Domain switching in single-phase multiferroics

Multiferroics are a time-honoured research subject by reason for their tremendous application potential in the information industry, such as in multi-state information storage devices and new types of sensors. An outburst of studies on multiferroicity has been witnessed in the 21st century, although this field has a long research history since the 19th century. Multiferroicity has now become one of the hottest research topics in condensed matter physics and materials science. Numerous efforts have been made to investigate the crosscoupling phenomena among ferroic orders such as ferroelectricity, (anti-)ferromagnetism, and ferroelasticity, especially the coupling between electric and magnetic orderings that would account for the magnetoelectric (ME) effect in multiferroic materials. The magnetoelectric properties and coupling behavior of single phase multiferroics are dominated by their domain structures. It was also noted that, however, the multiferroic materials exhibit very complicated domain structures. Studies on domain structure characterization and domain switching are a crucial step in the exploration of approaches to the control and manipulation of magnetic (electric) properties using an electric (magnetic) field or other means. In this review, following a concise outline of our current basic knowledge on the magnetoelectric (ME) effect, we summarize some important research activities on domain switching in single-phase multiferroic materials in the form of single crystals and thin films, especially domain switching behavior involving strain and the related physics in the last decade. We also introduce recent developments in characterization techniques for domain structures of ferroelectric or multiferroic materials, which have significantly advanced our understanding of domain switching dynamics and interactions. The effects of a series of issues such as electric field, magnetic field, and stress effects on domain switching are been discussed as well. It is intended that an integrated viewpoint of these issues, as provided here, will further motivate synergistic activities between the various research groups and industry towards the development and characterization of multiferroic materials. Disciplines Engineering | Physical Sciences and Mathematics Publication Details Jia, T., Cheng, Z., Zhao, H. & Kimura, H. (2018). Domain switching in single-phase multiferroics. Applied Physics Reviews, 5 (2), 021102-1-021102-23. This journal article is available at Research Online: http://ro.uow.edu.au/aiimpapers/3163 Domain switching in single-phase multiferroics Tingting Jia, Zhenxiang Cheng, Hongyang Zhao, and Hideo Kimura Citation: Applied Physics Reviews 5, 021102 (2018); doi: 10.1063/1.5018872 View online: https://doi.org/10.1063/1.5018872 View Table of

Multiferroics are a time-honoured research subject by reason for their tremendous application potential in the information industry, such as in multi-state information storage devices and new types of sensors.An outburst of studies on multiferroicity has been witnessed in the 21st century, although this field has a long research history since the 19th century.Multiferroicity has now become one of the hottest research topics in condensed matter physics and materials science.Numerous efforts have been made to investigate the cross-coupling phenomena among ferroic orders such as ferroelectricity, (anti-)ferromagnetism, and ferroelasticity, especially the coupling between electric and magnetic orderings that would account for the magnetoelectric (ME) effect in multiferroic materials.The magnetoelectric properties and coupling behavior of single phase multiferroics are dominated by their domain structures.It was also noted that, however, the multiferroic materials exhibit very complicated domain structures.Studies on domain structure characterization and domain switching are a crucial step in the exploration of approaches to the control and manipulation of magnetic (electric) properties using an electric (magnetic) field or other means.In this review, following a concise outline of our current basic knowledge on the magnetoelectric (ME) effect, we summarize some important research activities on domain switching in single-phase multiferroic materials in the form of single crystals and thin films, especially domain switching behavior involving strain and the related physics in the last decade.We also introduce recent developments in characterization techniques for domain structures of ferroelectric or multiferroic materials, which have significantly advanced our understanding of domain switching dynamics and interactions.The effects of a series of issues such as electric field, magnetic field, and stress effects on domain switching are been discussed as well.It is intended that an integrated viewpoint of these issues, as provided here, will further motivate synergistic activities between the various research groups and industry towards the development and characterization of multiferroic materials.V C 2018 Author(s).All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).https://doi.org/10.1063/1.5018872Authors to whom correspondence should be addressed: cheng@uow.edu.au and kimura.hideo@nims.go.jpMultiferroics are a wonderful research subject in respect to their great application potential in the information industry, e.g., multi-state information storage devices and new types of sensors. 1,2[8][9][10] The earliest study on the magnetoelectric (ME) effect was reported in the 19th century.In 1894, a prediction of the possibility of an intrinsic ME effect was put forward by Pierre Curie based on the lattice symmetry theory, while Debye defined the terminology of the "ME effect" in 1926.Dzyaloshinskii gave a generic prediction of the ME effect in Cr 2 O 3 in 1959, 11 and then Cr 2 O 3 crystal was discovered to be the first materials with the ME property one year later. 12Due to poor quality materials, the development of magnetoelectric materials was quite limited until 2003.The Ramesh group then reported large ferroelectricity and the magnetic property in BiFeO 3 (BFO) epitaxial thin film. 13The Tokura group discovered that magnetism causes ferroelectricity in TbMnO 3 . 14Cheong found a similar phenomenon in TbMn 2 O 5 . 15All of these investigations have encouraged studies on multiferroics all over the world since then.So far, besides the most well-studied ferroic orderings in multiferroic materials (ferroelectricity, ferromagnetism, and ferroelasticity), new orderings such as ferrotoroidal and ferrovalley have been discovered. 16,17Furthermore, there are still many possibilities in exploring new orderings such as spontaneous switchable orbital orderings, vortices, and chiralities, which will enrich future research 5 (Fig. 1).In multiferroic material processes, with any two or more of the primary ferroic orderings, the cross coupling among these ferroic orderings will definitely promote the development of fundamental physics and potential applications, e.g., integrated units and microdevices such as microelectromechanical systems (MEMS) devices, microsensors, and high-density information storage media.
The original definition of the ME effect describes the influence of a magnetic (electric) field on the polarization (magnetization) of a material.From the classification of material constituents, multiferroic ME materials can be generally divided into two types: single-phase and composite.In a single phase multiferroic, the ME properties and coupling behavior are largely determined by their domain structures.It should be pointed out that the multiferroic materials usually exhibit complicated domain structures.Studies on domain structure characterization and domain switching behaviour represent a crucial step in the exploration of approaches to control and manipulate magnetic (electric) properties using an electric (magnetic) field or other means.
The advances in thin film growth technology have provided a controlled way of synthesizing high quality thin films and have allowed the properties of existing materials to be modified by strain engineering, which has opened the door to the design of practical devices based on ME coupling. 18In case of single-phase multiferroics in the form of thin films, most of the published work is devoted to hexagonal manganites such as ErMnO 3 and YMnO 3 (YMO); 19,20 another series of single phase materials are solid solution perovskite ME materials.Bi-based perovskite (mostly pure or chemically doped BiFeO 3 (BFO) 21-23 has also been investigated.
In this review, following a concise outline of our basic knowledge on the ME effect, we summarize some important research activities on domain switching in single-phase multiferroic materials in the form of single crystals and thin films, especially domain switching behavior involving strain.We also introduce recent developments in characterization techniques on domain structures of ferroelectric or multiferroic FIG. 1. Schematic illustration of interactions in multiferroics.The wellestablished primary ferroic orderings, e.g., ferroelectricity (P), ferromagnetism (M), and ferroelasticity (e), can be switched by electric (E), magnetic (H), and stress (r) fields, respectively.Physicists are also exploring new feroric orderings, i.e., ferrotoroidic (T) 16 and ferrovalley (V) 17 orderings, which should be switchable by EÁH and kÁp.The "O" represents other possibilitiessuch as spontaneous switchable orbital orderings, vortices, and chiralities. 5aterials which have significantly advanced our understanding of domain switching dynamics and interactions.The effects of a series of issues, such as electric field, magnetic field, and stress effects on domain switching are discussed as well.It is intended that an integrated viewpoint on these issues, as provided here, will further motivate synergistic activities between the various research groups and industries towards the development and characterization of multiferroic materials. 24

II. ME EFFECTS IN MULTIFERROIC SINGLE CRYSTALS AND THIN FILMS
The magnetoelectric (ME) effect as it is generally defined relates to the coupling between electric polarization (P) and magnetization (M) that is induced by magnetic field (H) and\or electric field (E) in a solid.A systematic progression of contributions to the ME effect is obtained from the expansion of the free energy of a material, 25 i.e., with E and H as the electric field and magnetic field, respectively.Differentiation leads to the polarization and to the magnetization where Ps and Ms denote the spontaneous polarization and magnetization, whereas ê and l are the electric and magnetic susceptibilities.The tensor â corresponds to induction of polarization by a magnetic field or of magnetization by an electric field, which is designated as the linear ME effect.It is supplemented by higher-order ME effects like those parameterized by the tensors b and ĉ .The vast majority of research on the ME effect is devoted to the linear ME effect and it is generally acceptable to omit the prefix 'linear' and simply to refer to the linear manifestation as the "ME effect."It is further shown that the ME response can be described by the following equation: 26 with v e ii and v m jj being the electric and magnetic susceptibilities.This means that the ME effect can only be large in a ferroelectric and/or ferromagnetic materials.

A. ME effect in BiFeO 3
8][29] It has highly desirable ferroelectric Curie temperature (T C ) of 1103 K and antiferromagnetic N eel temperature (T N ) of 643 K. 30 Due to its large electrical leakage and high density of defects, bulk BFO has been less interesting for a long time.This is partly due to difficulties in preparing high quality, single phase BFO, and researchers have presented several methods to overcome these issues.In 2003, the Ramesh group observed a residual polarization as large as P r $55 lC/cm 2 along the [001] direction in high-quality epitaxial BFO thin films deposited on SrTiO 3 substrate. 13Meanwhile, a large magnetization was also claimed.Besides the large spontaneous polarization, strong magnetization, and high critical temperatures, ME coupling at room temperature, which is another attractive property, is claimed in BFO, which thus presents almost all the required properties for practical applications, stimulating research on every aspect of BFO as a multiferroic in both bulk and film/heterostructure forms in the subsequent years till today.
The structure of BFO can be described as follows: as illustrated in Fig. 2, a rhombohedral unit cell is built of two distorted perovskite blocks, which are connected along the polar-h111i axis.In this structure, the two oxygen octahedra of the cells connected along the h111i direction are rotated clockwise by 613.8 ; the Fe-ion is shifted along the same axis away from the centre position of the oxygen octahedron by 0.135 A ˚.The ferroelectricity in BFO is attributed to a large displacement of the Bi-ions relative to the FeO 6 octahedra.BFO was reported as a G-type antiferromagnetic which possessed a cycloidal spin structure with a period of $620 A ˚.31 This spin structure was found to be incommensurate with the structural lattice and was superimposed on the antiferromagnetic order.It was also revealed that, if the moments were oriented perpendicular to the h111i-polarization direction, the symmetry also permits a small canting of the moments in the structure, resulting in a weak ferromagnetic moment of the Dzyaloshinskii-Moriya (DM) type.
Direct observation of changes in the nature of the antiferromagnetic domain structure in BFO with respect to an applied electric field was realized by combining piezoresponse force microscopy (PFM) imaging of ferroelectric domains and X-ray photoemission electron microscopy (PEEM) imaging of antiferromagnetic domains. 18This research revealed that the ferroelastic switching events (i.e., 71 and 109 ) lead to a corresponding rotation of the antiferromagnetization plane in BFO (Fig. 2).This has opened the way for following studies of perovskite multiferroics in attempts to gain control of ferromagnetism at room temperature. 32

B. ME effect in hexaferrites
In hexaferrites, the origin of their ferroelectricity is generally driven by magnetism that sensitively responds to an applied magnetic field.The magnetically induced ferroelectrics often show giant ME effects, 8 remarkable changes in electric polarization in response to a magnetic field. 35Kitagawa et al. found that in a hexagonal ferrite, Sr 3 Co 2 Fe 24 O 41 shows magnetoelectricity at room-temperature. 36Figures 3(a) and 3(b) show the magnetic field dependence of the magnetization and the electric polarization at different temperatures (100 K, 200 K, and 300 K), respectively.These features become more evident when the magnetization curve is compared with that of Ba 3 Co 2 Fe 24 O 41 , which is a simple planar ferrimagnet at 300 K, and can be explained by the transformation from the transverse-conical ordered state [middle panel of Fig. 3(c)] into the ferromagnetic state.Thus, it is expected that the magnetically induced ferroelectrics could provide new types of device applications based on the ME effect, such as memory devices in which magnetic and/or ferroelectric domains are controlled by an electric and/or magnetic field.
YMnO 3 exhibits both ferroelectricity with spontaneous polarization ($5.6 lC cm À2 ) 20 and antiferromagnetic properties.It also shows a strong coupling between the electric and magnetic orders.Hexagonal YMnO 3 belongs to the P6 3 cm space group with lattice parameters: a ¼ 6.125 A ˚and c ¼ 11.41A ˚. Its unique structure consists of distorted MnO 5 bipyramids layer interleaved by distorted layers of rare earths.The origin of the polarization in YMnO 3 (and thus the ferroelectricity) is a consequence of the interplay in the network between frustrated Mn 3þ -O 2À -Mn 3þ in-plane exchange paths and Mn 3þ -O 2À -O 2À -Mn 3þ inter-plane exchange paths (Fig. 4).Theoretical studies have demonstrated that various possibilities for the rearrangement of the spins without losing the ferroelectricity exist in YMO, which leads to the possibility that various magnetic structures can be formed. 10The thermal properties of YMnO 3 compound have been studied as well.It is reported that the thermal conductivity of hexagonal YMnO 3 exhibits an isotropic suppression in the cooperative paramagnetic state, followed by a sudden increase upon magnetic ordering.The reason for this unprecedented behavior without an associated static structural distortion in geometrically frustrated magnets was considered to be a result of the strong coupling between acoustic phonons and low energy spin fluctuations.By substituting the magnetic element Ho for Y in the ferroelectric active sites, an even larger effect was observed, indicating a strong influence of multiferroicity. 37

C. ME effect in charge-ordered multiferroics
A charge-frustrated materials system RFe 2 O 4 (R ¼ Dy, Lu, Y, etc.) with triangular lattices has recently received great attention.LuFe 2 O 4 is a member of the mixed valence material RFe 2 O 4 family; it has attracted great attention due to its potential as a multiferroic. 38The crystal structure consists of the alternate stacking of triangular lattices of the rare-earth element, iron, and oxygen (Fig. 5).Fe 2þ and Fe 3þ coexist equally at the same sites in the triangular lattice.Because the average Fe valence is 2.5þ, the Fe 2þ and Fe 3þ ions can be regarded as an excess and a deficiency of half an electron, respectively.The ferrimagnetic Curie temperature of LuFe2O4 is around 230 K.The ferroelectric charge ordering transition in this material occurs around 340 K.At temperature higher than 340 K, Fe 2þ and Fe 3þ are randomly distributed in the triangular lattice.With decreasing temperature, the interaction between Fe ions leads to a preference for Fe 2þ and Fe 3þ as nearest neighbors in the triangular lattice in order to minimize the Coulomb energy, which is similar to the case of spin frustration.Thus, in each bilayer, the ratio of Fe 2þ to Fe 3þ is 2:1 in the lower layer, while it is 1:2 in the upper layer.The particular charge ordering of Fe 2þ and Fe 3þ ions leads to a charge imbalance between the two layers and thus produces corresponding electric dipoles, which results in ferroelectricity in this system. 39Fe ions also carry unpaired spins corresponding to the oxidation states, and the exchange interactions between Fe ions yield ferrimagnetism with geometrical frustration due to the triangular nature of the lattice.Yang et al. compared ferroelectric domains and magnetic domains of LuFe 2 O 4 using electrostatic force microscopy (EFM) and magnetic force microscopy (MFM). 40A big difference in the length scale between the ferroelectric and magnetic domains was observed.The possible reason for this difference is that the ferroelectric polarization depends on separation of the electric dipoles in the iron oxide bilayer, while the magnetization is determined by the direction of the magnetic moments of the un-cancelled component between Fe 2þ (S ¼ 2) and Fe 3þ (S ¼ 5/2) in the ferromagnetic configuration.Generally, appearance of magnetic domain walls (DWs) inside a ferroelectric domain would be excluded considering the high DW energy of LuFe 2 O 4 due to its exceptionally high magnetocrystalline anisotropy.

D. ME effect in Aurivillius phase multiferroics
The Aurivillius-phase ferroelectrics were first discovered by Smolenskii's group in the late 1950, 9 who studied a large number of the family members.The structure is built of a sandwich structure which consists of ABO 3 perovskite blocks interleaved by Bi 2 O 2 planes.Recently, a novel class of Aurivillius phase layer structure materials with the general formula of (Bi 2 O 2 ) 2þ (A m-1 B m O 3mþ1 ) 2-(m: number of pseudo-perovskite layers) has come to our attention.Oxides in this family such as Bi mþ1 Ti 3 Fe mÀ3 O 3mþ3 (BTFO) which consist of (Bi 2 O 2 ) 2þ layers alternating with pseudo-perovskite units consisting of (Bi m-1 Ti 3 Fe m-3 O 3mþ1 ) 2-layers exhibit fascinating properties with a relatively high Curie temperature (T c ), fatigue free switching characteristics, and the propensity to form long period structures. 42The layered structure enables the incorporation of magnetic ions with þ3 to þ5 oxidation states in B sites of the perovskite units, which possibly allows both ferroelectricity and ferromagnetism through cations with unoccupied d orbitals and partially filled d orbitals occupying adjacent perovskite units.Through this structure, BTFO compounds could potentially accommodate the normally conflicting electronic structure requirements for single phase multiferroics (Fig. 6). 43hao et al. deposited single-phase Bi 5 Ti 3 FeO 15 thin films with nearly (00l)-orientation by pulsed laser deposition.They demonstrated a large room-temperature magnetoelectric coupling in a Bi 5 Ti 3 FeO 15 thin film which had a high ferroelectric Curie temperature (1000 K). 44 Room-temperature multiferroic behaviour was demonstrated by a large modulation in its magnetopolarization and magnetodielectric responses.Local structural characterization by transmission electron microscopy complementary with Mossbauer spectroscopy results revealed the existence of Fe-rich nanoregions, which may be the origin of its short-range magnetic ordering above room temperature.In the Bi 5 Ti 3 FeO 15 film, together with a stable ferroelectric order, the spin canting in magnetic-ion-based nanoregions via the DM interaction yield a ME coupling of 400 mV/OeÁcm at room temperature.(Fig. 7).

III. DOMAINS AND DWS
Domains are regions with a uniform orientation of the relevant order parameter: for example, the polarization or the magnetization. 45,46At least two orientations of the order parameter (domain states) are allowed for any ferroic material; thus, a typical ferric material consists of multiple domains, each representing one of the allowed domain states.The interfaces between domains are called DWs.They can have a width ranging from less than 1 nm to more than 100 nm.They denote the region across which the order parameter reorients between adjacent domains.Domains and DWs are crucial for the control of many material properties, such as coercivity, resistance, and/ or fatigue.The ME coupling of a multiferroic material is rooted in the coupling between its individual magnetic and ferroelectric domain. 47Although advanced functionalities are often based on complex domain architectures, early investigations were focused on symmetry analysis and experiments on a single domain state of a single-crystal multiferroic material. 48n example is the study of the reversal of the electric order parameter by a magnetic field (or vice versa) via the linear ME effect.Domain patterns were initially imaged by linear optics, FIG.
6. Crystal structure of Bi mþ1 Ti 3 Fe mÀ3 O 3mþ3 .and ferroelectric domains were visualized after chemical surface etching or via optical birefringence in materials with simultaneous elastic deformation.Ferromagnetic domains were resolved by the magneto-optical Faraday or Kerr effect.

A. Domains and DWs in ferroic materials
Since ferroic (ferroelectrics, ferromagnets, and ferroelastics) phases contribute to at least two distinct orientations of the order parameter, they result in the formation of domains, which are divided by DWs (Fig. 8).Domains are defined as a representing long-range order with respect to at least one typical property of the material.When orientation states are changed, the interfaces (DWs) move; thus, the domain structure can be manipulated by external fields, which is a central feature of ferric materials. 49omain size is determined by the competition between the energy of the domains (itself dependent on the boundary conditions, as emphasized above) and the energy of the DWs.The energy density of the domains is proportional to the domain size where U is the volume energy density of the domain and w is the domain width.Smaller domains therefore have smaller depolarization, demagnetization, and elastic energies.But the energy gained by reducing domain size is balanced by the fact that this requires increasing the number of DWs, which are themselves energetically costly.The walls' energy density per unit area of thin film is where r is the energy density per unit area of the wall and d is the thickness of the film.Adding up the energy costs of domains and DWs, and minimizing the total with respect to the domain size, leads to the famous square root dependence, which is also called the Landau-Lifshitz-Kittel scaling relation: 50 The exact mathematical treatment of the "perfect stripes" model assumes that the DWs have zero or at least negligible thickness compared to the width of the domains.In reality, however, DWs do have a finite thickness d, which depends on material constants.Scott rewrote the square root dependence as where G is a dimensional parameter.This equation is useful to estimate DW thickness.When the square of the domain size is divided by the wall thickness as Eq. ( 3), all ferric materials look the same, and researchers calculated the value as follows: [51][52][53] G ¼ 1:765 where v x and v z are the in-plane susceptibility and out-ofplane susceptibility, respectively.Actually, the dependence on material properties is weak because they are inside a square root.The square root law should break down in certain circumstances where the size of the domains becomes comparable to the thickness of the film, so that the depolarization field is beyond the threshold. 54

B. Domains and DWs in ferroelectric materials
In ferroelectric crystals, domains usually show stripe patterns with alternating polarization.Such a domain pattern is due to a competition between the reduction in energy achieved by mixing two types of domain and the energetic cost of the DWs, thus improving alignment of the average polarization with the external field.The competition of energies determines an equilibrium DW spacing.It is also possible that the minimum energy state consists of several such laminates, sandwiched together to form a multi-rank lamination.
By changing the relative sample dimensions, the orientation of the domains could be modulated through the energy competition between the domains and the DWs, as shown in Fig. 9.To minimize the overall surface energy, the domains in BaTiO 3 arrange themselves so as to have the depolarizing fields only on the narrowest dimension of the column. 51,55n ferroelectrics, space inversion is broken, while time inversion is broken for ferrimagnets.In these cases, 180 DWs separate regions of opposite polarity, which tend to be parallel to the polar axis.Since the magnetic or electrostatic repulsion of the spins or dipoles is energetically costly, head-to-head 180 walls cannot possibly be formed at the wall, although 180 headto-head domains have been studied for decades in ferroelectrics.When they annihilate each other, large voltage pulses are emitted, called "Burkhouse pulses." 56The voltage spikes are orders of magnitude larger than thermal noise.Wei et al. directly visualized DWs in a ferroelectric Pb(Zr, Ti)O 3 single crystal using high-resolution transmission electron microscopy (HRTEM). 57s shown in Fig. 10, they found that the domains were about 10 times thicker than the neutral walls.Interesting, they found that the polarization reversal occurs over a few unit cells, and a small decrease in the out-of-plane (z-axis) polarization can be seen on either side of the wall, thus confirming the N eel-like character. 55

C. Domains in ferromagnetic materials
A magnetic domain is a region within a ferromagnetic material in which the magnetization is in a uniform direction.Since the magnetization is related to the ordering of microscopic spins in ferromagnetic materials, the type of domain structure is defined by the energy balance between the energy cost of divergent or unclosed field lines originating from the magnetic structure and the energy cost of the DW.In most ferromagnets, the magnetization rotates from one domain to the next with no preferred handedness.Figure 11 shows standard magnetic domain structures within microcrystalline grains in a piece of NdFeB alloy.The dipoles of the magnetic domains spontaneously align due to the exchange interaction.Domain walls (DWs) are the regions between two domains in which the magnetic moments gradually change direction.A zero length domain wall (i.e., the magnetic moments are oriented 180 with respect to each other at the domain interface) costs energy due to the exchange interaction that tends to align the magnetic moments.It is therefore energetically much more favorable to cant the magnetic moments gradually over a region at the interface: the domain wall.Two kinds of domain walls exist, as is shown in the images below, which differ in the direction of canting.The more common one is the Bloch wall, but in thinner films a N eel wall is often favored.Bloch walls are predicted to be the lowest energy walls in perpendicularly magnetized systems.
Figure 12 shows a spin-polarized low-energy electron microscopy (SPLEEM) measurement of the DW spin structure in a [Co/Ni] n multilayer stack epitaxially grown on a Pt(111) substrate. 58As shown in Fig. 12, The magnetization within the DWs always points from the in-plane components of DWs, which are displayed as grey domains (-M z ) to black domains (þM z ), which represent the perpendicular magnetization component, indicated that the spin structure in the 12. Real-space observation of chiral N eel walls in [Co/Ni] n multilayer. 58 , where D ij is the DMI vector, and S i and S j are magnetic spin moments located on neighboring atomic sites i and j.The DM interaction can be adjusted to stabilize either left-handed or right-handed N eel walls, or non-chiral Bloch walls by adjusting an interfacial spacer layer between the multilayers and the substrate.

D. Domains in multiferroics
The coupling between the magnetic and electric dipoles in multiferroic and magnetoelectric materials holds promise for conceptually novel electronic devices.Multiferroic hexagonal rare earth manganates exhibit a dense network of boundaries between six degenerate states of their crystal lattice, which are locked to both ferroelectric and magnetic DWs.Geng et al. directly visualized magnetoelectric domains in multiferroic h-ErMnO 3 using magnetoelectric force microscopy (MeFM), which can be employed to detect electric field-induced magnetization (M E ). 59 The ferroelectric domain pattern on the (001) surface of h-ErMnO 3 is identical to that for the magnetoelectric domains (Fig. 13 Hexagonal YMnO 3 (YMO) has received much attention as a representative geometrical frustrated multiferroic because of its large coupling between the magnetic and electric ferroic orders. 19,60,61Figure 14(a) shows a dark-field transmission electron microscope (TEM) image of YMO crystal, where so-called "cloverleaf" domains were observed elongated along the c-axis. 62An enlargement of a vortex as is shown in Fig. 14(b) clearly demonstrates the existence of topological domains in YMO.It was found that vortices with at least two domain boundaries along the c-axis (transverse DW, TDW) are stable during TEM observations.Along a TDW, no charge is exposed, whereas a small amount of charge is exposed at a longitudinal domain boundary (LDW) at the core.A four-leaf clover-like vortex appeared to be fundamentally unstable, however, as shown in Fig. 14(c), as the contrast became blurred near the vortex.All of the domain boundaries in the four-leaf vortex was possibly perpendicular to the c-axis, revealing that the DW conductivity in the vortex depends on the topological nature of the domains.The six crystallographic domains join at a defect line with positive and negative polarization alternating around the defect.There are two possible configurations of the domain sequences: vortex configuration as aþ, bÀ, cþ, aÀ, bþ, and cÀ and antivortex configuration as aþ, cÀ, bþ, aÀ, cþ, and bÀ.Thus, the electric alternating sign of polarization and the domain walls flip the electric polarization.Domain structures of BFO have been intensively investigated.Rhombohedral BFO possess 71 , 109 , and 180 ferroelectric DWs formed on (100) and other planes that satisfy the requirement that 6h 6 k þ l ¼ 0, respectively.All three wall orientations have been observed, as shown in Fig. 15.It was found that electrical conduction in BFO only observed at 109 and 180 DWs, while the 71 DW showed no conduction 63 (Fig. 15).Cross-sectional transmission electron microscopy (TEM) images of BFO thin film indicated that a charged domain wall (CDW) can form at the film surface as a result of the formation of a triangular charge-neutral nanodomain. 49These hidden nanodomains associated with the CDWs could also significantly affect the film conductivity in the local region.
In ferroelectrics, one of most important research topics associated with DWs is their enhanced conductivity compared to the surrounding domains. 64,65Recent experimental investigations have demonstrated that a quasi-two-dimensional (2D) electron gas can form at CDWs, leading to steady metallic conductivity 10 9 times that of the bulk. 66,67Li et al. reported reversible switching of stable nanoscale CDWs and corresponding nanodomains induced by an electric field applied across a cross-sectional sample of an epitaxial BFO thin film deposited on TbScO 3 substrate. 47A cross-sectional dark-field diffraction contrast TEM image of a system with a stable CDW is shown in Fig. 16.Since the "head-to-head" CDWs in rhombohedral-like BFO thin films possess a tetragonal-like structure, the process of creating or erasing a CDW in the film would involve a dynamic transition between different lattice symmetries induced by an applied electric field.Dramatic resistive switching is observed as the length of the CDW passes a critical value, leading to robust resistance changes (off/on ratio % 10 5 ) in ferroelectric memories, including ferroelectric tunneling junctions and switchable ferroelectric diodes.

E. DW characterized using transmission electron microscopy
High-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) imaging together with electron-energy loss spectroscopy (EELS) analysis is highly sensitive to atomic-number contrast, which is quite powerful in semiconductor, catalysis, ceramics, and particle analysis applications.The enhanced ME effects in multiferroics are often seen as depending on the dynamics of multiferroic DWs, in analogy to the large-scale hysteretic behavior of the ferromagnetic or ferroelectric DWs (FE-DWs). 23,68Resolving the mechanism of DW conductivity is essential for developing the functional potential of DWs.If the accumulated defects are largely responsible for the DW conductivity, a relationship may be foreseen between the type of charge carrier (oxygen vacancies, cation vacancies, electrons, or holes) and the DW motion under applied electric field.Understanding this relationship would be particularly important for the development of devices based on DW nanoelectronics and for those devices relying on polycrystalline (bulk) ferroelectrics.Rojac et al. investigated DW conduction in BFO due to accumulated charged defect in DWs using advanced transmission electron microscopy techniques. 23They found that the mobile charged defects (Fe 4þ and Bi vacancies) accumulated in the domain walls were responsible for the electrical conductivity at the DWs in BFO, as shown in Fig. 17.The defects show p-type behavior, which is different from the classic ferroelectrics such as BaTiO 3 where oxygen vacancies always accumulated in the domain walls.Rojac et al. also found that by varying the atmosphere during thermal annealing at high temperature ($700 C), the local domain-wall conductivity can be tailored.It is interesting that we can control the local conductivity in ferroelectrics by control the defect in the domain walls, which will benefit future devices based on domain walls.

F. Domain characterization using scanning probe microscopy
Scanning probe microscopy (SPM) has become a powerful tool to probe and manipulate materials, structures, and systems on the nanoscale.Since the original development of the atomic force microscope (AFM) in the 1980s, to study the atomic forces between samples and a scanning probe tip, a variety of various imaging modes of SPM have been proposed and implemented, expanding the capabilities of SPM to a wide range of functional properties.Despite the widespread success of contact-mode AFM in topographic imaging, dynamic force microscopy (DFM), which images with an oscillating cantilever, was developed to improve the resolution in many cases, particularly for soft samples.With the growing requirement for measurements on various samples with functional properties, AFMs have found an extremely broad range of applications for probing electrical, magnetic, and mechanical properties, by multiple frequency techniques, beyond simple topographic imaging.Piezoresponse force microscopy (PFM) is widely used to investigate ferroelectric domain structures.Figure 18 shows typical examples of domain structures observed by PFM. 69Domain patterns of ceramic PbZr x Ti 1-x O 3 (PZT), lithographic pattern of polycrystalline PZT thin film, and epitaxial BFO thin film were directly visualized using PFM.Typical piezoelectric and ferroelectric behavior, such as domain facing, polarization reversal, and DW motion, could be analyzed.
Beyond the study of phenomena, spectroscopy analysis was developed to address quantitatively the local switching characteristics of ferroelectric materials. 70The hysteresis in so-called switching spectroscopy piezoresponse force microscopy (SS-PFM) results from the nucleation of a single domain generated under a sharp tip, and the PFM signal follows the development of domains at a single location (Fig. 19), while macroscopic hysteresis occurs due to the nucleation, growth, and interaction of multiple separated domains.The PFM hysteresis loop shape is PR ¼ d eff 1 À 5br wall p 2 = È ð8P s V dc Þg, where PR represents the piezoelectric response, d eff is the effective electromechanical response of the material, b is a proportionality coefficient, r wall is the direction-independent domain wall energy, d wall is the direction-independent DW energy, and P s is the polarization.According to this equation, the shape of the hysteresis loop is determined solely by the DW energy and the spontaneous polarization.Besides the PFM technology, Kelvin probe force microscopy (KPFM) is another widely used technique to study ferroelectricity. 71,72

IV. DOMAIN SWITCHING IN MULTIFERROIC SINGLE CRYSTALS AND THIN FILMS
A. Domain switching under electric field Cross-coupling of ordering parameters in multiferroic materials by multiple external stimuli other than electric field (E) and magnetic field (H) is highly desirable from both practical application and fundamental study points of view.In our previous work, the ferroelectric domain switching phenomena in Bi 0.9 La 0.1 FeO 3 (BLFO) thin film were studied by PFM in a contact mode (Fig. 20).E manipulation of ferroelectricity in BLFO thin film was observed by applying a DC voltage.The locally applied E induces polarization switching and ferroelastic domain switching due to the electro-elastic coupling. 73oreover, when we applied positive dc bias in the inner box, which had been switched two times in an order of þ15 V and À15 V, the magnetic domains in this polycrystalline thin film could be switched back again, indicating that magnetization reversal could also be achieved by applying electric field.When an electric field is applied on the thin film, direct 180 polarization switching is difficult due to the requirement of high activation energy, which is usually through the combination of 71 and 109 ferroelastic switching.The antiferromagnetic ordering in BLFO is G-type, and the orientation of the antiferromagnetic magnetization is coupled to the ferroelastic strain and is always perpendicular to the ferroelectric polarization. 18Therefore, the 71 and 109 ferroelastic switching are related to the reorientation of the antiferromagnetic plane and changing the orientation of the easy magnetization plane.Thus, an electric field can change the ferroelastic strain state in a nanoregion of BLFO thin film, leading to a reorientation of the antiferromagnetic order and resulting in magnetic domain switching.
Recently, topological structures in ferroelectrics and multiferroics have received substantial attention.Some singular regions with low dimensionalities have been considered as topological defects, e.g., two-dimensional (2D) topological defects including ferroic DWs and one-dimensional (1D) defects such as flux-closure vortex and skyrmion states, which have emerged as hot topics in combination with multiferroic functionalities.Li et al. recently fabricated epitaxial BFO nanodots on SrTiO 3 substrate and characterized the domain structures in these arrays. 75If the nanodots have a purely upward vertical component of polarization together with headto-head charge DWs in the initial state, negative charges can be attracted to the top surfaces of the nanodots to screen the polarization, leading to negative charge states.In contrast, the positive charge states form in the nanodots with a purely downward vertical component of polarization along with tail-to-tail charge domains, and mixed charge states occur on those nanodots containing both upward and downward polarization domains, as well as charged DWs.After a reconstruction of the domain structure of these nanodots, they can evolve into different types of center domains in the final stage.Three types of domains were observed, as shown in Fig. 21: centerconvergent domains, center-divergent (convergent reverse) domains, and double-center domains.The three types of domain were identified by their appearance in PFM images at first.By further investigation, the authors found that all of the three types of center domain structures have the head-to-head or tail-to-tail charge cores.It may come from the surface and edge effects in low dimensional systems or charge accumulation on the top surface.
The electrical switching behavior of domains within the nanodots has been investigated by applying an electric voltage of 68 V, as shown in Fig. 22.A complete reversal of contrast patterns was observed in both vertical and lateral phases.Interesting, the switched domains are reversible by electric field according to the experimental results, as shown in Fig. 22, and the switched domains are individually addressable.Furthermore, retention experiment results indicated that the center domains remained stable, even for a duration up to 24,000 min at room temperature under ambient conditions.The domains in nanodots appear to be reversibly switchable and robust under electric field, which enables further possibilities for artificial control of the topological domain states by electric field, which is promising for applications in novel information devices.

B. Magnetically induced domain switching
Rare-earth manganite materials (ReMnO 3 ) have been receiving great attention because this family exhibits a wealth of fundamental physics and technological possibilities.Depending on the size of the Re ion, ReMnO 3 exhibits either an orthorhombic or a hexagonal structure. 76The room-temperature crystal structure of TbMnO 3 is the orthorhombic distorted perovskite structure (space group Pbnm; a cycloidal spin structure emerges below the transition temperature T C ¼ 27 K and breaks the inversion symmetry, giving rise to a spontaneous electric polarization along the c-axis. 77Matsubara et al. used second harmonic generation (SHG) microscopy to investigate the effects of an externally applied magnetic field on the ferroelectric domains in the multiferroic TbMnO 3 on changing the direction of electric polarization by 90 .Unexpectedly, the DWs, which were initially parallel to the polarization vector, did not change their shape or position.
Aurivillius phase thin films of Bi5Ti3(FexMn1-x)O15 recently were reported to be a candidate for room temperature multiferroics.Keeney et al. demonstrated that ferroelectric domain polarization switching could be induced by an applied magnetic field in Aurivillius-phase multiferroic thin films. 81As shown in Fig. 24, they performed PFM under a variable magnetic field to detect the piezoelectric-magnetic switching in a Bi 6 Ti 2.5 Fe 1.75 Mn 0.75 O 18 thin film, which directly proved magnetoelectric multiferroic coupling in the film.When a magnetic field of 250 mT was applied in the opposite (negative) direction, additional areas exhibiting polarization inversion were obtained.Since the film is not a single crystal epitaxial film, it is not possible to distinguish between 180 and 90 ferroelectric polarization switching under the application of magnetic field.Magnetoelectric switching has been observed in both lateral and vertical PFM experiments.

C. Stress induced domain switching
Investigations on the nanoscale of ferroelectric domain switching under mechanical force, due to loading by a SPM tip, are drawing increasing attention. 79,80Recently, mechanical-force-induced ferroelectric domain switching in multiferroics was reported by several groups. 76,81,82It is natural to ask whether such an external mechanical force could switch two or all three types of ferroic domains (ferroelectric, ferroelastic, and magnetic domains) in multiferroic materials.To investigate the influence of mechanical force on both the ferroelectric and the magnetic domains of a Bi 5 Ti 3 FeO 15 (BTF) film, we applied a set of vertical loading forces on the film.As shown in Fig. 25, the BTF thin film was firstly poled by þ20 V in an area of 8 Â 8 lm 2 to obtain an uniformly arranged "mono-domain"; then, the sample was scanned under a series of loading forces of 14 nN, 50 nN, 100 nN, 500 nN, 1000 nN, and 1300 nN, respectively, in an area of 4 Â 4 lm 2 in the centre; and finally, the switched area was read by scanning a larger area of 12 Â 12 lm 2 at 5 kHz in vertical PFM (VPFM), lateral PFM (LPFM), and MFM modes.For the VPFM images, when the tip force (F) is lower than 100 nN, no obvious switching is observed in the "force switching" area in the centre.On further increasing F, the contrast between the areas that were switched by E and F becomes more obvious.As the tip force is increased to 1300 nN, although the brightest contrast is obtained, some non-switched domains still exist in the centre of the VPFM image, indicating incomplete polarization reversal in the region switched by mechanical force.The LPFM images show a different switching phenomenon compared with the VPFM images: a bright pattern is obtained in the E-poled region, but the loading force seems have little effect on the ferroelectric domains along the in-plane (IP) direction because no obvious domain switching observed in the F-poled region in the centre.We consider that the sign of IP projection of the ferroelastic strain is opposite to the IP projection of piezostrain generated by an external mechanical force and the magnitude is bigger than for the latter, so that the back switching of ferroelastic domains becomes more obvious in the E-switched area.For the MFM images, the magnetic domain switching becomes more obvious with increasing F. We applied the E and F repeatedly in the same area, and the E-switched and F-switched patterns in MFM became more homogeneous when applied force was as high as 1300 nN.When the F was increased to 1300 nN, the magnetic domains in the F-poled region were mainly switched, indicating that the magnetization could be controlled by an external mechanical force.The increasing trend towards switching of magnetic domains with increasing load implies an enhancement of the magneto-elastic coupling with increasing tip stress in BTF thin film.According to the abovementioned experimental results, both ferroelectric and magnetic domains can be switched by F, indicating that the tip stress can induce not only local ferro-electro-elastic polarization switching but also ferroelastic-magnetic-domain switching.We need to note that the polarization reversal could not be observed when applying mechanical force without an initial positive dc voltage poling.In addition, no domain switching was observed if the thin film was initially poled by negative voltage.The tip stress induced switching pattern, as shown in Fig. 25(a), is not as bright as the E-induced switching pattern, due to the ferroelastic domain generation during the strain relaxation when the electric field and the mechanical force on the film are removed. 83he mechanical force introduces a piezostrain in nanoregions, which modifies the original elastic strain state generated from the thermal process during film deposition, 84 and results in a consequent reorientation of the local magnetism, driven by the strain coupling between small magnetic volume and ferroelastic domians. 85A second possibility is that before the mechanical force is applied, the film is already under a small in-plane stress because of the electric poling, producing a very small strain due to the high modulus.The addition of an electrostatic potential on the top of the film can be expected to cause cation displacement, and the existence of in-plane stress will ease this cation displacement, leading to a larger deformation, which would have an influence on the magnetic volume in the film as well. 86,87The switching process is illustrated in Fig. 25(d).We suppose that the rotational moment and polar distortions in BTF would be coupled under certain conditions involved in the strain state, as in BFO. 88The tip stress induced the E f to change the free energy profile asymmetrically, which would also take account of the factors for switching the domains.Further investigation on the coupling configuration between ferroelectric domains and magnetic domains would be complicated, so it is necessary to discover the ME coupling mechanism in high quality BTF single crystals.
We have demonstrated the manipulation of both ferroelectric and magnetic domains by electric field, magnetic field (Fig. 26), and mechanical force in a BTF thin film at room temperature.Due to the relaxation of ferroelastic domains in the BTF film and possible short-range magnetic ordering in Fe-rich nanoregions; however, the magneto-elastic coupling is not stable, E-induced magnetic domain switching fades away after the electric field is removed, while the successfully manipulation of both ferroelectric domains and magnetic domains by mechanical force proves the switching role of ferroelastic strain in the magnetoelectric coupling in BTF thin film, which would be important for further understanding the magneto-elastic-electric coupling in multiferroics.The mechanical switching of both ferroelectric and magnetic domain behaviour in multiferroics shows a complex intercoupling among polarization, magnetization, and strain, so it provides the possibility of manipulating one physical parameter by using one of the three external stimuli: magnetic field, electrical field, and mechanical force, which could yield an additional degree of freedom in novel multifunctional device design.coupling between the two varying order parameters in uncharged DWs of BFO drives the formation of the electrostatic potential step at the DW.The change in band gap exists, however, because of the deformation potential from inhomogeneous strain variations across the interface.Angledependency of the flexoelectric and electrostrictive mechanisms in circular domains of BFO was studied. 91The authors found that conductivity of DWs in BFO not only depends on orientation but also on the curvature of the wall (Fig. 27).Greater than 200% variation in the conductivity was achieved through I-V measurements along a charged curved DW, indicating a modulation of current at the DW.Morozovska et al. explained that an anisotropic elastic strain leads to anisotropic polarization rotations at the DW around the ring structure, which would then result in carrier accumulation at the DW.
Interestingly, skyrmions have recently been observed in a multiferroic material, Cu 2 OSeO 3 . 4The authors also found that the skyrmion lattice rotations in Cu 2 OSeO 3 could be manipulated by electric field.They also applied magnetic field (H) on the sample and found that a hexagonal lattice of skyrmions within a plane normal to H was formed in a narrow H-T region, but only below octahedral rotations (Fig. 28). 4 The intrinsic ME coupling in a skyrmion lattice can provide an alternative manipulation technique among the ferroic orders, which is different from the concept of spintransfer torques.A c-AFM image, taken with V tip ¼ À2.8 V, is shown in (c).To better visualize the conduction map, the outer ring in (c) was flattened to a single 2D map and plotted in (d). 92 calculations of a dipole skyrmion vortex in BFO. 93The DW possesses a quasi-continuous spectrum of voltage-tunable electronic states rather than acting as a rigid electronic conductor.Cu 2 OSeO 3 shows very unique domain structure: it shows multiple q-domains below Tc($60 K) H < 400 Oe; when applied magnetic field 800 Oe near the Tc, skyrmion structure was formed; when applied magnetic field higher than 800 Oe allow the q direction, single q-domain showed in the materials.Thus, in contrast to domains, the DW possesses memristor properties, which are shown to exhibit concrete conductance levels. 91The studies on the intrinsic dynamics of DWs are expected not only to influence future theoretical and experimental interpretations of the electronic phenomena but also point out the possibility of finding unique properties in multiferroic DWs, e.g., magnetization and magnetoresistance within an insulating antiferromagnetic matrix, influenced by order parameter coupling and localized secondary order parameters. 94,95 Prospective applications

Magnetic field detector based on multiferroics
By forming the multiferroic materials into a ring shape, one can achieve a vortex magnetic field detector (or current sensor) as an alternative to a commercially designed planar layered sensor.A current sensor with a highly sensitive magnetic vortex field has been realized to use a PZT ring, which is sandwiched between two terfenol-D rings that are magnetized around their circumference.The rings actually consist of multiple segments poled along the circumference direction.The magnetized rings had a response of up to 100 times higher than the 100 turn reluctance coil used for the same measurements. 96In a straight wire, a direct current will generate a vortex magnetic field around the wire.Since the value of the generated field is in proportion to the current, a ringshaped multiferroic detector would act as a vortex field and current detector. 97A magnetoelectric ring (MER) designed for current sensing is illustrated in Fig. 29.The proposed device can possibly enable vortex magnetic field detection and electric current sensing at high frequencies.The key challenge of the device, however, is the vortex ME voltage coefficient of the MER (a V;MER ¼ dV MER dH avg ).High quality multiferroic materials with a high vortex ME voltage coefficient and new device design, which can greatly amplify the MER, are very much expected.

Magnetic data storage based on multiferroics
Up to now, a prime goal for a multiferroic device, in which the magnetization is controlled by an electric field, is still to preferably work at low voltages, room temperature, and with ultrafast switching.Major accomplishments obtained so far are the repeatable, room-temperature magnetization reversal by an electric field demonstrated in BiFeO 3 -CoFe heterostructures and the realization of a multiferroic four-state memory operated at low temperatures. 98These are important steps towards the integration of multiferroics into devices, but crucial aspects, such as the dynamics, reliability, and fatigue, of these device concepts still have to be optimized in order to develop a competitive technology.In addition to this, alternative routes for the control of magnetism that use spin-orbit torque 99,100 exerted by a spin-polarized electric current have been presented, and any multiferroic device will need to compete with their functionality and performance.

Multiferroic photovoltaic/photocatalytic applications
The growing energy crisis and environmental issues demand alternative sources of green energy.Energy harvesting from ferroelectrics and multiferroics is a pioneering field of research on its own, but the combination of other ferroic properties is a valuable addition to it.The coupling of ferroic and optical properties has brought a revolution in the field of  111) planes, respectively, at different magnetic fields, with the magnetic field applied normal to the observed sample plane.In both cases, proper screw-spin texture appears for zero magnetic field, whereas a skyrmion lattice with the identical spin chirality is formed for H ¼ 800 Oe.A magnified view of (D) is shown in (E), where white arrows represent the magnetization direction.(H) Schematic illustration of a single magnetic skyrmion. 4 photovoltaics (PV).Ferroelectric and multiferroic photovoltaics have revitalized third generation solar cells through the discovery of very large photoresponses in a few ferroelectrics and multiferroic compounds such as BFO and Bi 2 FeCrO 6 (BFCO). 101,102The PV effect in ferroelectric (FE) materials was discovered about five decades back, although it attracted little attention before the discovery of a large photovoltage (15 V) in BFO thin films.The ferroelectric, optical, and photovoltaic properties are highly dependent on the microstructure, domain wall orientation, grain size, etc.The effect of the domain size and consequently the way of organizing the ferroelectric domains should be addressed in close connection with the diffusion length of the photo-generated charges carriers, which still has to be determined. 103The possibility of coupling between PV and ferroelectricity/ferromagnetism or multi-coupling between all functionalities makes this class of material fascinating for future research beyond its efficiency and capacity.

VI. SUMMARY
In summary, we have provided an overview on the ME effect and domain switching in multiferroic materials. 104So far, the development of multiferroics is continuing at great speed.Multiferroics represent an appealing topic due to their vast implications for fundamental physics, novel phenomena, various potential applications, etc.Therefore, we cannot cover all the topics, but we have tried to show the ME property in several representative multiferroics.Domains and DWs are essential to the functional properties of multiferroics.Nevertheless, there still many open questions waiting for further investigation, such as, what are the intrinsic properties of domains and DWs?What is the coupling mechanism with respect to new ferric orders and DWs, and it is intrinsic or extrinsic?How can we determine the linear ME coupling in a new multiferroic candidate?igures and captions are reproduced with permission from J. Appl.Phys.113(17), 17C733 (2013). 97Copyright 2013 AIP Publishing LLC.

FIG. 9 .
FIG. 9. Ferroelastic and ferroelectric 90 domains in single crystal nanocolumns of BaTiO 3 .Schematic illustration of the domain patterns typically observed in the nanocolumns under STEM with the electron beam parallel to the x-axis (left).Consideration of the depolarizing energy suggests that the nonaxial component of polarization in the domains will orient approximately perpendicular to the shortest dimension in the column.Decreasing the column dimension along the y-axis while keeping x constant (right) should eventually result in a reorientation of the nonaxial polarization and an associated change in the domain contrast as viewed down the x-axis.The STEM image (center) illustrates that domain orientation behaves exactly as expected.Figures and captions are reproduced with permission from A. Schilling et al., Nano Lett.7(12), 3787-3791 (2007).55Copyright 2007 American Chemical Society.
FIG.12.Real-space observation of chiral N eel walls in [Co/Ni] n multilayer.58(a) Schematic diagram of [Co/Ni] 3 grown on Pt(111) substrate.(b) Compound SPLEEM images highlighting the DWs.The color wheel represents the direction of in-plane magnetization in each image pixel.White arrows show the in-plane spin orientations in the DWs.(c) Schematic illustration of right-handed N eel wall.(d) Histogram of angle a in the DW boundary counted pixel-by-pixel in (b) shows a Gaussian distribution peaking at 180, which corresponds to a righthanded N eel wall.Figures and captions are reproduced with permission from G. Chen et al., Nat.Commun.4, 2671 (2013).Copyright 2013 Nature Publishing Group.

FIG. 16 .
FIG. 16.Bistability of the system associated with a CDW in BFO thin film.(a) Schematic illustration of the experimental set-up on a BFO/lanthanum strontium manganite (LSMO)/tin silicon oxide (TSO) heterostructure.(b) and (c) Crosssectional dark-field TEM images of different domain configurations in the sample.(d)-(g) High-angle annular darkfield (HAADF) scanning transmission electron microscopy (STEM) image of the four different regions.(i) Phase-field simulation of the polarization distribution in the plane of the image of the stable domain structure with a CDW in a BFO film.(j) Simulated polarization distribution in the plane of the image of the stable domain structure of the system without a CDW. 47Figures and captions are reproduced with permission from L. Li et al., Adv.Mater.28(31), 6574-6580 (2016).Copyright 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
FIG. 25.Mechanical force induced ferroelectric and magnetic domain switching in a Bi 5 Ti 3 FeO 15 thin film.(a) Topographic images and corresponding VPFM, LPFM, and MFM images before and after electric and mechanical switching.The BTF thin film was first poled by a positive electric bias of þ20 V over an area of 8 Â 8 lm 2 and then switched by mechanical forces of 14 nN, 50 nN, 100 nN, 500 nN, 1000 nN, and 1300 nN in the center over 4 Â 4 lm 2 , respectively; (b) the surface potential (DV) as a function of F; (c) magnetic response (D ) as a function of F; (d) schematic illustration of ferroelectric domain switching and magnetic domain switching on applying mechanical force. 24Figures and captions are reproduced with permission from T. T. Jia et al., NPG Asia Mater.9, e349 (2017).Copyright 2017 Nature Publishing Group.

FIG. 27 .
FIG. 27.Topological control of conductive states due to tail-tail and headhead charges at the DW.(a) Vertical PFM amplitude and (b) phase image of a ring written by þ9 V bias within a single lateral domain.The polarization vectors are shown in (b).A c-AFM image, taken with V tip ¼ À2.8 V, is shown in (c).To better visualize the conduction map, the outer ring in (c) was flattened to a single 2D map and plotted in (d).92 Figures and captions are reproduced with permission from J. Seidel et al., Adv.Electron.Mater.2(1), 1500292 (2016).Copyright 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

FIG. 28 .
FIG. 28.Skyrmions in multiferroicCu 2 OSeO 3 .Magnetic phase diagram under H jj [111], deduced for (A) bulk and (B) thin-film forms of Cu 2 OSeO 3 , respectively.(C-G)Images for the (110) and (111) planes, respectively, at different magnetic fields, with the magnetic field applied normal to the observed sample plane.In both cases, proper screw-spin texture appears for zero magnetic field, whereas a skyrmion lattice with the identical spin chirality is formed for H ¼ 800 Oe.A magnified view of (D) is shown in (E), where white arrows represent the magnetization direction.(H) Schematic illustration of a single magnetic skyrmion.4Figures and captions are reproduced with permission from S. Seki et al., Science 336(6078), 198-201 (2012).Copyright 2012 American Association for the Advancement of Science.
FIG. 28.Skyrmions in multiferroicCu 2 OSeO 3 .Magnetic phase diagram under H jj [111], deduced for (A) bulk and (B) thin-film forms of Cu 2 OSeO 3 , respectively.(C-G)Images for the (110) and (111) planes, respectively, at different magnetic fields, with the magnetic field applied normal to the observed sample plane.In both cases, proper screw-spin texture appears for zero magnetic field, whereas a skyrmion lattice with the identical spin chirality is formed for H ¼ 800 Oe.A magnified view of (D) is shown in (E), where white arrows represent the magnetization direction.(H) Schematic illustration of a single magnetic skyrmion.4Figures and captions are reproduced with permission from S. Seki et al., Science 336(6078), 198-201 (2012).Copyright 2012 American Association for the Advancement of Science.