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Spin-dependent tunneling in dielectric LaSrMnO films with mesoscopic conducting clusters
Physics Letters A 325 (2004) 79–85 www.elsevier.com/locate/pla
Spin-dependent tunneling in dielectric LaSrMnO films with mesoscopic conducting clusters V.D. Okunev a , Z.A. Samoilenko a , A. Abal’oshev b , M. Baran b , M. Berkowski b , P. Gierłowski b , S.J. Lewandowski b,∗ , A. Szewczyk b , H. Szymczak b , R. Szymczak b a Donetsk Physico-Technical Institute, Ukrainian National Academy of Sciences, 340114 Donetsk, Ukraine b Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
Received 12 October 2003; received in revised form 13 December 2003; accepted 15 March 2004 Communicated by R. Wu
Abstract The structure and electrical properties of laser-ablated LaSrMnO thin films containing mesoscopic clusters with metallic conductivity in an insulator matrix were studied. It is shown that the film properties, including temperature dependence of magnetoresistance and its behavior in high magnetic field, display features typical for spin-dependent tunneling. 2004 Published by Elsevier B.V. PACS: 72.50.+b; 77.65.Dq; 75.30.Vn Keywords: Manganite thin films; Metallic clusters; Insulator matrix; Magnetic ordering; Conductivity; Tunneling
The basic physical properties of the perovskite manganites R1−x Ax MnO3 , where R is the trivalent rare-earth ion and A = Sr, Ca, Ba is the divalent alkaline-earth ion, are determined by the interaction of their electron and magnetic subsystems. The specific behavior of these compounds, including their colossal magnetoresistance (CMR), depends on their atomic order and the presence of compositional or structural inhomogeneities [1–4]. In polycrystalline and granular samples, the crucial role is played by spin-dependent tunneling [1–3]. We show that the effects related to spin-dependent tunneling appear also
* Corresponding author.
E-mail address: [email protected] (S.J. Lewandowski). 0375-9601/$ – see front matter 2004 Published by Elsevier B.V. doi:10.1016/j.physleta.2004.03.032
in epitaxial La0.6 Sr0.2 Mn1.2O3−δ (LSMO) thin films exhibiting high quality crystalline structure, and can be explained, together with other transport properties, by the presence of clusters with metallic conductivity embedded in the dielectric host matrix. The nonstoichiometric composition of the investigated films was found to amplify the processes of cluster formation. Apparently the excess manganese ions facilitate this metal–insulator phase separation in the investigated samples. The type and concentration of the metallic clusters depends on the growth conditions of the films. In general, pulsed laser deposition (PLD) favors cluster growth. We have grown a set of 100 nm thick LSMO samples by excimer (KrF) PLD [5]. The samples were deposited at oxygen pressure of 300 mTorr
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and favors a more effective realignment of the atomic order under the effect of changing external parameters, like temperature or applied magnetic field. XRD patterns of Fig. 1 show that Mn ions form Mn–O bonds and occupy sites in mesoscopic clusters coherently built into the host matrix [6]. No Debye lines corresponding to additional phase were seen: the film structure appears to be heterogeneous, but not heterophase. The changes in chemical composition of the samples affect only relative intensities of the diffraction lines, but not their positions. We contend that the excess manganese is spread more or less uniformly in the sample volume. Representing the stoichiometric LaSrMnO as a solid solution of two compounds described by a generalized chemical formula M2 O3 (M = La, Mn, Sr), i.e., writing La1−x Srx MnO3 = (LaMnO3 )1−x (SrMnO3 )x , it can be seen that indeed the excess manganese forms structural groups with similar chemical composition in the solid solution of three compounds Fig. 1. Typical X-ray diffraction spectra of a LaSrMnO thin film on SrLaGaO4 . Differences between films on SrLaGaO4 (Ts = 670 ◦ C) and Nd3 Ga5 O12 (Ts = 700 ◦ C) are shown in the inset. The two photograms are original Laue patterns for: the stoichiometric film on LaAlO3 (top), and non-stoichiometric one on SrLaGaO4 (bottom). Both show dominant crystallographic ordering in planes parallel to the film surface.
onto single-crystalline substrates with different interatomic layer spacing: SrLaGaO4 (SLG), Nd3 Ga5 O12 and Gd3 Ga5 O12 . The growth temperature varied between 600 and 730 ◦ C; no post-annealing was applied. The recorded X-ray diffraction (XRD) patterns are composed of very intense and sharp interference maxima and of additional diffusive maxima (see Fig. 1). Such features are characteristic for films, which essentially are single-crystalline (cf. the Laue patterns in Fig. 1), but contain mesoscopic regions (clusters), in which the long-range order is perturbed by topological or compositional changes that preserve the existing bonds to the host matrix [7]. These clusters have intermediate zones instead of well-defined borders, and the size of such peripheral regions is comparable to the cluster size. The absence of fixed and sharp borders excludes the mechanisms related to trapping and localization of free charge carriers in surface states, typically observed for crystalline and granular samples,
La1−2x Srx Mn1+x O3 = (LaMnO3 )1−2x (SrMnO3 )x (Mn2 O3 )x , where x = 0.2. Θ dependence of intensities in diffusive maxima (Fig. 1) shows, however, that manganese can enter the lattice in a variety of higher ionization states resulting in shortened lengths of Mn–O bonds. This, as discussed in more detail later in the text, introduces local crystallographic disorder and provides the mechanism of cluster formation and metallic phase separation. A careful analysis of the XRD data for films grown at substrate temperatures Ts in the 450–730 ◦ C range shows that Ts increase is accompanied by structural changes in the film. For Ts < 650 ◦ C, we observe ¯ rhomboedric only thin films with single-phase R3c ◦ structure, while for Ts > 670 C there exists only the orthorhombic Pnma structure. Between 650 and 670 ◦ C a mixture of these two commensurate phases can be seen. At 290 K, the resistivity ρ of our films varied from 3.6 × 10−2 to 1.0 × 102 cm. At 4.2 K, the resistivity range was wider, 3.6 × 10−3 to 1.4 × 103 cm. Resistance R in function of temperature T exhibited a maximum Rmx , characteristic for these compounds [8, 9], at T = Tmx ≈ Tc , the temperature below which the
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Fig. 2. Temperature dependence of resistivity for LaSrMnO thin films on SrLaGaO4 (continuous lines) and Gd3 Ga5 O12 (dashed lines). The dotted line represents temperature dependence of the magnetoresistance ρ/ρ0 = [ρ(H ) − ρ(H = 0)]/ρ(H = 0) for H = 0.376 T of a thin film grown at 730 ◦ C on SrLaGaO4 .
semiconductor-like behavior of R(T ) (dR/dT < 0) is replaced by a metallic behavior (dR/dT > 0) (see Fig. 2). However, the metal–insulator transition in the vicinity of the Curie temperature was not observed. The measured electrical conductivity σ falls well below the value of minimum metallic conductivity predicted by Mott [10] σmn =
2 πe2 (B/V0 )crit , 4zh¯ a
(1)
where z is the coordination number, a is the distance between doping centers, V0 is amplitude of the random potential, and B is the width of the band. For our LSMO samples, we can assume (B/V0 )crit ≈ 1/2, and then Mott’s formula (1) yields σmn of the order of 100 −1 cm−1 , a value in good agreement with the estimates given in Refs. [11,12]. The majority of our samples exhibited conductivity between one and four orders of magnitude below these estimates. The decrease of the resistance at T < Tmx can be related to the increase of the metallic phase concentration Cm caused by magnetic ordering [13]. Decreased amplitude of the random potential and, as a consequence, changed position of the hole mobility edge, can decrease the concentration of localized holes and increase the size of the metallic clusters.
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The measured dependence of σ on temperature and applied electric field allows to reject hopping as the dominant physical mechanism of electrical conductivity in our samples. Similarly, charge injection and space charge limited currents cannot play such role, as these mechanisms result in non-linear conductivity. In our case, the I–V characteristics were perfectly linear, and the conductivity remained constant under bias voltage (or current) changes extending to 3–4 orders of magnitude. This leaves only tunneling between metallic clusters embedded in the dielectric matrix as the possible conduction mechanism. In such a case, the temperature and magnetic field dependence of resistance must reflect the features of spin-dependent tunneling. This conclusion is indeed confirmed by the experimental data. The magnitude of magnetoresistance (see Fig. 2) decreases monotonically with increasing temperature, i.e., behaves as in polycrystalline or granular samples, in which the basic conductivity mechanism appears to be spin-dependent tunneling [1,3]. Our measurements (Fig. 3) show that the rate of change of magnetoresistance is maximal in low magnetic fields, another characteristic feature of spin-dependent tunneling [1–3]. The dR/dH curves differ significantly only in low magnetic fields, below 3 kOe (see lower part of Fig. 3). With decreasing temperature, the slope dR/dH initially increases, reaches a maximum at 50 K (in the area of the minimum on the R(T )-curve), and then decreases. This is in very good agreement with our measurements of magnetization in function of temperature, M(T ), for zero field cooled (ZFC) and field cooled (FC) samples. The ZFC and FC curves differ only in the region of low temperatures and low (< 1 kOe) fields. In this region the FC curves exhibit saturation, while the ZFC ones are bell-shaped (see Fig. 4); both these features are characteristic for clusterized spin glasses [4]. The results of X-ray measurements are also in good agreement with the conduction mechanism relying on the tunneling of electrons between metallic clusters through highly resistive layers within the dielectric. The resistivity in this mechanism is given by the exponential function ρ = ρ0 exp(d/d0 ),
(2)
where d is the average distance between clusters. Let us assume that the clusters can be considered as quasi
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Fig. 3. LaSrMnO film on SrLaGaO4 substrate (Ts = 730 ◦ C). (a) Isothermal dependence of resistance on magnetic field. (b) Derivatives of the curves shown in (a).
Fig. 4. Temperature dependence of magnetization in different applied magnetic fields in ZFC and FC regimes for LaSrMnO thin films: (a) Ts = 600 ◦ C, (b) Ts = 650 ◦ C.
two-dimensional plates of size D and thickness D/3, oriented parallel to the sample surface, and arranged in a regular lattice. Then there are n = 1/(d + D)3 clusters in one cubic centimeter of the sample, and the concentration Cm of the metallic phase is given by
diffraction maxima due to the metallic clusters to the total intensity of coherent scattering [5]. For calculations involving metallic clusters, we selected these diffusive reflexes, which corresponded to interplane distances approximately equal to the length of Mn–O bonds [14], represented in Fig. 1 by A1 (Θ = (30–33) deg) and A0 (Θ = (33–37) deg) Θ ranges. The diffusive maxima were well separated, since we used the long-wave (Cr) radiation. We have found also that the clusters form a quasi twodimensional arrangement of manganese–oxygen planes of the orthorhombic (O) and rhombohedric (R) phases: 202–O, 203–R, 400–R, 004–O. This observation justifies the assumption, which led to Eqs. (3), (4). Clus-
Cm = (1/3)D 3 (d + D)−3 , and the resistivity becomes D −1/3 ρ = ρ0 exp (3Cm ) −1 . d0
(3)
(4)
The concentration of the metallic phase Cm = 0.09–0.26 was determined from X-ray measurements by calculating the ratio of the total intensity of X-ray
V.D. Okunev et al. / Physics Letters A 325 (2004) 79–85
Fig. 5. Resistivity vs. metallic cluster spacing for LaSrMnO thin films on different substrates, measured at T = 290 K.
ter size (D = 70–160 Å, depending on the sample), was estimated by measuring half-width of the maxima [5]. The average cluster size was confirmed also by the results of mean-field analysis of magnetization, based on the procedure proposed in [15]. Another independent estimation of Cm was provided by measurements of optical attenuation on free charge carriers. More precisely, this method allows to evaluate the product pCm , where p is the hole concentration [7]. Taking into account these findings, the reason why metallic conductivity is not observed in our samples becomes clear. The concentration of the metallic phase, although relatively high, is still below the percolation threshold, which for two-dimensional objects is shifted into the 0.4–0.6 range [16]. The percolation approach to the conductivity of manganites is validated also by more rigorous theoretical considerations [17]. Experimental confirmation of the exponential dependence of resistivity on cluster spacing d determined from the X-ray measurements is shown for several samples in Fig. 5. In the (log ρ, d) coordinates, the data form two straight lines with different slopes. The lower line corresponds to thin films on SLG substrates, which apparently favor the growth of samples with lower resistivity. Both data sets extrapolate for d → 0 to ρ0 ≈ 0.012 cm.
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The differences in atomic ordering of the samples shown in Fig. 5 are reflected in the X-ray data of Fig. 1 by the position of diffusive scattering maxima generated by the clusters. In the case of films deposited on SLG or Nd3 Ga5 O12 , the diffusive maxima due to the Mn–O metallic clusters (hatched areas) exhibit different intensities in regions A1 and A0 . Assuming that the increase of diffraction angle Θ corresponds to the decrease of interplanar distance d (2d sin Θ = nλ) and that the length of the Mn–O bond decreases when the ionization of Mn increases from Mn2+ to Mn3+ , these results indicate that the clusters differ in local mesoscopic order. Let us observe that in the film on SLG, where I (A0 ) > I (A1 ), dominate the densely packed planes with highly ionized manganese Mn(3–4)+, what should enhance the conductivity. On the other hand, the films grown on Nd3 Ga5 O12 , exhibit I (A0 ) < I (A1 ), i.e., in these films prevail clusters with more widely spread planes and Mn2+ –Mn3+ ions, what should yield lower film conductivity. These conclusions are in good agreement with the measurement results presented in Fig. 5, where at the same cluster spacing the LSMO films on SLG show clearly lower resistivities than the films on Nd3 Ga5 O12 . Assuming that at temperatures Tmx the thermal energy is comparable to the coupling (tunneling) energy W between clusters, which depends exponentially on the cluster spacing d, we can write kTmx = W = W0 exp −(d/d1 ) .
(5)
Taking into account Eq. (2) we obtain a powerdependence of ρmx on Tmx σ (Tmx ) ∼ (kTmx )β , ρmx ∼ (kTmx )−β ,
β = d1 /d0 ,
(6)
which is confirmed by our measurements. The plot of ρmx (Tmx ) is shown in Fig. 6. Eq. (6) with β = 10.7 is seen to hold over four orders of magnitude in ρ. In the temperature interval T = Tmx − Tmn between the two R(T ) extrema, the atomic, electronic, and magnetic subsystems actively interact. Disorder in the whole system is reduced due to magnetic ordering. As a result, the amplitude of the random potential decreases, and this leads to lower sample resistivity. Experimental data (see inset in Fig. 5) indicate a linear
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−1/3 D(T ) 0 3 Cm + η(Tmx − T ) −1 . ρ = ρ0 exp d0 (11) According to this result ρmn should decrease exponentially with increasing temperature difference Tmx − Tmn , and indeed this was observed for our samples (see Fig. 6). Eq. (11) cannot be solved analytically to yield an explicit relation between ρmn and ρmx . However, the experimental data show a power-law behavior (see the inset in Fig. 6) ρmn = (ρmx )ξ ,
Fig. 6. Temperature dependence of extremal values of resistivity, ρmn and ρmx , for LaSrMnO thin films on different substrates. The inset shows ρmn (ρmx ) dependence; black triangles mark numerical data obtained from Eq. (11).
relationship between Tmx and Tmn Tmn = αTmx + γ ,
(7)
where α = −0.46 and γ = 154.32. One can examine also the relationship between ρmx and ρmn . Let us assume that Cm on cooling the sample below Tmx increases: 0 Cm → Cm (T ) = Cm + η(Tmx − T ),
We can write then −1/3 D 3Cm (T ) ρ = ρ0 exp −1 . d0
T Tmx .
(8)
(9)
However, the cluster size D may depend also on the concentration Cm . To account for this dependence, we can apply the results of percolation theory, and treat the variation of D in the same manner as the variation of the correlation radius [16]. We obtain then crit −ν , D → D(T ) ≈ D Cm (T ) − Cm (10) where ν = 0.85 is the critical exponent of the correlation radius, and D is some characteristic length. In this manner the final expression for resistivity can be written as
where ξ = 1.25, and can be fitted by substituting into Eq. (11) η = 0.0017 K−1 , D = 44.18 Å, ρ0 = crit = 0.5. 0.012 cm, Cm Finally, let us remark that the derivation of Eq. (9) relies on the hypothesis that cluster size is temperature dependent. This hypothesis is based on the measurement of film properties in applied magnetic field. Temperature and field dependence of magnetization, M(T , H ), in the FC regime depends on the size of FM clusters embedded into AFM matrix. The magnetization of the smallest clusters can be easily oriented along the applied magnetic field, even at relatively high temperatures (see Fig. 4(a), (b), H = 100 Oe). With the increase of cluster size (at higher magnetic fields), the system can be saturated only at low temperatures (cf. M(T ) curves at H = 100 and 1000 Oe). At even higher magnetic fields (see M(T ) curves at 10 kOe), the influence of magnetic ordering on the structure and the size of clusters is so strong that the system does not saturate even in very low temperatures. Thus, we can conclude that the cluster size increases with decreasing temperature and increasing magnetic field. In this manner, the presumption of labile configuration of cluster structure in the film is confirmed and can be used to justify the dependence of metallic phase concentration and cluster size on temperature as given in Eqs. (7) and (10), with subsequent description of experimental data by Eq. (11). In other words, we are dealing with phase separation phenomena nucleating on the different crystallographic phases present in the investigated films. To conclude, the observed properties of LSMO thin films can be explained by spin-dependent tunneling between metallic clusters and by applying the percolation theory-based approach.
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Acknowledgement This work was supported by Polish Government (KBN) Grants PBZ-KBN-013/T08/19 and 7 T08A 00520.
References [1] J.S. Helman, B. Abeles, Phys. Rev. Lett. 37 (1976) 1429. [2] S. Lee, H.Y. Hwang, B.I. Shraiman, W.D. Ratcliff II, S.W. Cheong, Phys. Rev. Lett. 82 (1999) 4508. [3] A. Gupta, J.Z. Sun, J. Magn. Magn. Mater. 200 (1999) 24. [4] R.V. Demin, L.I. Koroleva, R. Szymczak, H. Szymczak, JETP Lett. 75 (2002) 331. [5] V.D. Okunev, Z.A. Samoilenko, V.M. Svistunov, A. Abal’oshev, E. Dynowska, P. Gierłowski, A. Klimov, S.J. Lewandowski, J. Appl. Phys. 85 (1999) 7282. [6] V.P. Pashchenko, S.I. Khartsev, O.P. Cherenkov, A.A. Shemyakov, Z.A. Samoilenko, A.D. Loiko, V.I. Kamenev, Inorg. Mater. 35 (1999) 1294. [7] V.D. Okunev, Z.A. Samoilenko, A. Abal’oshev, P. Gierłowski, A. Klimov, S.J. Lewandowski, Appl. Phys. Lett. 75 (1999) 1949.
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[8] A.J. Millis, P.B. Littlewood, B.I. Shraiman Phys. Rev. Lett. 74 (1995) 5144. [9] M.B. Salamon, M. Jaime, Rev. Mod. Phys. 73 (2001) 583. [10] N.F. Mott, Metal–Insulator Transitions, Taylor & Francis, London, 1990. [11] A.E. Kar’kin, D.A. Shulyatev, A.A. Arsenov, V.A. Cherepanov, E.A. Filonova, JETP 89 (1999) 358, Zh. Eksp. Teor. Fiz. 116 (1999) 671 (in Russian). [12] Z.A. Samoilenko, V.D. Okunev, E.I. Pushenko, T.A. Djachenko, A. Cherenkov, P. Gierłowski, S.J. Lewandowski, A. Abal’oshev, A. Klimov, A. Szewczyk, Technol. Phys. 48 (2003) 250. [13] N.G. Bebenin, R.I. Zainullina, V.V. Mashkautsan, V.S. Gaviko, V.V. Ustinov, Ya.M. Mukovskii, D.A. Shulyatev, JETP 90 (2000) 1027, Zh. Eksp. Teor. Fiz. 117 (2000) 1181 (in Russian). [14] Q. Huang, A. Santoro, J.W. Lynn, R.W. Erwin, J.A. Borchers, J.L. Peng, R.L. Greene, Phys. Rev. B 55 (1997) 14987. [15] J.I. Gittleman, Y. Goldstein, S. Bozowic, Phys. Rev. B 5 (1972) 3609. [16] B.I. Shklovskii, A.L. Efros, Electronic Properties of Doped Semiconductors, Springer-Verlag, Berlin, 1984. [17] L.P. Gor’kov, V.Z. Kresin, JETP Lett. 67 (1998) 985; M.O. Dzero, L.P. Gor’kov, V.Z. Kresin, Eur. Phys. J. B 14 (2000) 459.
Spin-dependent tunneling in dielectric LaSrMnO films with mesoscopic conducting clusters V.D. Okunev a , Z.A. Samoilenko a , A. Abal’oshev b , M. Baran b , M. Berkowski b , P. Gierłowski b , S.J. Lewandowski b,∗ , A. Szewczyk b , H. Szymczak b , R. Szymczak b a Donetsk Physico-Technical Institute, Ukrainian National Academy of Sciences, 340114 Donetsk, Ukraine b Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
Received 12 October 2003; received in revised form 13 December 2003; accepted 15 March 2004 Communicated by R. Wu
Abstract The structure and electrical properties of laser-ablated LaSrMnO thin films containing mesoscopic clusters with metallic conductivity in an insulator matrix were studied. It is shown that the film properties, including temperature dependence of magnetoresistance and its behavior in high magnetic field, display features typical for spin-dependent tunneling. 2004 Published by Elsevier B.V. PACS: 72.50.+b; 77.65.Dq; 75.30.Vn Keywords: Manganite thin films; Metallic clusters; Insulator matrix; Magnetic ordering; Conductivity; Tunneling
The basic physical properties of the perovskite manganites R1−x Ax MnO3 , where R is the trivalent rare-earth ion and A = Sr, Ca, Ba is the divalent alkaline-earth ion, are determined by the interaction of their electron and magnetic subsystems. The specific behavior of these compounds, including their colossal magnetoresistance (CMR), depends on their atomic order and the presence of compositional or structural inhomogeneities [1–4]. In polycrystalline and granular samples, the crucial role is played by spin-dependent tunneling [1–3]. We show that the effects related to spin-dependent tunneling appear also
* Corresponding author.
E-mail address: [email protected] (S.J. Lewandowski). 0375-9601/$ – see front matter 2004 Published by Elsevier B.V. doi:10.1016/j.physleta.2004.03.032
in epitaxial La0.6 Sr0.2 Mn1.2O3−δ (LSMO) thin films exhibiting high quality crystalline structure, and can be explained, together with other transport properties, by the presence of clusters with metallic conductivity embedded in the dielectric host matrix. The nonstoichiometric composition of the investigated films was found to amplify the processes of cluster formation. Apparently the excess manganese ions facilitate this metal–insulator phase separation in the investigated samples. The type and concentration of the metallic clusters depends on the growth conditions of the films. In general, pulsed laser deposition (PLD) favors cluster growth. We have grown a set of 100 nm thick LSMO samples by excimer (KrF) PLD [5]. The samples were deposited at oxygen pressure of 300 mTorr
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and favors a more effective realignment of the atomic order under the effect of changing external parameters, like temperature or applied magnetic field. XRD patterns of Fig. 1 show that Mn ions form Mn–O bonds and occupy sites in mesoscopic clusters coherently built into the host matrix [6]. No Debye lines corresponding to additional phase were seen: the film structure appears to be heterogeneous, but not heterophase. The changes in chemical composition of the samples affect only relative intensities of the diffraction lines, but not their positions. We contend that the excess manganese is spread more or less uniformly in the sample volume. Representing the stoichiometric LaSrMnO as a solid solution of two compounds described by a generalized chemical formula M2 O3 (M = La, Mn, Sr), i.e., writing La1−x Srx MnO3 = (LaMnO3 )1−x (SrMnO3 )x , it can be seen that indeed the excess manganese forms structural groups with similar chemical composition in the solid solution of three compounds Fig. 1. Typical X-ray diffraction spectra of a LaSrMnO thin film on SrLaGaO4 . Differences between films on SrLaGaO4 (Ts = 670 ◦ C) and Nd3 Ga5 O12 (Ts = 700 ◦ C) are shown in the inset. The two photograms are original Laue patterns for: the stoichiometric film on LaAlO3 (top), and non-stoichiometric one on SrLaGaO4 (bottom). Both show dominant crystallographic ordering in planes parallel to the film surface.
onto single-crystalline substrates with different interatomic layer spacing: SrLaGaO4 (SLG), Nd3 Ga5 O12 and Gd3 Ga5 O12 . The growth temperature varied between 600 and 730 ◦ C; no post-annealing was applied. The recorded X-ray diffraction (XRD) patterns are composed of very intense and sharp interference maxima and of additional diffusive maxima (see Fig. 1). Such features are characteristic for films, which essentially are single-crystalline (cf. the Laue patterns in Fig. 1), but contain mesoscopic regions (clusters), in which the long-range order is perturbed by topological or compositional changes that preserve the existing bonds to the host matrix [7]. These clusters have intermediate zones instead of well-defined borders, and the size of such peripheral regions is comparable to the cluster size. The absence of fixed and sharp borders excludes the mechanisms related to trapping and localization of free charge carriers in surface states, typically observed for crystalline and granular samples,
La1−2x Srx Mn1+x O3 = (LaMnO3 )1−2x (SrMnO3 )x (Mn2 O3 )x , where x = 0.2. Θ dependence of intensities in diffusive maxima (Fig. 1) shows, however, that manganese can enter the lattice in a variety of higher ionization states resulting in shortened lengths of Mn–O bonds. This, as discussed in more detail later in the text, introduces local crystallographic disorder and provides the mechanism of cluster formation and metallic phase separation. A careful analysis of the XRD data for films grown at substrate temperatures Ts in the 450–730 ◦ C range shows that Ts increase is accompanied by structural changes in the film. For Ts < 650 ◦ C, we observe ¯ rhomboedric only thin films with single-phase R3c ◦ structure, while for Ts > 670 C there exists only the orthorhombic Pnma structure. Between 650 and 670 ◦ C a mixture of these two commensurate phases can be seen. At 290 K, the resistivity ρ of our films varied from 3.6 × 10−2 to 1.0 × 102 cm. At 4.2 K, the resistivity range was wider, 3.6 × 10−3 to 1.4 × 103 cm. Resistance R in function of temperature T exhibited a maximum Rmx , characteristic for these compounds [8, 9], at T = Tmx ≈ Tc , the temperature below which the
V.D. Okunev et al. / Physics Letters A 325 (2004) 79–85
Fig. 2. Temperature dependence of resistivity for LaSrMnO thin films on SrLaGaO4 (continuous lines) and Gd3 Ga5 O12 (dashed lines). The dotted line represents temperature dependence of the magnetoresistance ρ/ρ0 = [ρ(H ) − ρ(H = 0)]/ρ(H = 0) for H = 0.376 T of a thin film grown at 730 ◦ C on SrLaGaO4 .
semiconductor-like behavior of R(T ) (dR/dT < 0) is replaced by a metallic behavior (dR/dT > 0) (see Fig. 2). However, the metal–insulator transition in the vicinity of the Curie temperature was not observed. The measured electrical conductivity σ falls well below the value of minimum metallic conductivity predicted by Mott [10] σmn =
2 πe2 (B/V0 )crit , 4zh¯ a
(1)
where z is the coordination number, a is the distance between doping centers, V0 is amplitude of the random potential, and B is the width of the band. For our LSMO samples, we can assume (B/V0 )crit ≈ 1/2, and then Mott’s formula (1) yields σmn of the order of 100 −1 cm−1 , a value in good agreement with the estimates given in Refs. [11,12]. The majority of our samples exhibited conductivity between one and four orders of magnitude below these estimates. The decrease of the resistance at T < Tmx can be related to the increase of the metallic phase concentration Cm caused by magnetic ordering [13]. Decreased amplitude of the random potential and, as a consequence, changed position of the hole mobility edge, can decrease the concentration of localized holes and increase the size of the metallic clusters.
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The measured dependence of σ on temperature and applied electric field allows to reject hopping as the dominant physical mechanism of electrical conductivity in our samples. Similarly, charge injection and space charge limited currents cannot play such role, as these mechanisms result in non-linear conductivity. In our case, the I–V characteristics were perfectly linear, and the conductivity remained constant under bias voltage (or current) changes extending to 3–4 orders of magnitude. This leaves only tunneling between metallic clusters embedded in the dielectric matrix as the possible conduction mechanism. In such a case, the temperature and magnetic field dependence of resistance must reflect the features of spin-dependent tunneling. This conclusion is indeed confirmed by the experimental data. The magnitude of magnetoresistance (see Fig. 2) decreases monotonically with increasing temperature, i.e., behaves as in polycrystalline or granular samples, in which the basic conductivity mechanism appears to be spin-dependent tunneling [1,3]. Our measurements (Fig. 3) show that the rate of change of magnetoresistance is maximal in low magnetic fields, another characteristic feature of spin-dependent tunneling [1–3]. The dR/dH curves differ significantly only in low magnetic fields, below 3 kOe (see lower part of Fig. 3). With decreasing temperature, the slope dR/dH initially increases, reaches a maximum at 50 K (in the area of the minimum on the R(T )-curve), and then decreases. This is in very good agreement with our measurements of magnetization in function of temperature, M(T ), for zero field cooled (ZFC) and field cooled (FC) samples. The ZFC and FC curves differ only in the region of low temperatures and low (< 1 kOe) fields. In this region the FC curves exhibit saturation, while the ZFC ones are bell-shaped (see Fig. 4); both these features are characteristic for clusterized spin glasses [4]. The results of X-ray measurements are also in good agreement with the conduction mechanism relying on the tunneling of electrons between metallic clusters through highly resistive layers within the dielectric. The resistivity in this mechanism is given by the exponential function ρ = ρ0 exp(d/d0 ),
(2)
where d is the average distance between clusters. Let us assume that the clusters can be considered as quasi
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Fig. 3. LaSrMnO film on SrLaGaO4 substrate (Ts = 730 ◦ C). (a) Isothermal dependence of resistance on magnetic field. (b) Derivatives of the curves shown in (a).
Fig. 4. Temperature dependence of magnetization in different applied magnetic fields in ZFC and FC regimes for LaSrMnO thin films: (a) Ts = 600 ◦ C, (b) Ts = 650 ◦ C.
two-dimensional plates of size D and thickness D/3, oriented parallel to the sample surface, and arranged in a regular lattice. Then there are n = 1/(d + D)3 clusters in one cubic centimeter of the sample, and the concentration Cm of the metallic phase is given by
diffraction maxima due to the metallic clusters to the total intensity of coherent scattering [5]. For calculations involving metallic clusters, we selected these diffusive reflexes, which corresponded to interplane distances approximately equal to the length of Mn–O bonds [14], represented in Fig. 1 by A1 (Θ = (30–33) deg) and A0 (Θ = (33–37) deg) Θ ranges. The diffusive maxima were well separated, since we used the long-wave (Cr) radiation. We have found also that the clusters form a quasi twodimensional arrangement of manganese–oxygen planes of the orthorhombic (O) and rhombohedric (R) phases: 202–O, 203–R, 400–R, 004–O. This observation justifies the assumption, which led to Eqs. (3), (4). Clus-
Cm = (1/3)D 3 (d + D)−3 , and the resistivity becomes D −1/3 ρ = ρ0 exp (3Cm ) −1 . d0
(3)
(4)
The concentration of the metallic phase Cm = 0.09–0.26 was determined from X-ray measurements by calculating the ratio of the total intensity of X-ray
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Fig. 5. Resistivity vs. metallic cluster spacing for LaSrMnO thin films on different substrates, measured at T = 290 K.
ter size (D = 70–160 Å, depending on the sample), was estimated by measuring half-width of the maxima [5]. The average cluster size was confirmed also by the results of mean-field analysis of magnetization, based on the procedure proposed in [15]. Another independent estimation of Cm was provided by measurements of optical attenuation on free charge carriers. More precisely, this method allows to evaluate the product pCm , where p is the hole concentration [7]. Taking into account these findings, the reason why metallic conductivity is not observed in our samples becomes clear. The concentration of the metallic phase, although relatively high, is still below the percolation threshold, which for two-dimensional objects is shifted into the 0.4–0.6 range [16]. The percolation approach to the conductivity of manganites is validated also by more rigorous theoretical considerations [17]. Experimental confirmation of the exponential dependence of resistivity on cluster spacing d determined from the X-ray measurements is shown for several samples in Fig. 5. In the (log ρ, d) coordinates, the data form two straight lines with different slopes. The lower line corresponds to thin films on SLG substrates, which apparently favor the growth of samples with lower resistivity. Both data sets extrapolate for d → 0 to ρ0 ≈ 0.012 cm.
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The differences in atomic ordering of the samples shown in Fig. 5 are reflected in the X-ray data of Fig. 1 by the position of diffusive scattering maxima generated by the clusters. In the case of films deposited on SLG or Nd3 Ga5 O12 , the diffusive maxima due to the Mn–O metallic clusters (hatched areas) exhibit different intensities in regions A1 and A0 . Assuming that the increase of diffraction angle Θ corresponds to the decrease of interplanar distance d (2d sin Θ = nλ) and that the length of the Mn–O bond decreases when the ionization of Mn increases from Mn2+ to Mn3+ , these results indicate that the clusters differ in local mesoscopic order. Let us observe that in the film on SLG, where I (A0 ) > I (A1 ), dominate the densely packed planes with highly ionized manganese Mn(3–4)+, what should enhance the conductivity. On the other hand, the films grown on Nd3 Ga5 O12 , exhibit I (A0 ) < I (A1 ), i.e., in these films prevail clusters with more widely spread planes and Mn2+ –Mn3+ ions, what should yield lower film conductivity. These conclusions are in good agreement with the measurement results presented in Fig. 5, where at the same cluster spacing the LSMO films on SLG show clearly lower resistivities than the films on Nd3 Ga5 O12 . Assuming that at temperatures Tmx the thermal energy is comparable to the coupling (tunneling) energy W between clusters, which depends exponentially on the cluster spacing d, we can write kTmx = W = W0 exp −(d/d1 ) .
(5)
Taking into account Eq. (2) we obtain a powerdependence of ρmx on Tmx σ (Tmx ) ∼ (kTmx )β , ρmx ∼ (kTmx )−β ,
β = d1 /d0 ,
(6)
which is confirmed by our measurements. The plot of ρmx (Tmx ) is shown in Fig. 6. Eq. (6) with β = 10.7 is seen to hold over four orders of magnitude in ρ. In the temperature interval T = Tmx − Tmn between the two R(T ) extrema, the atomic, electronic, and magnetic subsystems actively interact. Disorder in the whole system is reduced due to magnetic ordering. As a result, the amplitude of the random potential decreases, and this leads to lower sample resistivity. Experimental data (see inset in Fig. 5) indicate a linear
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−1/3 D(T ) 0 3 Cm + η(Tmx − T ) −1 . ρ = ρ0 exp d0 (11) According to this result ρmn should decrease exponentially with increasing temperature difference Tmx − Tmn , and indeed this was observed for our samples (see Fig. 6). Eq. (11) cannot be solved analytically to yield an explicit relation between ρmn and ρmx . However, the experimental data show a power-law behavior (see the inset in Fig. 6) ρmn = (ρmx )ξ ,
Fig. 6. Temperature dependence of extremal values of resistivity, ρmn and ρmx , for LaSrMnO thin films on different substrates. The inset shows ρmn (ρmx ) dependence; black triangles mark numerical data obtained from Eq. (11).
relationship between Tmx and Tmn Tmn = αTmx + γ ,
(7)
where α = −0.46 and γ = 154.32. One can examine also the relationship between ρmx and ρmn . Let us assume that Cm on cooling the sample below Tmx increases: 0 Cm → Cm (T ) = Cm + η(Tmx − T ),
We can write then −1/3 D 3Cm (T ) ρ = ρ0 exp −1 . d0
T Tmx .
(8)
(9)
However, the cluster size D may depend also on the concentration Cm . To account for this dependence, we can apply the results of percolation theory, and treat the variation of D in the same manner as the variation of the correlation radius [16]. We obtain then crit −ν , D → D(T ) ≈ D Cm (T ) − Cm (10) where ν = 0.85 is the critical exponent of the correlation radius, and D is some characteristic length. In this manner the final expression for resistivity can be written as
where ξ = 1.25, and can be fitted by substituting into Eq. (11) η = 0.0017 K−1 , D = 44.18 Å, ρ0 = crit = 0.5. 0.012 cm, Cm Finally, let us remark that the derivation of Eq. (9) relies on the hypothesis that cluster size is temperature dependent. This hypothesis is based on the measurement of film properties in applied magnetic field. Temperature and field dependence of magnetization, M(T , H ), in the FC regime depends on the size of FM clusters embedded into AFM matrix. The magnetization of the smallest clusters can be easily oriented along the applied magnetic field, even at relatively high temperatures (see Fig. 4(a), (b), H = 100 Oe). With the increase of cluster size (at higher magnetic fields), the system can be saturated only at low temperatures (cf. M(T ) curves at H = 100 and 1000 Oe). At even higher magnetic fields (see M(T ) curves at 10 kOe), the influence of magnetic ordering on the structure and the size of clusters is so strong that the system does not saturate even in very low temperatures. Thus, we can conclude that the cluster size increases with decreasing temperature and increasing magnetic field. In this manner, the presumption of labile configuration of cluster structure in the film is confirmed and can be used to justify the dependence of metallic phase concentration and cluster size on temperature as given in Eqs. (7) and (10), with subsequent description of experimental data by Eq. (11). In other words, we are dealing with phase separation phenomena nucleating on the different crystallographic phases present in the investigated films. To conclude, the observed properties of LSMO thin films can be explained by spin-dependent tunneling between metallic clusters and by applying the percolation theory-based approach.
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Acknowledgement This work was supported by Polish Government (KBN) Grants PBZ-KBN-013/T08/19 and 7 T08A 00520.
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