Measurements are reported on the magnetization reversal in submicron magnetic rings fabricated by high-resolution electron beam lithography and lift-off from cobalt thin films. For all dimensions investigated, with diameters of 300-800 nm and a thickness of 10-50 nm, the flux closure state is the stable magnetization configuration. However, with increasing diameter and decreasing film thickness a metastable near single domain state can be obtained during the reversal process in an in-plane

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... ed field. For the implementation of magnetic materials in high density data storage technologies, an optimization of the geometry and size of small magnetic elements is of importance. Generally, for a given material, the geometry determines which kind of magnetization configuration may be present, while the size and lateral extension control the balance between the demagnetization fields and exchange fields and thus the transformation of one magnetization configuration into another. Many investigations have been carried out so far on elements with simple geometries, such as squares [1], disks [2] [3] [4] , and rectangles with flat or pointed ends [5] [6] [7] . The application of such elements requires a reproducible switching mechanism from one cycle to the next and a narrow switching field distribution inside a large array of identical elements. In this respect, rectangular elements are less well suited due to the formation of end domains [7] and the sensitivity of the switching field on the exact sample shape. Furthermore, for circular disks the vortex formation and vortex displacement can lead to an irreproducible switching and thus a broadened switching field distribution [8] . In order to avoid such effects, recently a vertical magnetoresistive random access memory design was proposed based on a ring-shaped magnetic multilayer stack [8] . Such ring-shaped elements have the advantage that a flux closure (FC) structure can be stabilized without the formation of the central vortex, as in a circular disk [8] [9] [10] [11] , rendering the FC configuration the energetically more favorable state as compared to the single domain (SD) state. In this Letter, magneto-optic Kerr effect (MOKE) magnetometry and magnetic force microscopy (MFM) imaging combined with 2D and 3D numerical micromagnetic simulations are used to determine the stability range of the flux closure structure of polycrystalline Co rings as a function of film thickness and ring diameter. For all dimensions investigated, it is shown here that the FC state is the energetically lowest state. However, a metastable SD state can be realized at remanence after saturation in an in-plane applied field. The probability to trap this metastable SD state increases with decreasing film thickness and increasing outer diameter. A series of ring arrays were fabricated using electron beam lithography and lift-off techniques. First, a thin polymethylmethacrylate resist layer was spun onto thermally oxidized Si substrates. The resist layer was then patterned with a JEOL 5D2U vector scan generator at 50 keV beam energy. After development, a thin film of Co was first deposited by sputtering and subsequently removed from the unexposed parts of the samples in trichloroethylene. For each thickness of 10, 20, 30, 40, and 50 nm, the following rings of outer diameter (d o )͞inner diameter (d i ) were produced (in nm): 300͞100, 400͞100, 600͞200, 700͞300, and 800͞400. The rings of each type were arranged in an array of 160 mm 3 160 mm size, with a separation equal to d o . In order to simplify the electron beam lithography and also to make the flux closure configuration visible in the MFM images, all rings have an octagonal rather than a circular shape. In Figs. 1(a) and 1(b) two typical room temperature MOKE hysteresis loops are shown as a function of an in-plane applied field for rings of different thickness. There are several characteristic features in loop 1(a). Upon coming from positive saturation, the signal decreases abruptly at a positive critical field, reaches an almost constant plateau of width DH fc , and then decreases less abruptly into the reversed field direction. As confirmed by MFM imaging, the first abrupt switch corresponds to a transition from a single domain state into a flux closure state. The MFM contrast observed at field values corresponding to positions (i) and (ii) indicated in the loop of Fig. 1(a) is shown in Fig. 2(a) and 2(b) . The strong black and white contrast in Fig. 2(a) corresponds to a SD state, whereas the weaker alternating contrast shown in Fig. 2(b) corresponds to the FC state. The loop in Fig. 1(b) is qualitatively the same as in Fig. 1(a) , except that the transition from the SD into the FC 1102 0031-9007͞01͞86(6)͞1102(4)$15.00