LOW TEMPERATURE THERMAL MAGNETORESISTANCE OF Cr2O3

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LOW TEMPERATURE THERMAL

MAGNETORESISTANCE OF Cr2O3

J. Jolivet, A. de Goer, A. de Combarieu

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-990

LOW TEMPERATURE THERMAL MA6NET0RESI STANCE OF C r

2

0

3

J.M. Jolivet, A.M. de Goer and A. de Combarieu

Centre d'Etudes BualSaires de Grenoble, Service des Basses Temperatures, 86 X, 38041 Grenoble Cedex, France .

Résumé.- La conduction thermique de Cr2Û3 monocristallin a été mesurée de 0^,1 K à 100 K et sous champ magnétique jusqu'à 80 kG. On observe un ou deux pics de résistivitê au voisinage du champ de spin-flop (60 kG). Les résultats aux plus basses températures sont interprétés par une interaction phonon-magnon, le trans-port de la chaleur étant dû aux phonons seuls.

Abstract.- The thermal conductivity of a Cr203 single crystal has been measured from 0.1 R to 100 K and with an applied magnetic field up to 80 kG. One or two peaks of resistivity are observed near the spin-flop field (60 kG). The results at the lowest temperatures are explained by a magnon-phonon direct interaction, the heat transport being due only to phonons.

!. INTRODUCTION.- The possibility of heat transport by spwaves in magnetic insulators has been in-vestigated by several authors and evidence of a magnon contribution has been given in some cases

/l/. We present a study of the thermal conductivi-ty of Cr203, which is a well known simple antifer-romagnet : the magnon dispersion curves measured by neutron diffraction are well described in the Heisenberg model 111. As the magnon group velocity is larger than the longitudinal sound velocity, the phonon and magnon dispersion curves do not cross in zero magnetic field; when a field is applied parallel to c-axis, the energy of one ma-gnon branch decreases so that direct interaction between phonons and magnons is possible in the vicinity of the spin-flop transition which occurs for H : H . = 60 kG at low temperature 131.

sr

2. EXPERIMENTAL RESULTS.- The measurements have been performed with two apparatus, a dilution re-frigerator being used for the temperature range 0.07 - 1.2 K.

The sample was a cylinder cut from a single crystal grown by Verneuil process of length 15 mm, and diameter 3 mm.After the first thermal conductivity measurements (Figure la),the diameter has been reduced to 2.56 mm to eliminate the external part of the crystal which was of poor quality. The thermal conductivity was actually larger, as shown on figure 1 (curve lb), and the

measurements under magnetic field (0.2 K to 10 K) have been made on this smaller sample.

Fig. 1 : Thermal conductivity of Cr203versus tem-perature

0 - la : as received sample ( 0 - 3 m m ) ;

t - lb : sample with reduced diameter (0 = 2.56 nm) Straight line is the phonon Casimir's limit.

Typical results of measurements with applied ma-gnetic field parallel to sample axis (which was found to be at 3.5° from c-axis by subsequent X-rays measurements) are shown on figure 2 : the relative thermal resistivity W /W is plotted as

n o *It was supplied by Crystal-Tec, CENG, France.

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a function of H at several fixed temperatures.

Fig. 2 : Relative resistivity of Cr2O3 versus magnetic field. Upper part : experimental points and calculated curves for three temperatures; Lower parts : smooth curves drawn through experimental points for three other temperatures.

An increase of resistivity is observed near the spin-flop transition and two peaks are resolved

at the lowest temperatures (T<0.5 K). It must be noted that the overlap between the measurements taken on the two apparatus was not good for H%Hsfy because of a great sensitivity of the magneto thermal resistance to the actual orientation of H

relative to c-axis, which has been verified by

detailed measurements for different values of O =

(8,Tf)

at T

2

2 K and H = 60 kG.

The crystallographic quality of the crystal has been tested by neutron diffraction by Dr M. Schlenker at I.L.L. : a small region was found to be misoriented by 0.6', and the mosaic of the main part of the crystal was 12'..

3. DISCUSSION.- The experimental results can be explained supposing that the 'heat transport is due only to phonons (the application to Cr203 of

recent calculations /4/ supports this hypothesis). a) Zero-field thermal conductivity (curve Ib). At very low temperature (T cO.5 K) the ratio K / T ~ is constant and the absolute value (3.5x10-~

watts/cm K ~ ) is in good agreement with the boundary scattering limit for phonons (3.3~10-~). An attempt has been made to fit the K(T) curve within the Cal- laway model / 5 / , with a total inverse relaxation time ,-I= + where T;' includes all the

I S

intrinsic scattering terms and was introduced to described the dip observed near 4 K; it was found that a form of r i l proportional to w3 T~ x

Hwo Mwo

exp (-

w)

or to w exp (- -) (corresponding to ~ B T

possible non-resonant phonon-magnon interactions /6/)cannot give a good fit as the extra-scattering is resonant. The dip can be described by a phenome- nological relaxation rate . r i l = ~w~/(w'

-

WE)'

(with Hwo/kg = 15 K) so that the physical source of this scattering could be a paramagnetic impurity /7/ or some aggregates of defects /8/.

b) Magnetic-field effects (Figure 2). The observed magneto-thermal resistivity is explained by the direct interaction between phonons and magnons which occurs when the dispersion curves cross.

Fig. 3 : Spin waves frequencies us versus magnetic field. a

-

O = o, k = o; b

-

O = 3'

,

k = ko (see text); c

-

O = 3', and several values of k. On figures 3 we have plotted the spin-waves frequencies calculated in the Heisenberg model /2/,

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rent values of the wave vector k and the angle 0. The energy of dominant phonons at low temperatures is $w 2 4 k T and the corresponding wave vector

ph B

ko = w /C (where C is the mean sound velocity in Ph

an isotropic model) is quite small. It can be seen on figure 3 (b) that there are two crossing points A and B at different fields so that the existence of two peaks in the thermal resistivity is quali- tatively explained. When the temperature increa- ses, the width of the frequency distribution of

the thermal phonons is larger so that the peaks are not longer resolved.

A simple quantitative analysis has been done in the very low temperature range by consi- dering only two phonon scattering processes :

boundary scattering and direct phonon-magnon interaction described by a lorenztian relaxation

rate = Dr

,

the magnon L-ws(k,o,~U2

+

r2

frequencies being computed numerically. The best fits, shown as solid lines on figures 2(a) and (b) were obtained with O = 3', which is satisfactory in view of the 3.5' misorientation between the sample axis and the c-axis (see 5 2). The width

r

was found to be about 0.25 K and the crystal mosa'ic can account only for about 1/10 of this value. I' is also larger than the width given by

AFMR data /3/ so that the gap between the two branches of the coupled magneto-elastic dispersion curves must be considered. More detailed calculations are needed to test this point.

References

/I/ See for example Metcalfe, M.J., Rosenberg,H.M., J. Phys. C.

5

(1972) 459.

/2/ Samuelsen, E.J., Hutchings, M.T., Shirane,G., Physica

48

(1970) 13, Alikhanov et al., Phys. Status, Solidi

32

(1961) 41.

/3/ Foner, S., Phys. Rev.

130

(1963) 183. /4/ Sanders, D.J., Walton, D., Phys. Rev.

15

(1977) 1489.

/ 5 / Callaway, J. Phys. Rev.

113

(1959) 1046. /6/ Bachellerie, A., Joffrin, J., Levelut, A.,

J. Physique

32

(1971) 993.

/7/ de Goer, A.M., J. Physique

30

(1969) 389. /8/ Neumaier, K., J. Low Temp. Phys.

1-2

(1969) 27 /9/ Jolivet, J.M., to be published.

Acknowledgments.- We are very grateful to Dr