Growth and Interfacial Emergent Properties of Complex Oxide Thin Film Heterostructures

Abstract

Non-trivial/chiral spin textures like skyrmions originate from inversion symmetry breaking. Moreover, inversion symmetry breaking combined with strong spin-orbit coupling (SOC) can lead to a large Dzyaloshinskii-Moriya interaction (DMI). Electrically, these phenomena can be detected through what is called the topological Hall effect (THE). In artificially layered complex oxide thin film heterostructures composed of ferromagnetic or antiferromagnetic layers, this THE appears as an emergent property at the interfaces because it is not intrinsic to the bulk layer of such oxides. Thus these heterostructures provide a playground for the competition among DMI, exchange interaction, and magnetic anisotropy to produce novel non-coplanar spin textures and THE in a designable way due to inversion symmetry breaking at the interfaces. With the advancement in modern fabrication techniques, these properties can be tuned at will by engineering the interfaces of the heterostructures, especially due to crystal structure compatibility of these materials. In this chapter, growth, detection and manipulation of interfacial emergent phenomena in complex oxide heterostructures will be discussed.

1. Introduction

Magnetism and magnetic materials lie at the heart of all the electronic storage devices that we all know of (like, magnetic random access memory (MRAM), hard-disk drives (HDD), pen-drives). However, the ever-shrinking dimensions and ever-increasing demands in the storage areal density limit the data transfer rate in the present-day magnetic materials based devices.

Magnetic skyrmions (or simply, skyrmions), which are nanoscale swirling or chiral spin textures arising out of non-trivial real-space topology, are argued to have the potential to be the basis for next-generation magnetic storage devices. Because of the topological protection, these spin textures cannot be unwound without forming a discontinuity, providing them with high stability against external perturbations, even at small sizes. Along with skyrmions, there are other various chiral topological textures that are stabilized due to various magnetic interactions and can be classified by their unique topological properties. The basic requirement for such textures is to have strong spin-orbit coupling (SOC) along with inversion symmetry breaking, which gives rise to Dzyaloshinskii-Moriya interaction (DMI) [1, 2]. Interestingly, this DMI shows up as an anomalous topological contribution to the Hall effect, which thus is called the topological Hall effect (THE), and provides a tell-tale sign of the existence of chiral textures. Although many direct imaging techniques have been developed over the last few years, electrical detection by means of THE has also become a promising technique.

To harness topological textures practically, it is important to develop materials that can stabilize these textures across a wide range of temperatures, and develop all-electrical pathways to manipulate them. A large family of topological textures and control mechanisms have been discovered in magnetic metal-based heterostructures, or chiral magnets such as Heusler compounds [3] and $B_{20}$ systems [4, 5], making them favorites for developing skyrmionics. However, to no wonder, in nature only a few bulk materials have crystal structures that intrinsically aids to the formation of skyrmions. One way out is to design systems in such a manner that these phenomena can “emerge” due to some new interactions, which otherwise are absent in the bulk. Thin films offer this extra space where one can utilize the interfaces and surfaces to modify/tune the interactions separately from their bulk counterparts. Most often, these phenomena emerge at or near the surfaces/interfaces of thin films/heterostructures that are designed at will; due to which they are called “interfacial emergent phenomena”.

Correlated oxide magnets have sparked great attention because they provide the following specific advantages: (i) They host myriad of phases (like, magnetic, multiferroic, etc.) due to strong correlations among various degrees-of-freedom (i.e., charge, spin, orbital and lattice), which are quite susceptible to external perturbations. These couplings provide innovative practical avenues for controlling both intrinsic and emergent magnetic characteristics, such as anisotropy, symmetric exchange interactions, and DMI [6]. (ii) Because of their lower and configurable charge carrier densities, oxides are very responsive to electric fields, making them excellent candidates for non-volatile control. (iii) Additionally, using standard growth techniques, high-quality crystalline oxide thin films with carefully regulated interfaces and/or surfaces and heterostructures thereof, permitting spatial inversion symmetry breaking (with extremely low defects), can be fabricated at will. This chapter focuses on the two key proponents in the field of oxide skyrmionics: the creation of oxide heterostructures and detection and tuning mechanisms, which might set the course for practical oxide-based devices.

We start with a brief discussion on the basic physical interactions that can generate non-collinear or chiral spin textures, followed by their notions in electrical/magnetotransport properties. As a prelude to the electrical detection of such interactions/spin textures, we then discuss the various types of Hall effects and their phenomenological origin that show up in the experiments and cover a large part of the chapter on how to extract (from raw data) the topological Hall effect (THE), i.e. associated with such chiral spin structures. Finally, we discuss the ways one can harness these properties in complex oxide heterostructures. We go straight into the growth/development part of complex oxide heterostructures, followed by the detection and manipulation of the interfacial emergent properties in them. The recent progress in this field of research along with some future outlook is also concluded.

2. Brief basics of Skyrmions

2.1 Skyrmions

A magnetic skyrmion (or simply skyrmion) is a collection of magnetic moments forming non-coplanar/chiral texture. Mathematically it can be described by the topological skyrmion number ($N_{\mathit{sk}}$), which counts the times magnetic moments wraps a unit sphere, and is given by the following expression:

$$N_{\mathit{sk}}=\frac{1}{4\pi }\iint \overrightarrow{m}\left(\overrightarrow{r}\right)\cdot \left(\frac{\partial \overrightarrow{m}\left(\overrightarrow{r}\right)}{\partial x}\times \frac{\partial \overrightarrow{m}\left(\overrightarrow{r}\right)}{\partial y}\right)d^2\overrightarrow{r}$$E1

where $\overrightarrow{m}$($\overrightarrow{r}$) is the magnetic moment. For trivial spin arrangements/textures, like ferromagnet or antiferromagnet, $N_{\mathit{sk}}$ = 0. For magnetic vortices (as in magnetic nanostructures), $N_{\mathit{sk}}=\pm \frac{1}{2}$. For non-trivial spin textures like skyrmions, $N_{\mathit{sk}}$ = 1. There are two basic variations of skyrmions with different spin arrangements along the radial direction, viz., Bloch-type skyrmions and Néel-type skyrmions. In Bloch-type skyrmions, the spins rotate in the tangential planes (that is perpendicular to the radial directions), when moving from the Center to the circumference (periphery). Whereas, in a Néel-type skyrmions, the spins rotate in the radial planes when moving from the Center to the circumference. These are schematically shown in Figure 1. It is worth mentioning that there are other types of chiral spin textures apart from skyrmions and the skyrmion number topological charge can be used to identify the topological distinction of these different types of spin textures.

Figure 1.

Schematic of spin textures in two types of skyrmions: (a) Bloch-type skyrmion, (b) Néel-type skyrmion.

The type of chiral spin texture formation depends on the interplay of different magnetic interactions in a material.

2.2 Interactions involved in stabilizing chiral spin textures

There are various magnetic interactions that can generate skyrmions in magnetic systems, and at times, multiple such mechanisms may contribute simultaneously.

2.2.1 Dzyaloshinskii-Moriya interaction (DMI)

The Dzyaloshinskii-Moriya interaction (DMI) is an asymmetric exchange interaction that favors canting of spins in materials that would, in contrary, be ferromagnetic (FM) or antiferromagnetic (AF) with collinearly aligned spins (either parallel or anti-parallel). The DMI originates from spin-orbit coupling (SOC) and inversion symmetry breaking (typically through bulk crystal structure or multilayer heterostructure). Its Hamiltonian is written as:

$$H_{\mathit{DMI}}=\sum _{i,j}{\overrightarrow{D}}_{\mathit{ij}}\cdot \left({\overrightarrow{S}}_i\times {\overrightarrow{S}}_j\right)$$E2

where ${\overrightarrow{D}}_{\mathit{ij}}$ is the DMI vector. The direction of the DMI vector depends on the symmetry of the system. For bulk material with no inversion symmetry such as $B_{20}$ compounds, the ${\overrightarrow{D}}_{\mathit{ij}}$ is parallel to the vector that connects ${\overrightarrow{S}}_i$ and ${\overrightarrow{S}}_j$ [4, 7]. On the other hand, in multilayer heterostructure composed of a FM layer and a layer with strong SOC, the ${\overrightarrow{D}}_{\mathit{ij}}$ is often parallel to the interface [8], as shown in Figure 2.

Figure 2.

Schematic of the interfacial DMI mechanism that gives rise to emergent phenomena in thin film heterostructures.

2.2.2 Magnetic dipolar interaction

In magnetic thin films with perpendicular easy-axis anisotropy, the dipolar interaction favors an in-plane magnetization, whereas the anisotropy prefers an out-of-plane magnetization. The competition between these two interactions results in periodic stripes in which the magnetization rotates in the plane perpendicular to the thin film. An applied magnetic field perpendicular to the film turns the stripe state into a periodic array of magnetic bubbles or skyrmions.

Apart from these, frustrated exchange interactions and four-spin exchange interactions can also aid to the formation of chiral spin structures. However, in these two cases, the skyrmions are of atomic size length scales (often of the order of the lattice constant $\sim$1 nm).

In case of dipolar interactions, skyrmions are typically of the order of 100 nm to 1 $\mu$m, which is comparable to the period of the spiral determined by the ratio of the dipolar and exchange interactions. In case of DMI, the size is determined by the strength of DMI and is typically 5 nm – 100 nm. As a result, skyrmions in skyrmion crystals in cases (1) and (2) are larger than the lattice constant, and therefore the continuum approximation is justified. In these two cases, the energy density of the skyrmions is much smaller than the atomic exchange energy J, and the topological protectorate holds. In other words, discontinuous spin configurations — called monopoles — with energy of the order of J can create or annihilate the skyrmions.

In complex oxide based thin film heterostructures, one can easily comply with the dipole exchange interaction as well as the DMI interaction by harnessing the inversion symmetry breaking at the interfaces and/or surfaces of the heterostructures, using heavy Z-based elements (Z = atomic number) for strong SOC and of course the thickness to generate anisotropy along various directions with respect to the film plane.

2.3 Detection techniques

There are many various techniques for detection of skyrmions. These include advanced imaging techniques like magnetic force microscopy (MFM), Lorentz transmission electron microscopy (LTEM), spin polarized scanning tunneling microscopy (SP-STM), photoemission electron microscopy (PEEM), etc.; synchrotron radiation based techniques like x-ray magnetic circular dichroism (XMCD). But very intriguing and easy technique is the electrical one, the topological Hall effect (THE). Electrical detection can be easily performed nowadays with the available cryogenic and magnet based systems in any condensed matter physics laboratory.

3. Magnetotransport properties: the family of Hall effect

The Hall effect was discovered by Edwin Hall in 1879 (even before the discovery of the electron) when he observed the evolution of a transverse voltage in conductors for applied electric and magnetic fields which were mutually perpendicular (schematically shown in Figure 3(a)) [9]. Couple of years later, he again reported that the effect was ten times larger in ferromagnetic conductors than in non-magnetic conductors [10], which was hence termed as the “Anomalous” Hall effect (AHE). Then, about a century later, other members started to appear in the family, like the spin Hall effect (SHE), quantum Hall effect (QHE), planar Hall effect (PHE), quantum spin Hall effect (QSHE), to name a few. A recent addition to the family is the topological Hall effect (THE) that is related to the chiral spin textures in materials. All of these effects have different origin in themselves, except for the fact that the experimental arrangements remain same (and hence this arrangement is commonly called the “Hall configuration”). For simplicity and distinguishablity, the original Hall effect is often called as the ordinary Hall effect (OHE). The schematic of the Hall configuration is shown in Figure 3.

Figure 3.

Basic configuration for Hall effect measurement: (a) for bulk or layered (thin film) samples, (b) for patterned thin film samples in the form of “Hall bar”.

Needless to say that this section can form a chapter in itself; so we will try to keep it simple for the readers and discuss phenomenologically some of the important Hall effects, i.e., OHE, AHE, and ofcourse THE, those are of interest for this chapter.

3.1 Ordinary Hall effect (OHE)

When electric current ($I$) flows (say along $x$-direction) through a metal or a semiconductor placed in a perpendicular magnetic field (${\mu }_{0}H$, say along $z$-direction), the charge carriers inside the material are deflected from the straight path by the magnetic field as per the Lorentz force (given by Eq. (3)).

$$\overrightarrow{F}=q\left[\overrightarrow{E}+\left(\overrightarrow{v}\times \overrightarrow{B}\right)\right]$$E3

This results in charge accumulation on the sides (in $y$-direction) preferably depending on the type of charge carrier, giving rise to a transverse voltage along the $y$-direction (i.e., mutually perpendicular to that of both $I$ and ${\mu }_{0}H$). This voltage is called the Hall voltage ($V_{\mathit{xy}}$); and in a non-magnetic material it is proportional to the applied magnetic field. The Hall resistance ($R_{x}y$ = $V_{\mathit{xy}}$/$I_{\mathit{xx}}$) due to OHE is expressed as $R_{\mathit{OHE}}$ = ${\mu }_0{R}_{0}H$, where $R_0$ is the ordinary Hall coefficient.

3.2 Anomalous Hall effect (AHE)

In conducting magnetic materials with uniform magnetization ($M$), like ferromagnets, an anomalous contribution to the Hall signal is often observed in addition to the OHE, which is called “anomalous” Hall effect (AHE). AHE occurs intrinsically due to the spin-orbital coupling as a result of the “fictitious” magnetic field added by the magnetization and thus the anomalous Hall resistance is proportional to the magnetization $M_z$, expressed as:

$$R_{\mathit{AHE}}=R_A{M}_z$$E4

where $R_A$ is the anomalous Hall coefficient. However, apart from intrinsic source (i.e., $M$), there can be extrinsic sources (impurity scattering like, side-jump or skew scattering) can contribute to the anomalous Hall signal. Information of the contributing source (intrinsic or extrinsic) is generally contained in the $R_A$: For intrinsic sources, $R_A$$\propto$$R_{\mathit{xx}}^2$; and for extrinsic sources $R_A$$\propto$$R_{\mathit{xx}}$ (where $R_{\mathit{xx}}$ is the longitudinal resistance of the sample).

Thus AHE basically occurs due to the effect of magnetic field on the spin orientation in momentum (reciprocal) space and not in position (real) space that makes it different from topological Hall effect which is associated with spin arrangements in real space (Figure 4).

Figure 4.

Schematics of THE typical signatures of Hall resistances arising from different types of Hall effects: (a) OHE only, (b) AHE only, and (c) THE only.

3.3 Topological Hall effect (THE)

In materials with topologically protected real space chiral spin textures, such as skyrmions, strong exchange coupling occurs between the moments of the conduction electrons and the local magnetic moments at each sites. The spin of the electrons adiabatically follow the spin texture and thus pick up a quantum-mechanical Berry phase, which obviously is sensitive to the topology of the texture. The Berry phase is considered to give rise to another “virtual” (or emergent, or effective) spatially varying magnetic field, $b_{\mathit{eff}}$. As a result, the conduction electrons “feel” the emergent virtual magnetic field ($b_{\mathit{eff}}$) arising from the spin textures and are deflected perpendicularly to the applied current direction, resulting in the so-called topological Hall effect (THE). This THE appears as a bump or dip during the hysteretic Hall resistivity measurements. Thus, unlike OHE or AHE, it is obviously neither proportional to external magnetic field (${\mu }_{0}H$) nor to the magnetization ($M$) of the sample.

In contrast, the topological Hall voltage signal is proportional to emergent magnetic field ($b_{\mathit{eff}}$). In case of skyrmions, the $b_{\mathit{eff}}$ contains the information of the skyrmion density; it is proportional to $n_{\mathit{sk}}$, and hence for skyrmions, the THE voltage is inversely proportional to the size of the skyrmions. The topological Hall resistivity can be given by the following equation [11]:

$${\rho }_{\mathit{\text{THE}}}=\frac{{\mathit{PR}}_0{b}_{\mathit{eff}}}{\mathit{en}}=\frac{P{\mathrm{\Phi }}_0}{d_{\mathit{sk}}^2\mathit{en}}$$E5

Here, $P$- spin polarization of carriers, $d_{\mathit{sk}}$- distance between skyrmions, $n$- carrier density and ${\mathrm{\Phi }}_0$ is the quantum flux ($h/e$). The skyrmion density ($n_{\mathit{sk}}$) gives rise to the emergent magnetic field as $b_{\mathit{eff}}$ = $n_{\mathit{sk}}{\mathrm{\Phi }}_0$. Thus from Eq. (5), one can say that separation of skyrmions ($d_{\mathit{sk}}$) varies as $n_{\mathit{sk}}^{-1/2}$. Eq. (5) can thus also be re-written as

$${\rho }_{\mathit{\text{THE}}}={\mathit{PR}}_0{n}_{\mathit{sk}}{\mathrm{\Phi }}_0$$E6

It must be mentioned here, that, in case of skyrmions, the emergent magnetic field ($b_{\mathit{eff}}$) is expected to be independent of temperature and often is very high (may range from few tens of Tesla to few hundreds of Tesla) [12].

It is highlighted here that the appearance of distinctive bumps or dips in Hall resistivity signal of such chiral magnetic systems is a direct consequence of stabilization of non-collinear topological spin textures. However, it should be noted that complications in AHE, e.g., arising from the electronic band structure or sign change of the dominant scattering mechanism might influence the Hall resistivity signal equivalently [13], resulting in similar transport features. The emergence of a bump/dip characteristic in the Hall effect, for example, may not hold strict for skyrmions; and thus cannot always suffice as an unambiguous evidence for identifying non-collinear “topological” spin textures [14, 15]. Hence, along with THE detection, other imaging/x-ray based techniques (as mentioned above) might be required to support the claim of skyrmions as the origin of THE.

In any case, the acquired total Hall resistance signal contains the three components: OHE, AHE and THE. It is thus necessary to discuss in detail how to extract individual components in order to eliminate any experimental artifacts [16].

3.3.1 THE signal extraction technique

Step-1: During experiments with unpatterned thin film samples (say, as in Figure 2(a)), electrical four-probe (or van der Pauw) contacts are often made with conductive paints or solders by eye estimation, which adds the longitudinal magnetoresistance (MR) component in the Hall resistance due to the inevitable misalignment of the electrodes. This has to be removed, first, by using $R_{\mathit{xy}}$($H$)$\uparrow$ = [$R_{\mathit{xy}}^{\mathit{raw}}$($H$)$\uparrow$ - $R_{\mathit{xy}}^{\mathit{raw}}$(−$H$)$\downarrow$]/2, where $R_{\mathit{xy}}^{\mathit{raw}}$($H$)$\uparrow$ stands for the measured raw data in the $4^{\mathit{th}}$ and $1^{\mathit{st}}$ quadrants with the magnetic field scanning from -$\mid {\mu }_0{H}_{\mathit{max}}\mid$ to +$\mid {\mu }_0{H}_{\mathit{max}}\mid$ and $R_{\mathit{xy}}^{\mathit{raw}}$(−$H$)$\downarrow$ the measured raw data in the $2^{\mathit{nd}}$ and $3^{\mathit{rd}}$ quadrant for the reversed field scanning. Similarly, the $R_{\mathit{xy}}$($H$)$\downarrow$ branch was extracted using [$R_{\mathit{xy}}^{\mathit{raw}}$($H$)$\downarrow$ - $R_{\mathit{xy}}^{\mathit{raw}}$(−$H$)$\uparrow$]/2. In this way one can eliminate the longitudinal (MR) contribution due to misalignment of electrodes. Apart from this, another way to eliminate it from appearing in the Hall data is by pattering the thin film samples in the form of Hall bar. This leaves us with pure Hall signal ($R_{\mathit{xy}}$) which contains the contributions: $R_{\mathit{xy}}^{\mathit{\text{total}}}$ = ${\mu }_0{R}_{0}H$ + $R_A{M}_z$ + ${\mathit{PR}}_0{b}_{\mathit{eff}}$.

Step-2: The ordinary Hall resistance component (which varies linearly with the applied magnetic field) is subtracted from the total Hall resistance loop by slope-deduction method at the high field region. This leaves us with the AHE and THE components: $R_{\mathit{xy}}^{\mathit{\text{total}}}$ - $R_{\mathit{OHE}}$ = $R_{\mathit{AHE}}$ + $R_{\mathit{\text{THE}}}$.

Step-3: Finally the AHE component ($R_{\mathit{AHE}}$) is subtracted from the above equation to obtain only $R_{\mathit{\text{THE}}}$ contribution. There are two methods to find $R_{\mathit{AHE}}$: one is by measuring out-of-plane magnetization ($M_z$) and the $R_A$ from longitudinal resistivity (as mentioned in Section 3.2). The other method is by fitting with trial tanh or Langevin functions to estimate the AHE, which though is a crude method. Finally what remains is the $R_{\mathit{\text{THE}}}$ signal only. The complete process is shown schematically in Figure 5. In the next sections we discuss the origin of and ways to manipulate the topological Hall effect in complex oxide heterostructures.

Figure 5.

Steps for extracting THE THE signal from typical Hall data:- (a) gray curve: $R_{\mathit{xy}}^{\mathit{\text{total}}}$. Find OHE by slope-deduction method (red curve) at high field region. (b) after performing Step-2 (mentioned in text), dark gray curve: $R_{\mathit{AHE}}$ + $R_{\mathit{\text{THE}}}$. (c) $R_{\mathit{AHE}}$ determined from magnetization ($M-H$) data. (d) Finally after performing Step-3 (as in text), what remains is THE pure THE resistivity signal (black curve).

4. Oxide Heterostructures

The quest for magnetic textures in oxides have taken new thrust very recently after the celebrated discovery of chiral spin texture in La_1.37Sr_1.63Mn₂O₇ compound [17]. In this manganite compound, promisingly low threshold current density ($J_c$$\sim$ 10⁷ A/m²) was recorded for their electrically driven motion. Since then, over the years, various layer-by-layer or step-flow oxide growth techniques have emerged, which have enabled the creation of high-quality interfaces for novel heterostructure design. Interface engineering in complex oxide heterostructures has developed into a flourishing field as various intriguing physical phenomena can be demonstrated which are otherwise absent in their constituent bulk compounds [18]. Such capability has opened doors for stabilizing Néel-type skyrmions by engineering the interfacial DMI.

4.1 Growth of oxide heterostructures

Practical applications demand high-quality thin film growth. Owing to some significant advances in the fabrication techniques of high quality oxide heterostructures and the structural compatibility of these kind of complex oxides, the minute tuning of interfacial properties can be routinely achieved. Advanced techniques such as sputtering, pulsed laser deposition (PLD), and molecular beam epitaxy (MBE) have been successfully used to produce high-quality crystalline manganite thin films. Moreover, the presence of a substrate adds another degree of freedom, the external pressure in the form of stress. This is why one of the major characteristics of epitaxial thin films is the strain, which induces modifications in the physical properties (structure, transport and magnetic order) with respect to the bulk.

On the other hand, most of the interfacial emergent properties are highly sensitive to the structure of the interfaces/surfaces, since they arise out of various modified exchange interactions across the interfaces or at the surfaces/terminations (as we will soon explore in upcoming sections of this chapter), and may easily get lost due to presence of slightest of defects.

Intuitively, one has to create a very clean engineered surface or interface to play with such emergent phenomena.

5. Interfacial emergent properties of oxide Heterostructure

As discussed in earlier sections that THE arising from stabilized chiral spin structures or skyrmions require DMI. Considering that the DMI arises from spin-orbit coupling combined with broken inversion symmetry, it is possible to artificially introduce DMI at the surface/interface of complex oxide heterostructures, as discussed below.

Although the individual layers as whole may not show exotic/non-trivial spin structures, various mechanisms like strain, exchange interaction, proximity effect, etc., at the interfaces or surfaces may induce such phenomena and hence, in these heterostructures these properties are called “interfacial emergent” properties.

5.1 Origin and tuning of interfacial DMI

Skyrmions were observed in epitaxial ultrathin ferromagnetic films in the proximity of heavy metal layers, which are subject to giant “emergent” DMIs induced at the interface that breaks inversion symmetry and the strong SOC with neighboring heavy metal. The first investigated system in this class showing “emergent” DMI was heterostructure of Fe monolayer grown on Ir(111) [19].

It is well know that $3d$ transition metal ions rarely show any SOC effect and thus are unlikely to show DMI alone. Rather $4d$ and $5d$ ions are a very good candidate for DMI as they bear inherent strong SOC. For example, SrRuO${}_3$ (SRO) (a $4d$ transition metal oxide) has a SOC strength of $\sim$150 m$e$V, while 5$d$ transition metal oxide SrIrO₃ (SIO) has SOC strength of $\sim$450 meV, 3 times larger than that of SRO [20].

Thus $4d$ and $5d$ based oxides provide platform for engineering the interfacial DMI along with the manganites (Mn based ($3d$) oxides), which have myriad of magnetic phases. The most versatile candidates are SrRuO₃ (SRO), SrIrO₃ (SIO), BaTiO₃ (BTO) and La_2/3Sr_1/3MnO₃ (LSMO); additionally, they posses very common crystal structure- the ABO₃ Perovskite structure and hence high quality layer-by-layer growth can be easily achieved. In the following sub-sections, some recent progress in this field is presented, highlighting the origin and tuning mechanisms of the interfacial DMI, detected electrically through topological Hall effect.

5.1.1 Bilayer structures with strong SOC based oxide

The first investigated system in this class was epitaxial bilayer heterostructure of SRO and SIO in 2016 [11]. SIO is a paramagnet which can host $5d$ electrons with strong spin-orbit coupling [21], and SRO is an itinerant ferromagnet with a Curie temperature ($T_{\mathrm{C}}$) of $\sim$160 K [22]. The bilayers were grown by PLD on SrTiO₃ (STO) substrate with different SRO layer thickness ($m$, basically the number of unit cells) ranging from 4 to 7 unit cells, while keeping the SIO layer thickness fixed at 2 unit cells (uc). So in the layered structure STO//SRO ($m$ uc)/SIO (2 uc), the interface between SRO and SIO provided the broken inversion symmetry and the SIO layer provided the strong SOC, mimicking an effective “heavy metal” layer. The systematics of the magnetic and transport properties of the bilayers were governed by SRO and could be precisely controlled by tuning SRO layer thickness, $m$.

Using techniques mentioned as in Section 3.3.1 above, THE component was extracted from the Hall resistivity data for each measurements, where AHE components were derived by measuring the Kerr rotation angle (the Kerr signal magnitude is proportional to $M$ and thus to AHE as well). Among the samples, the THE was highest for $m$ = 4 uc. With increasing $m$ to 5 uc, similar peak structure related to THE could be observed, however, the THE component decreased. Upon further increasing $m$, THE decreased and vanished at only $m$=7 uc.

At the high magnetic field regions (say $\pm$9 T) where the magnetization gets saturated, the spins at the Ru sites align ferromagnetically (in corresponding directions depending on field), which lead to absence of spin chirality and the Hall resistivity in those high field regions could be attributed to AHE only. Decreasing the field from 9 T to 0 T, it remains in the ferromagnetic (FM) state with positive magnetization, which corresponds to the observed finite AHE and the negligible THE. With further decrease of the magnetic field from 0 to −0.8 T, absolute value of THE sharply increases upto −0.06 T and then gradually decreases to zero at around −0.4 T. This field (−0.4 T) coincides with the field at which the hysteresis in $M$ vs. ${\mu }_{0}H$ loop closes. This is indicative of the fact that some specific spin structure with finite scaler spin chirality might have been induced when the FM spins started to reverse. The appearance of hysteresis in magnetization and THE in Hall resistivity at simultaneous field range indicates a coexistence between co-planar FM phase and the scalar spin chiral phase.

As discussed earlier, the most plausible chiral spin texture responsible for THE is magnetic skyrmion which gives rise to the emergent magnetic field. This emergent magnetic field strongly affects the electron transport and marginally affects the magnetization.

Due to the broken inversion symmetry at SRO/SIO interface and the strong SOC of SIO, the finite DM vector pointed in the in-plane direction, which might give rise to a Néel-type magnetic skyrmion. The fact, THE appeared only when 4 $\ge$$m$$\le$ 6, suggests that it was derived from interfacial DMI.

It is worth mentioning that in contrast to the very narrow $T-H$ window of THE in bulk $B_{20}$ compounds (which exhibit Bloch type skyrmions), the THE in oxide bilayer heterostructures was found within a wide $T$ range upto around 90 K. The thickness variation also revealed the stabilization of 2-D nature of the Néel-type skyrmions.

Moreover, utilizing Eqs. (5) and (6) with P $\sim$ -9.5 $\%$ for SRO [23], the distance between skyrmions in these bilayers was approximately estimated to be around 10 nm to 20 nm. This provided an estimation of the length scales of the skyrmions, which was always larger than the film thickness ($\sim$2 nm in this case) and confirmed the two-dimensional nature of the skyrmions.

5.1.2 Single layer ultrathin film

In another contrasting work, a few years ago, THE was observed in a single layer SRO film grown on STO insulating substrate; but this time, astonishingly, without the presence of any $5d$ based metal oxides like SrIrO₃ [24]. Here the thickness of SRO films ranged from 3 nm to 10 nm, all having tetragonal structure. From structural characterizations it was observed that the strained SRO films in tetragonal phase showed rotation of the RuO₂ octahedra about the c-axis, which could persist upto several tens of nm.

In this case also, the THE appeared in the vicinity of the magnetization reversal, which was consistent with the previous result as mentioned above. Furthermore, the amplitude of the THE resistivity increased with increasing $T$ from 20 K to 80 K, and above 85 K, THE signal vanished. The itinerant magnetic property and the strong perpendicular magnetic anisotropy in these single layer SRO films are indicative of the fact that the non-trivial topological spin texture responsible for the THE must be the Néel skyrmion.

Needless to say, the terminating surface provides the broken symmetry for this single layer system, while Ru ions at the surfaces are the sources of SOC. This gave rise to the DMI, where DM vector also point along the film plane. The oxygen octahedral rotation due to combination of substrate induced strain and natural termination of top layer has a significant effect on THE of the SRO single layer.

Further, in order to elucidate on the origin of SOC of Ru ions at the surface layers, Hall transport was measured in presence of extra electric field, provided by ionic liquid gating. Although the electric field generated from the ionic liquid could be much higher as compared to that with conventional voltage gating, the penetration depth of the electric field might only be a nm or less due to the high carrier density of the SRO. It was observed that upon applying negative gate bias, the THE diminished. The reason is as follows: Upon applying gate bias, the momentum space around the Fermi level of SRO changed [25]. The electric potential gradient near the SRO surface resulted in a change in the inversion asymmetry, which modulated the SOC in that region. This is reminiscent of the phenomenon observed in case of Rashba-type band splitting and spin splitting [26, 27]. The combined contribution of change in SOC and change in inversion asymmetry affected the DMI, which resulted in the enhancement or suppression of THE with the polarity of gate bias.

As earlier, in the single layer SRO films, the emergence of the THE was observed at reduced dimensions, for thickness 3 nm to 6 nm but not in 10 nm film. This, along with the gate voltage modulation of the THE indicated that 2-D Néel skyrmions formed at the surface of the SRO single layer films.

5.1.3 Bilayer heterostructure with ferroelectric layer

Now that we have explored the idea of tuning the THE by applying electric field through ionic gating on SRO single layer films, one might be intuitively tempted to utilize ferroelectric materials in the proximity of SRO layers, as ferroelectric materials could be easily manipulated by electric field since they have the added advantage of inherent inversion symmetry breaking.

Heretofore, tuning of interfacial DMI due to lattice distortions driven by ferroelectricity at the SrRuO₃/BaTiO₃ (BTO) interface was investigated in detail [28]. Ultrathin bilayer heterostructures of SRO/BTO were prepared on STO substrate with SRO as the bottom layer. The SRO layer thickness $t_{\mathit{SRO}}$ was varied between 4 and 8 uc and BTO layer thickness $t_{\mathit{BTO}}$ was varied between 3 and 20 uc.

FE-driven ionic displacements in BTO could cross the interface and continue for several unit cells into SRO, a phenomenon what is known as the FE proximity effect [29]. The inevitable lattice distortion due to FE proximity effect could break the inversion symmetry of the SRO structure near SRO/BTO interface. The degree of this inversion symmetry breaking in SRO could be elucidated as the vertical ionic displacement between Ru and O (${\delta }_{\mathit{Ru}-O}$) ions in the RuO₂ plane, taking into account a c-axis-oriented FE polarization. In such a case also, one can expect a emergent DMI in the ferroelectrically distorted SRO lattice, where DM vector should lie in-plane, perpendicular to the Ru-O-Ru chains. Accordingly, it is expected that this in-plane DMI at the vicinity of SRO/BTO interface might stabilize Néel-type magnetic skyrmions, giving rise to emergent THE.

As obvious, The Hall signals of SRO/BTO samples depend strongly on the individual layer thicknesses. In this case, the THE signal persisted upto $T$$\sim$ 80 K, but for a much larger field range, with peak around ±1.65 T and vanished at around ±3.9 T.

To estimate the basic skyrmionic properties from the THE signal, the evolution of $n_{\mathit{sk}}$ (estimated from Eq. (6)) with sample structures (basically $t_{\mathit{SRO}}$ and $t_{\mathit{BTO}}$). With increasing $t_{\mathit{SRO}}$ from 4 to 6 uc, $n_{\mathit{sk}}$ decreased rapidly by almost an order of magnitude, which implied that the DMI was stronger in the vicinity of the SRO/BTO interface. On the other hand, $n_{\mathit{sk}}$ also decreased with decreasing $t_{\mathit{BTO}}$ below 8 uc due to suppression of the FE polarization. This trend further demonstrated that skyrmions could be driven by FE, through the proximity effect.

Further, because of a strong correlation between the interfacial DMI and FE, the manipulation of skyrmions with changes in ferroelectric polarization of BTO layer was also explored. For this, the BTO layer had to be electrically poled into pre-designed domain structures which led to local switching of the BTO polarization in the patterned Hall bars of the bilayer structures. This was performed using a conducting AFM tip at room temperature; voltage bias of -(+)8 V led to upward (downward) poling; and then the Hall measurements were performed at low temperatures. The local switching of the BTO polarization (in the out-of-plane/c-axis direction in this case) due to poling led to changes in the ${\delta }_{\mathit{Sr}-\mathit{Ru}}$ near the SRO/BTO interface. This further led to changes in ${\delta }_{\mathit{Ru}-O}$ from the pristine state, which remarkably affected the THE signal. It was observed that the uniformly upward-poled Hall bar exhibited enhancement in polarization which slightly enhanced the ${\rho }_{\mathit{\text{THE}}}$ as compared with that in pristine FE state. However, upon complete downward poling, polarization changed and as a result ${\rho }_{\mathit{\text{THE}}}$ decreased by about 80 $\%$. The magnetic field and temperature range of THE also got reduced due to downward poling which signified a substantial reduction in $n_{\mathit{sk}}$.

Thus, by downscaling the FE domain size in the above procedures, one might not only be able to tune the overall skyrmion properties microscopically but also could control the nucleation/deletion of individual skyrmions.

5.1.4 Bilayers heterostructures composed of manganites

Enlightened by the observations thin films and heterostructures as mentioned in previous sub-sections, an intuitive question appears: whether the emergent THE observed in these complex oxide heterostructures only appear specifically in the presence of SRO, which itself exhibits a relatively large SOC with $4d$ transition-metal Ru? Hence, it became desirable to investigate the magnetotransport properties in heterostructures composed of SIO and other magnetic oxides. In this subsection, we discuss briefly the emergent THE observed for the first time in the $3d$ perovskite La_0.7Sr_0.3MnO₃ (LSMO) in SIO/LSMO heterostructures deposited epitaxially on the (001) STO substrates [30].

Although the magnetic easy axis of LSMO is commonly known to lie in-plane along $<110>$ direction on STO (001)-oriented substrate, it was reported that the easy axis could shift to $<100>$ direction when interfaced with a SIO layer of thickness $<$ 5 uc due to strong SOC of SIO layer [31]. Hence the heterostructures used for the study of THE were composed of 2 uc SIO followed by 6–10 uc LSMO; the final structure being STO//SIO (2 uc)/LSMO ($m$ uc), $m$ = 6,8,10.

As shown in Figure 6, the emergent THE peak appeared in a wide temperature range of upto 200 K, and exhibited a gradual broadening with decreasing temperature, very similar trend seen in other oxide heterostructure systems as mentioned above and in typical skyrmion hosting materials like the $B_{20}$ alloys [7]. Moreover, the giant THE resistivity of $\sim$ 1.0 $\mu \mathrm{\Omega }$.cm (in average) was significantly higher than those reported in complex oxide heterostructures composed of SRO/SIO, SRO/BTO or SRO films, demonstrating the feasibility of using the proximity effect of SIO to create novel spin textures in oxide magnetic heterostructures.

Figure 6.

(a) Upper panel: AHE + THE combined signal at 200 K for SIO (2 uc)/LSMO (8 uc) heterostructure; lower panel: Only THE resistivity at 200 K for THE same sample. (b) $H$-$T$ phase diagram of THE THE resistivity for same heterostructure generated from Hall measurements at various temperatures. (c) Ordinary Hall co-efficient at various temperatures obtained from Hall measurements for THE same heterostructure. (d) Upper panel: Peak value of THE THE resistivity at various temperatures measured several times and on several samples of THE same heterostructure SIO (2 uc)/LSMO (8 uc), that showed THE reproducibility of THE THE signal; lower panel: The effective fictitious magnetic field obtained from Eq. (5), which was almost constant with temperature, confirmed that the emergent THE was due to formation of skyrmions as a result of interfacial DMI. [reprinted (adapted) with permission from [30]. Copyright (2019), American Chemical Society.]

To confirm the interfacial origin of the THE observed in the LSMO/SIO heterostructures, Hall effect measurements were performed on separate LSMO single layer films and on LSMO (8 uc)/STO (2 uc)/SIO (2 uc) trilayer heterostructures, both grown on STO substrates. Distinctively, no THE signals were observed in those two samples (single layer and trilayer). Although the absence of THE in LSMO single layer films was upto expectation, the absence of THE in the trilayer samples could only be ascribed to the inserted non-magnetic insulating STO layer, which interrupted the strong interfacial DMI between the LSMO and SIO layers.

The effective emergent magnetic field $b_{\mathit{eff}}$, associated with the real space Berry phase, was also found to be independent of temperature upto 200 K as shown in Figure 6(d), with an average value of around 12 Tesla. Such a strong stability against temperature indicated that the origin of emergent THE might be due to skyrmions.

In another work, interfacial atomic layer control of THE by deliberately controlling the competition between chiral DMI and intrinsic collinear FM in $3d$-$5d$ heterostructures composed of LaMnO₃/SrIrO₃ was demonstrated [32]. This interfacial symmetry control led to a large THE, which was believed to be originated from a highly robust chiral magnetic phase, potentially hosting skyrmions.

6. Further scope

Heterostructure engineering in complex oxide systems with polycrystalline heavy metal layers like, Pt or W instead of strong SOC based oxides is now an active sub-domain of research which is worth investigating, since the interfacial DMI is key for stabilization of Néel type skyrmions.

It has long been felt for the utilization of oxides in the field of flexible electronics. This requirement has triggered the research on growth and characterization of complex oxide thin films like on various flexible substrates like, mica, polymide tapes, etc. [33, 34] using common epitaxial lift-off techniques with the aid of sacrificial layers. A thorough and exhaustive study on the film growth and transfer on flexible substrates, their characterization (using AFM or electron microscopy techniques) and further establishing a direct relationship between strain and magnetic, magnetotransport properties are now being investigated in details.

7. Conclusions

To conclude, we presented the detection technique of interfacial emergent phenomena like interfacial DMI by means of topological Hall effect (THE) in complex oxide heterostructures, which only provides a tell-tale sign of the existence of chiral textures.

We also presented recent progresses towards various methods of achieving and tuning the inversion asymmetry and spin-orbit coupling to tailor minutely the interfacial DMI in those kind of thin film heterostructures, based on some recent works. To illustrate, we presented examples from each of the following methods: tuning the structure through atomic (unit cell) layer control at interface of $4d$/$5d$ based heterostructures (SRO/SIO); harnessing octahedral rotation due to strain in ultrathin single layer SRO films; utilizing ferroelectric polarization to tune the RuO${}_2$ octahedra in SRO/BTO heterostrcutures; using the exchange interactions among the Mn spins in ($3d$-$5d$) based heterostrcutures (LSMO/SIO) and superlattices (LMO/SIO) by means of unit cell modification along with the strong SOC of the $5d$ layers at the interfaces.

For the device application thin film heterostructures are very important. We expect that the recent progresses will aid to the future skyrmion based devices for the manipulation by current, electric field and/or by some other techniques as well, so that the information can be used for the memory devices and logic implementation.

Acknowledgments

The author acknowledges Dr. Samik DuttaGupta and Mr. Arnab Bhattacharya of SINP, Kolkata, for scientific discussions. Finally, the author acknowledges TCG CREST, Kolkata, for the Post-Doctoral fellowship.

Conflict of interest

The author declares no conflict of interest.