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Spin-polarized intergrain tunneling model for low-field magnetoresistance in polycrystalline manganites
Journal of Magnetism and Magnetic Materials 202 (1999) 405}409
Spin-polarized intergrain tunneling model for low-"eld magnetoresistance in polycrystalline manganites Pin Lyu, D.Y. Xing*, Jinming Dong Department of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People's Republic of China Received 4 January 1999; received in revised form 11 March 1999
Abstract Based on the spin-polarized intergrain tunneling, the origin of temperature-dependent low-"eld magnetoresistance (MR) is presented for the polycrystalline manganites. In consideration of the spin-#ip intergrain tunneling arising from the Mn ion impurities in the grain-boundary regions, it is shown that the variation of the electronic spin polarization and the inelastic intergrain tunneling induced by the collective excitations of local spins at the grain boundaries are simultaneously responsible for the rapid decay of the low-"eld MR ratio with increasing temperature. The theoretical results are in agreement with the experimental data of the polycrystalline manganites. 1999 Elsevier Science B.V. All rights reserved. PACS: 72.15.Gd; 75.30.Kz; 75.50.Cc Keywords: Spin-dependent tunneling; Low-"eld magnetoresistance; Perovskite manganite
1. Introduction A great deal of attention has recently been focused on the colossal magnetoresistance (CMR) in the perovskite manganites La A MnO with \V V A"Sr, Ca, Ba, Pb [1}4]. The single-crystal manganites and the epitaxial manganite "lms with a single grain boundary exhibit CMR e!ect near the Curie temperature ¹ when subjected to ap plied magnetic "elds of several tesla. The basic
* Corresponding author. Tel.: #86-25-359-6995; fax: #86-25330-0535. E-mail address: [email protected] (D.Y. Xing)
physics for the CMR e!ect is the strong Hund coupling and the double exchange mechanism [5}7]. Also, large low-"eld magnetoresistance (MR) e!ect was observed in the manganite ceramics [8] and the polycrystalline manganite "lms [9,10] at ¹(¹ , and the experiments have suc cessfully allowed the high-"eld CMR e!ect to be separated from the low-"eld MR e!ect using arti"cial grain boundaries [11,12]. It is obvious that the spin-polarized intergrain tunneling plays a crucial role in the low-"eld MR e!ect. A characteristic feature of the low-"eld MR is its rapid decay with increasing temperature, and the MR e!ect seems to vanish at a certain temperature below ¹ [8}10]. This temperature-dependent behavior of the low"eld MR is similar to that of the tunneling MR in
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 3 3 8 - 8
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the manganite tunnel junctions [13}16]. In spite of their completely di!erent forms, the origin of the low-"eld MR is expected to be interpreted by the same spin-dependent tunneling mechanism through the insulating layer in the manganite tunnel junctions and across the grain boundaries in the polycrystalline manganites [17]. In the previous work [18,19], we have presented the mechanism of the tunneling magnetoresistance and its temperature dependence for the manganite tunnel junctions. To fully understand the origin of temperature-dependent low-"eld MR and the role of the grain boundaries in the manganite ceramics and the polycrystalline manganite "lms, it is highly desirable to extend our work to be suitable for the polycrystalline manganite systems.
transformation is applied to Eq. (1):
ck
cos(h/2) sin(h/2) dk t " t , (2) ck !sin(h/2) cosh/2) dk s s where h is the relative angle of the magnetization directions of the two neighboring manganite grains, and may be controlled by an applied magnetic "eld via the domain-rotation process. Consequently, Eq. (1) is reduced to H " 2 kp N
h h ¹kp cos !ip¹ kp sin dRk cp N N 2 2
h h dRk cp #h.c. , # p¹kp sin #i¹ kp cos \N N 2 2 (3)
2. Spin-polarized intergrain tunneling model Let us consider two adjacent microcrystalline manganite grains separated by grain boundary. Each grain has its own magnetic domain. Electron tunneling across the grain boundary removes an electron with momentum p and spin p from one grain, and creates an electron in the other grain with momentum k and spin p for spin conservation or !p for spin #ipping. For collinear con"gurations, the tunneling Hamiltonian describing such an electron tunneling process is H " (¹kpcRk cp #i¹ kpcRk cp #h.c.), (1) 2 kp N N \N N N where ¹kp and ¹ kp are the spin-conserving and spin-#ip tunneling matrix elements, respectively. The imaginary i for the spin-#ip tunneling matrix element means the incoherence of the spin-conserving and spin-#ip tunneling processes. The spin-#ip tunneling term has been introduced to the tunneling Hamiltonian for the conventional ferromagnetic tunnel junctions [20] and the manganite tunnel junctions [18,19]. In order to get the general tunneling Hamiltonian in any magnetization con"gurations of the adjacent manganite grains, we take the spin quantization axis in each grain to be along its magnetization direction. The following well-known spinor
with p"1 (p"!1) in the round brackets of Eq. (3) for the subscript p in the operator cp representN ing the spin-up (spin-down) state. The electrons that participate in the tunneling current have their energies very near the chemical potential on both sides of the grain boundary. It is an adequate approximation to treat the transfer rates "¹kp" and "¹ kp" as their average values "¹" and "¹ ", respectively. Using the standard Green's function techniques [21], the tunneling conductance at zero bias is derived from Eq. (3) as
2pe "¹" G(h)"
h h cos #c sin [N (k)N (k) t t 2 2
h h #N (k)N (k)]# sin #c cos s s 2 2
;[N (k)N (k)#N (k)N (k)] , t s s t
(4)
where we have introduced the parameter c, de"ned by c""¹ "/"¹", to characterize the spin-#ip intergrain tunneling e!ect arising from the Mn ion impurities in the grain-boundary regions. N (k) t and N (k) are the majority and minority densities s of states at the chemical potential k for the e elec trons in the manganites, respectively. In consideration of the inelastic intergrain tunneling induced by the local spin collective excitations at the grain boundaries, c should be
P. Lyu et al. / Journal of Magnetism and Magnetic Materials 202 (1999) 405}409
renormalized as [19,22] gk ¹ c"c! ln(1!e\# I 2). pD
(5)
Here g is a parameter describing the inelastic intergrain tunneling e!ect. This inelastic tunneling process includes the spin #ipping due to the emission or absorption of the local spin collective excitations. D"D /1SX2, with D is the spin sti!ness of 1 1 the local spin collective excitation spectrum. E is the spin gap due to anisotropy. At low temperatures, we have 1SX2"S and D "DS, with S" 1 and D taken close to its measured value of the single-crystal bulk La A MnO [23,24]. \V V Then the conductance is rewritten as pe G(h)" "¹"[N (k)#N (k)] s t
;[1#P cos h#c(1!P cos h)],
(6)
where the electronic spin polarization P is N (k)!N (k) s . P" t (7) N (k)#N (k) t s The transmission coe$cient "¹" is proportional to exp(!2is) with the decaying wave vector i" (2mH(
pe G" "¹"[N (k)#N (k)] dhg(h) s t
;[1#P cos h#c(1!P cos h)],
(8)
where g(h) is distribution function. The average 1cos h2 is [25] 1cos h2"M,
(9)
where M is the relative magnetization of the system. In deriving Eq. (9) the correlation between the
407
magnetic moments of the neighboring grains is neglected. M is varied from 0 to 1 when the magnetic "eld is applied to the system from 0 to its saturated value. Finally, the system conductance is obtained as pe G" "¹"[N (k)#N (k)] s t
;[1#PM#c(1!PM)],
(10)
with the resistance given by R"1/G. According to its de"nition, *R/R "[R(0)!R(H)]/R(H), the MR ratio is given by *R (1!c)PM " . (11) R 1#c When the applied "eld reaches its saturated value, i.e., M"1, we have the maximum MR ratio,
*R (1!c)P " . (12) R 1#c It is easily seen that the formalism of the maximum MR for the polycrystalline manganites is di!erent from that for the manganite tunnel junctions [19], i.e., (*R/R ) "2(1!c)P/[(1!P)#c(1#P)]. This is due to their completely di!erent structures. In the manganites the electron-spin polarization is sensitively dependent on the variation of the electronic structure with temperature [26]. The relation of the spin polarization P and the electron normalized magnetization m(¹) in the manganites is obtained as [19] (1!m(¹) (1#m(¹)! P" . (1#m(¹)# (1!m(¹)
(13)
The normalized electron magnetization can be described by
¹!¹ h(¹!¹ ) (14) ¹ !¹ with ¹ ;¹ and h(x) being the unit step function, h(x)"1 for x'0 and h(x)"0 for x(0. This temperature dependence of the electron magnetization is in agreement with the experimental results. For ¹(¹ , we have m(¹)"1 and so P"100%, the manganites exhibiting the half-metallic feature m(¹)" 1!
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[26}29]. For ¹ (¹)¹ , the behavior of the electronic normalized magnetization m(¹) is expected to be similar to that of the bulk manganese perovskite La Sr MnO since there exists only the S# con"guration for the local spin and the itinerant electron due to the strong Hund coupling. When ¹'¹ , the electron spins become dis ordered and there is no electronic magnetization.
3. Results and discussions Fig. 1 shows our theoretical result (solid line) calculated from Eqs. (12)}(14) and the experimental data [8] of the low-"eld MR ratio for polycrystalline manganites La Sr MnO . It should be mentioned that the experimental data of the MR ratio in Ref. [8] have been transformed to be suitable for its present de"nition. We have chosen c"0.61 and g" . The c value suggests that there exists strong spin-#ip scattering by Mn ions [18,30] in the grain-boundary regions, and the g value has the same order of magnitude as that used for the manganite tunnel junctions [19] and the conventional ferromagnetic tunnel junctions [22]. The material parameters used in the numerical calculation are taken close to their single-crystal bulk values: D"8.0 meV, E "0.25 meV, ¹ "50 K, and ¹ "380 K. It is found that there is a good agreement between the theoretical and experimental results. At low temperatures ¹(¹ , the spin collective excitations can be described by the spin wave picture. The maximum MR ratio decreases steadily with increasing temperature due to the magnoninduced spin-#ip inelastic intergrain tunneling while the electron-spin polarization remains 100%. For ¹'¹ , however, not only the spin-#ip inelas tic intergrain tunneling induced by the spin collective excitations at the grain boundaries but also the decreasing of the electron-spin polarization with temperature are simultaneously responsible for the rapid decay of the MR ratio. In particular, the spin collective excitations at the grain boundaries and the impurity states of Mn ions in the grain-boundary regions are the main reasons that the magnetoresistance e!ect vanishes at about ¹+300 K lower than ¹ +380 K of La Sr MnO .
Fig. 1. Maximum low-"eld MR ratio versus temperature for the polycrystalline manganites. The points are experimental data taken from Ref. [8], and the solid line is the theoretical result calculated from Eqs. (12)}(14) using the parameters D"8.0 meV, E "0.25 meV, c"0.61, and g" .
Therefore, the rapid decay of the low-"eld MR ratio seems to be dominated by the joint e!ect of the variation of the electron-spin polarization with temperature and the spin collective excitations at the grain boundaries.
4. Summary We have presented the origin of temperaturedependent low-"eld magnetoresistance for the polycrystalline manganite systems. In consideration of the spin-#ip intergrain tunneling arising from the Mn ion impurities in the grain-boundary regions, it is shown that the variation of the electron-spin polarization and the inelastic intergrain tunneling induced by the collective excitations of local spins at the grain boundaries are simultaneously responsible for the rapid decay of the low"eld MR ratio with increasing temperature. The theoretical results are in agreement with the experimental data of the polycrystalline manganites. This indicates that there exits the same spin-dependent tunneling mechanism for the low-"eld MR in the manganite tunnel junctions, the manganite ceramics, and the polycrystalline manganite "lms in spite of their structures having di!erent forms.
P. Lyu et al. / Journal of Magnetism and Magnetic Materials 202 (1999) 405}409
The consideration on the spin-polarized intergrain tunneling presented above may be conducive to understanding and explanation of the low-"eld magnetoresistance e!ects observed recently in other interesting systems, such as half-metallic CrO "lms [31] and its powder compacts [32], the pyrochlore manganite Tl Mn O [33], and the or der double perovskite Sr FeMoO [34]. Acknowledgements This work was supported by the National Natural Science Foundation of China. One of the authors (P.L.) was also supported by Motorola Scholarship.
References [1] K. Chahara, T. Ohno, M. Kasai, Y. Kozono, Appl. Phys. Lett. 63 (1993) 1990. [2] R. von Helmolt, J. Wecker, B. Holzapfel, L. Schultz, K. Samwer, Phys. Rev. Lett. 71 (1993) 2331. [3] S. Jin, T.H. Tiefel, M. McCormack, R.A. Fastnacht, R. Ramesh, L.H. Chen, Science 264 (1994) 413. [4] A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, Phys. Rev. B 51 (1995) 14103. [5] C. Zener, Phys. Rev. 82 (1951) 403. [6] P.W. Anderson, H. Hasegawa, Phys. Rev. 100 (1955) 675. [7] P.G. de Gennes, Phys. Rev. 118 (1960) 141. [8] H.Y. Hwang, S.-W. Cheong, N.P. Ong, B. Batlogg, Phys. Rev. Lett. 77 (1996) 2041. [9] R. Shreekala, M. Rajeswari, K. Ghosh, A. Goyal, J.Y. Gu, C. Kwon, Z. Trajanovic, T. Boettcher, R.L. Greene, R. Ramesh, T. Venkatesan, Appl. Phys. Lett. 71 (1997) 282. [10] X.W. Li, A. Gupta, G. Xiao, G.Q. Gong, Appl. Phys. Lett. 71 (1997) 1124. [11] N.D. Mathur, G. Burnell, S.P. Isaac, T.J. Jackson, B.-S. Teo, J.L. MacManus-Driscoll, L.F. Cohen, J.E. Evetts, M.G. Blamire, Nature (London) 387 (1997) 266.
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[12] K. Steenbeck, T. Eick, K. Kirsch, K. O'Donnell, E. Steinbei, Appl. Phys. Lett. 71 (1997) 968. [13] Y. Lu, X.W. Li, G.Q. Gong, G. Xiao, A. Gupta, P. Lecoeur, J.Z. Sun, Y.Y. Wang, V.P. Dravid, Phys. Rev. B 54 (1996) R8357. [14] J.Z. Sun, W.J. Gallagher, P.R. Duncombe, L. KrusinElbaum, R.A. Altman, A. Gupta, Y. Lu, G.Q. Gong, G. Xiao, Appl. Phys. Lett. 69 (1996) 3266. [15] J.Z. Sun, L. Krusin-Elbaum, P.R. Duncombe, A. Gupta, R.B. Laibowitz, Appl. Phys. Lett. 70 (1997) 1769. [16] M. Viret, M. Drouet, J. Nassar, J.P. Contour, C. Fermon, A. Fert, Europhys. Lett. 39 (1997) 545. [17] J.-H. Park, E. Vescovo, H.-J. Kim, C. Kwon, R. Ramesh, T. Venkatesan, Phys. Rev. Lett. 81 (1998) 1953. [18] P. Lyu, D.Y. Xing, J. Dong, Phys. Rev. B 58 (1998) 54. [19] P. Lyu, D.Y. Xing, J. Dong, Phys. Rev. B, accepted for publication. [20] R.Y. Gu, D.Y. Xing, J. Dong, J. Appl. Phys. 80 (1996) 7163. [21] G.D. Mahan, Many-Particle Physics, Plenum, New York, 1981, p. 798. [22] S. Zhang, P.M. Levy, A.C. Marley, S.S.P. Parkin, Phys. Rev. Lett. 79 (1997) 3744. [23] M.C. Martin, G. Shirane, Y. Endoh, K. Hirota, Y. Moritomo, Y. Tokura, Phys. Rev. B 53 (1996) 14285. [24] T.G. Perring, G. Aeppli, S.M. Hayden, S.A. Carter, J.P. Remeika, S.-W. Cheong, Phys. Rev. Lett. 77 (1996) 711. [25] J. Inoue, S. Maekawa, Phys. Rev. B 53 (1996) R11927. [26] Y. Okimoto, T. Katsufuji, T. Ishikawa, A. Urushibara, T. Arima, Y. Tokura, Phys. Rev. Lett. 75 (1995) 109. [27] J.-H. Park, C.T. Chen, S.-W. Cheong, W. Bao, G. Meigs, Chakarian, Y.U. Idzerda, Phys. Rev. Lett. 76 (1996) 4215. [28] J.Y.T. Wei, N.-C. Yeh, R.P. Vasquez, Phys. Rev. Lett. 79 (1997) 5150. [29] J.-H. Park, E. Vescovo, H.-J. Kim, C. Kwon, R. Ramesh, T. Venkatesan, Nature (London) 392 (1998) 794. [30] F. Guinea, Phys. Rev. B 58 (1998) 9212. [31] H.Y. Hwang, S.-W. Cheong, Science 278 (1997) 1607. [32] J.M.D. Coey, A.E. Berkowitz, Ll. Balcells, F.F. Putris, A. Barry, Phys. Rev. lett. 80 (1998) 3815. [33] H.Y. Hwang, S.-W. Cheong, Nature (London) 389 (1997) 942. [34] K.-I. Kobayashi, T. Kimura, H. Sawada, K. Terakura, Y. Tokura, Nature (London) 395 (1998) 677.
Spin-polarized intergrain tunneling model for low-"eld magnetoresistance in polycrystalline manganites Pin Lyu, D.Y. Xing*, Jinming Dong Department of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People's Republic of China Received 4 January 1999; received in revised form 11 March 1999
Abstract Based on the spin-polarized intergrain tunneling, the origin of temperature-dependent low-"eld magnetoresistance (MR) is presented for the polycrystalline manganites. In consideration of the spin-#ip intergrain tunneling arising from the Mn ion impurities in the grain-boundary regions, it is shown that the variation of the electronic spin polarization and the inelastic intergrain tunneling induced by the collective excitations of local spins at the grain boundaries are simultaneously responsible for the rapid decay of the low-"eld MR ratio with increasing temperature. The theoretical results are in agreement with the experimental data of the polycrystalline manganites. 1999 Elsevier Science B.V. All rights reserved. PACS: 72.15.Gd; 75.30.Kz; 75.50.Cc Keywords: Spin-dependent tunneling; Low-"eld magnetoresistance; Perovskite manganite
1. Introduction A great deal of attention has recently been focused on the colossal magnetoresistance (CMR) in the perovskite manganites La A MnO with \V V A"Sr, Ca, Ba, Pb [1}4]. The single-crystal manganites and the epitaxial manganite "lms with a single grain boundary exhibit CMR e!ect near the Curie temperature ¹ when subjected to ap plied magnetic "elds of several tesla. The basic
* Corresponding author. Tel.: #86-25-359-6995; fax: #86-25330-0535. E-mail address: [email protected] (D.Y. Xing)
physics for the CMR e!ect is the strong Hund coupling and the double exchange mechanism [5}7]. Also, large low-"eld magnetoresistance (MR) e!ect was observed in the manganite ceramics [8] and the polycrystalline manganite "lms [9,10] at ¹(¹ , and the experiments have suc cessfully allowed the high-"eld CMR e!ect to be separated from the low-"eld MR e!ect using arti"cial grain boundaries [11,12]. It is obvious that the spin-polarized intergrain tunneling plays a crucial role in the low-"eld MR e!ect. A characteristic feature of the low-"eld MR is its rapid decay with increasing temperature, and the MR e!ect seems to vanish at a certain temperature below ¹ [8}10]. This temperature-dependent behavior of the low"eld MR is similar to that of the tunneling MR in
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 3 3 8 - 8
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P. Lyu et al. / Journal of Magnetism and Magnetic Materials 202 (1999) 405}409
the manganite tunnel junctions [13}16]. In spite of their completely di!erent forms, the origin of the low-"eld MR is expected to be interpreted by the same spin-dependent tunneling mechanism through the insulating layer in the manganite tunnel junctions and across the grain boundaries in the polycrystalline manganites [17]. In the previous work [18,19], we have presented the mechanism of the tunneling magnetoresistance and its temperature dependence for the manganite tunnel junctions. To fully understand the origin of temperature-dependent low-"eld MR and the role of the grain boundaries in the manganite ceramics and the polycrystalline manganite "lms, it is highly desirable to extend our work to be suitable for the polycrystalline manganite systems.
transformation is applied to Eq. (1):
ck
cos(h/2) sin(h/2) dk t " t , (2) ck !sin(h/2) cosh/2) dk s s where h is the relative angle of the magnetization directions of the two neighboring manganite grains, and may be controlled by an applied magnetic "eld via the domain-rotation process. Consequently, Eq. (1) is reduced to H " 2 kp N
h h ¹kp cos !ip¹ kp sin dRk cp N N 2 2
h h dRk cp #h.c. , # p¹kp sin #i¹ kp cos \N N 2 2 (3)
2. Spin-polarized intergrain tunneling model Let us consider two adjacent microcrystalline manganite grains separated by grain boundary. Each grain has its own magnetic domain. Electron tunneling across the grain boundary removes an electron with momentum p and spin p from one grain, and creates an electron in the other grain with momentum k and spin p for spin conservation or !p for spin #ipping. For collinear con"gurations, the tunneling Hamiltonian describing such an electron tunneling process is H " (¹kpcRk cp #i¹ kpcRk cp #h.c.), (1) 2 kp N N \N N N where ¹kp and ¹ kp are the spin-conserving and spin-#ip tunneling matrix elements, respectively. The imaginary i for the spin-#ip tunneling matrix element means the incoherence of the spin-conserving and spin-#ip tunneling processes. The spin-#ip tunneling term has been introduced to the tunneling Hamiltonian for the conventional ferromagnetic tunnel junctions [20] and the manganite tunnel junctions [18,19]. In order to get the general tunneling Hamiltonian in any magnetization con"gurations of the adjacent manganite grains, we take the spin quantization axis in each grain to be along its magnetization direction. The following well-known spinor
with p"1 (p"!1) in the round brackets of Eq. (3) for the subscript p in the operator cp representN ing the spin-up (spin-down) state. The electrons that participate in the tunneling current have their energies very near the chemical potential on both sides of the grain boundary. It is an adequate approximation to treat the transfer rates "¹kp" and "¹ kp" as their average values "¹" and "¹ ", respectively. Using the standard Green's function techniques [21], the tunneling conductance at zero bias is derived from Eq. (3) as
2pe "¹" G(h)"
h h cos #c sin [N (k)N (k) t t 2 2
h h #N (k)N (k)]# sin #c cos s s 2 2
;[N (k)N (k)#N (k)N (k)] , t s s t
(4)
where we have introduced the parameter c, de"ned by c""¹ "/"¹", to characterize the spin-#ip intergrain tunneling e!ect arising from the Mn ion impurities in the grain-boundary regions. N (k) t and N (k) are the majority and minority densities s of states at the chemical potential k for the e elec trons in the manganites, respectively. In consideration of the inelastic intergrain tunneling induced by the local spin collective excitations at the grain boundaries, c should be
P. Lyu et al. / Journal of Magnetism and Magnetic Materials 202 (1999) 405}409
renormalized as [19,22] gk ¹ c"c! ln(1!e\# I 2). pD
(5)
Here g is a parameter describing the inelastic intergrain tunneling e!ect. This inelastic tunneling process includes the spin #ipping due to the emission or absorption of the local spin collective excitations. D"D /1SX2, with D is the spin sti!ness of 1 1 the local spin collective excitation spectrum. E is the spin gap due to anisotropy. At low temperatures, we have 1SX2"S and D "DS, with S" 1 and D taken close to its measured value of the single-crystal bulk La A MnO [23,24]. \V V Then the conductance is rewritten as pe G(h)" "¹"[N (k)#N (k)] s t
;[1#P cos h#c(1!P cos h)],
(6)
where the electronic spin polarization P is N (k)!N (k) s . P" t (7) N (k)#N (k) t s The transmission coe$cient "¹" is proportional to exp(!2is) with the decaying wave vector i" (2mH(
pe G" "¹"[N (k)#N (k)] dhg(h) s t
;[1#P cos h#c(1!P cos h)],
(8)
where g(h) is distribution function. The average 1cos h2 is [25] 1cos h2"M,
(9)
where M is the relative magnetization of the system. In deriving Eq. (9) the correlation between the
407
magnetic moments of the neighboring grains is neglected. M is varied from 0 to 1 when the magnetic "eld is applied to the system from 0 to its saturated value. Finally, the system conductance is obtained as pe G" "¹"[N (k)#N (k)] s t
;[1#PM#c(1!PM)],
(10)
with the resistance given by R"1/G. According to its de"nition, *R/R "[R(0)!R(H)]/R(H), the MR ratio is given by *R (1!c)PM " . (11) R 1#c When the applied "eld reaches its saturated value, i.e., M"1, we have the maximum MR ratio,
*R (1!c)P " . (12) R 1#c It is easily seen that the formalism of the maximum MR for the polycrystalline manganites is di!erent from that for the manganite tunnel junctions [19], i.e., (*R/R ) "2(1!c)P/[(1!P)#c(1#P)]. This is due to their completely di!erent structures. In the manganites the electron-spin polarization is sensitively dependent on the variation of the electronic structure with temperature [26]. The relation of the spin polarization P and the electron normalized magnetization m(¹) in the manganites is obtained as [19] (1!m(¹) (1#m(¹)! P" . (1#m(¹)# (1!m(¹)
(13)
The normalized electron magnetization can be described by
¹!¹ h(¹!¹ ) (14) ¹ !¹ with ¹ ;¹ and h(x) being the unit step function, h(x)"1 for x'0 and h(x)"0 for x(0. This temperature dependence of the electron magnetization is in agreement with the experimental results. For ¹(¹ , we have m(¹)"1 and so P"100%, the manganites exhibiting the half-metallic feature m(¹)" 1!
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P. Lyu et al. / Journal of Magnetism and Magnetic Materials 202 (1999) 405}409
[26}29]. For ¹ (¹)¹ , the behavior of the electronic normalized magnetization m(¹) is expected to be similar to that of the bulk manganese perovskite La Sr MnO since there exists only the S# con"guration for the local spin and the itinerant electron due to the strong Hund coupling. When ¹'¹ , the electron spins become dis ordered and there is no electronic magnetization.
3. Results and discussions Fig. 1 shows our theoretical result (solid line) calculated from Eqs. (12)}(14) and the experimental data [8] of the low-"eld MR ratio for polycrystalline manganites La Sr MnO . It should be mentioned that the experimental data of the MR ratio in Ref. [8] have been transformed to be suitable for its present de"nition. We have chosen c"0.61 and g" . The c value suggests that there exists strong spin-#ip scattering by Mn ions [18,30] in the grain-boundary regions, and the g value has the same order of magnitude as that used for the manganite tunnel junctions [19] and the conventional ferromagnetic tunnel junctions [22]. The material parameters used in the numerical calculation are taken close to their single-crystal bulk values: D"8.0 meV, E "0.25 meV, ¹ "50 K, and ¹ "380 K. It is found that there is a good agreement between the theoretical and experimental results. At low temperatures ¹(¹ , the spin collective excitations can be described by the spin wave picture. The maximum MR ratio decreases steadily with increasing temperature due to the magnoninduced spin-#ip inelastic intergrain tunneling while the electron-spin polarization remains 100%. For ¹'¹ , however, not only the spin-#ip inelas tic intergrain tunneling induced by the spin collective excitations at the grain boundaries but also the decreasing of the electron-spin polarization with temperature are simultaneously responsible for the rapid decay of the MR ratio. In particular, the spin collective excitations at the grain boundaries and the impurity states of Mn ions in the grain-boundary regions are the main reasons that the magnetoresistance e!ect vanishes at about ¹+300 K lower than ¹ +380 K of La Sr MnO .
Fig. 1. Maximum low-"eld MR ratio versus temperature for the polycrystalline manganites. The points are experimental data taken from Ref. [8], and the solid line is the theoretical result calculated from Eqs. (12)}(14) using the parameters D"8.0 meV, E "0.25 meV, c"0.61, and g" .
Therefore, the rapid decay of the low-"eld MR ratio seems to be dominated by the joint e!ect of the variation of the electron-spin polarization with temperature and the spin collective excitations at the grain boundaries.
4. Summary We have presented the origin of temperaturedependent low-"eld magnetoresistance for the polycrystalline manganite systems. In consideration of the spin-#ip intergrain tunneling arising from the Mn ion impurities in the grain-boundary regions, it is shown that the variation of the electron-spin polarization and the inelastic intergrain tunneling induced by the collective excitations of local spins at the grain boundaries are simultaneously responsible for the rapid decay of the low"eld MR ratio with increasing temperature. The theoretical results are in agreement with the experimental data of the polycrystalline manganites. This indicates that there exits the same spin-dependent tunneling mechanism for the low-"eld MR in the manganite tunnel junctions, the manganite ceramics, and the polycrystalline manganite "lms in spite of their structures having di!erent forms.
P. Lyu et al. / Journal of Magnetism and Magnetic Materials 202 (1999) 405}409
The consideration on the spin-polarized intergrain tunneling presented above may be conducive to understanding and explanation of the low-"eld magnetoresistance e!ects observed recently in other interesting systems, such as half-metallic CrO "lms [31] and its powder compacts [32], the pyrochlore manganite Tl Mn O [33], and the or der double perovskite Sr FeMoO [34]. Acknowledgements This work was supported by the National Natural Science Foundation of China. One of the authors (P.L.) was also supported by Motorola Scholarship.
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