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Off-Specular Polarized Neutron Reflectometry from Periodic Arrays of Lithographically Structured Co Dots† H. Fritzsche,*,‡ Margriet J. Van Bael,§ and K. Temst§ Hahn-Meitner-Institut Berlin, Department SF1, Glienicker Strasse 100, 14109 Berlin, Germany, and Laboratorium voor Vaste-Stoffysica en Magnetisme, KU Leuven, Celestijnenlaan 200 D, Belgium Received September 30, 2002. In Final Form: February 14, 2003 We studied the off-specular intensity in polarized neutron reflectivity from regular arrays of circular and rectangular Co dots with sizes in the micrometer range. The dots were lithographically prepared and placed on a square lattice with a period of 10 µm, the rectangular dots having an aspect ratio of 4:1. In both cases, we observed enhanced intensity at particular angles off the specular condition. The positions of these satellites are correlated to the lateral periodicity of the ferromagnetic dots. The magnetic information could be revealed by measuring the off-specular intensity as a function of the magnetic field applied in-plane parallel to the rows of the dots. The magnetization reversal process could be analyzed by separating the spin-flip and non-spin-flip contributions to the off-specular signal. The measured spin-flip intensities clearly prove that for both samples the magnetization reversal is dominated by domain wall movement and not by a uniform rotation of single-domain particles.
Introduction Recent advances in lithography techniques have induced a growing interest in artificially fabricated periodic magnetic structures with all three dimensions in the micron or nanometer range. On one hand, these nanomagnets are ideal systems to test theorems in magnetostatics and micromagnetics in mesoscopic systems; on the other hand, technological applications such as magnetic data storage media or magnetic sensors are in progress. The central issue is the correlation of the magnetic properties of these patterned structures with the size and the shape of the single unit. The crucial point is to determine and to understand the magnetization reversal process which decides whether the magnetic sample is a good candidate for technological applications or not. The magnetic properties of these structured magnets are typically investigated by magneto-optical Kerr effect (MOKE) measurements,1-4 superconducting quantum interference device (SQUID) magnetometry,5,6 transport measurements,7,8 or magnetic force microscopy (MFM).5,9-12 Recently we succeeded in applying the technique of offspecular polarized neutron reflectometry (OSPNR) to such * Corresponding author. Tel: +49-30-80 62 31 41. Fax +49-3080 62 25 23. E-mail:
[email protected]. † Part of the Langmuir special issue dedicated to neutron reflectometry. ‡ Hahn-Meitner-Institut Berlin. § KU Leuven. (1) Cowburn, R. P.; Koltsov, D. K.; Adeyeye, A. O.; Welland, M. E. Appl. Phys. Lett. 1998, 73, 3947. (2) Schmitte, T.; Schemberg, T.; Westerholt, K.; Zabel, H.; Scha¨dler, K.; Kunze, U. J. Appl. Phys. 2000, 87, 5630. (3) Cowburn, R. P.; Koltsov, D. K.; Adeyeye, A. O.; Welland, M. E.; Tricker, D. M. Phys. Rev. Lett. 1999, 83, 1042. (4) Vavassori, P.; Metlushko, V.; Grimsditch, M.; Ilic, B.; Neuzil, P.; Kumar, R. Phys. Rev. B 2000, 61, 5895. (5) Van Bael, M. J.; Temst, K.; Moshchalkov, V. V.; Bruynseraede, Y. Phys. Rev. B 1999, 59, 14674. (6) Otani, Y.; Kohda, T.; Novosad, V.; Fukamichi, K.; Yuasa, S.; Katayama, T. J. Appl. Phys. 2000, 87, 5621. (7) Martin, J. I.; Jaccard, Y.; Hoffmann, A.; Nogue´s, J.; George, J. M.; Vicent, J. L.; Schuller, I. K. J. Appl. Phys. 1998, 84, 411. (8) Shimazu, Y.; Ohkubo, M.; Morinaga, K. J. Magn. Magn. Mater. 2002, 240, 17.
a magnetic dot array.13,14 By measuring the spin-flip and non-spin-flip intensity of off-specularly scattered neutrons, it is possible to study the process of magnetization reversal with the traditional advantages of PNR: to study buried layers, to have no diamagnetic/paramagnetic background problems as in SQUID magnetometry, to measure the parallel and perpendicular components of the sample’s in-plane magnetization simultaneously, and to have no change of the magnetic structure by the probe as may be the case in MFM measurements.9 Experimental Section We prepared two different dot arrays. One sample consisted of circular dots with a diameter of 4 µm, and the other one consisted of rectangular dots with a length of 4 µm and a width of 1 µm. Both kinds of dots were placed in a square lattice with a period of 10 µm with a total patterned area of 4 cm2. The circular dots were fabricated by UV lithography, whereas electron beam lithography was used for the rectangular dots. All other steps in the preparation process were identical. Oxidized Si wafers were covered with a resist mask, in which the film was deposited by molecular beam epitaxy under ultrahigh vacuum conditions. Each dot consisted of a trilayer of the form 7.5 nm Au/20 nm Co/7.5 nm Au. In the end, a lift-off step in boiling acetone removed the resist completely. X-ray diffraction indicates that the disks are polycrystalline. The sample preparation was described in more detail elsewhere.13,15 The samples were always kept at ambient temperature, and the external magnetic field was applied in the sample plane perpendicular to the scattering plane (see Figure 1). The experiments were performed at the neutron reflectometer V6 of (9) Kleiber, M.; Ku¨mmerlen, F.; Lo¨hndorf, M.; Wadas, A.; Weiss, D.; Wiesendanger, R. Phys. Rev. B 1998, 58, 5563. (10) Demand, M.; Hehn, M.; Ounadjela, K.; Stamps, R. L.; Cambril, E.; Cornette, A.; Rousseaux, F. J. Appl. Phys. 2000, 87, 5111. (11) Seynaeve, E.; Rens, G.; Volodin, A. V.; Temst, K.; Van Haesendonck, C.; Bruynseraede, Y. J. Appl. Phys. 2001, 89, 531. (12) Pulwey, R.; Zo¨lfl, M.; Bayreuther, G.; Weiss, D. J. Appl. Phys. 2002, 91, 7995. (13) Temst, K.; Van Bael, M. J.; Fritzsche, H. Appl. Phys. Lett. 2001, 79, 991. (14) Temst, K.; Van Bael, M. J.; Fritzsche, H. J. Magn. Magn. Mater. 2001, 226-230, 1840. (15) Temst, K.; Van Bael, M. J.; Moshchalkov, V. V.; Bruynseraede, Y. J. Appl. Phys. 2000, 87, 4216.
10.1021/la026625n CCC: $25.00 © 2003 American Chemical Society Published on Web 03/25/2003
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Figure 1. Scattering geometry for specular and off-specular reflectivity.
Figure 3. Ri-Rf map of the reflected intensity measured with up-neutrons for the case of saturation (H ) 2400 Oe) with H parallel to the rows of the circular Co dots.
Figure 2. Projection of the PSD picture onto the z axis after integration along the y axis, measured for 10 min with spin-up neutrons at an angle Ri ) 0.62°. the Hahn-Meitner-Institut16 using a wavelength of 0.466 nm. The neutrons were polarized before and analyzed after the scattering process by means of Si-FeCo supermirrors.17 The neutrons were recorded by a position sensitive detector (PSD)18 with an active area of about 180 × 180 mm2 and a spatial resolution of 1.5 mm. The scattering geometry is sketched in Figure 1. The incoming neutron beam hits the sample surface at an angle Ri. The specular neutrons are reflected at an angle Rf ) Ri, whereas all other neutrons reflected at an angle Rf * Ri contribute to the off-specular signal. In the classical picture of diffraction, the wave vector of the off-specularly reflected neutrons is changed by the addition (subtraction) of a reciprocal vector
qx )
2π 2π (cos(Rf) - cos(Ri)) ) n λ d
n ) 1,2,...
(1)
due to the periodicity of the dots with a distance d. In this classical reflectometry setup with very good collimation in the z direction and a relaxed collimation in the y direction, we are only sensitive to the off-specular scattering in the x direction (i.e., in the scattering plane), whereas off-specular scattering in the y direction (i.e., out of the scattering plane) is not visible and is simply integrated.
Results (a) Circular Co Dots. By using a PSD, we can monitor the specular and off-specular intensity simultaneously. Raw experimental data taken for the saturated sample at an angle Ri ) 0.62° with an acquisition time of 10 min are shown in Figure 2. The measurement was performed with up-neutrons and the magnetic field applied along the rows of Co dots. The intensity integrated along the y direction, (16) Mezei, F.; Golub, R.; Klose, F.; Toews, H. Physica B 1995, 213214, 898. (17) Krist, T.; Pappas, C.; Keller, T.; Mezei, F. Physica B 1995, 213214, 939. (18) Boulin, C. J.; Kempf, R.; Gabriel, A.; Koch, M. H. J. Nucl. Instrum. Methods Phys. Res., Sect. A 1988, 269, 312.
perpendicular to the scattering plane, is displayed as a function of the z direction. Four peaks are visible, from left to right: (1) the direct beam (not hitting the sample at all) plus the transmitted part which is not diffracted, (2) the transmitted beam after having been diffracted, (3) off-specular reflection, and (4) specular reflection. The second peak could in principle also be due to refraction, but for the used substrate (Si) the effect of refraction cannot be resolved experimentally because the deviation from the direct line-of-sight is only 0.04°. Most of the intensity of the direct beam was absorbed by a B4C plate which was placed at a distance of about 30 cm from the sample position in order to minimize the background contribution from the direct beam. To get an overview of the off-specularly scattered intensity as a function of Ri, we performed scans in an Ri range between 0.16° and 1°. It is quite convenient to display the measured data in an Ri-Rf map as done in Figure 3. The calculation of the reflection angle Rf is straightforward if the distance between sample and detector is known and the distance between the detector channels is calibrated. In such an Ri-Rf map, the specular reflectivity corresponds to the diagonal Ri ) Rf and all off-diagonal intensity represents off-specular reflectivity. In Figure 3, one clearly can see the decreasing intensity along the diagonal for increasing Ri (the normal specular reflectivity curve) and enhanced off-specular intensity at distinct positions. It is more instructive to transform such an Ri-Rf map into a wavelength-independent reciprocal qx-qz map. The component of the scattering vector in the sample plane, qx, is calculated via eq 1, whereas the outof-plane scattering vector component qz is calculated as
qz )
2π (sin(Rf) + sin(Ri)) λ
(2)
For the case of specular reflection, this equation simplifies to the well-known relation qz ) 4π/λ sin Ri. Such a reciprocal space map converted from the Ri-Rf map of Figure 3 is displayed in Figure 4. Now the specular reflection corresponds to the intensity along the line qx ) 0. The off-specular intensity is visible at all sites with qx * 0. A clear periodicity along the qx axis is present. The reciprocal space period equals 0.62 µm-1, corresponding
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Figure 4. Reciprocal space map of the reflected intensity measured with up-neutrons for the case of saturation (H ) 2400 Oe). It represents a conversion from the Ri-Rf map shown in Figure 3.
to a real-space period of 10.0 µm as can be calculated by eq 1. That is precisely the distance between the dots along the edges of the square lattice and hence proves the validity of the kinematic approximation made in eq 1. This kind of structural information can also be obtained by X-ray diffraction (XRD) as has been shown already earlier.15,19 The major advantage of PNR is the ability to probe the magnetic properties. However, the magnetic information is not observed in the specular reflectivity curves20 because the magnetic dots cover only an area of 12.5% of the total sample surface. Hence, the specularly reflected intensity is dominated by the nonmagnetic substrate. The magnetic information shows up in the offspecular satellites which are due to the periodicity of the magnetic dot lattice. This can be nicely seen in Figure 5 where we recorded the intensity of the specular and offspecular reflection as well as the intensity of the transmitted and diffracted part of the beam at a fixed angle of incidence as a function of an external magnetic field. We applied spin analysis after the reflection, and so we were able to measure the non-spin-flip intensities I- and I++ as well as the spin-flip intensities I- + and I+ -. Before the measurement, the sample was first saturated in a negative field. Because of that negative saturation, the spin-up and spin-down intensities are reversed at zero field, that is, I- - > I++. When the magnetic field is increased, the difference between I- - and I++ decreases up to the coercive field at about 70 Oe where I- - ) I++. When the field is increased further, the difference again increases but now with I++ > I- - indicating that the magnetization was reversed. There is only a small contribution of the spin-flip intensity to the total signal. Nevertheless, the spin-flip intensity is clearly visible up to 100 Oe and vanishes at 150 Oe when the sample is saturated. This shows that the component of the magnetization perpendicular to the external field is rather small throughout the magnetization reversal process. The spin-flip intensity can be increased when saturating the sample and then rotating by 90°. A magnetic field scan with that kind of treatment before the measurement is (19) Rafaja, D.; Valvoda, V.; Kub, J.; Temst, K.; Van Bael, M. J.; Bruynseraede, Y. Phys. Rev. B 2000, 61, 16144. (20) Fritzsche, H.; Temst, K.; Van Bael, M. J. Appl. Phys. A 2002, 74 [Suppl.], S1535.
Figure 5. The non-spin-flip intensities I- - and I++ and the spin-flip intensities I- + and I+ - of the circular dots as a function of an increasing external magnetic field at the position of the specular reflection (a), the off-specular reflection (b), and the diffracted and transmitted intensity (c) measured at an incident angle of Ri ) 0.62°. Prior to the measurements, the sample was saturated in a negative field.
Figure 6. The non-spin-flip intensities I- - and I++ and the spin-flip intensities I- + and I+ - of the circular dots as a function of an increasing external magnetic field at the position of the first-order satellite at an incident angle of Ri ) 0.62°. Prior to the measurements, the sample was saturated and turned by 90°.
shown in Figure 6. The difference between I- - and I++ is much smaller and the spin-flip intensity much higher at small fields when compared to Figure 5. That means that there is a larger component of the sample’s magnetization perpendicular to the field direction but also a component parallel to the external field (otherwise I- - should equal I++).
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Figure 7. The non-spin-flip intensities I- - and I++ and the spin-flip intensities I- + and I+ - as a function of an increasing external magnetic field applied along the long side of the rectangular dots at the position of the first-order satellite measured at an incident angle of Ri ) 0.62°. Prior to the measurements, the sample was saturated in a negative field.
(b) Rectangular Co Dots. To investigate the influence of the shape anisotropy on the magnetization reversal process, we performed the same measurements on circular and rectangular dots. A magnetic field scan at the position of the first satellite when applying the field along the long side (easy axis) of the dots can be seen in Figure 7. Prior to the measurements, the sample was saturated in the negative field direction. Therefore, at zero field, the magnetization is antiparallel to the external field and I- is larger than I++. When the magnetic field is increased, the magnetization of the dots starts being reversed as can be concluded from the decreasing I- - intensity. At the coercive field at about 175 Oe, I- - equals I++, and the saturation value is reached at about 250 Oe. The spin-flip intensity is very small, indicating that there is a negligible component of the magnetization perpendicular to the applied field during the magnetization reversal. Figure 8 shows the spin-flip and non-spin-flip intensities of the off-specular intensity when applying an external magnetic field along the short side, that is, along the magnetic hard axis of the dots. Prior to this measurement, the dots were saturated along their long side (easy axis) creating a strong remanence along the easy axis. So, when the sample is turned by 90°, a large spin-flip signal occurs since the magnetization is perpendicular to the neutron spin. When the reversal process is started by increasing the magnetic field, the spin-flip signal decreases and simultaneously the splitting between the I- - and I++ intensity increases, reaching the saturation value at about 250 Oe. When the field is removed, the intensities revert to their original values due to the induced shape anisotropy.21 Discussion and Conclusion By measuring the spin-flip and non-spin-flip intensities, it is possible to get information on the in-plane magnetization components parallel and perpendicular to the field direction. That opens up the possibility to distinguish directly between different possible magnetization reversal models. The negligible spin-flip intensity for both sample types leads to the conclusion that the magnetization is definitely not reversed by a coherent rotation. In that case, the spin-flip intensity should have a pronounced peak at the coercive field similar to the situation at zero field after having turned the rectangular dots by 90° as shown in Figure 8. (21) Temst, K.; Van Bael, M. J.; Moshchalkov, V. V.; Bruynseraede, Y.; Fritzsche, H.; Jonckheere, R. Appl. Phys. A 2002, 74 [Suppl.], S1538.
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Figure 8. The non-spin-flip intensities I- - and I++ and the spin-flip intensities I- + and I+ - as a function of an increasing external magnetic field applied along the short side of the rectangular dots at the position of the first-order satellite measured at an incident angle of Ri ) 0.62°. Prior to the measurements, the sample was saturated along the long side of the dots and then turned by 90°.
Figure 9. Hysteresis curve measured with MOKE as a function of an external magnetic field applied along the short side of the rectangular dots (open circles) and along the long side of the rectangular dots (full circles).
Micromagnetic calculations along with MFM measurements performed on dots with diameters in the micron range22 show that the ground state is a vortex or multivortex state. The magnetization reversal in the double-vortex state occurs via propagation of the vortices from the center to the edges of the dots with increasing field. Micromagnetic calculations23 performed on circular dots with 4 µm diameter also show a multivortex state as the ground state. However, it is impossible to decide unambiguously on the basis of the OSPNR data whether the magnetization is reversed via vortices or by domain wall movement. We can only exclude a coherent rotation because of the lack of spin-flip intensity near the coercive field. Edge roughness of the dots may favor the formation of domains, whereas in the simulations only perfect disks were considered. Additionally, the recorded MFM pictures (not shown here) prove that the circular dots deviate slightly from perfect circles. Hence, a small shape anisotropy could be induced, which also favors domain formation. Regardless of the reversal process, we clearly observe a reduced remanence compared to the saturation value and we can state that only small magnetization (22) Prejbeanu, I. L.; Natali, M.; Buda, L. D.; Ebels, U.; Lebib, A.; Chen, Y.; Ounadjela, K. J. Appl. Phys. 2002, 91, 7343. (23) Donahue, M. J.; Porter, D. G. OOMMF Software; NISTIR 6376; National Institute of Standards and Technology: Gaithersburg, MD; http://math.nist.gov/oommf/.
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components perpendicular to the external field are present throughout the whole magnetization process. The rectangular shape of the dots creates a magnetic easy axis (long side) and a magnetic hard axis (short side). This leads to a preferential orientation of the magnetization along the long side of the dots in zero field, as can be seen in Figure 8 where the intensity is displayed as a function of the external field along the short side of the dots after the sample had been rotated by 90°. The magnetization keeps its previous orientation along the long side of the dots. Hence, a large spin-flip signal is observable. From the magnetization reversal along the long side of the dots shown in Figure 7, it is evident that the remanence is slightly reduced compared to the saturation value. That is in agreement with MOKE measurements displayed in Figure 9. The reason for that reduction might be the presence of small edge domains which are beyond the resolution limits of MFM. To summarize, we successfully performed OSPNR studies on magnetic dot arrays. For circular and rectan-
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gular dots, we could detect enhanced reflected intensity at distinct angles off the specular condition. This offspecular intensity occurs at those positions where the neutrons have gained additional momentum of qx ) (n × 2π/d corresponding to the distance d between the dots. Beyond that structural information, it is possible to gain detailed information on the magnetic structure by measuring the spin-flip and non-spin-flip intensities at those off-specular satellite positions. Acknowledgment. We are grateful to R. Jonckheere from IMEC vzw in Leuven, Belgium, for e-beam lithography work. This work was supported by the Fund for Scientific Research-Flanders (FWO), by the Flemish GOA and Belgian IUAP Programs, and by the European Commission under the Human Potential Program (HPRI1999-CT00020). K.T. and M.J.V.B. are postdoctoral researchers of the FWO. LA026625N
