Proceedings of the 21st International Conference on Low Temperature Physics Prague, August 8-14, 1996

Part $6 - Plenary and invited papers

Q u a n t u m e f f e c t s in s p i n d y n a m i c s o f q u a s i - o n e - d i m e n s i o n a l a n t i f e r r o m a g n e t s

Igor A. Zaliznyak ~,* Lonis-Pierre Regnault b, and Daniel Petitgrand c

a p. KapitT.a Institute for Physical Problems, ul. Kosygina, 2, 117334 Moscow, Russia

b D~paxtement de Recherche Fondamentale sur la Mati~re Condens~e, Service de Physique Statistique, Magn6tisme et Supraconductivite, MDN, Centre d'l~tudes Nucl~aires, 85X, 38041 Grenoble Cedex, Prance

c Laboxatoixe L6on Bfillouin, Centre d']~tudes Nucl~aires de Saclay, 91191 Gif-sur-Yvette Cedex, Prance

Some experiments related to the quantum nature of spins that strongly manifest itself in the quasi- one-dimensional antiferromagnets axe discussed with a reference to CsNiCla and related compounds. In particular, the field dependence of the low-temperature staggered magnetization that is substantially reduced by zero-point motion of spins was measured by neutron diffraction and is shown to account for the nonlinear homogeneous susceptibility. We also present a comparison between the spin dynamics of Sffil CsNiCla and Sffi5/2 CsMnBrs above their N~el ordering temperatures measured by inelastic neutron scattering. It provides another spectacular evidence of the fundamental difference between the chains of integer and half-integer spins predicted by Haldane.

1. I N T R O D U C T I O N

Quantum fluctuations are known to be of a paramount importance for the quasi-one di- mensional systems, leading to the destruction of a long-range order as one-dimensionul limit is approached. For the linear Heisenberg antifer- romagnetic spin chain 7 / = J~"~.,~S,~S,~+I, J > 0 at finite temperature the absence of the long- range order was rigorously proven in the famous theorem by Hohenberg-Mermin-Wagner. In 1991 Pitaevskii and Stringaxi generalized the theorem for the TriO case, excluding the order also from the ground state (g.s.) and rigorously confirming the accepted point of view which was based on the quasiclassical spin-wave calculations. During the last decade an important breakthrough in un- derstanding the nature of the quantum disorder in the ground state of 1D Heisenberg antiferro- magnet had occurred. In fact, for the specific case of Sffil/2 an exact ansatz solution of the problem was found by H. Bethe [1] as fax as in 1932. Despite the disorder in the g.s. of Bethe ansatz, the single-time spin-spin correla- tions demonstrate rather slow, power-like decay:

^Ct ^Or (S 8 S~)N L ~ . Hence, the correlation length is infinite and the excitation spectrum is gapless. It corresponds to the continuum of the allowed energies: ~ J sin q <_ ~ua(q) <_ 7rJ sin q. Most of the excitations spectral weight is located near the lower boundary of the continuum and produces a picture resembling the usual N~el magnons in the spin-wave theory, valid in 1D only for infi- nite spins. After a very successful attempt was made in 1974 by Villain [2] to reconcile the spin- wave theory with the disordered g.s. of the 1D antiferromagnet implying a power-like correlated Bethe-ansatz-llke disorder, rather simple and gen- erally accepted picture was produced [3]. Namely, as on the scale of the magnon wavelength spin correlations do not decay noticeably except for the infinitesimal vicinities of the center qffi0 and the boundary qffi~r of the Brillouin zone (which become finite with T>0), spin wave excitations should look essentially the same as in the ordered phase. It was only in 1983 that Haldane [4]

* Present address: Reactor Rad la t ion Division, Nat ional

Inst i tute of Standards and Technology, Gai thersburs , MD

20899.

3232 Czech. J. Phys. 46 (1996), Suppl. $6

QUANTUM EFFECTS IN SPIN DYNAMICS OF QUASI-ONE-DIMENSIONAL ANTIFERROMAGNETS

pointed out that such classical picture with dou- blet gapless excitations is valid only for the chains with half-integer spins. The chain of the integer spins was, on the contrary, predicted to demon- strate all the standard features of the renormal- ized ID ~-model on which it can be mapped in the quasiclassical limit. Namely, it possesses a singlet disordered ground state with exponentially decaying correlations "a ̂ a ,~ (S~ S~) ~ e -I" l /(. The

Inl~ excitations are triplet corresponding to the total spin of the chain Stot=l and separated from the g.s. by an energy gap which is A H ,~, Je -'rs at the bottom of the dispersion curve (at the AFM point q = ~r).

CsNiCI3 and related ABX3 halide compounds (RbNiCI3, CsMnBrs, CsMnI3, CsVBr3, etc.) are among the subjects of the most intense studies aimed at clarifying the nature of quantum disor- der in the g.s. in view of the Haldane conjecture. They contain the antiferromagneticany coupled 3d ions located at the nodes of the hexagonal lattice and can be viewed as a set of the spin chains stretched along z aTis and forming a plane tri- angular lattice in the zy basal plane. Dominant interaction in their spin Hamiltonian

(1) is the Heisenberg exchange with the intrachain coupling 3 being 1-3 orders of magnitude larger than t h e inerchain J~, D << J is a single-ion anisotropy. In fact, CsNiC13 and all isomorphous Sffil ABX3 compounds known to date possess insufficiently small ratio J~/J to preserve the quantum disorder. Henceforth, they undergo a 3D antiferromagnetic ordering at some small but finite T jr (of course, this is impliticly the case for an demi-integer spin compounds). On one hand, this complicates the experimental verifica- tion of the results obtained for the disordered ID chains. But on the other hand, it gives a unique opportunity to study how the long-range order is affected by quantum spin motion "on the way" to be destroyed, compare the effect for different spin values a n d clarify the applicability limits of the spin-wave theory.

2. STATIC P R O P E R T I E S AT T--,0

One of the most interesting features of the quasi-one-dlmensional antiferromagnets indicative

of strong quantum fluctuations is unusually low, far from the classical expectation g/zBS, value of the saturated at T--,0 ordered magnetic mo- ment. The average ordered spin value was mea- sured to be about 0.5 of the nominal S=l in CsNiC13, 0.65 in RbNiC13 [5] and 0.66 of S=5/2 in CsMnBr3 [6]. In the harmonic spin wave theory the spin reduction is captured as a first 1/S correction to the staggered magnetization (or g.s. energy) arising from zero-point contribution of classical magnons. It was noticed as fax as in 1972 [7] that despite such large deviations of the ordered spins from the nominal values make the harmouic theory rather doubtful, the calcu- lated spin reductions appear to be in quite good agreement with the experiment. Recently this point was studied and reconfirmed for a large variety of quasi-one-dlmensional antiferromagnets [8, 9, 10]. We should note here that knowledge of the Hamiltonian (l) parameters necessary to calculate the static properties of an antiferromag- net is usually gained from fittin 8 the measured magnon dispersion with the classical spin-wave calculations. Large 1/S corrections to the stag- gered spin observed in the quasi 1D antiferro- magnets imply that spin wave frequencies can also be strongly renormalized (by the nonlinear "interaction" terms in the bosonic equivalent of the spin Hamiltonian). For small corrections the functional form of the magnon dispersion should not change and roughly they can be taken into account by employing the renormalized values J, f l and /5 which can differ by 10-50% from the Hamiltonian bare values. In fact, in CsNiCl3 also the functional form of the spin wave spec- trum as measured by neutron scattering [ll] is incompatible with the linear spin wave theory, making the actual Jt and D values even more uncertain. However, the logarithmic dependence 6S ... l n ( J / J ~) of the leadin 8 contzibution to the spin reduction in the spin-wave calculations makes it unsensitive to the uncertainty in s ~, D for large J/J~ which explains the good agreement with the experiment mentioned above [10] .

Another interestin 8 point is the influence of the quantum corrections on the homogeneous sus- ceptibility and magnetization process. CsNiCI3 family compounds order into a complex non- collinear six sublattice structure, for which the spin reorientation can be reasonably analyzed on- ly in the approximation of classical spins. Sur- prisingly, it appears that despite a strong spin

Czechoslovak Journal of Physics, Vol. 46 (1996), Suppl. $6 3233

1.A. Zaliznyak ct al.

reduction such analysis correctly reproduce all essential features of the magnetization curves.

. 8

"5 .6

(D r . 4

C "-I

% v -

.2

Magnetization'in CsNiCI.,- . . . . / 2 . . . . T = 1 . 8 K ~ , / / ' /

0 0 20 40 60 80

H(kOe) Fig. I. As an example we show in Fig.l the magne- tizations measured in CsNiC13 (T~. ~4.5K) at Tffi-I.gK which is believed to be sufficiently small to freeze the thermal fluctuations. Solid circles correspond to H / z (ffiCe hexagonal axis) which is the easy magnetization axis for this crystal (D <0), open circles - to H[[z; jump around H,! ~ 20 kOe is a spin-flop transition. Broken curves are calculated from the Hamiltonian (1) for the classical spins with 3ffi345GHs, 3'ffigGHz, /~ •0.6GHz and gffi2.15 as obtained [12] from fitting the AFMR and neutron scattering data. There are some evident important discrepancies which are due to the quantum effects. First, the susceptibility appears to be reduced from its classical expectation value. Its relative reduction was experimentally found to be approximately proportional to the relative spin reduction 6S /S [8, 13]. Later on this was confirmed by the cal- cnlations showing that the leading contribution to both is proportional to the same large logarithm ln(J ' /3) . This contrasts to the effect of thermal fluctuations which destroy the staggered magne- tization in the antiferromagnet almost without changing the susceptibility. Two other discrepan- cies with the classical spins approximation are the large magnetization anisotropy at fields above the spin-flop and its marked nonlinear growth with H. In [10] an at tempt was made to account for these peculiar features by calculating the leading 1/S quantum corrections to the ground state en- ergy and magnetization. The resultant curves are shown in Fig.l by the solid lines. They were cal- cnlated using the value 3ffi275GHz obtained from

the spin-flip (saturation) field which was recently measured in high field magnetization experiments by H. A. Katori et.al. [14] and is believed to be the bare J value in the Hamiltonian. It should also be mentioned that not knowing the bare value of the anisotropy constant D we cho- sen it to be D •l.6GHz, which gives the best agreement for the fluctuations-induced magnetiza- tion anisotropy. With such D value the classical spin-flop field Hs] ffi 4 S ~ - J , which is actually shown in the figure, appears to be larger than observed (in the classical calculations it agrees well because it is essentially a reference point to calculate D). An attempt to calculate the same first order in 1/S correction lead to an imagi- nary value of the spin-flop field. It means that including only the first order 1/S corrections to the g.s. energy results in an error that is larger than the energy difference of the non-spin-flop and spin-flop phases.

RbNiCI 3, <S>2(H)

1.5x10 s ~

.~ 1.0x10 s

~. 0.5x10 s t:]) c7)

m

0 0

I O=(1/3,1/3,1), T=5.1 K

20 40 60 80 100

H(kOe) Fig.2. Another evident deficiency of such approximation is its inability to reproduce correctly the nonlin- ear growth of the magnetization at high fields. Mainly it comes from the increase in the average ordered spin that is due to the suppression of the quantum reduction by the magnetic field, as was suggested in [8] and is also supported by the recent calculations. This point can be di- rectly verified in the experiment if one measure both the nonlinea~ magnetization and the field dependence of the magnetic Bragg peak intensity in neutron diffraction. We have performed such a study with S=I RbNiCI3 which is magnetical- ly isostructural with CsNiC13, but with slightly

3234 Czech. J. Phys. 46 (1996), Suppl. S6

QUANTUM EFFECTS IN SPIN DYNAMICS OF QUASI-ONE-DIMENSIONAL ANTIFERROMAGNETS

higher ] value and TN ~ I l K . Neutron diffraction experiments were performed at T ~ 5 K with DN3 lifting arm double axis spectrometer at the Siloe reactor at CEN-Grenoble. The sample of about 0.5 cm 3 with the mosaicity of 0.5 ~ was mount- ed with its Co axis vertical in the vertical field 10T cryomagnet. In this configuration we used the = 0.828.~ incident neutrons obtained with C u ( l l l ) monochromator to provide the wavevec- tot transfer qffi(h/3,k/3,1) within the angular ac- cess range .~ I0 ~ of the cryomagnet split. Tight diaphragms secured the 40" collimations before and after the sample. Square points in Fig.2 connected by solid line below the spin-flop and guided by the broken line above it represent the field dependence of the integral intensity of the (I/3,1/3,1) Bragg peak rocking curve which is proportional to the square of the sublattice or- dered spin. An increase by more than 20% at 97kOe is clearly observed (of course, we consid- er only the region above the spin-flop transition which is not affected by the geometrical factors due to spin reorientation). Open circles show the assumed (S) increase from the magnetiza- tion measurement performed with SQUID mag- netometer (they axe obtained as a ratio of the measured magnetization to one calculated for the classical spins from (1)). The effect observed in RbNiC13 is less pronounced than that in CsNiC13 (Fig.l) because of its weaker one-dimensionality and larger zero-fidd ordered spin value. Appar- ently, within the error our data confirm that the nonlinear growth of the magneti,.ation in the quasi-lD antiferromagnet is mostly due to the sublattice spin increase, so that quantum correc- tions to the sublattices canting angles (if any) are almost not affected by the field.

3. S P I N D Y N A M I C S A B O V E 3D O R D E R

Despite CsNiC13 and related Sffil compounds were extensively studied in view of the Haldane conjecture, neither of them have small enough J'/J ratio to possess quantum-disordered singlet g.s. Their true ground states are renormalized classical NEd states with the long-range 3D AFM order. At T--,0 spin dynamics is dominated by more or less usual magnons renormalized by zero- point fluctuations and gapless Goldstone modes axe present at the AFM points of the Brillouin �9 .one. Essentially the same situation holds for CsMnBr3 and other S=5/2 or S=3/2 isostructural quasi-lD compounds. Thus, 3D order at T--*0

completely smears the essential difference between the integer and half-integer spin antiferromagnet- ic chains constituting such systems. However, with T increasing above TN the 3D correlations should disappear outside the critical region, and in the temperature range TN <~<T<<~ 2J spin dy- namics of the quasi-lD antiferromagnet should be close to that of the corresponding spin chain. Thus, examination of the temperature evolution of the spin dynamics in such compounds can pro- vide a nice tool to view the difference between the AFM spin chains of integer and half-integer spins. Of course, to make a definitive conclusion about the existence or absence of the gap one should measure the energy profile of the fluctua- tions spectrum at the softest point of the systems Bdllouin zone, i.e. at the 3D antiferromagnetic Bragg positions. We performed such compara- tive study between CsNiCI3 (Sffil) and CsMnBr3 (S=5/2).

The dynamic structure factor S(q, w) was studied by inelastic neutron scattering using 4F1 and 4F2 triple axis cold neutron spectrometers installed at the Orphee reactor of the Labora- toire LEon Brillouin, CEN-Saclay. The exper- imental setup was essentially the same for all experiments. Rather large single crystal of ei- ther compound (,~lcm 3) grown from the melt by Bridgeman technique was mounted in the temperature-vaxiable ILL standard orange cryo- star with [110] and [001] (chain) lattice direc- tions lying in the horizontal scattering plane. All crystals excellently cleaved through the binary planes which made possible their rather precise preliminary visual orientation. The spectrometers were run in the constant q! = 1.25~i -1 mode with the hoxizontal collimations 4 0 " - 4 0 " - 4 0 " in the case of CsMnBr3 and almost relaxed collimations 6 0 " - 6 0 ' - 60" for CsNiCI3. Such setups gave the optimum relation between the neutron flux and energy resolution, which was P~ " 0.02THs in the first case and _~ 0.025THz in the second case (FWHM of the incoherent scattering peak at w = 0). High-energy neutrons produced in higher order reflections from PG double monochroma- tot system were removed by the nitrogen-cooled beryllium filter.

Essential problem in studying the low-energy spin dynamics arise from the nuclear incoherent scattering which dominate the neutrons cross- section around w = 0. A way to overcome this problem and obtain an accurate incoherent back-

Czechoslovak Journal of Physics, Vol. 46 (1996), Suppl. $6 3235

I.A. Zaliznyak ct at.

. ~ 1400

1200

~. 1000

0 600

.r 200

E 150

100

so 8

0

CsMnBr3

.9 1.0 1,1

0.20THz

.9 1.0 1.1

Q=(1/3,1/3,q) T=12K

800

600

400

200

0

0.05THz

.9 1.0 1.1

800 0.10THz'

600

4OO

0 .9 1.0 1.1 i05~ ] 0.30THZ - 200 O.'4OTHZ

I 150

100 i 100

50 ~ 50

0 0 .9 1.0 1.1 .9 1,0 1.1

Fig.3.

1000 I

E 0

0 0

q (rlu) q (rlu) q (flu)

CsNiCI 3 Q=(1/3,1/3,q) T=7.0K

200 0.05THz

950 150

900 100 ~

850 50

800.8 .9 1,0 1.1 1.2 0.8 ,9 1.0 1.1 1.2

200 0.10THz

150

100

0 .8 .9 1.0 1.1 1.2 .~ 200 0.15THz 200 0.20THz 200

150 150 150

�9 1 0 0 ~ 1 0 0 100 ..

50 50 50

8 0.8 .9 1.0 1.1 "1.2 0.8 .9 1.0 1.1 1.2 0.8 .9' 1.0 1.1 1.2

q (du) q (flu) q (du) Fig.4.

3236 Czech. J. Phys. 46 (1996), Suppl. $6

Q U A N T U M E F F E C T S 1N S P I N D Y N A M I C S O F Q U A S I - O N E - D I M E N S I O N A l , A N T I F E R I t O M A G N E T S

ground subtracted data is to perform a set of constant energy scans at different fixed energy transfers. To study the spectral composition of the low-frequency part of the dynamic correla- tion function S(q, co) at Q=(1/3,1/3,1) which is the 3D AFM Bragg point in our compounds we performed a number of such scans varying qffi(1/3,1/3,q). The step in q was chosen to be 0.01 around qffil and 0.02 on the tails of the peaks, well smaller than the observed q-width of the excitations. The step in energy 0.025THz was imposed by the available instrumental reso- lution. The results of such scanning in CsMnBr3 at Tffi-12K~ 1.5T~v are shown in Fig.3 by the open circles. The error bars are 2 ~ statistical error, and solid curves are simple gaussian fits. It is clear that scattering rapidly decreases with increasing energy, being the strongest at w ffi 0. As energy becomes larger than the temperature (12K ~0.25THz) the dispersion shows up and one observes well defined short-wavelength exci- tations moving apart from qffil. Scans at other temperatures revealed essentially the same pic- ture with strong critical scattering present at T -~K~ 1.1TN.

Completely different picture was observed at the same relative to TN temperature Tffi-7K~ 1.5Ttr in CsNiC13, Fig.4. Despite rather large error bars it is quite clear that peak at qffil is almost absent at w = 0THz and 0.025THz. It def- initely appears only at 0.05THz and reaches the maximal value at 0.1-0.15THz. Then, similarly to the previous case, for w > T ~ 0.15THz sepa- rate excitations appear dispersed from qffil. This picture persists at all temperatures, and even as T is decreased to T--4.9K~ 1.012T~r there is no evidence for the critical scattering, the maximal peak being at finite energy ..~0.05THz. The cor- responding background subtracted energy profiles of S(q, co) at q~1/3,1/3,1) and different tem- peratures obtained in our experiments are shown in Fig.5. Data for CsMnBr3 (Fig.5,a) demon- strate a strong critical correlations peak at 9K, transforming into a diffuse peak, still visible at T ~ 24K~ 3T~r, as temperature increases. Energy scans at all q can be nicely fitted by the Vil- lains expression for the disordered 1D spin chains [2] (solid curves) which is essentially a sum of the two Lorentzians centered at w and -w. On the contrary, the energy scans for CsNiC13 show well-defined maxima which energy increase with the temperature. This picture is characteristic of

the temperature-damped gapful excitations. Solid lines show the corresponding fits by S(q,w) of the damped harmonic oscillator which is in fact a difference of two Lorentzians centered at aJ and -co multiplied by the detailed balance constraint [15]. Their width appear to scale .~T while the position grow with a tendency to saturate at •0 .~0.25THz, close to the expected value of the Haldane gap for CsNiCI3 spin chains.

6OO

E O

,', 4 0 0

e"

r

2 2oo

e"

Z

Fig5,a.

0 0

3OO

r

E O

e-

.=_ c-

--I

e-

Z

0 0

CsMnBr3, Q=(1/3,1/3,1)

V

�9 13

.2 .4 .6

, , , (THz)

T=24.3K T=15.5K T=12.0K T=9.0K

1.0

CsNiCI 3, Q=(113,1/3,1)

.1 .2 .3

w (THz) Fig.5,b.

4. C O N C L U S I O N S

.4

We studied the effect of quantum spin fluc- tuations on the static properties of the ordered phase and spin dynamics in the "1D" region in some quasi-lD antiferromagnets of CsNiCI3 fam- ily. Nonlinear magnetization growth beyond the

Czechoslovak Journal of Physics, Vol. 46 (1996), Suppl. $6 3237

I.A. Zaliznyak et al.

spin reorientation region is observed in majority of such compounds at T<< TN. It is explained by the increase of the ordered spin value due to the suppression of quantum spin reduction by magnetic field. Such an increase of the staggered magnetization was measured by neutron diffrac- tion in RbNiC13. Within the experimental accu- racy it was shown to give the complete account for the nonlinear magnetization growth. Togeth- er with the spin-wave calculations this demon- strate that quantum zero-point spin motion leads at small fields to approximately equivalent rela- tive reductions of the staggered and homogeneous magnetisatious.

The "intermediate asymptotic" behavior of the dynamic spin correlations in CsNiCls and CsMnBr~ was studied by inelastic neutron scat- tering in the quantum-critical temperature region TN <<T<< 23 above the 3D ordering. In the case of S=5/2 (CsMnBr3) strong 3D critical scatter- ing was observed at the magnetic Bragg position Q=(1/3,1/3,1). With the increasing temperature it transformed into a broad diffuse peak centered at zero energy, in agreement with the classical- ly expected picture. In S=I CsNiCI3 even at T-.~ 1.01TN classical 3D critical fluctuations were not observed. Measured energy profiles of neutron scattering at Q=(1/3,1/3,1) revealed temperature damped but very well-defined gapful ex:citations. This provides another spectacular evidence of the gap in the excitation spectrum of the 1D an- tfferromagnet with integer spin as predicted by Haldane. It would be, of course, very exciting to tune the 3 ' /3 ratio and study the transition from the N6el to the Haldane phase at T- .0 , but experimental realization of such procedure is difficult to imagine. However, one can try to use for example an external pressure to change the Hamiltouian constants as was recently proposed by C. Brohohn. We plan such experiments for the nearest future.

[4] F. D. M. Haldane, Phys. Lett. 93 A, 464 (1983); F. D. M. HaJdane, Phys. Rev. Lett. 50, 1153 (1983).

[5] W. B. Yelon and D. E. Cox, Phys. Rev. B 6, 204 (1972); Phys. Rev. B 7, 2024 (1973).

[6] M. Eibshuts, R. C. Sherwood, F. S. L. Hsu, and D. E. Cox, AIP Conf. Proc. 17, 864 (1972).

[7] P. A. Montano, E. Cohen and A. Shekhter, Phys. Rev. B 6, 1053 (1972).

[8] I. A. Zalisnyak, Solid State Commun. 84, 573 (1992).

[9] D. Welts, J. Phys.: Cond. Matt. 5, 3643 (1993).

[10] M. E. Zhitomirsky and I. A. ZAli~uyak, Phys. Rev. B 53, 3428 (1995).

[11] R. M. Morra, W. J. L. Buyers, R. L. Arm- strong and K. Hirakawa, Phys. Rev. B 38, 543 (1988); Z. Tun, W. J. L. Buyers, R. L. Armstrong, K. HirAk~_wa and B. Briat, Phys. Rev. B 42, 4677 (1990).

[12] I. A. Zalisnyak, L. A. Prosorova and A. V. Chubukov, J. Phys.: Condens. Matter 1, 4743 (1989).

[13] S. I. Abarzhi, A. N. Bashan, L. A. Prozoro- va, and I. A. Zalisnyak, J. Phys.: Cond. Matt. 4, 3307 (1992).

[14] H. A. Katori, Y. Ajiro, T. Asano, and T. Goto, ISSP Techn. Rep. No. 2950 (1995).

[15] I. A. Zaliznyak, L.-P. Regnault, D. Petit- grand, Phys. Rev. B 50, 15824 (1994).

5. A C K N O W L E D G E M E N T

This work was partially supported by the INTAS project N 93-1107-Ext.

R E F E R E N C E S [1] H. A. Bethe, Z. Phys. 71, 205 (1931).

[2] J. Villain, J. de Physique 35, 27 (1974).

[3] M. Steiner, J. VRlain and C. G. Wiusdor, Adv. Phys. 25, 87 (1976).

3238 Czech. J. Phys. 46 (1996), Suppl. S6