NANO LETTERS
Magnetic Configurations of 30 nm Iron Nanocubes Studied by Electron Holography
2008 Vol. 8, No. 12 4293-4298
E. Snoeck* and C. Gatel CNRS, CEMES, F-31055 Toulouse, France, and UniVersite´ de Toulouse, UPS, CEMES, BP 94347, F-31055 Toulouse Cedex, France
L. M. Lacroix, T. Blon, S. Lachaize, J. Carrey, and M. Respaud UniVersite´ de Toulouse, INSA, UPS, LPCNO, 135 aVenue de Rangueil, F-31077 Toulouse, France
B. Chaudret LCC-CNRS, route de Narbonne, 31055 Toulouse, France Received July 8, 2008; Revised Manuscript Received October 29, 2008
ABSTRACT Ferromagnetic nanomaterials exhibit unique magnetic properties common to materials with dimensions approaching the atomic scale and have potential applications in magnetic data storage. Technological applications, however, require that the detailed magnetic behaviors and configurations of individual and interacting magnetic nano-objects be clarified. We determined the magnetic remnant configurations in single crystalline 30 nm Fe nanocubes and groups of nanocubes using off-axis electron holography in a transmission electron microscope. Our measurements on an isolated cube reveal a vortex state whose core size has been determined. Two neighboring nanocubes with adjacent {100} surfaces exhibit a ferromagnetic dipolar coupling, while similar magnetic interactions between four cubes in a square arrangement induce a bending of the magnetic induction, i.e., a magnetic flux closure state. The various configurations were successfully simulated by micromagnetic calculations.
Research into ferromagnetic nanomaterials, i.e., nanoparticles, disks, nanowires, dots, etc., is driven by large potential applications in magnetic recording and storage.1-3 However, successful technological applications of these materials will require detailed knowledge of the magnetic behavior and configurations of isolated and interacting magnetic nanoobjects. As an example, the critical size for which the magnetic configuration of a ferromagnetic nano-object switches from a single domain state to a vortex state (and then to a multidomain state) will depend not only on their size but also on their magnetic anisotropy, on their shape, and on possible magnetic interactions between the nanoobjects and/or between the object and the substrate. Some theoretical studies have aimed to tackle such a question for magnetic nanoelements of different shapes.4,9 Experimental magnetic studies are however needed on “model systems” to investigate more precisely these phenomena and to support these theoretical studies. Most nanosystems are prepared * Corresponding author: e-mail,
[email protected]; phone, +33 (0)562 25 78 91; fax, +33 (0)562 25 79 99. 10.1021/nl801998x CCC: $40.75 Published on Web 11/12/2008
2008 American Chemical Society
using top-down techniques, which may induce numerous defects and uncontrolled parameters such as the substrate/ nano-object interaction. As an alternative route, different chemical processes allow well-controlled nano-objects to be made.10,11 Among them, the organometallic approach has a proven efficiency to synthesis monodisperse nanomaterials with precise shape and structure in a size range that can be tuned between a few nanometers to hundreds of nanometers.12 Adjusting the synthesis conditions may moreover induce an organization of the nano-objects13 allowing a detailed study of their interactions. Several techniques are used to study the local magnetic properties of materials, including spin-polarized scanning tunneling microscopy (SP-STM),14-16 micro-SQUID magnetometry,17 magnetic force microscopy (MFM),18,19 photoemission electron microscopy (PEEM),20 and Lorentz microscopy.21 Except for SP-STM, these techniques lack sufficient spatial resolution for the study of magnetic configurations inside nanometer-sized magnetic materials and, particularly, for fine analysis of the vortex-core
Figure 1. Electron holography and micromagnetic simulations for a single isolated Fe nanocube. (a) TEM image reveals the cubic structure and an external iron oxide layer surrounding the nanocube. (b) Phase image corresponding to the magnetic contribution to the phase shift with 0.05 rad isophase contours. Note the cylindrical symmetry of the magnetic flux line. (c) Vector map of the in-plane components of the magnetic induction revealing the vortex state. (d) Micromagnetic simulation (with bulk Ms) of the in-plane induction (the location and the number of arrows are not related with the discretization points).
structures. On the other hand, electron holography (EH) combines the high spatial resolution of transmission electron microscopy (TEM) with the capability of quantitatively analyzing local magnetic configurations and locally measuring the magnetization.22,26 Off-axis EH is an interferometric technique that measures the phase shift of a high-energy electron wave that has passed through a material. The phase shift is sensitive to electric and magnetic fields in the sample. As a result, local magnetic properties in nanoscale materials can be mapped and quantitatively compared with simulations. The possibility to realize both high-resolution structural and magnetic investigations on exactly the same well-defined nano-object in a unique apparatus, combined to the micromagnetic calculations on the observed system, opens also the possibility to correlate exactly the magnetic configuration to the structural nanoparticle properties (geometry, crystalline structure, defects, etc.). In this work, we developed this EH approach to investigate the magnetic properties of Fe 30 nm single crystalline nanocubes. These Fe nanocubes, whose size is at the frontier between the monodomain and the vortex states, can be considered as model nano-objects to study the influence of shape and size on magnetic properties. We employed offaxis EH to map the room-temperature remnant magnetic configurations in several systems, i.e., isolated nanocubes (Figure 1), two neighboring cubes face to face (Figure 4), and four cubes in a square arrangement (Figure 6) (results on four in-line cubes are also reported as Supporting Information). Micromagnetic calculations were carried out to map the simulated magnetic configurations and to compare 4294
them with the experimental ones. The measurements revealed the major role played by dipolar effects, either on isolated or on interacting systems. Fitting the experimental induction maps with models allows us to determine the magnetic parameters of the Fe nanocube as well as an estimate of the vortex core dimensions. The nanocubes were synthesized using the organometallic method (see Supporting Information), which results in quasimonodispersed cubes with 30 nm sides. Statistical measurements of the size of the nanocubes revealed a dispersion of about 10% giving a thickness to length ratio of 1 ( 0.1. The TEM images (e.g., Figure 1a) reveal uniform contrast within the nanocubes, and high-resolution TEM experiments indicate that the Fe nanocubes are body-centered cubic (bcc) with {100} type facets and that a 2 nm thin layer of iron oxide (most likely Fe3O4) surrounds each particle. This oxide appears when transferring the sample into the TEM. It is responsible for the slightly perturbed contrast observed in the TEM micrographs (Figure 1a). Neighboring Fe particles have {100} surfaces face to face. Isolated Nanocube. Two remnant magnetic configurations +S and -S of an isolated cube were obtained after saturating the cube magnetization with a 1.7 T magnetic field along [10-1] and [-10-1] directions (their respective in-plane projections H1 and H2 are reported in Figure 1a). The two resulting holograms were subtracted in order to obtain the magnetic contribution to the phase shift (see Supporting Information). The phase image for the isolated nanocube is displayed in Figure 1b with 0.05 rad isophase contours superimposed. The in-plane induction vectors deduced from the phase image are displayed in Figure 1c; they exhibit an axial symmetry with an axis perpendicular to the (001) face slightly displaced with respect to the center of this facet. Magnetic domain structures in a material are determined by the total energy of the system. In bulk ferromagnetic materials, magnetic domains generally form structures that reduce their magnetostatic energy. In very small structures, however, the exchange energy dominates and the magnetization is approximately uniform, which results in single domain configurations. At intermediate sizes in low anisotropy nanomaterials (as iron), spin configurations may be in a vortex state.6,27 In such magnetic configurations, the spins achieve a complete flux closure in the vortex plane to minimize the magnetostatic energy, except for the spins located at the vortex core which rotate out of plane to minimize the exchange energy. At the vortex core, the flux is perpendicular to the vortex plane. The vortex can be described in terms of chirality of the spin rotation (clockwise (CW) or counterclockwise (CCW)) and polarity (up or down) of the vortex core. The calculated maps in panels b and c of Figure 1 could be identified as the mapping of the magnetic configuration of the cube, only at the condition that +S and -S remnant states are perfectly antisymmetrical. In order to verify this requirement, we performed an extensive series of micromagnetic simulations. First, we calculated the equilibrium magnetic configurations of iron nanocubes with 〈100〉 easy axis anisotropy and perfect cubic shape in the absence of an Nano Lett., Vol. 8, No. 12, 2008
applied magnetic field. Considering the bulk parameters for iron (saturation magnetization, exchange stiffness, and magnetic anisotropy, see Supporting Information), we compared the energies of the single domain state (flower state) and a vortex state for different particle sizes. These calculations predict that the magnetic configuration of an isolated iron nanocube is a single-domain state for cubes with dimensions less than 28 nm and a vortex state for larger cubes. This single-domain limit is consistent with previous micromagnetic calculations on small cubic particles with uniaxial anisotropy.6,7 Our simulations showed that the energies are identical for vortex states with axes oriented along [100], [010], or [001] (and also for flower states with the three equivalent 〈100〉 axes). We also found that neither chirality nor polarity influences the energy of the vortex state. Finally, since the exact thickness of the cube cannot be determined from the two-dimensional TEM images, we checked that slight changes in the perfect cubic shape do not drastically modify the final magnetic configuration. For the observed 30 nm nanocube, the calculations predict that, without any applied magnetic field, the vortex state occurs for thicknesses between 22 and 38 nm. Moreover, to reproduce the experimental procedure, we have simulated the two +S and -S remnant states “applying” on a simulated 30 nm perfect nanocube 1.7 T magnetic field successively along the two [10-1] and [-10-1] directions. In this case, our micromagnetic simulations predict that only two vortex directions remain stable at the remanence, i.e., those with axes parallel to [001] and [100]. In addition, assuming that a residual magnetic field of the objective lens parallel to the optic axis may contribute to the stabilization of only one vortex state (see Supporting Information), we include in the simulations a small magnetic field (15 mT) parallel to [00-1]. We observe that it favors the vortex whose axis is parallel to [001]. The chirality can be CW or CCW but it has to be reversed between H1 and H2 in order to map the vortex state after subtraction of the two remnant +S and -S states. Thus we conclude that panels b and c of Figure 1 do correspond to the induction maps of a vortex remnant state whose simulation is reported in Figure 1d. Even if such a vortex state costs exchange energy, it minimizes the magnetic flux circulation outside of the magnetic element. Because the magnetic element is a cube, the magnetization at the corners creates pseudomagnetic charges on surfaces inducing flux closure outside the cube. We observed this external flux closure experimentally (see the zoom inset Figure 1c), and its presence is confirmed by the micromagnetic calculations (Figure 1d). We quantitatively compared the EH data to the micromagnetic simulations in order to measure the local magnetic moment and study the tridimensional shape of the vortex. Figure 2a shows the experimental and simulated profiles of the in-plane component of the magnetic induction (Bxy). The experimental error on the magnetic induction measurements is about 0.25 T (due to thickness uncertainty). Profiles were taken in the [010] direction across the vortex core. The simulated profiles were convoluted with a Gaussian curve of 2.5 nm standard deviation to take into account the spatial Nano Lett., Vol. 8, No. 12, 2008
Figure 2. Quantitative comparison of the simulated and observed magnetic properties of the isolated Fe nanocube. (a) Simulated and experimental profiles of the in-plane induction (Bxy) along the [010] direction across the vortex core (see text). (b) Calculated profiles of the component of the magnetization parallel to the vortex axis (Mz) on the same line scan as (a). Dotted lines indicate the Fe3O4 layers introduced in the calculation.
resolution due to the spatial-frequency filter (2.5 nm) applied in the Fourier space when reconstructing the holograms. With bulk Ms (1.72 × 106 A/m), the simulation reproduces the general shape of the experimental profile, but a better agreement is obtained using a slightly reduced Ms (1.6 × 106 A/m). The experimental in-plane induction profile is asymmetrical compared with the simulated profiles. Whereas the simulations lead to vortex states perfectly centered in the cube, our observation displays a vortex core which is slightly displaced with respect to the cube center. This difference in the vortex core position is however small (2 nm) and could be partly simulated by a slight tilt (about 5°) of the [001] direction of the cube with respect to the direction of the residual field (i.e., the optical axis) and/or structural imperfections. The small 7% reduction of Ms agrees with our macroscopic magnetic measurements performed on the Fe-nanocube colloidal solutions. Reducing Ms below 7% in the simulations leads to the appearance of vortices with axes in directions 〈111〉 which do not fit the experimental data. Diminishing Ms even more (
