THERMAL CONDUCTIVITY IN THE SOLITON BEARING FERROMAGNETIC SYSTEM CHAB

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THERMAL CONDUCTIVITY IN THE SOLITON

BEARING FERROMAGNETIC SYSTEM CHAB

H. de Gronckel, W. de Jonge, K. Kopinga, L. Lemmens

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C8, Suppl6ment au no 12, Tome 49, dkcembre 1988

THERMAL CONDUCTIVITY IN THE SOLITON BEARING FERROMAGNETIC

SYSTEM CHAB

H. A. M. de Gronckel, W. J. M. de Jonge, K. Kopinga, L. F. ~emmensl

Department of Physics, Eindhoven University of Technology, P.O. Box 513, 5600-MB Eindhoven, The Nether- lands

Abstract. -The thermal conductivity of [C6H11NH3] CuBr3 (CHAB) has been measured in the region 1.5 K <T

<

10 K and B

<

7 T. Comparison of the data with a model describing the heat conduction by magnons and solitons shows a systematic deviation,.most likely due to the neglect of heat transport by the phonon system.

In spite of the large interest in the occurrence of solitons in certain classes of one-dimensional magnetic systems [I-31, up till now little attention has been paid to the effect of these non-linear excitations on the thermomagnetic transport properties. In this report data are presented on the thermal conductivity of a well known soliton bearing system, the S = 112 ferromagnetic chain system [ C ~ H I I N H ~ ] CuBra (CHAB) [4], and confronted with the results of a recently proposed model 151.

The thermal conductivity X of CHAB was measured [6] by a steady state longitudinal heat flow method. The experiments were performed in the range 1.5 K

<

T

<

10 K with the heat flow chosen parallel to the chain direction and a magnetic field (B

<

7 T) applied along the a, b or c axis. A typical set of data collected with the magnetic field applied parallel to the c axis (which is located in the easy plane, allowing the pres- ence of soliton-like excitations) is shown in figure 1.

The zero-field thermal conductivity is shown in figure 2.

Now we will turn t o a comparison of our data with the results of the model proposed by Wysin and Ku- mar [5], which considers the heat transport of only the magnetic excitations via a Boltzmann equation with

the collisions treated by a constant relaxation time. It is also assumed that interactions between the magnetic excitations can be ignored. Within this framework the contributions of solitons and magnons to the thermal

-

conductivity, denoted by A,,, and A,,, respectively, can be added linearly, and are given by

TsolCO

X.,I=-~EO (PEo)-''~ exp (-PEo) x

P

6

Here rrnag(,,l) represents the relaxation time of the

magnons (solitons) and @ = l / k ~ T . Eo is the soliton rest energy, co is the magnon gap and co is the magnon velocity.

If we insert the values appropriate to CHAB, i.e., ~ ~ / k ~ = 3 4 . 3 & K and EO = 2.64&

K

( B in Tesla),

in equations (1) and (2) and assume equal relaxation times for solitons and magnons (rsOl=rmag), we obtain a theoretical prediction that is reflected by the dashed curves in figure 1. Inspection of this figure reveals that, in contrast to the data, the predicted thermal conductivity X B / X ~ monotonically decreases with increasing magnetic field. If we - intuitively - assume the relaxation of the solitons to be much slower than that of the magnons, and correspondingly take rsol=10 rmag1 the high field behavior of XB/XO remains unaltered, but a maximum is predicted a t fields below 0.5 Tesla. This maximum, which in the model is associated with a soliton contribution, is not reflected by our data. One should note, however, that in this field region classical soliton theory is formally no longer valid (PEo

>

5) [7], and therefore any prediction involving a large soliton contribution in this region should be considered with some reservations.

Before discussing a possible origin of the systematic discrepancy,between theory and experiment, we would like to recall the successful interpretation of earlier thermal conductivity measurements on TMMC and DMMC in terms of scattering of the phonons by the magnetic excitations [8]. In the spirit of that interpretation, the gradual increase of the experimental data on XB/XO of CHAB with field indicates that in this compound the magnetic excitations also effectively act as a scattering mechanism. Since no clear minimum in XB/XO is observed, the contribution of solitons seems to be rather small. Figure 1 already showed that the calculations based on the model proposed by Wysing and Kumar yield a decrease of X B / X ~ at high fields, instead of the experimentally observed increase. Since the same qualitative tendency is observed in TMMC 191, we conclude that this discrepancy is most likely a '~nstitute for Applied Mathematics, University of Antwerp (RUCA), Groenenborgerlaan 171, B 2020 Antwerpen, Belgium.

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C8 - 1450 _{JOURNAL DE PHYSIQUE}

.

1 . 0 ?

.

CHAB- \i.. Q Ilc,

B

llc

K

----

-- ----_

_{- - - _ _}

0.2

-

Fig. 1. - Isothermal field dependence of the normalized thermal conductivity XB/Xo in CHAB for B along the c axis. Dashed lines reflect the results of the model of ref- erence [5] with rSol=rmag Dotted lines for T = 3.56 K and T = 7.13 K reflect similar calculations with r,,l= lormag Solid lines represent calculations based on a reso- nant soliton-phonon interaction model for the same ratio of magnetic and nonmagnetic scattering as for TMMC [S, 91.

consequence of the fact that in their model the transport of thermal energy by the phonon system itself is not taken into account.

Fig. 2. - Zero-field thermal conductivity Xo of CHAB as a function of temperature for a fresh s:~ngle-crystal.

Finally we like to emphasize that; the experimental data on CHAB and TMMC show a completely differ- ent behavior as far as the soliton contribution to X is concerned. It is not clear whether this difference is merely accidental or that it is related to the mechanism of the soliton-phonon scattering, which may be more effective for an antiferromagnetic (TMMC) than for a ferromagnetic chain system (CHAB). Measure- ments on other ferromagnetic solitoil-bearing systems, e.g., CsNiFs, as well as a theoretical approach in which both phonons and magnetic excitations are considered, could help to clarify this issue.

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(1978) 1137.

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33 (1980) 171.

[3] Kopinga, K., Tinus, A. M. C., De Jonge, W. J.

M., Phys. Rev. B 29 (1984) 2868.

[4] Kopinga, K., Tinus, A. M. C., De Jonge, W. J.

M., Phys. Rev. B 25 (1982) 4685;

Kopinga, K., Tinus, A. M. C., De Jonge, W. J. M., De Vries, G. C., Phys. Rev. B 36 (1987) 5398.

[5] Wysin, G . M., Kumar, P., Phys. Rev. B 13

(1987) 7063.

[6] Buys, J:A. H. M., De Jonge, W. J. M., Phys. Rev. B 25 (1982) 1322.

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[8] Buys, J. A. H. M., De Jonge, 7N. J. M., J. Phys.

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[9] De Gronckel, H. A. M., De Jonge, W. J. M.,

Kopinga, K., Lemmens, L. F., Phys. Rev. B 37