Letter pubs.acs.org/NanoLett
Collective Magnetism at Multiferroic Vortex Domain Walls Yanan Geng,† N. Lee,† Y. J. Choi,†,‡ S.-W. Cheong,† and Weida Wu*,† †
Department of Physics and Astronomy and Rutgers Center for Emergent Materials, Rutgers University, Piscataway, New Jersey 08854, United States ‡ Department of Physics and IPAP, Yonsei University, Seoul 120-749, South Korea S Supporting Information *
ABSTRACT: Cross-coupled phenomena of multiferroic domains and domain walls are of fundamental scientific and technological interest. Using cryogenic magnetic force microscopy, we find alternating net magnetic moments at ferroelectric domain walls around vortex cores in multiferroic hexagonal ErMnO3, which correlate with each other throughout the entire vortex network. This collective nature of domain wall magnetism originates from the uncompensated Er3+ moments at domain walls and the self-organization of the vortex network. Our results demonstrate that the collective domain wall magnetism can be controlled by external magnetic fields and represent a major advancement in the manipulation of local magnetic moments by harnessing cross-coupled domain walls. KEYWORDS: Multiferroic, vortex, domain walls, ErMnO3, uncompensated moments, magnetic force microscopy
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transmission electron microscopy, conductive atomic force microscopy, and piezoresponse force microscopy (PFM) at room temperature.18,19 The formation of 6-state vortices originates from the cyclic arrangement of 6 interlocked structural antiphase (α, β, γ) and ferroelectric (±) ground states (i.e., α+, β−, γ+, α−, β+, γ−),18,20,21 which is also observed in other hexagonal manganites.21,22 This intriguing network of vortex−antivortex pairs has a profound connection to graph theory, where 6-valent planar graphs with even-gons are twoproper-colorable.23 In addition, it has been shown that the formation of vortices in h-REMnO3 may be used to test the Kibble−Zurek model of cosmology.21,24 Furthermore, it turns out that charged domain walls can be stabilized in h-REMnO3 due to the topology of the vortex network. These topologically protected charged walls can be conducting and exhibit unexpected piezoelectric response.22,25,26 Despite much exciting progress on the 6-state vortex physics, the magnetic nature of these vortices was still unknown. Previous second harmonic generation (SHG) studies have suggested that ferroelectric domain walls (DWs) in millimetersize YMnO3 always pin 180° antiferromagnetic DWs. However, free 180° antiferromagnetic DWs also exist.27 To date, SHG has been unable to resolve vortex domain structure because of spatial resolution limitations (∼10 μm).28 Thus, it is of fundamental interest to explore the magnetic nature of crosscoupled structural antiphase-ferroelectric DWs (60° or 120° due to their antiphase relationship) with resolved vortex
opological defects, such as domain walls and vortices, are pervasive in complex matter such as superfluids, liquid crystals, the Earth’s atmosphere, and the early universe.1,2 Topological defects have been fruitful playgrounds for emergent phenomena.3,4 Recently, vortex-like topological defects, called magnetic skyrmions, were observed in helical magnets with broken inversion symmetry.5 The interplay between the topological spin texture of skyrmions and the spins of conduction electrons may lead to novel spintronic applications.6 Multiferroics are materials with coexisting magnetic and ferroelectric orders, where inversion symmetry is also broken.7 The cross-coupling between two ferroic orders can result in strong magnetoelectric coupling. This coupling can be used for manipulating spins with electric fields. Therefore, multiferroics are promising for energy efficient memory and sensor applications.8−11 Because the formation of domains is the hallmark of any ferroic order,12 it is of both fundamental and technological interest to visualize crosscoupled domains or walls in multiferroics. However, most multiferroics are antiferromagnets with vanishing magnetic moments, which makes imaging the domains or domain walls technically challenging. Hexagonal (h-) REMnO3 (RE = Sc, Y, Ho, ..., Lu) are an interesting family of multiferroics with high temperature ferroelectricity (TC ≈ 1200 − 1500 K)13 and antiferromagnetism (TN ≈ 70−120 K).14 Ferroelectricity is induced by structural instabilities which lead to trimerization15−17 and alleviates, presumably, the frustration of the antiferromagnetic interactions of Mn3+ spins on triangular lattices. Indeed, a 120° antiferromagnetic order of Mn3+ spins in the ab-plane sets in below the Néel temperature (TN). Recently, an intriguing 6state vortex-domain structure in YMnO3 is revealed by © XXXX American Chemical Society
Received: January 28, 2012 Revised: October 21, 2012
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dx.doi.org/10.1021/nl301432z | Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. Coupled antiphase-ferroelectric and antiferromagnetic domain walls with alternating magnetic moments around multiferroic vortex cores. a, room temperature PFM image on the (001) surface of a single crystal h-ErMnO3. The red and blue colors in the PFM image correspond to the up and down ferroelectric domains, respectively. b (c), MFM image measured at 5.5 K in a 0.2 T OOP magnetic field after −0.2 T (+0.2 T) field cooling from 100 K (>TN) to 5.5 K. The MFM images were taken at the same location as the PFM image. The color scale (Δf) is 0.8 Hz, and the lift height is 50 nm. d, a cartoon sketch shows the setup of the MFM experiment (see method in Supporting Information for details). e, the line profile of the MFM signal along the blue line in b, vertical green lines note the position of the DWs as indicated by the green arrows in b. f, a perspective view of PFM (a) and MFM (c) images with arrows representing the orientation of the uncompensated magnetic moments at structural antiphaseferroelectric DWs.
domain structure.29 Visualizing antiferromagnetic domains or DWs (especially in h-REMnO3) has been an experimental challenge, particularly due to the lack of suitable high resolution imaging techniques (Supporting Information, discussion 1). Using a homemade low-temperature magnetic force microscope (MFM),30 we observed and report here remarkable alternating net magnetic moments at interlocked antiphaseferroelectric DWs around vortex cores in multiferroic hErMnO3. Our results suggest that the intriguing DW magnetism originates from uncompensated Er3+ spins polarized by the Mn3+ antiferromagnetic order via anisotropic exchange interactions.31,32 More interestingly, the alternating DW net moments correlate over the entire vortex network and can be controlled by cooling in a magnetic field through TN. Figure 1a shows a room temperature PFM image taken on the (001) surface of a single crystal h-ErMnO3, where six alternating up (red) and down (blue) ferroelectric domains merge at a vortex core. Figure 1b (c) shows an MFM image measured at 5.5 K in a 0.2 T out-of-plane (OOP) magnetic field after −0.2 T (+0.2 T) field cooling from 100 K (>TN ≈ 80 K). The MFM images were taken at the same location as the PFM image (Figure 1a). Clearly there are line features with alternating bright and dark colors in the MFM images (Figure 1b and c), correlating with the antiphase-ferroelectric DWs around the vortex core in the PFM image (Figure 1a). Figure 1d shows the MFM measurement setup where a 50 nm Au film was deposited on the sample surface (after PFM measurements), to eliminate electrostatic stray fields from OOP ferroelectric domains. The MFM tip moment is normal to the sample surface, so that the MFM signal (cantilever resonant frequency shift Δf ∝ force gradient) is due to the OOP stray magnetic field gradient from the sample.33 Note that the
contrast inversion between Figure 1b and c is due to the reversal of local net moments because the orientation of the MFM tip moment is determined by the external magnetic field (0.2 T ≫ μ0Hc ≈ 0.02 T). Reversing the tip moment by external magnetic fields at low temperatures merely inverted the MFM contrast (see Supporting Information, Figure S1). The MFM signal along a line drawn in Figure 1b is shown in Figure 1e. The single peak profile (width ∼400 nm) of the MFM signal suggests that the local magnetization at DWs is parallel to the c-axis (see Supporting Information Figure S2 for more line profiles and cartoon explanation of OOP moments). The MFM contrast of DWs is essentially constant in 0.02−0.7 T, which excludes the possibility of local susceptibility differences as its origin34 (see Supporting Information, Figure S1). Therefore, the MFM signal, at DWs, originates from local net moments along the c-axis. In this article, we focus on the MFM results in low fields (5) on two different crystals from the same batch (see Supporting Information, Figure S3). Previous micromagnetic analysis of 180° antiferromagnetic DWs in h-YMnO3 suggested that oscillatory uncompensated Mn3+ spins rotate across the antiferromagnetic-ferroelectric
Figure S4 for the complete data set). The DW contrast, defined as the difference between bright and dark DWs, decreases sharply for T < 10 K, then more slowly at higher temperature as shown in Figure 3g, which resembles the Curie−Weiss behavior, but is inconsistent with the temperature dependence of the Mn3+ order parameter (the green dashed line in Figure 3g).36 Assuming that the MFM signal is proportional to the size of the DW net moments, we obtained a good fit (the red solid line in Figure 3g) of the temperature dependence of the DW contrast by using a phenomenological doublet model. In this model, the effective doublet ground state of Er3+ ions is split by the exchange fields from neighboring Mn3+ spins38 (Supporting Information, Discussion 2). Indeed, the DW contrast of the C
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Figure 4. A simple mode of uncompensated Er3+ moments at DWs in B2 phase. a, Mn3+ spins configuration of B2 magnetic symmetry. Solid (dotted) green triangles represent Mn3+ trimers at z = c/2 (z = 0) layer. Mn3+ ions and spins are not shown in the rest of the cartoons for clarity. b and c, the local distortion and spin configuration of Er3+ ions in type I and type II domain walls in ErMnO3, respectively. Yellow (white) circle corresponds to an Er3+ ion distorting out of (into) paper. “+” (“−”) denotes the induced Er3+ moment is out of (into) paper. d, Illustration of spin configuration of the moments of each Er3+ atomic plane in b and c near DWI and DWII domain walls; the arrows inside the red boxes represent uncompensated moments at the DWs.
realistic model of magnetic DWs would require proper consideration of the exchange and anisotropy energies and the symmetries of the order parameters.29 It has been suggested that there are two types of interlocked structural antiphaseferroelectric DWs which alternate around vortex cores, which may be the structural origin of the two types of magnetic DWs.18,43 Assuming atomically sharp Mn3+ spin variation at DWs, a single Mn3+ spin configuration in domains across DWs, and abrupt structural distortion variation across the two types of DWs, we find opposite uncompensated Er3+ moments polarized by DM exchange fields at the two types of DWs (see Supporting Information, Figure S6 and Discussion 3). The results of our simple model are shown in Figure 4b and c. A simplified form is shown in Figure 4d. Using the aforementioned caveats, our MFM results provide additional evidence of the existence of the two types of antiphase-ferroelectric DWs in h-REMnO3. Furthermore, our MFM studies also reveal that there are two distinct DW states [(DWI, DWII) = (↑,↓) or (↓,↑)] in the B2 phase that can be controlled by field cooling the sample through TN with different magnetic field orientations (Figure 1b and c). We define DWs with dark (bright) color in the MFM image, which have uncompensated moments parallel (antiparallel) with the orientation of the cooling magnetic field as DWI (DWII). It is possible that the DWI has a larger uncompensated magnetization than DWII near TN so that it is always parallel to the orientation of the cooling field. Unfortunately, our MFM results are not sufficient to pin down this possibility. We note that there are two degenerate Mn3+ spin states of B2 symmetry, which are related to each other by time reversal symmetry (Supporting Information, Figure S7). Based on our simple model, the two degenerate Mn3+ spin states provide a natural origin of the two magnetic DW states [(DWI, DWII) = (↑,↓) or (↓,↑)] because the DM exchange field switches sign when the orientation of the
MFM data essentially disappears above 80 K, in excellent agreement with TN ≈ 80 K, which can be inferred from the bulk susceptibility data (inset of Figure 3g). The doublet model has been successful in explaining the bulk (i.e., domains) partial RE3+ ordering in other h-REMnO3 materials (RE = Ho, Tm, Yb) as has been revealed by X-ray magnetic resonant scattering, neutron diffraction, and Mössbauer spectroscopy.38−40 The good agreement we find between the doublet model and our MFM data suggests that this model is also applicable for the DW magnetism. Therefore, we propose that the DW net magnetic moments come from uncompensated Er3+ spins polarized by the exchange fields from neighboring Mn3+ spins. It is believed that the effective exchange fields originate from anisotropic exchange interactions, for which the antisymmetric components are the well-known Dzyaloshinskii−Moriya (DM) interactions.31,32 The presence of DM interactions are the key ingredient for noncollinear spin orders, which induce ferroelectricity by breaking inversion symmetry and become multiferroic.7,41 In multiferroic h-REMnO3, the DM interactions between RE3+ and Mn3+ spins are likely responsible for inducing the partial RE3+ antiferromagnetic order.38−40 The dipolar interactions between RE3+ and Mn3+ spins are of order of 1 K and thus are too weak to account for the observed coupling strength (∼10 K).38 However, dipolar interactions between RE3+ ions may be responsible for the additional RE3+ ordering below 5 K.35,38 In zero or low magnetic field (
