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Uniaxial anisotropy in magnetite thin film—Magnetization studies
ARTICLE IN PRESS
Physica B 382 (2006) 147–150 www.elsevier.com/locate/physb
Uniaxial anisotropy in magnetite thin film—Magnetization studies A. Wiechec´, J. Korecki, B. Handke, Z. Ka˛ kol, D. Owoc, D.A. Antolak, A. Koz"owski Department of Solid State Physics, Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krako´w, Poland Received 29 July 2005; received in revised form 17 February 2006; accepted 17 February 2006
Abstract Magnetization and electrical resistivity measurements have been performed on a stoichiometric single crystalline magnetite Fe3O4 thin film (thickness of ca. 500 nm) MBE deposited on MgO (1 0 0) substrate. The aim of these studies was to check the influence of preparation method and sample form (bulk vs. thin film) on magnetic anisotropy properties in magnetite. The film magnetization along /0 0 1S versus applied magnetic field has been determined both in the direction parallel and perpendicular to the film surface, and at temperatures above and below the Verwey transition. We have found, in agreement with published results, that the in-plane field of 10 kOe was not sufficient to saturate the sample. This can be understood if some additional factor, on top of the bulk magnetocrystalline anisotropy, is taken into account. r 2006 Elsevier B.V. All rights reserved. PACS: 75.70.i; 75.30.Gw Keywords: Magnetic thin films: properties; Magnetic anisotropy
1. Introduction Magnetite is well known both for its extensive use in traditional recording media and the role in the emerging field of spintronics [1]. This material also exhibits the discontinuous Verwey phase transformation at T V ¼ 124 K where many physical properties, including magnetic anisotropy, change abruptly. Magnetic properties, both below and above the Verwey transition, have been well documented in bulk single crystals [2–4] revealing interesting phenomena, as e.g. the changeover of easy magnetization axis at TV, switching of this axis at ToTV, etc. It is interesting whether these phenomena are also present in thin film single crystals, the forms of widest possible application. The aim of the paper is to study the magnetization process in magnetite thin films. The results may be particularly interesting in view of the reports [5] concerning additional source of anisotropy in this class of materials, on top of usual magnetocrystalline and dipole effect. High-temperature bulk magnetite has its easy, intermediate and hard axes along cubic /1 1 1S, /1 1 0S and Corresponding author.
E-mail address: [email protected] (A. Koz"owski). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.02.013
/0 0 1S directions, respectively. Below the Verwey transition the easy axis switches to [0 0 1] direction, while [1 1 0] and [1 1 0] become intermediate and hard axes. Since at TV magnetite also undergoes the structural phase transformation from high-temperature cubic to monoclinic, each of cubic /1 0 0S may become an easy axis and the material breaks into several kind of twins unless special field-cooling procedure and external stress is applied [2,3,6]. The simplest way to force the particular [0 0 1] to become an easy axis in bulk magnetite is to apply external magnetic field H42 kOe along this [0 0 1]. This procedure was applied here for 500 nm thin crystalline film and we have studied the field-cooling effect on the low temperature magnetization process. The magnetization process is compared to that in bulk single crystal and the implications of our findings are discussed.
2. Experiment and results The single crystalline magnetite film was grown [7] by Fe-vapor deposition from a MBE source at the rate of about 1 nm/min, under the O2 partial pressure in the 106 mbar range. The substrate, MgO(0 0 1), was cleaved in 57
ARTICLE IN PRESS A. Wiechec´ et al. / Physica B 382 (2006) 147–150
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N2 atmosphere and then annealed for 1 h at 900 K in UHV to assure atomic cleanness and perfect structure of the exposed surface (verified with AES and LEED). The optimum growth was achieved by keeping the substrate during deposition at 520 K, the standard preparation temperature for many previous studies [8]. pffiffiffiThepffiffisample ffi was checked by in-situ LEED, displaying ð 2 2ÞR451 reconstruction and the in situ CEMS showed spectrum typical for the bulk stoichiometric magnetite. The sample quality was also checked by AC resistivity (frequency 7 Hz) measurements, performed by standard 4-point method with ultrasonically bonded contacts. The results are shown in Fig. 1 and the typically observed [9,10] broadening of the transition region and the decreased resistivity drop at TV were found, as compared to bulk crystals. Similar widening of the transition region was recorded in X-ray diffraction measurements of the identical sample [11]. The reason for these effects is most probably the strain exerted by the substrate and accentuated by the antiphase boundaries [9]. Magnetic measurements were performed with a vibrating sample magnetometer at 290, 115 and 77 K. The sample holder with the MgO substrate was measured separately, and the signal was taken into account in the analysis. Magnetite film’s surface was set parallel to the magnetometer axis in such a way that both the [0 0 1] in-plane and the [0 1 0] out-of-plane axes could be set parallel to the magnetic field direction (see the inset in Fig. 2) and all the in-field measurements were done accordingly. At T ¼ 290 K these directions coincide with the hard magnetization axis of bulk magnetite, and the difference between magnetization processes in those two directions should be the measure of dipolar interactions (shape anisotropy). The results of measurements at T ¼ 290 K, as compared to the bulk characteristics [3] are shown on Fig. 2. Note, that for the bulk sample, magnetic field refers to the external field Hext corrected by demagnetization field
250
10
200
8
single crystalline 500nm film of Fe3O4 on MgO
7 6 5
cooling
4 3 heating
2 1 0 -1 3
4
5
6
7
HD (H eff ¼ H ext H D ; H D ¼ ð4p=3ÞM in case of sphere) to allow comparison with the thin film in-plane data where H D ¼ 0. The out-of-plane magnetization is plotted vs. Hext. The following facts are noteworthy:
the saturation was not achieved up to 10 kOe, even in inplane direction, contrary to a bulk sample where Heffo1 kOe is needed to saturate the sample along hard axis, magnetization processes along /1 0 0S for a bulk and the thin film (in-plane) are different even though M(Heff-0) matches closely.
100
Tv = 124.47 K Tv = 121.34 K
9
In(R/R250)
T (K)
150
Fig. 2. Reduced magnetization of magnetite thin film along /1 0 0S perpendicular (off-plane) and parallel (in plane) to the film surface, compared to relevant bulk characteristics (where the demagnetization field along /1 0 0S has been subtracted from the external field Hext) and the model curve (stars). Note, that magnetization values are normalized to their value at 10 kOe, which is not the saturation field for the thin film. Open hexagons point to M(H) calculated based on the results from Ref. [15]. The inset defines symbols used in energy minimization.
8
9
10
11
12
1000/T (K-1) Fig. 1. The results of AC resistivity measurements. The data were recorded both on cooling and heating. The histeresis is due to the thermometer lag (the histeresis in the bulk sample is appr. 0.03 K).
For low temperature measurements the film was fieldcooled at 10 kOe along the /1 0 0S in-plain direction. M(H) were then measured both in the same direction (that, after field-cooling procedure, should constitute the easy magnetization axis) and along the off-plain /1 0 0S (i.e. magnetically non specific direction). The results are shown on Fig. 3 and it is clear that the magnetization process along the in-plane /1 0 0S (bulk easy direction) is strikingly distinct from that for the bulk sample. In particular, the field of 11 kOe was not sufficient to saturate the sample, like at 290 K. Also Mo¨ssbauer spectroscopy measurements performed on the same film at 80 K, after field cooling at 250 kOe, showed that the local magnetization probed by effective magnetic fields at the 57Fe nuclei is not aligned in the film plane [12]. In order to check whether principal magnetocrystalline axes are the same as in a bulk sample we have cooled the
ARTICLE IN PRESS
M/Ms
A. Wiechec´ et al. / Physica B 382 (2006) 147–150
Heff, Hext (Oe) Fig. 3. Magnetization of magnetite thin film at 77 K, along /1 0 0S perpendicular (bulk circles) and parallel (bulk squares) to the film surface, after the sample was field-cooled in in-plane H ¼ 10 kOe. The data for the zero-field cooled sample (open triangles) and relevant bulk characteristics (here demagnetization field along /1 0 0S has been subtracted from the external field) are shown for comparison. The arrow indicates axis switching and the stars are the best fit of the model. Error bars indicate absolute sample holder signal uncertainty.
sample in zero external magnetic field (ZFC, zero-field cooling process). In this case the sample should have broken into structural domains with the low temperature easy axis pointing along different /1 0 0S directions. The results of subsequent measurements (with H parallel to the in-plane [0 0 1]) are shown in Fig. 3, revealing the totally different characteristics than in the field-cooled sample. Apparently, no unique easy axis is set, but the sample partly orients under the increasing magnetic field, and M(H) for lowering field roughly resembles that for fieldcooled sample. The additional confirmation that the applied fieldcooling procedure basically establishes the unique easy axis comes from the appearance of axis switching phenomenon [2] marked with the arrow in Fig. 3. Namely, when the sample is magnetized along /1 0 0S perpendicular to the easy direction (established by the field cooling procedure) at temperatures slightly lower than TV, some structural reorientation may take place and this /1 0 0S direction can, at least partly, become a new easy axis. Although the experimental evidence for this phenomenon is blurred here mainly due to strong demagnetization field, the break in M(H) curve is apparent. 3. Discussion The magnetization process after ZFC and the axisswitching phenomenon prove that the easy magnetic direction was uniquely established. It is now interesting to explain why in such a situation the results of magnetization experiments (and the results of Mo¨ssbauer measurements [12]) are distinct from those for bulk
149
samples both at high and low temperatures. Our explanation is based assuming some additional contribution to the magnetic anisotropy, roughly independent of temperature. Also, since the ratio M(Heff-0)/MS is very close to 0.58 which corresponds to cos(54.71), the value predicted in case the magnetization vector points along easy /1 1 1S, it is tempting to suggest that /1 1 1S is still the easy axis in thin magnetite films at high temperature but with considerably higher anisotropy field, than in the bulk material. This kind of contribution to the magnetic anisotropy and the lack of saturation in thin films have already been found [5,13] and explained by the preparation induced structural domain pattern. In particular, the first step in layer-by-layer growth mechanism is the formation of two-dimensional islands that eventually coalesce. Whereas the resulting oxygen sublattice is continuous (and closely matches the oxygen sublattice of the MgO substrate), Fe cations may form rows pointing at several directions or mutually shifted, leading to so-called anti-phase boundaries [14] (APBs). A new type of magnetic interactions may develop in APBs, in particular relatively weak intrasublattice interactions may now become strong and antiferromagnetic. This process can lead to the observed difficulties with saturation and can cause the magnetic moment within APBs to point out of plain. Our measurements confirm that such a process may be the case here. We have first tried to simulate our M(H) data by the model based on the results of nuclear resonance scattering (NRS) of synchrotron radiation [15] of 15 nm epitaxial magnetite film grown on MgO and oriented as our sample. In this paper, it is assumed that due to strong anitferromagnetic interactions within APB spins tend to align perpendicular to the film plane close to the boundary position and lay flat far from it due to shape anisotropy. The angle j(x) between spins and the in-plane direction at the distance x from the APB is calculated based on NRS results and micromagnetic model without crystalline anisotropy term. The profile of the spin angle j(x) may depend on magnetic domain size z (equal to the distance between APBs) and the domain size in our sample may differ from the mean value of 106 nm reported in Ref. [15]. Nevertheless, for all conceivable domain sizes (20 nmozo400 nm) we have used the same j(x) from Ref. [15] and have set jðxÞ ¼ 0 (spins laying in plane) for 52oxoz52 nm, i.e. for all points far enough from the APB. The results are shown on Fig. 2 for z ¼ 106 nm and we have found that for any domain size z, the model M(H) dependence is too flat to reproduce our experimental results reasonably. Although our approach is oversimplified (j(x) should be calculated for each z), the results above suggest that actual crystalline anisotropy can not be postponed. To account for it, we have assumed that p-part of the sample (equal to the APBs density of 0.06 as estimated from TEM images [13]) has a strong uniaxial anisotropy pointing in the /1 1 1S direction, in agreement with the data for 290 K. This contribution from APBs, different from that sug-
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gested in Ref. [15], is temperature independent, so at ToTV the 1p part of the sample has magnetocrystalline anisotropy typical for a bulk monoclinic magnetite, while in the remaining part of the sample the same uniaxial anisotropy dominates. This leads to the following approximate formula for the energy density below TV: E ¼ p E u þ ð1 pÞ E A þ E H , where, at T below TV (monoclinic symmetry), energy contributions are E u ¼ K u cos2 b, i.e., uniaxial anisotropy term originating from APBs, 1 ~ K a sin y½cos j sin j2 2 1 þ K aa sin4 y½cos j sin j4 4 1 þ K~ b sin2 y½cos j þ sin j2 2 that describes magnetocrystalline anisotropy for monoclinic symmetry [3], and, finally, EA ¼
temperature K1 and K2 anisotropy constants from measurements on bulk samples [3]. Although, the reasonable agreement with experiment (in particular at low temperatures) was found, it is clear that a more realistic model should be invented, e.g. accounting for the magnetization direction in the APB’s normal to the film plane, as found by Kalev and Niesen [15]. Virtually, the same M(H) curves as those described above were found after 2 kOe field-cooling along in-plane /1 0 0S at T ¼ 115 K. In conclusion, we have found that although 2 kOe fieldcooling procedure along in-plane /1 0 0S partially makes this axis an easy magnetization direction in single crystalline magnetite film, as in a bulk sample, the magnetization process differs considerably from that for bulk specimens. It can qualitatively be explained by some type of additional uniaxial contribution to the magnetocrystalline anisotropy resulting from antiphase boundaries. This energy is approximately one order of magnitude larger than the anisotropy energy for bulk magnetite at low T. Acknowledgements
E H ¼ M s H cos y is the Zeeman term, common for the entire sample. Angles b, j and y are explained in the inset of Fig. 2 and in the calculations we have used magnetization values Ms equal to 551 emu/cm3 (T ¼ 290 K) and 575 emu/cm3 (77 K), as the highest M values measured. Minimizing the energy versus j and y and taking into account that M ¼ M s cos y leads to the formula rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 pffiffiffi M M M 2 2 1 þ 1 Ms Ms Ms 3K~ b ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 , 2pK u MsH M M M ð1 pÞ 2 M s 1 M s þ K~ 1 M s
This work is financially supported by the KBN State Committee for Scientific Research. References [1] [2] [3] [4] [5]
b
from which Ku can be calculated provided K~ b is known. The optimal value of K~ b ¼ 8 105 erg=cm3 (compared to 3.25 105 erg/cm3 for bulk samples [3]) is chosen taking into account that the right hand site of the above formula should not depend on H; consequently, the best Ku was 2 107 erg/cm3 and the M(H) calculated based on these values is shown on Fig. 3. This is conceivable that magnetocrystalline properties of thin films grown on MgO may differ from those of bulk samples. Although the lattice mismatch between magnetite and the MgO in the (0 0 1)-plane is small (0.3%), the substrate inevitably exerts negative pressure on magnetite crystal structure that can affect physical properties [9,11]. The application of the model (with K u ¼ 22 107 erg=cm3 ) to the high-temperature magnetization process is presented in Fig. 2, where we have used room
[6] [7] [8] [9] [10] [11]
[12] [13]
[14]
[15]
A. Gupta, J.Z. Sun, J. Magn. Magn. Mater. 200 (1999) 24. B.A. Calhoun, Phys. Rev. 94 (1954) 1577. Z. Ka˛ kol, J.M. Honig, Phys. Rev. B 40 (1989) 9090. Z. Ka˛ kol, J. Solid State Chem. 88 (1990) 104. D.T. Margulies, F.T. Parker, M.L. Rudee, F.E. Spada, J.N. Chapman, P.R. Aitchison, A.E. Berkowitz., Phys. Rev. Lett. 79 (1997) 5162. K. Abe, Y. Miyamoto, S. Chikazumi, J. Phys. Soc. Jpn 41 (1976) 1894. B. Handke, et al., J. Radioanal. Nucl. Chem. 246 (2000). N. Spiridis, B. Handke, T. S´l˛ezak, J. Barbasz, M. Zaja˛ c, J. Haber, J. Korecki, J. Phys. Chem. 108 (2004) 14356. K. Balakrishnan, S.K. Arora, I.V. Shvets, J. Phys.: Condens. Matter 16 (2004) 5387. D. Reisinger, P. Majewski, M. Opel, L. Alff, R. Gross, App. Phys. Lett. 85 (2004) 4980. B. Handke, A. Koz"owski, K. Parlin´ski, J. Przewoz´nik, T. S´l˛ezak, A.I. Chumakov, L. Niesen, Z. Ka˛ kol, J. Korecki, Phys. Rev. B 71 (2005) 144301. E. de Grave, B. Handke, private communication. T. Hibma, F.C. Voogt, L. Niesen, P.A.A. van der Heijden, W.M. de Jonge, J.J.T.M. Donkers, P.J. van der Zaag, J. Appl. Phys. 85 (1999) 5291. J.F. Bobo, D. Basso, E. Snoeck, C. Gatel, D. Hrabovsky, J.L. Gauffier, L. Ressier, R. Mamy, S. Visnovsky, J. Hamrle, J. Teillet, A.R. Fert, Eur. Phys. J. B 24 (2001) 43. L.A. Kalev, L. Niesen, Phys. Rev. B 67 (2003) 224403.
Physica B 382 (2006) 147–150 www.elsevier.com/locate/physb
Uniaxial anisotropy in magnetite thin film—Magnetization studies A. Wiechec´, J. Korecki, B. Handke, Z. Ka˛ kol, D. Owoc, D.A. Antolak, A. Koz"owski Department of Solid State Physics, Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krako´w, Poland Received 29 July 2005; received in revised form 17 February 2006; accepted 17 February 2006
Abstract Magnetization and electrical resistivity measurements have been performed on a stoichiometric single crystalline magnetite Fe3O4 thin film (thickness of ca. 500 nm) MBE deposited on MgO (1 0 0) substrate. The aim of these studies was to check the influence of preparation method and sample form (bulk vs. thin film) on magnetic anisotropy properties in magnetite. The film magnetization along /0 0 1S versus applied magnetic field has been determined both in the direction parallel and perpendicular to the film surface, and at temperatures above and below the Verwey transition. We have found, in agreement with published results, that the in-plane field of 10 kOe was not sufficient to saturate the sample. This can be understood if some additional factor, on top of the bulk magnetocrystalline anisotropy, is taken into account. r 2006 Elsevier B.V. All rights reserved. PACS: 75.70.i; 75.30.Gw Keywords: Magnetic thin films: properties; Magnetic anisotropy
1. Introduction Magnetite is well known both for its extensive use in traditional recording media and the role in the emerging field of spintronics [1]. This material also exhibits the discontinuous Verwey phase transformation at T V ¼ 124 K where many physical properties, including magnetic anisotropy, change abruptly. Magnetic properties, both below and above the Verwey transition, have been well documented in bulk single crystals [2–4] revealing interesting phenomena, as e.g. the changeover of easy magnetization axis at TV, switching of this axis at ToTV, etc. It is interesting whether these phenomena are also present in thin film single crystals, the forms of widest possible application. The aim of the paper is to study the magnetization process in magnetite thin films. The results may be particularly interesting in view of the reports [5] concerning additional source of anisotropy in this class of materials, on top of usual magnetocrystalline and dipole effect. High-temperature bulk magnetite has its easy, intermediate and hard axes along cubic /1 1 1S, /1 1 0S and Corresponding author.
E-mail address: [email protected] (A. Koz"owski). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.02.013
/0 0 1S directions, respectively. Below the Verwey transition the easy axis switches to [0 0 1] direction, while [1 1 0] and [1 1 0] become intermediate and hard axes. Since at TV magnetite also undergoes the structural phase transformation from high-temperature cubic to monoclinic, each of cubic /1 0 0S may become an easy axis and the material breaks into several kind of twins unless special field-cooling procedure and external stress is applied [2,3,6]. The simplest way to force the particular [0 0 1] to become an easy axis in bulk magnetite is to apply external magnetic field H42 kOe along this [0 0 1]. This procedure was applied here for 500 nm thin crystalline film and we have studied the field-cooling effect on the low temperature magnetization process. The magnetization process is compared to that in bulk single crystal and the implications of our findings are discussed.
2. Experiment and results The single crystalline magnetite film was grown [7] by Fe-vapor deposition from a MBE source at the rate of about 1 nm/min, under the O2 partial pressure in the 106 mbar range. The substrate, MgO(0 0 1), was cleaved in 57
ARTICLE IN PRESS A. Wiechec´ et al. / Physica B 382 (2006) 147–150
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N2 atmosphere and then annealed for 1 h at 900 K in UHV to assure atomic cleanness and perfect structure of the exposed surface (verified with AES and LEED). The optimum growth was achieved by keeping the substrate during deposition at 520 K, the standard preparation temperature for many previous studies [8]. pffiffiffiThepffiffisample ffi was checked by in-situ LEED, displaying ð 2 2ÞR451 reconstruction and the in situ CEMS showed spectrum typical for the bulk stoichiometric magnetite. The sample quality was also checked by AC resistivity (frequency 7 Hz) measurements, performed by standard 4-point method with ultrasonically bonded contacts. The results are shown in Fig. 1 and the typically observed [9,10] broadening of the transition region and the decreased resistivity drop at TV were found, as compared to bulk crystals. Similar widening of the transition region was recorded in X-ray diffraction measurements of the identical sample [11]. The reason for these effects is most probably the strain exerted by the substrate and accentuated by the antiphase boundaries [9]. Magnetic measurements were performed with a vibrating sample magnetometer at 290, 115 and 77 K. The sample holder with the MgO substrate was measured separately, and the signal was taken into account in the analysis. Magnetite film’s surface was set parallel to the magnetometer axis in such a way that both the [0 0 1] in-plane and the [0 1 0] out-of-plane axes could be set parallel to the magnetic field direction (see the inset in Fig. 2) and all the in-field measurements were done accordingly. At T ¼ 290 K these directions coincide with the hard magnetization axis of bulk magnetite, and the difference between magnetization processes in those two directions should be the measure of dipolar interactions (shape anisotropy). The results of measurements at T ¼ 290 K, as compared to the bulk characteristics [3] are shown on Fig. 2. Note, that for the bulk sample, magnetic field refers to the external field Hext corrected by demagnetization field
250
10
200
8
single crystalline 500nm film of Fe3O4 on MgO
7 6 5
cooling
4 3 heating
2 1 0 -1 3
4
5
6
7
HD (H eff ¼ H ext H D ; H D ¼ ð4p=3ÞM in case of sphere) to allow comparison with the thin film in-plane data where H D ¼ 0. The out-of-plane magnetization is plotted vs. Hext. The following facts are noteworthy:
the saturation was not achieved up to 10 kOe, even in inplane direction, contrary to a bulk sample where Heffo1 kOe is needed to saturate the sample along hard axis, magnetization processes along /1 0 0S for a bulk and the thin film (in-plane) are different even though M(Heff-0) matches closely.
100
Tv = 124.47 K Tv = 121.34 K
9
In(R/R250)
T (K)
150
Fig. 2. Reduced magnetization of magnetite thin film along /1 0 0S perpendicular (off-plane) and parallel (in plane) to the film surface, compared to relevant bulk characteristics (where the demagnetization field along /1 0 0S has been subtracted from the external field Hext) and the model curve (stars). Note, that magnetization values are normalized to their value at 10 kOe, which is not the saturation field for the thin film. Open hexagons point to M(H) calculated based on the results from Ref. [15]. The inset defines symbols used in energy minimization.
8
9
10
11
12
1000/T (K-1) Fig. 1. The results of AC resistivity measurements. The data were recorded both on cooling and heating. The histeresis is due to the thermometer lag (the histeresis in the bulk sample is appr. 0.03 K).
For low temperature measurements the film was fieldcooled at 10 kOe along the /1 0 0S in-plain direction. M(H) were then measured both in the same direction (that, after field-cooling procedure, should constitute the easy magnetization axis) and along the off-plain /1 0 0S (i.e. magnetically non specific direction). The results are shown on Fig. 3 and it is clear that the magnetization process along the in-plane /1 0 0S (bulk easy direction) is strikingly distinct from that for the bulk sample. In particular, the field of 11 kOe was not sufficient to saturate the sample, like at 290 K. Also Mo¨ssbauer spectroscopy measurements performed on the same film at 80 K, after field cooling at 250 kOe, showed that the local magnetization probed by effective magnetic fields at the 57Fe nuclei is not aligned in the film plane [12]. In order to check whether principal magnetocrystalline axes are the same as in a bulk sample we have cooled the
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Heff, Hext (Oe) Fig. 3. Magnetization of magnetite thin film at 77 K, along /1 0 0S perpendicular (bulk circles) and parallel (bulk squares) to the film surface, after the sample was field-cooled in in-plane H ¼ 10 kOe. The data for the zero-field cooled sample (open triangles) and relevant bulk characteristics (here demagnetization field along /1 0 0S has been subtracted from the external field) are shown for comparison. The arrow indicates axis switching and the stars are the best fit of the model. Error bars indicate absolute sample holder signal uncertainty.
sample in zero external magnetic field (ZFC, zero-field cooling process). In this case the sample should have broken into structural domains with the low temperature easy axis pointing along different /1 0 0S directions. The results of subsequent measurements (with H parallel to the in-plane [0 0 1]) are shown in Fig. 3, revealing the totally different characteristics than in the field-cooled sample. Apparently, no unique easy axis is set, but the sample partly orients under the increasing magnetic field, and M(H) for lowering field roughly resembles that for fieldcooled sample. The additional confirmation that the applied fieldcooling procedure basically establishes the unique easy axis comes from the appearance of axis switching phenomenon [2] marked with the arrow in Fig. 3. Namely, when the sample is magnetized along /1 0 0S perpendicular to the easy direction (established by the field cooling procedure) at temperatures slightly lower than TV, some structural reorientation may take place and this /1 0 0S direction can, at least partly, become a new easy axis. Although the experimental evidence for this phenomenon is blurred here mainly due to strong demagnetization field, the break in M(H) curve is apparent. 3. Discussion The magnetization process after ZFC and the axisswitching phenomenon prove that the easy magnetic direction was uniquely established. It is now interesting to explain why in such a situation the results of magnetization experiments (and the results of Mo¨ssbauer measurements [12]) are distinct from those for bulk
149
samples both at high and low temperatures. Our explanation is based assuming some additional contribution to the magnetic anisotropy, roughly independent of temperature. Also, since the ratio M(Heff-0)/MS is very close to 0.58 which corresponds to cos(54.71), the value predicted in case the magnetization vector points along easy /1 1 1S, it is tempting to suggest that /1 1 1S is still the easy axis in thin magnetite films at high temperature but with considerably higher anisotropy field, than in the bulk material. This kind of contribution to the magnetic anisotropy and the lack of saturation in thin films have already been found [5,13] and explained by the preparation induced structural domain pattern. In particular, the first step in layer-by-layer growth mechanism is the formation of two-dimensional islands that eventually coalesce. Whereas the resulting oxygen sublattice is continuous (and closely matches the oxygen sublattice of the MgO substrate), Fe cations may form rows pointing at several directions or mutually shifted, leading to so-called anti-phase boundaries [14] (APBs). A new type of magnetic interactions may develop in APBs, in particular relatively weak intrasublattice interactions may now become strong and antiferromagnetic. This process can lead to the observed difficulties with saturation and can cause the magnetic moment within APBs to point out of plain. Our measurements confirm that such a process may be the case here. We have first tried to simulate our M(H) data by the model based on the results of nuclear resonance scattering (NRS) of synchrotron radiation [15] of 15 nm epitaxial magnetite film grown on MgO and oriented as our sample. In this paper, it is assumed that due to strong anitferromagnetic interactions within APB spins tend to align perpendicular to the film plane close to the boundary position and lay flat far from it due to shape anisotropy. The angle j(x) between spins and the in-plane direction at the distance x from the APB is calculated based on NRS results and micromagnetic model without crystalline anisotropy term. The profile of the spin angle j(x) may depend on magnetic domain size z (equal to the distance between APBs) and the domain size in our sample may differ from the mean value of 106 nm reported in Ref. [15]. Nevertheless, for all conceivable domain sizes (20 nmozo400 nm) we have used the same j(x) from Ref. [15] and have set jðxÞ ¼ 0 (spins laying in plane) for 52oxoz52 nm, i.e. for all points far enough from the APB. The results are shown on Fig. 2 for z ¼ 106 nm and we have found that for any domain size z, the model M(H) dependence is too flat to reproduce our experimental results reasonably. Although our approach is oversimplified (j(x) should be calculated for each z), the results above suggest that actual crystalline anisotropy can not be postponed. To account for it, we have assumed that p-part of the sample (equal to the APBs density of 0.06 as estimated from TEM images [13]) has a strong uniaxial anisotropy pointing in the /1 1 1S direction, in agreement with the data for 290 K. This contribution from APBs, different from that sug-
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gested in Ref. [15], is temperature independent, so at ToTV the 1p part of the sample has magnetocrystalline anisotropy typical for a bulk monoclinic magnetite, while in the remaining part of the sample the same uniaxial anisotropy dominates. This leads to the following approximate formula for the energy density below TV: E ¼ p E u þ ð1 pÞ E A þ E H , where, at T below TV (monoclinic symmetry), energy contributions are E u ¼ K u cos2 b, i.e., uniaxial anisotropy term originating from APBs, 1 ~ K a sin y½cos j sin j2 2 1 þ K aa sin4 y½cos j sin j4 4 1 þ K~ b sin2 y½cos j þ sin j2 2 that describes magnetocrystalline anisotropy for monoclinic symmetry [3], and, finally, EA ¼
temperature K1 and K2 anisotropy constants from measurements on bulk samples [3]. Although, the reasonable agreement with experiment (in particular at low temperatures) was found, it is clear that a more realistic model should be invented, e.g. accounting for the magnetization direction in the APB’s normal to the film plane, as found by Kalev and Niesen [15]. Virtually, the same M(H) curves as those described above were found after 2 kOe field-cooling along in-plane /1 0 0S at T ¼ 115 K. In conclusion, we have found that although 2 kOe fieldcooling procedure along in-plane /1 0 0S partially makes this axis an easy magnetization direction in single crystalline magnetite film, as in a bulk sample, the magnetization process differs considerably from that for bulk specimens. It can qualitatively be explained by some type of additional uniaxial contribution to the magnetocrystalline anisotropy resulting from antiphase boundaries. This energy is approximately one order of magnitude larger than the anisotropy energy for bulk magnetite at low T. Acknowledgements
E H ¼ M s H cos y is the Zeeman term, common for the entire sample. Angles b, j and y are explained in the inset of Fig. 2 and in the calculations we have used magnetization values Ms equal to 551 emu/cm3 (T ¼ 290 K) and 575 emu/cm3 (77 K), as the highest M values measured. Minimizing the energy versus j and y and taking into account that M ¼ M s cos y leads to the formula rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 pffiffiffi M M M 2 2 1 þ 1 Ms Ms Ms 3K~ b ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 , 2pK u MsH M M M ð1 pÞ 2 M s 1 M s þ K~ 1 M s
This work is financially supported by the KBN State Committee for Scientific Research. References [1] [2] [3] [4] [5]
b
from which Ku can be calculated provided K~ b is known. The optimal value of K~ b ¼ 8 105 erg=cm3 (compared to 3.25 105 erg/cm3 for bulk samples [3]) is chosen taking into account that the right hand site of the above formula should not depend on H; consequently, the best Ku was 2 107 erg/cm3 and the M(H) calculated based on these values is shown on Fig. 3. This is conceivable that magnetocrystalline properties of thin films grown on MgO may differ from those of bulk samples. Although the lattice mismatch between magnetite and the MgO in the (0 0 1)-plane is small (0.3%), the substrate inevitably exerts negative pressure on magnetite crystal structure that can affect physical properties [9,11]. The application of the model (with K u ¼ 22 107 erg=cm3 ) to the high-temperature magnetization process is presented in Fig. 2, where we have used room
[6] [7] [8] [9] [10] [11]
[12] [13]
[14]
[15]
A. Gupta, J.Z. Sun, J. Magn. Magn. Mater. 200 (1999) 24. B.A. Calhoun, Phys. Rev. 94 (1954) 1577. Z. Ka˛ kol, J.M. Honig, Phys. Rev. B 40 (1989) 9090. Z. Ka˛ kol, J. Solid State Chem. 88 (1990) 104. D.T. Margulies, F.T. Parker, M.L. Rudee, F.E. Spada, J.N. Chapman, P.R. Aitchison, A.E. Berkowitz., Phys. Rev. Lett. 79 (1997) 5162. K. Abe, Y. Miyamoto, S. Chikazumi, J. Phys. Soc. Jpn 41 (1976) 1894. B. Handke, et al., J. Radioanal. Nucl. Chem. 246 (2000). N. Spiridis, B. Handke, T. S´l˛ezak, J. Barbasz, M. Zaja˛ c, J. Haber, J. Korecki, J. Phys. Chem. 108 (2004) 14356. K. Balakrishnan, S.K. Arora, I.V. Shvets, J. Phys.: Condens. Matter 16 (2004) 5387. D. Reisinger, P. Majewski, M. Opel, L. Alff, R. Gross, App. Phys. Lett. 85 (2004) 4980. B. Handke, A. Koz"owski, K. Parlin´ski, J. Przewoz´nik, T. S´l˛ezak, A.I. Chumakov, L. Niesen, Z. Ka˛ kol, J. Korecki, Phys. Rev. B 71 (2005) 144301. E. de Grave, B. Handke, private communication. T. Hibma, F.C. Voogt, L. Niesen, P.A.A. van der Heijden, W.M. de Jonge, J.J.T.M. Donkers, P.J. van der Zaag, J. Appl. Phys. 85 (1999) 5291. J.F. Bobo, D. Basso, E. Snoeck, C. Gatel, D. Hrabovsky, J.L. Gauffier, L. Ressier, R. Mamy, S. Visnovsky, J. Hamrle, J. Teillet, A.R. Fert, Eur. Phys. J. B 24 (2001) 43. L.A. Kalev, L. Niesen, Phys. Rev. B 67 (2003) 224403.