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Fabrication of electrodes on charge–density–wave nanoscale crystals
Physica C 426–431 (2005) 1736–1740 www.elsevier.com/locate/physc
Fabrication of electrodes on charge–density–wave nanoscale crystals Katsuhiko Inagaki *, Takeshi Toshima, Satoshi Tanda, Kazuhiko Yamaya Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Kita 8 Nishi 13 Kita-ku, Sapporo 060-8628, Japan Received 23 November 2004; accepted 18 January 2005 Available online 26 July 2005
Abstract The reduction of the system size may lead to new developments in macroscopic quantum systems such as superconductors and charge–density–wave systems. In order to investigate such effects, thin films and thin wires are generally fabricated by an evaporation technique. However, this technique can only be applied to a limited number of materials; hence, a more versatile technique is required. In this study, we provide the results of our recent study on the fabrication of electrodes on nanoscale crystals. Gold electrodes, which were 400 nm in width, were fabricated by a standard lift-off technique on o-TaS3 charge–density–wave nanocrystals, which were prepared by deposition on silicon substrates. The interface resistance was higher than 100 GX just after evaporation and was decreased significantly by electron beam irradiation. The electrodes were tested down to 80 mK and were found to be fairly durable for cryogenic measurement. 2005 Elsevier B.V. All rights reserved. PACS: 72.15.Nj; 73.63.Bd; 81.07.Bc Keywords: Charge–density–wave; Electron beam lithography; Contact resistance; TaS3
1. Introduction The reduction of the system size may lead to new developments in macroscopic quantum systems such as superconductors and charge–density–wave (CDW) systems. CDW occurs on *
Corresponding author. Tel./fax: +81 11 706 7293. E-mail address: [email protected] (K. Inagaki).
account of macroscopic quantum coherence, accompanied by the lattice deformation of the wavevector 2kF [1]. By applying an electric field larger than a threshold value, the entire CDW slides along the sample, contributing to nonlinear electric conduction. As the most fascinating example of the nanoscale effect in CDW, the reversal of the sign of voltage drop was observed in the nanoscale NbSe3 and TaS3 [2]. The investigation of the
0921-4534/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2005.01.083
K. Inagaki et al. / Physica C 426–431 (2005) 1736–1740
nanoscale CDW system will be key to the realization of prospective applications, such as field effect transistors [3], electron pumps [4], and ultrafast memory [5], which exploit the quantum collective motion of CDW. Moreover, the recent discovery of MX3 (M = Nb, Ta; X = Se, S) topological (ring, Mo¨bius, and figure-of-eight) crystals has created a novel field of possible CDW devices that exploit the interference of long-range CDW order through their nontrivial topology [6]. In order to investigate such new effects, thin films and wires are generally fabricated by an evaporation technique. For example, the fabrication of a thin film of Rb0.30MoO3, which also undergoes CDW transition, by pulsed-laser deposition has been reported [7]. However, this technique can only be applied to a limited number of materials, and the quality of the sample is generally worse than that of single crystals. A promising solution is a hybrid process that combines the growth of single crystals and the lithography technique [2,7]. In this article, we provide the results of our recent study on the fabrication of electrodes on nanoscale crystals. Gold electrodes, which were 400 nm in width, were fabricated on o-TaS3 charge–density–wave nanocrystals by the standard lift-off technique.
2. Experimental In order to obtain nanoscale o-TaS3 samples, we synthesized single crystals by the chemical vapor transport method. A pure tantalum sheet and sulfur powder were placed in a quartz tube. The quartz tube was evacuated to 1 · 10 6 Torr and heated in a furnace at 530 C for 5 h. Since we required rather smaller crystals, the reaction duration that was considerably shorter than the typical condition was chosen. After the growth of the crystals, one end of the quartz tube was quenched in a liquid nitrogen bath in order to prevent the condensation of excess sulfur gas on the crystals. The crystals were sonicated in toluene for 15 min and kept free from perturbation for several hours in order to sediment unwanted larger crystals. Subsequently, the dispersion was deposited on a silicon substrate with a thermal oxide
1737
layer of 1 lm. Prior to the deposition on the substrate, 50 nm thick gold markers and contact pads were prepared. After blow-drying, the crystals were examined with an optical microscope. The obtained crystals were typically 0.2 lm in width and 10–100 lm in length. Electrodes were fabricated by standard electron beam lithography with a scanning electron microscope (SEM) (JSM-5200, JEOL) equipped with a homemade writing system. Polymethylmethacrylate (PMMA) resist was spun to a thickness of 500 nm and prebaked for 1 h at 170 C. Based on the position of the crystal with respect to the markers, a mask pattern was designed and loaded onto an electron beam writer. The thin gold film (50 nm in thickness) was evaporated after the developing process by methyl isobutyl keton diluted with isopropylalcohol (1:2). An adhesive titanium layer was optionally evaporated between the gold film and the substrate in order to investigate whether the adhesive layer affects the contact resistance. The lift-off was performed with acetone at room temperature. Another process was required to obtain ohmic contact. It has commonly been found in previous studies that ohmic contact was scarcely obtained and several methods were used to reduce the contact resistance [2,8]. In this study, we heated each electrode locally by the irradiation of an electron beam with an SEM (JSM-820, JEOL). The electron current was monitored at both the sample stage and the probe current detector inserted in the beam line. Only a small negligible electron beam current (<10 9 A) was required to specify the sample. Once the contact to be heated was located on the SEM screen, we increased the beam current to 1 · 10 6 A by using the larger aperture and the high bias. Subsequently, the beam position was fixed at a desirable position using the ‘‘SPOT’’ feature of the SEM for typically 30 s. The appearance of the contact did not change after the electron beam treatment.
3. Results and discussions Fig. 1 shows the scanning electron micrograph of an o-TaS3 crystal on a silicon substrate before
1738
K. Inagaki et al. / Physica C 426–431 (2005) 1736–1740
lift-off stage; this was probably because of the strong affinity between the o-TaS3 surface and PMMA. Opting for an electron beam resist rather than PMMA may solve the problem. The use of the Ti adhesive layer increased the yield at lift-off although it affected contact resistance. This problem will be discussed later. Fig. 2(a) shows the room temperature I–V characteristics of the sample both before (the broken line) and after (the solid line) electron beam treatment. The resistance was initially larger than 100 GX, and it decreased rapidly to 21 kX after 30 s of electron beam irradiation at an acceleration voltage of 25 kV and a typical beam current of 1 · 10 6 A. Since the resistance was obtained from a two-terminal measurement, it includes the sample resistance, contact resistance, and the currentlimiting series resistor of 2 kX. By considering the sample dimension (2 · 0.2 · 0.2 lm3), the resistivity is calculated to be 3 · 10 4 Xm. This is two orders larger than the bulk resistivity. The cross
I (pA)
100
Au 50 nm
0 21.9 kΩ
–100 –2 (a)
and after it was attached with the gold electrodes. The figure shows that the gold electrodes were well defined and located precisely on the nanocrystal. The width of the electrode was 400 nm with a separation of 1 lm. Each electrode connects to a bonding pad (100 · 100 lm2). We fabricated gold electrodes for several nanocrystals; however, approximately half of them failed. In most cases of failure, the crystal was washed away at the
2
V (mV) 10 Au 50 nm/Ti 20 nm
I (pA)
Fig. 1. Scanning electron micrograph of an o-TaS3 nanocrystal (a) before and (b) after being attached with gold electrodes. The gold markers shown in (a) were prepared before the deposition of the nanocrystal, and the locations relative to the markers were used to fabricate the beam pattern of the second lithography.
0
0
–10 (b)
–5
0
5
V (V)
Fig. 2. I–V characteristics of TaS3 nanocrystals with (a) 50 nm thick gold electrodes and (b) 50 nm thick gold electrodes with a 20 nm thick Ti adhesive layer. The broken and solid lines in each pane represent data before and after the electron beam treatment, respectively. The solid curve in (a) shows that the Ohmic conduction of 21.9 kX is successfully achieved for the electrodes without the Ti adhesive layer. On the other hand, the use of the Ti adhesive layers impedes ohmic conduction (b).
K. Inagaki et al. / Physica C 426–431 (2005) 1736–1740
section that actually effects electric conduction is 10 2 times the image that appears in the micrograph, if the resistivity is the same as that of the bulk sample. Previous studies of o-TaS3 thin wires describe a similar tendency [9]. Ohmic conduction was not obtained for the electrode with the Ti adhesive layer. Fig. 2(b) shows the I–V curves before (the broken line) and after (the solid line) electron irradiation. The curve did not change after the electron beam was irradiated for a period longer than 30 s. Titanium is chemically active and easily forms a bond with other materials. Hence, it is often used as an adhesive layer between the substrate and the electrode. Based on the obtained I–V curves, we believe that the thin Ti layer was oxidized or sulfurized when it was deposited onto the o-TaS3 surface, and it became a tunnel barrier. During electron beam irradiation in the SEM, the sample occasionally gets contaminated with carbonate. We believe that this does not have a significant effect on the transport measurements due to the following reasons: (1) The sample size is typically 10–100 lm in length, and we use the optical microscope to locate the sample. (2) Since gold electrodes are evaporated after the deposition of the sample, the metal layer covers and protects the contact area during irradiation. (3) The electron beam is irradiated only on the metal-sample contact, which is to be heated locally although a weak electron beam is scattered when we located the sample. The difference between the I–V characteristics shown in Fig. 2(a) and (b) supports our observation. We conducted a preliminary study of the electric properties of o-TaS3 nanocrystals. We observed some distinct behavior in the nanocrystals with regard to the temperature dependence of resistance and in the I–V characteristics at low temperatures. The Peierls transition became vague; this was probably because of strong onedimensional (1D) fluctuation. The temperature dependence was represented as the 1D variablerange-hopping conduction. The observed I–V characteristics at low temperatures suggested that the electric transport in the nanocrystals was affected by the sample dimensions. Samples with the smallest cross section exhibited nonlinear con-
1739
duction governed by the 1D soliton nucleation. The details will be published separately [10]. The fabricated electrodes were found to be very durable. We cooled the electrodes to 80 mK several times and did not observe any degradation in them. Their electric properties underwent only little change even after a 6-month storage period. This is indeed remarkable because conventional methods to attach the electrodes on MX3 crystals are fragile and can only be used for a couple of measurements. Hence, our method will be of importance for the future application of MX3 nanocrystals to electronics. Further, there might be no reason why the technique should not be applied to any type of nanocrystals that are possibly too small for their electric properties to be measured. For instance, among the MX3 family, we have already tested NbS3, which exhibits CDW at room temperatures, and obtained good results. We also plan to measure high-Tc cuprates and other exotic materials.
Acknowledgements The authors thank Prof. Pertti Hakonen, Helsinki University of Technology, Prof. Noriyuki Hatakenaka and Prof. Munehiro Nishida, Hiroshima University, Dr. Shinya Uji, National Institute of Materials Sciences, and Prof. Andrew Cleland, University of California, Santa Barbara, for their fruitful discussions and experimental support. This work was partly supported by the Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science and the 21st Century COE program (Topological Science and Technology).
References [1] G. Gru¨ner, Density Waves in Solids, Addison-Wesley Longman, Reading, 1994. [2] H.S.J. van der Zant, E. Slot, S.V. Zaitsev-Zotov, S.N. Artemenko, Phys. Rev. Lett. 87 (2001) 126401. [3] T.L. Adelman, S.V. Zaitsev-Zotov, R.E. Thorne, Phys. Rev. Lett. 74 (1995) 5264. [4] M.I. Visscher, G.E.W. Bauer, Appl. Phys. Lett. 75 (2002) 1007.
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K. Inagaki et al. / Physica C 426–431 (2005) 1736–1740
[5] D. Mihailovic`, D. Dvorsek, V.V. Kabanov, J. Demsar, L. Forro, H. Berger, Appl. Phys. Lett. 80 (2002) 871. [6] S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, Nature 417 (2002) 397. [7] O.C. Mantel, C.A.W. Bal, C. Langezaal, C. Dekker, H.S.J. van der Zant, J. Appl. Phys. 86 (1999) 4440.
[8] D.V. Borodin, S.V. Zaitsev-Zotov, F.Ya. Nad, Sov. Phys. JETP 63 (1986) 184. [9] S.V. Zaitsev-Zotov, V.Ya. Pokrovskii, P. Monceau, JETP Lett. 73 (2001) 25. [10] K. Inagaki, T. Toshima, S. Tanda, J. Phys. Chem. Solid, in press.
Fabrication of electrodes on charge–density–wave nanoscale crystals Katsuhiko Inagaki *, Takeshi Toshima, Satoshi Tanda, Kazuhiko Yamaya Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Kita 8 Nishi 13 Kita-ku, Sapporo 060-8628, Japan Received 23 November 2004; accepted 18 January 2005 Available online 26 July 2005
Abstract The reduction of the system size may lead to new developments in macroscopic quantum systems such as superconductors and charge–density–wave systems. In order to investigate such effects, thin films and thin wires are generally fabricated by an evaporation technique. However, this technique can only be applied to a limited number of materials; hence, a more versatile technique is required. In this study, we provide the results of our recent study on the fabrication of electrodes on nanoscale crystals. Gold electrodes, which were 400 nm in width, were fabricated by a standard lift-off technique on o-TaS3 charge–density–wave nanocrystals, which were prepared by deposition on silicon substrates. The interface resistance was higher than 100 GX just after evaporation and was decreased significantly by electron beam irradiation. The electrodes were tested down to 80 mK and were found to be fairly durable for cryogenic measurement. 2005 Elsevier B.V. All rights reserved. PACS: 72.15.Nj; 73.63.Bd; 81.07.Bc Keywords: Charge–density–wave; Electron beam lithography; Contact resistance; TaS3
1. Introduction The reduction of the system size may lead to new developments in macroscopic quantum systems such as superconductors and charge–density–wave (CDW) systems. CDW occurs on *
Corresponding author. Tel./fax: +81 11 706 7293. E-mail address: [email protected] (K. Inagaki).
account of macroscopic quantum coherence, accompanied by the lattice deformation of the wavevector 2kF [1]. By applying an electric field larger than a threshold value, the entire CDW slides along the sample, contributing to nonlinear electric conduction. As the most fascinating example of the nanoscale effect in CDW, the reversal of the sign of voltage drop was observed in the nanoscale NbSe3 and TaS3 [2]. The investigation of the
0921-4534/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2005.01.083
K. Inagaki et al. / Physica C 426–431 (2005) 1736–1740
nanoscale CDW system will be key to the realization of prospective applications, such as field effect transistors [3], electron pumps [4], and ultrafast memory [5], which exploit the quantum collective motion of CDW. Moreover, the recent discovery of MX3 (M = Nb, Ta; X = Se, S) topological (ring, Mo¨bius, and figure-of-eight) crystals has created a novel field of possible CDW devices that exploit the interference of long-range CDW order through their nontrivial topology [6]. In order to investigate such new effects, thin films and wires are generally fabricated by an evaporation technique. For example, the fabrication of a thin film of Rb0.30MoO3, which also undergoes CDW transition, by pulsed-laser deposition has been reported [7]. However, this technique can only be applied to a limited number of materials, and the quality of the sample is generally worse than that of single crystals. A promising solution is a hybrid process that combines the growth of single crystals and the lithography technique [2,7]. In this article, we provide the results of our recent study on the fabrication of electrodes on nanoscale crystals. Gold electrodes, which were 400 nm in width, were fabricated on o-TaS3 charge–density–wave nanocrystals by the standard lift-off technique.
2. Experimental In order to obtain nanoscale o-TaS3 samples, we synthesized single crystals by the chemical vapor transport method. A pure tantalum sheet and sulfur powder were placed in a quartz tube. The quartz tube was evacuated to 1 · 10 6 Torr and heated in a furnace at 530 C for 5 h. Since we required rather smaller crystals, the reaction duration that was considerably shorter than the typical condition was chosen. After the growth of the crystals, one end of the quartz tube was quenched in a liquid nitrogen bath in order to prevent the condensation of excess sulfur gas on the crystals. The crystals were sonicated in toluene for 15 min and kept free from perturbation for several hours in order to sediment unwanted larger crystals. Subsequently, the dispersion was deposited on a silicon substrate with a thermal oxide
1737
layer of 1 lm. Prior to the deposition on the substrate, 50 nm thick gold markers and contact pads were prepared. After blow-drying, the crystals were examined with an optical microscope. The obtained crystals were typically 0.2 lm in width and 10–100 lm in length. Electrodes were fabricated by standard electron beam lithography with a scanning electron microscope (SEM) (JSM-5200, JEOL) equipped with a homemade writing system. Polymethylmethacrylate (PMMA) resist was spun to a thickness of 500 nm and prebaked for 1 h at 170 C. Based on the position of the crystal with respect to the markers, a mask pattern was designed and loaded onto an electron beam writer. The thin gold film (50 nm in thickness) was evaporated after the developing process by methyl isobutyl keton diluted with isopropylalcohol (1:2). An adhesive titanium layer was optionally evaporated between the gold film and the substrate in order to investigate whether the adhesive layer affects the contact resistance. The lift-off was performed with acetone at room temperature. Another process was required to obtain ohmic contact. It has commonly been found in previous studies that ohmic contact was scarcely obtained and several methods were used to reduce the contact resistance [2,8]. In this study, we heated each electrode locally by the irradiation of an electron beam with an SEM (JSM-820, JEOL). The electron current was monitored at both the sample stage and the probe current detector inserted in the beam line. Only a small negligible electron beam current (<10 9 A) was required to specify the sample. Once the contact to be heated was located on the SEM screen, we increased the beam current to 1 · 10 6 A by using the larger aperture and the high bias. Subsequently, the beam position was fixed at a desirable position using the ‘‘SPOT’’ feature of the SEM for typically 30 s. The appearance of the contact did not change after the electron beam treatment.
3. Results and discussions Fig. 1 shows the scanning electron micrograph of an o-TaS3 crystal on a silicon substrate before
1738
K. Inagaki et al. / Physica C 426–431 (2005) 1736–1740
lift-off stage; this was probably because of the strong affinity between the o-TaS3 surface and PMMA. Opting for an electron beam resist rather than PMMA may solve the problem. The use of the Ti adhesive layer increased the yield at lift-off although it affected contact resistance. This problem will be discussed later. Fig. 2(a) shows the room temperature I–V characteristics of the sample both before (the broken line) and after (the solid line) electron beam treatment. The resistance was initially larger than 100 GX, and it decreased rapidly to 21 kX after 30 s of electron beam irradiation at an acceleration voltage of 25 kV and a typical beam current of 1 · 10 6 A. Since the resistance was obtained from a two-terminal measurement, it includes the sample resistance, contact resistance, and the currentlimiting series resistor of 2 kX. By considering the sample dimension (2 · 0.2 · 0.2 lm3), the resistivity is calculated to be 3 · 10 4 Xm. This is two orders larger than the bulk resistivity. The cross
I (pA)
100
Au 50 nm
0 21.9 kΩ
–100 –2 (a)
and after it was attached with the gold electrodes. The figure shows that the gold electrodes were well defined and located precisely on the nanocrystal. The width of the electrode was 400 nm with a separation of 1 lm. Each electrode connects to a bonding pad (100 · 100 lm2). We fabricated gold electrodes for several nanocrystals; however, approximately half of them failed. In most cases of failure, the crystal was washed away at the
2
V (mV) 10 Au 50 nm/Ti 20 nm
I (pA)
Fig. 1. Scanning electron micrograph of an o-TaS3 nanocrystal (a) before and (b) after being attached with gold electrodes. The gold markers shown in (a) were prepared before the deposition of the nanocrystal, and the locations relative to the markers were used to fabricate the beam pattern of the second lithography.
0
0
–10 (b)
–5
0
5
V (V)
Fig. 2. I–V characteristics of TaS3 nanocrystals with (a) 50 nm thick gold electrodes and (b) 50 nm thick gold electrodes with a 20 nm thick Ti adhesive layer. The broken and solid lines in each pane represent data before and after the electron beam treatment, respectively. The solid curve in (a) shows that the Ohmic conduction of 21.9 kX is successfully achieved for the electrodes without the Ti adhesive layer. On the other hand, the use of the Ti adhesive layers impedes ohmic conduction (b).
K. Inagaki et al. / Physica C 426–431 (2005) 1736–1740
section that actually effects electric conduction is 10 2 times the image that appears in the micrograph, if the resistivity is the same as that of the bulk sample. Previous studies of o-TaS3 thin wires describe a similar tendency [9]. Ohmic conduction was not obtained for the electrode with the Ti adhesive layer. Fig. 2(b) shows the I–V curves before (the broken line) and after (the solid line) electron irradiation. The curve did not change after the electron beam was irradiated for a period longer than 30 s. Titanium is chemically active and easily forms a bond with other materials. Hence, it is often used as an adhesive layer between the substrate and the electrode. Based on the obtained I–V curves, we believe that the thin Ti layer was oxidized or sulfurized when it was deposited onto the o-TaS3 surface, and it became a tunnel barrier. During electron beam irradiation in the SEM, the sample occasionally gets contaminated with carbonate. We believe that this does not have a significant effect on the transport measurements due to the following reasons: (1) The sample size is typically 10–100 lm in length, and we use the optical microscope to locate the sample. (2) Since gold electrodes are evaporated after the deposition of the sample, the metal layer covers and protects the contact area during irradiation. (3) The electron beam is irradiated only on the metal-sample contact, which is to be heated locally although a weak electron beam is scattered when we located the sample. The difference between the I–V characteristics shown in Fig. 2(a) and (b) supports our observation. We conducted a preliminary study of the electric properties of o-TaS3 nanocrystals. We observed some distinct behavior in the nanocrystals with regard to the temperature dependence of resistance and in the I–V characteristics at low temperatures. The Peierls transition became vague; this was probably because of strong onedimensional (1D) fluctuation. The temperature dependence was represented as the 1D variablerange-hopping conduction. The observed I–V characteristics at low temperatures suggested that the electric transport in the nanocrystals was affected by the sample dimensions. Samples with the smallest cross section exhibited nonlinear con-
1739
duction governed by the 1D soliton nucleation. The details will be published separately [10]. The fabricated electrodes were found to be very durable. We cooled the electrodes to 80 mK several times and did not observe any degradation in them. Their electric properties underwent only little change even after a 6-month storage period. This is indeed remarkable because conventional methods to attach the electrodes on MX3 crystals are fragile and can only be used for a couple of measurements. Hence, our method will be of importance for the future application of MX3 nanocrystals to electronics. Further, there might be no reason why the technique should not be applied to any type of nanocrystals that are possibly too small for their electric properties to be measured. For instance, among the MX3 family, we have already tested NbS3, which exhibits CDW at room temperatures, and obtained good results. We also plan to measure high-Tc cuprates and other exotic materials.
Acknowledgements The authors thank Prof. Pertti Hakonen, Helsinki University of Technology, Prof. Noriyuki Hatakenaka and Prof. Munehiro Nishida, Hiroshima University, Dr. Shinya Uji, National Institute of Materials Sciences, and Prof. Andrew Cleland, University of California, Santa Barbara, for their fruitful discussions and experimental support. This work was partly supported by the Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science and the 21st Century COE program (Topological Science and Technology).
References [1] G. Gru¨ner, Density Waves in Solids, Addison-Wesley Longman, Reading, 1994. [2] H.S.J. van der Zant, E. Slot, S.V. Zaitsev-Zotov, S.N. Artemenko, Phys. Rev. Lett. 87 (2001) 126401. [3] T.L. Adelman, S.V. Zaitsev-Zotov, R.E. Thorne, Phys. Rev. Lett. 74 (1995) 5264. [4] M.I. Visscher, G.E.W. Bauer, Appl. Phys. Lett. 75 (2002) 1007.
1740
K. Inagaki et al. / Physica C 426–431 (2005) 1736–1740
[5] D. Mihailovic`, D. Dvorsek, V.V. Kabanov, J. Demsar, L. Forro, H. Berger, Appl. Phys. Lett. 80 (2002) 871. [6] S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, Nature 417 (2002) 397. [7] O.C. Mantel, C.A.W. Bal, C. Langezaal, C. Dekker, H.S.J. van der Zant, J. Appl. Phys. 86 (1999) 4440.
[8] D.V. Borodin, S.V. Zaitsev-Zotov, F.Ya. Nad, Sov. Phys. JETP 63 (1986) 184. [9] S.V. Zaitsev-Zotov, V.Ya. Pokrovskii, P. Monceau, JETP Lett. 73 (2001) 25. [10] K. Inagaki, T. Toshima, S. Tanda, J. Phys. Chem. Solid, in press.