~ Solid State Communications, Vol. 85, No. 7, pp. 597-599, 1993. Printed in Great Britain.

0038-1098/9356.00+.00 Pergamon Press Ltd

FINITE SEGMENTS, "FREE SPINS" AND RANDOM EXCHANGE IN SPIN S=I QUASI ONE-DIMENSIONAL ANTIFERROMAGNETS

H. Mutka 1, C. Payen 2 and P. Molini62 lInstitute Laue-Langevin, B.P. 156, F-38042 Grenoble Cedex 9, France

2Institut des Mat6riaux, 2 me de la Houssini~re, F-44072 Nantes Cedex 03, France

(Received 2 December 1992 by P. Burlet)

Magnetic susceptibity of representative examples of S=I Heisenberg antfferromagnetic chains, AgVP2S6 and NENP, has a divergent low temperature contribution, in spite of the fact that the bulk susceptibility should vanish due to the presence of the Haldane gap. The divergence follows a power law T -a with a = 0.6 that is quite different from free spin paramagnetism. We propose that this contribution is due to fmite segments that weakly interact to form a Random Exchange system.

In the field of one-dimensional magnetism finite system properties have a particular importance. The states of short isolated segments can be calculated exactly and trends due to changes of parameter values can be used in extrapolat- ing true bulk behaviour. On the experimental side finite size is unavoidable because a truly perfect one-dimen- sional system is practically impossible to produce. On the other hand isolated finite segments are also difficult to find and by consequence the connection to easily calcu- lated properties may be lost. A practical problem persists in the extraction of the true finite size or bulk properties from experiment because of this controversy.

The spin S=I antiferromagnetic Heisenberg chain has recently been shown to possess very interesting finite size properties [1-4]. Because of the finite correlation length the end points of an open chain start to feel a cer- tain independence. Segments of any length with even or odd number of spins are no more simply associated with a spinless S= 0 (singlet) or a spin S = 1 (triplet) ground state, but they are both almost fourfold degenerate systems. There is a correspondence with a weakly coupled pair of spin S =1/2 entities localized at both ends of the segment, see Fig. 1. At high temperatures, and for long segments the situation resembles a pair of free spins S ffi 1/2.

In case of an assembly of truly independent seg- ments of random length this produces rather simple ther- modynamics. At temperatures and fields that are small compared to the Haldane gap only the finite size effects give susceptibility and magnetization, because the bulk excitations are not populated. The segments that are long enough have a Curie-like susceptibility with S = 1/2 char- acteristics, and there is a length and temperature depen- dent gradual crossover towards coupled spin dimers. For a given distribution of segment lengths P(n), or a equiva- lently of coupling strentgh P(J), the susceptibility z(T) and the magnetization M(H,T) are easily calculated as properly weighted sums of corresponding quantities of spins S= 1/2 coupled in pairs. However, in case of appreciable coupling between the segments the situation may be very different. One may expect something similar to the case that was examined intensively some ten years ago in the context of organic charge transfer salts, the Random Exchange Heisenberg Antiferromagnetic Chain or REHAC [5-9]. Coupling between the segments leads to a system in which the apparent exchange values do not seem to have any lower limit, and the thermodynamic properties are singu-

lax at T = 0 K. Nevertheless the collective behaviour is clearly apparent in thermodynamic functions x(T), M(H,T) that may show quasi universal properties independent of the original form of P(n) or P(J).

In the present communication we wish to demon- strate such effects in the representative physical realiza- tions of S=I spin chains, namely AgVP2S 6 [10, 11,12] and NENP[13]. Low temperature susceptibility and magneti- zation measurements on AgVP2S 6 show quite particular temperature dependence and scaling that is distinctly dif- ferent from free spin or independent spin pair behaviour. Also in NENP, recent data obtained in a collective effort [14], although originally interpreted by Curie-Weiss type law, have a very similar temperature dependence of sus- ceptibility down to ultra-low temperatures. There seems to be little qualitative difference in the properties of different physical systems and different segment length distribu- tion.

Susceptibility data of AgVP2S 6 from Payen et al. [11] and of NENP form Avenel et al. [14] show a srik- ingly similar, rapid crossover from the high temperature behaviour typical of S=I spin chain to a divergent low temperature dependence, Fig. 2. At low temperature both materials have a non-Curie power-law dependence of sus-

C o n t i n u u m o f spin w a v e slates

G a p = J /2 .5

even odd

n

Spli t t ing = (- I ) J exp(-n/g')

Fig.l The singlet-triplet splitting of the lowest states of the t'mite open segment of a S =1 Heisenberg chain goes exponentially to zero with increasing length n [i]. The correlation length is of the order of ¢ = 6. The lowest states are similar to the spin S = I/2 pair with a coupling that becomes negligeable for long segments.

597

598

10 -I

0

"3 10 .2

!0 -s

10 "4 10 -3 10 -1 101

QUASI ONE-DIMENSIONAL ANTIFERROMAGNETS

" ~ I I x \ I I I

X x \ \

x x x ~ \ \ \ x \ x xX~X X xx

, ,

T(K)

Fig.2 Log-log plot of the temperature dependence o f , susceptibility for AgVP2S6 (o) and NENP(x). The latter is extracted from graphs of ref. [14]. Both curves follow at low temperature the T -0.6 dependence (solid line). A Curie law for 0.01 free spins S -1 is given for comparison (dashed line).

ceptibility z(T) = C/~a, with a = 0.6. The crossover tem- perature, as well as the magnitude of the low temperature susceptibility depend on sample preparation but the func- tional dependence retains the same power-law with a similar exponent. Note that this power law describes the temperature dependence much better and in a wider range of temperature than a Curie-Weiss form Xo + C/(T-O).

The field dependence of magnetization was measured on AgVP2S6 (a powder sample different from the one reported in Fig. 1) to examine closer the departure from the free-spin behaviour. Data was taken with a SQUID magnetometer up to H = 5 T at temperatures T = 1.8, 3, 5 and I0 K. On the Fig. 3 one can see that M(H,T) does not follow the H/T scaling typical of free spin paramagnetism. Stimulated by the earlier work [5,15] on random exchange chains we then plot the data as M/T l-a versus I-I/T which gives an excellent agreement with c~ = 0.6, Fig.4. This scaling behaviour indicates that

M(H,T) = T l - a f ( H / T) (1)

I I o

O O O O

O O °

I I I I

I 104 2 104 3 104

H/T (Oe/K)

120 / ' ' '

o D 100 oo o°

O0 O0 000 0 0 0 0

:;o<oo° ooo° 60 ~o o

oOO0 0 0 oo o

40 '~

20

0 0 10 °

Fig.3 Magnetization vs. H/T for a powder sample of AgVP2S 6. From left to right the curves are for T ffi 10, 5, 3 and 1.8 K.

Vol. 85, No. 7

where f(H/7") deviates strongly from Brillouin functions of S=1/2 or S=I, especially in that there is a notable low- field curvature but no saturation at high field.

These results point out the collective nature of the low temperature magnetism. Most of the features are simi- lar to those encountered in the S=1/2 REHAC. This is not surprising since the above explained properties of the open S=I segment give a natural reason for a divergent distribution of coupling strength. In fact a random distri- bution of cuts with a fraction c (missing magnetic ions on the chain) produces a collection of segments with a dis- tribution of lengths [15]

P(n) = c(l - c) n (2) and by consequence of couplings

P(IJI) = ~JI -e. (3) Following the treatment of Exchange Coupled Pairs pro- posed as a model for REHAC [15], this situation is solv- able for independent segments. However, due to the mod- ulation of sign of Y (see Fig.i) one does not produce the observed characteristics, eq. (1). For independent seg- ments the calculated susceptibility is dominated by the the odd segments and is rather close to Curie-behaviour. Some coupling between the segments is clearly necessary, be it a next nearest neighbour exchange across the cuts or a transversal 3D coupling between the chains. Another difficulty of the very straightforward coupled pair ap- proach is that one expects in from eq. (2), (3) that ct = e 1-1/(~c) depends on the fault concentration and this is not experimentally observed. However, one may recall that quite similar values of ct can describe different systems, due to the quasi universal properties found for the REHAC with various initial distributions of J [8,9].

Anyhow, the similarity of the susceptibility results on AgVP2S6 and NENP is intriguing and calls for more experimental work. The role of 3D effects, that may in- duce order contrary to the pure S=1 system [16], has to examined in more detail. We plan to continue with com- parative measurements on the Sffi3/2 system AgCrP2S 6 [17]. Preliminary data on single crystals of both AgVP2S 6 and AgCrP2S6 indicates somewhat similar collective anisotropy of susceptibility even though the S=3/2 case does not seem to have any REHAC character. Study of

120

, 100

"6 80

60

I I I I I

40

20

0

0 100

/ / 00000 O0 / 00 .......

/>- ' I I I I I

1 10 4 2 10 4 3 10 4

H/T(Oe/K)

Fig.4 Scaled magnetization M/T 0.4 versus H/T for AgVP2S6. The low temperature data falls on a quasi-uni- versal curve. Brillouin functions (for S =1/2, 1, broken and dashed lines) reproducing the low field susceptibility (H < 1000 Oe) do not follow the strongly curved and non- saturating master curve.

Vol. 85, No. 7 QUASI ONE-DIMENSIONAL ANTIFERROMAGNETS 599

intentionally doped systems may be useful. Some work has been done on NENP doped with magnetic ions (Cu with S=1/2). With a few 10 -3 Cu the low temperature sus- ceptibility is almost Curie-like in a narrow temperature range [18]. With 6 % Cu the magnetization at T = 2 K is close to Brillouin function [13]. For non-magnetic dopants the static susceptibility was not reported [3]. It looks like the Cu impurity coupled to the chain ends [2] is a rather independent three spin subsystem and the temperatures above 2 K may be too high for observation of the collec-

tive effects in the extrinsic susceptibility. The essential energy scale is well below J and the collective random ex- change properties are found at T << 0.1J, T <I K for NENP.

In conclusion, nominally pure AgVP2S6 and NENP seem to be good examples on REHAC behaviour. This is probably the first time such effects are seen in rather clean ID systems ofweU localised spins. It may be that the particular features of the S=I open chains, espe- cially the lack of long range order even in the quasi 1D case, favor this kind of properties.

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