Vortex rotation control in Permalloy disks with small circular voids

Transcription

1 JOURNAL OF APPLIED PHYSICS 99, Vortex rotation control in Permalloy disks with small circular voids P. Vavassori a and R. Bovolenta National Research Center S3, INFM-CNR, I Modena, Italy and Dipartimento di Fisica, Università di Ferrara, via Saragat 1, Ferrara, Italy V. Metlushko Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, Illinois B. Ilic Cornell Nanofabrication Facility, School of Applied and Engineering Physics, Cornell University, Ithaca, New York Received 22 August 2005; accepted 17 January 2006; published online 1 March 2006 We studied the magnetization reversal of Permalloy disks with a small circular void either concentric or decentered. In both systems the reversal takes place via the nucleation and annihilation of a magnetic vortex. By applying the diffracted magneto-optic technique combined with numeric micromagnetic simulations we retrieved the information about the sense of rotation of the magnetization in the vortex state. For the disks with the concentric void no preferential rotation has been observed. For the case of decentered void, the sense of rotation of all probed disks is deterministically controlled by appropriately choosing the direction of the externally applied field and the void position with respect to the disk center American Institute of Physics. DOI: / Ferromagnetic nanoelements developing magnetic vortex structures are attracting a great deal of interest for their potential application in high density data storage technology and because of the underlying physics governing the vortex formation/annihilation process, the vortex core displacement under the action of an external field, and its dynamic behavior. 1,2 The application of such nanomagnets as device elements in magnetic recording media and random access memories requires the perfect controllability of the magnetization circulation at room temperature. For this reason, methods to achieve the required control over the magnetization circulation in the vortex state in ferromagnetic nanoscale disks and rings are continuously investigated, and various solutions, more or less reliable, to achieve such a control have been reported. 3 6 In a disk the magnetization circulation in the vortex was proved to be controllable by introducing a slight ad hoc asymmetry e.g., a flattening into the geometric shape of the circular dots. 3 More recently, the attention has moved to ring nanostructures because of the higher stability shown by the vortex state in this geometric shape and the higher scalability below 100 nm as compared to the circular disk. In such nanoelements a control over the magnetization circulation has been achieved by introducing notches in the ring that act as pinning centers for the domain walls of the so called onion state, which has been found to be the seed state preceding the vortex formation, 4 or by making the ring asymmetric. 5,6 The pinning of magnetic vortex by point defects has also been studied. 7 Besides the capability of writing the desired magnetization circulation in the element, one has to be able to read the stored information. Among the methods for reading the stored information in the a Electronic mail: vavassori@fe.infn.it form of magnetization circulation, the one which is the most likely candidate for practical applications, is the use of magnetotransport measurements. Magnetoresistive measurements have indeed proven to be successful for retrieving information about the field dependence of magnetization configurations inside laterally confined systems when applied to both disk and ring cases. However, in the case of rings, the retrieval of the information about the sense of rotation is rather complicated and the magnetoresistive signals involved are quite small. 8 We recently showed that in the case of disks, magnetoresistive measurements can be carried out in which the two senses of rotation of the magnetization in the vortex state result in magnetoresistances having opposite signs and, thus, are easily detectable. 9 The success of the method relies on the shifting and distortion of the vortex structure as the external field is swept the vortex shifts perpendicular to the applied field direction, with a consequent distortion of the circular magnetization distribution that results in easily detectable variation of magnetoresistance 9. The aim of the present investigation is to find a method to reliably select the vortex circulation in soft Py disks, which stabilizes the vortex state as much as happens in a ring structure but, at the same time, ensures the controllable displacement of the vortex structure through the disk as the external field is swept. We have found that these goals can be achieved with the introduction of a slightly decentered small circular void into the disk. The void acts as a pinning center for the vortex state after its nucleation. If the void is small enough compared to the disk diameter, the application of an external field can shift the vortex, producing a distortion of the vortex configuration as required for the application of magnetoresistance for determining the sense of rotation of the vortex. It is worth noting that we obtained a sense of /2006/99 5 /053902/7/$ , American Institute of Physics

2 Vavassori et al. J. Appl. Phys. 99, scattering plane has not yet been developed, we will restrict our analysis to diffracted beams in the scattering plane plane xz, where z is the normal to the sample surface. In some detail, the D-MOKE loops in this geometry are due to the variation of the magnetic part of the scattered intensity I d m n of the nth diffracted order with field given by I d m n Re f d n Re f d m n A n Im f d m n +Im f d n Im f m d n + A n Re f m d n, 1 where f d n = S exp ing x ds is called the nonmagnetic form factor, where G =2 /d d is the array period along the direction x parallel to the scattering plane is the reciprocal lattice vector of the array parallel to the scattering plane, and the integral is carried out over a single dot. The magnetization information in the diffracted beams is contained in the so called magnetic form factor f d m n = S m y exp ing x ds, where m y is the component of the magnetization perpendicular to the scattering plane direction y. For particles with a shape having a center of inversion symmetry, f d n is a real number and Eq. 1 simplifies to 10 FIG. 1. Scanning electron images of a portion of the two patterns: symmetric rings upper panel and asymmetric rings lower panel. circulation of the magnetization in the vortex state, which is opposite compared to that reported in Ref. 6 for the same direction of the externally applied field and the void position with respect to the disk center. Since in Ref. 6 disks with a much larger decentered elliptical void where used, the observed difference suggests that the mechanisms determining the vortex circulation depend critically on the shape and size of the void. The samples investigated here are two arrays of 25-nm-thick Permalloy dots, with nominal diameter of 1.0 m arranged on a square lattice with a period of 2.00 m, prepared using e-beam lithography and lift-off techniques. A small circular void with a nominal diameter of 160 nm has been patterned into each disk. The circular void is concentric to the disk in one sample and slightly decentered in the other. Figure 1 shows the scanning electron microscopy images of the two samples. The magnetization reversal in these structures has been studied using the diffracted magneto-optic Kerr effect D- MOKE combined with numerical micromagnetic simulations; this technique has proven to be able to determine the magnetization circulation in circular Py nanomagnets. 10 The incident beam of a HeNe laser wavelength of nm for the D-MOKE experiments is polarized in the plane of incidence p polarization and the magnetic field is applied perpendicularly to the plane of incidence, as described in Refs. 10. This arrangement corresponds to the transverse MOKE geometry where the changes in the sample magnetization lead to changes in the intensity of reflected and diffracted beams, leaving their polarization state unchanged. Since the theory for magnetic effects in diffracted beams out of the I d m n Re f d m n A n Im f d m n. The number A n depends on the angles that the incidence and diffracted beams form with the sample normal and the optical and magneto-optical coefficients of the material and is treated usually as an adjustable parameter. For n=0, i.e., in the case of the reflected beam, the signal I d m 0 is just proportional to the average value of m y in all the probed dots. In this case, the MOKE loops are identical to those measured using standard averaging techniques such as superconducting quantum interference device SQUID and vibrating sample magnetometry. As shown in Ref. 10, this magnetic form factor can provide details of the magnetization structures inside the elements of an array with a spatial resolution below the laser light wavelength. In the case of vortex state in Permalloy circular disks, we showed that the loss of center of inversion symmetry in the magnetization distribution when the vortex is nucleated leads to a large imaginary part of the magnetic form factor, which changes sign upon changing the sense of rotation of the magnetization. 10 As a results, if all dots or their great majority develop a vortex state having the same magnetization circulation viz., there is spatial coherence for the disk switching, the diffracted loops, especially for n 2, will show characteristic features e.g., peaks, shoulders, and negative coercive field that substantially change upon rotation of the sample by 180 about its normal viz., upon changing the sense of rotation in the vortex state. This happens when an asymmetry is intentionally introduced in the shape of the disks or the fabrication defects do not have a random nature. 10 In the case of equal number of disks developing vortex with clockwise and counterclockwise circulations viz., no spatial coherence for the disk switching because of the random nature of defects, the imaginary part of the magnetic form factor averages to zero and no differences will appear between diffracted loops recorded, rotating the sample by

3 Vavassori et al. J. Appl. Phys. 99, FIG. 2. Measured D-MOKE hysteresis curves of the pattern with symmetric rings; indicates the angle of rotation of the sample about its surface normal. The arrows with numbers in the upper panel mark the nucleation of different magnetic configurations. With solid symbols is shown the portion of the hysteresis loop for decreasing external fields; the open symbols refer to the portion of the hysteresis loop for increasing external fields. Figure 2 shows D-MOKE hysteresis loops, up to the second order diffracted beam, measured from the disks with the concentric void. The loop recorded from the reflected beam shows a three-step reversal path see the labeled arrows in the upper panel of Fig. 2. The loops from the diffracted beams on the right column of Fig. 2 have been recorded upon rotating the sample by 180 about its normal with respect to those in the left column. According to our previous results, if the vortex rotation is the same in all probed disks and this is related to the sample orientation relative to the applied field, a rotation of the sample by 180 would result in an opposite vortex rotation and, in turn, in a very different diffracted loops shape, particularly in the case of second order ones where these effects should be very large. Based on the arguments presented above, the fact that the loops shape remains substantially unvaried upon rotating the sample is a strong indication that the vortex rotation is not spatially coherent in the set of disks probed in the measurements about disks within our beam spot size of 1 mm 2. This means that the disk switching is dominated by the random nature of fabrication defects deviations from the perfect circular shape of the disk and/or the void, nonperfectly concentric position of the void, edges roughness, etc.. To calculate the hysteresis loops we first simulated the field-dependent magnetization distribution in a single dot using the OOMMF code. 11 The material parameters used for the calculation are those contained in the OOMMF program for Permalloy viz., saturation magnetization M S = A/m, exchange stiffness constant A= J/m 3, no magnetocrystalline anisotropy; the damp-

4 Vavassori et al. J. Appl. Phys. 99, FIG. 3. Calculated D-MOKE hysteresis curves of symmetric rings assuming an equal number of disks nucleating a vortex state with clockwise and counterclockwise circulations. With solid symbols is shown the portion of the hysteresis loop for decreasing external fields; the open symbols refer to the portion of the hysteresis loop for increasing external fields. ing coefficient used in the simulations is 0.5 and we used a cell size of 5 nm, which corresponded the average grain size in our Permalloy film determined from transmission electron microscopy data. At each field the magnetization distribution is extracted, and the real and imaginary parts of the form factors calculated using Eq. 2. In Fig. 3 we show the calculated loops from the zeroth to the second order assuming Im f d m n =0 in Eq. 2, viz., an equal number of particles nucleating a vortex state with clockwise and counterclockwise circulations. For the zeroth through second order loops the agreement between the measured and calculated loops is excellent, confirming thus that the reversal is occurring through the nucleation of vortices without spatial coherence of the sense of rotation. We note here that the jumps shown by experimental loops are broader than those displayed by the calculated loops. This is not surprising considering that the calculations are performed on a perfect ideal particle. The inevitable fabrication defects, such as deviation from the ideal shape, edge roughness, and material inhomogeneities, yield to a distribution of nucleation fields and to pinning effects of the magnetic configuration developing during the reversal that make the features of the measured loops broader than those of the calculated loops. Despite these shortcomings, the micromagnetics allows also the identification of the origin of three steps in the reflected loops. The first step label 1 in the upper panel of Fig. 2 is due to the vortex nucleation; once nucleated the vortex core moves towards the center of the disk as the external field is varied, where it is pinned by the void small plateau in the loop. The core depinning occurs at a certain field, giving rise to the second step label 2 in the upper panel of Fig. 2. Eventually, at a high enough field, the core reaches the disk border and the vortex state annihilates, yielding the third step in the loop label 3 in the upper panel of Fig. 2. The measured D-MOKE loops of the disks with the decentered void are shown in Fig. 4. The loops are quite different from the previous case. The reflected loop displays now a two-step reversal process, and the diffracted loops do not remain unvaried upon rotation of the sample. In particular, both first and second order diffracted loops change completely upon rotation of the sample by 180 about its normal compare left and right columns in Fig. 4. In Fig. 5 we show the calculated loops from the zeroth to the second order obtained setting A l = 0.8 and A 2 = 0.65 in Eq. 2 and with the void position relative to the center of the disk and the applied field as sketched in the insets. Also sketched in Fig. 5 is the sense of rotation of vortex magnetization obtained from the micromagnetic simulations for the two orientations of the particles. The reversal of vortex rotation yields a change in sign of the Im f d m n which accounts very well for the observed change of shape of the D-MOKE loops. However, in the present case, where also the nonmagnetic form factor is complex i.e., the particles do not have a center of inversion symmetry, some cautions must be taken before drawing any conclusion about the sense of rotation of the vortex using Eq. 2. One should use instead the complete equation 1, which can be conveniently rewritten as follows: I d m n Re f d m n A n Im f d m n + R n Im f d m n + A n Re f d m n, where R n =Im f d n /Re f d n. The first term contributing to the diffracted intensity is the same as that for symmetric particles Eq. 2, while the second term, due to the asymmetric shape of the particle, can be neglected only for vanishing or negligible imaginary component of the nonmagnetic form factor. In particular, the ratio R n changes sign it is Im f d n that changes sign upon rotation of the particle by 180. In the case of the orientation of the particles as sketched in the insets of Figs. 4 and 5, the calculations give R 1 =0.025 and R 2 =0.1, indicating that, from a practical standpoint, the small size of the decentered void allows us to neglect the effects of the imaginary component of the nonmagnetic form factor and to use Eq. 2 also in this case. Therefore, the observed changes in shape of the diffracted loops upon rotation of the sample by 180 must be ascribed 3

5 Vavassori et al. J. Appl. Phys. 99, FIG. 4. Measured D-MOKE hysteresis curves of the pattern with asymmetric rings. The insets sketch the orientation of the rings with respect to the applied field. The arrows with numbers in the upper panel mark the nucleation of different magnetic configurations. With solid symbols is shown the portion of the hysteresis loop for decreasing external fields; the open symbols refer to the portion of the hysteresis loop for increasing external fields. to the reversed sense of rotation of the magnetization in the vortex state, as sketched in the insets of Fig. 5. We can thus conclude that the excellent agreement between the measured and calculated loops demonstrates that all disks, or at least the great majority of the disks, 12 nucleate vortices with the same sense of rotation and that this can be deterministically selected by choosing the position of the void with respect to the disk center and the direction of the applied field. Details of the magnetic configurations developing during the reversal are shown in Fig. 6. They show that the magnetization direction remains pinned in the narrow channel determined by the decentered position of the void and the disk edge with respect to the applied field direction, and this is the driving mechanism that yields the sense of rotation of magnetization in the vortex state. This behavior is different from those reported in Ref. 6 for the case of disks with a much larger decentered elliptical void, where the magnetization in the channel reverses first, as the external field is reduced to zero. This suggests that the vortex state nucleation process is very dependent on the size, shape, and position of the decentered void. The clarification of these aspects requires more theoretical and experimental work. The first step in the reflected loop in Fig. 4 corresponds to the vortex nucleation and immediate displacement of its core into the void label 1 in the upper panel of Fig. 4. As the field is increased, the vortex state starts to distort label 2 in Fig. 4, shifting towards the disk edge till to its annihilation, yielding the sec-

6 Vavassori et al. J. Appl. Phys. 99, FIG. 5. Calculated D-MOKE hysteresis curves of asymmetric rings assuming a well defined magnetization circulation in the vortex state. The insets sketch the orientation of the rings with respect to the applied field and the magnetization circulation in the vortex state nucleating during the reversal. With solid symbols is shown the portion of the hysteresis loop for decreasing external fields; the open symbols refer to the portion of the hysteresis loop for increasing external fields. ond step in the loop label 3 in the upper panel of Fig. 4. A highly distorted intermediate state is clearly visible in the magnetic configuration at 400 Oe shown in Fig. 6. From the measured loops of Fig. 4 we can evaluate that the field range over which the progressive distortion of the vortex state takes place is between about 100 and 350 Oe. The distortion of the vortex produces a clear peak in the second order diffracted loops, well reproduced by calculations compare the second order loops of Figs. 4 and 5. Important for application, the field range over which the vortex state exists can be widely varied by modifying the ratio between the diameter and the thickness of the dot. We finally note that the calculated fields at which these steps occur are slightly different higher from those observed experimentally, but this is not surprising considering that the calculations are performed on a perfect ideal particle. In conclusion we showed how it is possible to deterministically set the sense of rotation of the magnetization in the vortex state in a circular Permalloy disk by introducing a small circular void, slightly decentered with respect to the disk center. Our results show that, at variance with conventional ring structures, if the void is small enough, the vortex displacement inside the disk is still ensured as the external field is varied. These two features are most useful for potential applications in magnetic storage technology of devices that rely on the vortex circulation as the information bit and on the magnetoresistance effect as the method for reading the stored bit. ACKNOWLEGMENTS Financial support from the projects FIRB RBNE017XSW and PRIN of MIUR, project NANO&NANO of University of Ferrara, and by the U.S. NSF, Grant Nos. DMR and ECS is acknowledged. M. Grimsditch is gratefully acknowledged for fruitful discussions.

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