I. Magnet-Superconductor Hybrids
Introduction. The year 2011 completes a century of superconductivity (SC) discovery. It experiences now a renaissance associated with advances in nanotechnology. Among of the most promising of new materials are Ferromagnet-Superconductor Hybrids (FSH). This field, started about ten years ago (by me [1-3] among other researchers), has matured with dozen of research groups around the world and several topical conferences. The latest topic review  has almost 500 relevant references. The whole field can be roughly divided into two main parts by the types of systems under study: (i) those where the proximity effect plays no important role (even if present) and (ii) those where the proximity defines the physics of the system (see reviews [5,6]). My work was focused on the first situation. The recent experimental results in this research area were reviewed in [4,5,7]. The main element of magnetic nanostructure in such systems is a magnetic “dot”, which typically is pancake shaped with thickness about 40-50nm, diameter of several hundred nm and period of magnetic nanostructure in the micron range. The fringe magnetic field from such “magnetic pancakes” is typically in the mT range. The superconducting part is usually a 50–100 nm thin film. The London penetration depth is typically much larger than the film thickness, and the coherence length (well below TC) is several times smaller than the film thickness. Studies of such systems have revealed interesting phenomena: “magnetic field induced superconductivity” , “domain wall” superconductivity  and several others. Detailed reviews of the experimental findings can be found in [4,5,7]. The more traditional field of vortex pinning has also experienced a renaissance with introduction of magnet superconductor nanostructures to take advantage of the magnetic interaction between vortices and the nanomagnets. The latter can have a complicated magnetic moment configuration e.g. a magnetic vortex with a singularity of the normal component of the magnetization at the center of the dot . Different shape dots, different orientation of magnetic moment, different symmetry of the dot array – all have contributed to a wide range of pinning situations described in detail in the excellent review .
i. Development of the new class of materials: Magnetic Nanorods-Superconductor Hybrids, which have high critical current in a Tesla range external magnetic field. In a strong external field the critical current can be several orders of magnitude stronger than in the control superconducting film.
ii. Demonstration of validity of the above approach for YBCO films.
iii. Studies of vortex pinning due to only magnetic interaction of vortices with external magnetic nanostructures. Corresponding critical current can be enhanced by up to two orders of magnitude.
iv.First studies of the magnetic and transport properties of superconducting films on alumina templates filled with magnetic nanowires.
v. Development of methods to control independently the diameter of nanowires and the period of these nanowire arrays embedded into an alumina template.
These results were published in [11-20].
Fig. 1. Left: Magnetic Nanorods embedded in a superconducting film. Center: Schematic presentation of the magnetic nanostripes atop an insulating layer separating them from the superconducting film; Right: Schematic picture of superconducting film atop of an alumina template with magnetic nanowires.
Fig.2. Left: AFM picture of Ni nanocolumn array with 2 microns period, column diameter 70nm and height 350nm; Center: Magnetic Force Microscope (MFM) image of Co nanorods in a PMMA matrix; Right: Scanning Hall Probe Microscope (SHPM) scan of the alternating magnetic field distribution of the magnetic nanostructure. All pictures are unpublished data from our group at TAMU.
We have used two different routes to create nanometer scale Tesla range strong magnetic fields: (i) with nanolithography (Fig. 1, left, center) and (ii) with alumina templates (Fig. 1, right). These two methods have provided samples to study the phase diagram, flux pinning and magnetic properties in magnet superconductor hybrids. In the overwhelming majority of magnetic micro/nano structures studied previously the magnetization is in-plane ; consequently, the component of the magnetic field normal to the film is rather weak. Even when the magnetization is normal to the plane, as in CoPt films, the component of magnetization normal to the film is also weak, due to the small aspect ratio of the magnetic elements (see discussion in Sec. 3). In contrast to previous studies we have fabricated magnetic columnar nanostructures with high aspect ratio (5) magnetic (Ni, Co) columns which have a diameter small enough (70nm) to preserve the magnetization direction (parallel to the column) even at room temperature. Atomic Force Microscope (AFM) and Magnetic Force Microscope images of the same array of 350 nm high and about 70nm diameter Ni nanorods grown electrochemically in a PMMA template prepared by electron beam nanolithography are shown in Fig.2 left and center respectively. After fabrication the PMMA film was lifted, resulting in a remarkably stable array of Ni or Co nanorods. Magnetic Properties of such arrays were studied with Magnetic Force Microscope (MFM) and Scanning Hall Probe Microscope (SHPM) without lift-off of PMMA. Fig. 2 shows images of Co nanorods in the PMMA matrix. Center image has been obtained with MFM. Bright and dark colors correspond to different magnetic field directions normal to the film. Right image has been made with a Scanning Hall Probe Microscope (SHPM). The SHPM scan at 200nm above the surface shows an alternating magnetic field distribution with a two micron period. Bright and dark spots correspond to opposite magnetic field directions normal to the film.
Fig. 3. Left: SEM image of the superconducting Pb/Bi film (left part) with imbedded nickel nanorods (white dots). Right part of the image shows array of Ni nanorods without superconducting film. Bright cups atop of Ni nanorods at left side appear due to Pb/Bi deposition. Right: Resistivity vs magnetic field for control film (red squares) and hybrid system (blue circles) .
Fig. 4. Left: Resistivity near the transition temperature shows strong hysteresis and matching field effect. Right: Critical current as a function of field at T = 7.7K for a PbBi film (Tc = 7.9K ) for hybrid (red dots) and control (black dots) film (our unpublished data) .
Magnetic Nanorods: a SEM picture of a superconducting film with embedded Ni nanorods is shown in Fig. 3 left. The thickness of the quenched-condensed Pb82Bi18 film is 100nm. The Ni nanorods have a diameter of 70nm and height of about 350nm. The typical dependence of resistivity on magnetic field is shown in Fig. 3 right and Fig. 4 left. They all demonstrate very strong hysteresis. In the control sample (Fig. 3 right) superconductivity exists in the range of about 0.02T, in the hybrid sample the width of the superconducting range is more than 0.1T. The data close to TC in Fig. 4 left demonstrates a strong matching effect with deep minima in resistivity at field values which are interger multiples of the matching field H1 corresponding to one flux quantum per unit cell of the Ni nanorod lattice. Matching effect was first observed in [21,22]. Fig. 4 right shows typical critical current dependence on magnetic field for the control sample (black dots) and the hybrid one. The “butterfly” shape of the critical current curves is due to the strong hysteresis effect in hybrid samples. Similar behavior is presented in a systematic way in Fig.5. It shows that the main effect of the magnetic nanostructures is to dramatically increase the field range in which the system remains superconducting.
Fig. 5. Critical currents in control (top) and hybrid system (bottom) with embedded nanorods .
Fig. 5 compares critical currents for hybrid sample (array of Ni nanorods, 70nm diameter, 350 nm height) embedded in the PbBi film with control sample. Fig.5 shows that the main effect of the magnetic nanostructures is to dramatically increase the field range in which the system remains superconducting.
Fig. 6. Left: Phase diagram for control (open symbols) sample and for hybrid (closed symbols) PbBi film ; Right: Numerical simulation of the phase diagram.
Fig. 6 shows measured and calculated phase diagrams for hybrid sample. Two main effects of magnetic nanorods array are hysteresis and the shift of the maximum transition temperature by about 250Oe due to the internal field created by magnetic nanorods.
Parallel Magnetic and Superconducting Nanowires. We have fabricated two-dimensional periodic arrays of parallel magnetic and superconducting nanowires on a silicon substrate. Parallel magnetic (nickel) nanowires of cross-section 90 nm by 300 nm form a periodic array with Pb82Bi18 superconducting nanowires of cross-section 200 nm by 100 nm (see Fig. 7). These nanostructures were characterized with Scanning Electron Microscopy (SEM) and their room temperature magnetic properties were studied with Magnetic Force Microscopy (MFM). The phase diagram was determined by electrical transport measurements. Depending on the temperature, the second critical field was 2 to 3 times larger than that of a homogeneous Pb82Bi18 superconducting control film. The superconducting phase diagram and transport properties exhibit strong hysteresis in a magnetic field .
Fig. 7. Left: Magnetic force microscope (MFM) phase angle image (lift height 50 nm) taken at room temperature along the surface of a Ni nanowire array, Right: the phase angle profile along the white line in the image.
Fig. 8. Left: Schematic cross section of the nanostructure; Right: Superconducting phase diagrams for the control sample (squares) and hybrid sample (circles). Measuring current for the hybrid sample was parallel to the Ni stripes. Insert: Expanded phase diagram for temperatures near 7 K .
The second critical field at a given temperature, HC2(T) and the superconducting critical temperature at a given applied magnetic field, TC(H), were defined from the resistance data. The phase diagram near TC in Fig. 8 is similar to the one predicted by mean field theory . This is not surprising. However, in the region of high fields, close to one Tesla, the apparent second critical field HC2 determined by resistivity measurements is 2 times higher for the hybrid sample than that of the control film. This is surprising. Indeed, HC2 is a thermodynamic characteristic of a superconductor. The external field from the magnetic nanowires cannot change this thermodynamic value. Possible proximity effects can only decrease HC2. The explanation of this behavior relys on two important characteristics of our MSN system: large values of the magnetic field generated by the Ni nanowires and huge gradients of this magnetic field across each superconducting nanowire. The average value of the magnetic field from the Ni nanowires can be estimated from the shift to the highest TC(H) which occurs at about 0.15T. The minimum value of the field is apparently smaller than 0.15T. Though we did not measure the magnetic field on the top/bottom of the magnetic nanowire, from experiments in our lab it is reasonable to suggest that it is close to half of the internal field of a magnetized Ni crystal, i.e. about 0.3 T. Note that the direction of the magnetic field on the top/bottom of the magnetic nanowires is opposite to its direction inside the superconducting nanowires. When we apply an external field parallel to the magnetization of Ni nanowires, this field is opposite in direction to the field generated by the Ni nanowires in the superconducting nanowires. Due to the continuous variation of the field generated by the Ni nanowire, the total field in the superconducting nanowires will vary over a wide range of values, thus providing regions with total field smaller than HC2 of the control film in a range of fields of the order of several HC2. This inhomogeneous field distribution can explain the results shown in Fig. 8 right.
Fig. 9. Left: SEM image of YBCO film deposited on a STO substrate on which Co nanostructures in a triangular lattice (spacing ~500nm) were created; Right: Critical currents of hybrid and control samples versus magnetic fields applied perpendicular to the YBCO film plane at 50K and 55K (unpublished).
YBCO film with Co nanostructures. The above results for critical current and HC2 in hybrid systems show that magnetic nanorod arrays are very effective in pinning vortices. It would be extremely important to extend this approach to YBCO thin films. Indeed, micron thick YBCO films are used in the so-called “second generation” YBCO power cables, which operate under the condition of relatively small, self generated magnetic fields. The coherence length in YBCO is small and HC2 is high. Thus the density of magnetic rods can be much higher than in a PbBi film without deterioration in the superconducting properties. We have started to explore different routes to fabricate magnetic nanorods-YBCO hybrids. Fig. 8 left shows a SEM picture of one such hybrid, Fig. 8 right shows the critical currents for the control and hybrid films. Though the critical current for hybrid film is higher than for the control film, the YBCO film quality of both is poor with low TC = 65K. We plan further work to improve sample quality. This will provide a new test bed to check theoretical models of columnar magnetic /nonmagnetic defect pinning and vortex matter in a hybrid magnet /YBCO system. This study may also show new routes to increase critical currents in YBCO cables. This is unpublished result.
Magnetic Pinning. We have fabricated systems where vortices in the superconducting film can be pinned only due to the magnetic interaction with the underlying magnetic nanostructures, not due to interaction of the vortex core with defects embedded in the superconducting film. We have used a stripe geometry for
the magnetic nanostructure and measured the transport properties of a superconducting film under the influence of a Tesla range spatially alternating magnetic field created by magnetic nanostructures placed outside the superconducting film with an insulating barrier between them so that they interact only via the magnetic field. For micron scale systems we have placed a superconducting film atop the stripe magnetic nanostructure as in Figs. 10, 11. In a simple theoretical model for purely magnetic pinning the vortices have no barrier for motion along the stripes and have a significant barrier in the perpendicular direction. Thus, critical current perpendicular to the magnetic stripes should be much smaller than in the direction parallel to the stripes. Precisely this type of behavior has been observed for magnetic stripe structures with 10 micron period (Figs. 10,11). The magnetic field distribution from the stripe magnetic structure in Fig. 10 left has been measured with SHPM and is shown in Fig. 10 right. Critical current in the direction parallel to the stripes is orders of magnitude stronger than in the perpendicular direction as shown in Fig. 11 right . Anisotropy of critical current in directions parallel and perpendicular to the stripes was also observed in magnetic structure with a 275 micron period .
Fig. 10. Left: Scanning Electron Microscope image of the Co stripes embedded into photoresist (Su8) ; Center: Magnetic field image of these Co stripes measured with SHPM at 5 kOe applied field ; Right: Magnetic field profile across these Co stripes .
Fig. 11: Left: Sample geometry and magnetic field pattern for the system with 10mm period; Right: Critical current density JC(H). Insert: I-V curves at 4.2K and 5kOe for both current directions (perpendicular and parallel to the array). The difference in JC at zero applied field is due to the remnant magnetization of the Co stripes .
A simple estimate for the critical current density is given by JC m0-1dB/dx . dB/dx is estimated to be 5x102 T/m in an external field 0.15 T from the data in Fig. 2b in Ref. for the sample with period 275mm and 4x104 T/m in an external field 0.5T for the sample with period 10mm from Fig. 10 right, i.e. about 100 times larger than in . Though the external field was different, we expect that the field gradient does not depend strongly on the external field simply since the magnetization is saturated in these external fields. The critical current density at 4.2K as a function of magnetic field for the sample with period 10mm is given in Fig.11 right. In  the critical current density at 4.2K in a 0.3T field for the sample with period 275mm is about 105 A/cm2. From Fig. 11 right the critical current density at 0.3T for the sample with period 10mm is about 107 A/cm2 which is 100 times larger than that found in  for the sample with period 275mm. This is in surprisingly good agreement taking into account that prefactors in the formula for structures which differ in scale by a factor of 30 should be different. We do not claim that we have rigorously proved this simple formula for the critical current density, but this result does provide strong arguments for its validity. The absolute value of the critical current density can also be checked. Indeed substituting m0 and the field gradient we estimate JC0.3x107A/cm2 which is in order of magnitude agreement with the experimental result of about 107A/cm2. A similar estimate also works for the structure with a 275mm period.
Fig. 12. Left: SEM image of a superconducting Sn film with magnetic stripes atop it. Stripes have square 120nm X 120 nm cross-section and 500nm period. Center: Black curve - critical current parallel to the magnetic stripes, red – perpendicular. Right: Logarithm of the ratio of critical currents parallel and perpendicular to the magnetic stripes vs magnetic field (presented at 2010 March meeting).
We have also studied magnetic pinning for an array of Ni stripes with 120nm X 120nm cross-section and a 500nm period. In this case the magnetic nanostructure was deposited atop of a PbBi superconducting film as schematically shown in Fig. 1 center. The SEM image is shown in Fig. 12 left. This system also demonstrates strong anisotropy in critical current in the direction parallel and perpendicular to the stripes as shown in Fig. 12 center, right. The above discussed experimental examples prove the concept of “magnetic pinning”. We plan further studies of this phenomena with magnetic stripes of different cross-section, material and period.
Alumina Template with Co nanorods.We have demonstrated a new approach to independently tune the geometric parameters of the ordered nanowire arrays embedded in porous anodic aluminum oxide (AAO) membranes . The nanowire spacing is first selected by choosing the proper anodization voltage during the anodization process of the AAO membranes. The pore diameter of the membranes is enlarged by subsequent chemical etching, or reduced by isotropic sol-gel coating of TiO2 on the inner surfaces of the pores. Co nanowires are then deposited into the TiO2 nanotube array by the conventional electrochemical deposition. By this technique, the lattice parameter may be adjusted independently from the pore diameter, and thus the nanorod diameter.
Fig. 13. Schematic
diagram describing the fabrication of a nanowire-nanotube hybrid array. a)
The vacant AAO membrane with a honeycomb pore array. b) TiO2 was
coated into the pores as well as the membrane surfaces. c) An Au electrode
was deposited on one surface and Co was then electroplated into the TiO2
nanotubes. d) The surfaces of the structure shown in c) were polished to
monitor the process of the fabrication by SEM/TEM or for subsequent coating
with superconducting film.
Fig. 13. Schematic diagram describing the fabrication of a nanowire-nanotube hybrid array. a) The vacant AAO membrane with a honeycomb pore array. b) TiO2 was coated into the pores as well as the membrane surfaces. c) An Au electrode was deposited on one surface and Co was then electroplated into the TiO2 nanotubes. d) The surfaces of the structure shown in c) were polished to monitor the process of the fabrication by SEM/TEM or for subsequent coating with superconducting film.
Fig. 14 Left: Cross sectional TEM image of TiO2 nanotubes coated into a commercial AAO templates. Inset: Schematic diagram of the sample ion milling. Center: SEM image of the Co nanowire-TiO2 nanotube hybrid array in AAO membrane. Inset: EDS spectrum showing Al, Ti and Co peaks; Right: Cross-sectional TEM image of Co nanowire-TiO2 nanotube hybrids in AAO membrane. Inset: EDS mappings of Al, O, Ti and Co .
Fig.13 illustrates the fabrication steps in this approach to independent control of nanorod size and spacing. Fig. 14 displays TEM/SEM images to illustrate the uniformity of the TiO2 coating and successful filling of the TiO2 nanotubes with Co to create nanorod array. In developing and testing this technique we have used commercial AAO templates which are much more poorly ordered and less uniform than those we can fabricate. Although it will be much more time consuming to grow our AAO templates, that will be a necessary step, both to insure a higher degree of order and control of the pore spacing for the samples we will use to study superconductivity and vortex matter in staggered field.
Thus, Scanning electron microscopy (SEM) and transimission electron microscopy (TEM) measurements show a high nanowire filling factor in the pores and a clean interface between the Co nanowires and TiO2 nanotubes and confirm the power of this unique technique for fabrication of large ordered magnetic or non-magnetic nanorod arrays with independent control of the rod diameter and spacing. One of the figures from Ref.  has been used for the journal cover. This work has been featured in the media ( http://nanotechweb.org/cws/article/lab/38377 )
Superconducting Film on Alumina Template with Co nanorods. We have fabricated anodic aluminum oxide (AAO) templates with 50 nm pore diameter, which were then filled with electroplated Co nanowires to form an organized array of magnetic nanowires. The case of similar system without Co nanowires was studied in . The period of the honeycomb pore structure was 120 nm. Superconducting Pb/Bi(18%) films, of thickness 40 nm, were then thermally evaporated onto the AAO membrane filled with the Co nanowire array. The Co filled AAO membranes were held at liquid nitrogen temperature during the evaporation. This process produced a hybrid nanomagnet-superconductor system with a magnetic field having a strong spatial variation in the superconducting film. We have observed hysteretic superconducting properties and an enhanced critical current at high fields. However, the influence of the underlying Co nanostructure on the superconducting properties was much smaller than expected. We plan further studies to elucidate the situation. Fig. 16 left shows a SEM image of the alumina template filled with Co nanowires. This system demonstrates hysteresis (Fig. 16 center). The MFM image shows alternating direction of the Co nanowires magnetization normal to the membrane. Dark red and pink colors correspond to different (up/down) magnetization directions. Critical current dependence on the magnetic field for hybrid (filled points) and control films are shown in Fig. 16 right.
Fig. 16 Left: (a) SEM image of the Co nanowire array embedded in the AAO membrane; (b) The room temperature magnetization hysteresis curve of the Co nanowire array in an external magnetic field parallel to the nanowires. Right: MFM “phase” image of an alumina template with cobalt nanorods at room temperature. Pink and dark red colors correspond to opposite (up/down) magnetization directions .
Fig. 17 Left (a) Resistivity as a function of temperature for the Pb/Bi films deposited on the Co nanowire array (open circles) and on a glass slide (solid circles), respectively. (b) Hysteretic field-induced suppression of superconductivity in the Pb/Bi film on a Co nanowire array at T = 7.78 K (b), 7.4 K (c), and 7 K (d). : Right: Critical current for hybrid and control samples .
Ref.  has been featured in the Virtual Journal of Nanoscale Science and Technology and Ref.  in the Virtual Journal of Applied Superconductivity.
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