Magnetic configurations in nanostructured Co2MnGa thin film elements

The magnetic configuration of nanostructured elements fabricated from thin films of the Heusler compound Co2MnGa was determined by high-resolution x-ray magnetic microscopy, and the magnetic properties of continuous Co2MnGa thin films were determined by magnetometry measurements. A four-fold magnetic anisotropy with an anisotropy constant of K 1 ≈ 1.5 ?> kJ m−3 was deduced, and x-ray microscopy measurements have shown that the nanostructured Co2MnGa elements exhibit reproducible magnetic states dominated by shape anisotropy, with a minor contribution from the magneto-crystalline anisotropy, showing that the spin structure can be tailored by judiciously choosing the geometry.


Introduction
Due to a number of interesting magnetic and electronic properties, such as high spin polarization, elevated Curie temperatures, shape memory effects, and high magneto-optical constants, Heusler compounds are a widely studied class of materials [1][2][3][4][5][6][7][8]. In particular, these materials are interesting for spintronic applications, where the combination of high spin polarization [3,4], high Curie temperatures [9], and large values of the magnetization allow for a great variety of applications, such as spin polarized materials for applications as magnetic layers in magneto-resistance junctions [1,10,11], and also more complex devices such as artificial multiferroic systems based on magneto-electric coupling [12].
In order to use these interesting properties for applications within the field of spintronics, it is necessary to characterize the behavior of these materials in application relevant geometries. In particular, as the current lithographical technologies allow for the fabrication of nanoscale devices, the detailed characterization of the magnetic configuration of these materials at the nanoscale is a fundamental step towards applications.
Co 2 MnGa (CMG) is a Co-based Heusler compound exhibiting a spin polarization of P 0.55 ≃ at room temperature [13], which can be epitaxially grown as thin films on different substrates such as GaAs [14] and MgO [13]. Due to the use of gallium in the Z site of the X 2 YZ Heusler compound, CMG exhibits a higher oxidation resistance than other Co-based Heusler compounds with atoms such as Al or Si more prone to oxidation at the Z site [15]. In the work presented in this article, we analyze the influence of geometric confinements at the nanoscale on the magnetic configuration of CMG nanostructures by x-ray magnetic microscopy. We find that the magnetization configuration of nanostructured CMG elements is mainly determined by the contribution of shape anisotropy, thus rendering this material particularly interesting for applications, as its magnetic configuration can be reproducibly and reliably controlled solely by shape anisotropy, and thus by engineering the geometry of the single elements. . The as-deposited films were annealed at a temperature of 550°C for 300 s, changing their crystalline order from the B2 to the L2 1 phase, as observed by in-situ reflection high-energy electron diffraction (RHEED) measurements [16] and ex-situ x-ray diffraction (XRD) scans (Bruker D8 Diffractometer) after the deposition. In order to prevent the oxidation of the CMG, a capping layer consisting of 3 nm of Al was sputter deposited on top of the CMG film. The capping layer was removed by Ar sputtering (available in-situ at the x-ray magnetic microscopy beamlines) prior to imaging by magnetic microscopy.

Experimental
Magnetic hysteresis loops of the continuous CMG films were acquired by superconducting quantum interference measurements (SQUID, from Quantum Design), and by longitudinal magneto-optical Kerr effect (MOKE) measurements performed at room temperature employing a red ( 635 λ = nm) low noise laser diode (Coherent).
Nanostructures of various sizes and geometries were fabricated from the CMG thin films by means of focused ion beam (FIB) lithography (FEI Helios NanoLab 600i), employing a 30 kV accelerated Ga + ion beam. As shown in figure 1(a), where a scanning electron micrograph of the CMG nanostructures fabricated by FIB lithography is shown, this technique allows for the fabrication of well-defined and magnetically decoupled structures, as shown in figure 1(b), where a magnetic image of the same nanostructures is shown. The fabrication of the nanostructures by FIB lithography did not induce any detectable damage in the capping layer on the nanostructures outside of the exposed regions.
The magnetic configuration of the nanostructured CMG has been imaged using photoemission electron microscopy (PEEM), exploiting the x-ray magnetic circular dichroism (XMCD) at the Co L 3 edge (about 780 eV) to obtain a magnetic contrast [16]. These measurements were carried out at the Nanospectroscopy beamline at Elettra [17] and at the CIRCE beamline at ALBA [18], both equipped with an Elmitec SPELEEM setup (type LEEM III). An in-situ electromagnet, integrated with the PEEM sample holder [19], was employed to apply a magnetic field to the nanostructures along the [110] direction of the CMG in order to manipulate their magnetic configuration. All the measurements have been carried out at room temperature and in the remnant state.

Results and discussion
As shown in figure 2(a), θ-2 θ XRD scans of the CMG films exhibit only (00l) reflections, and no secondary phases or orientations were observed. In figure 2(b), ϕ-scans carried out on the (111) reflections of the CMG demonstrate the presence of a clear four-fold symmetry with L2 1 order induced by high temperature annealing [16]. Furthermore, by comparing the respective peak positions of the CMG films and the MgO substrate as shown in figure 2(b), a 45 • in-plane rotation of the CMG unit cell with respect to that of the MgO substrate has been observed. The CMG films analyzed in this work exhibit a saturation magnetization M s of about 3.2 B μ per formula unit at 5 K (determined by SQUID magnetometry) [15]. The M s reduces by 6% at room temperature, indicating a Curie temperature well above 300 K. As shown in figure 3, from angle-resolved longitudinal MOKE measurements of the CMG films it was possible to identify a four-fold magnetic anisotropy, with the easy axes along the 110 〈 〉 crystallographic directions. To determine the magnitude of the four-fold anisotropy constant K 1 of the CMG thin films, we employed the Stoner-Wohlfarth formalism [20], describing the magnetization of the CMG as a single rotating macro-spin, and expressing the magnetic free energy density as follows [20]: with θ being the angle between the magnetization vector M of the material and the applied magnetic field vector H, and ϕ the angle between the easy axis of the four-fold anisotropy term and the applied magnetic field vector H. As can be observed in (1), the Stoner-Wohlfarth model does not include the magnetic free energy terms that describe the contribution of the formation of magnetic domains. However, for the reversible part of the hysteresis loops (i.e. when relaxing the external magnetic field from the saturation value H s to zero), in particular along directions close to the hard-axes, the Stoner-Wohlfarth model constitutes a reasonable approximation for the behavior of the thin film magnetization [7,21]. We calculated the minimum of the magnetic free energy density given in (1), obtaining a function H ( ) K 1 θ θ = | and fitted it to the reversible part of the hysteresis loops of the CMG measured by MOKE magnetometry, with K 1 as the fitting parameter. As shown in figure 4, where a fit for the reversible part of the CMG hysteresis loop for an angle 30 ϕ =°is shown, it is possible to obtain a reasonable fit for a value of the fourfold anisotropy constant of K 1500 150 1 = ± J m −3 , which is comparable to other Co-based Heusler compound thin films [1].
Also, in agreement with the behavior of other Co-based Heusler compound thin films [8,22], the coercive field of the CMG thin films exhibits a maximum along the 100 〈 〉 directions and rapidly decreases at neighboring angles, as shown in figure 3. This behavior was interpreted as being due either to the formation of a checkerboard domain pattern at the switching of the magnetization [8], or as being due to magnetic frustration effects during the reversal process [22]. It was not possible to verify the microscopic origin of this increase in the coercive field for the analyzed CMG thin films, as XMCD-PEEM imaging can be carried out only close to the magnetic remnant state.
After having determined the main properties of the continuous CMG films, we now turn our attention to the analysis of the influence of geometric confinement on the magnetic domain structure of the CMG. The magnetic configuration of the nanostructured CMG elements, determined by XMCD-PEEM imaging, is compared with micromagnetic simulations, carried out by numerical time integration of the Landau-Lifshitz-Gilbert equation with a finite-difference method. The calculations were performed with the help of the MicroMagnum framework [23], using a value of A 4 10 11 = × − J m −1 for the exchange stiffness, and the values of the saturation magnetization and magneto-crystalline anisotropy given above. These values lead to an exchange length of ca. 13 nm, and thus a numerical discretization with a cell of x y 5 5 × = × nm 2 was used. The value of the exchange length was estimated by carrying out a simulation of the same structure (in this particular case, of a nanostructured CMG square with 1 μm × 1 μm edges along the 110 〈 〉 crystalline directions of the CMG) with different values of the exchange stiffness, and comparing the simulated state with the experimentally determined magnetic configuration.
In figure 5(a), a series of images acquired at the remnant state (after the application of a magnetic field of ca. 50 mT along the [1 1 0] direction of the CMG) of nanostructured squares of different sizes and orientations is presented. In particular, the squares were oriented with their edges either along the 100 〈 〉 or the 110 〈 〉 directions of the CMG. As can be observed in figure 5(a), the preferred magnetic domain configuration is the flux-closure Landau state [24] for both orientations of the square edges for square edges of 2 μm and below. However, as can be observed in figure 5(a), for larger squares (i.e. an edge size of 4 μm and above) the contribution of the magneto-crystalline anisotropy term can be observed: if the edges of the square nanostructure are pointing along the 110 〈 〉 crystallographic directions of the CMG, it is possible to observe an undistorted Landau flux-closure state also for the larger squares. Instead, if the edges of the nanostructured square are pointing along the 100 〈 〉 directions, a deformed Landau flux-closure state can be observed. These results are in agreement, as shown in figure 5(b), with the micromagnetic simulations.
As shown in figure 6, where the micromagnetic simulations of the nanostructured squares with a 4 μm edge size are presented, the effect of the different orientation of the square edges with respect to the magneto-  Furthermore, circular nanostructured elements with different diameters were analyzed both with XMCD-PEEM imaging and by determining their magnetic configuration with the help of micromagnetic simulations. As shown in figures 7(a) and (b), both the XMCD-PEEM imaging and the micromagnetic simulations reveal that the favored magnetic state for the nanostructured elements is the vortex state. These results show that by fabricating circular nanostructures it is possible to reliably stabilize the vortex domain configuration independently (at least, for the analyzed dimensions, which are of relevance for spintronic applications) from the diameter of the nanostructured element.
Finally, to study the spin structure of magnetic domain walls in the CMG, which is of critical importance for numerous spintronic applications such as for example current induced domain wall motion, ring-shaped nanostructures were analyzed, as shown in figure 8. After the initialization with a magnetic field along the [1 1 0] direction, the rings were predominantly in the onion state [25], exhibiting both a head-to-head and a tail-to-tail domain wall, with predominantly vortex-type wall configurations [26]. In contrast, for wide rings with a high local curvature, such as the 1 μm wide ring with a diameter of 2 μm shown in figure 8, the flux closure state seems to be energetically favored. Micromagnetic simulations of the nanostructured rings were also carried out. However, in this case, the favored magnetic configuration is the magnetic onion state with transverse wall configurations [26]. The reason behind this discrepancy between the simulated and experimentally determined magnetic configurations could be the different temperatures at which the two analyses were carried out: the micromagnetic simulations were carried out at an effective temperature of 0 K, while the XMCD-PEEM imaging experiments were carried out at room temperature. Such differences in the temperature can lead to the stabilization of a different magnetic domain wall configuration, as observed e.g. for La 0.7 Sr 0.3 MnO 3 nanostructured half-ring elements [27].
We thus find that the magnetic configuration of small CMG nanostructures is largely determined by the shape-anisotropy for the geometries analyzed in the work presented here. From the results of the micromagnetic simulations, it is possible to observe that, for the square nanostructures with their edges oriented along the 100 〈 〉   crystalline directions of the CMG (i.e. the hard axes of the cubic anisotropy), that the contributions of the shape and magneto-crystalline anisotropies become comparable for squares with an edge of ca. 4 μm and, for these and dimensions above these, the magnetic configuration is no longer dominated by the sole contribution of shape anisotropy.

Conclusions
In conclusion, the magnetic configurations of the FIB-nanostructured CMG Heusler compound have been characterized by means of XMCD-PEEM imaging. The films were heteroepitaxially grown on MgO (001) substrates by RF sputtering, and exhibit an L2 1 order after suitable annealing, as confirmed by XRD and RHEED measurements. MOKE measurements allowed us to observe that the CMG thin films in the L2 1 order exhibits a four-fold symmetry for the magnetic easy axes, which lay along the 110 〈 〉 crystalline directions of the CMG. The magnitude of the cubic anisotropy term was estimated to be K 1500 150 1 = ± J m −3 . As observed in XMCD-PEEM imaging and confirmed by micromagnetic simulations, the magnetic configuration of the CMG nanostructures is governed, for dimensions below ca. 4 μm, by shape anisotropy, thus allowing for the control of the magnetic configuration in the patterned CMG elements, making this material a good candidate for spintronic applications. The results reported in this paper focus on the analysis of the magnetic configurations of nanostructured CMG elements resulting from the combined (magnetic) contributions of the Co and Mn atoms. A possible future study could be the analysis of the atomic magnetic moments arising from the Co and Mn atoms in the CMG, which would also allow for the comparison of the effect of different growth conditions (e.g. with CMG films grown on GaAs substrates [28]) on the magnetic properties of this material. Figure 8. XMCD-PEEM images of nanostructured CMG rings of different diameters d and widths w. The preferred domain wall structure is given by a vortex wall, while for a high ring curvature (i.e. w = 1 μm, and d = 2 μm), the ring exhibits a single magnetic fluxclosure domain. No preferential orientation with respect to the crystallographic axes of the CMG for the magnetic domain walls has been observed. The grayscale arrows indicate the direction of the magnetic contrast in the images.