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Time relaxation of dielectric constant in the commensurate phase of TlGaSe2
Solid State Communications 129 (2004) 761–764 www.elsevier.com/locate/ssc
Time relaxation of dielectric constant in the commensurate phase of TlGaSe2 F.A. Mikailova,b,*, E. Bas¸arana, E. S¸entu¨rka,c, L. Tu¨mbeka, T.G. Mammadovb, V.P. Alievb a
Department of Physics, Gebze Institute of Technology, Gebze, 41400 Kocaeli, Turkey b Institute of Physics, Azerbaijan Academy of Sciences, 370143 Baku, Azerbaijan c Department of Physics, Sakarya University, 54100 Sakarya, Turkey Received 3 December 2003; accepted 29 December 2003 by P. Wachter
Abstract The results of measurements of the time dependences of the dielectric constant of TlGaSe2 in the commensurate ferroelectric phase are presented. From the result of the observation of the decay of 1 at different stabilized temperatures below the commensurate phase transition temperature after cooling from the incommensurate phase, the presence of two different characteristic relaxation time constants with the same temperature behaviour has been revealed. This peculiarity is considered as a result of a coexistence of two polar sublattices in the temperature range below 110 K. According to these results, the previously reported dielectric anomaly at about 103 K is considered as a final lock-in phase transition accompanied by the forming of the antiferroelectric state in TlGaSe2. q 2004 Elsevier Ltd. All rights reserved. PACS: 77.80.B; 78.20.C; 61.44.F Keywords: A. Ferroelectrics; D. Dielectric response; D. Phase transitions
1. Introduction Much interest has recently focused on ternary layered chalcogenide TlGaSe2 compound, which possesses both ferroelectric and semiconductor properties and exhibits successive incommensurate and commensurate phase transitions [1 – 8]. TlGaSe2 crystallizes in monoclinic system 6 at room and belongs to a space symmetry group of C2h temperature [1]. The crystal structure of TlGaSe2 is characterized by metal-chalcogen layers composed of Ga4Se10 polyhedron complexes representing a combination of four elementary GaSe4 tetrahedra linked by common chalcogene atoms at the corners. Monovalent Tl ions are located in the trigonal cavities between metal-chalcogen * Corresponding author. Address: Department of Physics, Gebze Institute of Technology, Gebze, 41400 Kocaeli, Turkey. Tel.: þ 90262-6538497-1297; fax: þ90-262-6538490. E-mail address: [email protected] (F.A. Mikailov). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2003.12.034
layers. On cooling, TlGaSe2 crystal undergoes successive structural phase transitions to an incommensurate (at the temperature Ti , 120 K) and commensurate (at Tc , 107 K) phases [2]. According to the structural investigations [3], the transition to the incommensurate phase is associated with condensation of a soft mode at a point in the Brillouin zone characterized by qi ¼ ðd; d; 0:25Þ; where (d ¼ 0:02) is the incommensuration parameter. The commensurate ferroelectric phase transition at the temperature of Tc , 107 K is accompanied with condensation of the soft mode at qc ¼ ð0; 0; 0:25Þ and the quadrupling of the unit cell volume along the direction of perpendicular to the layers. However, the presence of the ferroelectric soft mode with Curie temperature at about Tc , 107 K and with the Curie constant , 103 was discovered as a result of submillimeter spectra and dielectric constant measurements [4]. The spontaneous polarization vector of the ferroelectric
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phase lies in the plane of layers. In addition to these successive phase transitions, a transition to a weak ferroelectric phase was recently observed by authors [5], which explained this result by using the model of two nonequivalent sublattices, proposed by Dvorak and Ishibashi [6]. The peculiarities and possible mechanisms of the successive phase transitions in TlGaSe2 were discussed in a number of publications published in recent years. A very interesting result has been observed in [7], after measuring the temperature dependencies of the dielectric constant of TlGaSe2 under bias electric field: the commensurate phase transition temperature exhibited unusual behaviour which is attributed to antiferroelectric one. The results of optical absorption [8], heat capacity [9] and acoustic emission [10] experiments revealed the presence of two additional phase transitions in TlGaSe2 at the temperatures about 101–103 K and 246– 253 K. Authors [10] reported that the phase transition takes place at about 246 K into the incommensurate phase, while the transition at 101 K reveals ferroelectric-commensurate peculiarities. As is known, the presence of incommensurately modulated structures in crystals leads to the occurrence of long-lived metastable states in the temperature interval of the successive commensurate phase transitions. This provokes a thermal hysteresis of the dielectric susceptibility, which has been observed for TlGaSe2 by authors [11]. A thermal hysteresis is usually attributed to defect-induced pinning of discommensurations, which prevents the crystal from reaching thermal equilibrium after the incommensurate – commensurate phase transition. A slow time evolution of the dielectric constant of TlInS2 while approaching thermal equilibrium attracts much interest because of its importance for understanding the kinetics of the commensurate phase transitions. The present paper reports the results of measurements of time dependencies of the dielectric constant of TlInS2 in the commensurate ferroelectric phase after cooling the crystal.
ments, which allowed to scan the temperature with a rate of about 0.2 K/min and to stabilize the temperature with accuracy better than 0.05 K. The temperature was measured by GaAlAs diode sensor with an accuracy of 0.01 K. The measurements were performed in the temperature range of 80– 300 K. The system was fully computer controlled. The software for controlling the experimental set-up was written by us in isual Borland Delphi programming language.
3. Results and discussion The temperature dependence of the dielectric constant of TlInS2 measured during cooling and heating cycles is shown in Fig. 1. As it is seen from the figure, the temperature dependence of the dielectric susceptibility exhibits a remarkable temperature hysteresis in the vicinity of phase transitions. Figure shows that the most prominent thermal hysteresis has been observed in the temperature interval is lower than the ferroelectric commensurate phase transition at Tc , 110 K: The observed phenomenon is attributed to the formation of long-living metastable states caused by pinning effects of a domain-like soliton structure. The presence of this state is an evidence of the coexistence of at least two different phases in the mentioned temperature range. The existence of the metastable chaotic state in the commensurate ferroelectric phase of TlGaSe2 has been proposed from Raman lineshape analysis in [12], and molecular luminescent marker measurements [13]. In order to check the relaxational behaviour of the metastable states and the kinetics of the phase transformations in the mentioned temperature interval, the time variation of the dielectric constant at different fixed temperatures in the range of 95 –105 K has been investigated. Measurements were performed at nine different temperatures. The sample was cooled from the paraelectric phase down to 110 K, then the temperature was stabilized and the time dependencies were measured. The results are
2. Experimental details The crystals were grown in evacuated quartz tubes by using a modified Bridgman method. The samples, in rectangular form, were oriented along the polar axis, which lies in the cleavage plane (the morphology of crystals permits cleavage to plane parallel plates with mirror-like surfaces). The plates were gently polished, cleaned and covered with silver paste. The dimensions of the electrodes were 5 £ 5 mm2 with an inter-electrode distance of 1 mm. Measurements of the real and imaginary parts of the dielectric susceptibility were performed with a HP 4194A Impedance Gain/Phase Analyser at frequency of 5 kHz. A closed-cycle helium cryostat system and Lakeshore 340 model temperature controller were used in the measure-
Fig. 1. Dielectric susceptibility versus temperature of TlGaSe2 on cooling and heating runs of 0.5 K/min at 5 kHz.
F.A. Mikailov et al. / Solid State Communications 129 (2004) 761–764
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presented in Fig. 2. The equilibrium values of the dielectric constant 11 at fixed temperatures have been chosen as the averages between the values of 1ðTÞ measured during heating and cooling. It is evident that the time evolution of 1 can be best fitted with: pffiffiffiffi 1t ¼ 11 þ ð10 2 11 Þexpð2 t=tÞ where 10 and 11 are the dielectric constant values at t ¼ 0 and t ¼ 1; respectively, t is a relaxation time constant. In order to evaluate the characteristic relaxation time constants, the {ln½ðð10 2 11 Þ=1t 2 11 }2 versus t curves have been constructed. The results are depicted in Fig. 3. All curves are seen to be linear functions of time. It is evident that the relaxation times can be obtained by determining the reciprocal values of the slope ratios of these lines. As is seen from the figure, there are two different relaxation behaviours for each of the time dependencies. Naturally, these relaxation times are connected with different phases coexisting in the mentioned temperature interval. Thus, it is possible to study the kinetics of the phase transformations by changing the temperature during the chaotic state using the temperature dependencies of the relaxation times. Finally, we can obtain information about the temperature evolution of the metastable state. The temperature dependencies of the relaxation times t1 and t2 are presented in Fig. 4. It is seen that by reducing the temperature from 110 K, both of relaxation times show a slight increase. As is seen from the figure, a considerable increase of the relaxation times takes place at the temperature about 103 K. After such behaviour the time constants saturate on further decreasing the temperature. Such a saturation of two different relaxation time constants can be treated as a result of the stabilization of two coexisting polar structures formed in a result of successive phase transitions at higher temperatures. It is worth to mention the fact, that the possibility of the coexistence of different polar regions in TlGaSe2 in the temperature
Fig. 2. Time dependences of the dielectric constant D1 ¼ ð1t 2 11 of TlInS2 at fixed temperatures inside the temperature interval 95 – 105 K after cooling the sample from the paraelectric state.
Fig. 3. Time dependences of ðln gÞ2 ðg ¼ ½ð10 2 11 Þ=ð1t 2 11 Þ in TlGaSe2.
interval below 95 K was suggested by authors [7] in a result of observing non-trivial dielectric hysteresis loops with four polarization regions. In a frame of this consideration and taking into account the temperature behaviour of the relaxation times presented in Fig. 4, we can make a suggestion about the character of anomalies of various physical properties at the temperature 103 K. On lowering the temperature below 110 K the transformation of the crystal structure to the chaotic state exists. This state is characterized by the coexistense of both the discommensurations (or solitons) of high temperature incommensurate state and the two different polar regions appeared during the phase transformation at 110 K. On further lowering the temperature the transformation from the chaotic to commensurate phase takes place at about 103 K, which can be treated also as a final lock-in transition.
Fig. 4. Temperature dependences of the relaxation times t1 and t2 of the coexisting phases in the metastable chaotic state of TlGaSe2.
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4. Conclusion Thus, from the results of above mentioned dielectric measurements one can make a suggestion about the coexistence of two lattice instabilities in this crystal, which brings to formation of two polar sublattices. This is another confirmation of the necessity of applying of the twosublattice model, suggested by authors [6], and applied to the crystal with the analogous structure TlInS2 in [14]. In this frame, the antiferroelectric properties in TlGaSe2, observed in [7] and the phase transition at 65 K, presented earlier by authors [5], can be successfully described in a frame of the model of strong-interacting two polar sublattices. The anomaly at 103 K observed recently by measurements of various physical properties of TlGaSe2 can be considered as a lock-in transition from metastable chaotic to commensurate antiferroelectric state.
References [1] W. Henkel, H.D. Hochheimer, C. Carlone, A. Werner, S. Ves, H.G.v. Schnering, Phys. Rev. B26 (1982) 3211.
[2] R.A. Aliev, K.R. Allakhverdiev, A.I. Baranov, N.R. Ivanov, R.M. Sardarly, Sov. Phys. Solid State 26 (1984) 775. [3] D.F. McMorrow, R.A. Cowley, P.D. Hatton, J. Banys, J. Phys.: Condens. Matter 2 (1990) 3699. [4] A.A. Volkov, Yu.G. Goncharov, G.V. Kozlov, S.P. Lebedev, A.M. Prokhorov, R.A. Aliev, K.R. Allakhverdiev, JETP Lett. 37 (1984) 517. [5] K.R. Allakhverdiev, F.M. Salaev, F.A. Mikailov, T.S. Mamedov, JETP Lett. 56 (1992) 153. [6] V. Dvorak, Y. Ishibashi, J. Phys. Soc. Jpn 41 (1976) 548. [7] K.R. Allakhverdiev, N.D. Akhmed-zade, T.G. Mamedov, T.S. Mamedov, M.Y. Seidov, Low Temp. Phys. 26 (2000) 56. [8] K.R. Allakhverdiev, M.A. Aldzanov, T.G. Mamedov, E.Yu. Salaev, Solid State Commun. 58 (1986) 295. [9] M.A. Aldzanov, N.G. Guseinov, Z.N. Mamedov, Phys. Status Solidi A 100 (1987) K145. [10] Y.P. Gololobov, V.M. Perga, I.N. Salivonov, E.E. Shchigol, Sov. Phys. Solid State 34 (1992) 59. [11] F.A. Mikailov, E. Bas¸aran, E. S¸entu¨rk, L. Tu¨mbek, T.G. Mammadov, V.P. Aliev, Phase Transitions 76 (12) (2003) 1057. [12] A.A. Anikeev, V.M. Burlakov, M.R. Yakheev, Phys. Solid State 32 (1990) 2131. [13] Y.P. Gololobov, S.A. Shilo, I.A. Yurchenko, Phys. Solid State 33 (9) (1991) 2781. [14] F.A. Mikailov, E. Bas¸aran, T.G. Mammadov, M.Yu. Seidov, E. S¸entu¨rk, Physica B 334/1-2 (2003) 13–20.
Time relaxation of dielectric constant in the commensurate phase of TlGaSe2 F.A. Mikailova,b,*, E. Bas¸arana, E. S¸entu¨rka,c, L. Tu¨mbeka, T.G. Mammadovb, V.P. Alievb a
Department of Physics, Gebze Institute of Technology, Gebze, 41400 Kocaeli, Turkey b Institute of Physics, Azerbaijan Academy of Sciences, 370143 Baku, Azerbaijan c Department of Physics, Sakarya University, 54100 Sakarya, Turkey Received 3 December 2003; accepted 29 December 2003 by P. Wachter
Abstract The results of measurements of the time dependences of the dielectric constant of TlGaSe2 in the commensurate ferroelectric phase are presented. From the result of the observation of the decay of 1 at different stabilized temperatures below the commensurate phase transition temperature after cooling from the incommensurate phase, the presence of two different characteristic relaxation time constants with the same temperature behaviour has been revealed. This peculiarity is considered as a result of a coexistence of two polar sublattices in the temperature range below 110 K. According to these results, the previously reported dielectric anomaly at about 103 K is considered as a final lock-in phase transition accompanied by the forming of the antiferroelectric state in TlGaSe2. q 2004 Elsevier Ltd. All rights reserved. PACS: 77.80.B; 78.20.C; 61.44.F Keywords: A. Ferroelectrics; D. Dielectric response; D. Phase transitions
1. Introduction Much interest has recently focused on ternary layered chalcogenide TlGaSe2 compound, which possesses both ferroelectric and semiconductor properties and exhibits successive incommensurate and commensurate phase transitions [1 – 8]. TlGaSe2 crystallizes in monoclinic system 6 at room and belongs to a space symmetry group of C2h temperature [1]. The crystal structure of TlGaSe2 is characterized by metal-chalcogen layers composed of Ga4Se10 polyhedron complexes representing a combination of four elementary GaSe4 tetrahedra linked by common chalcogene atoms at the corners. Monovalent Tl ions are located in the trigonal cavities between metal-chalcogen * Corresponding author. Address: Department of Physics, Gebze Institute of Technology, Gebze, 41400 Kocaeli, Turkey. Tel.: þ 90262-6538497-1297; fax: þ90-262-6538490. E-mail address: [email protected] (F.A. Mikailov). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2003.12.034
layers. On cooling, TlGaSe2 crystal undergoes successive structural phase transitions to an incommensurate (at the temperature Ti , 120 K) and commensurate (at Tc , 107 K) phases [2]. According to the structural investigations [3], the transition to the incommensurate phase is associated with condensation of a soft mode at a point in the Brillouin zone characterized by qi ¼ ðd; d; 0:25Þ; where (d ¼ 0:02) is the incommensuration parameter. The commensurate ferroelectric phase transition at the temperature of Tc , 107 K is accompanied with condensation of the soft mode at qc ¼ ð0; 0; 0:25Þ and the quadrupling of the unit cell volume along the direction of perpendicular to the layers. However, the presence of the ferroelectric soft mode with Curie temperature at about Tc , 107 K and with the Curie constant , 103 was discovered as a result of submillimeter spectra and dielectric constant measurements [4]. The spontaneous polarization vector of the ferroelectric
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F.A. Mikailov et al. / Solid State Communications 129 (2004) 761–764
phase lies in the plane of layers. In addition to these successive phase transitions, a transition to a weak ferroelectric phase was recently observed by authors [5], which explained this result by using the model of two nonequivalent sublattices, proposed by Dvorak and Ishibashi [6]. The peculiarities and possible mechanisms of the successive phase transitions in TlGaSe2 were discussed in a number of publications published in recent years. A very interesting result has been observed in [7], after measuring the temperature dependencies of the dielectric constant of TlGaSe2 under bias electric field: the commensurate phase transition temperature exhibited unusual behaviour which is attributed to antiferroelectric one. The results of optical absorption [8], heat capacity [9] and acoustic emission [10] experiments revealed the presence of two additional phase transitions in TlGaSe2 at the temperatures about 101–103 K and 246– 253 K. Authors [10] reported that the phase transition takes place at about 246 K into the incommensurate phase, while the transition at 101 K reveals ferroelectric-commensurate peculiarities. As is known, the presence of incommensurately modulated structures in crystals leads to the occurrence of long-lived metastable states in the temperature interval of the successive commensurate phase transitions. This provokes a thermal hysteresis of the dielectric susceptibility, which has been observed for TlGaSe2 by authors [11]. A thermal hysteresis is usually attributed to defect-induced pinning of discommensurations, which prevents the crystal from reaching thermal equilibrium after the incommensurate – commensurate phase transition. A slow time evolution of the dielectric constant of TlInS2 while approaching thermal equilibrium attracts much interest because of its importance for understanding the kinetics of the commensurate phase transitions. The present paper reports the results of measurements of time dependencies of the dielectric constant of TlInS2 in the commensurate ferroelectric phase after cooling the crystal.
ments, which allowed to scan the temperature with a rate of about 0.2 K/min and to stabilize the temperature with accuracy better than 0.05 K. The temperature was measured by GaAlAs diode sensor with an accuracy of 0.01 K. The measurements were performed in the temperature range of 80– 300 K. The system was fully computer controlled. The software for controlling the experimental set-up was written by us in isual Borland Delphi programming language.
3. Results and discussion The temperature dependence of the dielectric constant of TlInS2 measured during cooling and heating cycles is shown in Fig. 1. As it is seen from the figure, the temperature dependence of the dielectric susceptibility exhibits a remarkable temperature hysteresis in the vicinity of phase transitions. Figure shows that the most prominent thermal hysteresis has been observed in the temperature interval is lower than the ferroelectric commensurate phase transition at Tc , 110 K: The observed phenomenon is attributed to the formation of long-living metastable states caused by pinning effects of a domain-like soliton structure. The presence of this state is an evidence of the coexistence of at least two different phases in the mentioned temperature range. The existence of the metastable chaotic state in the commensurate ferroelectric phase of TlGaSe2 has been proposed from Raman lineshape analysis in [12], and molecular luminescent marker measurements [13]. In order to check the relaxational behaviour of the metastable states and the kinetics of the phase transformations in the mentioned temperature interval, the time variation of the dielectric constant at different fixed temperatures in the range of 95 –105 K has been investigated. Measurements were performed at nine different temperatures. The sample was cooled from the paraelectric phase down to 110 K, then the temperature was stabilized and the time dependencies were measured. The results are
2. Experimental details The crystals were grown in evacuated quartz tubes by using a modified Bridgman method. The samples, in rectangular form, were oriented along the polar axis, which lies in the cleavage plane (the morphology of crystals permits cleavage to plane parallel plates with mirror-like surfaces). The plates were gently polished, cleaned and covered with silver paste. The dimensions of the electrodes were 5 £ 5 mm2 with an inter-electrode distance of 1 mm. Measurements of the real and imaginary parts of the dielectric susceptibility were performed with a HP 4194A Impedance Gain/Phase Analyser at frequency of 5 kHz. A closed-cycle helium cryostat system and Lakeshore 340 model temperature controller were used in the measure-
Fig. 1. Dielectric susceptibility versus temperature of TlGaSe2 on cooling and heating runs of 0.5 K/min at 5 kHz.
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presented in Fig. 2. The equilibrium values of the dielectric constant 11 at fixed temperatures have been chosen as the averages between the values of 1ðTÞ measured during heating and cooling. It is evident that the time evolution of 1 can be best fitted with: pffiffiffiffi 1t ¼ 11 þ ð10 2 11 Þexpð2 t=tÞ where 10 and 11 are the dielectric constant values at t ¼ 0 and t ¼ 1; respectively, t is a relaxation time constant. In order to evaluate the characteristic relaxation time constants, the {ln½ðð10 2 11 Þ=1t 2 11 }2 versus t curves have been constructed. The results are depicted in Fig. 3. All curves are seen to be linear functions of time. It is evident that the relaxation times can be obtained by determining the reciprocal values of the slope ratios of these lines. As is seen from the figure, there are two different relaxation behaviours for each of the time dependencies. Naturally, these relaxation times are connected with different phases coexisting in the mentioned temperature interval. Thus, it is possible to study the kinetics of the phase transformations by changing the temperature during the chaotic state using the temperature dependencies of the relaxation times. Finally, we can obtain information about the temperature evolution of the metastable state. The temperature dependencies of the relaxation times t1 and t2 are presented in Fig. 4. It is seen that by reducing the temperature from 110 K, both of relaxation times show a slight increase. As is seen from the figure, a considerable increase of the relaxation times takes place at the temperature about 103 K. After such behaviour the time constants saturate on further decreasing the temperature. Such a saturation of two different relaxation time constants can be treated as a result of the stabilization of two coexisting polar structures formed in a result of successive phase transitions at higher temperatures. It is worth to mention the fact, that the possibility of the coexistence of different polar regions in TlGaSe2 in the temperature
Fig. 2. Time dependences of the dielectric constant D1 ¼ ð1t 2 11 of TlInS2 at fixed temperatures inside the temperature interval 95 – 105 K after cooling the sample from the paraelectric state.
Fig. 3. Time dependences of ðln gÞ2 ðg ¼ ½ð10 2 11 Þ=ð1t 2 11 Þ in TlGaSe2.
interval below 95 K was suggested by authors [7] in a result of observing non-trivial dielectric hysteresis loops with four polarization regions. In a frame of this consideration and taking into account the temperature behaviour of the relaxation times presented in Fig. 4, we can make a suggestion about the character of anomalies of various physical properties at the temperature 103 K. On lowering the temperature below 110 K the transformation of the crystal structure to the chaotic state exists. This state is characterized by the coexistense of both the discommensurations (or solitons) of high temperature incommensurate state and the two different polar regions appeared during the phase transformation at 110 K. On further lowering the temperature the transformation from the chaotic to commensurate phase takes place at about 103 K, which can be treated also as a final lock-in transition.
Fig. 4. Temperature dependences of the relaxation times t1 and t2 of the coexisting phases in the metastable chaotic state of TlGaSe2.
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4. Conclusion Thus, from the results of above mentioned dielectric measurements one can make a suggestion about the coexistence of two lattice instabilities in this crystal, which brings to formation of two polar sublattices. This is another confirmation of the necessity of applying of the twosublattice model, suggested by authors [6], and applied to the crystal with the analogous structure TlInS2 in [14]. In this frame, the antiferroelectric properties in TlGaSe2, observed in [7] and the phase transition at 65 K, presented earlier by authors [5], can be successfully described in a frame of the model of strong-interacting two polar sublattices. The anomaly at 103 K observed recently by measurements of various physical properties of TlGaSe2 can be considered as a lock-in transition from metastable chaotic to commensurate antiferroelectric state.
References [1] W. Henkel, H.D. Hochheimer, C. Carlone, A. Werner, S. Ves, H.G.v. Schnering, Phys. Rev. B26 (1982) 3211.
[2] R.A. Aliev, K.R. Allakhverdiev, A.I. Baranov, N.R. Ivanov, R.M. Sardarly, Sov. Phys. Solid State 26 (1984) 775. [3] D.F. McMorrow, R.A. Cowley, P.D. Hatton, J. Banys, J. Phys.: Condens. Matter 2 (1990) 3699. [4] A.A. Volkov, Yu.G. Goncharov, G.V. Kozlov, S.P. Lebedev, A.M. Prokhorov, R.A. Aliev, K.R. Allakhverdiev, JETP Lett. 37 (1984) 517. [5] K.R. Allakhverdiev, F.M. Salaev, F.A. Mikailov, T.S. Mamedov, JETP Lett. 56 (1992) 153. [6] V. Dvorak, Y. Ishibashi, J. Phys. Soc. Jpn 41 (1976) 548. [7] K.R. Allakhverdiev, N.D. Akhmed-zade, T.G. Mamedov, T.S. Mamedov, M.Y. Seidov, Low Temp. Phys. 26 (2000) 56. [8] K.R. Allakhverdiev, M.A. Aldzanov, T.G. Mamedov, E.Yu. Salaev, Solid State Commun. 58 (1986) 295. [9] M.A. Aldzanov, N.G. Guseinov, Z.N. Mamedov, Phys. Status Solidi A 100 (1987) K145. [10] Y.P. Gololobov, V.M. Perga, I.N. Salivonov, E.E. Shchigol, Sov. Phys. Solid State 34 (1992) 59. [11] F.A. Mikailov, E. Bas¸aran, E. S¸entu¨rk, L. Tu¨mbek, T.G. Mammadov, V.P. Aliev, Phase Transitions 76 (12) (2003) 1057. [12] A.A. Anikeev, V.M. Burlakov, M.R. Yakheev, Phys. Solid State 32 (1990) 2131. [13] Y.P. Gololobov, S.A. Shilo, I.A. Yurchenko, Phys. Solid State 33 (9) (1991) 2781. [14] F.A. Mikailov, E. Bas¸aran, T.G. Mammadov, M.Yu. Seidov, E. S¸entu¨rk, Physica B 334/1-2 (2003) 13–20.