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Au(1 1 1)
Journal of Magnetism and Magnetic Materials 492 (2019) 165648
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Research articles
Orthogonal bistable magnetic domains in Co/Au(1 1 1)
T
S. Pütter Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science at Heinz Maier-Leibnitz Zentrum, Lichtenbergstr. 1, 85747 Garching, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Thin films Spin reorientation transition Perpendicular magnetic anisotropy Phase of coexistence
The thickness-driven spin-reorientation transition of Co/Au(1 1 1) is studied via in situ Kerr microscopy. On varying the premagnetization conditions in external field of in-plane or normal orientation, the magnetic switching into a final remanent state from an in-plane field is investigated. The quantitative analysis of the Kerr rotation derived from Kerr microscopy images allows the determination of the population of different magnetic phases as a function of thickness. Coexisting magnetic phases with preferred in-plane and out-of-plane magnetization orientation are identified. The overall switching behaviour is explained by thermal activation of magnetic domains. We show that there is a population of orthogonal bistable magnetic domains, which can be remanently switched between out-of-plane and in-plane orientation by the appropriate magnetic field. This quantity is related to the intersection of the population of states for in-plane and out-of-plane magnetization.
1. Introduction Spin reorientation transitions (SRT) are a fascinating topic in magnetism as the magnetic orientation changes due to a parameter like temperature or thickness. SRTs have been studied in bulk [1] as well as in ultrathin film systems for a long time, e.g. Refs. [2–5]. A spin-reorientation is characterized by the change of magnetization orientation due to the competition of magnetic anisotropies like magnetocrystalline, surface or shape anisotropy. For uniaxial anisotropy, the free energy density fA in second order approximation is given by
fA = K1eff sin2 α + K2sin4 α
(1)
where α is the angle of the magnetization with respect to the system’s easy axis [6]. For thin films, α describes the angle between the magnetization and the surface normal. The effective anisotropy K1eff is composed of the first order anisotropy constant K1 and the shape ani1 sotropy, i. e. K1eff = K1 − 2 μ0 Ms2; Ms denotes the saturation magnetization and μ0 the vacuum permeability. K2 is the anisotropy constant of second order. As the anisotropy constants depend on temperature and/ or film thickness, their balance changes with these parameters and, as a consequence, the orientation of the magnetization may also change. Two different types of transitions are generally distinguished [3,7,8]. A transition via magnetization canting is characterized by a continuous change of the magnetization orientation from out-of-plane to in-plane (K2 > 0 ). It has been unraveled as function of temperature [9–12] and thickness [13–19]. For the second type, in-plane and out-ofplane magnetization orientation may coexist within the transition region (K2 < 0 ). This transition has been discussed for various thin film
systems, e. g. Co/Fe/Cu(1 0 0) [20], Fe/Cu(1 0 0) [21,22], Co/Au(1 1 1) [23–27], Co0.9Fe0.1/MgO/Co0.9Fe0.1[28] and Au/Co/Au(1 1 1) [29,30], but only at few discrete thicknesses. Theory predicts a continuous increase/decrease of the population of in-plane and out-of-plane domains [31–33], which means the investigation of the balance between the two different orientations will give further insight into the magnetism of spin reorientation transitions. For the study of reorientation transitions, methods with high lateral resolution [9–11,15,23–25,34,35] but also integral methods like hysteresis loops [26,28] or magnetic susceptibility [36,37] have been utilized. In this publication, we study the SRT of Co wedges grown on Au (1 1 1) utilizing in situ Kerr microscopy. Protecting cap layers for ex situ studies may change the thickness of the SRT drastically [30,38] and might even alter the type of SRT. By extracting line profiles from Kerr microscopy images of different remanent states, the Kerr rotation is quantitatively studied in dependence of film thickness. We observe coexisting magnetic phases of inplane and out-of-plane orientation with varying population within the reorientation. Additionally, these magnetic domains are bistable, i. e. they can be remanently switched in out-of-plane and in-plane direction. The observed switching behaviour is explained by thermal activation of magnetic domains. 2. Experimental Sample preparation and experiments were performed at room temperature in ultra high vacuum (UHV) ( p = 2·10−10 mbar). The surface of the Au(1 1 1) single crystal was prepared by 1 keV Ar ion
E-mail address: [email protected]. https://doi.org/10.1016/j.jmmm.2019.165648 Received 14 January 2019; Received in revised form 25 July 2019; Accepted 28 July 2019 Available online 29 July 2019 0304-8853/ © 2019 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 492 (2019) 165648
S. Pütter
sputtering at about 37° to the sample plane and subsequent annealing at 650 °C for 30 min. The quality of the surface was checked by Auger electron spectroscopy and low energy electron diffraction. The 22 × 3 reconstruction [39,40] was obtained for the clean Au(1 1 1) surface. Cobalt films were grown epitaxially [41] by electron beam evaporation at a rate of 0.4 ML/min (ML = monolayer). The evaporation rate was calibrated by means of intensity oscillations of medium energy electron diffraction [42] with an estimated error of about 5%. To gain an overview about the thickness dependent magnetic behaviour at a glance, wedges were grown by slowly moving a sample mask during Co evaporation. To ensure repeatability of the experiments several Co wedges were prepared and studied. They all revealed similar magnetic behaviour. Here, we focus on two wedges. For Co wedge W1 the slope and the thickness range are 0.56 ML/mm and 3.0 − 5.2 ML and for wedge W2 they are 0.40 ML/mm and 3.5–5.0 ML, respectively. The width of the displayed wedges is 1.5 mm. The Kerr microscope for in situ investigation is similar to the one described in Ref. [43], except that a halogen lamp is used for illumination and the light is polarized/analyzed by Glan–Thompson prisms. The angle of incidence of the s-polarized light is 45°. The reflected light is analyzed by a polarizer tilted δ = 38 mrad out of extinction. The beam is guided through a long-distance microscope and finally detected by a charge-coupled device camera. The lateral resolution of the in situ Kerr microscope is estimated to be approx. 40μ m, which means that domains cannot be resolved. The typical domain size of Co/Au(1 1 1) at the SRT is below 2 μm (Refs. [25,44]) and may be even as small as 120 nm, see Ref. [10]. Similar to hysteresis measurements an overview about the magnetic behaviour in different fields is gained. Quantitative magnetic analysis of Kerr microscopy is gained from normalized difference images, which are calculated pixel-wise from two micrographs at different magnetic states, i. e. ΔI = (If − Ii )/(Ii + If ) with Ii and If as the intensities of the initial and the final state, respectively. The resulting intensity is proportional to the Kerr rotation θ . Considering only difference images minimizes topographic contributions. However, due to small vibrations of the sample holder inside the UHV chamber the topography remains visible. Line profiles, i. e. the Kerr rotation in dependence of the Co film thickness can be extracted from Kerr images by averaging the gray scale values at constant Co thickness within a width of 6 mm and rescaling according to the formulae above. Both, polar and longitudinal Kerr effect may contribute to the Kerr signal [45]. However, the ratio between polar and longitudinal Kerr rotation was found to be 30:1 at the angle of incidence of 45° by using formulae given by Zak et al. [46], the Voigt constant from Ref. [47] and tabulated values for the index of refraction [48]. It follows that the polar Kerr rotation measured with the Kerr microscope will be dominant for Co/Au(1 1 1) even with applied in-plane field. As the longitudinal Kerr rotation is well below the detection limit of the in situ Kerr microscope we may say that the Kerr signal will only be of polar origin. Hence, the detected Kerr rotation is proportional to the magnetization component that is in out-of-plane direction, i. e. normal to the sample plane. For simultaneous in situ detection of hysteresis loops in in-plane field two magneto-optical Kerr effect (MOKE) setups were utilized at 9° and 45° angles of incidence with s-polarized light. The setups are similar to the one described in Ref. [42]. For detection of the Kerr ellipticity ε a λ/4 -plate is inserted in front of the analyzer to cancel the window birefringence [49]. The polarizer is tilted by δ = 12.6 mrad out of extinction. For quantitative analysis, the Kerr ellipticity is calculated by ε = (I+M − I−M )·δ /(4I0) , considering the intensities I±M at opposite magnetic states and the intensity in absence of magnetic signals, I0 [49]. The sensitivity for polar and longitudinal Kerr effect in Co/Au(1 1 1) changes when the Kerr ellipticity is investigated. At 9° angle of incidence the ratio between polar and longitudinal Kerr ellipticity is 33:1, i.e. similar to the Kerr rotation at 45° mainly a polar signal is detected.
Fig. 1. Polar Kerr images of Co/Au(1 1 1) wedge W1 obtained from remanent states after applying magnetic fields of opposite sign (a) normal to the sample plane (± 35 mT), and (b) in the sample plane (± 110 mT). On the bottom of each image the non-ferromagnetic Kerr response of the Au substrate is visible. On top of the figure a side view of the Co wedge is sketched. The coarse structure of image (a) results from the realingment procedure of the sample, see Section 2.
The longitudinal ellipticity at 45°, however, is a superposition of polar and longitudinal signal according to the ratio 6:1, while the polar Kerr ellipticity for 9° and 45° is quite similar. Hence, a measurement at 45° will consist of polar and longitudinal ellipticity. A rough separation of the polar and longitudinal contributions at 45° can be obtained by substracting the Kerr ellipticities at 45° and 9° which will result in the longitudinal ellipticity. A more detailed investigation with sophisticated separation of the components has been performed by Ding et al. [26]. A magnetic field was applied either normal to or within the sample plane (parallel to constant thickness direction of the wedge). Remanent states were produced by slow reduction of the applied field to zero. For the application of normal magnetic fields the sample had to be moved out of the position for Kerr microscopy. Special care was taken for realignment of the sample. 3. Results and discussion 3.1. Kerr microscopy of Co/Au(1 1 1) in opposite magnetic fields Fig. 1 shows the magnetization reversal in Co wedge W1 grown on Au(1 1 1) after applying opposite magnetic fields normal to the sample plane and in-plane. The thickness range spans from 3 ML (left) to 5.2 ML Co (right). Both images exhibit the same part of the Co wedge with individual contrast enhancement. The Kerr signal of the gold substrate at the bottom of each image gives reference for zero magnetic response. Due to the dominant polar Kerr effect, only changes of out-of-plane magnetization are detected, see Section 2. In order to keep things simple, throughout this publication only remanent states are compared after successively applying initial and final magnetic field. Utilizing magnetic fields of H⊥ = ± 35 mT normal to the surface (first with negative then with positive sign) results in a magnetic contrast (darkgray) of the remanent states from lowest thickness up to du = 4.7 ML, Fig. 1(a). Obviously, the out-of-plane magnetization is stable in this range as the magnetic field is well above the saturation field in this direction [42]. Applying in-plane fields of H= = ± 110 mT also reveals magnetic contrast, but only in a very narrow thickness range of about 0.3 ML, Fig. 1(b). Higher contrast enhancement was applied to make the Kerr signal visible, i.e. the Kerr signal is smaller than in normal field. Hysteresis curves recorded in inplane field at thickness >du demonstrate in-plane easy axis [42]. In the following, we will show that the thickness interval exhibiting contrast in in-plane fields is related to the spin-reorientation transition of Co/Au (1 1 1). As the Kerr microscope is exclusively sensitive to magnetic changes in out-of-plane direction, it appears most surprising to find a contrast at 2
Journal of Magnetism and Magnetic Materials 492 (2019) 165648
S. Pütter
Fig. 3. Kerr ellipticity loops of 4.3 ML Co/Au(1 1 1) measured in different MOKE geometries. For the measurement in in-plane field two different MOKE setups were used, one with 9° angle of incidence and the second one with 45° angle of incidence. Due to the different sensitivities of the polar and longitudinal Kerr effect, a separation of the true longitudinal Kerr ellipticity is achieved, see text.
Fig. 2. The polar Kerr rotation θ as a function of Co thickness (wedge W2 ). The initial remanent states were created by applying a positive/negative in-plane ( A/ B ) and a positive/negative normal field (C / D ), respectively. The final state was always the remanent state after applying a positive in-plane field. The inset shows a side view sketch of the field directions with respect to the sample plane.
field with normal component. Additionally, the same switching process as for profile C contributes, but with opposite sign. As the absolute value of the Kerr rotation varies with the configuration, we conclude that the magnetization does not switch as a whole, i. e. as a macrospin, which is usually assumed for coherent magnetization rotation [50], but rather in fractions depending on the prehistory. This, however, leads to the conclusion that we confirm the spin reorientation via coexisting phases. If there was a transition via canting of the magnetization, the Kerr signal in profile C should be zero, as the canted state cannot be altered with respect to the out-of-plane magnetization component by the in-plane field. Magnetization reversal within region II was also studied utilizing hysteresis loops. An example is given for 4.3±0.1 ML Co/Au(1 1 1) in Fig. 3. The thickness was chosen to be within the reorientation transition of the as grown film [24]. As the investigation by Kerr microscopy was performed with considerable time delay to the growth process, surface diffusion of Au or contamination by carbon (residual gas) shifted the spin reorientation to higher thickness [29,51–53]. Hence, the hysteresis loops refer to a nominal film thickness of about 4.65 ML for the Kerr microscopy experiment and will be justified later in this publication. The hysteresis loops in Fig. 3 were simultaneously recorded in inplane field at different angles of incidence with varying sensitivity for polar and longitudinal Kerr ellipticity, see Section 2. While at 9° angle of incidence the polar Kerr ellipticity εpol is dominant, a superposition of longitudinal and polar contribution is expected in ε45 at 45° angle of incidence. Hence, the longitudinal Kerr ellipticity is derived from εlong = |ε45 − εpol |. The separated longitudinal Kerr loop εlong in Fig. 3 reveals an inplane hysteresis with saturation field of about 29 mT and squareness, i. e. the ratio of remanence to saturation magnetization, of 0.26. The polar loop εpol also exhibits hysteresis for the out-of-plane magnetization at low in-plane field and non-zero remanence. The decreasing εpol at higher in-plane field is related to the torque acting on the out-ofplane magnetization by the in-plane field. Clearly, the magnetization decomposes into in-plane and out-of-plane domains when the in-plane field with normal component is applied to the Co film. Consistently, magnetic domains are also stabilized in normal field, as shown in the inset of Fig. 3. The polar Kerr loop in normal magnetic field exhibits a squareness of 0.25. To conclusively check the statement of a spin reorientation transition via coexisting phases we calculate E = D + C which should coincide with B according to the argumentation above. Taking into account
all after applying in-plane fields. We have to conclude that the in-plane field is slightly misaligned, which means that there is a non-zero normal field component. As the magnetic contrast is dark in both images of Fig. 1, it follows that the positive in-plane field comes with a positive normal component. An earlier investigation of the misalignment revealed that the normal component is about 2% of the nominal in-plane field strength, i. e. ≈ 2.2 mT for the used in-plane field [45].
3.2. Influence of premagnetization in different directions Next, we study the influence of the in-plane field (H= = +110 mT) on different premagnetized states, which were produced by applying initial magnetic fields either in-plane (A: H= = +110 mT and B: H= = −110 mT) or normal to the sample plane (C: H⊥ = +35 mT and D: H⊥ = −35 mT). A side view of the field directions with respect to the sample plane is sketched as inset in Fig. 2. The results are given in the same figure as line profiles calculated from Kerr images in remanence of Co wedge W2 with higher thickness resolution than W1, see Section 2. Negative values of the Kerr rotation correspond to dark gray scale values in Fig. 1. The error in the Kerr rotation is estimated to be 10 μrad. Profile A is the comparison of two nominal identical states that have been achieved after applying the same positive in-plane field successively twice. The result is zero with some noise in the complete thickness range. This demonstrates that the remanent state is reproduced. For profile B the initial state was produced in negative in-plane field, similar to Fig. 1(b). Due to lack of sensitivity to the longitudinal Kerr effect, the signal cannot be attributed to in-plane magnetization switching. Therefore, we conclude, that the in-plane field with its normal component causes a reversal of out-of-plane magnetization. After applying first positive normal and then positive in-plane field profile C is gained. In this case the normal field component is not affecting the switching process as the fields are parallel. However, it may stabilize the out-of-plane magnetization with the consequence, that the signal in profile C is smaller than expected. Nevertheless, a polar Kerr signal is obtained between dl = 4.4 ML and du = 4.7 ML, which we define as region II, see Fig. 2. We conclude that the out-of-plane magnetization is switched remanently into the film plane by the in-plane field. The largest signal is observed when the remanent state achieved in negative normal field is taken as reference (profile D). From the previous findings we infer that the magnetization is switched from negative into positive out-of-plane orientation, again due to the in-plane 3
Journal of Magnetism and Magnetic Materials 492 (2019) 165648
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the noise of about 20μ rad of each of the addends, E and B match quite well, see Fig. 4. In concordance with the assumption that C may be smaller than expected due to magnetization stabilization by the normal component of the in-plane field, the absolute Kerr rotation of E is larger than B. Finally, we compare our measurements with out-of-plane magnetization reversal, Fig. 4. Profile S results from the application of opposite normal fields, similar to Fig. 1(a). The higher noise level in S is related to the difficulty to resume the sample position for taking the second Kerr micrograph after moving the sample for applying the normal magnetic field. According to our assumptions, the magnetic signal which is caused by the misaligned in-plane field on premagnetized magnetic states of opposite out-of-plane orientation is included in profile F = D − C . As can be seen, F and S are identical above 4.6 ML Co. Obviously, below 4.6 ML the in-plane field with its normal component is not strong enough to switch all of the out-of-plane magnetization and F is smaller than S. The slight linear increase of |S| with thickness is attributed to the linear thickness dependence of the Kerr signal and is given as straight line [54]. To summarize, the thickness dependent magnetic properties of Co/ Au(1 1 1) can be divided into three regions, see Figs. 2 and 4. In region I, below dl = 4.4 ML, the magnetization cannot be remanently switched into the in-plane direction (see profile C in Fig. 2), while the normal magnetic field switches the magnetization between out-of-plane orientations (profile S in Fig. 4). In region III, above du = 4.7 ML, the Kerr signal is negligible for all pretreatments, revealing no changes of the out-of-plane magnetization. Here, only in-plane switching processes can be expected but the experimental setup is not sensitive to it. However, hysteresis measurements of similar Co thin films confirm that the magnetization is in-plane [42]. Between dl and du (region II), a magnetic population switches remanently between out-of-plane and inplane orientation which is a clear proof of the coexistence of two phases in the spin-reorientation transition. As the profiles vary with thickness, the population of the in-plane and out-of-plane magnetization changes across the transition region.
Fig. 4. Polar Kerr rotation θ for different magnetization processes (wedge W2 ). B results from remanent states of opposite in-plane fields, S is produced by remanent states of opposite normal fields. The sum/difference of C and D (Fig. 2) is given in E and F, respectively. The larger noise in S results from the preparation procedure as the sample had to be moved for obtaining Kerr images of the remanent states in normal field. The small linear increase of the absolute Kerr rotation on thickness increase is attributed to the linear thickness dependency of the Kerr rotation (Fit for Co thickness <4.5 ML).
3.4. The population of the magnetic phases Finally, we aim at a quantitative determination of the thickness dependent population of the magnetic phases within the SRT of Co/Au (1 1 1). Profile S, which was obtained from the magnetization reversal in normal magnetic fields of ±35 mT (Fig. 4), is almost constant below dl which means the normal field fully reverses the out-of-plane magnetization. Hysteresis measurements on similar Co films reveal rectangular shape [42]. The total number of states with out-of-plane magnetization orientation S ∗ is obtained by rescaling S with respect to the linear thickness dependence of the Kerr signal. In fact, S ∗ is similar to the thickness resolved squareness of hysteresis loops in normal field. A smooth decrease of S ∗ is observed in region II of Fig. 5. Hence, the squareness of 0.25 for the as grown Co film (Fig. 3) refers to about 4.65 ML Co in the Kerr microscopy study. Different models for the occupation of magnetic phases within the SRT have been discussed in literature. The perfect delay convention as well as the Maxwell convention postulate a sudden change of the uniform magnetization either when one local minimum disappears in the energy landscape, i. e. at du or at equal minima depth [50]. Our results, however, reveal a continuous reduction of S ∗ upon thickness increase which is covered by neither of the models. A continuous change of the magnetization, however, is expected for canted magnetic reorientation. Hence, this option comes into play again. In this case the total number of states S ∗ should vary with the ∗ = sinα = −K1eff /(2K2) [6]. Taking into accanting angle α like Scant count bulk anisotropies1 and film thickness d as variable, the best fit for ∗ Scant with K1s and K2s as parameters is given in Fig. 5. The result does not follow the data points at all. Hence, canting is again excluded. An alternative model for the interpretation of the SRT of Co/Au (1 1 1) considers thermal activation of so called magnetic volumes which may overcome the energy barrier between in-plane and out-ofplane magnetization orientation given by Eq. 1. Rodary et al. [58] relate the magnetic volumes with the granular structure of the Co film. Co growth is known to proceed via merging of self–organized structures on the Au(1 1 1) surface and grain boundaries remain even after coalescence of the islands [58,59]. These grain boundaries, however, can induce a strong local variation of magnetic exchange and/or anisotropy
3.3. Calculation of surface anisotropies As the spin-reorientation transition of coexistence has been identified in the former section, the knowledge can be utilized to quantify the surface anisotropies taking into account the critical thicknesses of region II. The phenomenological ansatz for the thickness dependent anisotropies [2] is given by Ki (d ) = Ki,v + Ki,s/ d (where the indices v and s denote the volume and surface contributions and i = 1, 2 are the first and second order). Following the anisotropy flow concept of Millev 1 et al. [8], we derive from K1s = ( 2 μ0 Ms2 − K1v )·d u with d u = 4.70 ± 0.05 1 ML and bulk values for the first order surface anisotropy K1s = 0.76 ± 0.02 mJ/m2. In first approximation, Ms is considered to be constant, though there is evidence for thickness dependence [56,57]. The second order surface anisotropy is obtained from 1 1 K2s = 2 ( 2 μ0 Ms2 − K1v )(dl − d u) − K2v ·dl and dl = 4.40 ± 0.05 ML. We find K2s = −0.13 ± 0.02 mJ/m2. The values for K1s and K2s agree perfectly with values from literature. As discussed in Section 3.2, the SRT is expected to shift with respect to as grown Co/Au(1 1 1) due to considerable time delay after the growth process. A shift is related to larger absolute values of the surfaces anisotropies. Consequently, the derived values for K1s and K2s lie in between the values for as-grown (K1s = 0.66 mJ/m2, K2s = −0.12 mJ/ m2[23]) and annealed Co/Au(1 1 1) (K1s = 0.80 mJ/m2, K2s = −0.14 mJ/ m2[24]).
1 The volume anisotropy of first and second order are K1v = 5.0·105 J/m3 and K2v = 1.25·105 J/m3. The saturation magnetization is Ms = 1.44·106 A/m (All values taken from Ref. [55]). One monolayer of Co is 2 Å.
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between in-plane and out-of-plane orientation as they are part of both populations. However, C ∗ is higher than P ∗ below 4.6 ML, which means that the population of in-plane states after switching the in-plane field off is higher than in thermal equilibrium. In fact, the waiting time for recording the Kerr image after reducing the magnetic field to zero for the final state in S ∗ was much longer than for C ∗. While it was about 10 min for the first case it was only few ten seconds for the second case. Hence, we assume that the magnetization did not reach the thermal equilibrium magnetization population and C ∗ is larger. Magnetization reversal investigations on Au/Co/Au(1 1 1) samples support this assumption [62]. Further time dependent investigation of the switching behaviour would be necessary to facilitate this statement. However, this is beyond the scope of these measurements. To conclude, the thickness dependent population of bistable orthogonal domains in the SRT of Co/Au(1 1 1) was resolved for the first time. It is worth mentioning that Oepen et al. [24] have discussed another kind of bistability for annealed Co/Au(1 1 1). They could magnetize the virgin domain state within the SRT in out-of-plane direction and recover the virgin domain state by annealing the sample above its Curie temperature. Due to lack of an in-plane field, bistability between in-plane and out-of-plane magnetization orientation was not shown.
Fig. 5. Total number of states for different magnetization orientations (wedge W2 ). The number of out-of-plane states S ∗ decreases in thickness range II, while the total number of states which can be remanently switched between out-ofplane and in-plane orientation of magnetization C ∗ shows a maximum. The black line is the fit of S ∗. The green line is calculated by P ∗ = 1 − S ∗ . The blue line represents the fit assuming a canted reorientation transition and the red line with crosses shows the intersection of S ∗ and 1 − S ∗. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
4. Summary In conclusion, we have studied the thickness dependent spin reorientation transition of Co/Au(1 1 1) by in situ Kerr microscopy. The switching behavior in external in-plane fields reveals the coexistence of two phases with in-plane and out-of-plane magnetization orientation. A quantitative analysis of the Kerr signal derived from Kerr images allowed to determine the strength of the population of the different contributions as a function of thickness. The number of states within the intersection of the two phases is shown to be orthogonal bistable, i. e. they switch remanently between out-of-plane and in-plane orientation. The behavior is attributed to the existence of magnetic domains which are thermally activated to overcome the energy barrier for the different magnetization orientations.
and may act as pinning centers of magnetic domain walls. Hence, the resulting magnetic domains can be considered as magnetic volumes. Also for He+ irradiated Pt/Co/Pt thin films a correlation between structure and domains was observed [12]. The magnetic behaviour of the magnetic domains can be treated by a master rate equation introducing occupation probabilities for in-plane and out-of-plane magnetic states. According to the Boltzmann distribution law in thermal equilibrium the population of these states will depend on their energy difference ΔE , the magnetic domain volume V (d ) = l 2·d with domain length l and temperature T. Hence, the number of states with out-of-plane magnetization is given by
S∗ =
1 . 1 + exp(−ΔE ·V / kB T )
Acknowledgments (2)
Experimental work was performed with the equipment and financial support of the Max-Planck-Institut für Mikrostrukturphysik, Halle, Germany. Fruitful discussions and support of H. P. Oepen, University of Hamburg, Germany, and J. Kirschner, Max-Planck-Institut für Mikrostrukturphysik, Halle, Germany, are gratefully acknowledged. The author is also very thankful to R. Frömter, S. Mühlbauer and P. Schöffmann for carefully reading the manuscript.
From Eq. (1) the thickness dependent energy barrier between in-plane and out-of-plane magnetization orientation is derived in thermal equilibrium, ΔE (d ) = K1eff (d ) + K2 (d ) . The domain length l is the only fit parameter in S ∗. The model (black straight line) fits the data points very well, see Fig. 5. For the domain size we obtain l = 24 ± 1 nm, which coincides perfectly with the derived value by Rodary et al. [58] of 27 ± 5 nm and also agrees with experimentally found Co grain sizes [58,60,61]. However, this domain size is well below the resolution of optical microscopes and imaging methods with high lateral resolution have to be applied to prove the existance of these domains. Finally, we discuss the population of the magnetic states per thickness interval C ∗ that can be switched from out-of-plane to in-plane magnetization orientation in dependence of the Co thickness, Fig. 5. C ∗ is obtained by correcting profile C (Fig. 2) for the thickness dependent Kerr rotation and rescaling with a factor of two which takes into account that C results from magnetization switching from out-of-plane to in-plane while S originates from reversal of opposite out-of-plane orientation. C ∗ coincides with S ∗ when its value is approx. 0.5, at about 4.6 ML. On further thickness increase both number of states decrease congruently because S ∗ limits the number of states which may be switched by the normal field. Vice versa, the number of states per thickness interval which may be remanently switched with in-plane field is defined by P ∗ = 1 − S ∗. Hence, we expect C ∗ to be related to the intersection of S ∗ and P ∗, see Fig. 5. Only the states within the intersection may switch
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Research articles
Orthogonal bistable magnetic domains in Co/Au(1 1 1)
T
S. Pütter Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science at Heinz Maier-Leibnitz Zentrum, Lichtenbergstr. 1, 85747 Garching, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Thin films Spin reorientation transition Perpendicular magnetic anisotropy Phase of coexistence
The thickness-driven spin-reorientation transition of Co/Au(1 1 1) is studied via in situ Kerr microscopy. On varying the premagnetization conditions in external field of in-plane or normal orientation, the magnetic switching into a final remanent state from an in-plane field is investigated. The quantitative analysis of the Kerr rotation derived from Kerr microscopy images allows the determination of the population of different magnetic phases as a function of thickness. Coexisting magnetic phases with preferred in-plane and out-of-plane magnetization orientation are identified. The overall switching behaviour is explained by thermal activation of magnetic domains. We show that there is a population of orthogonal bistable magnetic domains, which can be remanently switched between out-of-plane and in-plane orientation by the appropriate magnetic field. This quantity is related to the intersection of the population of states for in-plane and out-of-plane magnetization.
1. Introduction Spin reorientation transitions (SRT) are a fascinating topic in magnetism as the magnetic orientation changes due to a parameter like temperature or thickness. SRTs have been studied in bulk [1] as well as in ultrathin film systems for a long time, e.g. Refs. [2–5]. A spin-reorientation is characterized by the change of magnetization orientation due to the competition of magnetic anisotropies like magnetocrystalline, surface or shape anisotropy. For uniaxial anisotropy, the free energy density fA in second order approximation is given by
fA = K1eff sin2 α + K2sin4 α
(1)
where α is the angle of the magnetization with respect to the system’s easy axis [6]. For thin films, α describes the angle between the magnetization and the surface normal. The effective anisotropy K1eff is composed of the first order anisotropy constant K1 and the shape ani1 sotropy, i. e. K1eff = K1 − 2 μ0 Ms2; Ms denotes the saturation magnetization and μ0 the vacuum permeability. K2 is the anisotropy constant of second order. As the anisotropy constants depend on temperature and/ or film thickness, their balance changes with these parameters and, as a consequence, the orientation of the magnetization may also change. Two different types of transitions are generally distinguished [3,7,8]. A transition via magnetization canting is characterized by a continuous change of the magnetization orientation from out-of-plane to in-plane (K2 > 0 ). It has been unraveled as function of temperature [9–12] and thickness [13–19]. For the second type, in-plane and out-ofplane magnetization orientation may coexist within the transition region (K2 < 0 ). This transition has been discussed for various thin film
systems, e. g. Co/Fe/Cu(1 0 0) [20], Fe/Cu(1 0 0) [21,22], Co/Au(1 1 1) [23–27], Co0.9Fe0.1/MgO/Co0.9Fe0.1[28] and Au/Co/Au(1 1 1) [29,30], but only at few discrete thicknesses. Theory predicts a continuous increase/decrease of the population of in-plane and out-of-plane domains [31–33], which means the investigation of the balance between the two different orientations will give further insight into the magnetism of spin reorientation transitions. For the study of reorientation transitions, methods with high lateral resolution [9–11,15,23–25,34,35] but also integral methods like hysteresis loops [26,28] or magnetic susceptibility [36,37] have been utilized. In this publication, we study the SRT of Co wedges grown on Au (1 1 1) utilizing in situ Kerr microscopy. Protecting cap layers for ex situ studies may change the thickness of the SRT drastically [30,38] and might even alter the type of SRT. By extracting line profiles from Kerr microscopy images of different remanent states, the Kerr rotation is quantitatively studied in dependence of film thickness. We observe coexisting magnetic phases of inplane and out-of-plane orientation with varying population within the reorientation. Additionally, these magnetic domains are bistable, i. e. they can be remanently switched in out-of-plane and in-plane direction. The observed switching behaviour is explained by thermal activation of magnetic domains. 2. Experimental Sample preparation and experiments were performed at room temperature in ultra high vacuum (UHV) ( p = 2·10−10 mbar). The surface of the Au(1 1 1) single crystal was prepared by 1 keV Ar ion
E-mail address: [email protected]. https://doi.org/10.1016/j.jmmm.2019.165648 Received 14 January 2019; Received in revised form 25 July 2019; Accepted 28 July 2019 Available online 29 July 2019 0304-8853/ © 2019 Elsevier B.V. All rights reserved.
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sputtering at about 37° to the sample plane and subsequent annealing at 650 °C for 30 min. The quality of the surface was checked by Auger electron spectroscopy and low energy electron diffraction. The 22 × 3 reconstruction [39,40] was obtained for the clean Au(1 1 1) surface. Cobalt films were grown epitaxially [41] by electron beam evaporation at a rate of 0.4 ML/min (ML = monolayer). The evaporation rate was calibrated by means of intensity oscillations of medium energy electron diffraction [42] with an estimated error of about 5%. To gain an overview about the thickness dependent magnetic behaviour at a glance, wedges were grown by slowly moving a sample mask during Co evaporation. To ensure repeatability of the experiments several Co wedges were prepared and studied. They all revealed similar magnetic behaviour. Here, we focus on two wedges. For Co wedge W1 the slope and the thickness range are 0.56 ML/mm and 3.0 − 5.2 ML and for wedge W2 they are 0.40 ML/mm and 3.5–5.0 ML, respectively. The width of the displayed wedges is 1.5 mm. The Kerr microscope for in situ investigation is similar to the one described in Ref. [43], except that a halogen lamp is used for illumination and the light is polarized/analyzed by Glan–Thompson prisms. The angle of incidence of the s-polarized light is 45°. The reflected light is analyzed by a polarizer tilted δ = 38 mrad out of extinction. The beam is guided through a long-distance microscope and finally detected by a charge-coupled device camera. The lateral resolution of the in situ Kerr microscope is estimated to be approx. 40μ m, which means that domains cannot be resolved. The typical domain size of Co/Au(1 1 1) at the SRT is below 2 μm (Refs. [25,44]) and may be even as small as 120 nm, see Ref. [10]. Similar to hysteresis measurements an overview about the magnetic behaviour in different fields is gained. Quantitative magnetic analysis of Kerr microscopy is gained from normalized difference images, which are calculated pixel-wise from two micrographs at different magnetic states, i. e. ΔI = (If − Ii )/(Ii + If ) with Ii and If as the intensities of the initial and the final state, respectively. The resulting intensity is proportional to the Kerr rotation θ . Considering only difference images minimizes topographic contributions. However, due to small vibrations of the sample holder inside the UHV chamber the topography remains visible. Line profiles, i. e. the Kerr rotation in dependence of the Co film thickness can be extracted from Kerr images by averaging the gray scale values at constant Co thickness within a width of 6 mm and rescaling according to the formulae above. Both, polar and longitudinal Kerr effect may contribute to the Kerr signal [45]. However, the ratio between polar and longitudinal Kerr rotation was found to be 30:1 at the angle of incidence of 45° by using formulae given by Zak et al. [46], the Voigt constant from Ref. [47] and tabulated values for the index of refraction [48]. It follows that the polar Kerr rotation measured with the Kerr microscope will be dominant for Co/Au(1 1 1) even with applied in-plane field. As the longitudinal Kerr rotation is well below the detection limit of the in situ Kerr microscope we may say that the Kerr signal will only be of polar origin. Hence, the detected Kerr rotation is proportional to the magnetization component that is in out-of-plane direction, i. e. normal to the sample plane. For simultaneous in situ detection of hysteresis loops in in-plane field two magneto-optical Kerr effect (MOKE) setups were utilized at 9° and 45° angles of incidence with s-polarized light. The setups are similar to the one described in Ref. [42]. For detection of the Kerr ellipticity ε a λ/4 -plate is inserted in front of the analyzer to cancel the window birefringence [49]. The polarizer is tilted by δ = 12.6 mrad out of extinction. For quantitative analysis, the Kerr ellipticity is calculated by ε = (I+M − I−M )·δ /(4I0) , considering the intensities I±M at opposite magnetic states and the intensity in absence of magnetic signals, I0 [49]. The sensitivity for polar and longitudinal Kerr effect in Co/Au(1 1 1) changes when the Kerr ellipticity is investigated. At 9° angle of incidence the ratio between polar and longitudinal Kerr ellipticity is 33:1, i.e. similar to the Kerr rotation at 45° mainly a polar signal is detected.
Fig. 1. Polar Kerr images of Co/Au(1 1 1) wedge W1 obtained from remanent states after applying magnetic fields of opposite sign (a) normal to the sample plane (± 35 mT), and (b) in the sample plane (± 110 mT). On the bottom of each image the non-ferromagnetic Kerr response of the Au substrate is visible. On top of the figure a side view of the Co wedge is sketched. The coarse structure of image (a) results from the realingment procedure of the sample, see Section 2.
The longitudinal ellipticity at 45°, however, is a superposition of polar and longitudinal signal according to the ratio 6:1, while the polar Kerr ellipticity for 9° and 45° is quite similar. Hence, a measurement at 45° will consist of polar and longitudinal ellipticity. A rough separation of the polar and longitudinal contributions at 45° can be obtained by substracting the Kerr ellipticities at 45° and 9° which will result in the longitudinal ellipticity. A more detailed investigation with sophisticated separation of the components has been performed by Ding et al. [26]. A magnetic field was applied either normal to or within the sample plane (parallel to constant thickness direction of the wedge). Remanent states were produced by slow reduction of the applied field to zero. For the application of normal magnetic fields the sample had to be moved out of the position for Kerr microscopy. Special care was taken for realignment of the sample. 3. Results and discussion 3.1. Kerr microscopy of Co/Au(1 1 1) in opposite magnetic fields Fig. 1 shows the magnetization reversal in Co wedge W1 grown on Au(1 1 1) after applying opposite magnetic fields normal to the sample plane and in-plane. The thickness range spans from 3 ML (left) to 5.2 ML Co (right). Both images exhibit the same part of the Co wedge with individual contrast enhancement. The Kerr signal of the gold substrate at the bottom of each image gives reference for zero magnetic response. Due to the dominant polar Kerr effect, only changes of out-of-plane magnetization are detected, see Section 2. In order to keep things simple, throughout this publication only remanent states are compared after successively applying initial and final magnetic field. Utilizing magnetic fields of H⊥ = ± 35 mT normal to the surface (first with negative then with positive sign) results in a magnetic contrast (darkgray) of the remanent states from lowest thickness up to du = 4.7 ML, Fig. 1(a). Obviously, the out-of-plane magnetization is stable in this range as the magnetic field is well above the saturation field in this direction [42]. Applying in-plane fields of H= = ± 110 mT also reveals magnetic contrast, but only in a very narrow thickness range of about 0.3 ML, Fig. 1(b). Higher contrast enhancement was applied to make the Kerr signal visible, i.e. the Kerr signal is smaller than in normal field. Hysteresis curves recorded in inplane field at thickness >du demonstrate in-plane easy axis [42]. In the following, we will show that the thickness interval exhibiting contrast in in-plane fields is related to the spin-reorientation transition of Co/Au (1 1 1). As the Kerr microscope is exclusively sensitive to magnetic changes in out-of-plane direction, it appears most surprising to find a contrast at 2
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Fig. 3. Kerr ellipticity loops of 4.3 ML Co/Au(1 1 1) measured in different MOKE geometries. For the measurement in in-plane field two different MOKE setups were used, one with 9° angle of incidence and the second one with 45° angle of incidence. Due to the different sensitivities of the polar and longitudinal Kerr effect, a separation of the true longitudinal Kerr ellipticity is achieved, see text.
Fig. 2. The polar Kerr rotation θ as a function of Co thickness (wedge W2 ). The initial remanent states were created by applying a positive/negative in-plane ( A/ B ) and a positive/negative normal field (C / D ), respectively. The final state was always the remanent state after applying a positive in-plane field. The inset shows a side view sketch of the field directions with respect to the sample plane.
field with normal component. Additionally, the same switching process as for profile C contributes, but with opposite sign. As the absolute value of the Kerr rotation varies with the configuration, we conclude that the magnetization does not switch as a whole, i. e. as a macrospin, which is usually assumed for coherent magnetization rotation [50], but rather in fractions depending on the prehistory. This, however, leads to the conclusion that we confirm the spin reorientation via coexisting phases. If there was a transition via canting of the magnetization, the Kerr signal in profile C should be zero, as the canted state cannot be altered with respect to the out-of-plane magnetization component by the in-plane field. Magnetization reversal within region II was also studied utilizing hysteresis loops. An example is given for 4.3±0.1 ML Co/Au(1 1 1) in Fig. 3. The thickness was chosen to be within the reorientation transition of the as grown film [24]. As the investigation by Kerr microscopy was performed with considerable time delay to the growth process, surface diffusion of Au or contamination by carbon (residual gas) shifted the spin reorientation to higher thickness [29,51–53]. Hence, the hysteresis loops refer to a nominal film thickness of about 4.65 ML for the Kerr microscopy experiment and will be justified later in this publication. The hysteresis loops in Fig. 3 were simultaneously recorded in inplane field at different angles of incidence with varying sensitivity for polar and longitudinal Kerr ellipticity, see Section 2. While at 9° angle of incidence the polar Kerr ellipticity εpol is dominant, a superposition of longitudinal and polar contribution is expected in ε45 at 45° angle of incidence. Hence, the longitudinal Kerr ellipticity is derived from εlong = |ε45 − εpol |. The separated longitudinal Kerr loop εlong in Fig. 3 reveals an inplane hysteresis with saturation field of about 29 mT and squareness, i. e. the ratio of remanence to saturation magnetization, of 0.26. The polar loop εpol also exhibits hysteresis for the out-of-plane magnetization at low in-plane field and non-zero remanence. The decreasing εpol at higher in-plane field is related to the torque acting on the out-ofplane magnetization by the in-plane field. Clearly, the magnetization decomposes into in-plane and out-of-plane domains when the in-plane field with normal component is applied to the Co film. Consistently, magnetic domains are also stabilized in normal field, as shown in the inset of Fig. 3. The polar Kerr loop in normal magnetic field exhibits a squareness of 0.25. To conclusively check the statement of a spin reorientation transition via coexisting phases we calculate E = D + C which should coincide with B according to the argumentation above. Taking into account
all after applying in-plane fields. We have to conclude that the in-plane field is slightly misaligned, which means that there is a non-zero normal field component. As the magnetic contrast is dark in both images of Fig. 1, it follows that the positive in-plane field comes with a positive normal component. An earlier investigation of the misalignment revealed that the normal component is about 2% of the nominal in-plane field strength, i. e. ≈ 2.2 mT for the used in-plane field [45].
3.2. Influence of premagnetization in different directions Next, we study the influence of the in-plane field (H= = +110 mT) on different premagnetized states, which were produced by applying initial magnetic fields either in-plane (A: H= = +110 mT and B: H= = −110 mT) or normal to the sample plane (C: H⊥ = +35 mT and D: H⊥ = −35 mT). A side view of the field directions with respect to the sample plane is sketched as inset in Fig. 2. The results are given in the same figure as line profiles calculated from Kerr images in remanence of Co wedge W2 with higher thickness resolution than W1, see Section 2. Negative values of the Kerr rotation correspond to dark gray scale values in Fig. 1. The error in the Kerr rotation is estimated to be 10 μrad. Profile A is the comparison of two nominal identical states that have been achieved after applying the same positive in-plane field successively twice. The result is zero with some noise in the complete thickness range. This demonstrates that the remanent state is reproduced. For profile B the initial state was produced in negative in-plane field, similar to Fig. 1(b). Due to lack of sensitivity to the longitudinal Kerr effect, the signal cannot be attributed to in-plane magnetization switching. Therefore, we conclude, that the in-plane field with its normal component causes a reversal of out-of-plane magnetization. After applying first positive normal and then positive in-plane field profile C is gained. In this case the normal field component is not affecting the switching process as the fields are parallel. However, it may stabilize the out-of-plane magnetization with the consequence, that the signal in profile C is smaller than expected. Nevertheless, a polar Kerr signal is obtained between dl = 4.4 ML and du = 4.7 ML, which we define as region II, see Fig. 2. We conclude that the out-of-plane magnetization is switched remanently into the film plane by the in-plane field. The largest signal is observed when the remanent state achieved in negative normal field is taken as reference (profile D). From the previous findings we infer that the magnetization is switched from negative into positive out-of-plane orientation, again due to the in-plane 3
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the noise of about 20μ rad of each of the addends, E and B match quite well, see Fig. 4. In concordance with the assumption that C may be smaller than expected due to magnetization stabilization by the normal component of the in-plane field, the absolute Kerr rotation of E is larger than B. Finally, we compare our measurements with out-of-plane magnetization reversal, Fig. 4. Profile S results from the application of opposite normal fields, similar to Fig. 1(a). The higher noise level in S is related to the difficulty to resume the sample position for taking the second Kerr micrograph after moving the sample for applying the normal magnetic field. According to our assumptions, the magnetic signal which is caused by the misaligned in-plane field on premagnetized magnetic states of opposite out-of-plane orientation is included in profile F = D − C . As can be seen, F and S are identical above 4.6 ML Co. Obviously, below 4.6 ML the in-plane field with its normal component is not strong enough to switch all of the out-of-plane magnetization and F is smaller than S. The slight linear increase of |S| with thickness is attributed to the linear thickness dependence of the Kerr signal and is given as straight line [54]. To summarize, the thickness dependent magnetic properties of Co/ Au(1 1 1) can be divided into three regions, see Figs. 2 and 4. In region I, below dl = 4.4 ML, the magnetization cannot be remanently switched into the in-plane direction (see profile C in Fig. 2), while the normal magnetic field switches the magnetization between out-of-plane orientations (profile S in Fig. 4). In region III, above du = 4.7 ML, the Kerr signal is negligible for all pretreatments, revealing no changes of the out-of-plane magnetization. Here, only in-plane switching processes can be expected but the experimental setup is not sensitive to it. However, hysteresis measurements of similar Co thin films confirm that the magnetization is in-plane [42]. Between dl and du (region II), a magnetic population switches remanently between out-of-plane and inplane orientation which is a clear proof of the coexistence of two phases in the spin-reorientation transition. As the profiles vary with thickness, the population of the in-plane and out-of-plane magnetization changes across the transition region.
Fig. 4. Polar Kerr rotation θ for different magnetization processes (wedge W2 ). B results from remanent states of opposite in-plane fields, S is produced by remanent states of opposite normal fields. The sum/difference of C and D (Fig. 2) is given in E and F, respectively. The larger noise in S results from the preparation procedure as the sample had to be moved for obtaining Kerr images of the remanent states in normal field. The small linear increase of the absolute Kerr rotation on thickness increase is attributed to the linear thickness dependency of the Kerr rotation (Fit for Co thickness <4.5 ML).
3.4. The population of the magnetic phases Finally, we aim at a quantitative determination of the thickness dependent population of the magnetic phases within the SRT of Co/Au (1 1 1). Profile S, which was obtained from the magnetization reversal in normal magnetic fields of ±35 mT (Fig. 4), is almost constant below dl which means the normal field fully reverses the out-of-plane magnetization. Hysteresis measurements on similar Co films reveal rectangular shape [42]. The total number of states with out-of-plane magnetization orientation S ∗ is obtained by rescaling S with respect to the linear thickness dependence of the Kerr signal. In fact, S ∗ is similar to the thickness resolved squareness of hysteresis loops in normal field. A smooth decrease of S ∗ is observed in region II of Fig. 5. Hence, the squareness of 0.25 for the as grown Co film (Fig. 3) refers to about 4.65 ML Co in the Kerr microscopy study. Different models for the occupation of magnetic phases within the SRT have been discussed in literature. The perfect delay convention as well as the Maxwell convention postulate a sudden change of the uniform magnetization either when one local minimum disappears in the energy landscape, i. e. at du or at equal minima depth [50]. Our results, however, reveal a continuous reduction of S ∗ upon thickness increase which is covered by neither of the models. A continuous change of the magnetization, however, is expected for canted magnetic reorientation. Hence, this option comes into play again. In this case the total number of states S ∗ should vary with the ∗ = sinα = −K1eff /(2K2) [6]. Taking into accanting angle α like Scant count bulk anisotropies1 and film thickness d as variable, the best fit for ∗ Scant with K1s and K2s as parameters is given in Fig. 5. The result does not follow the data points at all. Hence, canting is again excluded. An alternative model for the interpretation of the SRT of Co/Au (1 1 1) considers thermal activation of so called magnetic volumes which may overcome the energy barrier between in-plane and out-ofplane magnetization orientation given by Eq. 1. Rodary et al. [58] relate the magnetic volumes with the granular structure of the Co film. Co growth is known to proceed via merging of self–organized structures on the Au(1 1 1) surface and grain boundaries remain even after coalescence of the islands [58,59]. These grain boundaries, however, can induce a strong local variation of magnetic exchange and/or anisotropy
3.3. Calculation of surface anisotropies As the spin-reorientation transition of coexistence has been identified in the former section, the knowledge can be utilized to quantify the surface anisotropies taking into account the critical thicknesses of region II. The phenomenological ansatz for the thickness dependent anisotropies [2] is given by Ki (d ) = Ki,v + Ki,s/ d (where the indices v and s denote the volume and surface contributions and i = 1, 2 are the first and second order). Following the anisotropy flow concept of Millev 1 et al. [8], we derive from K1s = ( 2 μ0 Ms2 − K1v )·d u with d u = 4.70 ± 0.05 1 ML and bulk values for the first order surface anisotropy K1s = 0.76 ± 0.02 mJ/m2. In first approximation, Ms is considered to be constant, though there is evidence for thickness dependence [56,57]. The second order surface anisotropy is obtained from 1 1 K2s = 2 ( 2 μ0 Ms2 − K1v )(dl − d u) − K2v ·dl and dl = 4.40 ± 0.05 ML. We find K2s = −0.13 ± 0.02 mJ/m2. The values for K1s and K2s agree perfectly with values from literature. As discussed in Section 3.2, the SRT is expected to shift with respect to as grown Co/Au(1 1 1) due to considerable time delay after the growth process. A shift is related to larger absolute values of the surfaces anisotropies. Consequently, the derived values for K1s and K2s lie in between the values for as-grown (K1s = 0.66 mJ/m2, K2s = −0.12 mJ/ m2[23]) and annealed Co/Au(1 1 1) (K1s = 0.80 mJ/m2, K2s = −0.14 mJ/ m2[24]).
1 The volume anisotropy of first and second order are K1v = 5.0·105 J/m3 and K2v = 1.25·105 J/m3. The saturation magnetization is Ms = 1.44·106 A/m (All values taken from Ref. [55]). One monolayer of Co is 2 Å.
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between in-plane and out-of-plane orientation as they are part of both populations. However, C ∗ is higher than P ∗ below 4.6 ML, which means that the population of in-plane states after switching the in-plane field off is higher than in thermal equilibrium. In fact, the waiting time for recording the Kerr image after reducing the magnetic field to zero for the final state in S ∗ was much longer than for C ∗. While it was about 10 min for the first case it was only few ten seconds for the second case. Hence, we assume that the magnetization did not reach the thermal equilibrium magnetization population and C ∗ is larger. Magnetization reversal investigations on Au/Co/Au(1 1 1) samples support this assumption [62]. Further time dependent investigation of the switching behaviour would be necessary to facilitate this statement. However, this is beyond the scope of these measurements. To conclude, the thickness dependent population of bistable orthogonal domains in the SRT of Co/Au(1 1 1) was resolved for the first time. It is worth mentioning that Oepen et al. [24] have discussed another kind of bistability for annealed Co/Au(1 1 1). They could magnetize the virgin domain state within the SRT in out-of-plane direction and recover the virgin domain state by annealing the sample above its Curie temperature. Due to lack of an in-plane field, bistability between in-plane and out-of-plane magnetization orientation was not shown.
Fig. 5. Total number of states for different magnetization orientations (wedge W2 ). The number of out-of-plane states S ∗ decreases in thickness range II, while the total number of states which can be remanently switched between out-ofplane and in-plane orientation of magnetization C ∗ shows a maximum. The black line is the fit of S ∗. The green line is calculated by P ∗ = 1 − S ∗ . The blue line represents the fit assuming a canted reorientation transition and the red line with crosses shows the intersection of S ∗ and 1 − S ∗. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
4. Summary In conclusion, we have studied the thickness dependent spin reorientation transition of Co/Au(1 1 1) by in situ Kerr microscopy. The switching behavior in external in-plane fields reveals the coexistence of two phases with in-plane and out-of-plane magnetization orientation. A quantitative analysis of the Kerr signal derived from Kerr images allowed to determine the strength of the population of the different contributions as a function of thickness. The number of states within the intersection of the two phases is shown to be orthogonal bistable, i. e. they switch remanently between out-of-plane and in-plane orientation. The behavior is attributed to the existence of magnetic domains which are thermally activated to overcome the energy barrier for the different magnetization orientations.
and may act as pinning centers of magnetic domain walls. Hence, the resulting magnetic domains can be considered as magnetic volumes. Also for He+ irradiated Pt/Co/Pt thin films a correlation between structure and domains was observed [12]. The magnetic behaviour of the magnetic domains can be treated by a master rate equation introducing occupation probabilities for in-plane and out-of-plane magnetic states. According to the Boltzmann distribution law in thermal equilibrium the population of these states will depend on their energy difference ΔE , the magnetic domain volume V (d ) = l 2·d with domain length l and temperature T. Hence, the number of states with out-of-plane magnetization is given by
S∗ =
1 . 1 + exp(−ΔE ·V / kB T )
Acknowledgments (2)
Experimental work was performed with the equipment and financial support of the Max-Planck-Institut für Mikrostrukturphysik, Halle, Germany. Fruitful discussions and support of H. P. Oepen, University of Hamburg, Germany, and J. Kirschner, Max-Planck-Institut für Mikrostrukturphysik, Halle, Germany, are gratefully acknowledged. The author is also very thankful to R. Frömter, S. Mühlbauer and P. Schöffmann for carefully reading the manuscript.
From Eq. (1) the thickness dependent energy barrier between in-plane and out-of-plane magnetization orientation is derived in thermal equilibrium, ΔE (d ) = K1eff (d ) + K2 (d ) . The domain length l is the only fit parameter in S ∗. The model (black straight line) fits the data points very well, see Fig. 5. For the domain size we obtain l = 24 ± 1 nm, which coincides perfectly with the derived value by Rodary et al. [58] of 27 ± 5 nm and also agrees with experimentally found Co grain sizes [58,60,61]. However, this domain size is well below the resolution of optical microscopes and imaging methods with high lateral resolution have to be applied to prove the existance of these domains. Finally, we discuss the population of the magnetic states per thickness interval C ∗ that can be switched from out-of-plane to in-plane magnetization orientation in dependence of the Co thickness, Fig. 5. C ∗ is obtained by correcting profile C (Fig. 2) for the thickness dependent Kerr rotation and rescaling with a factor of two which takes into account that C results from magnetization switching from out-of-plane to in-plane while S originates from reversal of opposite out-of-plane orientation. C ∗ coincides with S ∗ when its value is approx. 0.5, at about 4.6 ML. On further thickness increase both number of states decrease congruently because S ∗ limits the number of states which may be switched by the normal field. Vice versa, the number of states per thickness interval which may be remanently switched with in-plane field is defined by P ∗ = 1 − S ∗. Hence, we expect C ∗ to be related to the intersection of S ∗ and P ∗, see Fig. 5. Only the states within the intersection may switch
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