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Zero-field muon-spin-rotation study of hole antiferromagnetism in low-carrier-density Y1−xCaxBa2Cu3O6
Physica C 311 Ž1999. 19–22
Zero-field muon-spin-rotation study of hole antiferromagnetism in low-carrier-density Y1yxCa x Ba 2 Cu 3 O6 C.E. Stronach
a,)
, D.R. Noakes a , X. Wan a,1, Ch. Niedermayer b, C. Bernhard E.J. Ansaldo c
b,2
,
a
c
Physics Department, Virginia State UniÕersity, Petersburg, VA 23806, USA b Physics Institute, UniÕersity of Konstanz, D-78434 Konstanz, Germany Physics Department, UniÕersity of Saskatchewan, Saskatoon, SK S7N 0W0 Canada
Received 10 March 1998; revised 25 September 1998; accepted 28 September 1998
Abstract We have studied magnetic correlations in the low-carrier-doping regime of Y1yx Ca x Ba 2 Cu 3 O6 . Samples with carrier densities psh s 0.015–0.035 Ž x s 0.03–0.07. were studied in the temperature range 2.6–200 K using the zero-field time differential muon spin rotation ŽZF TD mSR. technique. An oscillating signal, of 4.1 MHz Ž; 300 G. in the low-temperature limit ŽT ™ 0 K., indicative of antiferromagnetism, was found in each sample. This frequency diminished slightly with increasing Ca concentration. Two distinct regimes of frequency as a function of temperature are separated by a kink, which is interpreted as an independent ordering of the spins of the doped holes. The doped-hole spin-freezing temperature is doping dependent and occurs in the range 20.8–33 K. Even in the low-carrier-density regime, the long-range antiferromagnetic ordering is still strongly frustrated by the spin-glass mechanism through calcium doping. Apparent transitions between the 3D frozen-hole antiferromagnetic state and the spin-glassy state with diffusing holes were observed. Clearly the same magnetic interaction mechanisms are operating in both low-carrier-density ŽY,Ca.-123 and ŽLa,Sr. 2 CuO4 . q 1999 Elsevier Science B.V. All rights reserved. PACS: 74.25.Ha; 74.72.Bk; 76.75.q i Keywords: Muon spin relaxation; Y1y x Ca x Ba 2 Cu 3 O6 ; Doped-hole spin freezing; Antiferromagnetic ordering
1. Introduction In HTSC materials, there is a complex interplay between the antiferromagnetic ŽAF., spin-glassy ŽSG.
)
Corresponding author. Tel.: q1-804-524-5915; Fax: q1-804524-5914; E-mail: [email protected] 1 Current address: Physics Department, College of William and Mary, Williamsburg, VA 23187, USA. 2 Current address: Max-Planck-Institut fur ¨ Festkorperforschung, ¨ D-70569 Stuttgart, Germany.
and superconducting ŽSC. states which strongly depends on the doped charge carriers Žholes.. Most research has concentrated on the phase diagram in the La,SrrBa-214 w1–7x and Bi,Sr-2212 systems w8,9x where clear evidence of antiferromagnetic ordering was found below the transition temperature, Tf . For the YBCO system, previous work concentrated on the effects of Fe or O doping w10,11x on the magnetic-alloy ordered state. In the case of calcium doping ŽY1y x Ca x Ba 2 Cu 3 O6 series., samples with doping x F 0.20 were studied with muon spin relax-
0921-4534r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 8 . 0 0 5 8 7 - 5
C.E. Stronach et al.r Physica C 311 (1999) 19–22
20
Fig. 1. ZF-mSR spectra at 3, 26 and 160 K for x s 0.07. Solid lines are fits discussed in the text.
ation ŽmSR. w12–14x, 3 and strong magnetic correlations were observed only for x F 0.10 w15x. Later, it was confirmed that superconductivity appears only above a threshold concentration of x s 0.12 w16x. It appears that doping higher than x s 0.12 tends to destroy the antiferromagnetic ordering in the sample. The Y1y x Ca x Ba 2 Cu 3 O6 system is very suitable for study of this phenomenon since it allows one to directly control the hole concentration in the CuO 2 sheets, psh .
nential ŽFME. and nonrelaxing, was used to fit all the asymmetry data, 2 2
P Ž t . s A1eys 1 t cos Ž 2p f 1 t . q A 2 eyl 2 t q A 3 eyl 3 t q A 4 ,
Ž 1.
where A1 and s 1 are the amplitude and relaxation rate, respectively, for the OG volume fraction; A 2 and l2 are the analogous values for the SME fraction; A 3 and l3 are those for the FME fraction, and A 4 is the nonrelaxing amplitude. f 1 is the OG transverse oscillation frequency. Typical ZF asymmetry spectra are shown in Fig. 1.
2. Experiment and analysis Samples of Y1y x Ca x Ba 2 Cu 3 O6 with dopings, x s 0.03, 0.05, 0.06, 0.07, were studied on the M13 beamline at TRIUMF. Standard zero-field time differential muon spin rotation ŽZF TD mSR. spectra were measured in the temperature range 2.6–200 K. A multisignal depolarization function which includes four main fractions: oscillating Gaussian ŽOG., slow monotonic exponential ŽSME., fast monotonic expo-
3 For an introduction to mSR, see Ref. w12x; the study of magnetic materials with mSR is reviewed by Schenck and Gygax w13x.
3. Results For the x s 0.03 sample, over the whole experimental temperature range Ž2.6–200 K., there is only a gradual change in the strength of the magnetic ordering and the OG signal persisted to the highest temperature measured. This suggests the doping of calcium is too low to destroy the antiferromagnetic ordering in the sample. The frequency of the OG signal is close to 4.1 MHz at low temperature, indicating that muons are located at a site with an internal magnetic strength of 300 G. For the sample with x s 0.05 doping, there is more complex behavior. In general, the FME signal dominates at lower temperatures and the SME signal
C.E. Stronach et al.r Physica C 311 (1999) 19–22
dominates at higher temperatures. Furthermore, there is a sudden exchange of fractions among several signals at about 24 K. The mSR spectra of the x s 0.06 sample are similar to those of the x s 0.05 sample. The amplitudes of the OG, SME and FME signals remain nearly flat across the whole temperature range 1.8 to 120 K except at about 29 K where there is an exchange fraction between the SME and FME signals. The theoretical depolarization function Ž1. also works well on the x s 0.07 sample. The effect of doping x s 0.07 or carrier density psh s 0.035 on the YBCO substrate is evident, in that near and above 19 K there was no OG signal at all. The disappearance of the OG signal, combined with the continued presence of monotonic exponential depolarization, is indicative of a transition to a spin-glassy state.
4. Discussion Among all the doping and temperature-dependent parameter plots, the frequency of the OG signal ŽFig. 2. is the most interesting one. A sudden change in
21
Fig. 3. Phase diagram of Y1y x Ca x Ba 2 Cu 3 O6 . Higher magnetic transition temperature data with full dark square symbols were taken by the NMR method. Data with full dark up-triangle symbols were reported by previous ZF-mSR measurements. Our results for the lower magnetic transition temperatures are shown with hollow circles. In the SC regime, no more magnetic correlations are visible on the time scale of ZR-mSR. Lines are guides for the eye. The corresponding results on La 2y x Sr x CuO4 are given in Refs. w2,12x.
the temperature dependence of the local magnetic field strength was found in all samples at a temperature Tf that was determined by data analysis, and which we identify as the onset of freezing of the spins of the doped holes within the Cu-antiferromagnetic state w16,17x. A phenomenological model that fits this Žlines on Fig. 2. is: T
ž /
,
for T - Tf Ž 2a .
for T ) Tf .
Ž 2b .
f Ž T . s f 0 q sT q fg 1 y s f 0 q sT ,
Fig. 2. Temperature dependence of the precession frequency of the oscillating Gaussian ŽOG. signal in the four samples. The lines show the least-squares fit of Eqs. Ž2a. and Ž2b..
p
Tf
For the x s 0.07 sample, the above model gives a fit for the transition temperature of Tf s 33 K, but the OG signal in the experimental spectra disappears suddenly above 19 K. This suggests that the dopedhole spin freezing by itself is not enough to cause the local antiferromagnetic ordering required to generate a unique local field at the muon site which we would have observed as coherent oscillation. The dopedhole spin freezing may set in at a temperature as high as 33 K in the x s 0.07 sample, but apparently
22
C.E. Stronach et al.r Physica C 311 (1999) 19–22
the copper moments do not come into alignment until there is a first-order Žjump. transition at ; 19 K. In fact, since the Tf ’s are rising as the TN ’s are falling, it may be that the mechanisms causing the two orderings oppose each other, whichever is stronger suppressing the other’s transition temperature. The modified alloy magnetic phase diagram, which includes our analysis for Y1y x Ca x Ba 2 Cu 3 O6 , is shown in Fig. 3. It confirms the previous ZF-mSR study result w15x that the antiferromagnetic transition temperature for the x s 0.05 sample is 24 K. Furthermore, Fig. 3 shows that in the 33 K fit Tf for x s 0.07 falls on a simple extrapolation of the doped-hole spin-freezing transition line of points, while the observed Tf s 19 K falls basically on the extrapolation to the lower psh of the line of Tf ’s of the spin-glassy state Žup triangles.. Meanwhile the TN line is descending so steeply it is hard to tell which extrapolation it should go through. The similarity between the phase diagram of Y1y x Ca xBa 2 Cu 3 O6 and that of La 2yx Sr x CuO4 w7,18x is also noteworthy. This strongly suggests that the same mechanisms are operating in these two systems of high-Tc superconductors.
5. Conclusions It has been demonstrated that the ZF-mSR method is a powerful tool for investigating the magnetic transition Žphase diagram. at low temperature inside the Y1y x Ca x Ba 2 Cu 3 O6 sample, which allows a direct study of the mechanism behind the interplay between AF and SC. A multiple-signal analysis was presented, from which it was determined that the lower magnetic transition temperature in the Y1y x Ca x Ba 2 Cu 3 O6 is doping dependent even in the low-carrier-density regime, and occurs in the range 20.8–33 K. This not only confirms the previous ZF-mSR result but also adds three new transition
temperatures in the phase diagram in the antiferromagnetic regime. Clearly the same magnetic interaction mechanisms are operating in both low-carrierdensity ŽY,Ca.-123 and ŽLa, Sr. 2 CuO4 .
Acknowledgements CES, DRN and XW were supported in part by US DOE grant DE-FG05-88ER-45353 and US Air Force Office of Scientific Research grant F49620-97-10297. CN and CB were supported by the German Bundesministerium fur ¨ Bildung, Wissenschaft, Forschung und Technologie ŽBMBF.. TRIUMF is supported by the National Research Council of Canada. The assistance of Dr. Sydney Kreitzman and the TRIUMF technical staff is warmly appreciated.
References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x w11x w12x w13x
w14x w15x w16x w17x w18x
N. Nishida et al., Jpn. J. Appl. Phys. 26 ŽL. Ž1987. 1856. J.I. Budnick et al., Phys. Lett. A 124 Ž1987. 106. A. Weidinger et al., Phys. Rev. Lett. 62 Ž1989. 102. K. Kumagai et al., Hyp. Int. 86 Ž1994. 473. I. Watanabe et al., Hyp. Int. 86 Ž1994. 603. F.C. Chou et al., Phys. Rev. Lett. 71 Ž1993. 2323. D.C. Johnston et al., Physica C 235–240 Ž1994. 257. C.J. Boardman et al., Hyp. Int. 86 Ž1994. 525. P.A.J. De Groot et al., Hyp. Int. 86 Ž1994. 591. K. Nagamine et al., Hyp. Int. 86 Ž1994. 569. S.G. Barsov et al., Hyp. Int. 86 Ž1994. 543. E.B. Karlsson, Solid State Phenomena as seen by Muons, Protons and Excited Nuclei, Clarendon, Oxford, 1995. A. Schenck, F.N. Gygax, in: K.H.J. Buschow ŽEd.., Handbook on Magnetic Materials, Vol. 9, Elsevier, Amsterdam, 1995, p. 57. P. Dalmas de Reotier et al., J. Phys.: Condens. Matter 9 Ž1997. 9113. Ch. Niedermayer, Progress Report, Private communication, 1996. Ch. Niedermayer et al., Hyp. Int. 105 Ž1997. 131. R.J. Gooding et al., Phys. Rev. B 49 Ž1994. 6067. Ch. Niedermayer et al., Phys. Rev. Lett. 80 Ž1998. 3843.
Zero-field muon-spin-rotation study of hole antiferromagnetism in low-carrier-density Y1yxCa x Ba 2 Cu 3 O6 C.E. Stronach
a,)
, D.R. Noakes a , X. Wan a,1, Ch. Niedermayer b, C. Bernhard E.J. Ansaldo c
b,2
,
a
c
Physics Department, Virginia State UniÕersity, Petersburg, VA 23806, USA b Physics Institute, UniÕersity of Konstanz, D-78434 Konstanz, Germany Physics Department, UniÕersity of Saskatchewan, Saskatoon, SK S7N 0W0 Canada
Received 10 March 1998; revised 25 September 1998; accepted 28 September 1998
Abstract We have studied magnetic correlations in the low-carrier-doping regime of Y1yx Ca x Ba 2 Cu 3 O6 . Samples with carrier densities psh s 0.015–0.035 Ž x s 0.03–0.07. were studied in the temperature range 2.6–200 K using the zero-field time differential muon spin rotation ŽZF TD mSR. technique. An oscillating signal, of 4.1 MHz Ž; 300 G. in the low-temperature limit ŽT ™ 0 K., indicative of antiferromagnetism, was found in each sample. This frequency diminished slightly with increasing Ca concentration. Two distinct regimes of frequency as a function of temperature are separated by a kink, which is interpreted as an independent ordering of the spins of the doped holes. The doped-hole spin-freezing temperature is doping dependent and occurs in the range 20.8–33 K. Even in the low-carrier-density regime, the long-range antiferromagnetic ordering is still strongly frustrated by the spin-glass mechanism through calcium doping. Apparent transitions between the 3D frozen-hole antiferromagnetic state and the spin-glassy state with diffusing holes were observed. Clearly the same magnetic interaction mechanisms are operating in both low-carrier-density ŽY,Ca.-123 and ŽLa,Sr. 2 CuO4 . q 1999 Elsevier Science B.V. All rights reserved. PACS: 74.25.Ha; 74.72.Bk; 76.75.q i Keywords: Muon spin relaxation; Y1y x Ca x Ba 2 Cu 3 O6 ; Doped-hole spin freezing; Antiferromagnetic ordering
1. Introduction In HTSC materials, there is a complex interplay between the antiferromagnetic ŽAF., spin-glassy ŽSG.
)
Corresponding author. Tel.: q1-804-524-5915; Fax: q1-804524-5914; E-mail: [email protected] 1 Current address: Physics Department, College of William and Mary, Williamsburg, VA 23187, USA. 2 Current address: Max-Planck-Institut fur ¨ Festkorperforschung, ¨ D-70569 Stuttgart, Germany.
and superconducting ŽSC. states which strongly depends on the doped charge carriers Žholes.. Most research has concentrated on the phase diagram in the La,SrrBa-214 w1–7x and Bi,Sr-2212 systems w8,9x where clear evidence of antiferromagnetic ordering was found below the transition temperature, Tf . For the YBCO system, previous work concentrated on the effects of Fe or O doping w10,11x on the magnetic-alloy ordered state. In the case of calcium doping ŽY1y x Ca x Ba 2 Cu 3 O6 series., samples with doping x F 0.20 were studied with muon spin relax-
0921-4534r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 8 . 0 0 5 8 7 - 5
C.E. Stronach et al.r Physica C 311 (1999) 19–22
20
Fig. 1. ZF-mSR spectra at 3, 26 and 160 K for x s 0.07. Solid lines are fits discussed in the text.
ation ŽmSR. w12–14x, 3 and strong magnetic correlations were observed only for x F 0.10 w15x. Later, it was confirmed that superconductivity appears only above a threshold concentration of x s 0.12 w16x. It appears that doping higher than x s 0.12 tends to destroy the antiferromagnetic ordering in the sample. The Y1y x Ca x Ba 2 Cu 3 O6 system is very suitable for study of this phenomenon since it allows one to directly control the hole concentration in the CuO 2 sheets, psh .
nential ŽFME. and nonrelaxing, was used to fit all the asymmetry data, 2 2
P Ž t . s A1eys 1 t cos Ž 2p f 1 t . q A 2 eyl 2 t q A 3 eyl 3 t q A 4 ,
Ž 1.
where A1 and s 1 are the amplitude and relaxation rate, respectively, for the OG volume fraction; A 2 and l2 are the analogous values for the SME fraction; A 3 and l3 are those for the FME fraction, and A 4 is the nonrelaxing amplitude. f 1 is the OG transverse oscillation frequency. Typical ZF asymmetry spectra are shown in Fig. 1.
2. Experiment and analysis Samples of Y1y x Ca x Ba 2 Cu 3 O6 with dopings, x s 0.03, 0.05, 0.06, 0.07, were studied on the M13 beamline at TRIUMF. Standard zero-field time differential muon spin rotation ŽZF TD mSR. spectra were measured in the temperature range 2.6–200 K. A multisignal depolarization function which includes four main fractions: oscillating Gaussian ŽOG., slow monotonic exponential ŽSME., fast monotonic expo-
3 For an introduction to mSR, see Ref. w12x; the study of magnetic materials with mSR is reviewed by Schenck and Gygax w13x.
3. Results For the x s 0.03 sample, over the whole experimental temperature range Ž2.6–200 K., there is only a gradual change in the strength of the magnetic ordering and the OG signal persisted to the highest temperature measured. This suggests the doping of calcium is too low to destroy the antiferromagnetic ordering in the sample. The frequency of the OG signal is close to 4.1 MHz at low temperature, indicating that muons are located at a site with an internal magnetic strength of 300 G. For the sample with x s 0.05 doping, there is more complex behavior. In general, the FME signal dominates at lower temperatures and the SME signal
C.E. Stronach et al.r Physica C 311 (1999) 19–22
dominates at higher temperatures. Furthermore, there is a sudden exchange of fractions among several signals at about 24 K. The mSR spectra of the x s 0.06 sample are similar to those of the x s 0.05 sample. The amplitudes of the OG, SME and FME signals remain nearly flat across the whole temperature range 1.8 to 120 K except at about 29 K where there is an exchange fraction between the SME and FME signals. The theoretical depolarization function Ž1. also works well on the x s 0.07 sample. The effect of doping x s 0.07 or carrier density psh s 0.035 on the YBCO substrate is evident, in that near and above 19 K there was no OG signal at all. The disappearance of the OG signal, combined with the continued presence of monotonic exponential depolarization, is indicative of a transition to a spin-glassy state.
4. Discussion Among all the doping and temperature-dependent parameter plots, the frequency of the OG signal ŽFig. 2. is the most interesting one. A sudden change in
21
Fig. 3. Phase diagram of Y1y x Ca x Ba 2 Cu 3 O6 . Higher magnetic transition temperature data with full dark square symbols were taken by the NMR method. Data with full dark up-triangle symbols were reported by previous ZF-mSR measurements. Our results for the lower magnetic transition temperatures are shown with hollow circles. In the SC regime, no more magnetic correlations are visible on the time scale of ZR-mSR. Lines are guides for the eye. The corresponding results on La 2y x Sr x CuO4 are given in Refs. w2,12x.
the temperature dependence of the local magnetic field strength was found in all samples at a temperature Tf that was determined by data analysis, and which we identify as the onset of freezing of the spins of the doped holes within the Cu-antiferromagnetic state w16,17x. A phenomenological model that fits this Žlines on Fig. 2. is: T
ž /
,
for T - Tf Ž 2a .
for T ) Tf .
Ž 2b .
f Ž T . s f 0 q sT q fg 1 y s f 0 q sT ,
Fig. 2. Temperature dependence of the precession frequency of the oscillating Gaussian ŽOG. signal in the four samples. The lines show the least-squares fit of Eqs. Ž2a. and Ž2b..
p
Tf
For the x s 0.07 sample, the above model gives a fit for the transition temperature of Tf s 33 K, but the OG signal in the experimental spectra disappears suddenly above 19 K. This suggests that the dopedhole spin freezing by itself is not enough to cause the local antiferromagnetic ordering required to generate a unique local field at the muon site which we would have observed as coherent oscillation. The dopedhole spin freezing may set in at a temperature as high as 33 K in the x s 0.07 sample, but apparently
22
C.E. Stronach et al.r Physica C 311 (1999) 19–22
the copper moments do not come into alignment until there is a first-order Žjump. transition at ; 19 K. In fact, since the Tf ’s are rising as the TN ’s are falling, it may be that the mechanisms causing the two orderings oppose each other, whichever is stronger suppressing the other’s transition temperature. The modified alloy magnetic phase diagram, which includes our analysis for Y1y x Ca x Ba 2 Cu 3 O6 , is shown in Fig. 3. It confirms the previous ZF-mSR study result w15x that the antiferromagnetic transition temperature for the x s 0.05 sample is 24 K. Furthermore, Fig. 3 shows that in the 33 K fit Tf for x s 0.07 falls on a simple extrapolation of the doped-hole spin-freezing transition line of points, while the observed Tf s 19 K falls basically on the extrapolation to the lower psh of the line of Tf ’s of the spin-glassy state Žup triangles.. Meanwhile the TN line is descending so steeply it is hard to tell which extrapolation it should go through. The similarity between the phase diagram of Y1y x Ca xBa 2 Cu 3 O6 and that of La 2yx Sr x CuO4 w7,18x is also noteworthy. This strongly suggests that the same mechanisms are operating in these two systems of high-Tc superconductors.
5. Conclusions It has been demonstrated that the ZF-mSR method is a powerful tool for investigating the magnetic transition Žphase diagram. at low temperature inside the Y1y x Ca x Ba 2 Cu 3 O6 sample, which allows a direct study of the mechanism behind the interplay between AF and SC. A multiple-signal analysis was presented, from which it was determined that the lower magnetic transition temperature in the Y1y x Ca x Ba 2 Cu 3 O6 is doping dependent even in the low-carrier-density regime, and occurs in the range 20.8–33 K. This not only confirms the previous ZF-mSR result but also adds three new transition
temperatures in the phase diagram in the antiferromagnetic regime. Clearly the same magnetic interaction mechanisms are operating in both low-carrierdensity ŽY,Ca.-123 and ŽLa, Sr. 2 CuO4 .
Acknowledgements CES, DRN and XW were supported in part by US DOE grant DE-FG05-88ER-45353 and US Air Force Office of Scientific Research grant F49620-97-10297. CN and CB were supported by the German Bundesministerium fur ¨ Bildung, Wissenschaft, Forschung und Technologie ŽBMBF.. TRIUMF is supported by the National Research Council of Canada. The assistance of Dr. Sydney Kreitzman and the TRIUMF technical staff is warmly appreciated.
References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x w11x w12x w13x
w14x w15x w16x w17x w18x
N. Nishida et al., Jpn. J. Appl. Phys. 26 ŽL. Ž1987. 1856. J.I. Budnick et al., Phys. Lett. A 124 Ž1987. 106. A. Weidinger et al., Phys. Rev. Lett. 62 Ž1989. 102. K. Kumagai et al., Hyp. Int. 86 Ž1994. 473. I. Watanabe et al., Hyp. Int. 86 Ž1994. 603. F.C. Chou et al., Phys. Rev. Lett. 71 Ž1993. 2323. D.C. Johnston et al., Physica C 235–240 Ž1994. 257. C.J. Boardman et al., Hyp. Int. 86 Ž1994. 525. P.A.J. De Groot et al., Hyp. Int. 86 Ž1994. 591. K. Nagamine et al., Hyp. Int. 86 Ž1994. 569. S.G. Barsov et al., Hyp. Int. 86 Ž1994. 543. E.B. Karlsson, Solid State Phenomena as seen by Muons, Protons and Excited Nuclei, Clarendon, Oxford, 1995. A. Schenck, F.N. Gygax, in: K.H.J. Buschow ŽEd.., Handbook on Magnetic Materials, Vol. 9, Elsevier, Amsterdam, 1995, p. 57. P. Dalmas de Reotier et al., J. Phys.: Condens. Matter 9 Ž1997. 9113. Ch. Niedermayer, Progress Report, Private communication, 1996. Ch. Niedermayer et al., Hyp. Int. 105 Ž1997. 131. R.J. Gooding et al., Phys. Rev. B 49 Ž1994. 6067. Ch. Niedermayer et al., Phys. Rev. Lett. 80 Ž1998. 3843.