Low-field giant magnetoresistance in layered magnetic rings

PHYSICAL REVIEW B 74, 224401 共2006兲

Low-field giant magnetoresistance in layered magnetic rings F. J. Castaño, D. Morecroft, and C. A. Ross Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA 共Received 30 August 2006; published 4 December 2006兲 The low-field magnetization reversal of NiFe/ Cu/ Co multilayer mesoscopic elliptical and circular rings has been investigated via magnetoresistance measurements and micromagnetic modeling. Minor loop measurements, in which the NiFe layer is cycled for a fixed Co layer configuration, show qualitatively different behavior depending on whether the Co layer is present in a vortex or an onion state. Micromagnetic simulations are in excellent agreement with the experimental data and confirm the dominant role played by magnetostatic interactions between the Co and NiFe layers, as a result of stray fields from the domain walls present in the layers. Multiple stable remanent resistance levels can be obtained by cycling the rings at modest fields. DOI: 10.1103/PhysRevB.74.224401

PACS number共s兲: 75.47.⫺m, 85.75.Dd, 73.43.Qt, 85.70.Kh

I. INTRODUCTION

The physical properties of small, lithographically defined multilayered magnetic solids have attracted considerable fundamental and applied research, fueled by the advantages of using these structures in memory1,2 and logic3 applications. The magnetotransport behavior in compositionally modulated elements ranks among the most interesting, since it is the preferred read-back mechanism in integrated devices.4 The basic architecture of these small elements comprises a soft 共free兲 magnetic layer separated from a hard or pinned magnetic layer using a nonmagnetic metallic spacer layer5 or a thin insulating tunnel barrier.6 The resistance of these structures is well understood in terms of giant- or tunneling magnetoresistance 共GMR or TMR兲, respectively.7,8 Multilayered elements with dimensions in the deepsubmicrometer regime, exhibiting a robust and reproducible magnetization reversal, characterized by the existence of well-defined magnetic configurations or states, are requirements for many magnetoelectronic applications. Single-layer thin-film magnetic rings are known to show several stable and metastable states, but there is little published work on the more complex magnetotransport behavior of multilayer magnetic rings. Thin-film rings are characterized by the existence of the bidomain or “onion” state,9 which contains two 180° domain walls at opposite ends of a diameter, and the flux-closed or “vortex” state, in which the magnetization is oriented circumferentially. The existence of flux-closed magnetic configurations in ferromagnetic bodies with physical boundaries was first deduced by Landau10 and is favored in rings, compared to thin-film disks, because of the absence of the highly energetic vortex core in a ring. Considerable experimental and modeling work11–19 has established the magnetic phase diagram of single-magnetic-layer rings, typically made from NiFe or Co, illustrating the diameters, widths, and thicknesses at which the vortex and onion states are stable. The onion state is typically stable at remanence. A transition from the onion state to the vortex state occurs when one of the walls unpins and traverses the structure, eventually 1098-0121/2006/74共22兲/224401共9兲

annihilating with the other wall to generate the vortex state. Vortex-to-onion transitions occur at higher reverse fields by the nucleation and propagation of a reverse domain. Multilayered rings have recently been shown to display both GMR20–22 and TMR,23 with a magnetization reversal characterized by multiple stable resistance levels separated by abrupt transitions. Significantly, we have found that the reversals of the magnetic layers in NiFe/ Cu/ Co layered rings are qualitatively different from those in a single layer ring,20 and are dominated by magnetostatic interactions between the layers caused by the stray fields from domain walls present in each ring. Additionally, in current-in-plane GMR measurements, the measured variation of resistance with applied field is strongly dependent on the contact configuration used in the four-point measurement, and indeed the contact configuration may be adjusted to tailor the magnetotransport response of the rings.24–28 In this article, we describe in detail the low-field behavior of both circular and elliptical NiFe/ Cu/ Co rings, and demonstrate dramatic differences in reversal of the NiFe layer, depending on whether the Co layer is in an onion or a vortex state. This low-field behavior is of key importance in the performance of magnetoelectronic devices, for example, magnetic random access memories,29 based on rings. II. EXPERIMENTAL METHODS AND MODELING

The device fabrication process entailed three lithography levels and liftoff processing. Electron-beam 共e-beam兲 and optical lithography were used for pattern generation and ultrahigh-vacuum sputtering or e-beam evaporation followed by liftoff for the metallization steps. First contact patterns of Ti 共4 nm兲 / Au 共30 nm兲 was defined by optical lithography on a Si共100兲 wafer with 50-nm-thick thermal oxide. The pattern consisted of 42 macroscopic pads linking seven 600 ⫻ 400 ␮m2 areas, each with six isolated metallic wires. E-beam lithography was then used to define constant-width elliptical 共aspect ratio ⫽ 2兲 and circular ring patterns in each of the seven open areas, followed by the deposition and liftoff of the NiFe/ Cu/ Co/ Au pseudo-spin-valve 共PSV兲 thin film. Rings were made from polycrystalline NiFe4 / Cu6.5/ Co8; NiFe4 / Cu5 / Co7; NiFe4 / Cu4 / Co8;

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©2006 The American Physical Society


CASTAÑO, MORECROFT, AND ROSS

NiFe6 / Cu6 / Co8; and NiFe6 / Cu4 / Co5 共numbers refer to film thicknesses in nanometers兲 PSV structures, coated with a 3–4 nm-thick Au layer to prevent oxidation. The rings had widths of 80 nm and above, and lateral edge roughness below 10 nm. Finally, connecting-wire patterns from the rings to the Ti/ Au pads were written in resist, after precise alignment to the magnetic rings. The final connecting wires were made by liftoff of a sputter-deposited Ta 共2 nm兲 / Cu 共80–140 nm兲 bilayer to complete the devices. Elliptical and circular PSV ring devices with outer diameter from 1.7 ␮m to 20 ␮m and widths ranging from 80 nm to 400 nm were fabricated. The ring resistance was measured at room temperature with a four-point technique, using a constant rms current of 10 ␮A and ac lock-in detection at 1 kHz. The devices were first magnetized in-plane using fields of ⬃10 kOe, and then the resistance was measured while the field was symmetrically swept, typically up to ⬃1500 Oe. The chips were positioned between the poles of an electromagnet on a precision rotating stage that allowed for accurate alignment of the applied field along the axis of the devices. We describe here GMR measurements for large field amplitudes in which both the NiFe and Co layers reverse 共major loops兲, and for small field amplitudes in which the NiFe layer reverses for a fixed Co layer configuration 共minor loops兲. In all cases the applied field direction was parallel to the position of the current leads 关as shown in Fig. 1共b兲兴. When an electrical current is injected into a ring using two contacts, it divides between the two sides of the ring. The rings can therefore be modeled as two resistors connected in parallel: R1 and R2 关Fig. 1共d兲兴. The measured resistance is V12 / I = 共RAR2兲 / 共R1 + R2兲, where RA is the resistance of the ring section between the voltage leads. Therefore, the resistance measured is sensitive to changes in magnetic configuration anywhere within the ring. The magnetotransport behavior of the unpatterned PSV films is dominated by giant magnetoresistance, and the GMR ratios of the films, 兵关⌬R共H兲 − ⌬R共HMax兲兴 / ⌬R共HMax兲其 ⫻ 100%, were 0.8% 共NiFe4 / Cu6.5/ Co8兲; 1.2% 共NiFe4 / Cu5 / Co7兲; 1.4% 共NiFe4 / Cu4 / Co8兲; 0.9% 共NiFe6 / Cu6 / Co8兲; and 1.3% 共NiFe6 / Cu4 / Co5兲. These values are lowered by the shunting effect of the Au layer but are comparable with reported data on similar NiFe/ Cu/ Co stacks.30 The Cu spacer thickness is sufficiently large that the exchange coupling between the two magnetic layers is negligible. Despite the different ring dimensions, the GMR ratios for all the devices made from each PSV were similar: 1.2% ± 0.06% 共NiFe4 / Cu6.5/ Co8兲; 1.85% ± 0.08% 共NiFe4 / Cu5 / Co7兲; 2.3% ± 0.05% 共NiFe4 / Cu4 / Co8兲; 1.55% ± 0.05%共NiFe6 / Cu6 / Co8兲; and 2.1% ± 0.05% 共NiFe6 / Cu4 / Co5兲, respectively. The devices show GMR ratios up to 40% higher than their corresponding unpatterned PSV films, which may be attributed to an improved magnetization alignment parallel to the edges of the patterned rings. The magnetization reversal in elliptical and circular PSV rings was modeled using the three-dimensional object oriented micromagnetic framework 共OOMMF兲 simulation software.31 Two ring structures were used for the modeling: 共a兲 a 2-␮m-long axis, 1-␮m-short axis, 120-nm-wide

FIG. 1. 共Color online兲共a兲 Side-view scanning electron micrograph 共SEM兲 of a NiFe/ Cu/ Co/ Au elliptical ring device. Plan-view SEMs corresponding to 1.9-␮m-long elliptical rings 共b兲, 共c兲 and 2 -␮m-diameter circular PSV rings 共d兲, 共e兲 with different widths. Schematics of the contact configurations 共d兲 used for magnetotransport measurements and the different resistances 共R1, R2, and RA兲 of the electrical circuit 共d兲 used for the modeling.

NiFe4 / Cu4 / Co8 elliptical ring, discretized using 4 ⫻ 4 ⫻ 4 nm3 cubic cells; and 共b兲 a 2-␮m-long axis, 200-nm-wide NiFe6 / Cu6 / Co9 circular ring discretized using 5 ⫻ 5 ⫻ 3 nm3 cells. The Landau–Lifschitz–Gilbert equation was then solved for the magnetization in each cell,32 using standard parameters for NiFe 共exchange constant A = 1.3 ⫻ 10−6 erg/ cm, saturation moment Ms = 860 emu/ cm3, anisotropy K1 = 5 ⫻ 103 erg/ cm3兲 and Co 共A = 3 ⫻ 10−6 erg/ cm, Ms = 1400 emu/ cm3, K1 = 5.2⫻ 106 erg/ cm3兲, and the damping constant ␣ was set to 0.5. Both major and minor GMR loops in applied fields up to 1000 Oe with directions parallel to the positions of the current leads in the devices were modeled. Furthermore, based on the relative orientation of the magnetization between adjacent cells in the NiFe and Co rings deduced from the micromagnetic simulations, both major and minor loops were computed assuming that the change in the resistance of a region of the ring can be calculated using ⌬R = RP + 共RAp − RP兲关共1 − cos ␪兲 / 2兴, where RP and RAp are the resistances when the magnetization vectors of the Co and NiFe are parallel and antiparallel, respectively, and ␪ is the angle between the magnetization vectors in adjacent cells in the Co and NiFe rings. In the modeling, 关共RAp − RP兲 / RP兴 ⫻ 100% was taken as 1.2% and 1.8% for the elliptical and circular rings, respectively.

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LOW-FIELD GIANT MAGNETORESISTANCE IN… III. RESULTS AND DISCUSSION A. Major loops of multilayer rings

Each branch of the major GMR loops from both circular and elliptical PSV rings displayed three distinct resistance levels 共labeled as S1, S2, and S3 in Fig. 2兲. The highest 共S1兲 and lowest 共S3 or Ssat兲 levels can be attributed20 to antiparallel and parallel configurations, respectively, of onion states in the soft NiFe and hard Co layers. On the other hand, the intermediate level 共S2兲 corresponds to a configuration in which the hard Co layer is in a vortex state and the NiFe is in a reverse onion state. In state S2, the magnetization of half of the Co ring is parallel to that of the NiFe ring and the other half antiparallel; thus, the resistance of S2 is halfway between that of S1 and S3 in the contact geometry used here. The low-field S3-to-S1 transition in these major loops is determined by the reversal of the NiFe layer, while the two higher field steps are governed by the Co ring, transitioning from onion-to-vortex 共S1-to-S2兲 and vortex-to-reverse onion 共S2-to-S3兲 with increasing field.20 For rings patterned from a given multilayer, decreasing the outer diameter and ring width leads to an increase in switching fields, evident for example in Fig. 2共c兲. This trend is in agreement with the results for single-layer rings reported elsewhere.11–14 On the other hand, Co rings with similar dimensions can display significantly different S1-to-S2 and S2-to-S3 transitions depending on the thicknesses of the Cu spacer and NiFe soft layers.20 This may be compared with single-layer polycrystalline Co circular rings with similar dimensions, in which the onion-to-vortex and vortex-to-onion switching fields are determined solely by the dimensions of the rings.12 Decreasing the Co layer thicknesses 关Fig. 2共b兲兴 or decreasing the Cu spacer thickness 关Fig. 2共d兲兴 results in lower switching fields for the S1-to-S2 and S2-to-S3 transitions. Additionally, single-layer Co rings within the thickness range of 5–8 nm do not typically show a vortex state,12 i.e., they transition directly from a forward onion state to a reverse onion state, because the onion state has lower total energy at all fields. In comparison, the Co layers in the PSV stacks show vortex states that can be stable over wide field ranges, even for the thinnest 共5 nm兲 rings 关Figs. 2共b兲 and 2共d兲兴. Vortex stability ranges of up to 150 Oe and 700 Oe were measured for the circular and elliptical PSV rings, respectively. The qualitative differences between single-layer Co rings and the Co layers within the PSV rings is suggestive of a fundamentally different reversal mechanism in the two cases. The reversal of the Co layer in the PSV rings is dominated by the magnetostatic coupling between the Co and the NiFe layers in the stack, rather than solely by the intrinsic dimensions 共outer diameter and width兲 of the rings, as in single-layer rings. Similarly, the reversal of the NiFe layer in the PSV rings is dominated by magnetostatic interactions from the stray fields of the domain walls in the onion-state Co layer, and shows little or no vortex stability, in contrast with single-layer NiFe rings of the same dimensions. The importance of these magnetostatic interlayer interactions will be evident when we consider the minor-loop reversal of the NiFe layer in the following sections. Finally, circular and elliptical rings may be compared. Even though the elliptical rings were narrower than their

FIG. 2. Major magnetoresistance loops corresponding to elliptical 共a兲, 共b兲 and circular 共c兲, 共d兲 pseudo-spin-valve rings with different dimensions and NiFe/ Cu/ Co stacks. The legends give the ring diameter, width, and layer thicknesses.

circular counterparts, elliptical structures showed a lower S1-to-S2 transition than circular rings patterned from the same PSV film, and for fields applied along the long axis, elliptical PSV rings displayed a significantly more stable Co vortex state than did circular structures.

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As the reverse field is increased, the Co ring transitions into a vortex state 共S2 resistance level兲. Again, unlike the reversal of a single-layer Co ring, the reversal of the Co layer in the PSV ring is influenced by the stray fields from the NiFe domain walls. The Co layer reversal in the PSV ring proceeds by nucleation and growth of a reverse domain, and the resulting Co vortex state can contain residual 360° walls, which are especially prevalent in circular rings, but also found in elliptical rings. 共Vortex states containing 360° walls were also reported in single-layer rings and described as “twisted” states.34兲 The modeling 关Fig. 3共a兲兴 confirms the significantly higher stability of the Co vortex state for elliptical compared to circular rings. A further field increase converts the Co vortex into a reverse onion state by domain nucleation and propagation, and also results in the eventual disappearance of any remaining 360° walls in both NiFe and Co layers. The qualitatively different reversal process in the multilayer compared to single-layer rings seen in the model, which results from magnetostatic interactions between the layers, is in good agreement with the measured GMR of the rings. B. Minor loops for onion-state hard layer

FIG. 3. 共a兲 GMR curves computed from micromagnetic simulations for elliptical and circular PSV rings. 共b兲 Micromagnetic snapshots of the magnetic configurations in the Co and NiFe layers for a circular PSV ring at resistance levels S1 and S2. The small arrows show the magnetization in the cells inside each ring and the schematics the overall domain structures and the positions of 180° walls 共single bar兲 and 360° walls 共double bar兲.

The shape of the GMR curves computed from micromagnetic simulations 共Fig. 3兲 shows a remarkable resemblance to the experimental results for both elliptical and circular rings 共Fig. 2兲. As the field is decreased from saturation, both the soft and hard rings are in parallel onion configurations 共Ssat or S3兲. The domain walls in the onion configurations of both rings contain head-to-head and tail-to-tail 180° domain walls with a transverse spin structure. At low reverse fields, reverse domains nucleate at both ends of the NiFe layer and propagate along the sides of the ring to form a reverse onion state, leading to the S1 configuration in which the NiFe onion is antiparallel to the Co onion state. Unlike the reversal of a single-layer NiFe ring, this reversal mechanism can leave residual 360° walls in both sides of the NiFe layer 关shown as double lines in Fig. 3共b兲兴. In this configuration the NiFe ring may be described as a “twisted onion” state, in analogy to previous micromagnetic simulations on PSV nanorings.33 The 360° walls have a minor effect on the GMR of the ring. As observed in narrow single-layer-rings,34,35 these walls are metastable and eventually annihilate at sufficiently high reverse fields.

In these measurements the rings were initially saturated in a field of +5000 Oe. The field was reduced to a value in the range −100 Oe to −200 Oe, which is within the stability range of the S1 configuration, then cycled in the range of ±100 Oe or ±200 Oe. Under these conditions, the Co layer remains in a forward-onion state, while the soft NiFe layer is cycled. These minor loops show the expected S1 and Ssat 共or S3兲 resistance levels, but additional resistance plateaus 关labeled as S0 and S0R in Figs. 4共a兲 and 4共c兲兴 are also observed. The intermediate states are asymmetric, both in stability and in resistance level. S0 is significantly more stable than S0R, and in the circular rings S0R did not appear at all, except in the smallest samples. The stability of these states varies with the ring dimensions and layer thicknesses. The switching fields of the NiFe layer increase on decreasing the ring width and diameter, similar to observations made in the major loops. Switching fields are lower for thicker NiFe 关Fig. 4共a兲兴 and also lower for thicker Cu and Co layers 关Figs. 4共b兲 and 4共c兲兴. The stability of the intermediate S0 and S0R configurations was greatest for narrow, elliptical rings made from the NiFe4 / Cu6.5/ Co8 film. The minor loops are offset with respect to zero field, and this shift decreases with an increase in the diameter and width of the rings. While the minor loops for elliptical rings are always offset 共ranging from 20 Oe to 90 Oe兲, circular rings display no offset for the larger structures. Some of the smallest circular rings 共2 ␮m diam, 220 nm wide兲 have a large enough offset, compared to the switching field, that the NiFe layer has reversed before the applied field has changed sign, and the remanent state therefore consists of antiparallel NiFe and Co onion states 关Fig. 4共c兲兴. To understand this behavior, the minor loop of an elliptical ring was modeled, as shown in Fig. 5. The model is in excellent agreement with the observed intermediate states,

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LOW-FIELD GIANT MAGNETORESISTANCE IN…

FIG. 4. Minor GMR curves measured by cycling the NiFe with the Co layer in an onion state for 共a兲, 共b兲 elliptical and 共b兲, 共c兲 circular PSV-ring devices with different dimensions.

including their different resistances, and the offset of the loop from zero field. Recall that in the initial S1 configuration, the NiFe ring is in a twisted-onion state containing both head-on 180° walls and residual 360° walls. On reversing the field from this configuration, the NiFe ring first transitions into a vortex 共S0 configuration兲 with additional domain walls located above the 180° walls in the Co onion state 关Fig. 5共b兲兴. Increasing the reverse field slightly decouples these domain walls, allowing them to move through the structure to create an onion state parallel to the Co onion state 共Ssat兲. Following the field sequence in the experiment, the field direction was then reversed again. This returned the ring to the S1 configuration, via an intermediate state of small stability corresponding to the S0R configuration, which in the simulation contains several domains. The reversal of the NiFe into the S0R state occurs by domain propagation starting from

FIG. 5. 共a兲 Minor GMR loop computed from micromagnetic simulations corresponding to a PSV-elliptical ring. The inset shows experimental minor GMR loops from a 1.7-␮m-long, 120-nm-wide NiFe4 / Cu6.5/ Co8 elliptical ring showing the reversibility of the S0 and S0R configurations. 共b兲 Micromagnetic snapshots of the magnetic configurations in the Co and NiFe 共Permalloy, Py兲 rings for an elliptical PSV ring at resistance levels S1, S0, Ssat, and S0R, respectively.

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both ends of the ring, influenced by magnetostatic coupling from the walls in the hard Co ring. The offset of the minor loop is ⬃100 Oe and hence, is in reasonable agreement with the experimental results from PSV rings with similar dimensions. These minor loops show the profound influence of interactions, both in determining the reversal mechanism of the rings and in stabilizing configurations with correlated domain wall positions in the two magnetic layers. The origins of coupling between soft and hard 共or pinned兲 layers have been extensively investigated in unpatterned, multilayered films.36,37 These structures may simultaneously display various exchange interactions, direct or indirect, which can be positive 共parallel兲 or negative 共antiparallel兲 in nature. In the present case, coupling arising from oscillatory exchange is negligible in the PSV stacks due to the relatively thick Cu spacer layer, and Néel’s “orange-peel” coupling36 is assumed to be small since the films have low roughness. Therefore, the main contribution to the coupling in the rings is from the magnetostatic interactions from the stray fields of the domain walls present in the layers. The domain walls in narrow rings are expected to be transverse, 180° head-to-head or tail-totail walls,11–19 as well as 360° walls formed by interacting pairs of 180° walls.34 During the minor loop cycling, the Co configuration is almost unchanged and the S1-to-S0 switching field in the minor loop can be considered as the escape field 共Hesc兲 needed, for example, for a head-to-head domain wall in the NiFe to unpin or dissociate from the stray field of a tail-to-tail wall in the Co. Fuller and Sullivan38,39 showed that experimental escape fields in unpatterned films lay well below theoretical values, calculated by treating the domain walls as linear dipoles.39 The same modeling predicts escape fields on the order of several hundred Oe in the PSV rings, while the experimental values are typically in the range of ⬃50–100 Oe. Interestingly, experimental minor loops show that the S0 configuration can be cycled into the S0R resistance levels when the field is reversed 关see inset in Fig. 5共a兲兴 and eventually into the S1 configuration at low applied fields 共5–25 Oe兲. Hence, the soft layer in a PSV ring can display three stable remanent configurations, in contrast to the two remanent states achieved in elongated magnetic multilayered elements,2,5 which may be useful in applications. The switching of the NiFe rings when the Co is in an onion state differs significantly from that of single-magneticlayer NiFe or Co rings, which require the nucleation of domain walls for the vortex-to-onion transition.11–19 Overall, the reversal revealed by the simulations is consistent with the experimental results, and the reversibility of the S0 and S0R configurations supports the hypothesis that complex domain wall configurations exist in the soft NiFe rings at both these intermediate resistance levels. The low-field switching displayed by the soft layer in PSV rings suggests a nucleationfree reversal dominated by the coupling and decoupling of domain walls in the hard and soft layers. C. Minor loops for vortex-state hard layer

We now turn to the case of minor loops measured when the hard Co layer is present in a vortex state. As previously

FIG. 6. Minor loops with the Co rings in vortex configurations for both elliptical and circular PSV rings with different dimensions and PSV stacks. 共a兲 The applied field is swept from positive saturation 共resistance Ssat兲 to the S1 resistance level and then to the S2 resistance level 共solid points兲, followed by the return to remanence and the switching of the soft ring into state SPaV and then state S2R 共open points兲. Minor loops after positive 共b兲 and negative 共c兲 saturation. Branches returning from the SPaV and SApV levels to remanence 共triangles兲 are also included. 共d兲 Minor loop from a circular ring starting from the S2 state.

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described, the S2 resistance level corresponds to the Co layer being magnetized in a vortex state, which may contain 360° walls. If the ring is magnetized into the S2 plateau and the field is then removed, the resistance remains unchanged 关Fig. 6共a兲兴, indicating that the magnetic states of the Co and NiFe layers that exist at S2 are preserved at remanence. The soft NiFe layer may now be cycled with a small field amplitude while the Co layer remains in a vortex configuration. On cycling the NiFe ring 关Figs. 6共b兲 and 6共c兲兴 the resistance changes abruptly, increasing to S1, or decreasing to Ssat. These resistance levels are attributed to the transition of the NiFe layer into a vortex state, which may be either antiparallel 共resistance level S1兲 or parallel 共resistance level Ssat兲 to the vortex state in the Co layer. These two states have been labeled as parallel vortex, SPaV, and antiparallel vortex, SApV, in Figs. 6共b兲 and 6共c兲. This switching behavior was observed in both elliptical and circular rings 关Fig. 6共d兲兴. It is noteworthy that the NiFe vortex state has considerable stability range, of the order of 100 Oe, in these minor loops, while in the major loops the NiFe vortex state was not evident. Increasing the field amplitude further causes a second abrupt transition, returning the NiFe to an onion state 共of opposite sense compared to the starting onion state兲 to recreate a different S2 configuration that is labeled S2R. An interesting feature of the minor loops is the existence of slightly different remanent resistances for the S2R state compared to the S2 state. For example, in the ring of Fig. 6共b兲, bringing the ring to remanence from the S2 state formed at −230 Oe gives a GMR of 0.6% 共solid points兲. However, if the field is then increased to +230 Oe, the ring forms the SPaV state and then the S2R state. Returning the S2R state to remanence gives a GMR of 0.7%. The difference in resistance is attributed to the presence of domain wall configurations 共such as 360° walls兲 generated on cycling the soft NiFe ring, while the hard Co ring remains in a vortex configuration. Figure 6共c兲 shows the same behavior but starting from opposite saturation. In addition to these two remanent states, if the ring is cycled into the SApV state or the SPaV state and then returned to remanence, its resistance remains at the S1 or Ssat level, respectively. Hence, the PSV ring displays a total of four distinct remanence resistance levels when the soft layer is cycled with the hard layer in a vortex configuration. This is seen in other geometries, for example, the circular ring in Fig. 6共d兲 displays four remanence levels with GMR ratios of 0%, 0.68%, 0.94%, and 1.6%, respectively. The selection of chirality of the double-vortex state, i.e., the formation of either SApV or SPaV on each branch of the minor loop, is highly reproducible for multiple cycles 共⬃100兲 of a given ring. For example, the ring shown in Figs. 6共b兲 and 6共c兲 showed S2 − ⬎ SPaV and S2R − ⬎ SApV transitions consistently in the minor loop. However, initial saturation of the ring at different fields, prior to the minor loop measurement, can lead to different 共but consistent兲 minor loop behavior, such as the formation of SApV on both branches of the minor loop. The choice of chirality is determined by the initial movement direction of the walls in the NiFe layer, which is presumably dependent on details of the magnetic configuration prior to reversal. Unlike the asymmetric minor loops found when the Co layer is in an onion state 共Fig. 4兲, the switching fields in the

FIG. 7. 共a兲 Modeled minor loop for a 2-␮m-long, 120-nm-wide NiFe4 / Cu4 / Co8 elliptical ring. From positive saturation the field is reduced, and the ring transitions from the parallel onion state 共Ssat兲 to state S1 and then to state S2 at −200 Oe. Increasing the field again drives the ring into an antiparallel vortex state, SApV, then into state S2R. 共b兲 Snapshots corresponding to the micromagnetic configurations present in the antiparallel double-vortex configuration 共SApV兲, as well as the S2 and S2R levels.

minor loops measured with the Co ring in a vortex configuration 共Fig. 6兲 are considerably more symmetric with respect to zero applied field, even for the smallest and narrowest PSV rings investigated. From the results shown in Figs. 6共b兲–6共d兲 the highest offsets with respect to zero field for the four transitions experienced by the soft rings are ⬃10 Oe and ⬃2 Oe for elliptical and circular rings, respectively, which are up to an order of magnitude below those measured

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in the same devices when the Co rings were magnetized in onion configurations, indicative of weaker magnetostatic, interactions in the minor loops of the Co vortex state. Computed minor loops starting with the hard ring in a vortex configuration 共Fig. 7兲 are again in excellent agreement with measurements following the same cycling procedure 关Fig. 6共a兲兴. On reducing the field from the S2 plateau, the NiFe switches via reverse domains that sweep through the NiFe to create a vortex state. The simulation shows the presence of 360° walls in both the NiFe and the Co layer in this particular ring geometry. In the antiparallel vortex state shown in Fig. 7共b兲, the 360° walls in the Co and NiFe layers are arranged above each other and of opposite sense, forming a coupled structure with small stray field. These results support a model for reversal of the soft ring that is dominated by domain wall movement. IV. SUMMARY

The low-field magnetoresistance behavior of Co/ Cu/ NiFe multilayer rings has been explored in detail. The reversal behavior of the soft layer shows major qualitative differences depending on whether the hard layer is configured in a vortex or an onion state, and also differs profoundly from that of single-layer rings. The differences are a result of magnetostatic interactions between the magnetic layers resulting from the stray fields of the domain walls present in the rings. These include both 180° walls, and metastable 360° walls that are formed by the interaction of two 180° walls. Exchange interactions are negligible in these multilayer stacks, and the excellent agreement between micromagnetic modeling and the observed magnetoresistance behavior supports the expectation that magnetostatic interactions dominate the behavior of the rings. It must be emphasized that the reversal process of the soft layers described here is highly reproducible and consistent throughout all the devices fabricated. Reversing the soft layers over hundreds of field cycles yields switching field distributions with maxi-

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mum widths of ⬃2 Oe. Magnetic-history-induced asymmetries in reversal, resulting from using different measurement geometry or cycling the hard layer from an unsaturated state, have been recently reported in similar devices.28 Nevertheless, such asymmetries do not occur if the voltage leads are located away from the regions where the NiFe layer starts reversing24,25 and the devices are saturated at high field prior to cycling. The soft layer in these ring devices can reverse at low magnetic fields, making them appealing for device architectures in which the elements are written or configured using the fields generated by currents passing through conductive wires arranged in proximity to the patterned magnetic elements.2 Alternatively, a spin-polarized current may be used to accomplish the reversal of PSV structures directly40 at current densities of the order of 106 A / cm2, and we have demonstrated this effect in some ring devices. The rings show a range of states accessible through minor loop cycling that is not found in the major loops. A number of stable or metastable states can exist at remanence. For example, when the hard layer is in a vortex state, four distinct resistance levels 共SApV, S2R, S2, SPaV兲 can be created by cycling the ring at modest field amplitudes. Since the remanent configurations are key to the operation of magnetoelectronic storage and logic devices, the existence of multiple remanent resistance levels can allow for two or more bitsper-cell in storage devices, as well as an increase in functionality of logic devices. This could provide an alternative path toward increased data densities, beyond that afforded by miniaturization of the devices. ACKNOWLEDGMENTS

The authors would like to thank H. I. Smith for the use of nanofabrication facilities, as well as W. Jung and I. A. Colin of MIT and T. J. Hayward of Cambridge University for fruitful discussions. This work was supported by the National Science Foundation, the Singapore-MIT Alliance, and the Marie Curie Foundation.

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