperature; Quantum molecular magnet; V15
1. Introduction Low-dimensional quantum spin systems, such as one-dimensional spin chains and magnetic molecular clusters, have attracted much attention because of their interesting quantum phenomena, for example, quantum fluctuation and quantum tunneling [1]. Among many molecular magnets, V15-polyoxyvanadate molecules, K6 ½V15 As6 O42 ðH2 OÞ8H2 O is characterized by a remarkable layer structure in an each quasi-spherical cluster, *Corresponding author. E-mail address: [email protected] (T. Sakon).
which has an overall trigonal symmetry with C3 axis along the c-axis [2]. A cluster containing 15 vanadium ions V4þ (S ¼ 12 in each V ion), consists of three distinct layers. Two hexagons (6 ions and 2 layers, total 12 ions) separate by a triangle (three ions). Interesting phenomenon in an interacting finite spin system is a quantum effect which manifests in well-defined discrete energy levels [3]. Some low-energy states are concerned with the low-temperature behavior. Ajiro et al. [4] carried out the experimental ESR and magnetic susceptibility study. The ESR spectrum shows a quite distinct behavior in the three temperature regions: a temperature between 300 and 100 K (region I),
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.01.051
ARTICLE IN PRESS T. Sakon et al. / Physica B 346–347 (2004) 206–210
an intermediate temperature region between 100 and 20 K (region II), and a low-temperature region below 20 K (region III). At region I, the effective magnetic moment meff X3 and gradually decreases with lowering temperature. At region II, meff is about 3 and almost constant at this temperature. At region III, meff decreases with lowering temperature. They also analyzed of angular-dependent behaviors and they provided that the triangle unit is well decoupled from the hexagon units. In this paper, we extended the measurement to lower temperature and investigate the magnetic properties by the ESR measurements between 4.2 and 0:5 K at region III, which is much lower than the energy gap. We also measured ESR above 3 T at ultra-low temperature and the magnetic field dependence of this spin system is discussed.
207
A clear peak was observed at 4:2 K for the external magnetic field m0 H ¼ 2:1 T: With lowered temperature, the peak becomes broader, which means that the amount of the microwave absorption W becomes larger. In V15, the most closed hexagonal V atoms are coupled antiferromagnetically by an exceeding large exchange interaction Jhex =kB B1000 K: This is obtained from the first principle density-functional calculation by Kortus et al. [6] Therefore, the number of total spins Shex of low-energy states of two hexagons in the ground state is zero. The higher total spin states are irrelevant to the magnetization at low temperature below 4:2 K: Therefore we consider only about three spins in a triangle. The energy levels of a triangle unit are two Kramers doublets with Stri ¼ 1 2 as the ground state and a low lying excited quartet state with Stri ¼ 32; which is separated from the ground state by an energy gap D ¼ Jtri : The
2. Experimental apparatus 4.2 K
3. Results and discussion The temperature dependence of the transmission spectra of the microwave for Hjjc is shown in Fig. 1. The microwave frequency is 57:831 GHz:
3.1 K
2.8 K 2.3 K
Transmission (arb. unit)
This experimental study has been performed at High Field Laboratory for Superconducting materials, Institute for Materials Research, Tohoku University. We have developed an ESR measurement system at ultra-low temperatures using a vector network analyzer (AB millime! ter Co. Ltd.) that makes low power microwaves and an ultrahigh sensitive analyzer and 3 He cryostat [5]. The microwave frequency was between 45 and 110 GHz and the transmission method using a cavity was used. In this system, the power of the microwave supplied to the sample is few mW: Rectangular pipes are used for the wave guide. In order to avoid heat leaks through wave guide, thermal anchors and filters are installed at the best positions. The size of the sample is 0:5 0:5 0:5 mm3 : Superconducting magnet was used in this study. The homogeneity of this magnet is 105 T=cm:
2.0 K
1.7 K
1.4 K 1.2 K 0.8 K
0.5 K
V15 f = 57.831 GHz
1.5
2.0
2.5
3.0
Magnetic Field (T) Fig. 1. ESR transmission spectra of the microwave for Hjjc and the microwave frequency is 57:831 GHz:
ARTICLE IN PRESS T. Sakon et al. / Physica B 346–347 (2004) 206–210
208
total magnetic susceptibility wtot is expressed by this formula.
properly by the Boltzmann factors, and the absorption power P is given more accurately by [8]
wtot ¼ wtri þ 2whex :
Ppðe2b 1Þð2eb þ ed ð3eb þ eb þ 3e3b ÞÞ=
ð1Þ
At low temperature ðT5Jhex =kB B1000 KÞ; whex ¼ 0; because the ground state of the spins of the hexagonals is singlet. The susceptibility of the triangle wtri is expressed as wtri ¼ ðg2 m2B =4kB TÞð1 þ 5 expðD=kB TÞÞ= ð1 þ expðD=kB TÞÞ:
ð3Þ
where b ¼ hn=kB T; and d ¼ D=kB T: The temperature dependence of ESR absorption power P at about 60 GHz (Fig. 4) and 110 GHz (Fig. 5) is shown. Filled circles and filled triangles are data
ð2Þ
Fig. 3. Schematic drowning of the energy level in a triangle unit.
H //c-axis 57.8310 GHz H //ab-plane 55.2888 GHz calculation (∆ = 3.7 K)
1.0
P ( arb. unit)
Based on this model, Ajiro et al. [4] analyzed their X-band ESR and magnetic susceptibility results and they obtained that the gap D between the ground state and a low-lying excited state in the triangle unit is 3:7 K: In ordinary case where kB Tbhn; the ESR absorption power P is proportional to the magnetic susceptibility wtri : Therefore, the effective magnetic moment meff per cluster is pffiffiffiffiffiffiffi given by the relation meff p PT ; using the definition wtri ¼ m2eff =3kB T: Fig. 2 shows the temperature dependence of meff thus obtained. Closed circles and crosses are experimental values for Hjjc and Hjjab-plane respectively. Solid line is a calculated value from Eq. (2). Overall qualitative behavior is well reproduced with D ¼ 3:7 K: This result indicates the ground state of V15 ions of the triangle is doublet with Stri ¼ 12: However, in the case where kB Tphn; the populations of the energy levels illustrated in Fig. 3, have to be weighted
3.0
eff
Effective Magnetic Moment M (µΒ)
ð2ðeb þ eb Þ þ ed ðe3b þ eb þ eb þ e3b ÞÞ;
2.5
2.0
1.5
V15 (∆ = 3.7 K) ESR (H //c-axis 57.8310 GHz) ESR (H //ab-plane 55.2888 GHz) calculation (Eq.(2) )
0.5
1.0 0
1
2
3
4
5
T (K)
Fig. 2. Temperature dependence of the effective magnetic moment meff per cluster.
0
1
2
3
4
5
T (K) Fig. 4. Temperature dependence of an absorption power P at 60 GHz:
ARTICLE IN PRESS T. Sakon et al. / Physica B 346–347 (2004) 206–210
obtained by ESR measurements for Hjjc-axis and Hjjab-plane, respectively. Solid lines are results of the calculation by Eq. (3). D is 3:7 K: The experimental data are normalized at 4:2 K: At low temperature, experimental data are smaller than the calculated values, but the characteristic features of the experimental results are well reproduced by Eq. (3). As shown in Fig. 4, there is a peak around 1 K at 60 GHz: On the other hand, at 110 GHz in Fig. 5, the power P gradually increases with lowering temperature. The temperature and frequency dependence of P is well explained by this model. Now, we confirm again that the ground state of V15 ions of the triangle is doublet with Stri ¼ 12: The magnetization measurement at ultra-low temperature below 1 K shows meta-magnetic transition around 3 T; which is due to a crossover between Stri ¼ 12 and Stri ¼ 32 [7]. The energy gap, which was obtained from their study, is as same as the value of our study. At 0:5 K; the ESR spectra are measured at some frequencies. The resonant frequency of the ESR is
209
proportional to the magnetic fields. The obtained g-value is about 1.97. This is as same as g-value obtained from X-band ESR measurements studied by Ajiro et al. [4]. The characteristic of V15 is that the ESR spectra are much broader than the spectra of other molecular magnets. The ESR line width increases nearly in proportion to the resonance frequency. Temperature dependence of the line width DH for Hjjc-axis is shown in Fig. 6. The frequency is 57:831 GHz (filled triangles) and 107:956 GHz (filled circles). At each frequency, line width goes broader with lowering temperature. It should be noted that these behaviors are quite different from those in the usual paramagnetic crystal for which the line width goes to zero for T-0 and H-N as the spin system is aligned at low temperature and in a strong magnetic field since DH is proportional to 2 ð/Hloc S /Hloc S2 Þ1=2 ¼ /dðHloc Þ2 S1=2 ;
ð4Þ
where Hloc represents the local field [9]. The present result suggests that the local field increases
3.0 0.4
ESR (H //c-axis 107.9562 GHz) ESR (H //ab-plane 109.6344 GHz) calculation (∆ = 3.7 K)
V15 H // c-axis
2.5
Line Width (T)
P (arb. unit)
0.3
2.0
0.2 107.9562 GHz
1.5 0.1
57.831 GHz
1.0 0 0
0
1
2
3
4
5
T (K) Fig. 5. Temperature dependence of an absorption power P at 110 GHz:
1
2
3
4
T (K) Fig. 6. Temperature dependence of the ESR line width. The frequency is 57:831 GHz (filled triangles) and 107:956 GHz (filled circles).
ARTICLE IN PRESS 210
T. Sakon et al. / Physica B 346–347 (2004) 206–210
with lowering temperature and increasing field in highly contrast with the usual case. One problem is the splitting of the ground state two doublets due to DM interaction. The splitting is about 100 mK [10]. Therefore the effect of the splitting should be considered when we analyze the line width of the ESR spectrum. Theoretical investigation is needed for clarify this problem. In conclusion, ESR investigations were performed at low temperatures down to 0:5 K using a Vector Network Analyzer. A resonant peak was observed clearly. Both the width and height increase with lowering temperature, which indicates the intensity of the ESR absorption signal increases steadily. From the analysis of temperature dependence of the signal intensity, we found that the magnetic moments of V15 drastically decrease with lowering temperature. This result indicates the ground state of spins of V15 ions is doublet with S ¼ 12:
References [1] B. Barbara, L. Thomas, F. Lionti, I. Chiorescu, A. Sulpice, J. Magn. Magn. Mater. 200 (1999) 167. [2] D. Gatteschi, L. Pardi, A.L. Barra, A. Muller, J. Doring, Nature 354 (1991) 463. [3] I. Chirescu, W. Wernsdorfer, A. Muller, H. Bogge, B. Barbara, Phys. Rev. Lett. 84 (2000) 3454. [4] Y. Ajiro, Y. Inagaki, H. Itoh, T. Asano, T. Sakon, M. Motokawa, B. Barbara, Quantum Properties of LowDimensional Antiferromagnets Vol. 80, Kyushu Univ. Press, Fukuoka, Japan, 2002. [5] T. Sakon, K. Koyama, M. Motokawa, Rev. Sci. Instrum. 73 (2002) 1242. [6] J. Kortus, C.S. Helberg, M.R. Pederson, Phys. Rev. Lett. 86 (2001) 3400. [7] I. Chirescu, W. Wernsdorfer, A. Muller, H. Bogge, B. Barbara, J. Magn. Magn. Mater. 221 (2000) 103. [8] C.P. Slichter, Principles of Magnetic Resonance, Springer, Berlin, Heidelberg, 1978. [9] I. Svare, G. Seidel, Phys. Rev. 134 (1964) A172. [10] S. Miyashita, N. Nagaosa, Prog. Theor. Phys. 106 (2001) 533.