Eider
Berganza
*ab,
Miriam
Jaafar
*ac,
Jose A.
Fernandez-Roldan
ad,
Maite
Goiriena-Goikoetxea
ef,
Javier
Pablo-Navarro
g,
Alfredo
García-Arribas
fh,
Konstantin
Guslienko
ij,
César
Magén
gkl,
José M.
De Teresa
gkl,
Oksana
Chubykalo-Fesenko
a and
Agustina
Asenjo
a
aInstituto de Ciencia de Materiales de Madrid, CSIC, 28049 Madrid, Spain
bInstitute of Nanotechnology, KIT Campus North, 76344 Eggenstein-Leopoldshafen, Germany. E-mail: eider.eguiarte@kit.edu
cDepartamento de Física de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
dDepartamento de Física, Universidad de Oviedo, Federico García Lorca s/n, Oviedo 33007, Spain
eDepartment of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA
fDepartamento de Electricidad y Electrónica, Universidad del País Vasco (UPV/EHU), 48940 Leioa, Spain
gLaboratorio de Microscopías Avanzadas (LMA) - Instituto de Nanociencia de Aragón (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain
hBasque Center for Materials, Applications and Nanostructures (BCMaterials), UPV/EHU Science Park, 48940 Leioa, Spain
iDepartment of Materials Physics, University of the Basque Country (UPV/EHU), 20018 Donostia, Spain
jIKERBASQUE, the Basque Foundation for Science, 48013 Bilbao, Spain
kInstituto de Ciencia de Materiales de Aragón (ICMA), Universidad de Zaragoza-CSIC, 50009 Zaragoza, Spain
lDepartamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
First published on 19th June 2020
Topologically non-trivial structures such as magnetic skyrmions are nanometric spin textures of outstanding potential for spintronic applications due to their unique features. It is well known that Néel skyrmions of definite chirality are stabilized by the Dzyaloshinskii–Moriya exchange interaction (DMI) in bulk non-centrosymmetric materials or ultrathin films with strong spin–orbit coupling at the interface. In this work, we show that soft magnetic (permalloy) hemispherical nanodots are able to host three-dimensional chiral structures (half-hedgehog spin textures) with non-zero tropological charge. They are observed at room temperature, in absence of DMI interaction and they can be further stabilized by the magnetic field arising from the Magnetic Force Microscopy probe. Micromagnetic simulations corroborate the experimental data. Our work implies the existence of a new degree of freedom to create and manipulate complex 3D spin-textures in soft magnetic nanodots and opens up future possibilities to explore their magnetization dynamics.
Most of the published papers report on magnetic skyrmions in systems with broken inversion symmetry, that display Dzyaloshinskii–Moriya exchange interaction (DMI) either in ultra-thin multilayers of transition metals4 and materials with strong spin–orbit coupling5,6 or in non-centrosymmetric B20 compounds. Both Néel (hedgehog) and Bloch skyrmions can be stabilized in the above-mentioned cases due to the interplay of exchange interaction, DMI and uniaxial perpendicular magnetic anisotropy.7,8 DMI can also induce skyrmions in materials with easy-plane magnetic anisotropy.9,10 Moreover, the magnetization configuration of Néel and Bloch skyrmions is chiral, i.e., only one rotation sense of the magnetization direction is energetically favourable, depending on the DMI nature. A separate question is the stabilization of the Néel and Bloch skyrmions in nanostructured materials such as nanodots, where the confinement plays a very important role and changes the skyrmion stability conditions.11
On the other hand, the so-called curvature driven effects in nanomagnetic systems constitute a very active research field.12,13 It has been established that the sample curvature can be considered as a source of an effective magnetic anisotropy and trigger magnetochiral effects.14,15 In 1D systems as magnetic nanowires, for instance, the curvature and geometrical confinement have proved to stabilize skyrmionics textures with no need of DMI.16,17
Planar soft magnetic permalloy (Py, NiFe alloy) dots are believed to host magnetic vortices only.18 However, the shape and curvature may produce additional effects as the theoretically predicted 3D Bloch-type skyrmions in hemispherical or spherical nanoparticles.19 Nevertheless, hemispherical shaped soft nanomagnets have not been investigated systematically. Despite the existence of Néel-like skyrmions in thick films with out-of plane anisotropy has been recently reported,20 so far nobody has observed the stabilization of chiral structures in confined systems with neither DMI nor perpendicular magnetic anisotropy.
During the last decade, essential progress of the experimental techniques enabled the detection of magnetic vortices,21 bubbles22 or skyrmions23 by using various imaging techniques on the nanoscale. The importance of imaging individual nano-objects lies in its capability to directly visualize these spin textures or even to control them.24,25 Several techniques such as Photo Emission Electron Microscopy (PEEM)5 or Electron Holography (EH)26 are commonly used to study magnetic configurations of individual nano-objects. Nevertheless, the family of Scanning Probe Microscopy techniques (Spin Polarized Scanning Tunneling Microscopy, SP-STM,27 Magnetic Exchange Force Microscopy, MExFM,28,29 Magnetic Force Microscopy, MFM,30 and NV-magnetometry31) provide higher resolution images as well as remarkable sensitivity.
In this article, we study sub-100 nm diameter Py (Ni80Fe20) hemispherical shaped nanodots with no uniaxial out-of-plane magnetic anisotropy or DMI. Many previous works studying cylindrical Py nanodots reported the stabilization of flux-closure vortex state or a single domain state due to the low magnetocrystalline anisotropy.18,32 However, half-skyrmionic (Néel-type) spin textures were unexpectedly detected in the present study using MFM. The evolution of the magnetic configuration under externally applied in-plane (IP) fields, together with micromagnetic simulations leave no doubts of the existence of stable three-dimensional configurations with non-zero topological charge, which behave as chiral radial vortices in such Py nanodots.
As a first approach, magnetic imaging was performed after subjecting the sample to a saturating out-of-plane (OOP) magnetic field. The resulting MFM image, shown in Fig. 1a, resembles a magnetic vortex because their core can clearly distinguished from the surrounding area. Magnetic vortices present in-plane (IP) closed-flux magnetization with a core at the centre, where the OOP magnetization component can be either positive or negative and their chirality can be clock- or counter-clockwise.34,35
In the vortex configuration, since the MFM signal is mainly sensitive to the OOP component of the magnetization, a repulsive (bright) or attractive (dark) contrast is expected at the vortex core when the tip stray field and the core polarization are antiparallel (repulsive interaction) or parallel (attractive interaction), respectively, as Fig. 1b illustrates. Thus, the core contrast could be simply reversed by changing the magnetization of the MFM tip.
Keeping this in mind, MFM experiments were repeatedly performed on a previously saturated sample, whose magnetic state is left unchanged during the imaging process. Surprisingly, despite changing the MFM probe polarization, the contrast at the centre of the Py nanodots is always positive (corresponding to an antiparallel tip-core configuration, as illustrated in Fig. 1c). Moreover, the contour of the magnetic configuration of the sample is quite intense, considering that the MFM in-plane configuration should lead to a faint contrast. All in all, the results point at the existence of an alternative configuration to the expected magnetic vortex. Further experiments (presented in ESI2†) were done in order to discard any crosstalk with electrostatic interactions, given that they are also strong at the scale of a few tens of nanometers.
Moreover, the final movement direction of the core depends entirely on the vortex chirality and it is therefore independent of its core magnetization direction.36,37
The application of in situ magnetic field during MFM measurements is frequently used to shed light upon the magnetic configuration and its dynamic behaviour. In this case, Variable Field-MFM (VF-MFM) is performed applying the field along the in-plane direction. The results display an unexpected behaviour where the movement of the core is parallel or antiparallel to the external magnetic field. These results are incompatible with the conventional vortex configuration and they necessarily imply the presence of some radial magnetization component.
In order to investigate the kind of magnetic configurations that fulfil such condition, micromagnetic simulations have been performed. Similarly to conventional vortices, where the combination of the two possible core polarities plus the two chiralities give rise to 4 energy degenerate states, one might also expect to find 4 stable states in the system that concerns us, combining the two polarities and two radial components. To reveal the stability of the magnetic configurations, micromagnetic simulations were carried out using Object Oriented Micromagnetic Framework (OOMMF).38 Hemispherical Py nanoparticles were modelled choosing a configuration with a core pointing perpendicular to the plane, an outer part pointing opposite to the core magnetization and a radially magnetized shell as initial condition. To mimic the existence of internal tensions generated by the dot fabrication process, a radial magnetic anisotropy of 2.5 × 105 J m−3 was chosen.
As a matter of fact, micromagnetic simulations show that 4 different states are stable states-resulting from the combination of 2 different core polarities P and 2 radial chiralities RC- (see Fig. 2, where cross sectional and basal planes of the nanodot magnetic configurations are shown). However, due to the lack of cylindrical symmetry of the nanodot, they do not present equal energy values. Micromagnetic simulations estimate that the total energy of the configurations displayed in Fig. 2a and b is E = 1.934 × 10−17 J, while those in 2c and d present E = 1.701 × 10−17 J value. Therefore, they do reveal the existence of 3D chiral magnetization configurations, hereinafter referred to as half-hedgehog spin textures, with a half-Néel skyrmion in the dot basal plane.39
VF-MFM imaging shows, however, that not all the simulated configurations are possible in the studied system. In the two sequences shown below, the magnetization of the tip is fixed in up or down direction, while the sample is initially demagnetized in both cases. As it was previously mentioned, the MFM images display the same contrast (bright core, corresponding to repulsive interaction) in both sequences where all the cores are antiparallel to the tip magnetization. When magnetic in-plane field is applied along the x direction (see Fig. 3a and b), the white cores move antiparallel to the field direction (sequence I). In sequence II, the experiment is repeated with opposite tip polarity (Fig. 3d), which gives a different result, since the core moves parallel to the magnetic field. The combination of the two sequences proves that the displacement of the core (antiparallel or parallel to the applied field) depends on the polarity of the tip. The core displacement can be better seen on the profiles of the MFM data displayed in Fig. 3e.
Simulations in Fig. 3b and d reproduce the magnetic configurations with a radial vortex on the base plane as a minimum energy state and prove that the configuration is stable in hemispheres of 70 nm in diameter. Notice that the out-of-plane (mz) magnetization component is represented in a colour scale and that a transversal dot cross section is shown to emphasize the movement of the core. The stability of both positive (and negative) polarity half-hedgehog configurations is proven, with the radial component of the magnetization pointing in (and out), in good agreement with the observations. Results unveil that the core diameter is narrow at the base and it grows in size approaching the nanodot surface. Additionally, when it is subjected to external field, the magnetic moments of the base respond later than the ones closer to the dot upper surface.
Therefore, the comparison of simulations and experiment shows that only structures with one chirality are observed.40
A similar coupling effect between polarity and the domain wall chirality was reported for vortex-like structures in spherical dots.19
At this point we can claim that the stray field of the tip plays a critical role on the definition of the magnetic configuration of the nanodots, considering that a positive or negative core structure can be induced by applying an out-of-plane field in the appropriate direction. This explains why the images obtained in the MFM measurements (i.e., faint core and dark contour, on Fig. 1c) stay the same regardless of the magnetization direction of the tip: the relative orientation of sample–tip magnetization remains always the same. Notice that in this system, the MFM tip does not produce the usual reversible process where the sample magnetization aligns parallel to the tip magnetic moment. The tip creates a perturbation that induces a metastable state, where the dot external part keeps the radial component of the tip stray field while the core is magnetized antiparallel to it.
More importantly, it should be made clear that despite all four configurations in Fig. 2 being energy minimum states, only the two lower energy configurations have been experimentally detected (Fig. 2c and d). This conclusion can be extracted through careful interpretation of the VF-MFM images in Fig. 3. A more detailed explanation can be found in ESI3.†
We also note that the widely used concept of the topological charge (skyrmion number or degree of mapping) in 2D spin systems is not directly applicable to our dots because the magnetization depends on the thickness coordinate z, m (x, y, z). Despite this issue, several works in literature report 2D topological charge analysis in nanowires as a function of z dimension.17,41
In order to understand the evolution of the topological charge as a function of the dot thickness, we have calculated the 2D topological charge a function of the dot thickness coordinate in the dot, according to the following equation:
(1) |
The 2D topological charge (eqn (1)) is approximately equal to 0.4 at the base of the nanodot and it decreases when approaching the dot surface (Fig. 4a). A more rigorous approach to the topological charge in 3D case assumes calculation of the flux of the gyrocoupling density vector over the sample surface or introducing a Hopf invariant.42
At this point, the interpretation of the MFM images might be controversial due to the high intensity measured in the contour of the nanodots. For deep analysis of the MFM contrast, the intensities of the signal from the remnant state and the signal from the saturated nanodot are compared in ESI4.† At first sight, this might lead us to think that the topological charge of the configuration is higher than what we calculated. However, considering the stray field generated by the nanodot (Fig. 4b), with strong OOP field component close to the nanodot contour, a strong attractive interaction (dark contrast) between the MFM tip and the nanodot edge is expected.
The previous experiments shown in Fig. 1c and 3 have demonstrated that the MFM tip stray field nucleates the chiral structure. Johnson et al. already predicted the possibility of stabilizing skyrmionic spin textures in curved nanostructures assisted by an external stray field.43 In fact, the direction of the core can be chosen by selecting the polarization of the tip prior to scanning. Furthermore, none of the MFM images obtained so far present any kind of sudden changes or “jumps”, where the stability of the induced configuration might to some extent be questioned. Conversely, they seem to remain always stable during the scan, even if the retrace distance is on purpose enlarged (see ESI5†).
However, the influence of the MFM tip over the stability of the configuration is not yet clear. For further experiments addressing this topic, lower moment MFM tips were designed and characterized44,45 (see Table 1 and ESI6† for more details), which give us a gradient of tip stray fields with tuned intensity.
Making use of the series of VF-MFM based methods,46 the critical fields of the structures creation and annihilation have been determined, repeating the experiment with each one of the tips. In Fig. 5a, the field intervals for the half-hedgehog structure existence are depicted as a function of the stray field contrast of the probes.
Fig. 5 Assessment of the half-hedgehog stability as a function of the magnetic force gradient. (a) Correlation between OOP magnetic probe stray field (x axis) and the field range where the structure is stable (y axis). The black dots represent the experimental data obtained from the MFM based measurements described in ESI7.† Field sequences performed ith different tips show the decreasing saturating in-plane magnetic fields from (b)–(d). Image size is 250 × 250 nm. |
Notice that the stray field contrast value is given in Hz units, as the observable of the MFM contrast is the oscillation frequency channel due to the use of the Phase Locked Loop. Fig. 5b–d display representative standard MFM images of the structures under in situ applied magnetic fields, performed with probes of different stray field values. The colour code of frames of the MFM images in Fig. 5 is in accordance with that shown in Table 1. Interestingly, the annihilation field is almost 5 times larger when a commercial probe is used (tip 1, Fig. 5b) as compared to the values obtained for the nanorod probe (tip 3, Fig. 5d).
Thus, the larger stray fields lead to the stabilization of the half hedgehog 3D structures, turning it into a magnetically harder configuration. This phenomenon has been observed in previous works, where the local field of the MFM tip was used to manipulate the magnetic charges.47,48 In this work, the tip stray field serves as a tool to create and enhance the stability of the configurations. The set of images from Fig. 5d, which were scanned with the smallest possible stray field tip (4 Hz) speak for themselves, remarkably showing how just a very small stray field is needed to nucleate the half-hedgehog spin texture. Moreover, the configuration still stays relatively stable, i.e. it does not immediately vanish upon applied field.
On the other hand, in simulations, the configuration is stabilized specifically for 70 nm diameter hemispheres. However, additional experiments with slightly different samples show that the stabilization of the studied configuration is closely related to a specific dot geometry and aspect ratio. Some examples are shown in ESI7,† where a sample with a bigger size dispersion presents also single domain configurations, additionally to the here studied magnetic configurations.
We believe that the possibility of stabilizing chiral structures in permalloy nanodots without magnetic anisotropy and DMI opens new perspectives for the exploration of topologically non-trivial spin textures in soft magnetic systems that have not been yet considered, or novel magnetic configurations arising from curvature in nanoscale magnetic systems.
Footnote |
† Electronic supplementary information (ESI) available: Morphological and structural characterization (ESI1), study of the electrostatic contribution to the frequency shift (ESI2), MFM data interpretation (ESI3), topological charge (ESI4), imaging at different heights (ESI5), determination of critical fields and tip stray field values (ESI6), influence of geometrical parameters (ESI7). See DOI: 10.1039/d0nr02173c |
This journal is © The Royal Society of Chemistry 2020 |