The magnetization of the linear chain Heisenberg antiferromagnet CuCl22NC5H5, in high magnetic fields

Volume 34A, number 5

PHYSICS

LETTERS

22 March 1971

THE MAGNETIZATION OF THE LINEAR CHAIN HEISENBERG ANTIFERROMAGNET CuC1 22NC5H5, IN HIGH MAGNETIC FIELDS. M. MATSUURA * Natuurkundig Laboratorium Universiteit van A msterdam. Amsterdam-C. Nederland and Clarendon Laboratory. University of Oxford, Oxford. UK Received 4 February 1971

The magnetization curve of CuCI22NC5H5 agrees well with the theoretical prediction taking the intrachain interaction J/k as 13.5 K and the interchain interaction J~/~ as 0.04 J/k. 2~zte 17CC A—H O•Cu

fr—---—

Recent magnetic susceptibility measurements on copper dipyridine dichloride (CuC1 22NC5H5) [1] indicated a broad maximum at a temperature of about 18 K. The susceptibility curve above 1 K was in good agreement with the theoretical prediction for a linear chain Heisenberg antiferromagnet of S = 1 ‘2 by Bonner and Fisher [2] taking the interactionJ k as 13.5 K. The implication that CuC122NC5H5 approximates quite closely to a perfect linear chain antiferromagnet is justified by the fact that kTC’J ‘ 0.07, since TC must be less than 1 K the lower limit of the magnetic susceptibility measurements. The crystallographic analysis showed that 2~ions[3]are coupled along by twothe Cu [001] - Cl - direction Cu bonds Cu while along the [111] direction they are separated by large pyridine molecules. The arrangement is shown schematically in fig. 1. Thus the magnetic interaction is tion than along the [001] direction. expected to be much weaker along the [ill] direcThe heat capacity measurements [1] revealed a linear dependence with temperature in the liquid helium temperature range, which is consistent with the theoretical prediction of Bonner and Fisher. In order to obtain further information on the

perfect linear chain antiferromagnetic properties of this compound, magnetization measurements at 2 K(kT~J = 0.15) in fields as high as 350 kOe were performed using the high field magnet at the University of Amsterdam. The experimental result is shown in fig.2 and is compared with a theoretical curve using agvalue of 2.12 as obtained by E.S.R. on the same *

On leave from the Dept. of Phys.. Kyoto Univ., Kyoto, Japan.

274

387A

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-~

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~

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Fig. 1. A schematic arrangement of the crystal structure of CuCI22NC5H5. Two Cu-Cl-Cu bonds along the [001] direction. One possible exchange path Cu-NC5H5—C5H5N-Cu along the [ill] direction.

specimen and J/1~ = 13.5 K as derived from the magnetic susceptibility [1]. The and theoretical results agree wellexperimental in fields less than about 250 kOe (M/M 0 < 0.35). However, in fields greater than this value, a small but finite discrepancy is seen. It could be explained by assuming 2~ion site a negative which isinternal proportional field, H~, to the at mageach netization M along the external field direction. Cu The bulk demagnetization effect is too weak to explain this negative internal field. If it is attributable to a weak antiferromagnetic interchain interaction, then H 2J’ (S~ (1) Z

where z is the number of nearest neighbours in the adjacent chains and (S) is the average value of spin along the external field direction. From the best fit of the experimental results with the theoretical curve, using eq. (1), the ratio J’ J is derived as 0.04. According to Onsager [4], kTC/J = 0.25 for J”J = 0.01 and z = 2. Therefore, for CuCl 22NC5H~(J’/J - 0.04 and z = 8), we should expect kTC/J> 0.25 or TC > 3.4K while the experimental results indicated TC < 1K. This seems

Volume 34A, numberS ‘C

PHYSICS LETTERS

I/

M/M

0

I

develops inside each chain with decreasing temperature, and thus the pair correlation between

,i

06

the nearest neighbour spins in the same chain increases. Since the intrachain interaction is antiferromagnetic, theout. net Thus internal from interthese spins is cancelled thefield effective chain interaction is much weaker than that ob-

j

04

22 March 1971

tamed and perfect the system is expected to behave asabove a nearly linear chain antiferromagnet. At what temperature this compound

0.21

ceases to do so without any phase transition is an interesting future problem. 9Jl~H/IJ!

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1.0

2.0

30

40

5.0

Fig. 2. Magnetization of CuCI22NC5H5 at 2K(kT/J 0.15). Theoretical curve with J/k 13.5K, J’/J 0 and kT/J = 0. Theoretical curve with J/k = 13.5 K, J’/J 0 and kT/J 0.3. Theoretical curve with J/k = 13.5 K, J’/J 0.04 and kT/J 0.

The author expresses his thanks to Prof. A. R. Miedema for his helpful discussions and to Mr. W. Bruer for his assistance during the measurements. He is much indebted to Mr. M. R. Wells for his reading and advice on the manuscript.

References [11K. Takeda, M.Matsuura, S. Matsukawa, Y.Ajiro and

surprising 2~ion but may explained the following hasbetwo nearest inneighbours in way. of A the Cu adjacent chains (fig. 1). Owing to the each strong intrachain interaction, short range order

SINGLE-MODE

T. C. Haseda, J. Phys. Soc. Japan to be published. [2] J. A640.Bonner and M. E. Fisher, Phys. Rev. 135 (1964) [31J. D. Dunitz. Acta Cryst. 10 (1957) 367. [4] L. Onsager, Phys. Rev. 65 (1944) 90.

ELECTRON

COHERENCE

I. M. BOWRTNG, H. S. PERLMAN, G. J. TROUP and A. C. McLAREN Department of Physics, Monash University, Clayton, Victoria, 3168, Australia Received 8 January 1971

The results of applying quantum coherence theory to a single mode for a beam of non—interacting electrons are presented. -

We briefly report here the results of formalizing the coherence of a beam of non-interacting electrons, in a manner analogous to the Glauber formulation [1] for optical coherence. Some of the results obtained are well known, but they have neither been derived nor grouped together previously from considerations of coherence. A “single mode” (single cell in phase space) for an electron beam can be defined by exact analogy with that for a light beam, using the arguments of Kastler [2]. That the fulfillment of single-mode conditions implies first order coherence (the possibility of Young’s interference

area” and “coherence volume”, using the probability amplitude (Dirac field) in the same way as one uses the electromagnetic field for light. We assume an interaction of the electron beam with a detector of the form âb~,where a is the electron annihilation operator, and b+ is the creation operator for the detector: i.e. the detec-. tor is always in the ground state. Then the considerations put forward by Glauber for the 1atom photon-detector [1] become valid, mutatis mutandis, for the electron detector. We can now define the correlation functions G(~)(x 1...x~, x1...x~) = trace{~â~j... ~ a,2}

fringes) follows from definitions of “coherence 275