- Email: [email protected]
3MnO3 thin films on (0 0 1) Si substrates
Journal of Magnetism and Magnetic Materials 211 (2000) 206}211
Anisotropic magnetoresistance of (0 0 h), (0 h h) and (h h h) La Sr MnO thin "lms on (0 0 1) Si substrates 2@3 1@3 3 M. Bibes!, B. MartmH nez!, J. Fontcuberta!,*, V. Trtik", C. Ferrater", F. SaH nchez", M. Varela", R. Hiergeist#, K. Steenbeck# !Institut de Cie% ncia de Materials de Barcelona, CSIC, Bellaterra 08193, Catalunya, Spain "Universitat de Barcelona. Departament de Fn& sica Aplicada i O" ptica, Diagonal 647, Barcelona 08028, Catalunya, Spain #Institut fu( r Physikalishe Hochtechnologie e. V., Jena, (IPHT), Winzerlaer Str. 10, D-07745 Jena, Postfach 100239, Germany
Abstract The epitaxial growth of magnetoresistive La Sr MnO thin "lms with di!erent orientations on (0 0 1) Si substrates 2@3 1@3 3 has been successfully achieved by a suitable choice of the bu!er heterostructure. The out-of-plane and in-plane microstructure has been carefully analysed and related to the magnetocrystalline anisotropy. The dependence of the magnetoresistance (MR) as a function of the angle between the current and the applied "eld has been explored in a wide "eld range. At high "eld the magnetisation is saturated whatever the direction of the "eld and we observe the intrinsic anisotropic magnetoresistance (AMR) e!ect having a uniaxial anisotropy while at low "eld the magnetocrystalline anisotropy induces higher-order angle dependence of the magnetoresistance. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Thin "lms; Anisotropic magnetoresistance; Microstructure
1. Introduction In the last few years there has been an important renewed interest for alkaline-earth-substituted manganese perovskites of general formula La A MnO (A"Ba, Sr, Ca, Pb) [1,2]. Espe1~x x 3 cially for x"1 and around the ferromagnetic or3 dering temperature ¹ the magnetoresistive e!ect C is `colossala and has been extensively studied with the double objective of understanding the intrinsic phenomena as well as opening the way towards applications. In this paper we will try to contribute
* Corresponding author: Tel: #34-93-580-18-53; fax: #3493-580-57-29. E-mail address: [email protected] (J. Fontcuberta)
to both of these requisites: "rst we will roughly describe the elaboration process and the structural, magnetic and transport properties of our "lms grown on silicon substrates, and on the other hand, we will describe the "eld and temperature dependence of the magnetoresistance on the angle h between the current density J and the applied "eld H.
2. Experimental La Sr MnO (LSMO) thin "lms have been 2@3 1@3 3 prepared on (0 0 1)Si substrates by pulsed-laser deposition (PLD) using a KrF excimer laser. In a previous paper we showed that a suitable selection of the bu!er heterostructure allowed the selective growth of epitaxial (0 0 h), (0 h h) and (h h h)
0304-8853/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 7 3 5 - 0
M. Bibes et al. / Journal of Magnetism and Magnetic Materials 211 (2000) 206}211
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Fig. 1. (a) Schema of the orientation of the crystallites for (0 1 1)LSMO; (b) /-scan around the [1 1 2] direction of (0 1 1)LSMO.
SrTiO (STO) thin "lms on (0 0 1)Si. The hetero3 structures used as bu!er layers are: STO/CeO / 2 YSZ,1 STO/YSZ and STO/TiN/YSZ and the orientation of the uppermost layer is: (0 0 h), (0 h h) and (h h h), respectively. The upperlying STO is a suitable template "lm for the manganite layer deposition [4]. The LSMO layers, typically 100 nm thick, were then grown on top of the STO at a substrate temperature of 7503C and an oxygen pressure of 0.4 mbar. After deposition, the "lms were annealed in situ for 10 min under an oxygen pressure of 1 atm. The structural quality of the "lms was investigated with a four-circle X-ray di!ractometer. All crystallographic planes and directions referred to in this paper are indexed according to cubic notation. The magnetisation was measured by a quantum design squid magnetometer while all transport measurements were performed with a quantum design physical properties measurement system (PPMS) equipped with a horizontal rotator module.
3. Results X-ray di!raction analysis was performed in order to check the in-plane and out-of-plane texture. The
1 Yttria-stabilised zirconia.
latter was found to be in agreement with the (0 0 h), (0 h h) and (h h h) expected orientations although, a peak associated, with a small population of (0 h h)oriented crystallites was observed in the h}2h scan of the (h h h)-oriented "lm [4,5]. We will see that this point may be relevant to understand the magnetoresistance data but we will label the samples according to the majority population orientation: (0 0 1)LSMO, (0 1 1)LSMO and (1 1 1)LSMO. The in-plane texture was studied through /-scans around the [1 0 3], [1 1 2] and [1 0 1] directions for (0 0 1)LSMO, (0 1 1)LSMO and (1 1 1)LSMO respectively. (0 0 1)LSMO was found to present a complete in-plane texture and thus only one family of crystallites. As can be seen in Fig. 1b, (0 1 1)LSMO has a more complex /-scan diagram with four sets of three mimicking that of the STO layer [3]. The central peak of each set corresponds to crystallites aligned parallel to YSZ square mesh whereas smaller satellite peaks at $83 re#ects a double population of crystallites with orientation STO[1 1 1]//Si[0 1 1] as schematically indicated in Fig. 1a. The paving of the square YSZ lattice by the (0 1 1)STO rectangular mesh results in six di!erent in-plane orientations for the (0 1 1) STO (and (0 1 1)LSMO)) crystallites [6]. In Fig. 2b, we show the /-scan graph of the (1 1 1)LSMO sample. Four sets of three re#ections are detected corresponding to the following
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M. Bibes et al. / Journal of Magnetism and Magnetic Materials 211 (2000) 206}211
Fig. 2. (a) Schema of the orientation of the crystallites for (1 1 1)LSMO; (b) /-scan around the [1 0 1] direction of (1 1 1)LSMO.
Fig. 3. Dependence of the magnetoresistance MR"(o(h, H)!o(h"0, H))/o(h"0, H) on the angle h for the three samples at ¹"10 K and H"50 kOe (a) and H"1 kOe (b). Circles: (0 0 1)LSMO; squares: (0 1 1)LSMO; triangles: (1 1 1)LSMO. The curves are shifted up for (0 0 1)LSMO and down for (1 1 1)LSMO.
crystallographic relationships: LSMO[1011 ]// Si[1 0 0], LSMO[11 0 1]//Si[1 0 0], LSMO[1 0 11 ]// Si[0 1 0] and LSMO[11 0 1]//Si[0 1 0]. Since the height of the associated peaks are alike one should expect to describe the "lm with four almost equivalent families of crystallites depending on their inplane orientation. Fig. 2a shows these four families and their orientations relative to the TiN square mesh. Resistivity o(h, H) measurements have been performed for all the samples in order to investigate the dependence of the magnetoresistance MR" (o(h, H)!o(h"0, H))/o(h"0, H) on the angle
h between the current density J and the applied "eld H. The "eld was rotated within the "lm plane from 03 to 3603. The direction of J with respect to the crystallographic axis was "xed during the measurements. Consecutive MR(h) measurements were performed for di!erent values of the applied magnetic "eld starting with H"50 kOe and then decreasing H down to some hundreds of oersteds. As shown in Fig. 3a, at 10 K and H"50 kOe a clear sin2h dependence was obtained for (0 1 1)LSMO (squares) and (1 1 1)LSMO (triangles). This behaviour was also detected for (0 0 1)LSMO despite some irregularities in the
M. Bibes et al. / Journal of Magnetism and Magnetic Materials 211 (2000) 206}211
curve that may be attributed either to a non-saturation of the "lm for all angles [7] or the presence of residual non-ideally oriented crystallites. Apart from this second-order e!ect, the sin2h dependence re#ects the classical anisotropic magnetoresistance AMR whose contribution to the measured magnetoresistance can be written [8}10]: o(M)"o (DDMDD)#o (DDMDD)sin2(h#d), (1) 1 2 where d is the initial angle between J and the magnetisation vector M. At H"50 kOe, the "lm magnetisation is saturated [4] and DDMDD is constant and independent of h. Under these circumstances, the MR can be described by the phenomenological equation [11]: MR"c #c sin2(h#d). (2) 1 2 Indeed, the experimental data of Fig. 3a are in agreement with this angular dependence and thus disclose the AMR contribution to the MR. We note that this contribution is of about 0.2%. That is only a fraction of the MR observed in the 0}50 kOe range where MR can be as large as 40% at this temperature [4]. Upon reduction of the applied "eld, signi"cant distortions appear in the MR response and higher order components add to the intrinsic AMR dependence of Eq. (2). This e!ect can be clearly appreciated in the MR(h) data of Fig. 3b, taken at 10 K and H"1 kOe. These new terms arise from the contribution of the magnetocrystalline anisotropy of the "lms and possibly of the magnetic
209
domain structure. Thus, in principle, the MR(h) dependence of Fig. 3b could be rationalised in term of both contribution: the AMR and the magnetocrystalline anisotropy. Indeed, when the applied "eld becomes smaller than the anisotropy "eld, the magnetisation is no longer saturated for every direction of H and depends on the position of the "eld with respect to the easy and hard axis in the "lm plane. Using a biaxial anisotropy model for the magnetocrystalline anisotropy of a (0 1 1)LSMO "lm with fourfold in-plane symmetry, we can write the magnetisation: M"M #M sin(4h#e), (3) 1 2 where M is the value of average value of M when 1 rotating H, M the di!erence in magnetisation 2 between the `H parallel to an easy axisa and &&H parallel to a hard axis'' situations and e the initial angle between the "eld and the position of a hard axis, it turns out that MR"(c #c sin2(h#d))(c #c sin(4h#e)). (4) 1 2 3 4 The solid line through the data of Fig. 4a shows the best "t obtained using Eq. (4). It can be appreciated that this simple model reproduces rather well the data but fails at reproducing the sharp maxima. This discrepancy may come from the remaining presence of magnetic domains. However, the good agreement of the "t indicates that the magnetocrystalline anisotropy indeed contributes to the angle-dependent MR with a fourfold term. The sixfold term contribution implicit in
Fig. 4. (a) MR obtained at 10 K and 1 kOe for (0 1 1)LSMO (squares); "t from Eq. (4) (solid line) (b) MR obtained at 10 K and 1 kOe for (1 1 1)LSMO (squares); "t from Eq. (6) (solid line).
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M. Bibes et al. / Journal of Magnetism and Magnetic Materials 211 (2000) 206}211
Fig. 6. Field dependence of the angle-dependent MR for (1 1 1)LSMO (¹"10 K). Fig. 5. Torque measurements for the (1 1 1)LSMO sample at ¹"10 K and H"5 kOe (squares), 2 kOe (circles) and 1 kOe (triangles).
Eq. (4) is only of second order and is not apparent in the observed angle dependence. We now turn to the (1 1 1)LSMO "lm. The raw experimental data of Fig. 4b reveal prominent two and fourfold contributions to the MR. In order to relate the MR to the magnetocrystalline anisotropy we have performed torque measurements for "elds between 1 and 5 kOe (see Fig. 5). The initial position corresponds to the "eld parallel to the [0 1 1] direction of the Si substrate. Some hysteresis of the G has been observed but in Fig. 5 the average G(h) is shown. Both the "eld dependence of G(h) and this hysteresis indicate that the magnetocrystalline anisotropy as well as the domain structure contribute to G(h) in this "eld range. From the positions of the intersections between the torque curve and the G"0 straight line, we can deduce the positions of the remarkable axis of the sample. This analysis suggests that the sample possesses four hard axis at h+03, +903, +1803 and +2703 (G"0 and dG/dh'0) and four easy axis at h+403, +1403, +2203 and +3203 (G"0 and dG/dh(0) [12]. The Fourier transformation of G(h) shows a twofold and a fourfold term whose contributions change with "eld. Thus the magnetisation may be described by M"M #M sin(4h#e)#M sin(2h#/), (5) 1 2 3 which leads to the following equation for the magnetoresistance: MR"(c #c sin2(h#d))(c #c sin(4h#e) 1 2 3 4 #c sin(2h#/)). 5
(6)
In Fig. 4b we show the result of the "t by Eq. (6). The quality of "t is very good and reveals that in this (1 1 1)-oriented "lm, irrespective of the in-plane structure, the magnetocrystalline anisotropy contributes to the AMR with a fourfold dependence. Fig. 6 summarises the "eld dependence of the angle-dependent MR. As shown, the intrinsic AMR e!ect remains dominant for "elds down to about 2 kOe whereas at lower "elds two small peaks start to develop coming from the fourfold dependence related to the anisotropy of the magnetisation. We have also studied how the amplitude of the AMR changes with temperature. It turns that the normalised amplitude of the MR(h) curves recorded at high "eld (H'10 kOe) seems to follow the magnetisation as expected in metallic systems [13,14]. This behaviour is what one should expect a priori if the magnetisation is fully saturated (which is the case for our sample when H"10 kOe). However, from the comparison between manganite thin "lms having di!erent degrees of in-plane epm` taxy we have recently found that the high-"eld AMR contains two terms of distinct temperature dependence: one related to the bulk material and displaying a peak a ¹ and the other C associated with grain interfaces and increasing at low temperature [15]. It turns out that, in general, a non-monotonic temperature dependence of the normalised amplitude of the AMR, having a peak at ¹+¹ should be expected [16,17]. C In summary, in this work we investigated the in-plane magnetoresistance anisotropy of LSMO epitaxial (0 1 1) and (1 1 1) thin "lms grown on
M. Bibes et al. / Journal of Magnetism and Magnetic Materials 211 (2000) 206}211
appropriately bu!ered (0 0 1)Si substrates. The conventional twofold anisotropic magnetoresistance arising from the dependence of the resistance on the angle between the measuring current and the magnetisation has been clearly identi"ed in the high "eld regime. The temperature dependence of the AMR amplitude has been analysed for the particular (1 1 1)LSMO "lm and it has been found to follow the magnetisation. At "elds lower than the anisotropy "eld the in-plane angle dependence of the MR becomes more complex due to the contribution of the magnetocrystalline anisotropy and higher order terms appear in MR(h). Dominating fourfold terms exist in both (0 1 1) and (1 1 1)LSMO "lms irrespectively of the distinct microstructure. Further experiments are under way to get deeper understanding of the low-"eld magnetoresistance and magnetic anisotropy of these "lms.
Acknowledgements This work was supported by the CICYT (Grant Nos. MAT97-0699 and MAT96-0911), the Generalitat de Catalunya (Grant Nos. GRQ95-8029) and the CEE OXSEN TMR network. We would also like to thank Carles Frontera for his help on data processing.
211
References [1] M. McCormack, S. Jin, T.H. Tiefel, R.M. Fleming, J.M. Phillips, R. Ramesh, Appl. Phys. Lett. 64 (1994) 3045. [2] S. Jin, T.H. Tie#, M. McCormack, R.A. Fastnacht, R. Ramesh, L.H. Chen, Science 264 (1994) 413. [3] F. SaH nchez, R. Aguiar, V. TrtmH k, C. Guerrero, C. Ferrater, M. Varela, J. Mater. Res. 13 (1998) 1422. [4] J. Fontcuberta, M. Bibes, B. MartmH nez, V. TrtmH k, C. Ferrater, F. Sanchez, M. Varela, Appl. Phys. Lett. 74 (1999) 1743. [5] J. Fontcuberta, M. Bibes, B. MartmH nez, V. TrtmH k, C. Ferrater, F. Sanchez, M. Varela, J. Appl. Phys. 85 (1999) 4800. [6] D.G. Schlom, E.S. Hellman, E.H. Hartford Jr., C.B. Eom, J.C. Clark, J. Mannhart, J. Mater. Res. 11 (1998) 1336. [7] J.N. Eckstein, I. Bozovic, J. O'Donnell, M. Onellion, M.S. Rzchowski, Appl. Phys. Lett. 69 (1996) 1312. [8] E. Dan Dahlberg, K. Riggs, G.A. Prinz, J. Appl. Phys. 63 (1998) 4270. [9] R.I. Potter, Phys. Rev. B 10 (1974) 4626. [10] A.P. Malozemo!, Phys. Rev. B 32 (1985) 6080. [11] J. O'Donnell, M. Onellion, M.S. Rzchowski, J.N. Eckstein, I. Bozovic, Phys. Rev. B 55 (1997) 5873. [12] B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, Reading, MA, 1972, pp 215-225. [13] J. O'Donnell, M. Onellion, M.S. Rzchowski, J.N. Eckstein, I. Bozovic, J. Appl. Phys. 81 (1997) 4961. [14] P.A. Stampe, H.P. Hunkel, Z. Wang, G. Williams, Phys. Rev. B 52 (1995) 335. [15] M. Bibes, O. Gorbenko, B. MartmH nez, A. Kaul, J. Fontcuberta, presented at the EMRS-Spring meeting, Strasbourg 1999. [16] M. Ziese, S.P. Sena, J. Phys. Condens. Matter 10 (1998) 2727. [17] J. O'Donnell, M. Onellion, M.S. Rzchowski, J.N. Eckstein, I. Bozovic, to be published.
Anisotropic magnetoresistance of (0 0 h), (0 h h) and (h h h) La Sr MnO thin "lms on (0 0 1) Si substrates 2@3 1@3 3 M. Bibes!, B. MartmH nez!, J. Fontcuberta!,*, V. Trtik", C. Ferrater", F. SaH nchez", M. Varela", R. Hiergeist#, K. Steenbeck# !Institut de Cie% ncia de Materials de Barcelona, CSIC, Bellaterra 08193, Catalunya, Spain "Universitat de Barcelona. Departament de Fn& sica Aplicada i O" ptica, Diagonal 647, Barcelona 08028, Catalunya, Spain #Institut fu( r Physikalishe Hochtechnologie e. V., Jena, (IPHT), Winzerlaer Str. 10, D-07745 Jena, Postfach 100239, Germany
Abstract The epitaxial growth of magnetoresistive La Sr MnO thin "lms with di!erent orientations on (0 0 1) Si substrates 2@3 1@3 3 has been successfully achieved by a suitable choice of the bu!er heterostructure. The out-of-plane and in-plane microstructure has been carefully analysed and related to the magnetocrystalline anisotropy. The dependence of the magnetoresistance (MR) as a function of the angle between the current and the applied "eld has been explored in a wide "eld range. At high "eld the magnetisation is saturated whatever the direction of the "eld and we observe the intrinsic anisotropic magnetoresistance (AMR) e!ect having a uniaxial anisotropy while at low "eld the magnetocrystalline anisotropy induces higher-order angle dependence of the magnetoresistance. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Thin "lms; Anisotropic magnetoresistance; Microstructure
1. Introduction In the last few years there has been an important renewed interest for alkaline-earth-substituted manganese perovskites of general formula La A MnO (A"Ba, Sr, Ca, Pb) [1,2]. Espe1~x x 3 cially for x"1 and around the ferromagnetic or3 dering temperature ¹ the magnetoresistive e!ect C is `colossala and has been extensively studied with the double objective of understanding the intrinsic phenomena as well as opening the way towards applications. In this paper we will try to contribute
* Corresponding author: Tel: #34-93-580-18-53; fax: #3493-580-57-29. E-mail address: [email protected] (J. Fontcuberta)
to both of these requisites: "rst we will roughly describe the elaboration process and the structural, magnetic and transport properties of our "lms grown on silicon substrates, and on the other hand, we will describe the "eld and temperature dependence of the magnetoresistance on the angle h between the current density J and the applied "eld H.
2. Experimental La Sr MnO (LSMO) thin "lms have been 2@3 1@3 3 prepared on (0 0 1)Si substrates by pulsed-laser deposition (PLD) using a KrF excimer laser. In a previous paper we showed that a suitable selection of the bu!er heterostructure allowed the selective growth of epitaxial (0 0 h), (0 h h) and (h h h)
0304-8853/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 7 3 5 - 0
M. Bibes et al. / Journal of Magnetism and Magnetic Materials 211 (2000) 206}211
207
Fig. 1. (a) Schema of the orientation of the crystallites for (0 1 1)LSMO; (b) /-scan around the [1 1 2] direction of (0 1 1)LSMO.
SrTiO (STO) thin "lms on (0 0 1)Si. The hetero3 structures used as bu!er layers are: STO/CeO / 2 YSZ,1 STO/YSZ and STO/TiN/YSZ and the orientation of the uppermost layer is: (0 0 h), (0 h h) and (h h h), respectively. The upperlying STO is a suitable template "lm for the manganite layer deposition [4]. The LSMO layers, typically 100 nm thick, were then grown on top of the STO at a substrate temperature of 7503C and an oxygen pressure of 0.4 mbar. After deposition, the "lms were annealed in situ for 10 min under an oxygen pressure of 1 atm. The structural quality of the "lms was investigated with a four-circle X-ray di!ractometer. All crystallographic planes and directions referred to in this paper are indexed according to cubic notation. The magnetisation was measured by a quantum design squid magnetometer while all transport measurements were performed with a quantum design physical properties measurement system (PPMS) equipped with a horizontal rotator module.
3. Results X-ray di!raction analysis was performed in order to check the in-plane and out-of-plane texture. The
1 Yttria-stabilised zirconia.
latter was found to be in agreement with the (0 0 h), (0 h h) and (h h h) expected orientations although, a peak associated, with a small population of (0 h h)oriented crystallites was observed in the h}2h scan of the (h h h)-oriented "lm [4,5]. We will see that this point may be relevant to understand the magnetoresistance data but we will label the samples according to the majority population orientation: (0 0 1)LSMO, (0 1 1)LSMO and (1 1 1)LSMO. The in-plane texture was studied through /-scans around the [1 0 3], [1 1 2] and [1 0 1] directions for (0 0 1)LSMO, (0 1 1)LSMO and (1 1 1)LSMO respectively. (0 0 1)LSMO was found to present a complete in-plane texture and thus only one family of crystallites. As can be seen in Fig. 1b, (0 1 1)LSMO has a more complex /-scan diagram with four sets of three mimicking that of the STO layer [3]. The central peak of each set corresponds to crystallites aligned parallel to YSZ square mesh whereas smaller satellite peaks at $83 re#ects a double population of crystallites with orientation STO[1 1 1]//Si[0 1 1] as schematically indicated in Fig. 1a. The paving of the square YSZ lattice by the (0 1 1)STO rectangular mesh results in six di!erent in-plane orientations for the (0 1 1) STO (and (0 1 1)LSMO)) crystallites [6]. In Fig. 2b, we show the /-scan graph of the (1 1 1)LSMO sample. Four sets of three re#ections are detected corresponding to the following
208
M. Bibes et al. / Journal of Magnetism and Magnetic Materials 211 (2000) 206}211
Fig. 2. (a) Schema of the orientation of the crystallites for (1 1 1)LSMO; (b) /-scan around the [1 0 1] direction of (1 1 1)LSMO.
Fig. 3. Dependence of the magnetoresistance MR"(o(h, H)!o(h"0, H))/o(h"0, H) on the angle h for the three samples at ¹"10 K and H"50 kOe (a) and H"1 kOe (b). Circles: (0 0 1)LSMO; squares: (0 1 1)LSMO; triangles: (1 1 1)LSMO. The curves are shifted up for (0 0 1)LSMO and down for (1 1 1)LSMO.
crystallographic relationships: LSMO[1011 ]// Si[1 0 0], LSMO[11 0 1]//Si[1 0 0], LSMO[1 0 11 ]// Si[0 1 0] and LSMO[11 0 1]//Si[0 1 0]. Since the height of the associated peaks are alike one should expect to describe the "lm with four almost equivalent families of crystallites depending on their inplane orientation. Fig. 2a shows these four families and their orientations relative to the TiN square mesh. Resistivity o(h, H) measurements have been performed for all the samples in order to investigate the dependence of the magnetoresistance MR" (o(h, H)!o(h"0, H))/o(h"0, H) on the angle
h between the current density J and the applied "eld H. The "eld was rotated within the "lm plane from 03 to 3603. The direction of J with respect to the crystallographic axis was "xed during the measurements. Consecutive MR(h) measurements were performed for di!erent values of the applied magnetic "eld starting with H"50 kOe and then decreasing H down to some hundreds of oersteds. As shown in Fig. 3a, at 10 K and H"50 kOe a clear sin2h dependence was obtained for (0 1 1)LSMO (squares) and (1 1 1)LSMO (triangles). This behaviour was also detected for (0 0 1)LSMO despite some irregularities in the
M. Bibes et al. / Journal of Magnetism and Magnetic Materials 211 (2000) 206}211
curve that may be attributed either to a non-saturation of the "lm for all angles [7] or the presence of residual non-ideally oriented crystallites. Apart from this second-order e!ect, the sin2h dependence re#ects the classical anisotropic magnetoresistance AMR whose contribution to the measured magnetoresistance can be written [8}10]: o(M)"o (DDMDD)#o (DDMDD)sin2(h#d), (1) 1 2 where d is the initial angle between J and the magnetisation vector M. At H"50 kOe, the "lm magnetisation is saturated [4] and DDMDD is constant and independent of h. Under these circumstances, the MR can be described by the phenomenological equation [11]: MR"c #c sin2(h#d). (2) 1 2 Indeed, the experimental data of Fig. 3a are in agreement with this angular dependence and thus disclose the AMR contribution to the MR. We note that this contribution is of about 0.2%. That is only a fraction of the MR observed in the 0}50 kOe range where MR can be as large as 40% at this temperature [4]. Upon reduction of the applied "eld, signi"cant distortions appear in the MR response and higher order components add to the intrinsic AMR dependence of Eq. (2). This e!ect can be clearly appreciated in the MR(h) data of Fig. 3b, taken at 10 K and H"1 kOe. These new terms arise from the contribution of the magnetocrystalline anisotropy of the "lms and possibly of the magnetic
209
domain structure. Thus, in principle, the MR(h) dependence of Fig. 3b could be rationalised in term of both contribution: the AMR and the magnetocrystalline anisotropy. Indeed, when the applied "eld becomes smaller than the anisotropy "eld, the magnetisation is no longer saturated for every direction of H and depends on the position of the "eld with respect to the easy and hard axis in the "lm plane. Using a biaxial anisotropy model for the magnetocrystalline anisotropy of a (0 1 1)LSMO "lm with fourfold in-plane symmetry, we can write the magnetisation: M"M #M sin(4h#e), (3) 1 2 where M is the value of average value of M when 1 rotating H, M the di!erence in magnetisation 2 between the `H parallel to an easy axisa and &&H parallel to a hard axis'' situations and e the initial angle between the "eld and the position of a hard axis, it turns out that MR"(c #c sin2(h#d))(c #c sin(4h#e)). (4) 1 2 3 4 The solid line through the data of Fig. 4a shows the best "t obtained using Eq. (4). It can be appreciated that this simple model reproduces rather well the data but fails at reproducing the sharp maxima. This discrepancy may come from the remaining presence of magnetic domains. However, the good agreement of the "t indicates that the magnetocrystalline anisotropy indeed contributes to the angle-dependent MR with a fourfold term. The sixfold term contribution implicit in
Fig. 4. (a) MR obtained at 10 K and 1 kOe for (0 1 1)LSMO (squares); "t from Eq. (4) (solid line) (b) MR obtained at 10 K and 1 kOe for (1 1 1)LSMO (squares); "t from Eq. (6) (solid line).
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Fig. 6. Field dependence of the angle-dependent MR for (1 1 1)LSMO (¹"10 K). Fig. 5. Torque measurements for the (1 1 1)LSMO sample at ¹"10 K and H"5 kOe (squares), 2 kOe (circles) and 1 kOe (triangles).
Eq. (4) is only of second order and is not apparent in the observed angle dependence. We now turn to the (1 1 1)LSMO "lm. The raw experimental data of Fig. 4b reveal prominent two and fourfold contributions to the MR. In order to relate the MR to the magnetocrystalline anisotropy we have performed torque measurements for "elds between 1 and 5 kOe (see Fig. 5). The initial position corresponds to the "eld parallel to the [0 1 1] direction of the Si substrate. Some hysteresis of the G has been observed but in Fig. 5 the average G(h) is shown. Both the "eld dependence of G(h) and this hysteresis indicate that the magnetocrystalline anisotropy as well as the domain structure contribute to G(h) in this "eld range. From the positions of the intersections between the torque curve and the G"0 straight line, we can deduce the positions of the remarkable axis of the sample. This analysis suggests that the sample possesses four hard axis at h+03, +903, +1803 and +2703 (G"0 and dG/dh'0) and four easy axis at h+403, +1403, +2203 and +3203 (G"0 and dG/dh(0) [12]. The Fourier transformation of G(h) shows a twofold and a fourfold term whose contributions change with "eld. Thus the magnetisation may be described by M"M #M sin(4h#e)#M sin(2h#/), (5) 1 2 3 which leads to the following equation for the magnetoresistance: MR"(c #c sin2(h#d))(c #c sin(4h#e) 1 2 3 4 #c sin(2h#/)). 5
(6)
In Fig. 4b we show the result of the "t by Eq. (6). The quality of "t is very good and reveals that in this (1 1 1)-oriented "lm, irrespective of the in-plane structure, the magnetocrystalline anisotropy contributes to the AMR with a fourfold dependence. Fig. 6 summarises the "eld dependence of the angle-dependent MR. As shown, the intrinsic AMR e!ect remains dominant for "elds down to about 2 kOe whereas at lower "elds two small peaks start to develop coming from the fourfold dependence related to the anisotropy of the magnetisation. We have also studied how the amplitude of the AMR changes with temperature. It turns that the normalised amplitude of the MR(h) curves recorded at high "eld (H'10 kOe) seems to follow the magnetisation as expected in metallic systems [13,14]. This behaviour is what one should expect a priori if the magnetisation is fully saturated (which is the case for our sample when H"10 kOe). However, from the comparison between manganite thin "lms having di!erent degrees of in-plane epm` taxy we have recently found that the high-"eld AMR contains two terms of distinct temperature dependence: one related to the bulk material and displaying a peak a ¹ and the other C associated with grain interfaces and increasing at low temperature [15]. It turns out that, in general, a non-monotonic temperature dependence of the normalised amplitude of the AMR, having a peak at ¹+¹ should be expected [16,17]. C In summary, in this work we investigated the in-plane magnetoresistance anisotropy of LSMO epitaxial (0 1 1) and (1 1 1) thin "lms grown on
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appropriately bu!ered (0 0 1)Si substrates. The conventional twofold anisotropic magnetoresistance arising from the dependence of the resistance on the angle between the measuring current and the magnetisation has been clearly identi"ed in the high "eld regime. The temperature dependence of the AMR amplitude has been analysed for the particular (1 1 1)LSMO "lm and it has been found to follow the magnetisation. At "elds lower than the anisotropy "eld the in-plane angle dependence of the MR becomes more complex due to the contribution of the magnetocrystalline anisotropy and higher order terms appear in MR(h). Dominating fourfold terms exist in both (0 1 1) and (1 1 1)LSMO "lms irrespectively of the distinct microstructure. Further experiments are under way to get deeper understanding of the low-"eld magnetoresistance and magnetic anisotropy of these "lms.
Acknowledgements This work was supported by the CICYT (Grant Nos. MAT97-0699 and MAT96-0911), the Generalitat de Catalunya (Grant Nos. GRQ95-8029) and the CEE OXSEN TMR network. We would also like to thank Carles Frontera for his help on data processing.
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References [1] M. McCormack, S. Jin, T.H. Tiefel, R.M. Fleming, J.M. Phillips, R. Ramesh, Appl. Phys. Lett. 64 (1994) 3045. [2] S. Jin, T.H. Tie#, M. McCormack, R.A. Fastnacht, R. Ramesh, L.H. Chen, Science 264 (1994) 413. [3] F. SaH nchez, R. Aguiar, V. TrtmH k, C. Guerrero, C. Ferrater, M. Varela, J. Mater. Res. 13 (1998) 1422. [4] J. Fontcuberta, M. Bibes, B. MartmH nez, V. TrtmH k, C. Ferrater, F. Sanchez, M. Varela, Appl. Phys. Lett. 74 (1999) 1743. [5] J. Fontcuberta, M. Bibes, B. MartmH nez, V. TrtmH k, C. Ferrater, F. Sanchez, M. Varela, J. Appl. Phys. 85 (1999) 4800. [6] D.G. Schlom, E.S. Hellman, E.H. Hartford Jr., C.B. Eom, J.C. Clark, J. Mannhart, J. Mater. Res. 11 (1998) 1336. [7] J.N. Eckstein, I. Bozovic, J. O'Donnell, M. Onellion, M.S. Rzchowski, Appl. Phys. Lett. 69 (1996) 1312. [8] E. Dan Dahlberg, K. Riggs, G.A. Prinz, J. Appl. Phys. 63 (1998) 4270. [9] R.I. Potter, Phys. Rev. B 10 (1974) 4626. [10] A.P. Malozemo!, Phys. Rev. B 32 (1985) 6080. [11] J. O'Donnell, M. Onellion, M.S. Rzchowski, J.N. Eckstein, I. Bozovic, Phys. Rev. B 55 (1997) 5873. [12] B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, Reading, MA, 1972, pp 215-225. [13] J. O'Donnell, M. Onellion, M.S. Rzchowski, J.N. Eckstein, I. Bozovic, J. Appl. Phys. 81 (1997) 4961. [14] P.A. Stampe, H.P. Hunkel, Z. Wang, G. Williams, Phys. Rev. B 52 (1995) 335. [15] M. Bibes, O. Gorbenko, B. MartmH nez, A. Kaul, J. Fontcuberta, presented at the EMRS-Spring meeting, Strasbourg 1999. [16] M. Ziese, S.P. Sena, J. Phys. Condens. Matter 10 (1998) 2727. [17] J. O'Donnell, M. Onellion, M.S. Rzchowski, J.N. Eckstein, I. Bozovic, to be published.