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Elastic properties of lanthanum manganites
ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 321 (2009) 682–685
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Elastic properties of lanthanum manganites N.G. Bebenin , R.I. Zainullina, V.V. Ustinov Institute of Metal Physics, Ural Division, Russian Academy of Sciences, 18 Sofia Kovalevskaya St., Ekaterinburg 620041, Russia
a r t i c l e in f o
a b s t r a c t
Available online 27 November 2008
We give a brief overview of the data on elastic properties of the CMR manganites published during last decade. The main emphasis is put on the results obtained for single crystals. & 2008 Elsevier B.V. All rights reserved.
PACS: 75.47.Lx 62.65.+k Keywords: Manganite Ultrasound Elastic moduli
1. Introduction Rare-earth manganites Ln1xDxMnO3, where Ln stands for a rare earth and D is a divalent element, attract attention due mainly to the colossal magnetoresistance (CMR) effect observed near Curie temperature TC. It is generally recognized that the specific feature of the CMR compounds is the strong interaction between charge carriers, localized spins, and crystal lattice. A whole wealth of information on transport and magnetic properties of the CMR materials is available in literature, but elastic properties remain less studied. In the well-known reviews [1,2], the issues of propagation and attenuation of sound waves are not addressed. To fill the gap in part, we briefly overview the experimental data on elastic properties of ferromagnetic lanthanum manganites La1xDxMnO3, D ¼ Ca, Sr, and Ba, which were published during the last decade. The sound velocity and damping were studied at various frequencies. Most of the publications report the measurements that were carried out in the range from 1 kHz to 100 MHz; some authors report the internal friction Q1, which is a measure of sound damping, taken at frequencies around 1 Hz. The frequencies below 100 MHz will be referred to as ‘‘low’’ frequencies. Some interesting effects were also found in the high-frequency region, when the frequency f is about or higher than 1 GHz. It is reasonable to discuss the properties of the CMR manganites in the low- and high-frequency regions separately. The complex oxides, we wish to discuss, have the perovskite structure. The ideal cubic perovskite unit cell is, however, somewhat distorted, so that three structural phases are observed: Corresponding author. Tel.: +7 343 378 38 90; fax: +7 343 3745244.
E-mail address: [email protected] (N.G. Bebenin). 0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.11.024
the Jahn–Teller distored O0 and pseudocubic O* phases of the same orthorhombic Pnma space group and rhombohedral R phase with R3¯c symmetry [3].
2. Temperature dependence of the sound velocity The single crystals of manganites are usually twinned, so the cubic approximation, in which distortions of the unit cell are ignored, is widely used to indicate crystallographic directions. The temperature dependence of elastic moduli was reported for single crystals of La1xSrxMnO3, with x ¼ 0.17 [4] and x ¼ 0.12, 0.165, and 0.3 [5]. Fig. 1 shows the moduli Cij for x ¼ 0.17 in the cubic geometry. This single crystal undergoes the ferromagneticto-paramagnetic phase transition at TC ¼ 265 K and the structural Pnma-R3¯c transition at TS ¼ 285 K [4]. In the rhombohedral phase, all the moduli are larger than in the orthorhombic phase. The less pronounced peculiarities at the Curie temperature are affected by a magnetic field, which is a signature of the strong coupling of lattice and spin degrees of freedom. Similar results were reported by Hazama et al. [5]. In Ref. [5], Cij are given in the cubic geometry for La0.88Sr0.12MnO3, where the transition between the orthorhombic phases is observed, in the cubic and rhombohedral geometries for La0.835Sr0.165MnO3, which undergoes O–R transition, and in the rhombohedral geometry for La0.7Sr0.3MnO3 single crystal, which is always in the R3¯c phase. The single crystals of La1xSrxMnO3 family were also studied in Refs. [6–11]. It was shown that the sound velocity is independent of frequency up to f ¼ 90 MHz [11]. The information for La1xBaxMnO3 is not as detailed as that for La1xSrxMnO3. To our knowledge, only one paper [12] describes the elastic properties of La1xBaxMnO3 single crystals. In order to reveal the effect of the dopant type on the elastic properties, we
ARTICLE IN PRESS N.G. Bebenin et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 682–685
Fig. 1. Elastic moduli Cij of La0.83Sr0.17MnO3 single crystal reported in Ref. [4] for cubic geometry (open symbols) and Young’s modulus calculated for [1 0 0] and [111] directions using Eq. (1) (solid symbols).
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curve it is clearly seen. Perhaps, this is true for other CMR manganites. Looking at the curves in Fig. 2 and at Vl–T curve for Ca26 crystal shown in Fig. 3, we see that the increase of a divalent content results in an increase of the value and in a weakening of the temperature dependence of sound velocity. At low temperatures, Vl increases with the decrease in ionic radius of a divalent ion. The sound velocity in Ca26 is close to the sound velocity in Sr25, but noticeably larger than the velocity in Ba25. This can be related to the fact that ionic radius of Ca2+ (1.34 A˚) is close to that of La (1.38 A˚) and Sr2+ (1.44 A˚) and is small in comparison with the radius of Ba2+ (1.61 A˚). In the curves for all La–Ba crystals and for Sr20, there is a discontinuity caused by the structural Pnma-R3¯c transition. However, in the curve for Sr15, the peculiarity related to the structural transition at TS ¼ 365 K is rather weak, which is likely to occur because the direction of sound propagation is close to the four-fold cubic axis. The second-order ferromagnetic-to-paramagnetic phase transition gives rise to a weak peculiarity in the Vl–T curves. The Sr25 sample exhibits only this weak peculiarity because Sr25 is always in R3¯c phase. In the Vl–T curve for Sr20, there is a very small jump at about 400 K, which is a signature of a first-order transition [9]. In Ca26, the magnetic transition is of the first order and the longitudinal sound velocity drastically falls down in the range from 210 to 225 K, see Fig. 3. Above this range, the structural transition between the low-temperature orthorhombic phase and the high-temperature orthorhombic phase occurs [15]. The X-ray measurements [17] revealed that in La1–xSrxMnO3, the Pnma-R3¯c transition results in a jump in the unit cell volume of about Dv ¼ 0.15–0.20 A˚3 per formula unit, which at the first glace provides a simple explanation for the jump in the longitudinal sound velocity Vl. However, the X-ray study of La1–xBaxMnO3 [18,19] did not reveal an observable volume change at the transition. The Dv value in the La–Ba manganites is significantly smaller than in the La–Sr crystals, although the jump in Vl is larger. It follows that the Vl jump is determined by a rearrangement of ions in the cell and perhaps by interactions of the crystal lattice with magnetic and electronic subsystems of the crystal.
Fig. 2. Longitudinal sound velocity versus temperature for La–Sr and La–Ba manganites measured on heating [9,12,13]. The sound propagated along [1 0 3], [111], and [11 5] cubic directions of Sr15, Sr20, and Sr25, respectively. In all La–Ba crystals, the waves propagated along a direction close to [11 0].
show in Fig. 2 the temperature dependence of the longitudinal sound velocity Vl in La–Sr and La–Ba single crystals (x ¼ 0.15, 0.20, and 0.25) reported in Refs. [9,12,13]. For brevity, we denote a manganite by the symbol of a divalent ion and percentage, for example, Sr15 stands for La0.85Sr0.15MnO3, etc. The measurements of the elastic properties were performed in Refs. [9,12,13] by the composite oscillator method, which allows finding the Young’s modulus E. In the case of a single-crystalline cylinder with its axis along vector n, the Young’s modulus is given by Ref. [14] 1 C 11 þ C 12 1 2 þ ¼ PðnÞ (1) En ðC 11 þ 2C 12 ÞðC 11 C 12 Þ C 44 C 11 C 12 where P(n) ¼ nx2nz2+ny2nz2+nx2ny2 and the cubic symmetry is assumed. To illustrate the dependence of the Young’s modulus on n, we calculated En for n||[1 0 0] (P(n) ¼ 0) and n||[111] (P(n) ¼ 1/ 3) using the data of Darling et al. [4] for Sr17. In the first orientation, the peculiarity at the temperature of Pnma-R3¯c transition is hardly observable although in the E[111]–T
Fig. 3. Temperature dependence of longitudinal sound velocity for Ca26 [15] and Ca30 [16] single crystals measured on heating at 100 kHz and at 50 GHz, respectively.
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3. Internal friction Fig. 4 shows the internal friction Q1 versus temperature for Sr15 (TC ¼ 232 K) and Ba15 (TC ¼ 222 K) obtained by the composite oscillator method [9,12]. There are peaks caused by the PnmaR3¯c transition and weak peaks related to the magnetic transition. The peak at E400 K was found not only in Ba15, but also in other La–Ba crystals as well as in Sr20 and Sr25. This peak was attributed to the relaxation due to point defects. In the Sr15 curve below TC, one can see a peak at 202 K. Taking into consideration the results of the neutron scattering experiments [20], we infer that the peak at 202 K is due to the transition to the low-temperature charge-ordered state [9]. Similar peak is seen in the Ba15 curve at T ¼ 176 K. It is likely that in Ba15, the charge ordering occurs at T ¼ 176 K. At E100 K in the Sr15 curve and at E60 K in the Ba15 curve, we see pronounced peaks of the internal friction. Fig. 5 shows that such peak is observed in the Q1–T curves for all La–Ba crystals, and the peak diminishes and shifts toward lower temperatures as the Ba content increases. Moreover, the peak appears in La0.77Sr0.20Y0.03MnO3 (Sr20Y3 in short), although it was not found in Y-free La0.8Sr0.2MnO3 [21]. Therefore, the peak is observed if the ionic radius of lanthanum differs from the radius of a dopant significantly and/or if the dopant concentration is sufficiently low.
Fig. 4. Temperature dependence of internal friction in La0.85Sr0.15MnO3 and La0.85Ba0.15MnO3 single crystals measured on heating at frequency of about 100 kHz [9,12].
Fig. 5. Low-temperature peak of the internal friction measured on heating.
Fig. 6. Hysteretic behavior of the longitudinal sound velocity. Inset: the same for the velocity of torsion vibration.
This suggests that the low-temperature peak arises due to smallscale clusters.
4. Giant thermal hysteresis (GTH) Fig. 6 shows Vl–T curves measured on heating and cooling. The curves for other La–Sr and La–Ba manganites are similar. The Pnma-R3¯c transition results in the giant (of about 200–300 K) width of the hysteresis loop. It follows that when heating, there are Pnma inclusions in R3¯c matrix at T4TS. A simple phenomenological theory describing the GTH effect was proposed in Ref. [22]. Inset in Fig. 6 shows the velocity of torsion vibrations, Vtor, versus T for Sr20. One can see that Vtor is essentially less than Vl and the width of the hysteresis loop is about 20 K, i.e. much less than in the case of the longitudinal vibrations. The absence of GTH in the case of torsion waves can be explained as follows. The difference between Vl in R3¯c phase and Pnma phase increases with T at T4TS, so that the contribution of the Pnma inclusions into E remains observable although the volume of these inclusions decreases. In the case of torsion vibrations, the difference between the velocities rapidly decreases with growing T, which makes the contribution of the inclusions into the torsion modulus very small except close vicinity of TS.
5. High-frequency effects Bogdanova et al. [8] studied the propagation of sound waves of frequency f ¼ 770 MHz along [10 0] direction in La0.825Sr0.175MnO3 (TC ¼ 282 K) single crystal. The values of the longitudinal and transverse velocities reported in Ref. [8] are consistent with the data of Refs. [4,5]. Below TC, the attenuation of the longitudinal waves was found to increase rapidly with decreasing T, but the longitudinal vibrations give rise to transverse wave that travels through the sample with low attenuation. The transformation of the longitudinal wave into the transverse one occurred near the sample face. Yuhang Ren et al. [16] studied elastic properties of La0.7Ca0.3MnO3 single crystal at very high frequencies. It was found that values of the longitudinal sound velocity at 1010 Hz are more than by 50% larger than those deduced from the experiments at 103–106 Hz. It is clearly seen in Fig. 3, where we compare the temperature dependence of Vl reported in Ref. [16] with the data for La0.74Ca0.26MnO3 obtained in Ref. [15] at f100 kHz. It was pointed out in Ref. [16] that such a behavior, indicative of coupling to relaxation process, is similar to that of liquids, but unusual for a hard solid.
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6. Concluding remarks In our overview, we have considered the data for single crystals only. The experiments on polycrystalline samples are numerous but not so informative because of inevitable effects due to grain size, porosity, etc. For example, the temperature dependence of Young’s modulus reported in Ref. [23] for polycrystalline La0.67Ca0.33MnO3 is very smooth, even near TC, which is inconsistent with the fact that the magnetic transition is of the first order. The results considered above show that the sound velocity measurements is a good tool for detecting various crystal defects and allow one to find phase transitions, which are hardly observable by other techniques. They also clearly demonstrate that the boundary between the crystal phases is fuzzy in the CMR manganites.
Acknowledgments The work was supported by Grants RFBR 06-02-16085 and NSh 3257.2008.2. References [1] M.S. Salamon, M. Jaime, Rev. Mod. Phys. 73 (2001) 583. [2] E. Dagotto, Nanoscale Phase Separation and Colossal Magnetoresistance. The Physics of Manganites and Related Compounds, Springer, Berlin, 2002. [3] H. Kawano, R. Kajimoto, M. Kubota, H. Yoshizawa, Phys. Rev. B 53 (1996) R14709. [4] T.W. Darling, A. Migliori, E.G. Moshopoulou, S.A. Trugman, J.J. Neumeier, J.L. Sarrao, A.R. Bishop, J.D. Thompson, Phys. Rev. B 57 (1998) 5093.
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[5] H. Hazama, T. Goto, Y. Nemoto, Y. Tomioka, A. Asamitsu, Y. Tokura, Phys. Rev. B 62 (2000) 15012. [6] Yu.P. Gaidukov, N.P. Danilova, A.A. Mukhin, A.M. Balbashov, JETP Lett. 68 (1998) 153. [7] M. Paraskevopulos, F. Mayer, J. Hemberger, A. Loidl, R. Heichele, D. Maurer, V. Muller, A.A. Mukhin, A.M. Balbashov, J. Phys.: Condens. Matter 12 (2000) 3993. [8] Kh.G. Bogdanova, A.R. Bulatov, V.A. Golenishchev-Kutuzov, L.V. Elokhina, A.V. Kapralov, A.V. Korolev, E.A. Neifeld, M.M. Shakirzyanov, Phys. Solid State 45 (2003) 298. [9] R.I. Zainullina, N.G. Bebenin, A.M. Burkhanov, V.V. Ustinov, Ya.M. Mukovskii, Phys. Rev. B 66 (2002) 064421. [10] A.V. Goltsev, K.V. Dyakonov, N.F. Kartenko, L.A. Kulakova, V.V. Popov, E´.Z. Yakhkind, Ya.M. Mukovskii, V.P. Dyakonov, Phys. Solid State 47 (2005) 102. [11] Kh.G. Bogdanova, A.R. Bulatov, V.A. Golenishchev-Kutuzov, R.F. Mamin, A.A. Potapov, Phys. Solid State 49 (2007) 519. [12] R.I. Zainullina, N.G. Bebenin, A.M. Burkhanov, V.V. Ustinov, Ya.M. Mukovskii, J. AlloysCompd. 394 (2005) 39. [13] R.I. Zainullina, N.G. Bebenin, V.V. Mashkautsan, V.V. Ustinov, Ya.M. Mukovskii, J. Magn. Magn. Mater. 300 (2006) e137. [14] L.D. Landau, E.M. Lifshitz, Theory of Elasticity, second ed., Pergamon, London, 1970. [15] R.I. Zainullina, N.G. Bebenin, V.V. Ustinov, Ya.M. Mukovskii, D.A. Shulyatev, Phys. Rev. B 76 (2007) 014408. [16] Yuhang Ren, G. Lupke, Yufeng Hu, Qi Li, C.S. Hong, N.H. Hur, R. Merlin, Phys. Rev. B 74 (2006) 012405. [17] E.A. Neifeld, N.G. Bebenin, V.E. Arkhipov, K.M. Demchuk, V.S. Gaviko, A.V. Korolev, N.A. Ugryumova, Ya.M. Mukovskii, J. Magn. Magn. Mater. 295 (2005) 77. [18] V.S. Gaviko, N.G. Bebenin, Ya.M. Mukovskii, Phys. Rev. B 77 (2008) 224105. [19] P.G. Radaelli, M. Marezio, H.Y. Hwang, S.-W. Cheong, J. Solid State Chem. 122 (1996) 144. [20] Y. Yamada, O. Hino, S. Nohdo, R. Kanao, T. Inami, S. Katano, Phys. Rev. Lett. 77 (1996) 904. [21] R.I. Zainullina, N.G. Bebenin, V.V. Ustinov, Ya.M. Mukovskii,, J. Alloys Compd. 467 (2009) 22. [22] A.P. Saiko, S.A. Markevich, JETP Lett. 78 (2003) 332. [23] Y.Q. Ma, W.H. Song, R.L. Zhang, J.M. Dai, J. Yang, J.J. Du, Y.P. Sun, C.Z. Bi, Y.J. Ge, X.G. Qiu, Phys. Rev. B 69 (2004) 134404.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Elastic properties of lanthanum manganites N.G. Bebenin , R.I. Zainullina, V.V. Ustinov Institute of Metal Physics, Ural Division, Russian Academy of Sciences, 18 Sofia Kovalevskaya St., Ekaterinburg 620041, Russia
a r t i c l e in f o
a b s t r a c t
Available online 27 November 2008
We give a brief overview of the data on elastic properties of the CMR manganites published during last decade. The main emphasis is put on the results obtained for single crystals. & 2008 Elsevier B.V. All rights reserved.
PACS: 75.47.Lx 62.65.+k Keywords: Manganite Ultrasound Elastic moduli
1. Introduction Rare-earth manganites Ln1xDxMnO3, where Ln stands for a rare earth and D is a divalent element, attract attention due mainly to the colossal magnetoresistance (CMR) effect observed near Curie temperature TC. It is generally recognized that the specific feature of the CMR compounds is the strong interaction between charge carriers, localized spins, and crystal lattice. A whole wealth of information on transport and magnetic properties of the CMR materials is available in literature, but elastic properties remain less studied. In the well-known reviews [1,2], the issues of propagation and attenuation of sound waves are not addressed. To fill the gap in part, we briefly overview the experimental data on elastic properties of ferromagnetic lanthanum manganites La1xDxMnO3, D ¼ Ca, Sr, and Ba, which were published during the last decade. The sound velocity and damping were studied at various frequencies. Most of the publications report the measurements that were carried out in the range from 1 kHz to 100 MHz; some authors report the internal friction Q1, which is a measure of sound damping, taken at frequencies around 1 Hz. The frequencies below 100 MHz will be referred to as ‘‘low’’ frequencies. Some interesting effects were also found in the high-frequency region, when the frequency f is about or higher than 1 GHz. It is reasonable to discuss the properties of the CMR manganites in the low- and high-frequency regions separately. The complex oxides, we wish to discuss, have the perovskite structure. The ideal cubic perovskite unit cell is, however, somewhat distorted, so that three structural phases are observed: Corresponding author. Tel.: +7 343 378 38 90; fax: +7 343 3745244.
E-mail address: [email protected] (N.G. Bebenin). 0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.11.024
the Jahn–Teller distored O0 and pseudocubic O* phases of the same orthorhombic Pnma space group and rhombohedral R phase with R3¯c symmetry [3].
2. Temperature dependence of the sound velocity The single crystals of manganites are usually twinned, so the cubic approximation, in which distortions of the unit cell are ignored, is widely used to indicate crystallographic directions. The temperature dependence of elastic moduli was reported for single crystals of La1xSrxMnO3, with x ¼ 0.17 [4] and x ¼ 0.12, 0.165, and 0.3 [5]. Fig. 1 shows the moduli Cij for x ¼ 0.17 in the cubic geometry. This single crystal undergoes the ferromagneticto-paramagnetic phase transition at TC ¼ 265 K and the structural Pnma-R3¯c transition at TS ¼ 285 K [4]. In the rhombohedral phase, all the moduli are larger than in the orthorhombic phase. The less pronounced peculiarities at the Curie temperature are affected by a magnetic field, which is a signature of the strong coupling of lattice and spin degrees of freedom. Similar results were reported by Hazama et al. [5]. In Ref. [5], Cij are given in the cubic geometry for La0.88Sr0.12MnO3, where the transition between the orthorhombic phases is observed, in the cubic and rhombohedral geometries for La0.835Sr0.165MnO3, which undergoes O–R transition, and in the rhombohedral geometry for La0.7Sr0.3MnO3 single crystal, which is always in the R3¯c phase. The single crystals of La1xSrxMnO3 family were also studied in Refs. [6–11]. It was shown that the sound velocity is independent of frequency up to f ¼ 90 MHz [11]. The information for La1xBaxMnO3 is not as detailed as that for La1xSrxMnO3. To our knowledge, only one paper [12] describes the elastic properties of La1xBaxMnO3 single crystals. In order to reveal the effect of the dopant type on the elastic properties, we
ARTICLE IN PRESS N.G. Bebenin et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 682–685
Fig. 1. Elastic moduli Cij of La0.83Sr0.17MnO3 single crystal reported in Ref. [4] for cubic geometry (open symbols) and Young’s modulus calculated for [1 0 0] and [111] directions using Eq. (1) (solid symbols).
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curve it is clearly seen. Perhaps, this is true for other CMR manganites. Looking at the curves in Fig. 2 and at Vl–T curve for Ca26 crystal shown in Fig. 3, we see that the increase of a divalent content results in an increase of the value and in a weakening of the temperature dependence of sound velocity. At low temperatures, Vl increases with the decrease in ionic radius of a divalent ion. The sound velocity in Ca26 is close to the sound velocity in Sr25, but noticeably larger than the velocity in Ba25. This can be related to the fact that ionic radius of Ca2+ (1.34 A˚) is close to that of La (1.38 A˚) and Sr2+ (1.44 A˚) and is small in comparison with the radius of Ba2+ (1.61 A˚). In the curves for all La–Ba crystals and for Sr20, there is a discontinuity caused by the structural Pnma-R3¯c transition. However, in the curve for Sr15, the peculiarity related to the structural transition at TS ¼ 365 K is rather weak, which is likely to occur because the direction of sound propagation is close to the four-fold cubic axis. The second-order ferromagnetic-to-paramagnetic phase transition gives rise to a weak peculiarity in the Vl–T curves. The Sr25 sample exhibits only this weak peculiarity because Sr25 is always in R3¯c phase. In the Vl–T curve for Sr20, there is a very small jump at about 400 K, which is a signature of a first-order transition [9]. In Ca26, the magnetic transition is of the first order and the longitudinal sound velocity drastically falls down in the range from 210 to 225 K, see Fig. 3. Above this range, the structural transition between the low-temperature orthorhombic phase and the high-temperature orthorhombic phase occurs [15]. The X-ray measurements [17] revealed that in La1–xSrxMnO3, the Pnma-R3¯c transition results in a jump in the unit cell volume of about Dv ¼ 0.15–0.20 A˚3 per formula unit, which at the first glace provides a simple explanation for the jump in the longitudinal sound velocity Vl. However, the X-ray study of La1–xBaxMnO3 [18,19] did not reveal an observable volume change at the transition. The Dv value in the La–Ba manganites is significantly smaller than in the La–Sr crystals, although the jump in Vl is larger. It follows that the Vl jump is determined by a rearrangement of ions in the cell and perhaps by interactions of the crystal lattice with magnetic and electronic subsystems of the crystal.
Fig. 2. Longitudinal sound velocity versus temperature for La–Sr and La–Ba manganites measured on heating [9,12,13]. The sound propagated along [1 0 3], [111], and [11 5] cubic directions of Sr15, Sr20, and Sr25, respectively. In all La–Ba crystals, the waves propagated along a direction close to [11 0].
show in Fig. 2 the temperature dependence of the longitudinal sound velocity Vl in La–Sr and La–Ba single crystals (x ¼ 0.15, 0.20, and 0.25) reported in Refs. [9,12,13]. For brevity, we denote a manganite by the symbol of a divalent ion and percentage, for example, Sr15 stands for La0.85Sr0.15MnO3, etc. The measurements of the elastic properties were performed in Refs. [9,12,13] by the composite oscillator method, which allows finding the Young’s modulus E. In the case of a single-crystalline cylinder with its axis along vector n, the Young’s modulus is given by Ref. [14] 1 C 11 þ C 12 1 2 þ ¼ PðnÞ (1) En ðC 11 þ 2C 12 ÞðC 11 C 12 Þ C 44 C 11 C 12 where P(n) ¼ nx2nz2+ny2nz2+nx2ny2 and the cubic symmetry is assumed. To illustrate the dependence of the Young’s modulus on n, we calculated En for n||[1 0 0] (P(n) ¼ 0) and n||[111] (P(n) ¼ 1/ 3) using the data of Darling et al. [4] for Sr17. In the first orientation, the peculiarity at the temperature of Pnma-R3¯c transition is hardly observable although in the E[111]–T
Fig. 3. Temperature dependence of longitudinal sound velocity for Ca26 [15] and Ca30 [16] single crystals measured on heating at 100 kHz and at 50 GHz, respectively.
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3. Internal friction Fig. 4 shows the internal friction Q1 versus temperature for Sr15 (TC ¼ 232 K) and Ba15 (TC ¼ 222 K) obtained by the composite oscillator method [9,12]. There are peaks caused by the PnmaR3¯c transition and weak peaks related to the magnetic transition. The peak at E400 K was found not only in Ba15, but also in other La–Ba crystals as well as in Sr20 and Sr25. This peak was attributed to the relaxation due to point defects. In the Sr15 curve below TC, one can see a peak at 202 K. Taking into consideration the results of the neutron scattering experiments [20], we infer that the peak at 202 K is due to the transition to the low-temperature charge-ordered state [9]. Similar peak is seen in the Ba15 curve at T ¼ 176 K. It is likely that in Ba15, the charge ordering occurs at T ¼ 176 K. At E100 K in the Sr15 curve and at E60 K in the Ba15 curve, we see pronounced peaks of the internal friction. Fig. 5 shows that such peak is observed in the Q1–T curves for all La–Ba crystals, and the peak diminishes and shifts toward lower temperatures as the Ba content increases. Moreover, the peak appears in La0.77Sr0.20Y0.03MnO3 (Sr20Y3 in short), although it was not found in Y-free La0.8Sr0.2MnO3 [21]. Therefore, the peak is observed if the ionic radius of lanthanum differs from the radius of a dopant significantly and/or if the dopant concentration is sufficiently low.
Fig. 4. Temperature dependence of internal friction in La0.85Sr0.15MnO3 and La0.85Ba0.15MnO3 single crystals measured on heating at frequency of about 100 kHz [9,12].
Fig. 5. Low-temperature peak of the internal friction measured on heating.
Fig. 6. Hysteretic behavior of the longitudinal sound velocity. Inset: the same for the velocity of torsion vibration.
This suggests that the low-temperature peak arises due to smallscale clusters.
4. Giant thermal hysteresis (GTH) Fig. 6 shows Vl–T curves measured on heating and cooling. The curves for other La–Sr and La–Ba manganites are similar. The Pnma-R3¯c transition results in the giant (of about 200–300 K) width of the hysteresis loop. It follows that when heating, there are Pnma inclusions in R3¯c matrix at T4TS. A simple phenomenological theory describing the GTH effect was proposed in Ref. [22]. Inset in Fig. 6 shows the velocity of torsion vibrations, Vtor, versus T for Sr20. One can see that Vtor is essentially less than Vl and the width of the hysteresis loop is about 20 K, i.e. much less than in the case of the longitudinal vibrations. The absence of GTH in the case of torsion waves can be explained as follows. The difference between Vl in R3¯c phase and Pnma phase increases with T at T4TS, so that the contribution of the Pnma inclusions into E remains observable although the volume of these inclusions decreases. In the case of torsion vibrations, the difference between the velocities rapidly decreases with growing T, which makes the contribution of the inclusions into the torsion modulus very small except close vicinity of TS.
5. High-frequency effects Bogdanova et al. [8] studied the propagation of sound waves of frequency f ¼ 770 MHz along [10 0] direction in La0.825Sr0.175MnO3 (TC ¼ 282 K) single crystal. The values of the longitudinal and transverse velocities reported in Ref. [8] are consistent with the data of Refs. [4,5]. Below TC, the attenuation of the longitudinal waves was found to increase rapidly with decreasing T, but the longitudinal vibrations give rise to transverse wave that travels through the sample with low attenuation. The transformation of the longitudinal wave into the transverse one occurred near the sample face. Yuhang Ren et al. [16] studied elastic properties of La0.7Ca0.3MnO3 single crystal at very high frequencies. It was found that values of the longitudinal sound velocity at 1010 Hz are more than by 50% larger than those deduced from the experiments at 103–106 Hz. It is clearly seen in Fig. 3, where we compare the temperature dependence of Vl reported in Ref. [16] with the data for La0.74Ca0.26MnO3 obtained in Ref. [15] at f100 kHz. It was pointed out in Ref. [16] that such a behavior, indicative of coupling to relaxation process, is similar to that of liquids, but unusual for a hard solid.
ARTICLE IN PRESS N.G. Bebenin et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 682–685
6. Concluding remarks In our overview, we have considered the data for single crystals only. The experiments on polycrystalline samples are numerous but not so informative because of inevitable effects due to grain size, porosity, etc. For example, the temperature dependence of Young’s modulus reported in Ref. [23] for polycrystalline La0.67Ca0.33MnO3 is very smooth, even near TC, which is inconsistent with the fact that the magnetic transition is of the first order. The results considered above show that the sound velocity measurements is a good tool for detecting various crystal defects and allow one to find phase transitions, which are hardly observable by other techniques. They also clearly demonstrate that the boundary between the crystal phases is fuzzy in the CMR manganites.
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