TWO-DIMENSIONAL HEISENBERG FERROMAGNET : SUSCEPTIBILITY

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TWO-DIMENSIONAL HEISENBERG FERROMAGNET : SUSCEPTIBILITY

L. de Jongh, W. van Amstel

To cite this version:

L. de Jongh, W. van Amstel. TWO-DIMENSIONAL HEISENBERG FERROMAG- NET : SUSCEPTIBILITY. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-880-C1-881.

�10.1051/jphyscol:19711311�. �jpa-00214343�

JOURNAL DE _PHYSIQUE

Colloque C I , supplbment au no 2-3, Tome 32, FPvrier-Mars 1971, page C

- ⁸⁸⁰

TWO-DIMENSIONAL HEISENBERG FERROMAGNET : SUSCEPTIBILITY

L. J. D E JONGH and W. D. VAN AMSTEL

Natuurkundig Laboratorium der Universiteit van Amsterdam, The Netherlands

R h r n 6 .

- Des mesures de la susceptibilitk magnetique

de composes de Cu du type Cu(CnHzn~ 1NH3)2C14

ferromagnktisme en couche (n variant de

10) et de composCs isomorphes de Br ont ete effectutes. Des anomalies de variation de x ont

constatees

certaines temperatures TC de transition. Pour la plupart des composes

base de C1, la temperature

est voisine de

OK, pour ceux a base de Br TC

OK, bien que la cellule Blementaire varie d'un facteur

dans les series Ctudiees. Les resultats de mesure dans le domaine paramagnetique s'ajustent fort bien Aunresultat thwrique de developpernent en s h e de x. L'ajustement .permet de dCtermlner des valeurs de la constante d'echange Jlk.

L'existence de transition de phase dans un ferromagnktlque

2 dimensions de Heisenberg est discutke en fonction des valeurs trouvees ainsi pour JlkTc.

Abstract.

- The magnetic susceptibility

has been measured of the ferromagnetic layer-type CU-compounds C U ( C ~ H ~ ~ + I N H ~ ) ~ C I ~ , n varying from 1-10, and of isomorphous Br-compounds. Transition temperatures Tc have been found at which anomalies in x occur. For most of the C1-compounds TC =

OK, for the Br-series Tc

11 OK, while the unit-cell varies with a factor

through these series. The data in the paramagnetic region may be fitted quite well to the series-expansion result for x. From these fits values for the exchange-constants J/k have

derived. The consequences of the so obtained J/kTc -.values with respect to the poss~ble exlstence of a phase-transition for the Zdimensional Hei- senberg ferromagnet are d~scussed.

The susceptibility of the layer-type Cu-compounds Cu(C,H2,+,NH3),C14 and the isomorphous Br- compounds has been studied both in the paramagnetic region using fields of 4 and 10 kOe and near the tran- sition temperature Tc. We define Tc as the tempe- rature at which a peak in occurs (at about kT/J

In the latter 'region'we used an a. c.

method (zero field).

In table I we have listed the values for T, found for the various compounds. It is striking that T, ~ ' 7 . 5 0 K for the C1-compounds with n

Tc

11 OK for the Br-compounds with

2, while the vol~ime of the chemical unit cell varies with

factor

salts can be considered to a fair approximation as an assembly of nearly isolated magnetic layers.

dl and d2 are respectively the coppercopper distance within

a

layer

between neighbouring layers.

by Baker et al. [I]. As only a finite number (10) of terms in this expansion is known it will only be a reasonable representation of the susceptibility down to a certain temperature. We have used the series- result down to J/kT

0.6 because in this region the %TIC values calculated with 10 and 7 terms did not differ by more than 1 %, whi1.e .the uncertainty in the experimental %TIC values is a few percent. In the next step we ((scaled

the experimental C/xT versus Tc/T curves in the region 0.3

< 0.6 by a factor J/kTc, in order to bring them into coinci- dence with the theoretical C/xT versus J/kT curve.

The fact that this can be brought about (that J/kT, does not vary systematically with temperature) again demonstrates the two-dimensional behaviour. This statement is substantiated by the linear temperature- dependence of the specific heat at low temperatures [2].

A typical result is shown in figure 1 where the suscep-

Also listed in table

susceptibility of Cu(C2HsNH3)2C14 versus

J/kT

(dimensionless units).

constant Jlk, derived from the data in the paramagnetic

region. wk used the following procedure by measuf- tibility

C~(C,H,NH,),C~, has been fitted to the ing the diamagnetism isOmOrphOus

series result (full curve drawn through experimental Cd- and pd-compounds, we were

points for J/kT < 0.7). Also plotted are the mole- our data for diamagnetism. Our results were then cular field result, is the straight line

with the series-expansion of xT/C in .powers

of J/kT for the quadratic Heisenberg lattice given C/%T

- B/T

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711311

TWO-DIMENSIONAL HEISENBERG FERROMAGNE'T : SUSCEPTIBILITY C 1

-

(0 =

2 J/k for the quadratic lattice,

4) and the series-expansion result for the b. c. c. lattice which is the dotted curve (abcissa scaled by a factor 2).

This has been done to demonstrate the difference in the deviation from the molecular field result in two and three dimensions. It may be seen in figure 1 that the susceptibility is field dependent (for H

10 kOe) for J / k T > 0.8.

In figure 2 we have plotted the zero-field suscepti-

FIG. 2. -- Zero-field susceptibility results for three different compounds. The curves coincide for J / k T < 1.0 irrespective

of the sign of the interlayer interaction J2.

bility of powdered samples of three different compounds, in order to show that for J / k T < 1.0 all curves coincide. Nearer to Tc the anisotropy energy and the interaction between the Cu-layers J2 will, however small as compared to the interaction within a layer J , , greatly influence the magnitude and the temperature-dependence of the susceptibility by order- ing the ferromagnetic planes ferro- or antiferroma- gnetically with respect to each other (we have also observed weak ferromagnetism). For Cu(CH,NH,),Cl, the sign of J, is positive, for Cu(C,H,NH,),CI, it is negative. From figure 2 it follows that for tempe- ratures higher than J / k T < 1.0 the influence of the anisotropy and the coupling between the Cu-layers is negligibly small. In this temperature region there- fore, our results can be considered to be representative for the ideal square Heisenberg ferromagnet. Since our results extend to a region where the series expan- sion can no longer be trusted, we have listed in table I1

mean values of the C/xT versus J / k T curves in the region 0.5 < J / k T < 1. The C/xT-values of all compounds scatter evenly around this curve within a range which is 2 % of C/xT at J / k T

0.5, becoming 10 0/, at J / k T

1.05.

Considering the obtained values for J/kTc we would like to remark that the mean value J/kT,

1.75 , ^0.1

which we have previously [3] reported, has changed to J/kTc

2.0 + 0.2. This difference is due to the fact that the data reported in ref. [2] were taken in the region 0.1 < J / k T < 0.25 while the present results have been obtained in the region 0.1 < J / k T < 0.6 (the error in the correction for diamagnetism is negli- gible for J / k T

phous nonmagnetic salts were not yet available.

The values for J/kTc we have derived may be of importance because in recent years there has been, mainly theoretical, discussions about the existence or nonexistence of a phase-transition for the two- dimensional Heisenberg model. The specific heat results reported in the preceding paper suggest there is no phase transition in C , for the ideal model. It is possible however [4] that while long range order is ruled out at any finite temperature, there is a transition point at which the susceptibility, which is propor- tional to C, <

> diverges. Our results show a variation 1.81 < J/kT, < 2.26. This suggests that either the anisotropy or the interlayer exchange J2 may have an influence. What we need therefore is additional information on the anisotropy in the Cu- plane, which we are studying at this moment, in order to see whether the variation of J/kTc can be corre- lated to a variation in the anisotropy. In this respect it is gratifying that the compound Cu(C,,H,, NH,),CI,, in which thus far we have found the smallest anisotropy in x Gust above and at T,), has the highest JjkT,- value, as the effect of anisotropy would be to lower the J/kTc value. A conclusion which at this stage can be drawn from these susceptibility experiments alone is that if a J/kT, exists for the quadratic Heisen- berg ferromagnet its value will be higher than 2.26, which itself is 4.5 times larger than the molecular field result (See however also ref.

Acknowledgements. -

This work is part of the research program of the

Stichting voor Fundamenteel Onderzoek der Materie

and was made possible by financial support from the

Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek

References

[I] BAKER

GILBERT

EVE

and RUSH-

MIEDEMA

BROOKE (G. S.), 1967, Phys, Letters

25

[2] Preceding paper and results of COLPA

to be [4] STANLEY (H. E.) and KAPLAN

published.

[3]

B O ~ E R M A N

DE BOER

[5] MIEDEMA (A.

conference.