MR plotted as the percent of change of the resistance vs the magnetic field for the left and right tunnel junctions. The saturation resistance of the left and right junctions was 127 and 130 k ⍀ , respectively. 

Contexts in source publication

Context 1

... degradation of the barrier properties due to height gradients. We have fabricated multijunction arrays consisting of small elliptical, thin-film Co electrodes with film thickness of 50 Å ͑ bottom electrode ͒ or 100 Å ͑ top electrode ͒ . A scanning electron microscopy ͑ SEM ͒ micrograph of a three-junction array is shown in Fig. 1. An elliptical form of the electrodes was used to avoid the formation of magnetic domains in the electrode. The shape anisotropy of the ellipse favors magnetization parallel to the long axis of the ellipse. Figure 1 also shows a schematic of how the sample was measured. Two magnetic electrodes that form the electrical contact on each side of the structure are formed by shadow evaporation. These two contacts were held at the same potential, so that the measured resistance resulted from the three central tunnel junctions formed at the overlap of the elliptical electrodes. The film and lead resistance was checked and was typically ϳ 1 k ⍀ whereas the junctions were ϳ 100 k ⍀ , so that the tunnel resistance could be measured in a two-point configu- ration. The current–voltage characteristics at room temperature were linear, and the resistance was measured as a function of the external magnetic field. This magnetoresistance ͑ MR ͒ is given as a percent of change in resistance, relative to the resistance in the all-parallel alignment ͑ large magnetic field ͒ . For the sample geometry shown in Fig. 1 we often found that the MR exhibited complex switching behavior, which was not always reproducible. Figure 2 shows two measurements of the MR of the same sample at room temperature. In Fig. 2 ͑ a ͒ we offer an interpretation of the measured MR, where the groups of arrows denote the relative magnetic orientation of the four magnetic electrodes through which the tunnel current flows. Starting at large magnetic field, we have saturation, or parallel alignment, of all electrodes. As we sweep the field through zero towards saturation in the opposite direction, the MR remains constant until we cross zero field. As we continue to increase the magnetic field, we switch the electrodes’ magnetic orientation and observe a discrete change of the MR. With four electrodes we expect four distinct values of the MR if each electrode has only two orientations of its magnetization. Indeed, in Fig. 2 ͑ a ͒ we observed four levels of MR, roughly equally spaced, indicating uniformity of the tunnel junctions. Furthermore, the MR measurement is symmetric with respect to the direction of the field sweep, as expected. However, on some sweeps, this sample geometry showed more than four distinct MR values, as exhibited in Fig. 2 ͑ b ͒ , where five distinct levels of MR can be observed. In other samples we observed transient levels, which did not appear on every sweep. We interpret these intermediate levels to be a result of a complex magnetic state of the array, with domains forming at the tunnel junction surfaces. Another sample geometry we have studied is the double- tunnel junction shown in Fig. 3. In this geometry, two small capacitance junctions are formed close to one another by overlap of a narrow rectangular electrode with a wider electrode having rounded edges. Contact was made to each electrode so that the junctions could be measured individually. Figure 4 shows MR measurements of the left and right tunnel junctions taken at room temperature. The electrodes in this sample are the same as in Fig. 3, with width of 90 nm ͑ left junction ͒ and 70 nm ͑ right junction ͒ . Interpretation of these MR measurements is reasonably straightforward. Starting at large field, where all electrodes are saturated and in parallel magnetic alignment, we sweep through zero field. The MR of the right junction is essentially constant until 50 Oe, where an abrupt increase in MR occurs. On the other hand, the MR of the left junction undergoes a gradual increase until the abrupt increase at Ϯ 50 Oe. Because both the left junction and the right junction show an abrupt increase of MR at Ϯ 50 Oe, we can identify this feature in the MR as the wider, center electrode switching its direction of magnetization. As we continue to increase the magnitude of the field towards saturation in the opposite direction, we find a sudden drop of the MR of the left junction at Ϯ 250 Oe, indicating switching of the left electrode to alignment parallel with the center electrode. The same type of magnetic switching event occurs in the right junction at Ϯ 330 Oe. We note that the coercive field of the electrodes is inversely re- lated to the electrode width, as expected. Figure 5 shows the MR measurement of another double- tunnel junction structure where each of the junctions had slightly wider electrodes. In this sample the left junction had a width of 120 nm and the right junction had a width of 100 nm. The MR of the right junction ͑ dashed line in Fig. 5 ͒ shows behavior very similar to that of the 90 nm wide junction in the previous sample ͑ solid line in Fig. 4 ͒ . Starting from large field where all the electrodes are saturated and moving towards zero field, we see a gradual change of the MR of the right junction until the abrupt change at Ϯ 100 Oe where the center electrode switched. The right electrode and center electrodes are then antiparallel, and the MR does not change until Ϯ 300 Oe, where the right electrode switches. The left tunnel junction with width of 120 nm has much more complex switching behavior as seen by the solid line in Fig. 5. Starting from large field with parallel alignment and moving towards zero field, we find the MR indicates switching to nonparallel alignment before crossing zero field. Some rotation of the magnetization continues as we cross zero field, with complex switching to an intermediate alignment occurring at Ϯ 80 Oe, where the center electrode switches its direction of magnetization. This intermediate state persists until Ϯ 200 Oe, where the left electrodes switches to alignment parallel with the center electrode. The complex MR of the 120 nm wide junction indicates complex magnetic switching. A likely interpretation of the MR data is that the 120 nm wide electrode with rectangular shape forms domains at the corners of the electrode. Because these domains exist in the tunnel junction area, they affect the MR. The room temperature data presented here demonstrate how sensitive the magnetic switching of electrodes is to the geometry of the tunnel junction sample. We can see how the elliptical shape of the center electrode helps to suppress the formation of domains when the electrode is wide. We also observe how the electrode width plays an important role in the switching characteristics. The 70 nm wide junction exhibit relatively clean, single-domain-like switching of the magnetization. The 90 and 100 nm wide junctions both showed a gradual change of the MR, indicating rotation of the direction of magnetization. The 120 nm wide junction exhibited complex switching behavior, with an intermediate state at zero applied field, which could be explained by magnetic domain formation at the junction surface. The length scale of ϳ 70 nm, below which single-domain switching occurs, is consistent with estimates based on the theory of domain formation in small magnetic particles with uniaxial anisotropy. 10 Small magnetic particles are known to approach the single-domain state, in which all spins are aligned, as their size is reduced so that it becomes comparable to the intrinsic exchange length. The exchange length l ex 2 ε A / K m is defined from the ratio of the exchange stiffness constant, A , to the magnetostatic energy density of the mate- rial K m ϭ ␮ 0 M s 2 /2. For Co we have A ϳ 10 Ϫ 11 J/m and saturation magnetization M s ϳ 1.4 ϫ 10 5 A/nm, which gives l ex ϳ 3 nm. In the three-dimensional ͑ 3D ͒ case of a small cubic particle of size L , the single-domain limit is reached when L Ӎ 7 l ex , 10 or about 20 nm for Co particles. Our experimental geometry involves thin-film electrodes with thickness t ϳ 10 nm, much smaller than the transverse dimensions of the electrodes. The exchange length in the plane is thus en- hanced due to the strong demagnetization in the perpendicu- lar direction, l ex,2 D ϭ 4 ␲ A / K m t Ӎ 10 nm. Using the same cri- teria found for 3D particles, we expect that when the sample dimensions exceeds 7 l ex,2 D Ӎ 70 nm, domain formation is possible. This is consistent with our experimental MR data which showed that electrodes wider than 70 nm exhibited magnetic switching, which we interpreted as resulting from rotation of the magnetization and the formation of domains in the corners of the electrodes at the tunneling surface. The above arguments can be nicely demonstrated with micromagnetic simulations. 11 The simulations rotate finite blocks of spin ͑ cell size 5 nm ͒ to minimize the total magnetic energy ͑ exchange energy and magnetostatic energy ͒ for a given geometry. The intrinsic crystalline anisotropy was ne- glected since it is much smaller for our thin Co films than it is for bulk hexagonal-close-packed ͑ hcp ͒ Co, and ϳ 10–20 times smaller than the shape anisotropy ͑ϳ 1 kOe ͒ . In Fig. 6 we show the results of simulations of the magnetization of Co films with thickness t ϭ 10 nm and length L ϭ 500 nm for two different widths, w ϭ 140 and 70 nm. The simulations show that when the width is greater than ϳ 100 nm a ‘‘vortex state’’ domain structure Fig. 6 a can develop, depending on the magnetic history of the sample. On the other hand, narrower electrodes form single-domain states having essentially uniform magnetization and slight twisting of the magnetization, forming slight ‘‘ C ’’ and ‘‘ S ’’-type edge perturba- tions ͓ Figs. 6 ͑ b ͒ and 6 ͑ c ͔͒ . We have fabricated and measured magnetoresistance curves of nanoscale Co/AlO x /Co tunnel junctions. The MR data reveal complex magnetic switching which depends on the sample geometry and on the width of the tunnel junction electrodes. We ...

Context 2

... of the type discussed here. Magneto-Coulomb effects 1 and Coulomb blockade in small capacitance spin tunnel junction structure has been studied experimentally 2 and in theory. 3 Spin injection into superconductors 4 and nor- mal metals 5 in the mesoscopic regime is also currently of interest. When interpreting an experiment, it is important to understand the nanomagnetic switching properties of the sample. Here we show how the electrode geometry of small tunnel junctions plays an important role in the magnetic switching characteristics. Considerable experimentation was carried out to find a method of fabrication based on the standard two-angle, shadow evaporation technique used in the field of single charge tunneling. 6 We found that the all-polymer shadow mask typically used for Al tunnel junction fabrication is not strong enough to withstand Co evaporation from an e-gun source. We have used pre-evaporation of Al to strengthen the polymer mask. We also found it necessary to make multiple evaporations of Al on Co, with oxidation after each evaporation in order that a good tunnel junction could be formed. 7 A typical barrier formation sequence consisted of four steps of deposing 5 Å of Al at 0.3 Å/s with a subsequent in situ oxidation in 0.2 Torr of O 2 for 15 min. We find, similar to that reported in Ref. 8, that this multistep natural oxidation results in improved magnetotransport properties due to a more uniform oxide barrier. The magnetoresistance we observe of ϳ 10% is comparable with 10%–20% found in the literature for Co/AlO /Co tunnel junctions, 9 even though our junction geometry is not a perfect parallel-interface multilayer and one might expect some degradation of the barrier properties due to height gradients. We have fabricated multijunction arrays consisting of small elliptical, thin-film Co electrodes with film thickness of 50 Å ͑ bottom electrode ͒ or 100 Å ͑ top electrode ͒ . A scanning electron microscopy ͑ SEM ͒ micrograph of a three-junction array is shown in Fig. 1. An elliptical form of the electrodes was used to avoid the formation of magnetic domains in the electrode. The shape anisotropy of the ellipse favors magnetization parallel to the long axis of the ellipse. Figure 1 also shows a schematic of how the sample was measured. Two magnetic electrodes that form the electrical contact on each side of the structure are formed by shadow evaporation. These two contacts were held at the same potential, so that the measured resistance resulted from the three central tunnel junctions formed at the overlap of the elliptical electrodes. The film and lead resistance was checked and was typically ϳ 1 k ⍀ whereas the junctions were ϳ 100 k ⍀ , so that the tunnel resistance could be measured in a two-point configu- ration. The current–voltage characteristics at room temperature were linear, and the resistance was measured as a function of the external magnetic field. This magnetoresistance ͑ MR ͒ is given as a percent of change in resistance, relative to the resistance in the all-parallel alignment ͑ large magnetic field ͒ . For the sample geometry shown in Fig. 1 we often found that the MR exhibited complex switching behavior, which was not always reproducible. Figure 2 shows two measurements of the MR of the same sample at room temperature. In Fig. 2 ͑ a ͒ we offer an interpretation of the measured MR, where the groups of arrows denote the relative magnetic orientation of the four magnetic electrodes through which the tunnel current flows. Starting at large magnetic field, we have saturation, or parallel alignment, of all electrodes. As we sweep the field through zero towards saturation in the opposite direction, the MR remains constant until we cross zero field. As we continue to increase the magnetic field, we switch the electrodes’ magnetic orientation and observe a discrete change of the MR. With four electrodes we expect four distinct values of the MR if each electrode has only two orientations of its magnetization. Indeed, in Fig. 2 ͑ a ͒ we observed four levels of MR, roughly equally spaced, indicating uniformity of the tunnel junctions. Furthermore, the MR measurement is symmetric with respect to the direction of the field sweep, as expected. However, on some sweeps, this sample geometry showed more than four distinct MR values, as exhibited in Fig. 2 ͑ b ͒ , where five distinct levels of MR can be observed. In other samples we observed transient levels, which did not appear on every sweep. We interpret these intermediate levels to be a result of a complex magnetic state of the array, with domains forming at the tunnel junction surfaces. Another sample geometry we have studied is the double- tunnel junction shown in Fig. 3. In this geometry, two small capacitance junctions are formed close to one another by overlap of a narrow rectangular electrode with a wider electrode having rounded edges. Contact was made to each electrode so that the junctions could be measured individually. Figure 4 shows MR measurements of the left and right tunnel junctions taken at room temperature. The electrodes in this sample are the same as in Fig. 3, with width of 90 nm ͑ left junction ͒ and 70 nm ͑ right junction ͒ . Interpretation of these MR measurements is reasonably straightforward. Starting at large field, where all electrodes are saturated and in parallel magnetic alignment, we sweep through zero field. The MR of the right junction is essentially constant until 50 Oe, where an abrupt increase in MR occurs. On the other hand, the MR of the left junction undergoes a gradual increase until the abrupt increase at Ϯ 50 Oe. Because both the left junction and the right junction show an abrupt increase of MR at Ϯ 50 Oe, we can identify this feature in the MR as the wider, center electrode switching its direction of magnetization. As we continue to increase the magnitude of the field towards saturation in the opposite direction, we find a sudden drop of the MR of the left junction at Ϯ 250 Oe, indicating switching of the left electrode to alignment parallel with the center electrode. The same type of magnetic switching event occurs in the right junction at Ϯ 330 Oe. We note that the coercive field of the electrodes is inversely re- lated to the electrode width, as expected. Figure 5 shows the MR measurement of another double- tunnel junction structure where each of the junctions had slightly wider electrodes. In this sample the left junction had a width of 120 nm and the right junction had a width of 100 nm. The MR of the right junction ͑ dashed line in Fig. 5 ͒ shows behavior very similar to that of the 90 nm wide junction in the previous sample ͑ solid line in Fig. 4 ͒ . Starting from large field where all the electrodes are saturated and moving towards zero field, we see a gradual change of the MR of the right junction until the abrupt change at Ϯ 100 Oe where the center electrode switched. The right electrode and center electrodes are then antiparallel, and the MR does not change until Ϯ 300 Oe, where the right electrode switches. The left tunnel junction with width of 120 nm has much more complex switching behavior as seen by the solid line in Fig. 5. Starting from large field with parallel alignment and moving towards zero field, we find the MR indicates switching to nonparallel alignment before crossing zero field. Some rotation of the magnetization continues as we cross zero field, with complex switching to an intermediate alignment occurring at Ϯ 80 Oe, where the center electrode switches its direction of magnetization. This intermediate state persists until Ϯ 200 Oe, where the left electrodes switches to alignment parallel with the center electrode. The complex MR of the 120 nm wide junction indicates complex magnetic switching. A likely interpretation of the MR data is that the 120 nm wide electrode with rectangular shape forms domains at the corners of the electrode. Because these domains exist in the tunnel junction area, they affect the MR. The room temperature data presented here demonstrate how sensitive the magnetic switching of electrodes is to the geometry of the tunnel junction sample. We can see how the elliptical shape of the center electrode helps to suppress the formation of domains when the electrode is wide. We also observe how the electrode width plays an important role in the switching characteristics. The 70 nm wide junction exhibit relatively clean, single-domain-like switching of the magnetization. The 90 and 100 nm wide junctions both showed a gradual change of the MR, indicating rotation of the direction of magnetization. The 120 nm wide junction exhibited complex switching behavior, with an intermediate state at zero applied field, which could be explained by magnetic domain formation at the junction surface. The length scale of ϳ 70 nm, below which single-domain switching occurs, is consistent with estimates based on the theory of domain formation in small magnetic particles with uniaxial anisotropy. 10 Small magnetic particles are known to approach the single-domain state, in which all spins are aligned, as their size is reduced so that it becomes comparable to the intrinsic exchange length. The exchange length l ex 2 ε A / K m is defined from the ratio of the exchange stiffness constant, A , to the magnetostatic energy density of the mate- rial K m ϭ ␮ 0 M s 2 /2. For Co we have A ϳ 10 Ϫ 11 J/m and saturation magnetization M s ϳ 1.4 ϫ 10 5 A/nm, which gives l ex ϳ 3 nm. In the three-dimensional ͑ 3D ͒ case of a small cubic particle of size L , the single-domain limit is reached when L Ӎ 7 l ex , 10 or about 20 nm for Co particles. Our experimental geometry involves thin-film electrodes with thickness t ϳ 10 nm, much smaller than the transverse dimensions of the electrodes. The exchange length in the plane is thus en- hanced due to the strong demagnetization in the perpendicu- lar direction, l ex,2 D ϭ 4 ␲ A / K m t Ӎ 10 nm. Using the same cri- teria found for 3D ...