Electrical observation of asymmetric magnetization configurations in the vortex state of NiFe and Co rings

Chunghee Nam M D Mascaro B G Ng and C A Ross

Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

¹ Author to whom any correspondence should be addressed.

E-mail: caross@mit.edu

Received 27 August 2009, in final form 1 October 2009
Published 28 October 2009

1. Introduction

Small magnetic ring structures have been proposed for applications in non-volatile memory, logic and biosensor devices, and their magnetic configurations have been studied extensively, including the stable onion and vortex states and metastable states containing 360° domain walls (DWs) [1–17]. The onion state contains two 180° DWs, whose locations are determined by the direction of an in-plane applied magnetic field [4, 5]. In contrast, the vortex state is a flux-closure state without DWs, and has zero stray field at remanence [7]. The vortex state can have a clockwise (CW) or counter-clockwise (CCW) chirality, which may be useful in encoding data in high density information storage devices. In a symmetrical circular ring, the onion-to-vortex transition yields a vortex state of either chirality depending on which DW depins first and which direction it traverses the ring. The vortex chirality can be selected by breaking the symmetry of the ring [4, 14] or by using a current to translate the DWs around the ring in a specific direction [13]. Detection of the vortex chirality has been accomplished using magneto-optical measurements and giant magnetoresistance measurements in a single layer and multilayer rings, respectively [4, 16, 5].

Several groups [4, 10] have used anisotropic magnetoresistance (AMR) measurements to detect onion–vortex (O–V) transitions, but there is less reported work on the resistance changes that occur within the magnetic field range in which the vortex state is stable [10]. A vortex state at remanence has a circumferential magnetization that is oriented uniformly around the ring. However, a dc applied field can distort the vortex state [9, 10], leading to differences in resistance between the sections of the ring that are parallel and antiparallel to the field [10], and at higher field, to nucleation of a reverse domain and the formation of a reverse onion state. Dynamic measurements also reveal quantized spin wave modes in the vortex state corresponding to periodic distortions of the magnetization [11, 12]. It is therefore important to understand the details of magnetization distortion in the vortex state as a function of applied field, not only to better understand the reversal processes of rings but also to contribute to practical applications of ring devices. In this paper, we have followed the evolution of the vortex state in a NiFe ring using four-point AMR measurements which were used to deduce the vortex chirality. Measurements on a Co ring also demonstrate vortex distortion preceding the vortex–onion transition, which is consistent with recent observations of non-uniform rotation during Co nanowire switching [18].

2. Experiments

A circular magnetic ring 3 µm in diameter and 200 nm in width comprising a Ta (2 nm)/NiFe or Co (15 nm)/Cu(3 nm) stack with four non-magnetic electrical contacts was fabricated using similar processing steps to those described elsewhere [2, 5]. The sensing current (I) was applied using two contacts placed at opposite ends of a diameter, and voltage drop was measured using two voltage leads V₁ and V₂ located along one side of the ring, as shown in figure 1(a). The magnetic field was applied in-plane with an angle of α between the current leads and the applied field direction. Figure 1(a) defines the NiFe ring in terms of four resistors R_A, R_B, R_C and R₁. The measured resistance (R_m) between voltage contacts i and j can be written as [5]

The ring can be considered to be made of two halves, one with resistance R₁ and the other with resistance R₂, between which the current divides. R_B represents the resistance of the section of ring between the voltage contacts i and j. Micromagnetic modelling of the NiFe ring was carried out using the 2D NIST OOMMF code [19], where the simulated ring was discretized into 4 nm × 4 nm × 15 nm cells with exchange constant A  =  1.3 × 10^–6 erg cm^–1, saturation moment M_s  =  860 emu cm^–3, anisotropy K₁  =  5 × 10³ erg cm^–3 and damping constant α  =  0.1.

3. Results and discussion

3.1.  Major magnetoresistance loops for a NiFe ring

Figure 1(b) shows three successive measurements of the AMR as a function of a descending applied field at α  =  3π/8 ( =  68°) after positive saturation. At this angle, the DWs in the onion state are located between the voltage probes. The ring resistance shows a transition from state A (onion state) to B (vortex) to C (reverse onion) at fields of –85 Oe and –320 Oe, respectively. The vortex state has a higher resistance because the magnetization is everywhere parallel to the current flow so the resistivity ρ  =  ρ_⊥  +  (ρ_∥ – ρ_⊥) cos² θ is maximized, where θ is the angle between the current and magnetization directions and ρ_∥ and ρ_⊥ represent the resistivities at θ  =  0° and 90°, respectively. The decrease in resistance of the onion states with field magnitude is a result of increasing θ as the magnetization becomes aligned along the field direction.

Figures 2(a) and (b) illustrate four individual measurements on the NiFe ring at α  =  90° in a descending field and an ascending field, respectively. At this field angle, one of the DWs in the onion state is under the voltage contact, V₂, and does not contribute to the magnetoresistance [15]. In figure 2(a), after positive saturation the resistance slowly increases as the applied field is removed because the magnetization relaxes to be parallel to the edges of the ring. This relaxation is shown in the simulation result for field I in figure 2(c). The resistance peaks at remanence, then decreases slightly as the negative field increases. At –80 Oe, the ring transitions into a vortex state and there is a small increase in resistance. The resistance change is much smaller than that seen in figure 1(b) because most of the volume of NiFe occupied by the DW in section R_B is covered by the Au contact, which shunts the current.

The second panel of figure 2(c) shows simulations of the ring just after the vortex has formed (field II). The simulations generated either CW or CCW vortex chirality, and we selected a simulation result which had the same chirality as our experimental results for easier comparison with the experimental data. As the reverse field increases, a distortion or buckling is seen on the side of the ring magnetized opposite to the field. The distorted-vortex state is most prominent for reverse fields above –200 Oe, and a simulation is shown at field III in the third panel of figure 2(c) corresponding to a distorted vortex. The distorted configuration in the vortex state has been previously described as a `stressed vortex' in a 5 µm diameter, 500 nm wide, 35 nm thick NiFe ring at low temperature by Buntinx et al [10], although in this work the 2-point measurement geometry precluded detection of vortex chirality. At –330 Oe, a reverse domain nucleates in the buckled region and the ring transforms to a reverse onion state (field IV) with a sharp increase in resistance. There were no significant differences between ten successive measurements in a descending field, indicating that the same vortex chirality (clockwise, CW) was formed on each cycle.

In the micromagnetic model, the onion–vortex transition occurred at –190 Oe, larger than the experimental value, and the vortex-reverse onion transition occurred at –310 Oe, similar to the experimental value. The simulated magnetization states I, II, III and IV in figure 2(c) correspond to 0 Oe, –200 Oe, –300 Oe and –700 Oe, respectively.

Figure 2(b) shows data for an ascending field. Most AMR measurements show an increase in the resistance at  + 80 Oe, corresponding to the reverse onion-to-vortex transition, as seen in the lower AMR curve, followed by a decrease at  + 330 Oe for the vortex-to-onion transition. This indicates that the distorted-vortex region of the ring was on the side of the ring without the voltage contacts, implying that the vortex chirality was CW, as in the descending field data. However, the eighth AMR measurement out of a series of sixteen shows the opposite AMR behaviour, meaning that the vortex chirality was CCW in that cycle. This result can be compared with an earlier measurement of vortex chirality of NiFe and Co rings with various sizes on repeated cycling using electrical measurements, a magneto-optical technique and magnetometer measurements [4, 14, 16, 17]. One ring reversed via the same vortex chirality for typically 20 cycles, and the probability of a change in vortex chirality on a given cycle was 0.12–0.17, which is attributed to thermal effects [16]. The rarity of a change in vortex chirality in multiple cycles is consistent with the electrical data in this work.

3.2.  Minor magnetoresistance loops for a NiFe ring

Figures 3(a) and (b) show minor loop resistance measurements at α  =  90° for the NiFe ring, starting from saturation at ±5 kOe. In this ring, which typically switched via a CW vortex state on each cycle, the asymmetrical field-response of the two halves of the ring leads to qualitatively different minor loops. In figure 3(a), which started from positive saturation, the ring formed a vortex at –80 Oe, which was already shown in figure 2(a). As the field decreased further, the resistance decreased due to the vortex distortion of region R_B of the CW vortex. The field sweep was reversed at –320 Oe, just before the ring could transition into a reverse onion state. The ascending branch of the minor loop shows an increasing resistance between points I, II and III as the vortex distortion relaxes, and almost overlaps the descending branch between –320 Oe and –80 Oe because the voltage probes are placed within the unswitched half of the ring. An onion state forms at  + 330 Oe, at which point the resistance drops.

Micromagnetic simulations of the minor loop in figure 3(a) are shown in figure 3(c). The left image (I) indicates the CW vortex formed at –300 Oe after positive saturation, in which the upper half of the ring shows vortex distortion. The field was then increased to 0 Oe, and a fully symmetric vortex configuration is seen in the centre image (II). The magnetic field is then swept to  + 300 Oe, the right image (III), at which the lower part of the ring shows vortex distortion.

In figure 3(b), which starts from negative saturation, the reverse onion state is maintained until the field reaches  + 80 Oe, at which the vortex forms and the resistance rises sharply, because the voltage probes are now placed within the switched half of the ring. Changing the direction of the field sweep, the vortex state is retained until –330 Oe, but its resistance decreases due to distortion. At –330 Oe the reverse onion state is formed with an increase in resistance. As in figures 3(a) and (b), these changes are consistent with a CW vortex chirality. Both minor loops therefore indicate that reversal in this ring proceeded via a CW vortex, and the qualitative differences between the minor loops are a result of the placement of the voltage contacts on one side of the ring.

3.3.  Angular dependent magnetoresistance loops for a NiFe ring

Figures 4(a) and (b) show the AMR versus applied field for a range of applied field angles for the NiFe ring. At the angles shown in figure 4(a), the DWs are outside region R_B. The decrease in resistance of the vortex state with an increase in reverse field is again indicative of the formation of a CW vortex for all field angles in figure 4(a). The resistance change depends systematically on α. For a CW vortex in a negative field, as α is increased, R₁ increases while R₂ decreases, but the sum R₁  +  R₂ is constant. Also, R_B is independent of α at every applied magnetic field. Equation (1) therefore predicts that the measured resistance change in the V–O transition will decrease with increasing α, as observed.

Next, we compare the magnitude of the AMR from vortex distortion to that from the DWs in the NiFe ring by measuring AMR at α  =  68° and 90°, figure 4(b). The 90° data are given for two different cycles showing a CW and a CCW vortex. In the CW data, vortex distortion leads to a change in resistance of 0.3% over the range of existence of the vortex, –80 to –330 Oe. (The change in resistance in the CCW vortex is negligible.) In contrast, the 68° data are governed by the AMR of the DW located between the voltage contacts. At the O–V transition, the elimination of the DW gives an increase in resistance of 0.2%, while its creation at the V–O transition gives a decrease in resistance of 0.32%. (These differ because the onion configuration and the wall structure change with field.) The results show that vortex distortion, which gives local changes in magnetization direction of up to about 50° away from the edge of the ring, according to modelling, can give AMR effects that are comparable to those of a transverse DW.

3.4.  Major magnetoresistance loops for the Co ring

Figure 5(a) shows a Co ring device in which three voltage probes V₁, V₂ and V₃ are present. The voltages V₁₂, V₂₃ and V₁₃ were measured in a descending field at an angle α  =  90°, after positive saturation (figure 5(b)). The O–V transition occurs at –390 Oe and the V–O transition at –700 Oe. V₁₂ shows an increase in the resistance at the O–V transition and a slowly varying resistance for the vortex state, while V₂₃ shows a decrease in the resistance in the vortex state. This indicates that the lower half of the ring is distorted by the field, showing that the vortex is CCW. The small resistance decrease observed from V₁₃ represents a superposition of these changes. The change in AMR is greater for the Co ring than for the NiFe ring because the magnetization of Co is larger than that of NiFe, inducing more pronounced vortex distortion due to magnetostatic effects [20, 21].

4. Summary

The evolution of the vortex state in NiFe and Co magnetic rings has been examined using four-point AMR major and minor loop measurements combined with micromagnetic modelling. Reversible and irreversible resistance changes measurements are observed and related to the different magnetic behaviour of the two halves of the vortex, which are oriented differently with respect to the applied field. The vortex chirality can be deduced from changes in resistance measured between voltage probes placed asymmetrically on the rings, and measurements at different field angles enable domain-wall AMR and vortex distortion effects on resistance to be separated. An understanding of vortex distortion gives insight into the vortex–onion transition in rings, which is also relevant to the non-uniform reversal in narrow magnetic wires [22] used in racetrack or domain-wall memory devices [22, 23].

Acknowledgments

The support of the Nanoelectronics Research Initiative INDEX program and the National Science Foundation is acknowledged.

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