- Email: [email protected]
Cu(1 0 0)-films
Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
Correlation between the microscopic and macroscopic magnetic properties in ultrathin Fe/Cu(1 0 0)-films A. Berger!, B. Feldmann",#, H. Zillgen", M. Wuttig",* ! Physics Department, University of California, San Diego, USA " Institut fu( r Grenzfla( chenforschung und Vakuumphysik, Forschungszentrum Ju( lich, 52425 Ju( lich, Germany # Booz Allen & Hamilton, 40215 Du( sseldorf, Germany Received 12 June 1997; received in revised form 2 September 1997
Abstract The magnetic properties of ultrathin iron films on Cu(1 0 0), grown at 300 and 100 K, were investigated by the magneto-optic Kerr effect (MOKE). In the thickness range up to about 11 monolayers, we observe a rich variety of unusual magnetic phases and properties. In particular, Fe films deposited at 300 K exhibit a pronounced peak of the coercive field upon transition from the ferromagnetic phase to the live layer phase. We develop a domain model, which explains this behavior by correlating the microscopic and macroscopic magnetic properties. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Structure and magnetism; Micromagnetism; Thin films; Phase transition
1. Introduction Iron films epitaxially grown on Cu(1 0 0) exhibit a rich variety of structural and magnetic phases, depending upon film thickness and growth conditions (growth temperature, residual gas, etc.). In general, it is possible to stabilize three different phases of Fe. At large thickness, BCC(1 1 0) Fe is formed independent of the preparation procedure [1—3]. Below about 4 ML, the ferromagnetic (FM) FCC(1 0 0) Fe phase grows on the Cu(1 0 0)
* Corresponding author. Tel.: 49 2461 614733; fax: 49 2461 613907; e-mail: [email protected].
substrate after deposition at 300 K as well as after deposition at 100 K and annealing to 300 K [3]. But only after deposition at 300 K, the third phase which consists of antiferromagnetic (AF) FCC Fe with FM FCC surface layers can be stabilized in the thickness range between 4 and 11 ML [4—6]. This rich variety of structural and magnetic phases offers the unique possibility to explore the close correlation between film structure and magnetic properties, which explains the tremendous interest this material system has attracted in recent years. Fig. 1 summarizes magnetic and structural properties of ultrathin iron films [1—3]. The Kerr ellipticity measured at saturation field indicates how the magnetic moment of the iron films changes with
0304-8853/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 1 0 6 7 - 6
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A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
Fig. 1. Correlation of magnetism and structure: The upper portion displays the Kerr ellipticity at saturation field for films grown at 300 K (RT) on the left-hand side, and films deposited at 100 K and annealed to 300 K (LT) on the right-hand side. Solid circles denote perpendicular magnetization and open circles describe in-plane magnetization, respectively. In the lower portion, the corresponding side view of the film structure is depicted schematically with growing film thickness.
thickness (upper part of Fig. 1). The structural properties, in particular the interlayer spacing, are shown in the lower portion of Fig. 1. In this paper, we discuss the correlation of the microscopic properties with the macroscopic magnetic behavior, focusing especially on the relation between the thickness-dependent saturation magnetization M (d) and the coercive field H . In Sec4 # tion 2, we give a brief description of our setup and experimental procedures. Experimental results are presented and discussed in Section 3; in particular, a domain model is outlined which explains how the microscopic structural changes are correlated with the macroscopic magnetization properties.
2. Experimental The experiments in this study were performed in an ultra-high vacuum chamber, which contains all
facilities necessary to prepare the substrate and films as well as analyze their structural and magnetic properties. Only a brief description of the system will be given here, because the apparatus and our sample treatment have already been described elsewhere [4,7]. Fe was evaporated from a small disk of high purity (99.99%) which was heated by electron bombardment. During Fe deposition, the pressure in our UHV chamber stayed between 8]10~9 and 2]10~8 Pa and dropped quickly to a base pressure of 4]10~9 Pa after the source was turned off. The resulting contamination level of the Fe-films was below 2% of one monolayer. Fe was deposited at a sample temperature of 300 K (RT) and 100 K (LT) with a deposition rate between 0.5 and 2.0 ML/min. Films grown at 100 K were subsequently annealed to 300 K for 10 min to improve the structural order and decrease the surface roughness. Most of our samples
A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
were deposited with a wedge-like thickness variation. The thickness profile of such films was determined by the Auger electron intensity ratios, which were taken at various points on the wedge. The Auger electron intensity ratios had been previously calibrated by medium energy electron diffraction (MEED)-intensity oscillations which were measured during the deposition of films with homogeneous thickness [3]. The magnetic properties of the films were characterized using the magneto-optic Kerr effect (MOKE). Hysteresis loops were recorded in longitudinal and polar geometry employing a polarization modulation technique [4]. As a light source we used a He—Ne laser with a wavelength of 632.8 nm. The maximum field which could be applied was 1050 Oe. In addition to measurements on wedge-shaped samples, we took several data on homogeneous films to rule out that the thickness gradient of the wedge influenced the magnetic properties. No significant differences between the uniform and wedge-shaped films were detected.
3. Results and discussion Independent of the preparation condition FM FCC Fe is stabilized on Cu(1 0 0) up to approxi-
37
mately 4—5 ML in regions I and A (Fig. 1). This phase is characterized by a perpendicular magnetization and a sinusoidal shear of neighboring atomic rows in FCC [0 1 1]-direction and a corrugation with a periodicity of 4—5 atoms. This reconstruction is indicative for the structural instability of FM FCC iron and above a critical film thickness, the FM FCC phase can no longer be stabilized. Hence, the film structure changes above this thickness. Depending upon the growth temperature, two different phases are formed. For LT growth, the shear displacement and the interlayer distance increases and the FM FCC phase transforms directly into the BCC(1 1 0) iron phase for thicknesses above 5 ML (region B). Associated with this structural phase transition is a magnetic reorientation from perpendicular (region A) to in-plane orientation of the magnetization (region B). This can be clearly seen in Fig. 1 (right-hand side) where we observe an almost linear increase of the saturation magnetization up to a thickness of 5 ML. At this particular thickness, the out-of-plane saturation signal drops abruptly to zero and an in-plane Kerr signal appears. The coercive field, shown in Fig. 2 for LT as well as RT growth conditions, does not show any unusual behavior for the LT growth phase transition (A to B). In region A, the coercive field decreases monotonically with the film thickness, which can
Fig. 2. Thickness dependence of the polar (v) and longitudinal (L) coercive field measured for RT-films (left) and LT-films (right).
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A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
be interpreted as a thickness-dependent anisotropy [8]. In region B, the coercive field is rather small and almost independent of the thickness, a behavior which has been previously observed for other in-plane magnetized systems [9]. The physics of the RT grown films is considerably more complex. Not only do we observe a third phase, the FM live layer phase (II), as a function of the film thickness, but we also find a rather unusual behavior of the coercive field in this case. At about 4 ML thickness, we observe a phase transition from a fully magnetized FM FCC(1 0 0) phase I to the live layer phase II. As previous experiments showed, this live layer phase consists of a FM surface layer and shows indications for antiferromagnetic ordering in the interior of the film [6]. This phase transition is associated with a very large peak of the coercive field H as shown in # Fig. 2, even though the magnetization orientation is perpendicular in both cases. Furthermore, we observe that the peak in the coercive field is shifted to slightly higher thickness values (maximum at approximately 4.7 ML) compared to the transition of the saturation magnetization or saturation ellipticity as shown in Fig. 1. Nonetheless, it is obvious from a comparison of Figs. 1 and 2 that the observed H maximum is clearly related to the struc# tural and magnetic-phase transition (IPII). This is in perfect agreement with a conclusion derived previously by Bader et al. [10,11]. These authors already observed the coercivity maximum upon the phase transition from phase IPII (and phase IIPIII) for films grown at RT and concluded that the maximum of H is related to the structural # transition of the iron films. In the following, we will outline a domain model which will enable us to relate the macroscopic magnetization properties, i.e. the coercive field H , to the microscopic struc# tural and magnetic properties. In general, magnetization reversal is associated with three processes: coherent magnetization rotation, domain nucleation, and domain-wall displacement [12]. In our model, we do not consider the possibility of coherent magnetization rotation because the external magnetic field is applied along the easy axis of magnetization, i.e. there is no torque onto the magnetization vector. Therefore, the magnetization reversal as well as the coercive
field H should be characterized by domain effects # only. Furthermore, we restrict our model to the effect of domain wall displacement and do not consider the effect of domain nucleation here. This simplification of the problem would not be justified if we would attempt to describe the entire magnetization reversal process. But our goal here is the explanation of the H anomaly in the phase # transition region only. Thus, we can neglect the domain nucleation process, because it is highly unlikely that the domain nucleation field H would / show such an anomaly in that very thickness region. In general, H is determined by a competition / of the domain-wall energy necessary to form a nucleus and the Zeeman energy gained by this nucleus. Assuming different material parameters in phases I and II, this energy competition would result in two different values for H in phases I and / II and in a step-like change of the nucleation field as a function of film thickness. But this is not what we observe experimentally for H and, therefore, # the H anomaly has to be associated with domain# wall displacement effects. To motivate our model, let us first reconsider what is happening in the phase transition region. With growing film thickness, the ferromagnetic FCC phase becomes unstable and the FCC live layer phase is formed. This transition is not really abrupt as one can see from Fig. 1, where the transition region shows an extension of almost 2 ML thickness. But, of course, locally the film thickness is an integer and the film is hence either in phases I or II. Thus, the transition region corresponds to a lateral distribution of film regions being in phases I or II, i.e. the film represents a nonuniform system. It is well known that magnetically inhomogeneous materials show increased values of the coercive field [12]. This results from the fact that the domain wall energy in a non homogeneous material varies as a function of the position. Thus, domain walls can get trapped which corresponds to a larger magnetic field necessary for domain wall displacement and an increased value of the coercive field. After this general discussion, we are now able to formulate a model which describes the magnetization reversal in the transition regions I—II. Fig. 3 shows the geometry we assume for our
A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
39
Fig. 3. Model for a thin magnetic film with two magnetic phases. The upper part shows the top view of the film, the lower part the side view. The position of the domain wall with width w for the largest coercive force is shown for 0(b(0.5 (on the left side) and 0.5)b)1 (on the right side), respectively. Ferromagnetic domains and layers are shaded dark, paramagnetic or antiferromagnetic ones white. s is the distance between two domains of a structural phase, 2l the domain diagonal and d and d the number of ferromagnetic I II layers in phases I or II. x is the in-plane propagation direction of the domain wall.
domain-wall displacement model. The majority phase (I or II) is connected in the entire film plane and the minority phase is immersed in this background forming a regular grid of quadratic patches. In the framework of this model, the change in the different phase concentrations during film growth is now described as a change in the size of the minority patches. We introduce the phase ratio b, which is defined as the phase II area/total film area. For b(0.5, the minority phase II patches are growing (a) and accordingly for b'0.5 the phase I patches are decreasing with increasing film thickness (b). Even though the regular grid and the patch form we have chosen in Fig. 3 are highly artificial, this model has the advantage that the geometric structure is not changing for the entire phase transition region, i.e. patches of phases I and II have the same shape. Therefore, the model does not include any additional qualitative changes of the microstructure and we can isolate the effect of the relative phase contribution onto H . The bottom # part of Fig. 3 shows the assumed magnetization structure of the Fe film in the transition region. As we can see, the ferromagnetic thickness is now laterally varying according to the distribution of phases I and II patches. Therefore, the wall energy is a function of the position x. We furthermore
assume constant material parameters in phases I and II, so that the only change in the magnetic properties results from the different ferromagnetic thickness of the particular phase. The total energy as a function of the externally applied field H can now be written as E (x)"E (x)#E (x), 505 ; $8 with the Zeeman energy
PP
E (x)"!H ;
M d(x) dA 4 A and the domain-wall energy
(1)
(2)
E (x)"e (¼A (x)d #¼A (x)d ), (3) $8 $8 I I II II with M and H being the saturation magnetization 4 and the externally applied field, respectively. d(x) is the local magnetic thickness which can either be d or d (Fig. 3). e is the domain-wall energy I II $8 density, and ¼A (x) and ¼A (x) describe the surI II face area of phases I and II which is covered by the domain wall. These quantities ¼A and ¼A do not I II only depend on the wall position x but also on the relative magnitude of l, s, and the wall width w. The geometric quantities l and s are shown in Fig. 3 and we furthermore define d"d !d . For the I II
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A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
derivation of Eqs. (1)—(3), we have assumed that the energy density within the wall is constant and that the magnetization structure within the wall is such that the Zeeman energy contribution of the entire structure is equal to the case of an infinitely thin wall (w"0). Even though these assumptions do not correspond to a realistic domain-wall structure they should not significantly change the outcome of our calculation. Furthermore, more exact domainwall models have only been developed for uniform systems [12]. Thus, a laterally varying system as encountered here requires a rigorous micromagnetic approach which is beyond the scope of our investigation. Using the total energy Eqs. (1)—(3), we are now able to determine the coercive field as a function of the film thickness or the phase ratio b. First, let us consider how the domain wall behaves as a function of E (x). As long as E (x) has a local minimum 505 505 the domain wall is trapped within this minimum and further displacement requires a larger magnetic field H. Only if the field is large enough and E does not exhibit any local minimum anymore, 505 the domain wall is free to move throughout the entire sample. Thus, we can identify the coercive field as the minimum magnetic field at which the total energy function does not exhibit any local minimum anymore. In this way, we derive for the thickness-dependent coercive field
AB
As J2b w 2 H (b)" , , 0)b)2 # 2 w d #dw/s!dJ2b s I (4a)
AB AB
J2b w 2 H (b)"A )b)1, (4b) , 2 2 # s d #dw/s!dJ2b I 1 w 2 , (4c) H (b)"A , 1)b)1!2 # s d #dw/s 2 II As J2(1!b) H (b)" , # 2 w d !dw/s#dJ2(1!b) II w 2 )b)1, (4d) 1!2 s
AB
Fig. 4 shows an example of H in the transition # region as a function of b. One can clearly see that H exhibits a pronounced peak in the transition #
Fig. 4. Dependence of the polar coercive force on the fraction of phase II domains at the film surface b. The model was applied according to Eqs. (4a), (4b), (4c) and (4d) for the transition from I to II with d "3.7 ML, d "2 ML and w/s"33/80. I II
region. The peak originates from the fact, that the wall energy in phase II is significantly lower than in phase I due to the reduced magnetically effective thickness. Thus, the larger the phase II contribution gets, the more difficult it is to remove a domain wall from the phase II patches, i.e. the coercive field increases with b. We also see, that within our model H is vanishing if b approaches either 0 or 1, which # is the expected result, because b"0, 1 corresponds to a uniform phase. Within a uniform phase, domain-wall displacement does not require any significant magnetic field. So, our model does not describe H properly as one approaches a uniform # phase. As outlined before, this limited applicability is caused by the suppression of nucleation effects. Furthermore, we can see from Fig. 4 that the H # peak is not symmetric with respect to the phase ratio b. The peak is shifted towards larger values of b. The reason for this asymmetry is the asymmetric position of the domain-walls with respect to the minority phase as one can see in Fig. 3. For b(0.5, the domain wall tries to incorporate as much phase II (minority phase) regions as possible because this phase has the lower energy density per surface area. Therefore, the domain wall is located, at least partially, within the minority phase and can sense the size of this phase. Hence, H depends on the phase # ratio b and increases monotonically with b for b(0.5. For b'0.5, the domain wall now avoids the minority phase, because phase I has the higher
A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
energy density per surface area. Therefore, the domain wall is not necessarily influenced by any change of the phase I patch size. Up to a certain value of b, the coercive field is actually independent of b within our model (Fig. 4) Only when the minority patch size is of the order of the domain wall width w, the domain-wall displacement actually depends on this patch size and the coercive field changes accordingly. Thus, our model does not only explain the occurrence of a pronounced H peak in the phase # transition region; it also shows that this peak does not have to be symmetric with regard to the phase ratio b, but can be shifted to one side which is exactly what we observed in our experiment. Hence, our domain model fully explains the observed macroscopic magnetization behavior. It shows, in particular, that the thickness-dependent coercive field is intrinsically correlated with the non-uniform microscopic magnetization structure in the transition region IPII. Thus, we have achieved a detailed understanding of the correlation between the macroscopic magnetic behavior and the microscopic structural and magnetic characteristics, even though our domain model is certainly a very crude simplification of the actual microstructure within a real sample.
4. Summary Magnetic properties of ultrathin iron films on Cu(1 0 0) have been investigated. A close correlation between microscopic and macroscopic magnetic properties is found. In particular, Fe films deposited at 300 K exhibit a pronounced peak of the coercive field upon the transition from the ferromagnetic phase (I) to the live layer phase (II).
41
This thickness-dependent coercive field is intrinsically correlated with the non-uniform microscopic magnetization structure in the transition region IPII.
Acknowledgements Financial support by the Deutsche Forschungsgemeinschaft (Wu 243/2) is gratefully acknowledged. Work at UCSD was supported by the ONR-N000-1495-10541, NSF-DMR-94-00439 and the CMRR at UCSD. One of us (B.F.), gratefully acknowledges the support of the Konrad Adenauer Stiftung.
References [1] K. Kalki, D.D. Chambliss, K.E. Johnson, R.J. Wilson, S. Chiang, Phys. Rev. B 48 (1993) 18344. [2] M. Wuttig, B. Feldmann, J. Thomassen, F. May, H. Zillgen, A. Brodde, H. Hannemann, H. Neddermeyer, Surf. Sci. 291 (1—2) (1993) 14. [3] H. Zillgen, B. Feldmann, M. Wuttig, Surf. Sci. 321 (1994) 32. [4] J. Thomassen, F. May, B. Feldmann, M. Wuttig, H. Ibach, Phys. Rev. Lett. 69 (26) (1992) 3831. [5] W. Keune, T. Ezawa, W.A.A. Macedo, U. Glos, U. Kirschbaum, Physica B 161 (1989) 269. [6] D. Li, M. Freitag, J. Pearson, Z.Q. Qiu, S.D. Bader, J. Appl. Phys. 76 (10) (1994) 6425. [7] J. Thomassen, B. Feldmann, M. Wuttig, Surf. Sci. 264 (3) (1992) 406. [8] C. Chappert, P. Bruno, J. Appl. Phys. 64 (1988) 5736. [9] M.T. Kief, G.J. Mankey, R.F. Willis, J. Appl. Phys. 69 (1991) 5000. [10] S.D. Bader, Dongqi Li, Z.Q. Qiu, J. Appl. Phys. 76 (10) (1994) 6419. [11] Dongqi Li, M. Freitag, J. Pearson, Z.Q. Qiu, S.D. Bader, Phys. Rev. Lett. 72 (19) (1994) 3112. [12] D.J. Craik, R.S. Tebble, Ferromagnetism and Ferromagnetic Domains, North-Holland, Amsterdam, 1965.
Correlation between the microscopic and macroscopic magnetic properties in ultrathin Fe/Cu(1 0 0)-films A. Berger!, B. Feldmann",#, H. Zillgen", M. Wuttig",* ! Physics Department, University of California, San Diego, USA " Institut fu( r Grenzfla( chenforschung und Vakuumphysik, Forschungszentrum Ju( lich, 52425 Ju( lich, Germany # Booz Allen & Hamilton, 40215 Du( sseldorf, Germany Received 12 June 1997; received in revised form 2 September 1997
Abstract The magnetic properties of ultrathin iron films on Cu(1 0 0), grown at 300 and 100 K, were investigated by the magneto-optic Kerr effect (MOKE). In the thickness range up to about 11 monolayers, we observe a rich variety of unusual magnetic phases and properties. In particular, Fe films deposited at 300 K exhibit a pronounced peak of the coercive field upon transition from the ferromagnetic phase to the live layer phase. We develop a domain model, which explains this behavior by correlating the microscopic and macroscopic magnetic properties. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Structure and magnetism; Micromagnetism; Thin films; Phase transition
1. Introduction Iron films epitaxially grown on Cu(1 0 0) exhibit a rich variety of structural and magnetic phases, depending upon film thickness and growth conditions (growth temperature, residual gas, etc.). In general, it is possible to stabilize three different phases of Fe. At large thickness, BCC(1 1 0) Fe is formed independent of the preparation procedure [1—3]. Below about 4 ML, the ferromagnetic (FM) FCC(1 0 0) Fe phase grows on the Cu(1 0 0)
* Corresponding author. Tel.: 49 2461 614733; fax: 49 2461 613907; e-mail: [email protected].
substrate after deposition at 300 K as well as after deposition at 100 K and annealing to 300 K [3]. But only after deposition at 300 K, the third phase which consists of antiferromagnetic (AF) FCC Fe with FM FCC surface layers can be stabilized in the thickness range between 4 and 11 ML [4—6]. This rich variety of structural and magnetic phases offers the unique possibility to explore the close correlation between film structure and magnetic properties, which explains the tremendous interest this material system has attracted in recent years. Fig. 1 summarizes magnetic and structural properties of ultrathin iron films [1—3]. The Kerr ellipticity measured at saturation field indicates how the magnetic moment of the iron films changes with
0304-8853/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 1 0 6 7 - 6
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A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
Fig. 1. Correlation of magnetism and structure: The upper portion displays the Kerr ellipticity at saturation field for films grown at 300 K (RT) on the left-hand side, and films deposited at 100 K and annealed to 300 K (LT) on the right-hand side. Solid circles denote perpendicular magnetization and open circles describe in-plane magnetization, respectively. In the lower portion, the corresponding side view of the film structure is depicted schematically with growing film thickness.
thickness (upper part of Fig. 1). The structural properties, in particular the interlayer spacing, are shown in the lower portion of Fig. 1. In this paper, we discuss the correlation of the microscopic properties with the macroscopic magnetic behavior, focusing especially on the relation between the thickness-dependent saturation magnetization M (d) and the coercive field H . In Sec4 # tion 2, we give a brief description of our setup and experimental procedures. Experimental results are presented and discussed in Section 3; in particular, a domain model is outlined which explains how the microscopic structural changes are correlated with the macroscopic magnetization properties.
2. Experimental The experiments in this study were performed in an ultra-high vacuum chamber, which contains all
facilities necessary to prepare the substrate and films as well as analyze their structural and magnetic properties. Only a brief description of the system will be given here, because the apparatus and our sample treatment have already been described elsewhere [4,7]. Fe was evaporated from a small disk of high purity (99.99%) which was heated by electron bombardment. During Fe deposition, the pressure in our UHV chamber stayed between 8]10~9 and 2]10~8 Pa and dropped quickly to a base pressure of 4]10~9 Pa after the source was turned off. The resulting contamination level of the Fe-films was below 2% of one monolayer. Fe was deposited at a sample temperature of 300 K (RT) and 100 K (LT) with a deposition rate between 0.5 and 2.0 ML/min. Films grown at 100 K were subsequently annealed to 300 K for 10 min to improve the structural order and decrease the surface roughness. Most of our samples
A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
were deposited with a wedge-like thickness variation. The thickness profile of such films was determined by the Auger electron intensity ratios, which were taken at various points on the wedge. The Auger electron intensity ratios had been previously calibrated by medium energy electron diffraction (MEED)-intensity oscillations which were measured during the deposition of films with homogeneous thickness [3]. The magnetic properties of the films were characterized using the magneto-optic Kerr effect (MOKE). Hysteresis loops were recorded in longitudinal and polar geometry employing a polarization modulation technique [4]. As a light source we used a He—Ne laser with a wavelength of 632.8 nm. The maximum field which could be applied was 1050 Oe. In addition to measurements on wedge-shaped samples, we took several data on homogeneous films to rule out that the thickness gradient of the wedge influenced the magnetic properties. No significant differences between the uniform and wedge-shaped films were detected.
3. Results and discussion Independent of the preparation condition FM FCC Fe is stabilized on Cu(1 0 0) up to approxi-
37
mately 4—5 ML in regions I and A (Fig. 1). This phase is characterized by a perpendicular magnetization and a sinusoidal shear of neighboring atomic rows in FCC [0 1 1]-direction and a corrugation with a periodicity of 4—5 atoms. This reconstruction is indicative for the structural instability of FM FCC iron and above a critical film thickness, the FM FCC phase can no longer be stabilized. Hence, the film structure changes above this thickness. Depending upon the growth temperature, two different phases are formed. For LT growth, the shear displacement and the interlayer distance increases and the FM FCC phase transforms directly into the BCC(1 1 0) iron phase for thicknesses above 5 ML (region B). Associated with this structural phase transition is a magnetic reorientation from perpendicular (region A) to in-plane orientation of the magnetization (region B). This can be clearly seen in Fig. 1 (right-hand side) where we observe an almost linear increase of the saturation magnetization up to a thickness of 5 ML. At this particular thickness, the out-of-plane saturation signal drops abruptly to zero and an in-plane Kerr signal appears. The coercive field, shown in Fig. 2 for LT as well as RT growth conditions, does not show any unusual behavior for the LT growth phase transition (A to B). In region A, the coercive field decreases monotonically with the film thickness, which can
Fig. 2. Thickness dependence of the polar (v) and longitudinal (L) coercive field measured for RT-films (left) and LT-films (right).
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A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
be interpreted as a thickness-dependent anisotropy [8]. In region B, the coercive field is rather small and almost independent of the thickness, a behavior which has been previously observed for other in-plane magnetized systems [9]. The physics of the RT grown films is considerably more complex. Not only do we observe a third phase, the FM live layer phase (II), as a function of the film thickness, but we also find a rather unusual behavior of the coercive field in this case. At about 4 ML thickness, we observe a phase transition from a fully magnetized FM FCC(1 0 0) phase I to the live layer phase II. As previous experiments showed, this live layer phase consists of a FM surface layer and shows indications for antiferromagnetic ordering in the interior of the film [6]. This phase transition is associated with a very large peak of the coercive field H as shown in # Fig. 2, even though the magnetization orientation is perpendicular in both cases. Furthermore, we observe that the peak in the coercive field is shifted to slightly higher thickness values (maximum at approximately 4.7 ML) compared to the transition of the saturation magnetization or saturation ellipticity as shown in Fig. 1. Nonetheless, it is obvious from a comparison of Figs. 1 and 2 that the observed H maximum is clearly related to the struc# tural and magnetic-phase transition (IPII). This is in perfect agreement with a conclusion derived previously by Bader et al. [10,11]. These authors already observed the coercivity maximum upon the phase transition from phase IPII (and phase IIPIII) for films grown at RT and concluded that the maximum of H is related to the structural # transition of the iron films. In the following, we will outline a domain model which will enable us to relate the macroscopic magnetization properties, i.e. the coercive field H , to the microscopic struc# tural and magnetic properties. In general, magnetization reversal is associated with three processes: coherent magnetization rotation, domain nucleation, and domain-wall displacement [12]. In our model, we do not consider the possibility of coherent magnetization rotation because the external magnetic field is applied along the easy axis of magnetization, i.e. there is no torque onto the magnetization vector. Therefore, the magnetization reversal as well as the coercive
field H should be characterized by domain effects # only. Furthermore, we restrict our model to the effect of domain wall displacement and do not consider the effect of domain nucleation here. This simplification of the problem would not be justified if we would attempt to describe the entire magnetization reversal process. But our goal here is the explanation of the H anomaly in the phase # transition region only. Thus, we can neglect the domain nucleation process, because it is highly unlikely that the domain nucleation field H would / show such an anomaly in that very thickness region. In general, H is determined by a competition / of the domain-wall energy necessary to form a nucleus and the Zeeman energy gained by this nucleus. Assuming different material parameters in phases I and II, this energy competition would result in two different values for H in phases I and / II and in a step-like change of the nucleation field as a function of film thickness. But this is not what we observe experimentally for H and, therefore, # the H anomaly has to be associated with domain# wall displacement effects. To motivate our model, let us first reconsider what is happening in the phase transition region. With growing film thickness, the ferromagnetic FCC phase becomes unstable and the FCC live layer phase is formed. This transition is not really abrupt as one can see from Fig. 1, where the transition region shows an extension of almost 2 ML thickness. But, of course, locally the film thickness is an integer and the film is hence either in phases I or II. Thus, the transition region corresponds to a lateral distribution of film regions being in phases I or II, i.e. the film represents a nonuniform system. It is well known that magnetically inhomogeneous materials show increased values of the coercive field [12]. This results from the fact that the domain wall energy in a non homogeneous material varies as a function of the position. Thus, domain walls can get trapped which corresponds to a larger magnetic field necessary for domain wall displacement and an increased value of the coercive field. After this general discussion, we are now able to formulate a model which describes the magnetization reversal in the transition regions I—II. Fig. 3 shows the geometry we assume for our
A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
39
Fig. 3. Model for a thin magnetic film with two magnetic phases. The upper part shows the top view of the film, the lower part the side view. The position of the domain wall with width w for the largest coercive force is shown for 0(b(0.5 (on the left side) and 0.5)b)1 (on the right side), respectively. Ferromagnetic domains and layers are shaded dark, paramagnetic or antiferromagnetic ones white. s is the distance between two domains of a structural phase, 2l the domain diagonal and d and d the number of ferromagnetic I II layers in phases I or II. x is the in-plane propagation direction of the domain wall.
domain-wall displacement model. The majority phase (I or II) is connected in the entire film plane and the minority phase is immersed in this background forming a regular grid of quadratic patches. In the framework of this model, the change in the different phase concentrations during film growth is now described as a change in the size of the minority patches. We introduce the phase ratio b, which is defined as the phase II area/total film area. For b(0.5, the minority phase II patches are growing (a) and accordingly for b'0.5 the phase I patches are decreasing with increasing film thickness (b). Even though the regular grid and the patch form we have chosen in Fig. 3 are highly artificial, this model has the advantage that the geometric structure is not changing for the entire phase transition region, i.e. patches of phases I and II have the same shape. Therefore, the model does not include any additional qualitative changes of the microstructure and we can isolate the effect of the relative phase contribution onto H . The bottom # part of Fig. 3 shows the assumed magnetization structure of the Fe film in the transition region. As we can see, the ferromagnetic thickness is now laterally varying according to the distribution of phases I and II patches. Therefore, the wall energy is a function of the position x. We furthermore
assume constant material parameters in phases I and II, so that the only change in the magnetic properties results from the different ferromagnetic thickness of the particular phase. The total energy as a function of the externally applied field H can now be written as E (x)"E (x)#E (x), 505 ; $8 with the Zeeman energy
PP
E (x)"!H ;
M d(x) dA 4 A and the domain-wall energy
(1)
(2)
E (x)"e (¼A (x)d #¼A (x)d ), (3) $8 $8 I I II II with M and H being the saturation magnetization 4 and the externally applied field, respectively. d(x) is the local magnetic thickness which can either be d or d (Fig. 3). e is the domain-wall energy I II $8 density, and ¼A (x) and ¼A (x) describe the surI II face area of phases I and II which is covered by the domain wall. These quantities ¼A and ¼A do not I II only depend on the wall position x but also on the relative magnitude of l, s, and the wall width w. The geometric quantities l and s are shown in Fig. 3 and we furthermore define d"d !d . For the I II
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A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
derivation of Eqs. (1)—(3), we have assumed that the energy density within the wall is constant and that the magnetization structure within the wall is such that the Zeeman energy contribution of the entire structure is equal to the case of an infinitely thin wall (w"0). Even though these assumptions do not correspond to a realistic domain-wall structure they should not significantly change the outcome of our calculation. Furthermore, more exact domainwall models have only been developed for uniform systems [12]. Thus, a laterally varying system as encountered here requires a rigorous micromagnetic approach which is beyond the scope of our investigation. Using the total energy Eqs. (1)—(3), we are now able to determine the coercive field as a function of the film thickness or the phase ratio b. First, let us consider how the domain wall behaves as a function of E (x). As long as E (x) has a local minimum 505 505 the domain wall is trapped within this minimum and further displacement requires a larger magnetic field H. Only if the field is large enough and E does not exhibit any local minimum anymore, 505 the domain wall is free to move throughout the entire sample. Thus, we can identify the coercive field as the minimum magnetic field at which the total energy function does not exhibit any local minimum anymore. In this way, we derive for the thickness-dependent coercive field
AB
As J2b w 2 H (b)" , , 0)b)2 # 2 w d #dw/s!dJ2b s I (4a)
AB AB
J2b w 2 H (b)"A )b)1, (4b) , 2 2 # s d #dw/s!dJ2b I 1 w 2 , (4c) H (b)"A , 1)b)1!2 # s d #dw/s 2 II As J2(1!b) H (b)" , # 2 w d !dw/s#dJ2(1!b) II w 2 )b)1, (4d) 1!2 s
AB
Fig. 4 shows an example of H in the transition # region as a function of b. One can clearly see that H exhibits a pronounced peak in the transition #
Fig. 4. Dependence of the polar coercive force on the fraction of phase II domains at the film surface b. The model was applied according to Eqs. (4a), (4b), (4c) and (4d) for the transition from I to II with d "3.7 ML, d "2 ML and w/s"33/80. I II
region. The peak originates from the fact, that the wall energy in phase II is significantly lower than in phase I due to the reduced magnetically effective thickness. Thus, the larger the phase II contribution gets, the more difficult it is to remove a domain wall from the phase II patches, i.e. the coercive field increases with b. We also see, that within our model H is vanishing if b approaches either 0 or 1, which # is the expected result, because b"0, 1 corresponds to a uniform phase. Within a uniform phase, domain-wall displacement does not require any significant magnetic field. So, our model does not describe H properly as one approaches a uniform # phase. As outlined before, this limited applicability is caused by the suppression of nucleation effects. Furthermore, we can see from Fig. 4 that the H # peak is not symmetric with respect to the phase ratio b. The peak is shifted towards larger values of b. The reason for this asymmetry is the asymmetric position of the domain-walls with respect to the minority phase as one can see in Fig. 3. For b(0.5, the domain wall tries to incorporate as much phase II (minority phase) regions as possible because this phase has the lower energy density per surface area. Therefore, the domain wall is located, at least partially, within the minority phase and can sense the size of this phase. Hence, H depends on the phase # ratio b and increases monotonically with b for b(0.5. For b'0.5, the domain wall now avoids the minority phase, because phase I has the higher
A. Berger et al. / Journal of Magnetism and Magnetic Materials 183 (1998) 35—41
energy density per surface area. Therefore, the domain wall is not necessarily influenced by any change of the phase I patch size. Up to a certain value of b, the coercive field is actually independent of b within our model (Fig. 4) Only when the minority patch size is of the order of the domain wall width w, the domain-wall displacement actually depends on this patch size and the coercive field changes accordingly. Thus, our model does not only explain the occurrence of a pronounced H peak in the phase # transition region; it also shows that this peak does not have to be symmetric with regard to the phase ratio b, but can be shifted to one side which is exactly what we observed in our experiment. Hence, our domain model fully explains the observed macroscopic magnetization behavior. It shows, in particular, that the thickness-dependent coercive field is intrinsically correlated with the non-uniform microscopic magnetization structure in the transition region IPII. Thus, we have achieved a detailed understanding of the correlation between the macroscopic magnetic behavior and the microscopic structural and magnetic characteristics, even though our domain model is certainly a very crude simplification of the actual microstructure within a real sample.
4. Summary Magnetic properties of ultrathin iron films on Cu(1 0 0) have been investigated. A close correlation between microscopic and macroscopic magnetic properties is found. In particular, Fe films deposited at 300 K exhibit a pronounced peak of the coercive field upon the transition from the ferromagnetic phase (I) to the live layer phase (II).
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This thickness-dependent coercive field is intrinsically correlated with the non-uniform microscopic magnetization structure in the transition region IPII.
Acknowledgements Financial support by the Deutsche Forschungsgemeinschaft (Wu 243/2) is gratefully acknowledged. Work at UCSD was supported by the ONR-N000-1495-10541, NSF-DMR-94-00439 and the CMRR at UCSD. One of us (B.F.), gratefully acknowledges the support of the Konrad Adenauer Stiftung.
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