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Real-Space Observation of Helical Spin Order

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Science  20 Jan 2006:
Vol. 311, Issue 5759, pp. 359-361
DOI: 10.1126/science.1120639

Abstract

Helical spin order in magnetic materials has been investigated only in reciprocal space. We visualized the helical spin order and dynamics in a metal silicide in real space by means of Lorentz electron microscopy. The real space of the helical spin order proves to be much richer than that expected from the averaged structure; it exhibits a variety of magnetic defects similar to atomic dislocations in the crystal lattice. The application of magnetic fields allows us to directly observe the deformation processes of the helical spin order accompanied by nucleation, movement, and annihilation of the magnetic defects.

Magnetic materials are generally characterized by spin moments on respective atomic sites aligned all parallel or site-alternately antiparallel. However, many exceptions to this rule exist in which the direction of spin moments varies in space. A prototypical example is the gradual moment variation (Bloch type or Néel type) within the magnetic domain wall region in a ferromagnet (1) or the somewhat long-period (over several atomic sites) spin density wave as observed in Cr metal (2). The helical spin order (Fig. 1A) is another such example: Spins on some crystallographic planes are all parallel, but their direction rotates by a constant angle in going from one plane to a neighboring plane along the helical axis. The helical spin order was first proposed as a way to interpret neutron diffraction results for MnO2 crystal (3). Similar helical spin orders have been observed in materials such as rare-earth metals and alloys (4) as well as members of the metal silicide family, including MnSi (5, 6) and Fe1–xCoxSi (0.05 ≤ x ≤ 0.8) (7, 8).

Fig. 1.

Illustration of helical spin order. (A) Helical spin order with the helical axis along the x axis in an orthogonal xyz system. Spins are all parallel at a yz plane, and their direction rotates by a constant angle from one plane to a neighboring plane along the helical axis. (B) Magnetization distribution projected on the xy plane for this helical spin order, which changes as a sinusoidal wave.

The relative orientation of spin moments between magnetic planes affects the flow of electric current. The control of the spin-dependent charge transport in terms of the manipulation of the local magnetic structure forms the basis of spinelectronics or spintronics (912), as exemplified by the magnetoresistive field sensor in computer hard disks and the magnetic tunneling junction in magnetic random access memory (MRAM). In this context, the helical spin order can be viewed as a regular array of the magnetic domain walls every helical period. Therefore, the real-space observation of the local modification or deformation of the helical order (as induced by temperature change, magnetic field, and current injection) would provide a challenging arena to study the nanometric magnetic domain structure as well as to explore the possible spintronic application of such a self-organized magnetic nanostructure.

The family of Fe1–xCoxSi with cubic but non-centrosymmetric (B20) structure is known to exhibit a helical spin order, with a relatively long period (>30 nm) in a concentration range 0.05 ≤ x ≤ 0.8 (7, 8, 11). The helical spin order is due to the Dzyalosinsky-Moriya (DM) interaction because of the lack of centrosymmetry of the lattice (1316). The helix period is governed by the ratio of the DM interaction to the ferromagnetic spin exchange interaction (15, 16). The Néel temperature TN and the helix period for the x = 0.5 crystal we investigated here are 38 K and 90 nm along the [100] direction, respectively.

Figure 2 shows a typical image of the helical spin order of Fe0.5Co0.5Si as obtained by Lorentz transmission electron microscopy (17). Shown in Fig. 2, A and B, are overfocused Lorentz images taken near the [001] zone axis orientation at 40 and 20 K, respectively. The image at 20 K (< TN) clearly shows periodic stripe patterns running normal to the [100] axis. In the focused image the patterns disappeared, confirming that the image is magnetic in origin. The magnetization distribution obtained by the transport of intensity equation (TIE) analysis (18, 19) of the over- and under-focused images is shown in Fig. 2C. The direction and amplitude of the magnetization are represented by changes in color and brightness, respectively. The green and violet stripe pairs in the figure reflect the regions with opposite magnetic orientation; the darker area indicates the smaller amplitude of the local magnetization. The sinusoidal modulation in Fig. 2D (a profile of the amplitude of the magnetization along the line indicated in Fig. 2C) indicates that the spin order is helical, with a period of 90 nm along [100], in good agreement with the results determined by neutron diffraction (7, 8).

Fig. 2.

Real-space observation of the helical spin order in Fe0.5Co0.5Si. (A and B) Overfocused Lorentz images (defocus length +1.4 mm) obtained at 40 and 20 K, respectively. Electron incidence is nearly parallel to the [001] direction. Stripe contrasts seen in (B) are of magnetic origin. (C) A color representation of magnetization distribution [projected onto the (001) plane] obtained by the TIE method, corresponding to the state shown in (B); the direction and amplitude of the magnetization are represented by changes in color and brightness with respect to the color wheel. (D) Amplitude profile of the magnetization along the line shown in (C). The sinusoidal modulation indicates that the spin order is helical with a period of 90 nm along [100].

The real-space observation has, however, revealed the existence of defects of this periodic magnetic state, analogous to atomic boundary and dislocation in a crystalline lattice (1, 20). Figure 3 shows a low-magnification image of the magnetization distribution (17). An electron diffraction study confirmed that the observed area is a single crystallographic domain. The spin stripes are almost straight but are locally and slightly bent. In addition to the spin stripes, wavy dark line contrasts can be seen, nearly perpendicular to the helical axis. Careful observation shows that the spin stripes can be seen even inside the dark-contrast regions (Fig. 3B). The dark contrasts indicate the region where the helical spin order is less regular. Here, we define the helical magnetic “domain” as the region in which the periodic order of spins with the well-defined helical axis direction shows up apart from the presence of topological defects. Therefore, we may call the dark-contrast region a helical magnetic domain boundary.

Fig. 3.

Helical magnetic domain structure involving magnetic defects. (A) Magnetic domain boundaries are seen as dark wavy line contrasts in addition to the regular helical spin order. The image colors have the same meaning as in Fig. 2C. (B) Magnified image of the boxed part in (A), exhibiting a helical magnetic edge dislocation (arrow). (C) A schematic showing the helical magnetic domain and boundary. The fine and thick lines represent the regular helical spin order and the magnetic domain boundary, respectively. Note that the orientation of the helical axis (denoted by arrows) varies slightly from domain to domain through a boundary. (D) A schematic showing the magnetic edge dislocation.

The helical magnetic domain boundary is not straight but wavy and diffuse. The width between two neighboring boundaries (domain size) is hundreds of nanometers along the [100] direction. The domain structures are found to vary in shape and size after the sample is heated above TN and then cooled to the original temperature (20 K); they are also sensitive to magnetic fields, as shown below. Most of the neighboring domains are substantially characterized by the slight misorientation of the helical axis, not by a change of the helix period (Fig. 3C).

Another interesting feature is the existence of topological magnetic defects. A branching of the spin stripe (Fig. 3, B and D) looks just like an edge dislocation in crystal, whose geometry is described by an extra atomic half-plane inserted into the lattice (1). What we have observed in this magnetic system is the elementary edge dislocation whose Burgers vector b, defined as the plane difference, is (±½)d parallel to [100] (where d is a helix period). Many edge dislocations appear to gather around the domain boundaries and to connect the spin stripe smoothly across a boundary.

Our results raise questions about the origin and role of helical magnetic defects. In all ferromagnets, domain structure is inherent because domains form to reduce the magnetostatic energy (1, 21). This is not the case for the present helical magnet as well as for antiferromagnets (22, 23). However, helical magnetic domain boundaries are wavy and diffuse, and they mainly run normal to the helical axis, invalidating the magnetostatic mechanism. Furthermore, whenever the sample was cooled through the Néel temperature, the experiment showed similar images, but the dislocations and the domain boundaries did not always appear at the same locations in the sample. Thus, magnetic defects are not strongly pinned by atomic defects or by strain.

It is known that atomic defects such as boundary and dislocation play a crucial role in mechanical deformation (1, 20). For example, as materials deform under increasing stress, dislocations are generated, which in turn affect the deformation properties. By analogy, the magnetic defects may play some role in the deformation of the helical spin order. We therefore investigated the deformation dynamics of the helical spin order by applying magnetic fields. The sample was first cooled to 20 K and magnetic field H was then gradually increased along either the [110] or the [100] axis. Figure 4 shows the changes of helical magnetic domains of the same sample. In the case of H // [110] (Fig.4, A to D), the helical spin order is easily deformed to contain more magnetic defects. Even with small fields (<10 Oe), some magnetic domain boundaries and dislocations are observed to move. When the magnetic field is increased (Fig. 4B), new domain boundaries and dislocations are nucleated. The domain boundaries become more bent. The nucleation of the edge dislocations is possibly due to the tendency for the spin stripes to remain equidistant. With H ∼50 Oe, the helical axes locally begin to rotate from [100] to the magnetic field direction [110]. Upon further increasing H to 60 Oe, the spin stripes are almost rotated so that the helical axis is along the direction of H (Fig. 4C), although the image becomes noisy because of the presence of H. Upon decreasing the magnetic field to zero (Fig. 4D), some of the domains come back to the [100] axis while others remain with the [110] axis, resulting in the irreversible formation of magnetic domains. Note that magnetic fields do not alter the helix period. Such a change of the helical magnetic domains as induced by magnetic fields has been reported in neutron diffraction studies of MnSi (5) and FeGe (24). We have also made a “real-time” observation of the deformation with temperature under magnetic fields (25). When magnetic field is applied along the helical axis [100] (Fig. 4F), the helical magnetic domains grow in size, accompanying the annihilation of the magnetic defects. As a result, the spin stripes as well as the domain boundaries become regular and straight, in a manner analogous to the annealing process in crystal growth. Thus, the deformation of the helical magnetic domain is characterized by nucleation, movement, and annihilation of the magnetic defects.

Fig. 4.

Helical magnetic domain structure modified by applying magnetic field along the [110] or the [100] direction at 20 K. (A) Helical domain structure of the sample cooled to 20 K under the zero magnetic field. Electron incidence is nearly parallel to the [001] direction. (B) When the applied field H is 40 Oe, new magnetic domain boundaries and dislocations are nucleated. (C) With 60 Oe, the spin stripe rotates along the direction of the magnetic field [110]. The noisy image is due to a large image distortion by magnetic field. (D) Upon decreasing the field to zero, some domains remain with the helical axis along [110]. This transformation is irreversible with magnetic fields. (E) The same area as in (A). Note that the domain structures in (A) and (E) are different because of the different thermal history. (F) When magnetic field is applied along the [100] direction, the helical magnetic domains grow in size while edge dislocations diminish in number. The image colors have the same meaning as in Fig. 2C. Some magnetic edge dislocations are marked by open circles.

Our real-space observations of Fe0.5Co0.5Si have revealed the unexpected existence of magnetic defects such as magnetic domain boundary and dislocation. In addition, by applying magnetic fields, we have observed the field direction–dependent change of the magnetic domains, in which the magnetic defects mediate the nanometer-scale modification of the magnetic structure.

Supporting Online Material

www.sciencemag.org/cgi/content/full/311/5759/359/DC1

Materials and Methods

Fig. S1

References and Notes

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