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The relation between magnetoresistance and magnetocaloric effect in La0.85Ag0.15MnO3 manganite
Physica B 406 (2011) 1902–1905
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Physica B journal homepage: www.elsevier.com/locate/physb
The relation between magnetoresistance and magnetocaloric effect in La0.85Ag0.15MnO3 manganite A.G. Gamzatov n, A.B. Batdalov Amirkhanov Institute of Physics of Daghestan Scientific Center of RAS, Makhachkala 367003, Russia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 August 2010 Received in revised form 14 December 2010 Accepted 24 January 2011 Available online 24 February 2011
We present the temperature dependence of La0.85Ag0.15MnO3 resistivity in the temperature interval between 77 and 340 K and magnetic fields up to 26 kOe. We offer a method of separating tunnel magnetoresistance from total magnetoresistance. A change in both the magnetic entropy, which is caused by the magnetocaloric effect (MCE), and the magnetoresistance are shown to be connected through a simple relationship to La0.85Ag0.15MnO3. & 2011 Elsevier B.V. All rights reserved.
Keywords: Manganite Magnetoresistance Magnetocaloric effect
1. Introduction The effects of colossal magnetoresistance (CMR) and the magnetocaloric effect (MCE) are usually observed in manganites near magnetic phase transition temperatures. It is obvious that there exists a certain relationship between a change in magnetic entropy and the resistivity. The theoretical investigations of s–d exchange models [1], double exchange models [2] predict a temperatureindependent proportional constant between a change in magnetic entropy and resistivity. A relationship between resistivity and a change in magnetic entropy in manganites is given in Ref. [3], where the authors offered a new method for the estimation of the change in magnetic entropy from the data on the temperature and field dependencies of the specific resistance. In Ref. [4] it was shown that the relationship between the MCE and the magnetoresistance was observed not only in the manganites, but also for the samples of TmCu and TmAg. The authors in Ref. [5] showed that the relationship between the change in resistance and the change in magnetic entropy for La0.6Sr0.4CoO3, SrRuO3 and CoPt3 samples has a rather simple form: Dr DSM. We present the experimental results for the resistivity of La0.85Ag0.15MnO3 in the temperature interval between 77 and 340 K and magnetic fields up to 26 kOe and the analysis of r(T) data. A relationship connecting the magnetoresistance with a change in magnetic entropy for manganites is proposed.
n
Corresponding author. E-mail address: [email protected] (A.G. Gamzatov).
0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.01.075
According to Ref. [3], the correlation between DSM and r in manganites is Z H @ ln r DSM ðT,HÞ ¼ a dH, ð1Þ @T H 0 where the parameter a determines the magnetic properties of the sample and a ¼21.72 emu/g for La0.67Ca0.33MnO3 [3]. This relationship is valid in short temperature ranges near the magnetic phase transition temperature [3]. The values of DSM near TC derived by Eq. (1) and by the data on caloric measurements conforms to La0.9MnO3 well enough [6]. As mentioned above, the simplest correlation between Dr and DSM was suggested by the authors in Ref. [5], where the relationship between the entropy that changes because of the MCE, and the change in resistivity takes the form
rðT,HÞrðT,0Þ ¼ K½SðT,HÞSðT,0Þ,
ð2Þ
i.e., the relationship of the resistivity change to the change in magnetic entropy is a constant value that is independent from the temperature DH rsd ðTÞ=DH Smag ðTÞ ¼ K. This relationship is well satisfied for the samples La0.6Sr0.4CoO3, SrRuO3 and CoPt3, and poorly executed for polycrystalline manganite La0.825Sr0.175MnO3. The authors in Ref. [5] stated that the bad satisfiability of this relationship for La0.825Sr0.175MnO3 is connected with the occurrence of the electron phase separation and the additional magnetoresistance in manganites due to the Jahn–Teller effect. The direct proportional dependence between Dr and DSM for ferromagnetic compositions RAl2 (R¼ Pr, Nd, Tb, Dy, Ho, Er) was observed by the authors in Ref. [7] as well. Revealing the magnetic entropy change in manganites through resistivity data is considerably complicated. The fact is that the
A.G. Gamzatova, A.B. Batdalov / Physica B 406 (2011) 1902–1905
value of the MCE in magnetic materials is determined by the suppression of the spin-disordered state under the influence of the magnetic field, but such a suppression near the TC leads to the effect of colossal magnetoresistance in manganites. It is well known that besides the classical effect of magnetoresistance, (MRsd) other mechanisms (the Jahn–Teller effect, phase stratification, tunnel MR) contribute to the total magnetoresistance (MRtotal). In polycrystalline samples, the tunnel magnetoresistance (TMR) makes a contribution to MRtotal, which is based on the intergranular tunneling of current carriers through the grain limits and can reach significant values, especially at low temperatures [8–10]. Consequently, DSM values obtained by Eqs. (1) and (2) for polycrystalline manganites will not be reliable. At the same time, it is known that a number of ceramic manganites [11,12] show extensive MCE and CMR effects. The manganites doped with univalent ions of Ag, K, Na, etc. belong to this class of manganites, which could not be obtained in a monocrystalline state.
2. Result and discussions The value of the MCE is determined in granular magnetic structures, owing to the reorientation of the spins inside granules under the effect of the magnetic field. Because the probability of intergranular tunneling is determined by the mutual orientation of magnetic moments of the neighboring grains, the tunneling magnetoresistance, which is a consequence of processes occurring inside the granules, will not contribute significantly to the MCE value, i.e., DSM MRsd. The total magnetoresistance of granular ferromagnetic materials can be read as: MRtotal ¼MRsd þTMR, where TMR is a contribution caused by the intergrain tunneling of charge carriers. Then the relation between DSM and MRtotal for granular ferromagnetic manganites will have the form
TMRðTÞ ¼ ðð1 þP 2 Þ=ð1P 2 ÞÞ1,
ð5Þ
where P ¼ P0 ð1bT 3=2 Þ is the dependence of polarization on the temperature, b is a parameter depending on the type of material, and P0 is the total effective polarization of the spins at 0 K. Let us consider the mechanisms of the sharing of TMR from MRtotal by considering the example of the La0.85Ag0.15MnO3 sample using Eqs. (4) and (5). Fig. 1(a) shows the temperature dependence of the resistivity for La0.85Ag0.15MnO3 in the magnetic fields H¼ 0, 11, and 26 kOe and the temperature interval between 77 and 340 K. A temperature dependence of magnetoresistance for MRtotal in the fields of 11 and 26 kOe is presented there. As can be observed, a magnetoresistive effect near the metal-dielectric transition temperature approaches the values of 18% and 32% in fields of 11 and 26 kOe, respectively, and the magnetoresistive effect increases when temperature decreases. Such behavior is elicited by a dependence of tunneling between grains on the mutual orientation of magnetic moments of neighboring grains. Simultaneously, the magnetic field orienting the magnetic moments of neighboring grains results in an increase in tunneling, which means that the conductivity increases, i.e., the CMR effect occurs. Such a principle leads to an appearance of negative magnetoresistance far below TC, down to helium temperatures. Moreover
ð3Þ
where A is a parameter depending on the type of material, d ¼TMR/MRtotal, TMR-0 in monocrystals, and Eq. (3) takes the form of Eq. (2). In order to use Eq. (3), it is necessary to distinguish clearly the contributions from the TMR and MRsd. We are not aware of any experimental or theoretical work devoted to the separation of different contributions to the total magnetoresistance in magnetic materials, particularly in manganites. There are a great number of both theoretical and experimental studies, where the temperature motion of TMR has been analyzed in granular ferromagnets in broad temperature intervals [13–15], which could be used in the first approximation for manganites as well. The authors in Ref. [15] proposed an empirical relationship to describe the temperature dependence of magnetoresistance caused by intergranular spin-dependent tunneling in granular manganites: MR¼ (A þB/(1 T)), where A, B are the fitting constants. In Refs. [13,14] expressions were presented for the temperature dependence of the tunnel magnetoresistance of granular ferromagnets [13] and for the magnetic tunnel structure [14]. We will consider two different ideas proposed in those works for the separation of different contributions to the total magnetoresistance. According to Ref. [13] the temperature dependence of TMR for granular ferromagnets is determined by the expression TMRðT,HÞ ¼ P2 L2 ðm300 ð300=TÞ3=2 ðH=kTÞÞ,
Unlike in Ref. [13], another approach was used in Ref. [14] for the description of the tunnel magnetoresistance of magnetic tunnel structures; in the case of direct tunneling, the TMR temperature dependence will be as follows:
ð4Þ
where P is the spin polarization of conductivity electrons independent from the magnetic field, L(x) ¼coth(x) 1/x is the Langevin function where x ¼ m300 ð300=TÞ3=2 ðH=kTÞ, m300 is the fitting parameter defining a magnetic moment of granules and characterizing their sizes.
1.0
0.8
δ
DSM ¼ AðMRtotal TMRÞ or DSM ¼ A MRtotal ð1dÞ,
1903
0.6
0.4
0.2 100
150
200 T (K)
250
300
Fig. 1. (a) Temperature dependence of the resistivity of La0.85Ag0.15MnO3. On the right is shown the temperature dependence of MRtotal ¼(r0–rH)/r0 in a magnetic field H¼ 11 and 26 kOe. (b) Temperature dependence of the d parameter in a magnetic field H ¼11 kOe.
1904
A.G. Gamzatova, A.B. Batdalov / Physica B 406 (2011) 1902–1905
(see Fig. 1(a)), the tunnel contribution increases when the temperature decreases, because the probability of the tunneling carriers scattering at thermal fluctuations is lowered. As shown in Fig. 1(a) the TMR makes a significant contribution in MRtotal as well. A similar motion of the temperature dependence of the magnetoresistance is typical for most ceramic manganites. Obviously, the smaller the grain is, the greater the tunnel contribution in MRtotal will be [8,15]. An occurrence whereby d-1 can be observed under certain conditions near the TC, then DSM-0. Such cases occur in granular structures with friable packing and weak intergranular contacts. It is appropriate to say this about the MCE in one granule, and the total effect in this case will be fuzzy. Our attempts to measure the MCE of the sample with such a friable structure (La0.85Ag0.15MnO3), which was obtained by cold pressing under low pressure, showed through a direct method that the magnitude of the effect is much smaller than in dense ceramics and is strongly fuzzed. Fig. 1(b) shows the temperature dependence of the d. The experimental data was analyzed by Eqs. (4) and (5) for a temperature interval of 77–340 K, and the results are shown in Fig. 2(a). We assume that in using Eqs. (4) and (5) for an approximation of the experimental data of MRtotal(T), that the TMR temperature motion in manganites has either no features in
the transition region, or that these features are negligible. The temperature dependence of MRsd in the magnetic fields of 11 and 26 kOe obtained as MRsd ¼MRtotal(T)–TMR(T) is shown in Fig. 2(a). As seen in Fig. 2(a), a temperature motion of TMR(T) derived by Eq. (4) below 130 K disagrees strongly with the experimental findings, whereas Eq. (5) agrees well enough with the experimental data down to 77 K. It should be noted that the values of polarization degree P obtained from different models diverge. Therefore, according to the data in the model described by Eq. (4) PE0.4, and PE0.3 for the model described by Eq. (5). The analysis of r(T) behavior for La0.85Ag0.15MnO3 at low temperatures within a model of spin-polarized tunneling shows that PE0.6 at T¼5 K in a zero magnetic field [16]. This difference is connected to the approximation interval by means of Eqs. (4) and (5). Fig. 2(b) presents the temperature dependences of a change in magnetic entropy derived by Eqs. (1)–(3). In this figure, the temperature dependences of the MCE received from the data of the RT specific heat are shown DSM ðT,HÞ ¼ T12 ðCðT,HÞCðT,0ÞÞT 1 dT in the field of 11 kOe [11]. Fig. 2(b) proves that values of DSmax obtained by Eqs. (1)–(3) agree with caloric measurements near the TC. The data of caloric measurements diverge from DSM(T) behavior derived by Eqs. (1) and (2), when they are far from TC, especially when ToTC. Let us note that the correlation (2) reveals a large error for granular ferromagnetic materials when T4TC, while the results, which are obtained from Eq. (3) with the proportionality coefficient A¼14 J/kg K, agree well enough with the caloric measurement data for temperature intervals that are rather broad. Using Eq. (3), we calculate a change in the magnetic entropy in a field of 26 kOe, which is found to be 3.9 J/kg K; this is less than value of DSM ¼4.2 J/kg K obtained from direct measurements of magnetic entropy in the same magnetic field [11]. The results of the indirect methods will always differ from the results of direct measurements, thus DSM ¼4.8 J/kg K, which is obtained from the heat capacity data in magnetic field of 26 kOe [11], is several times higher than the results of direct measurements. Eq. (3) leads us to an interesting conclusion; the value of MRtotal ¼ ðr0 rH Þ=r0 r 1; the MCE cannot be larger than a certain constant value A in manganites at any value of the magnetic field, i.e., at MRtotal ¼ 1, DSM ¼A. The analyses in our previous work [9,11] showed that for La1 xAgxMnO3, the most permissible value of the MCE is about 14–15 J/kg K, and to achieve such a value of change in magnetic entropy, very strong magnetic fields are required. We should note that in manganites the field dependencies of the MCE and the CMR near the TC are saturated at fields of 40 kOe, and further growth of the magnetic field results only in a slight increase of the MCE value. The maximum MCE values vary within 5–10 J/kg K in fields of 50–90 kOe for caloric measurement data near the TC, DSM ¼10.2 J/kg K for La0.7Ca0.25Sr0.05MnO3 in a field of 50 kOe [17], and DSM ¼9.5 J/kg K for (La0.6Ca0.4)0.9Mn1.1O3 in a field of 90 kOe [18]. The maximum values of MCE in magnetic materials have been reported in a recent publication [19]. This work has presented an estimation of the maximum adiabatic change of the temperature per unit of the magnetic field, which can be achieved in magnetic materials, in principle. As shown in Ref. [19] DT can never exceed 18 K/T, and DT¼2.6–2.9 K/T for gadolinium. In conclusion, we note that Eq. (3) is yet another indirect method that determines the change in magnetic entropy from data of electrical measurements in manganites.
Fig. 2. (a) J—MRtotal experiment; a solid line means the approximation by formula (4) with the values of P¼ 0.41, m300 ¼1200 mB (mB – Bohr magneton); a dashed line marks the approximation by formula (5) with the values of P0 ¼0.32, b ¼ 3.42.10-8. ’—MRsd ¼MRtotal(T)–TMR(T), where instead of TMR(T) formula (5) was used. (b) Temperature dependence of DSM obtained by different methods.
Acknowledgment This study was supported by the Russian Foundation for Basic Research (Project no. 09-0896533), and the Program of the
A.G. Gamzatova, A.B. Batdalov / Physica B 406 (2011) 1902–1905
Physical Sciences Division of the Russian Academy of Sciences, titled ‘‘Highly Correlated Electrons in Solids and Structures’’. References [1] T. Kasuya, Prog. Theor. Phys. 16 (1956) 58. [2] K. Kubo, N. Ohata, J. Phys. Soc. Jpn. 33 (1972) 21. [3] C.M. Xiong, J.R. Sun, Y.F. Chen, B.G. Shen, J. Du, Y.X. Li, IEEE Trans. Magn. 41 (2005) 122. [4] R. Rawat, I. Das, J. Phys. Condens. Matter 13 (2001) L379. [5] N. Sakamoto, T. Kyomen, S. Tsubouchi, M. Itoh, Phys. Rev. B 69 (2004) 092401. [6] M. Patra, K. De, S. Majumdar, S. Giri, Appl. Phys. Lett. 94 (2009) 092506. [7] J.C.P. Campoy, E.J.R. Plaza, A.A. Coelho, S. Gama, Phys. Rev. B 74 (2006) 134410. [8] J. Yang, B.C. Zhao, R.L. Zhang, Y.Q. Ma, Z.G. Sheng, W.H. Song, Y.P. Suna, Solid State Commun. 132 (2004) 87. [9] I.K. Kamilov, A.G. Gamzatov, A.M. Aliev, A.B. Batdalov, Sh.B. Abdulvagidov, O.V. Melnikov, O.Y. Gorbenko, A.R. Kaul, J. Exp. Theor. Phys. 105 (2007) 774.
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[10] A.I. Tovstolytkin, V.M. Tsmots, L.I. Pan’kiv, P.G. Litovchenko, I.S. Pan’kiv, Low Temp. Phys. 36 (2010) 220. [11] I.K. Kamilov, A.G. Gamzatov, A.M. Aliev, A.B. Batdalov, A.A. Aliverdiev, Sh.B. Abdulvagidov, O.V. Melnikov, O.Y. Gorbenko, A.R. Kaul, J. Phys. D: Appl. Phys. 40 (2007) 4413. [12] I.K. Kamilov, A.G. Gamzatov, A.B. Batdalov, A.S. Mankevich, I.E. Korsakov, Phys. Solid State 52 (2010) 789. [13] E.Z. Meilikhov, JETP Lett. 69 (1999) 623. [14] Y. Lu, M. Tran, H. Jaffres, P. Seneor, C. Deranlot, F. Petroff, J.-M. George, B. Lepine, S. Ababou, G. Jezequel, Phys. Rev. Lett. 102 (2009) 176801. [15] S. Karmakar, S. Taran, B.K. Chaudhuri, Phys. Status Solidi (b) 241 (2004) 3563. [16] A.G. Gamzatov, A.B. Batdalov, O.V. Melnikov, O. Yu. Gorbenko, Low Temp. Phys. 35 (2009) 219. [17] Z.B. Guo, Y.W. Du, J.S. Zhu, H. Huang, W.P. Ding, D. Feng, Phys. Rev. Lett. 78 (1997) 1142. [18] E´.E. Zubov, R. Puzhnyak, V.P. Pashchenko, V.I. Mikha˘ılov, A. Esenchuk, S.F. Mironova, S. Pekhota, V.P. Dyakonov, V.N. Varyukhin, H. Szymczak, Phys. Solid State 51 (2009) 2090. [19] V.I. Zverev, A.M. Tishin, M.D. Kuz’min, J. Appl. Phys. 107 (2010) 043907.
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Physica B journal homepage: www.elsevier.com/locate/physb
The relation between magnetoresistance and magnetocaloric effect in La0.85Ag0.15MnO3 manganite A.G. Gamzatov n, A.B. Batdalov Amirkhanov Institute of Physics of Daghestan Scientific Center of RAS, Makhachkala 367003, Russia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 August 2010 Received in revised form 14 December 2010 Accepted 24 January 2011 Available online 24 February 2011
We present the temperature dependence of La0.85Ag0.15MnO3 resistivity in the temperature interval between 77 and 340 K and magnetic fields up to 26 kOe. We offer a method of separating tunnel magnetoresistance from total magnetoresistance. A change in both the magnetic entropy, which is caused by the magnetocaloric effect (MCE), and the magnetoresistance are shown to be connected through a simple relationship to La0.85Ag0.15MnO3. & 2011 Elsevier B.V. All rights reserved.
Keywords: Manganite Magnetoresistance Magnetocaloric effect
1. Introduction The effects of colossal magnetoresistance (CMR) and the magnetocaloric effect (MCE) are usually observed in manganites near magnetic phase transition temperatures. It is obvious that there exists a certain relationship between a change in magnetic entropy and the resistivity. The theoretical investigations of s–d exchange models [1], double exchange models [2] predict a temperatureindependent proportional constant between a change in magnetic entropy and resistivity. A relationship between resistivity and a change in magnetic entropy in manganites is given in Ref. [3], where the authors offered a new method for the estimation of the change in magnetic entropy from the data on the temperature and field dependencies of the specific resistance. In Ref. [4] it was shown that the relationship between the MCE and the magnetoresistance was observed not only in the manganites, but also for the samples of TmCu and TmAg. The authors in Ref. [5] showed that the relationship between the change in resistance and the change in magnetic entropy for La0.6Sr0.4CoO3, SrRuO3 and CoPt3 samples has a rather simple form: Dr DSM. We present the experimental results for the resistivity of La0.85Ag0.15MnO3 in the temperature interval between 77 and 340 K and magnetic fields up to 26 kOe and the analysis of r(T) data. A relationship connecting the magnetoresistance with a change in magnetic entropy for manganites is proposed.
n
Corresponding author. E-mail address: [email protected] (A.G. Gamzatov).
0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.01.075
According to Ref. [3], the correlation between DSM and r in manganites is Z H @ ln r DSM ðT,HÞ ¼ a dH, ð1Þ @T H 0 where the parameter a determines the magnetic properties of the sample and a ¼21.72 emu/g for La0.67Ca0.33MnO3 [3]. This relationship is valid in short temperature ranges near the magnetic phase transition temperature [3]. The values of DSM near TC derived by Eq. (1) and by the data on caloric measurements conforms to La0.9MnO3 well enough [6]. As mentioned above, the simplest correlation between Dr and DSM was suggested by the authors in Ref. [5], where the relationship between the entropy that changes because of the MCE, and the change in resistivity takes the form
rðT,HÞrðT,0Þ ¼ K½SðT,HÞSðT,0Þ,
ð2Þ
i.e., the relationship of the resistivity change to the change in magnetic entropy is a constant value that is independent from the temperature DH rsd ðTÞ=DH Smag ðTÞ ¼ K. This relationship is well satisfied for the samples La0.6Sr0.4CoO3, SrRuO3 and CoPt3, and poorly executed for polycrystalline manganite La0.825Sr0.175MnO3. The authors in Ref. [5] stated that the bad satisfiability of this relationship for La0.825Sr0.175MnO3 is connected with the occurrence of the electron phase separation and the additional magnetoresistance in manganites due to the Jahn–Teller effect. The direct proportional dependence between Dr and DSM for ferromagnetic compositions RAl2 (R¼ Pr, Nd, Tb, Dy, Ho, Er) was observed by the authors in Ref. [7] as well. Revealing the magnetic entropy change in manganites through resistivity data is considerably complicated. The fact is that the
A.G. Gamzatova, A.B. Batdalov / Physica B 406 (2011) 1902–1905
value of the MCE in magnetic materials is determined by the suppression of the spin-disordered state under the influence of the magnetic field, but such a suppression near the TC leads to the effect of colossal magnetoresistance in manganites. It is well known that besides the classical effect of magnetoresistance, (MRsd) other mechanisms (the Jahn–Teller effect, phase stratification, tunnel MR) contribute to the total magnetoresistance (MRtotal). In polycrystalline samples, the tunnel magnetoresistance (TMR) makes a contribution to MRtotal, which is based on the intergranular tunneling of current carriers through the grain limits and can reach significant values, especially at low temperatures [8–10]. Consequently, DSM values obtained by Eqs. (1) and (2) for polycrystalline manganites will not be reliable. At the same time, it is known that a number of ceramic manganites [11,12] show extensive MCE and CMR effects. The manganites doped with univalent ions of Ag, K, Na, etc. belong to this class of manganites, which could not be obtained in a monocrystalline state.
2. Result and discussions The value of the MCE is determined in granular magnetic structures, owing to the reorientation of the spins inside granules under the effect of the magnetic field. Because the probability of intergranular tunneling is determined by the mutual orientation of magnetic moments of the neighboring grains, the tunneling magnetoresistance, which is a consequence of processes occurring inside the granules, will not contribute significantly to the MCE value, i.e., DSM MRsd. The total magnetoresistance of granular ferromagnetic materials can be read as: MRtotal ¼MRsd þTMR, where TMR is a contribution caused by the intergrain tunneling of charge carriers. Then the relation between DSM and MRtotal for granular ferromagnetic manganites will have the form
TMRðTÞ ¼ ðð1 þP 2 Þ=ð1P 2 ÞÞ1,
ð5Þ
where P ¼ P0 ð1bT 3=2 Þ is the dependence of polarization on the temperature, b is a parameter depending on the type of material, and P0 is the total effective polarization of the spins at 0 K. Let us consider the mechanisms of the sharing of TMR from MRtotal by considering the example of the La0.85Ag0.15MnO3 sample using Eqs. (4) and (5). Fig. 1(a) shows the temperature dependence of the resistivity for La0.85Ag0.15MnO3 in the magnetic fields H¼ 0, 11, and 26 kOe and the temperature interval between 77 and 340 K. A temperature dependence of magnetoresistance for MRtotal in the fields of 11 and 26 kOe is presented there. As can be observed, a magnetoresistive effect near the metal-dielectric transition temperature approaches the values of 18% and 32% in fields of 11 and 26 kOe, respectively, and the magnetoresistive effect increases when temperature decreases. Such behavior is elicited by a dependence of tunneling between grains on the mutual orientation of magnetic moments of neighboring grains. Simultaneously, the magnetic field orienting the magnetic moments of neighboring grains results in an increase in tunneling, which means that the conductivity increases, i.e., the CMR effect occurs. Such a principle leads to an appearance of negative magnetoresistance far below TC, down to helium temperatures. Moreover
ð3Þ
where A is a parameter depending on the type of material, d ¼TMR/MRtotal, TMR-0 in monocrystals, and Eq. (3) takes the form of Eq. (2). In order to use Eq. (3), it is necessary to distinguish clearly the contributions from the TMR and MRsd. We are not aware of any experimental or theoretical work devoted to the separation of different contributions to the total magnetoresistance in magnetic materials, particularly in manganites. There are a great number of both theoretical and experimental studies, where the temperature motion of TMR has been analyzed in granular ferromagnets in broad temperature intervals [13–15], which could be used in the first approximation for manganites as well. The authors in Ref. [15] proposed an empirical relationship to describe the temperature dependence of magnetoresistance caused by intergranular spin-dependent tunneling in granular manganites: MR¼ (A þB/(1 T)), where A, B are the fitting constants. In Refs. [13,14] expressions were presented for the temperature dependence of the tunnel magnetoresistance of granular ferromagnets [13] and for the magnetic tunnel structure [14]. We will consider two different ideas proposed in those works for the separation of different contributions to the total magnetoresistance. According to Ref. [13] the temperature dependence of TMR for granular ferromagnets is determined by the expression TMRðT,HÞ ¼ P2 L2 ðm300 ð300=TÞ3=2 ðH=kTÞÞ,
Unlike in Ref. [13], another approach was used in Ref. [14] for the description of the tunnel magnetoresistance of magnetic tunnel structures; in the case of direct tunneling, the TMR temperature dependence will be as follows:
ð4Þ
where P is the spin polarization of conductivity electrons independent from the magnetic field, L(x) ¼coth(x) 1/x is the Langevin function where x ¼ m300 ð300=TÞ3=2 ðH=kTÞ, m300 is the fitting parameter defining a magnetic moment of granules and characterizing their sizes.
1.0
0.8
δ
DSM ¼ AðMRtotal TMRÞ or DSM ¼ A MRtotal ð1dÞ,
1903
0.6
0.4
0.2 100
150
200 T (K)
250
300
Fig. 1. (a) Temperature dependence of the resistivity of La0.85Ag0.15MnO3. On the right is shown the temperature dependence of MRtotal ¼(r0–rH)/r0 in a magnetic field H¼ 11 and 26 kOe. (b) Temperature dependence of the d parameter in a magnetic field H ¼11 kOe.
1904
A.G. Gamzatova, A.B. Batdalov / Physica B 406 (2011) 1902–1905
(see Fig. 1(a)), the tunnel contribution increases when the temperature decreases, because the probability of the tunneling carriers scattering at thermal fluctuations is lowered. As shown in Fig. 1(a) the TMR makes a significant contribution in MRtotal as well. A similar motion of the temperature dependence of the magnetoresistance is typical for most ceramic manganites. Obviously, the smaller the grain is, the greater the tunnel contribution in MRtotal will be [8,15]. An occurrence whereby d-1 can be observed under certain conditions near the TC, then DSM-0. Such cases occur in granular structures with friable packing and weak intergranular contacts. It is appropriate to say this about the MCE in one granule, and the total effect in this case will be fuzzy. Our attempts to measure the MCE of the sample with such a friable structure (La0.85Ag0.15MnO3), which was obtained by cold pressing under low pressure, showed through a direct method that the magnitude of the effect is much smaller than in dense ceramics and is strongly fuzzed. Fig. 1(b) shows the temperature dependence of the d. The experimental data was analyzed by Eqs. (4) and (5) for a temperature interval of 77–340 K, and the results are shown in Fig. 2(a). We assume that in using Eqs. (4) and (5) for an approximation of the experimental data of MRtotal(T), that the TMR temperature motion in manganites has either no features in
the transition region, or that these features are negligible. The temperature dependence of MRsd in the magnetic fields of 11 and 26 kOe obtained as MRsd ¼MRtotal(T)–TMR(T) is shown in Fig. 2(a). As seen in Fig. 2(a), a temperature motion of TMR(T) derived by Eq. (4) below 130 K disagrees strongly with the experimental findings, whereas Eq. (5) agrees well enough with the experimental data down to 77 K. It should be noted that the values of polarization degree P obtained from different models diverge. Therefore, according to the data in the model described by Eq. (4) PE0.4, and PE0.3 for the model described by Eq. (5). The analysis of r(T) behavior for La0.85Ag0.15MnO3 at low temperatures within a model of spin-polarized tunneling shows that PE0.6 at T¼5 K in a zero magnetic field [16]. This difference is connected to the approximation interval by means of Eqs. (4) and (5). Fig. 2(b) presents the temperature dependences of a change in magnetic entropy derived by Eqs. (1)–(3). In this figure, the temperature dependences of the MCE received from the data of the RT specific heat are shown DSM ðT,HÞ ¼ T12 ðCðT,HÞCðT,0ÞÞT 1 dT in the field of 11 kOe [11]. Fig. 2(b) proves that values of DSmax obtained by Eqs. (1)–(3) agree with caloric measurements near the TC. The data of caloric measurements diverge from DSM(T) behavior derived by Eqs. (1) and (2), when they are far from TC, especially when ToTC. Let us note that the correlation (2) reveals a large error for granular ferromagnetic materials when T4TC, while the results, which are obtained from Eq. (3) with the proportionality coefficient A¼14 J/kg K, agree well enough with the caloric measurement data for temperature intervals that are rather broad. Using Eq. (3), we calculate a change in the magnetic entropy in a field of 26 kOe, which is found to be 3.9 J/kg K; this is less than value of DSM ¼4.2 J/kg K obtained from direct measurements of magnetic entropy in the same magnetic field [11]. The results of the indirect methods will always differ from the results of direct measurements, thus DSM ¼4.8 J/kg K, which is obtained from the heat capacity data in magnetic field of 26 kOe [11], is several times higher than the results of direct measurements. Eq. (3) leads us to an interesting conclusion; the value of MRtotal ¼ ðr0 rH Þ=r0 r 1; the MCE cannot be larger than a certain constant value A in manganites at any value of the magnetic field, i.e., at MRtotal ¼ 1, DSM ¼A. The analyses in our previous work [9,11] showed that for La1 xAgxMnO3, the most permissible value of the MCE is about 14–15 J/kg K, and to achieve such a value of change in magnetic entropy, very strong magnetic fields are required. We should note that in manganites the field dependencies of the MCE and the CMR near the TC are saturated at fields of 40 kOe, and further growth of the magnetic field results only in a slight increase of the MCE value. The maximum MCE values vary within 5–10 J/kg K in fields of 50–90 kOe for caloric measurement data near the TC, DSM ¼10.2 J/kg K for La0.7Ca0.25Sr0.05MnO3 in a field of 50 kOe [17], and DSM ¼9.5 J/kg K for (La0.6Ca0.4)0.9Mn1.1O3 in a field of 90 kOe [18]. The maximum values of MCE in magnetic materials have been reported in a recent publication [19]. This work has presented an estimation of the maximum adiabatic change of the temperature per unit of the magnetic field, which can be achieved in magnetic materials, in principle. As shown in Ref. [19] DT can never exceed 18 K/T, and DT¼2.6–2.9 K/T for gadolinium. In conclusion, we note that Eq. (3) is yet another indirect method that determines the change in magnetic entropy from data of electrical measurements in manganites.
Fig. 2. (a) J—MRtotal experiment; a solid line means the approximation by formula (4) with the values of P¼ 0.41, m300 ¼1200 mB (mB – Bohr magneton); a dashed line marks the approximation by formula (5) with the values of P0 ¼0.32, b ¼ 3.42.10-8. ’—MRsd ¼MRtotal(T)–TMR(T), where instead of TMR(T) formula (5) was used. (b) Temperature dependence of DSM obtained by different methods.
Acknowledgment This study was supported by the Russian Foundation for Basic Research (Project no. 09-0896533), and the Program of the
A.G. Gamzatova, A.B. Batdalov / Physica B 406 (2011) 1902–1905
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