Magnetoelastic contribution to the elastic constants of terbium, dysprosium and erbium

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Magnetoelastic contribution to the elastic constants of terbium, dysprosium and erbium

M. Torikachvili, S. Gama, B. Kale, D. Pinatti, P. Donoho

To cite this version:

M. Torikachvili, S. Gama, B. Kale, D. Pinatti, P. Donoho. Magnetoelastic contribution to the elastic constants of terbium, dysprosium and erbium. Journal de Physique Colloques, 1979, 40 (C5), pp.C5- 30-C5-32. �10.1051/jphyscol:1979511�. �jpa-00218893�

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JOURNAL DE PHYSIQUE Colloque C5, supplkment a u no 5, ^Tome40, Mai 1979, page C5-30

Magnetoelastic contribution to the elastic constants of terbium, dysprosium and erbium (*)

M. S. Torikachvili, S. Gama, B. M. Kale, D. G. Pinatti Instituto de Fisica Gleb Wataghin, Universidade Estadual de Campinas, C.P. 1170, Campinas 13100, SP., Brasil

and P. L. Donoho

Department of Physics, Rice University, P.O. Box 1892, Houston, Texas 77001, USA

R6sum6. - On a mesure la variation de vitesse des ondes Clastiques longitudinales et de cisaillement dans des monocristaux de Tb, Dy et Er en fonction de l'aimantation et de la temperature. Un champ magnetique de 75 kOe Ctait utilist dans la gamme de temperature 4,2-300 K laquelle comprenait toutes les phases ordonnkes des mate- riaux. Pour rendre compte des ph6nomknes observes, on a vEtrifiC qualitativement que l'interaction magneto- Blastique doit &tre considtree jusqu'au 2e ordre pour les contraintes, et que l'knergie tlastique de 3' ordre ne peut pas Ctre negligCe.

Abstract. - We have measured the dependence of the longitudinal and shear elastic waves velocity of Tb, Dy and Er single-crystals on magnetization and temperature. Data were taken in magnetic fields up to 75 kOe, in the temperature range of 4.2-300 K, which included all the ordered phases of these materials. We found quali- tatively that to explain the observed behavior, the magnetoelastic interaction have to be treated u p to 2nd order in the strains and that the 3rd order elastic energy can not be neglected.

1 . Introduction. - The strong magnetoelastic coupling found in the heavy rare-earths elements is responsible for measurable effects on the dimensions and on the second order elastic constants (SOE) of these materials. In this work we correlate the SOE with the state of magnetization of the samples.

Using a model similar to that of Freyne [I], which details are going to be published elsewhere, we found that although the magnetostriction values found in the literature for Tb [2], Dy [3] and Er [4]

can be satisfactorily described by a magnetoelastic interaction linear in the strains, the SOE do not.

This is undoubtedly clear when analysing the behavior of the shear SOE of Tb (rotational strains included).

We found that it was important to consider the magnetoelastic interactions up to 2nd order in the strains and also the 3rd order elastic energy, to explain the measured non-degeneracy in the equi- valent ways of measuring the shear SOE's and the strong dependence they show on the direction of the basal plane magnetization, although these higher- order terms contributions to the magnetostriction are small. Detailed calculation of the magnetoelastic contribution to the SOE envolves many magnetoelastic coupling constants and is beyond

the purpose of this paper.

(*) Work partially supported by FAPESP and CNPq.

2. The experiment. - The SOE were determined with ultrasonic techniques, using the echo-overlap method. The magnetization curves were obtained with a vibrating sample magnetometer. The experiment was performed in a flowing-gas cryostat inserted in the bore of a 75 kOe superconductive magnet, and the SOE and magnetization. curves were determined in the same samples.

3. Experimental results. - 3.1 TERBIUM. - The magnitude of the dependence of Tb SOE on the

0 01 0.2 0 3 0 0.1 0 2 0 3 REDUCED MAGNETIZATION ( M / M O )

(a I b )

Fig. 1. - General behavior of Tb and Dy elastic constants on magnetization, in the paramagnetic phase of these materials.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979511

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MAGNETOELASTIC CONTRIBUTION TO THE ELASTIC CONSTANTS OF Tb, Dy AND Er C5-31

magnetization is more or less equal to that of Dy, in the paramagnetic region (figure 1). The non- degeneracy in 2 ways of measuring C,, is seen in the behavior of C , , , , and C3,,, (figure la), for magnetic field in the basal plane. The same effect occurs for Hd'c-axis (figure 2). Figure 3 shows that C,,,, is dependent on the direction of the applied field in the basal plane. The basal plane anisotropy is small in the paramagnetic region, so that this effect can only be attributed to the higher- order elastic and magnetoelastic terms. The contribution of the calculated 3rd order elastic energy to the magnetization dependence of Tb SOE is seen in figure 3 to be comparable, in magnitude, to the mea- sured dependence. The 3rd order elastic energy was determined using calculated 3rd order elastic constants (TOE) [5] and static strains calculated in a numerical model in which the magnetoelastic constants were chosen to force the calculated strains to be equal to those measured experimentally [2].

Fig. 2. - Non-degeneracy of C,3,3(u) and C,,,,(u). TO is the 3rd order elastic energy contribution to both these constants.

-

TERBIUM

-

T = 260 K

- -

Fig. 3. - Behavior of Tb C2,2, on magnetization, for H / / a and b. 1 and 2 represent the 3rd order elastic contribution when H / / a and Hlb, respectively.

3 . 2 DYSPROSIUM. ^-Using calculated TOE [6] and calculated strains, we observed also a large contribution of the 3rd order elastic energy to the expe- rimental behavior of C ,

, , ,

(figure 4).

(

D Y S P R O S I U M I

Fig. 4. - Behavior of Dy C,,,, on magnetization

3 - 3 ERBIUM. - We limit the discussion about Er to the anti-ferromagnetic phase, where the c-axis angular momentum component is sinusoidally modulated. The magnetization when the field is applied in the basal plane (hard plane) has a paramagnetic- like behavior. The field dependence of the longitudinal SOE C , ,

, ,

and C,,,, can be seen in figure 5. The field applied in the c-axis induces an anti-ferromagnetic-ferromagnetic transition that occurs at a temperature dependent critical field. C ,

, , ,

^{and C,,,,}

both show sudden changes near this field, which can be correlated with the changes in the magnetization curves.

1 MAGNETIC

0 12 2 4 3 6 4 8 6 0 7 2 FIELD ( K O e l (bl

Fig. 5. -Behavior of Er magnetization, C,,,, and C,,,, on magnetic field, in the sinusoidally modulated anti-ferromagnetic phase.

4. Conclusions. - We conclude that the observed behavior on Tb and Dy can only be explained satisfactorily when higher-order terms in the strains are taken into account (Er analysis is underway). These contributions are probably necessary in the theore- tical treatment because of the large magnetostriction values found in the heavy rare-earths, in the tempe- ratures and fields of the experiment.

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C5-32 M. S. TORIKACHVILI, S. GAMA, B. M. KALE, D . G. PINATTI A N D P. L. DONOHO

References

[I] FREYNE, F., Phys. Rev. B 5 (1972) 1327. [5] RAO, R. R. and RAMANAND, A., J. Phys. Chem. Solids 38 [2] RHYNE, J. J. and LEGVOLD, S., Phys. Rev. 138 (1965) A 507. (1977) 1035.

[3] CLARK, A. E., DESAVAGE, B. F. and BOZORTH, R., Phys. Rev. 138 [6] RAO, R. R. and MENON, C. S., J. Phys. Chem. Solids 34 (1973)

(1965) A 216. 1879.

[4] RHYNE, J. J. and LEGVOLD, S., Phys. Rev. 140 (1965) A 2143.