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Direct Observation of Internal Spin Structure of Magnetic Vortex Cores

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Science  18 Oct 2002:
Vol. 298, Issue 5593, pp. 577-580
DOI: 10.1126/science.1075302

Abstract

Thin film nanoscale elements with a curling magnetic structure (vortex) are a promising candidate for future nonvolatile data storage devices. Their properties are strongly influenced by the spin structure in the vortex core. We have used spin-polarized scanning tunneling microscopy on nanoscale iron islands to probe for the first time the internal spin structure of magnetic vortex cores. Using tips coated with a layer of antiferromagnetic chromium, we obtained images of the curling in-plane magnetization around and of the out-of-plane magnetization inside the core region. The experimental data are compared with micromagnetic simulations. The results confirm theoretical predictions that the size and the shape of the vortex core as well as its magnetic field dependence are governed by only two material parameters, the exchange stiffness and the saturation magnetization that determines the stray field energy.

Detailed understanding of the magnetism of nanostructures is a major requirement for the future progress in magnetic data storage technology. For example, circular nanostructures that exhibit a curling in-plane magnetic configuration (vortex) are considered as basic elements for the magnetoelectronic random access memory (MRAM) (1). The stability and switching behavior of such devices depend on the width of the vortex core, where the magnetization turns into the surface normal. Although detailed theoretical predictions on the width and spin structure of vortex cores are available (2, 3), they have never been proven experimentally.

Recently, magnetic vortex cores were verified by magnetic force microscopy (MFM) (4, 5). However, MFM suffers from three problems: (i) The lateral resolution of MFM typically is limited to ≈20 to 100 nm, which is larger than the vortex core. (ii) The magnetic stray field of the tip easily interferes with the vortex as the tip-sample distance becomes too small. (iii) The sensitivity is restricted to the out-of-plane component of the stray field gradient. All three problems are avoided by using spin-polarized scanning tunneling microscopy (SP-STM). First, SP-STM is capable of resolving magnetic domain walls (6) and superstructures down to the atomic scale (7). Second, it has recently been shown that any dipolar interaction between tip and sample can be avoided by the use of antiferromagnetic probe tips (8). Third, by varying the thickness of the antiferromagnetic layer deposited on the tip, we are able to prepare tips with either in-plane or out-of-plane sensitivity: thick chromium (Cr) films were found to be sensitive to the in-plane component of the sample magnetization, whereas thinner films [thickness <50 monolayers (ML)] resulted in an out-of-plane sensitivity (9). With this technique we studied the vortex core that appears on iron (Fe) nanoislands, revealing the lateral width of the vortex core, its shape, and its magnetic field dependence.

SP-STM is sensitive to the sample's surface local electron spin density. It makes use of the intrinsic spin polarization of a magnetic tip material serving as a spin filter. It has been shown experimentally (10, 11) and theoretically (12) that topographic and electronic contributions can be successfully separated from the spin signal by means of spectroscopic techniques. The differential conductance measured with spin-polarized scanning tunneling spectroscopy (SP-STS) at the locationr⃗ on the surface for a sample bias voltageU 0 can be written asEmbedded Image(1)where C = dI/dU(r⃗,U 0)SA is the spin-averaged differential conductance, P T =P T(E F) is the spin polarization of the tip at the Fermi energy E F, and P S =P S(E F +eU 0) is the spin polarization of the sample at the energy E F +eU 0 (13). The angle θ = θ(M⃗ T,M⃗ S(r⃗)) is enclosed by the tip magnetizationM⃗ T and the local sample magnetizationM⃗ S(r⃗) below the tip apex. On an electronically homogeneous surface,C(r⃗) andP S are independent of the locationr⃗. Therefore, any lateral variation of the dI/dU signal is caused by the cosθ term, which—at a fixed tip magnetization direction—is directly connected to the local orientation of the sample magnetizationM⃗ S(r⃗). In the case of antiferromagnetic tips, the magnetic moments cancel out each other and, hence, the net magnetization vanishes but the spin polarization of the outermost tip atom responsible for the tunneling process is preserved. Equation 1 is still valid for antiferromagnetic tips if the termM⃗ T is interpreted as the magnetic moment m⃗ of the atom at the tip apex. Throughout this report, we will continue to use the notation “tip magnetization” M⃗ T, though it actually means m⃗ T in the case of an antiferromagnetic tip.

The measurements were performed with a low-temperature scanning tunneling microscope (14) at a tip and sample temperature of 14 ± 1 K. A superconducting magnet supplied a magnetic field normal to the surface plane. Nanoscale magnetic particles were prepared under ultra-high vacuum conditions (pressure p ≤ 1 × 10 10 mbar) by means of self-organized growth of Fe on the (110) surface of a tungsten (W) single crystal. We evaporated 8 to 10 ML Fe on a stepped W(110) substrate held at room temperature. The sample was thermally annealed for 10 min at 800 ± 100 K, leading to the formation of elongated “islands” with lateral dimensions of 200 to 500 nm by 150 to 250 nm along the [001] and the [11̄0] directions, respectively, and an average heightD = 8 to 9 nm. The areas between the islands are covered with a single pseudomorphic ML of Fe (15).

The magnetic ground state of Fe islands of that lateral and vertical size is expected to be a vortex. The dimensions of the particles are too large to form a single-domain state because it would cost a relatively high stray field (or dipolar) energy. But they are also too small to form domains like those found in macroscopic pieces of magnetic material because the additional cost of domain wall energy cannot be compensated by the reduction of stray field energy. The magnetization continuously curls around the particle center, drastically reducing the stray field energy and avoiding domain wall energy. For topological reasons, the magnetization in the vortex core has been predicted to turn into the surface normal (Fig. 1).

Figure 1

Schematic of a vortex core. Far away from the vortex core the magnetization continuously curls around the center with the orientation in the surface plane. In the center of the core the magnetization is perpendicular to the plane (highlighted).

A constant current topograph of a single Fe island is shown in Fig. 2A. The quasi-hexagonal symmetry of the W(110) surface leads to tapered ends. Step edges of the underlying substrate are weakly visible as a diagonal height modulation caused by the different layer thickness of Fe and W. Though the dI/dU signal on top of such Fe islands is found to be spatially constant if measured with uncovered W tips (not shown), a spatial pattern can be recognized in the dI/dUmap (Fig. 2B) measured with a tip coated with more than 100 ML of Cr. This variation is caused by spin-polarized tunneling between the magnetic sample and the polarized tip. Because this particular tip also showed a strong domain contrast on the pseudomorphic Fe ML (6), the easy axis of which is the [11̄0] direction, we conclude that M⃗ Tis parallel to the surface plane and is approximately oriented along the [11̄0] direction. Four different regions, referred to as domains, can be distinguished in Fig. 2B. AssumingP T > 0 and P S> 0, the observed pattern can be explained by a local sample magnetizationM⃗ S(r⃗) that is parallel (bottom) and antiparallel (top) toM⃗ T, respectively. An intermediate contrast in the left and the right domain shows thatM⃗ T andM⃗ S(r⃗) are almost orthogonal (cosθ = 0). A corresponding domain pattern exhibiting a flux-closure configuration is indicated by the arrows inFig. 2B. However, because neither the absolute direction ofM⃗ T nor the sign ofP T and P S is known, the opposite sense of rotation would also be consistent with the data.

Figure 2

(A) Topography and (B) map of the dI/dU signal of a single 8-nm-high Fe island recorded with a Cr-coated W tip. The vortex domain pattern can be recognized in (B). Arrows illustrate the orientation of the domains. Because the sign of the spin polarization and the magnetization of the tip is unknown, the sense of vortex rotation could also be reversed. The measurement parameters were I = 0.5 nA and U 0 = +100 mV. The crystallographic orientations were determined by low-energy electron diffraction.

We have zoomed into the central region where the four “domains” touch and where the rotation of the magnetization into the surface normal is expected. Maps of the dI/dU signal measured with Cr-coated tips that are sensitive to the in-plane and out-of-plane component of M⃗ S are shown (Fig. 3, A and B, respectively). The dI/dU signal as measured along a circular path at a distance of 19 nm around the vortex core (circle in Fig. 3A) is plotted in Fig. 3C. The cosine-like modulation indicates that the in-plane component ofM⃗ S(r⃗) continuously curls around the vortex core. Figure 3B, which was measured with an out-of-plane sensitive tip on an identically prepared sample, exhibits a small bright area approximately in the center of the island. Because M⃗ T of this tip is perpendicular to the surface plane, Eq. 1 provides cosθ = 0 as long as theM⃗ S(r⃗) exhibits no out-of-plane component as in the domain regions. Therefore, the dI/dU map of Fig. 3B confirms that the local magnetizationM⃗ S(r⃗) in the vortex core is tilted normal to the surface (Fig. 1) (16). Figure 3D shows dI/dUline sections measured along the lines in (A) and (B) across the vortex core. It was predicted theoretically (2, 3) that the shape of a vortex core is determined by the minimum of the total energy, which is dominated by the exchange and the magnetostatic or demagnetization energy. Compared with the latter, the magneto-crystalline anisotropy energy, which is relevant for the width of bulk Bloch walls, and the surface anisotropy are negligible as long as thin films made of soft magnetic materials like Fe are used. For the thin-film limit (i.e., D = 0), it has been shown (2, 3) that the vortex width as defined by the slope of the in-plane magnetization component in the vortex center isw D=0 = 2A/Kd ≈ 6.4 nm, whereA is the exchange stiffness andK d = μ0 M sat 2/2 is the magnetostatic energy density with M sat as the saturation magnetization. This value is in reasonable agreement with the experimental result w exp = 9 ± 1 nm. The remaining discrepancy is caused by the finite thickness of the islands (D ≈ 2.5A/Kd) in agreement with more elaborate theory (2, 3).

Figure 3

Magnetic dI/dU maps as measured with an (A) in-plane and an (B) out-of-plane sensitive Cr tip. The curling in-plane magnetization around the vortex core is recognizable in (A), and the perpendicular magnetization of the vortex core is visible as a bright area in (B). (C) dI/dU signal around the vortex core at a distance of 19 nm [circle in (A)]. (D) dI/dU signal along the lines in (A) and (B). The measurement parameters were (A) I = 0.6 nA,U 0 = −300 mV and (B) I = 1.0 nA, U 0 = −350 mV.

Looking at the shape of the vortex core in more detail, Fig. 4A shows the dI/dUmap of an Fe island as measured with a mostly out-of-plane sensitive Cr-coated tip at zero field. Again, the vortex core appears as a bright spot approximately in the center of the island. A radial line profile is shown as a gray line in Fig. 4C. In order to improve the signal-to-noise ratio, the dI/dUsignal has been averaged on circles of a radiusd vc around the vortex core. Due to the circular symmetry (Fig. 1), this also removes any in-plane contribution to the measured signal, and only the part of the dI/dU signal that contains information on the perpendicular magnetization Mz remains.

Figure 4

dI/dU maps measured with an out-of-plane sensitive Cr tip at (A) zero field and (B) a perpendicular field μ0 H ext = −800 mT. The inset shows the vortex core at the position it is found at μ0 H ext = +800 mT. The measurement parameters were I = 0.5 nA and U 0 = −0.3 V. (C) Experimental (lines) and calculated data of the perpendicular magnetization of the vortex core at (•) zero field, (Δ) μ0 H ext= +800 mT, and (∇) μ0 H ext = −800 mT. (D) Magnified representation of the zero field data in (C). At a distance of ≈18 nm, both experimental and calculated data show a weak magnetization opposite to the magnetization in the vortex core.

The experimental results are compared with micromagnetic simulations (17) using Fe bulk parameters forA, M sat, and the magneto-crystalline anisotropy K. The resulting normalized perpendicular magnetizationMz /M sat is also shown in Fig. 4C (•). To compensate for the uncertainty in the knowledge of C and P S ·P T in Eq. 1, we scaled and shifted the experimental data. Thereby, we ensure for a value of 1 in the center of the core and 0 far away from the core as expected for the out-of-plane component. Excellent agreement between the measurement and the simulation is found. Experimental and calculated data are plotted at an enhanced y scale in Fig. 4D. Atd vc ≈ 18 nm, a weak component in the direction opposite to the central area appears in the calculated data (3, 4). It is also found experimentally. As already mentioned (3), this reversed component is caused by partial flux closure of the magnetic stray field of the vortex core. Although this effect only amounts to 1% ofM sat, it is recognizable in the experimental data.

We also investigated the influence of an external field on the vortex core. Figure 4B shows dI/dU maps of the island of Fig. 4A in a perpendicular field of μ0 H ext = −800 mT. The vortex core is pushed away from the center of the island, toward its right rim. This lateral movement is caused by a nonperfect alignment of the externally applied field with the island's surface normal (3). The application of a positive field (μ0 H ext= +800 mT) causes the vortex core to move in the opposite direction, toward the left rim. More important, averaged radial sections of the experimental dI/dU data reveal that the vortex becomes narrower as the external field is negative; as the field is positive, the vortex becomes broader. Qualitatively, this field-dependence can easily be understood: The energy, which has to be paid for the perpendicular magnetization of the vortex core, increases for an antiparallel and decreases for a parallel orientation to the external field. The micromagnetic simulations reproduce these trends quantitatively (19) and, moreover, show that the magnetization of the whole island, which was in-plane except for the vortex core at zero field, is tilted into the field direction.

  • * To whom correspondence should be addressed. E-mail: mbode{at}physnet.uni-hamburg.de

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