We present the fabrication of nano-magnet arrays, comprised of two sets of interleaving SmCo5 and Co nano-magnets, and the subsequent development and implementation of a protocol to program the array to create a one-dimensional rotating magnetic field. We designed the array based on the microstructural and magnetic properties of SmCo5 films annealed under different conditions, also presented here. Leveraging the extremely high contrast in coercivity between SmCo5 and Co, we applied a sequence of external magnetic fields to program the nano-magnet arrays into a configuration with alternating polarization, which based on simulations creates a rotating magnetic field in the vicinity of nano-magnets. Our proof-of-concept demonstration shows that complex, nanoscale magnetic fields can be synthesized through coercivity contrast of constituent magnetic materials and carefully designed sequences of programming magnetic fields.

Creation and control of nanoscale magnetic fields enable applications in diverse areas, such as nanoscale magnetic resonance imaging,1,2 nanoparticle manipulation,3,4 and engineering Majorana fermions for topological quantum computing.5–10 In particular, one approach to create Majorana fermions in a weakly spin-orbit-coupled material requires the presence of one-dimensional (1D) spatially rotating magnetic fields, which open up an artificial spin-orbit gap in the energy spectrum of a 1D system.5,6,10 The energy dispersion of such systems mimics a 1D system with strong spin-orbit coupling in the presence of an external magnetic field. When coupled to an s-wave superconductor, such systems can host Majorana modes at the ends of the 1D wire.11,12 One design proposed for creating 1D, spatially rotating magnetic fields is an array of nano-magnets with alternating polarization and with their magnetization axes perpendicular to the 1D system.5,6 With this design, it was shown through simulations that an artificial spin-orbit gap in Si is theoretically observable at temperatures accessible in dilution refrigerators.10 Here, we report the experimental realization of a dense array of nano-magnets with such alternating-polarization configuration. Specifically, we fabricated arrays of interleaving SmCo5 and Co nano-magnets. These two magnetic materials have distinct coercivities, allowing us to program individual sets of nano-magnets using designed sequences of external magnetic fields. The configuration of alternating polarization is achieved by first applying an external magnetic field higher than both coercivities and then reversing the magnetic field to flip the set of nano-magnets with the smaller coercivity. We chose to use SmCo5 and Co for our nano-magnet arrays because of their distinct coercivities (potentially > 10 kOe for SmCo5 vs < 1 kOe for Co), strong magnetization, and excellent thermal stability.13–15 

A high contrast in coercivity between two magnetic materials is a requisite toward programming the nano-magnets using external fields. As we will show below, room-temperature-deposited SmCo5 films are amorphous, and the coercivity is comparable to that of Co films. We thus first performed a series of annealing tests to identify an annealing temperature that would maximize the coercivity of SmCo5 films. A tri-layer stack of 150 nm Cr/400 nm SmCo5/30 nm Cr was deposited on a SiO2/Si wafer in a dc magnetron sputtering system using Cr and stoichiometric SmCo5 targets. Both Cr layers were used to prevent oxidation. After deposition, the Si wafer was diced into 1-cm2 pieces for the subsequent annealing steps. Each die was annealed for 30 min at a different temperature, ranging from 250 °C to 750 °C with the chamber pressure maintained at ∼10−7 Torr during annealing.

Using Rutherford backscattering spectrometry, the stoichiometry of the SmCo film was determined to be 16±1 atomic percent (at. %) Co and 83.9±0.5 at. % Sm, consistent with the composition of the sputter target. The amount of oxygen in the film was determined to be less than 1 at. %. Figure 1 shows the x-ray diffraction (XRD) spectra for the unannealed and annealed Cr/SmCo5/Cr films. The unannealed film produces only a weak Cr peak at 2θ ∼44.5°.16 The absence of diffraction peaks from SmCo5 indicates that the SmCo layer in the unannealed film is amorphous. Annealing at a temperature Tanneal > 500 °C produces a measurable SmCo5 crystalline phase that matches with the hexagonal closed packed (HCP) crystal structure with space group P6/mmm.16,17 For Tanneal > 675 °C, we observe oxidation of Sm, as indicated by a Sm2O3 peak.18 To examine the microstructures and crystallinity, transmission electron microscopy (TEM) studies were carried out on the films annealed at 250 °C and 650 °C. The cross-sectional TEM images, displayed in Fig. 2, show that the film annealed at 250 °C contains an amorphous SmCo5 layer, whereas the film annealed at 650 °C contains embedded nanocrystals, as shown in Fig. 2(a) and 2(d), respectively. This observation is further supported by the selected area electron diffraction (SAED) patterns of SmCo5 layers shown in Fig. 2(b) and 2(e). The halo features in Fig. 2(b) represent an amorphous structure and the diffraction rings in Fig. 2(e) indicate a polycrystalline structure. The indexing of the diffraction rings in Fig. 2(e) further verifies the HCP crystal structure of a SmCo5 layer. The Cr layer exhibited polycrystalline SAED patterns for Tanneal ∼ 250 °C, as shown in Fig. 2(c), and the grain sizes become comparable to the electron beam and the thickness of the TEM specimen for Tanneal ∼ 650 °C as shown in Fig. 2(f).

To determine the annealing temperature that would maximize the coercivity, we performed magnetization studies on the unannealed and annealed SmCo5 films. Using a Superconducting QUantum Interference Device (SQUID) magnetometer, we collected magnetic hysteresis loops at measurement temperature Tm = 5 K in applied magnetic fields up to 70 kOe, oriented parallel to the surface of the film (in-plane). Hysteresis loops of the unannealed and annealed films are plotted in Fig. 3(a), and the dependence of the coercivity HC, defined as the field at which the magnetization crosses zero, on Tanneal is shown in Fig. 3(b). The hysteresis loops are similar for the unannealed and annealed films for Tanneal < 500 °C and the small coercivities of these films can be attributed to their amorphous nature. Previous studies of amorphous SmCo5 films demonstrated relatively small coercivity compared to epitaxially grown films.19–21 Annealing at temperatures between 500 °C and 675 °C sharply increases the in-plane coercivity from 0.5 kOe to 15.5 kOe. Moreover, the onset of the rise in coercivity occurs at Tanneal ∼ 500 °C, coinciding with the temperature at which we observe a transition from an amorphous to a crystalline phase in our XRD data. The crystallized SmCo5 displays stronger ferromagnetic properties compared to the amorphous film21,22 We therefore attribute the enhancement in the coercivity to crystallization of SmCo5 when Tanneal > 500 °C. The coercivity decreases sharply for Tanneal > 675 °C, which is likely due to the onset of oxidation of Sm as discussed above. The optimal annealing temperature to enhance the in-plane coercivity of SmCo5 film is thus in the range of 600 °C to 700 °C. In this temperature range, we can achieve HC > 5 kOe. A separate SQUID magnetometry measurement on Co films yielded a coercivity of ∼200 Oe, resulting in high contrast in coercivity, HC,SmCo/HC,Co > 25.

After determining the optimal annealing condition to maximize the magnetic coercivity of the SmCo5 film, we developed a fabrication procedure for the nano-magnet arrays. More specifically, Cr/SmCo5/Cr was sputter-deposited onto SiO2/Si substrates with electron-beam-lithography-defined resist patterns, followed by lift-off and annealing at 600 °C for 30 minutes. This defined the first set of nano-magnets. Next, a second round of electron beam lithography, deposition of Co, and lift-off were carried out to form the desired interleaving SmCo5 and Co nano-magnets. Figure 4(a) shows an AFM image of an array of alternating Co and SmCo5 nano-magnets. In the final array, each SmCo5 or Co nano-magnet is 5 μm long and 150 nm wide, and the gap between adjacent SmCo5 and Co nano-magnets is 250 nm.

Programming of the nano-magnets was studied by applying a sequence of external magnetic fields along the long axis of the nano-magnets and imaging the nano-magnet array using magnetic force microscopy (MFM). The same nano-magnet array was used in all of the programming and imaging experiments. The sequence of the external magnetic field included (1) ramping the external magnetic field from zero to 50 kOe, which is higher than HC,SmCo and HC,Co, (2) reversing the magnetic field direction (thus passing the zero magnetic field point) and ramping to the reverse programming field -Hrev, and (3) ramping the magnetic field back to zero. The nano-magnets were then imaged with MFM. Figure 4(b) is an MFM image of the array before applying any programming magnetic field. The image shows bright or dark contrast on the ends of each nano-magnet, in addition to some isolated high-contrast spots inside the nano-magnets. These high-contrast areas represent the north (N) and south (S) poles of magnets. Most nano-magnets are single-domain, having exactly one bright and one dark spots at the two end points, while those nano-magnets with high-contrast spots inside are multiple-domain. We observe mostly alternating magnetization alignment even before applying an external programming magnetic field, which is likely due to the lower magnetostatic energy of this configuration.23 

Figure 4(c) shows single-domain nano-magnets and parallel alignment of magnetization after applying a programming field of 50 kOe. All of the nano-magnets are polarized along the same direction, as expected. Figure 4(d) shows the MFM image of the nano-magnet array after the application of a reverse programming field at Hrev = 1 kOe. Only a few Co nano-magnets have flipped polarization, suggesting that Hrev = 1 kOe is not sufficiently high to reverse the polarization of Co nano-magnets. This result indicates that HC,Co is strongly enhanced in our nano-magnet array compared to Co films. The strong enhancement could be due to the geometry, defects, and interactions between the nano-magnets. When the reverse magnetic field is increased to Hrev = 2 kOe, the polarization of all Co nano-magnets is now in the reverse direction, while the SmCo5 nano-magnets retain their original polarization direction, as shown in Fig. 4(e). Hrev = 2 kOe is thus the optimal reverse programming field for producing alternating polarization in the nano-magnets array and therefore a rotating magnetic field in the vicinity of nano-magnets. Figures 4(f) and 4(g) present the MFM images for Hrev = 3 kOe and 4 kOe, respectively. Surprisingly, at Hrev = 3 kOe, a significant portion of SmCo5 nano-magnets already flip their polarization, and at Hrev = 4 kOe, all of the nano-magnets reverse their polarization direction. This lower-than expected HC,SmCo is again likely due to the geometry, defects, and interactions between nano-magnets.

We use COMSOL Multiphysics, a commercial finite-element code, to model the nanoscale magnetic field due to the alternating magnetization of the nano-magnet array discussed above. Details of the simulation and numerical methods can be found in Ref. 10. Here we assume that the remanence of Co and SmCo5 nano-magnets is 1.76 and 1.07 T/μ0, respectively.15 In Fig. 5, we present the magnetic field along a hypothetical nanowire, placed 35 nm below and 37.5 nm away from the magnet tips horizontally. The inset of Fig. 5 represents nanomagnet arrays with alternating magnetization direction near a hypothetical axis where the 1D quantum wire is assumed to be located. The simulation result shows spatial rotation of the magnetic field along the 1D channel.

In conclusion, we first studied the microstructural and magnetic properties of annealed SmCo5 films. We found that sputtered amorphous SmCo5 films crystallize when annealed at Tanneal > 500 °C, resulting in enhanced coercivity. The optimal annealing temperature is in the range of 600 °C to 700 °C for achieving HC,SmCo > 5 kOe. We fabricated an array of interleaving SmCo5 and Co nano-magnets. Leveraging the high contrast in coercivity between annealed SmCo5 and unannealed Co, we programmed the nano-magnet array into a configuration with alternating polarization using a designed sequence of external magnetic fields. We showed from simulation result that the rotating magnetic field can be achieved by programming alternating polarization of nanomagnets. This demonstration represents an important step toward quantum materials engineering using nanoscale magnetic fields and opens the door to applications such as nanoscale magnetic resonance imaging and nanoparticle manipulation. Furthermore, the concept of leveraging the contrast in coercivity of the constituent materials for synthesizing nanoscale magnetic fields can be easily applied to other geometries and field patterns.

This work was funded by the Laboratory Directed Research and Development Program at Sandia National Laboratories (SNL). SNL is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. DOE, Office of Basic Energy Sciences, user facility. The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Work at Los Alamos National Laboratory (SQUID magnetometry and contributions to manuscript preparation) was funded by the US DOE, Office of Science, Basic Energy Sciences, Division of Materials Sciences and Engineering.

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