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Soft-acoustic phonon mode at the Jahn–Teller transition in LaMnO3
ARTICLE IN PRESS
Physica B 352 (2004) 353–357 www.elsevier.com/locate/physb
Soft-acoustic phonon mode at the Jahn–Teller transition in LaMnO3 M. Saint-Paul, P. Lejay Centre de Recherches sur les Tre`s Basses Tempe´ratures CNRS BP166 25 Av des Martyrs, 38042 Grenoble, France Received 29 June 2004; received in revised form 20 August 2004; accepted 21 August 2004
Abstract The elastic properties of LaMnO3 have been investigated by means of ultrasonic measurements. The longitudinal elastic constant C Ort 22 propagating along the b-axis exhibits a large softening around the Jahn–Teller transition TJT750 K accompanied by the orbital order-disorder transition r 2004 Elsevier B.V. All rights reserved. PACS: 75.30.Et; 75.30.Vn; 75.30.Kz; 62.20.DC Keywords: Jahn–Teller effect; Structural transition; Elastic softening
1. Introduction Since the discovery of the colossal magnetoresistance, much attention has been attracted to the perovskite manganese oxides [1]. In these materials, the charge, spin and orbital degrees of freedom play important roles because the large decrease of the resistivity is observed at the phase transition from a charge and orbital-ordered phase to a ferromagnetic metallic phase. LaMnO3 is of interest as the parent compound of the CMR Corresponding author. Tel.: +33-4-76-88-78-20; fax: +334-76-87-50-60. E-mail address: [email protected] (M. Saint-Paul).
materials and a large number of theoretical [2,3] and experimental [4–11] investigations have been undertaken on this material. In 3d transition-metal compounds with orbital degeneracy, one mechanism of the orbital ordering is based on the cooperative Jahn–Teller effects where the lattice distortion occurs and lifts the orbital degeneracy in the transition metal ion. LaMnO3 shows an orbital ordering below 750 K associated with the distortion of MnO6 octahedra. LaMnO3 undergoes a structural phase transition at TJT=750 K from the Jahn–Teller distorted orthorhombic phase to a high-temperature nearly cubic phase. This transition is accompanied by an orbital order–disorder transition. Abrupt changes in the electric resistivity and thermopower [9] have
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.08.014
ARTICLE IN PRESS 354
M. Saint-Paul, P. Lejay / Physica B 352 (2004) 353–357
been observed at this transition TJT. The structural phase transition can be described as an ordering of the local distortions that are thermally disordered above TJT, the first-order transition is accompanied by a sharp volume contraction and a large specific heat anomaly [4]. The 3d electron state of transition-metal ions has an electric quadrupole moment due to the orbital state as well as a magnetic dipole moment. The 3d electron state is perturbated by a modulation of the crystalline electric field potential due to lattice vibrations. The coupling of the quadrupole moment of the 3d electron to the lattice gives rise to anomalies of the elastic modes (Jahn–Teller effect) [3,11–13]. Elastic constants are very sensitive to structural phase transition, the elastic constant softening is the soft mode associated with the transition and reflects the instability of the lattice to a strain of a given symmetry [3,13]. The instability of the lattice to a strain of a given symmetry as evidenced by the corresponding elastic constant going to zero is a fundamental feature of a cooperative Jahn–Teller phase transition. When a crystal contains Jahn– Teller ions with a high concentration, local distortions interact with each other to order themselves cooperatively. This ordering disappears above a transition temperature. The properties of the elastic constants associated with this cooperative phenomenon were theoretically studied [3,12]. Considerable changes in several elastic constants at the structural phase transition associated with the quadrupole ordering for La1xSrxMnO3 have been observed [10]. Measurements of the longitudinal elastic constant C Ort propagating along the b-axis of 22 LaMnO3 in the temperature range 5–900 K are presented hereafter.
2. Experimental The single crystals were grown by the floating zone method. Feed and seed rods were prepared by high-temperature solid-state reaction. Powders of La2O3 (4N) and MnO (4N) were used as starting materials. The mixture was twice hydrostatically pressed at 10 kbars and sintered in air at
1200 1C for 24 h with an intermediate grinding to improve the sample homogeneity. The cylindered samples were placed on rods of the same chemical composition to prevent contamination from the alumina crucible. The final rods dimensions were 5 mm diameter for 80 mm length. A double-elliptical light furnace (Cyberstar, France) equipped with two 1000 W halogen lamps has been used for growing the LaMnO3 single crystals. The atmosphere was composed of highquality oxygen (20%) and argon (80%) at room pressure. The feeding rod and the seed were inversely rotated at 20 rpm and the transition speed was 2 mm/h. X-ray back-scattering Lau¨e diffraction proved the single crystalline state of the growth and the phase purity have been checked by X-ray powder diffraction on small crushed parts of the single crystal (Fig. 1). The Rielveld refinement carried out with the Pnma space group gives the following lattice constants: a=5.744 A˚, b=7.695 A˚ and c=5.539 A˚ in agreement with the lattice parameters reported in Ref. [6] using the P bnm space group. The b-axis of the orthorhombic phase corresponds to the z-axis of the high-temperature cubic cell and the x and y directions are 451 rotated from the orthorhombic a and c axis [6–7,10]. The LaMnO3 single crystal used in this study was cut is in the form of a cylindrical rod of length 10 and diameter 4 mm. with the rod axis parallel to b-axis. Below 300 K, the standard pulse echo technique was used at 15 MHz with LiNbO3 transducers bounded directly on the sample. At highest temperatures, the measurements had to be performed at a lower frequency of 2 MHz with the buffer rod method [14]. The sample was placed at room temperature between two stainless steel rods of length 200 mm and diameter 6 mm. The whole assembly was placed inside a tubular chamber within the furnace. The ultrasonic transducers were bounded at the ends of the wave guide rods outside the furnace. The sample was bounded at the other ends of the wave guide rods with a liquid Pt–Sn film. The selection of an appropriate binding material in the hightemperature range presented a severe problem.
ARTICLE IN PRESS M. Saint-Paul, P. Lejay / Physica B 352 (2004) 353–357
355
Fig. 1. X-ray powder diffraction of LaMnO3 at 300 K.
140
120
C22 (GPa)
The longitudinal velocity variation was measured by phase coherent detection. The phase delay due to the wave guides was measured without the sample in order to extract the value of the sound velocity of the sample. Changes in velocity were continuously measured. A relative velocity shift of about 104 could be determined below 300 K, at high temperatures a precision of 1% for the velocity is obtained. The temperature was determined by means of calibrated thermocouples and platinum resistors. Care was taken to change the temperature very slowly at a rate of 1 K/min.
100
80
60
3. Results and discussions The elastic stiffness constant C Ort 22 ¼ 140 GPa was deduced from the sound velocity V=5000 m/s. 2 C Ort 22 ¼ rV ; with the densityr ¼ 5:7:
Temperature dependence of C Ort 22 is shown in Figs. 1 and 2. C Ort shows a pronounced variation 22 around the transition temperature TJT=750 K. It starts to deviate at about 600 K from the normal decrease towards higher temperatures and goes through a sharp minimum at TJT. A thermal hysteresis of about 10 K between the heating and the cooling runs was observed. As shown in Fig. 2 C Ort mode exhibits 22 considerable softening in the vicinity of the transition temperature TJT.
0
200
400 T (K)
600
800
Fig. 2. Temperature dependence of the longitudinal elastic constant of C Ort 22 : The solid and open symbols indicate the temperature increasing and decreasing runs, respectively. The solid line is the anharmonic lattice contribution calculated with a Gru¨neisen parameter g=5.
In our experiment no noticeable anomaly occurs in the C Ort 22 measurement around the antiferromagnetic ordering temperature TN140 K. The anharmonic lattice contribution to the elastic constant C Ort 22 has been evaluated with the standard Ort 2 C Ort 22 C 22 0 ¼ g CðTÞT;
ARTICLE IN PRESS M. Saint-Paul, P. Lejay / Physica B 352 (2004) 353–357
where C Ort 22 0 is the elastic constant at T=0, g is the effective Gru¨neisen parameter which describes the anharmonic coupling of the external strain to the thermal phonon modes and is the Debye specific heat. The calculated anharmonic contribution with the Debye temperature YD=400 K and g=5 follows the experimental data below 600 K. For the discussion of the anomalous behaviour of C Ort 22 at TJT, we start with the cooperative Jahn–Teller phase transition [3,13].The orbital degrees of the 3d electrons of the transition metal provide the electric quadrupole moments of the ions. The strain coupling to quadrupole moments leads to the cooperative Jahn–Teller effects. The ultrasonic wave induces the elastic strain with various kinds of symmetry. In the case of a cubic crystal class, the longitudinal C11 propagating along the [0 0 1] direction induces the elastic strain ezz which consists of the volume strain B ¼ xx þ yy þpzz ffiffiffi the tetragonal strain u ¼ ð2zz xx yy Þ= 3 with G3(Eg) symmetry [10,11]. The shear elastic constant (C11C12)/2 mode propagating along [1 1 0] with the polarizing vector parallel to the ½1 1 0 induces the elastic strain n ¼ xx yy with G3(Eg) symmetry [10,11]. It is well known that the 3d electron state of the the Mn3+ ion splits into a doublet with Eg symmetry and a triplet with T2g symmetry. The quadrupole–strain interaction is described in [9–12]. The Eg doublet of the Mn3+ ion has p theffiffiffi quadrupole components O02 ¼ ð2l 2z l 2x l 2y Þ= 3 and O22 ¼ l 2x l ey_ with Eg symmetry. l x ; l y and l z are the angular momentum components. The quadrupoles O02 and O22 couple bilinearly to the pffiffiffi elastic strains u ¼ ð2zz xx yy Þ= 3 and v ¼ xx yy with the same symmetry [10–12] as H ¼ gG3 ðO02 u þ O22 v Þ; where gG3 is the coupling constant. Softening of the elastic constant (C11C12)/2 around the structural phase transition associated to the orbital ordering or quadrupolar ordering was observed in the previous ultrasonic measurement on the hole-doped manganite La1xSrx MnO3 with x=0.12 and 0.165 [10,11].
The function of temperature of this mode was described by the simple relation T Tc ; (1) C C0 T Y where C0 is the elastic constant in the high temperature phase TbTc, Y indicates the intersite quadrupole interaction. The difference between the two characteristic temperatures EJT=Tc Y indicates the Jahn-Teller coupling energy of the system. With our experimental set up, the shear (C11C12)/2 mode could not be generated directly through the sample and the direct observation of the shear (C11C12)/2 mode could not be achieved. Nevertheless the temperature behaviour of C Ort 22 reported in Figs. 2 and 3 was analyzed with Eq. (1). Above TJT=750 K, the temperature dependence of C Ort 22 in the heating run can be described by Eq. (1) with C0=120 GPa, Tc=600 K, Y=200 K EJT=TcY gives a Jahn–Teller coupling energy of 400 K which is much smaller than that given for this system [2]. A coupling constant gG3 of 2000 K is estimated from EJT and an intersite quadrupole 0 coupling gG of 20 K is evaluated from Y. Both
140
120
C22 (GPa)
356
100
80
60 600
650
700
750 T (K)
800
850
Fig. 3. Temperature dependence of the longitudinal elastic constant of C Ort 22 : The solid and open symbols indicate the temperature increasing and decreasing runs, respectively. The dashed line is the theoretical prediction given in Ref. [3] and Eq. (1) with Y=200 K and Tc=600 K.
ARTICLE IN PRESS M. Saint-Paul, P. Lejay / Physica B 352 (2004) 353–357
values are two times larger than those obtained in La1xSrxMnO3 compounds [10]. Below TJT the large temperature dependence of C Ort 22 (Fig. 3) is similar to that found for the intensity of the orbital ordering reflection measured by resonant X-ray scattering [5]. Strong distortion of the MnO6 octahedra is observed in the same temperature range [6]. A recent theoretical approach of the elastic behaviour has been given by Kataoka [3]. The author examines the antiferroorbital ordering due to the cooperative Jahn–Teller effect in LaMnO3. When a crystal contains Jahn–Teller ions with a high concentration, local distortions around the Jahn–Teller ions interact with each other to order them cooperatively. This ordering disappears above a transition temperature. LaMnO3 can be considered to belong to the antiparallel orbital ordering accompanied by antiparallel ordering of distortions. Softening of the (C11C12)/2 is predicted around the structural transition. The theoretical prediction of the temperature dependence of (C11C12)/2 has been extracted from Ref. [3]. The theoretical prediction corresponding to the parameter Y/Tc=0.3 and reported in Fig. 3 describes qualitatively well the experimental results. The theoretical behaviour is reduced to Eq. (1) in the high-temperature phase [3]. In conclusion, we have measured the longitudinal elastic constant C Ort 22 along the b-axis of LaMnO3 in a large temperature range up to 800 K. A large softening of the elastic mode C Ort 22 is
357
observed at the structural phase transition TJT=750 K associated with the orbital order disorder transition.
References [1] See for a review Y. Tokura, N. Nagaosa, Science 288 (2000) 462. [2] A.J. Millis, Phys. Rev. B 53 (1996) 8434. [3] M. Kataoka, J. Phys. Soc. Jpn. 70 (2001) 2353. [4] M.C. Sanchez, G. Subias, J. Garcia, J. Blasco, Phys. Rev. Lett. 90 (2003) 045503. [5] Y. Murakami, J.P. Hill, D. Gibbs, M. Blume, I. Koytama, M. Tanaka, H. Kawata, T. Arima, Y. Tokura, K. Hirota, Y. Endoh, Phys.Rev. Lett. 81 (1998) 582. [6] J. Rodriguez-Carvajal, M. Hennion, F. Moussa, A.H. Mouden, L. Pinsard, A. Revcolevschi, Phys. Rev. B 57 (1998) R3189. [7] F. Moussa, M. Hennion, J. Rodriguez-Carvajal, H. Moudden, L. Pinsard, A. Revcolevschi, Phys. Rev. B 54 (1996) 15149. [8] T. Chatterji, F. Fauth, B. Ouladdiaf, P. Mandal, B. Ghost, Phys. Rev. B 68 (2003) 053406. [9] J.-S. Zhou, J.B. Goodenough, Phys. Rev. B 60 (1999) R15002. [10] H. Hazama, T. Goto, Y. Nemoto, Y. Tomioka, A. Asamitsu, T. Tokura, Phys. Rev. B 62 (2000) 15012. [11] T. Goto, B. Lu¨thi, Adv. in Phys. 52 (2003) 67. [12] B. Lu¨thi, W. Rehwal, in: K.A. Muller, H. Thomas (Eds.), Structural Phase Transition Topics in Current Physics vol. 23, Springer, Berlin, 1981, p. 131. [13] R.L. Melcher, in: W.P. Mason, R.N. Thurston (Eds.), Physical Acoustics vol. XII, Academic press, New York, 1976, p. 1. [14] H.J. McSkimin, in: W.P. Mason (Ed.), Physical Acoustics vol. IA, Academic Press, New York, 1964, p. 271.
Physica B 352 (2004) 353–357 www.elsevier.com/locate/physb
Soft-acoustic phonon mode at the Jahn–Teller transition in LaMnO3 M. Saint-Paul, P. Lejay Centre de Recherches sur les Tre`s Basses Tempe´ratures CNRS BP166 25 Av des Martyrs, 38042 Grenoble, France Received 29 June 2004; received in revised form 20 August 2004; accepted 21 August 2004
Abstract The elastic properties of LaMnO3 have been investigated by means of ultrasonic measurements. The longitudinal elastic constant C Ort 22 propagating along the b-axis exhibits a large softening around the Jahn–Teller transition TJT750 K accompanied by the orbital order-disorder transition r 2004 Elsevier B.V. All rights reserved. PACS: 75.30.Et; 75.30.Vn; 75.30.Kz; 62.20.DC Keywords: Jahn–Teller effect; Structural transition; Elastic softening
1. Introduction Since the discovery of the colossal magnetoresistance, much attention has been attracted to the perovskite manganese oxides [1]. In these materials, the charge, spin and orbital degrees of freedom play important roles because the large decrease of the resistivity is observed at the phase transition from a charge and orbital-ordered phase to a ferromagnetic metallic phase. LaMnO3 is of interest as the parent compound of the CMR Corresponding author. Tel.: +33-4-76-88-78-20; fax: +334-76-87-50-60. E-mail address: [email protected] (M. Saint-Paul).
materials and a large number of theoretical [2,3] and experimental [4–11] investigations have been undertaken on this material. In 3d transition-metal compounds with orbital degeneracy, one mechanism of the orbital ordering is based on the cooperative Jahn–Teller effects where the lattice distortion occurs and lifts the orbital degeneracy in the transition metal ion. LaMnO3 shows an orbital ordering below 750 K associated with the distortion of MnO6 octahedra. LaMnO3 undergoes a structural phase transition at TJT=750 K from the Jahn–Teller distorted orthorhombic phase to a high-temperature nearly cubic phase. This transition is accompanied by an orbital order–disorder transition. Abrupt changes in the electric resistivity and thermopower [9] have
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.08.014
ARTICLE IN PRESS 354
M. Saint-Paul, P. Lejay / Physica B 352 (2004) 353–357
been observed at this transition TJT. The structural phase transition can be described as an ordering of the local distortions that are thermally disordered above TJT, the first-order transition is accompanied by a sharp volume contraction and a large specific heat anomaly [4]. The 3d electron state of transition-metal ions has an electric quadrupole moment due to the orbital state as well as a magnetic dipole moment. The 3d electron state is perturbated by a modulation of the crystalline electric field potential due to lattice vibrations. The coupling of the quadrupole moment of the 3d electron to the lattice gives rise to anomalies of the elastic modes (Jahn–Teller effect) [3,11–13]. Elastic constants are very sensitive to structural phase transition, the elastic constant softening is the soft mode associated with the transition and reflects the instability of the lattice to a strain of a given symmetry [3,13]. The instability of the lattice to a strain of a given symmetry as evidenced by the corresponding elastic constant going to zero is a fundamental feature of a cooperative Jahn–Teller phase transition. When a crystal contains Jahn– Teller ions with a high concentration, local distortions interact with each other to order themselves cooperatively. This ordering disappears above a transition temperature. The properties of the elastic constants associated with this cooperative phenomenon were theoretically studied [3,12]. Considerable changes in several elastic constants at the structural phase transition associated with the quadrupole ordering for La1xSrxMnO3 have been observed [10]. Measurements of the longitudinal elastic constant C Ort propagating along the b-axis of 22 LaMnO3 in the temperature range 5–900 K are presented hereafter.
2. Experimental The single crystals were grown by the floating zone method. Feed and seed rods were prepared by high-temperature solid-state reaction. Powders of La2O3 (4N) and MnO (4N) were used as starting materials. The mixture was twice hydrostatically pressed at 10 kbars and sintered in air at
1200 1C for 24 h with an intermediate grinding to improve the sample homogeneity. The cylindered samples were placed on rods of the same chemical composition to prevent contamination from the alumina crucible. The final rods dimensions were 5 mm diameter for 80 mm length. A double-elliptical light furnace (Cyberstar, France) equipped with two 1000 W halogen lamps has been used for growing the LaMnO3 single crystals. The atmosphere was composed of highquality oxygen (20%) and argon (80%) at room pressure. The feeding rod and the seed were inversely rotated at 20 rpm and the transition speed was 2 mm/h. X-ray back-scattering Lau¨e diffraction proved the single crystalline state of the growth and the phase purity have been checked by X-ray powder diffraction on small crushed parts of the single crystal (Fig. 1). The Rielveld refinement carried out with the Pnma space group gives the following lattice constants: a=5.744 A˚, b=7.695 A˚ and c=5.539 A˚ in agreement with the lattice parameters reported in Ref. [6] using the P bnm space group. The b-axis of the orthorhombic phase corresponds to the z-axis of the high-temperature cubic cell and the x and y directions are 451 rotated from the orthorhombic a and c axis [6–7,10]. The LaMnO3 single crystal used in this study was cut is in the form of a cylindrical rod of length 10 and diameter 4 mm. with the rod axis parallel to b-axis. Below 300 K, the standard pulse echo technique was used at 15 MHz with LiNbO3 transducers bounded directly on the sample. At highest temperatures, the measurements had to be performed at a lower frequency of 2 MHz with the buffer rod method [14]. The sample was placed at room temperature between two stainless steel rods of length 200 mm and diameter 6 mm. The whole assembly was placed inside a tubular chamber within the furnace. The ultrasonic transducers were bounded at the ends of the wave guide rods outside the furnace. The sample was bounded at the other ends of the wave guide rods with a liquid Pt–Sn film. The selection of an appropriate binding material in the hightemperature range presented a severe problem.
ARTICLE IN PRESS M. Saint-Paul, P. Lejay / Physica B 352 (2004) 353–357
355
Fig. 1. X-ray powder diffraction of LaMnO3 at 300 K.
140
120
C22 (GPa)
The longitudinal velocity variation was measured by phase coherent detection. The phase delay due to the wave guides was measured without the sample in order to extract the value of the sound velocity of the sample. Changes in velocity were continuously measured. A relative velocity shift of about 104 could be determined below 300 K, at high temperatures a precision of 1% for the velocity is obtained. The temperature was determined by means of calibrated thermocouples and platinum resistors. Care was taken to change the temperature very slowly at a rate of 1 K/min.
100
80
60
3. Results and discussions The elastic stiffness constant C Ort 22 ¼ 140 GPa was deduced from the sound velocity V=5000 m/s. 2 C Ort 22 ¼ rV ; with the densityr ¼ 5:7:
Temperature dependence of C Ort 22 is shown in Figs. 1 and 2. C Ort shows a pronounced variation 22 around the transition temperature TJT=750 K. It starts to deviate at about 600 K from the normal decrease towards higher temperatures and goes through a sharp minimum at TJT. A thermal hysteresis of about 10 K between the heating and the cooling runs was observed. As shown in Fig. 2 C Ort mode exhibits 22 considerable softening in the vicinity of the transition temperature TJT.
0
200
400 T (K)
600
800
Fig. 2. Temperature dependence of the longitudinal elastic constant of C Ort 22 : The solid and open symbols indicate the temperature increasing and decreasing runs, respectively. The solid line is the anharmonic lattice contribution calculated with a Gru¨neisen parameter g=5.
In our experiment no noticeable anomaly occurs in the C Ort 22 measurement around the antiferromagnetic ordering temperature TN140 K. The anharmonic lattice contribution to the elastic constant C Ort 22 has been evaluated with the standard Ort 2 C Ort 22 C 22 0 ¼ g CðTÞT;
ARTICLE IN PRESS M. Saint-Paul, P. Lejay / Physica B 352 (2004) 353–357
where C Ort 22 0 is the elastic constant at T=0, g is the effective Gru¨neisen parameter which describes the anharmonic coupling of the external strain to the thermal phonon modes and is the Debye specific heat. The calculated anharmonic contribution with the Debye temperature YD=400 K and g=5 follows the experimental data below 600 K. For the discussion of the anomalous behaviour of C Ort 22 at TJT, we start with the cooperative Jahn–Teller phase transition [3,13].The orbital degrees of the 3d electrons of the transition metal provide the electric quadrupole moments of the ions. The strain coupling to quadrupole moments leads to the cooperative Jahn–Teller effects. The ultrasonic wave induces the elastic strain with various kinds of symmetry. In the case of a cubic crystal class, the longitudinal C11 propagating along the [0 0 1] direction induces the elastic strain ezz which consists of the volume strain B ¼ xx þ yy þpzz ffiffiffi the tetragonal strain u ¼ ð2zz xx yy Þ= 3 with G3(Eg) symmetry [10,11]. The shear elastic constant (C11C12)/2 mode propagating along [1 1 0] with the polarizing vector parallel to the ½1 1 0 induces the elastic strain n ¼ xx yy with G3(Eg) symmetry [10,11]. It is well known that the 3d electron state of the the Mn3+ ion splits into a doublet with Eg symmetry and a triplet with T2g symmetry. The quadrupole–strain interaction is described in [9–12]. The Eg doublet of the Mn3+ ion has p theffiffiffi quadrupole components O02 ¼ ð2l 2z l 2x l 2y Þ= 3 and O22 ¼ l 2x l ey_ with Eg symmetry. l x ; l y and l z are the angular momentum components. The quadrupoles O02 and O22 couple bilinearly to the pffiffiffi elastic strains u ¼ ð2zz xx yy Þ= 3 and v ¼ xx yy with the same symmetry [10–12] as H ¼ gG3 ðO02 u þ O22 v Þ; where gG3 is the coupling constant. Softening of the elastic constant (C11C12)/2 around the structural phase transition associated to the orbital ordering or quadrupolar ordering was observed in the previous ultrasonic measurement on the hole-doped manganite La1xSrx MnO3 with x=0.12 and 0.165 [10,11].
The function of temperature of this mode was described by the simple relation T Tc ; (1) C C0 T Y where C0 is the elastic constant in the high temperature phase TbTc, Y indicates the intersite quadrupole interaction. The difference between the two characteristic temperatures EJT=Tc Y indicates the Jahn-Teller coupling energy of the system. With our experimental set up, the shear (C11C12)/2 mode could not be generated directly through the sample and the direct observation of the shear (C11C12)/2 mode could not be achieved. Nevertheless the temperature behaviour of C Ort 22 reported in Figs. 2 and 3 was analyzed with Eq. (1). Above TJT=750 K, the temperature dependence of C Ort 22 in the heating run can be described by Eq. (1) with C0=120 GPa, Tc=600 K, Y=200 K EJT=TcY gives a Jahn–Teller coupling energy of 400 K which is much smaller than that given for this system [2]. A coupling constant gG3 of 2000 K is estimated from EJT and an intersite quadrupole 0 coupling gG of 20 K is evaluated from Y. Both
140
120
C22 (GPa)
356
100
80
60 600
650
700
750 T (K)
800
850
Fig. 3. Temperature dependence of the longitudinal elastic constant of C Ort 22 : The solid and open symbols indicate the temperature increasing and decreasing runs, respectively. The dashed line is the theoretical prediction given in Ref. [3] and Eq. (1) with Y=200 K and Tc=600 K.
ARTICLE IN PRESS M. Saint-Paul, P. Lejay / Physica B 352 (2004) 353–357
values are two times larger than those obtained in La1xSrxMnO3 compounds [10]. Below TJT the large temperature dependence of C Ort 22 (Fig. 3) is similar to that found for the intensity of the orbital ordering reflection measured by resonant X-ray scattering [5]. Strong distortion of the MnO6 octahedra is observed in the same temperature range [6]. A recent theoretical approach of the elastic behaviour has been given by Kataoka [3]. The author examines the antiferroorbital ordering due to the cooperative Jahn–Teller effect in LaMnO3. When a crystal contains Jahn–Teller ions with a high concentration, local distortions around the Jahn–Teller ions interact with each other to order them cooperatively. This ordering disappears above a transition temperature. LaMnO3 can be considered to belong to the antiparallel orbital ordering accompanied by antiparallel ordering of distortions. Softening of the (C11C12)/2 is predicted around the structural transition. The theoretical prediction of the temperature dependence of (C11C12)/2 has been extracted from Ref. [3]. The theoretical prediction corresponding to the parameter Y/Tc=0.3 and reported in Fig. 3 describes qualitatively well the experimental results. The theoretical behaviour is reduced to Eq. (1) in the high-temperature phase [3]. In conclusion, we have measured the longitudinal elastic constant C Ort 22 along the b-axis of LaMnO3 in a large temperature range up to 800 K. A large softening of the elastic mode C Ort 22 is
357
observed at the structural phase transition TJT=750 K associated with the orbital order disorder transition.
References [1] See for a review Y. Tokura, N. Nagaosa, Science 288 (2000) 462. [2] A.J. Millis, Phys. Rev. B 53 (1996) 8434. [3] M. Kataoka, J. Phys. Soc. Jpn. 70 (2001) 2353. [4] M.C. Sanchez, G. Subias, J. Garcia, J. Blasco, Phys. Rev. Lett. 90 (2003) 045503. [5] Y. Murakami, J.P. Hill, D. Gibbs, M. Blume, I. Koytama, M. Tanaka, H. Kawata, T. Arima, Y. Tokura, K. Hirota, Y. Endoh, Phys.Rev. Lett. 81 (1998) 582. [6] J. Rodriguez-Carvajal, M. Hennion, F. Moussa, A.H. Mouden, L. Pinsard, A. Revcolevschi, Phys. Rev. B 57 (1998) R3189. [7] F. Moussa, M. Hennion, J. Rodriguez-Carvajal, H. Moudden, L. Pinsard, A. Revcolevschi, Phys. Rev. B 54 (1996) 15149. [8] T. Chatterji, F. Fauth, B. Ouladdiaf, P. Mandal, B. Ghost, Phys. Rev. B 68 (2003) 053406. [9] J.-S. Zhou, J.B. Goodenough, Phys. Rev. B 60 (1999) R15002. [10] H. Hazama, T. Goto, Y. Nemoto, Y. Tomioka, A. Asamitsu, T. Tokura, Phys. Rev. B 62 (2000) 15012. [11] T. Goto, B. Lu¨thi, Adv. in Phys. 52 (2003) 67. [12] B. Lu¨thi, W. Rehwal, in: K.A. Muller, H. Thomas (Eds.), Structural Phase Transition Topics in Current Physics vol. 23, Springer, Berlin, 1981, p. 131. [13] R.L. Melcher, in: W.P. Mason, R.N. Thurston (Eds.), Physical Acoustics vol. XII, Academic press, New York, 1976, p. 1. [14] H.J. McSkimin, in: W.P. Mason (Ed.), Physical Acoustics vol. IA, Academic Press, New York, 1964, p. 271.