Schematic view of the nucleation of a reversed domain, which is followed by a rapid domain expansion along the edge. Once the whole region parallel to the edge has reversed, the domain propagates perpendicular to this edge. 

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... less pronounced angular dependence as the island size increases. As a first step we compared reversal modes for different island sizes with the field applied perpendicular to the plane. Simulation results show that there is a critical size above which the reversal becomes governed by a nucleation of a reversed region of magnetization followed by a rapid domain wall motion. This nucleation field was found to be much larger that the field needed to move the domain wall. This suggests why the observed angle dependence of the switch- 4,5 ing field which follows a Stoner–Wohlfarth-like curve, and is explained below. Figure 1 compares the experimentally found angle dependence with micromagnetic simulations. The switching fields were normalized to the switching field at 0°. As a reference the theoretical Stoner–Wohlfarth prediction for the angle dependence of a single domain particle is also plotted ͑ bold solid curve ͒ . The thin solid curves show the experimental data for island sizes of 30, 50, and 100 nm. The dashed curves show the micromagnetic results for island sizes of 20 and 70 nm. A good qualitative agreement is found between experimentally measured values and the simulation with both showing a Stoner–Wohlfarth-like dependence. However, the normialized minimum is less than that obtained from the Stoner–Wohlfarth model. This effect is explained by the dispersion of easy axes directions. Without a dispersion of the easy axes, i.e., all grains have their easy axis perpendicular to the film plane, micromagnetic simulations show an angle dependence which is much closer to the Stoner–Wohlfarth curve. The second observation is a change of the curves with increasing size of the islands. Larger islands show a less strong dependence on the angle than smaller islands. Again this could be explained by varying the dispersion of the easy axes in the micromagnetic simulations, without dispersion this size effect disappears. It has to be pointed out, that micromagnetic simulations show a highly nonuniform reversal mode for island sizes above the domain wall width ␲ ͑ A / K int ͒ 1/2 of the material, which is ϳ 12 nm in our case, here A is the exchange constant and K int is the intrinsic ͑ magnetocrystalline ͒ anisotropy. Indeed the 70 nm islands switch by the nucleation of a reversed domain on some corner of the island, followed by a rapid expansion of this domain. However, the angle dependence still shows a Stoner–Wohlfarth behavior. The explana- tion of this is the low domain propagation field in this material, which is much smaller than the nucleation field needed to form the initial reversed nucleus. The switching field, and therefore also the angle dependence, is thus completely de- termined by the nucleation field of the initial, small reversed domain. This is also manifested in the perfectly squared hysteresis loops generated by the simulation. A simple estimate of the domain propagation field is shown below. In the following we estimate the field necessary to move a domain wall H w and compare this value with the field necessary to form a nucleation of reversed magnetization H N . For high anisotropy media such as those we are dealing with here, H N will be comparable to the intrinsic anisotropy field H k = 2 K int / J s but slightly reduced by the demagnetizing fac- tor of the patterned island. Two extreme cases are possible: ͑ 1 ͒ H w Ͼ H N : In this case the angular dependence will increase with increasing angle. ͑ 2 ͒ H w Ͻ H N : The nucleation is followed by rapid domain wall motion. The hysteresis loops are perfectly square, and we speak of a “switching field” H s , where H s = H N = H c . The angle dependence of the switching field will show the observed Stoner–Wohlfarth dependence for the nucleation of the reversed domain. For patterned media, both simulations and experiments show that the fields necessary to move a domain wall are much smaller than the fields necessary to form a nucleation of reversed magnetization. The angle dependence in patterned media thus depends on the angle dependence from this small nucleus, which will show a Stoner–Wohlfarth-like curve. If we had case ͑ 1 ͒ , then the angular dependence would show a different functional form, where the coercive field would always increase as function of the angle of the applied field. To estimate the domain propagation field we write the Gibbs free energy for the case where the reversed domain is already present E total Ϸ E domain wall + E zeeman = − H ext J s ͑ V 1 − V 2 ͒ + 4 F ͱ AK , where F is the total area of the domain wall, V 1 the total volume of the reversed domain, and V = V 1 + V 2 is the total volume of the island. In this estimate we neglected magnetostatic interactions. The field necessary to move the domain wall can then be obtained by the condition that ץ E total / ץ x Ͻ 0, where x is the direction of the motion of the domain wall. The value that one obtains will depend on the assumptions made about how the wall propagates. Figure 2 shows one possibility for the propagation of a domain wall, which is motivated by our simulation data for the 70 nm island. With this estimate we obtain H ϳ 300 kA/ m which is much lower than the intrinsic anisotropy field of 1200 kA/ m and also lower than the nucleation field in the simulation of about 600 kA/ m. Experimental values for the switching field are about 0.5 times lower that the simulated switching fields. This is reasonable, since our finite element model does not take into account structural defects at island surface. The angle dependence of the switching field of patterned islands shows the well-know Stoner–Wohlfarth form with a minimum at a field angle of 45° independent of the island size. Whereas a well-pronounced minimum for fields at 45° is expected for small island sizes that reverse by uniform rotation, the same behavior is found for large island sizes that clearly reverse by the nucleation and expansion of reversed domains. The Stoner–Wohlfarth-like behavior for samples that reverse by domain wall propagation can be explained by the angle dependence of the critical field that is required to nucleate a reversed domain. The theoretical results agree well with experimental data for Co/ Pd multilayer patterned ...