Influence of the Local Atom Configuration on a Hexagonal Skyrmion

Letter pubs.acs.org/NanoLett

Influence of the Local Atom Configuration on a Hexagonal Skyrmion Lattice Kirsten von Bergmann,* Matthias Menzel, André Kubetzka,* and Roland Wiesendanger Department of Physics, University of Hamburg, 20355 Hamburg, Germany S Supporting Information *

ABSTRACT: Spin-resolved scanning tunneling microscopy is used to reveal a commensurate hexagonal nanoskyrmion lattice in the hcp stacked Fe monolayer on Ir(111). The exact nature of the spin configuration is due to magnetic interactions between the Fe atoms and the Ir substrate, either originating from polarization effects, or due to a three-site hopping mechanism of the Dzyaloshinsky−Moriya interaction leading to a canting of the Dzyaloshinsky− Moriya vector with respect to the interface. KEYWORDS: Skyrmions, magnetism, STM, DM-interaction, TAMR

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alignment of spins Si and Sj with unique rotational sense: EDM = D(Si × Sj). Here, the maximum DM energy can only be gained for a certain configuration, and deviations from that will lower the total energy gain. Experimentally, skyrmion lattices have been found in chiral crystal structures1,2 and in an ultrathin biatomic PdFe layer on an Ir(111) substrate.4 In these systems the magnetic zero-field state is a spin spiral due to a competition between ferromagnetic exchange and DM interaction. Upon the application of an external magnetic field, a skyrmion lattice emerges which is eventually saturated to a ferromagnetic state. An example of a skyrmion lattice that exists also in the absence of an applied magnetic field is the square nanoskyrmion lattice in the fcc-stacked Fe monolayer on Ir(111), which has been identified using spin-polarized scanning tunneling microscopy (SP-STM) and density functional theory.3,12,13 This complex magnetic state contains roughly 13 atoms per skyrmion. It not only exists without external magnetic field but also stays unchanged in fields up to 9 T.6 A recent temperaturedependent study reported the decrease of magnetic corrugation amplitude with increasing T until it is no longer detected at about 28 K.14 The origin of the nanoskyrmion lattice is attributed to a small nearest neighbor Heisenberg exchange interaction due to the Fe−Ir hybridization which in combination with the DM interaction sets the period of the magnetic state; the four-spin interaction couples the spins to form a two-dimensional magnetic state, and this energy gain is maximized by the formation of a nanoskyrmion lattice with square symmetry.3 The polymorph of a material plays a significant role for its electronic and magnetic properties, e.g., α-Fe (bcc) is ferromagnetic while γ-Fe (fcc) has been classified as paramagnetic.15 In addition the stacking of hexagonal layers of

agnetic skyrmions are noncollinear magnetic states that can condense into two-dimensionally ordered states called skyrmion lattices.1−6 The magnetic texture of a skyrmion is characterized by spins covering the entire unit sphere, thereby representing a topologically distinct state as compared to the topologically trivial ferromagnetic state. When the magnetization in the center of a skyrmion is pointing up, then there is a coherent rotation of the magnetization with distance until the spins are pointing downward at the perimeter. Skyrmions occur with unique rotational sense for a given system due to the Dzyaloshinsky−Moriya (DM) interaction, which favors an orthogonal spin arrangement, and is a driving force for the formation of such noncollinear magnetic states. The DM interaction is due to spin−orbit coupling and can be nonzero when the inversion symmetry is broken. This is the case not only for chiral crystal structures but also at any surface or interface.3,4,6−9 Following the phenomenological symmetry selection rules from Moriya,10 the allowed directions of the DM vector can be deduced, and for chiral bulk structures typically helical spin spirals or skyrmions are proposed,1,2 whereas the DM vector at an interface typically leads to cycloidal spin rotations.3,4,6−9 Magnetic skyrmions offer great potential for future spintronic devices.5,8,11 One promising route is the use of multilayers, where the Dzyaloshinsky−Moriya (DM) interactionnecessary for the formation of a skyrmionis induced by the intrinsic inversion symmetry breaking at the interfaces.6,7 With state-of-the art technology multilayers can be manufactured on a large scale with a high degree of ordering. However, there are always defects like grain boundaries or impurities present, and up to now little is known about the influence of the precise atom arrangement on noncollinear spin textures. While for ferromagnetic Heisenberg exchange local disorder does not play a big role, it is well-known from antiferromagnetic systems that many atomic arrangements, e.g., triangularly arranged atoms, lead to geometric frustration. Similar results can be expected for the DM interaction D which favors an orthogonal © XXXX American Chemical Society

Received: February 6, 2015 Revised: March 13, 2015

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DOI: 10.1021/acs.nanolett.5b00506 Nano Lett. XXXX, XXX, XXX−XXX

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hcp islands is limited to some 10 nm as the growth of double layer Fe occurs for larger islands. To reinvestigate the magnetic state of hcp Fe on Ir(111), we have reduced the measurement temperature compared to a previous study.13 Figure 2 shows SP-STM17 constant-current

atoms has also been found to have an influence on the electronic and thus magnetic properties of condensed matter: While the calculated spin spiral dispersions for fcc and hcp stacking of Fe on Ir(111) are similar,13 SP-STM measurements at T = 13 K have demonstrated the existence of a nanoskyrmion lattice in fcc-Fe, but no magnetic signal was found for hcp-Fe islands in zero field.13 However, when an hcp area is attached to an fcc area, a rapidly decaying magnetic corrugation with a similar periodicity has been observed also in the hcp-Fe close to the lateral fcc/hcp interface.13 Recent theory investigations on the system of a Pd monolayer on fccFe/Ir(111) have proposed different spin spiral periods and skyrmion phase space behavior depending on the stacking of the overlayer.9 SP-STM measurements on the system of Mn on Ag(111) have led to the conclusion that within the noncollinear Néel state the fcc and hcp stacking exhibit different magnetization directions of the atoms.16 Here we present spin-resolved STM data of the hcp-Fe monolayer on Ir(111) that show a hexagonal skyrmion lattice as the magnetic ground state. Atomic-scale STM measurements allow the identification of the exact nature of this spin texture. These experimental observations can be explained only when the interactions of the Fe atoms with the Ir substrate atoms are taken into account, which break the 6-fold rotational symmetry of the hexagonal Fe layer. This demonstrates, that not only the macro-scale polymorph, but also the precise atom configuration can play a role for nanoscale magnetic properties of materials, selecting one out of several similar magnetic states. The system of Fe on Ir(111) is investigated in the submonolayer coverage regime using STM, and Figure 1

Figure 2. SP-STM constant-current images of hcp-Fe islands. (a) An hcp island without magnetic contrast and an fcc stripe with magnetic contrast at B = 0 T. (b) Same area as in a but in an applied magnetic field of B = +2 T, exhibiting a hexagonal magnetic superstructure in the hcp island. (c) Larger hcp island showing the hexagonal magnetic state at B = 0 T. (d) An hcp island with double layer Fe in the center showing different magnetic signals at B = 0 T, see magnified views at the bottom; the histograms show the height distribution of the two magnetic domains. (e) Same island as in d at B = +2T showing mostly the hexagonal magnetic superstructure with dark dots. (All: raw data, Cr-bulk tip, T = 7.5 K, U = +50 mV, I = 0.5 nA, scale bar and height color apply to all, except to insets of d).

images at T = 7.5 K. For hcp-Fe islands on the order of about 10 nm in size no magnetic contrast is observed at B = 0 T; see Figure 2a. However, when a magnetic field is applied normal to the surface (b) a magnetic superstructure emerges: it has a period of about 1 nm but opposed to the nearly square nanoskyrmion lattice of the fcc Fe monolayer (see bottom right), the symmetry is hexagonal, and dark dots periodic in directions, i.e., perpendicular to the island edges, are observed. Figure 2c and d display larger triangular shaped hcp islands, which exhibit the hexagonal magnetic superstructure already at zero magnetic field; the hcp island of Figure 2d has a double layer island in the center. We observe no influence of the island edge or the double-layer island on the magnetic state of the hcp-Fe monolayer, except for a 1−2 nm wide rim. Neither do we have any indications for confinement effects due to the boundaries, and thus we consider the observed hcp-Fe areas large enough to develop the magnetic ground state of an

Figure 1. Overview pseudo-3D topography image of Fe on Ir(111). At room temperature the Fe monolayer grows pseudomorphic as hcp or fcc monolayer high islands and fcc monolayer stripes at the Ir step edges (see also S1); on top of most islands double-layer high patches can be observed. (Image area 600 nm × 600 nm).

shows a topographic image. While deposition of Fe at elevated temperature leads to step flow growth at the Ir step edge only, at lower substrate temperature also triangular shaped islands with edges along close-packed atomic rows, i.e., directions, are observed.13 The stacking of the islands can be easily identified, where in Figure 1 (and throughout the paper) fcc-Fe forms upward pointing triangular islands and hcp-Fe triangular islands point downward (see also S1). While the Ir step edges nucleate the growth of fcc Fe stripes the majority of islands on the terraces is hcp. Thus, broad terraces are favorable for the study of hcp Fe areas. However, the size of uncovered B

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Nano Letters extended hcp-Fe monolayer. As obvious from the magnified images below, the island of Figure 2d shows different appearances: at the top left corner the magnetic state is imaged as a hexagonal pattern of bright dots, the top right area looks inverted with hexagonally ordered dark dots, and toward the bottom corner of the island the contrast vanishes. When a magnetic field is applied normal to the surface (Figure 2e), the hexagonal magnetic superstructure tends to become uniform, i.e., most parts of the island show the hexagonal pattern of dark dots. From this set of measurements, we can conclude that the magnetic ground state of hcp Fe on Ir(111) is hexagonal with a period of about 1 nm. At B = 0 T, we observe either no magnetic superstructure due to thermal excitations, i.e., rapid switching between different magnetic states close in energy, or we find one of two different hexagonal contrasts which we interpret as two oppositely magnetized domains. The imbalance of bright and dark areas within each domain (see height histograms in insets to Figure 2d) implies a net magnetic moment within the magnetic unit cell. This immediately explains the stabilization of the magnetic state due to a preference of one of the magnetic domains in external magnetic field. To propose a model for the spin structure of the magnetic ground state of the hcp-Fe monolayer on Ir(111), we compare our findings with previous periodic spin textures. The external magnetic field-stabilized hexagonal skyrmion lattice states in the chiral B20 materials1,2 and the system of PdFe4 are induced from a zero-field ground state of spin spirals with defined rotational sense. This mechanism for skyrmion lattice formation is different from the one proposed for fcc Fe on Ir(111),3 where the four-spin interaction couples spin spirals to form a two-dimensionally periodic magnetic state already without applied magnetic field. Inspired by these two different mechanisms for skyrmion lattice formation by the coupling of spin spirals (either by external magnetic field or by higher order terms) we propose that the hexagonal magnetic state of hcp-Fe can be described by a superposition of three cycloidal symmetry-equivalent spin spirals running along with identical rotational sense. The resulting multi-Q state has a net magnetic moment, in agreement with the experimental finding, and can be interpreted as a hexagonal skyrmion lattice. Without the detailed knowledge of the different magnetic interaction strengths we cannot elucidate the origin of the different symmetry of the nanoskyrmion lattices in hcp- and fcc-Fe, i.e., hexagonal and square, nor the reduced thermal stability of the magnetic state in hcp as compared to fcc. In contrast to the incommensurate magnetic state in fcc-Fe, we will show below that the magnetic unit cell for hcp-Fe is commensurate and contains 12 Fe atoms. The positioning of this commensurate magnetic state relative to the hexagonal atomic lattice can be done in different ways, yielding two different symmetry-inequivalent magnetic states (see also S2): either the maximum out-of-plane magnetization (up, red), i.e., the point of constructive superposition of all three spin spirals, is on top of an atom, see sketch in Figure 3a, and we will refer to this state as on-top-state; or it is in the center of a triangle spanned by three atoms, see sketch of the magnetic state in Figure 3b, called hollow-state from here on. Note that in the sketch for the hollow-state (b) the center of a downward pointing atom triangle was chosen (cf. dashed yellow triangle); when an upward pointing atom triangle is used one obtains the same state rotated by 180°. To compare the on-top- and hollow-state with our experimental data, we

Figure 3. Skyrmion lattice states with 12 atoms per skyrmion. (a,b) Sketches of the on-top- and the hollow-states, which are constructed by mapping the same multi-Q state onto the hexagonal atomic Fe lattice with the up magnetization (red) on top of an atom, and in between three atoms, respectively. Yellow arrows visualize the constituting spin spirals, where the length defines the full spin rotation by 360° starting from an up magnetization. Balls represent Fe atoms and arrows their magnetic moment direction; color refers to the out-of-plane component where red is up and green is down. Below are simulated SP-STM topographic images of the same area as displayed in the top panels with the tip magnetized in +z and −z (out-of-plane) direction.

simulate SP-STM images18 with out-of-plane magnetized tips, see bottom panels in Figure 3. Both of the proposed magnetic states show a hexagonal magnetic pattern as observed experimentally, meaning that from the measurement of Figure 2, we cannot distinguish if both or only one of the magnetic states is realized in our system. To characterize complex magnetic states it has proven to be useful to search for tunneling anisotropic magnetoresistance (TAMR) contrast and crosscheck it with the tunnel magnetoresistance (TMR) contrast from SP-STM measurements.19 TAMR contrast can be obtained with nonmagnetic STM tips and arises due to spin−orbit coupling within the magnetic sample (see also S3). Figure 4a displays a constant-current image of Fe on Ir(111), which shows fcc, hcp and Fe double layer areas as indicated. The nonmagnetic nature of the tip is confirmed by the typical TAMR contrast of the fcc nanoskyrmion lattice observed as stripes along the diagonal of the magnetic unit cell at small positive bias voltage.3 The hcp area is shown at a closer view in the constant-current image of Figure 4b. We find that the dominant TAMR contrast is hexagonal with bright dots at a distance of about 0.54 nm along a closed-packed row, i.e., twice the nearest neighbor distance, leading to 4 atoms in the supercell. To identify which of the two proposed spin structures, i.e., the on-top- or hollow-state, is realized in the hcp Fe monolayer on Ir(111), we simulate TAMR-STM images19 using the out-of-plane direction as quantization axis, see Figure 4c,d; in the simulation, γ is a measure for the strength of the TAMR contrast distinguishing between out-of-plane and in-plane magnetized atoms (see also S3). All simulated images show a hexagonal superstructure. However, for the on-top-state (c) a supercell with 12 atoms dominates and only the simulation for the hollow-state (d) with +γ is in agreement with the data: in the image all in-plane magnetized atoms (cf. Figure 3b) appear brighter. By comparison with simulated TAMR-STM images of slightly C

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Figure 4. Assignment of the magnetic state by TAMR-STM. (a) STM constant-current overview image with TAMR stripe contrast on fcc Fe at U = +10 mV, I = 0.5 nA, z-scale 30 pm. (b) STM constant-current image of the hcp Fe monolayer (area indicated in a by gray box) exhibiting hexagonally arranged dots as TAMR contrast at U = +20 mV, I = 5 nA, z-scale 20 pm (both: raw data, T = 7.5 K, B = 0 T). (c,d) Simulated TAMR-STM topographic images with |γ| = 0.1 for the ontop- and hollow-state, respectively, same area as in Figure 3a and b.

compressed or expanded hexagonal nanoskyrmion lattice states (see S4), we can rule out an incommensurability of the magnetic state with the atomic lattice, justifying the choice of commensurate spin spirals for the construction of the magnetic state. Thus, we conclude that the magnetic ground state of the hcp Fe monolayer on Ir(111) can be described by a commensurate multi-Q state that is positioned on the atomic lattice in a way that it forms the hollow-state, see sketch in Figure 3b. The selection of this specific magnetic state is due to the atomic-scale size of the skyrmions, which leads to slightly different interaction energies when a multi-Q state is mapped onto the atomic lattice in two symmetry inequivalent ways (see also S5). As demonstrated previously for the fcc Fe monolayer on Ir(111), TAMR contrast from different quantization axes can be observed, when allowed by symmetry.19 An island of the hcp-Fe monolayer is shown in Figure 5a,b. Here, we observe not only the hexagonal TAMR contrast with four atoms in the supercell at +12 mV (a), but at a bias voltage of −12 mV (b) also triangular depressions with the magnetic periodicity, i.e., twelve atoms per supercell, are found. A closer view of these two different appearances is shown in (c) and (d). The triangular shaped depressions can be reproduced in TAMRSTM simulations, see inset to Figure 5d, when also contributions from a different quantization axis are considered (see also S3). Areas with periodic TAMR contrast in (a) and (b) are separated by broad, slightly modulated brighter lines, which tend to be in the vicinity of the defects that are imaged as bright spots. A close inspection of the data reveals that the patterns of hexagonally arranged dots and triangular depressions are strictly periodic within one area but are phase-shifted across the broad lines. This means that the broad lines are the transition regions between phase shifted magnetic domains, i.e., the commensurate magnetic unit cells are shifted with respect to one another (see also S6). While we have now observed the occurrence of magnetic domains (Figure 2) and phase domains (Figure 5), it is striking

Figure 5. STM constant-current images with different TAMR contributions. (a,b) Hcp island with bright dots (U = +12 mV) and with triangular depressions (U = −12 mV), respectively. (c,d) Closer views of the hcp phase domain indicated by the box in a,b with STM topography simulations as insets (γ1 = +0.1 and γ1 = +0.1, γ2 = +0.1, respectively). (All: raw data, T = 4.2 K, B = 0 T; (a,b) I = 1 nA, z-scale 20 pm; (c,d) I = 3 nA, z-scale 15 pm).

that there are no rotational domains, i.e., the triangular depressions in all domains in Figure 5b point in the same direction. As already pointed out in connection with the sketch of the magnetic hollow-state, Figure 3b, a positioning of the multi-Q state relative to the atomic lattice is possible either with the up-magnetization in the center of a down- or an upward pointing atom triangle, see circles in Figure 6a,b. However, in the measurement of Figure 5b only one of these two possible hollow-states is observed and the sketches in Figure 6 are used in the following for a reasoning about the origin for this selection. When only the Fe−Fe magnetic interactions are considered the two states are degenerate in energy, and thus they cannot be responsible for the observation of only one of the states. Only when also magnetic interactions between the Fe atoms and the Ir atoms are taken into account the degeneracy of the two hollow states can be lifted, as the position of the magnetic states relative to the Ir atoms is different. In the following we want to propose two different mechanisms that can favor one state over the other. First, it is expected that the underlying Ir atoms get polarized by the adjacent Fe atoms.12 When comparing the sketches in Figure 6a and b, one finds that one of the hollow-states has an Ir atom in the center of the group of the three red atoms (a) and the other one does not (b). This implies that the size of the polarization of the Ir atoms is different for the two states (see also S7), which then results in an energy difference between the two states. D

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Ir substrate. We find that both the polarization of the Ir atoms, as well as the atomistic DM interaction, could be responsible for the lifting of the degeneracy between these two hollowstates. While we cannot judge which of the two identified mechanisms plays the decisive role here, we have demonstrated that the precise atomic configuration has a significant influence on the exact spin structure of nanoscale noncollinear states.

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ASSOCIATED CONTENT

* Supporting Information S

Further information on the stacking, the multi-Q state, the TAMR, the commensurability, interaction energies, phase domain boundaries, and polarization of the Ir atoms. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected].

Figure 6. Magnetic interaction with the substrate. (a,b) Sketch of the two different hollow-states due to a different positioning of the upmagnetization (red) of the magnetic state, leading to the three red Fe atoms arranged to form a down- or upward-pointing atom triangle, respectively (see circles); in a there is an Ir atom in the center of the group of the three up-magnetized (red) Fe atoms. (c,d) Sketches to illustrate the canting of the DM vector (blue) due to the 3-sites hopping mechanism for a pair of Fe atoms for each of the two states.

Author Contributions

K.v.B., M.M., and A.K. performed the experiments; A.K. performed the STM simulations; K.v.B. analyzed the data and wrote the manuscript; all authors discussed the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank S. Heinze for discussions and the DFG (SFB668) for financial support.

Another interaction with the substrate, which may also lift the degeneracy of the two hollow-states, is the DM interaction. While this interaction is also a pairwise interaction, it is considered to be mediated by the substrate, and a three-site hopping mechanism has been proposed20−22 where the electrons hop from one Fe atom via the heavy Ir atom, where they experience significant spin−orbit coupling, to the next Fe atom. Due to this hopping the DM vector is perpendicular to the plane spanned by these three atoms. For our system this means that the DM vector is not in the plane of the interface as usually assumed,8 which would lead to a degeneracy of the two states; instead it is canted, see Figure 6c,d, leading to different DM energies for the two hollow-states. For the example of the pair of Fe atoms shown in Figure 6c,d, one can easily see that the DM interaction energy (EDM = D(Si × Sj)) is different for the two cases. The DM energy can be calculated for each Fe−Fe atom pair of the two states and when we assume that the DM-interaction is similar to the one in the fcc Fe monolayer on Ir(111),3 i.e., D = −1.8 meV/Fe atom, this canting of the DM vector leads to a difference in total energy of 0.02 meV per atom or 0.26 meV per magnetic unit cell, with the state sketched in Figure 6a having the lower energy compared to Figure 6b due to the DM interaction. In conclusion, using SP- as well as TAMR-STM, we have revealed the spin structure of the hcp-stacked Fe monolayer on Ir(111). It forms a commensurate hexagonal nanoskyrmion lattice, which naturally has two magnetic domains with opposite net moments perpendicular to the plane. Comparing TAMRSTM measurements with simulations we can exclude the ontop-state and find that the hollow-state with 3-fold symmetry is the magnetic ground state. The experimental observation that only one of two possible rotational domains of the magnetic hollow-state (considering only the Fe atoms) is realized is attributed to the magnetic interaction of the Fe atoms with the

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