A glimpse at topological structures in multiferroic materials

Ferroic materials are defined by having an order parameter that can be oriented in more than one direction. Within a ferroic material, then, there can be regions (domains) with different orientation of the order parameter: magnetic domains in ferromagnets, polar domains in ferroelectrics, twins in ferroelastics. Domain walls, or domain boundaries, are the separations between adjacent domains. In the last few years, domain walls have moved from being regarded as an inevitable by-product of the domains, to regions of interest in their own right, with unique electronic properties that may be used as the active ingredient in new electronic device paradigms, in what has been called “domain wall nanoelectronics”. The present book chapter outlines the basic physics of domain walls from their thickness and internal structure to their properties and dynamics. We will draw the connection between the fundamental properties and their experimental observation. The last section will discuss current unresolved challenges in this exciting and emerging field.

Considerable work has focused on the use of epitaxial strain to engineer domain structures in ferroic materials. Here, we revisit the observed reduction of domain variants in rhombohedral BiFeO3 films on rare-earth scandate substrates. Prior work has attributed the reduction of domain variants to anisotropic in-plane strain, but our findings suggest that the monoclinic distortion of the substrate, resulting from oxygen octahedral rotation, is the driving force for variant selection. We study epitaxial BiFeO3/DyScO3 (110)O heterostructures with and without ultrathin, cubic SrTiO3 buffer layers as a means to isolate the effect of “symmetry mismatch” on the domain formation. Two-variant stripe domains are observed in films grown directly on DyScO3, while four-variant domains are observed in films grown on SrTiO3-buffered DyScO3 when the buffer layer is >2 nm thick. This work provides insights into the role of the substrate—beyond just lattice mismatch—in manipulating and controlling domain structure evolution in materials.

The effect of excess Ba concentration on the dielectric nonlinearity was investigated in Mn and V-doped BaTiO3 multi layer ceramic capacitors (MLCC) under the same grain size condition, which was described by the Preisach model utilizing the first order reversal curve (FORC) distribution. The high-field dielectric constant and its ac field dependence dramatically changed increasing to a maximum and then decreasing with the increase of Ba concentration. The saturation polarization which scales to the magnitude of spontaneous polarization also showed similar behavior. These results indicate that the dependence of the dielectric constant on the Ba concentration is associated with the variation of both domain wall contribution and the magnitude of the spontaneous polarization, which could be correlated with the same dependence on the Ba concentration of the reversible FORC distribution at zero bias and the irreversible FORC distribution near origin. In the corresponding bulk specimens of the dielectrics of MLCC, almost the same amount of the Ba2TiSi2O8 second phases were detected irrespective of Ba concentration, which shows that the excess Ba incorporate into BaTiO3. Thus, low and high Ba concentration corresponds to Ba-deficient and Ba-rich or Ti-deficient BaTiO3, respectively, which results in a small spontaneous polarization and low domain wall density. The intermediate Ba concentration for the maximum dielectric constant is supposed to be near stoichiometric condition in the ABO3 structure corresponding to large spontaneous polarization and high domain wall density. The excess Ba concentration and its resultant A/B stoichiometry is a crucial factor controlling dielectric properties.

Rashba spin-orbit torque derived from the broken inversion symmetry at ferromagnet/heavy metal interfaces has potential application in spintronic devices. In the conventional description of the precessional and damping components of the Rashba spin-orbit torque in magnetization textures, the decomposition coefficients are assumed to be independent of the topology of the underlying structure. Contrary to this common wisdom, for Schr\"odinger electrons trespassing ballistically across a magnetic domain wall, we found that the decomposition coefficient of the damping component is determined by the topology of the domain wall. The resultant damping Rashba spin-orbit torque is protected by the topology of the underlying magnetic domain wall and robust against small deviations from the ideal domain-wall profile. Our identification of a topological damping Rashba spin-orbit torque component in magnetic domain walls will help one to understand experiments on current-driven domain-wall motion in ferromagnet/heavy metal systems with broken inversion symmetry and to facilitate its utilization in innovative device designs.

We investigate the Gilbert damping and the magnetization switching of perpendicularly magnetized FeCoB-based free layers embedded in tunnel junctions adequate for spin-torque operated memories. We study the influence of the boron content in MgO / FeCoB /Ta systems alloys on their Gilbert damping after crystallization annealing. Increasing the boron content from 20 to 30\% increases the crystallization temperature, thereby postponing the onset of elemental diffusion within the free layer. This reduction of the interdiffusion of the Ta atoms helps maintaining the Gilbert damping at a low level of 0.009 without any penalty on the anisotropy and the magneto-transport properties up to the 400$^\circ$C annealing required in CMOS back-end of line processing. In addition, we show that dual MgO free layers of composition MgO/FeCoB/Ta/FeCoB/MgO have a substantially lower damping than their MgO/FeCoB/Ta counterparts, reaching damping parameters as low as 0.0039 for a 3 \r{A} thick Tantalum spacer. This confirms that the dominant channel of damping is the presence of Ta impurities within the FeCoB alloy. On optimized tunnel junctions, we then study the duration of the switching events induced by spin-transfer-torque. We focus on the sub-threshold thermally activated switching in optimal applied field conditions. From the electrical signatures of the switching, we infer that once the nucleation has occurred, the reversal proceeds by a domain wall sweeping though the device at a few 10 m/s. The smaller the device, the faster its switching. We present an analytical model to account for our findings. The domain wall velocity is predicted to scale linearly with the current for devices much larger than the wall width. The wall velocity depends on the Bloch domain wall width, such that the devices with the lowest exchange stiffness will be the ones that host the domain walls with the slowest mobilities.

Noncollinear ferroic materials are sought after as testbeds to explore the intimate connections between topology and symmetry, which result in electronic, optical, and magnetic functionalities not observed in collinear ferroic materials. For example, ferroaxial materials have rotational structural distortions that break mirror symmetry and induce chirality. When ferroaxial order is coupled with ferroelectricity arising from a broken inversion symmetry, it offers the prospect of electric‐field‐control of the ferroaxial distortions and opens up new tunable functionalities. However, chiral multiferroics, especially ones stable at room temperature, are rare. A strain‐stabilized, room‐temperature chiral multiferroic phase in single crystals of BaTiS3 is reported here. Using first‐principles calculations, the stabilization of this multiferroic phase having P63 space group for biaxial tensile strains exceeding 1.5% applied on the basal ab‐plane of the room temperature P63cm phase of BaTiS3 is predicted. The chiral multiferroic phase is characterized by rotational distortions of TiS6 octahedra around the long c‐axis and polar displacement of Ti atoms along the c‐axis. The ferroaxial and ferroelectric distortions and their domains in P63‐BaTiS3 are directly resolved using atomic resolution scanning transmission electron microscopy. Landau‐based phenomenological modeling predicts a strong coupling between the ferroelectric and the ferroaxial order making P63‐BaTiS3 an attractive test bed for achieving electric‐field‐control of chirality.

Members belonging to the Dion–Jacobson (DJ) family of layered perovskites have time and again proven to be the preferred materials of choice for the exploration and identification of polar structures. We report two noncentrosymmetric n = 2 DJ members, A′SmNb2O7 (A′ = Rb, Cs), prepared by high-temperature solid-state reactions, thus expanding the polar n = 2, DJ series as A′ANb2O7 (A′ = Rb, Cs; A = La, Pr, Nd, Sm, Bi). Optical second harmonic generation measurements utilizing 1064 nm substantiated the existence of Type I phase matchable compounds, and the efficiencies were 4 to 6 times higher than the standard KDP. Structural refinements by the Rietveld method confirm the polar orthorhombic space groups of I2cm and P21am, respectively, for RbSmNb2O7 [a = 5.4368(3) Å, b = 5.3944(3) Å, c = 21.9051(1) Å] and CsSmNb2O7 [a = 5.4669(5) Å, b = 5.4158(4) Å, c = 11.1437(1) Å]. The orthorhombic distortions and symmetry lowering were further supported by the Raman spectroscopy measurements. The difference in the orthorhombic a and b parameters (∼0.05 Å) possibly originates from the chemical pressure induced by the smaller ionic size of Sm3+ (1.24 Å, XII) as compared to other Ln3+ (La, Pr, Nd) ions. Ferroelectric switching of A′SmNb2O7 (A′ = Rb, Cs) oxides is demonstrated by the polarization hysteresis loops observed at room temperature with remanent polarization values of 5.3 and 2.0 μC/cm2 corresponding to the Rb and Cs analogues. Variable-temperature powder X-ray diffraction measurements confirmed the phase transition from polar to anti-polar transitions around temperatures ∼1273 and ∼1173 K, respectively, for the Rb and Cs analogues. Structural analysis results in the identification of prototype tetragonal (a ∼ 3.88 Å, c ∼ 11.20 Å) centrosymmetric structures relating the transition temperatures to potential Curie temperatures. The transitions coincide with the observed Curie point of 1113 K for CsSmNb2O7, from the temperature-dependent relative permittivity measurements, and a much higher temperature is expected for the Rb analogue.

Chiral magnetic textures in ultrathin perpendicularly magnetised multilayer film stacks with an interfacial Dzyaloshinskii-Moriya interaction have been the focus of much research recently. The chirality associated with the broken inversion symmetry at the interface between an ultrathin ferromagnetic layer and a heavy metal with large spin-orbit coupling supports homochiral N\'eel domain walls and hedgehog (N\'eel) skyrmions. Under spin-orbit torques these N\'eel type magnetic structures are predicted, and have been measured, to move at high velocities. However recent studies have indicated that some multilayered systems may possess a more complex hybrid domain wall configuration, due to the competition between interfacial DMI and interlayer dipolar fields. These twisted textures are expected to have thickness dependent N\'eel and Bloch contributions to the domain or skyrmion walls. In this work, we use the methods of Lorentz microscopy to measure quantitatively for the first time experimentally both; i) the contributions of the N\'eel and Bloch contributions and ii) their spatial spin variation at high resolution. These are compared with modelled and simulated structures which are in excellent agreement with our experimental results. Our quantitative analysis provides powerful direct evidence of the Bloch wall component which exists in these hybrid walls and will be significant when exploiting such phenomena in spintronic applications.

Ab initio density-functional theory calculations within the local density approximation were conducted to elucidate whether critical thickness for ferroelectricity intrinsically exists in free-standing polydomain ${\text{PbTiO}}_{3}$ ultrathin films, where there was no screening effect of electrodes. The ferroelectric polydomain state was found to be energetically favorable over the paraelectric state even in the thinnest film one unit-cell thick, indicating no intrinsic critical thickness existed. The ferroelectric distortions in the film were stabilized by the formation of ferromagneticlike closure domains, because the surface charge, which caused a depolarizing field, was sufficiently screened by the in-plane aligned polarization at the surface. Further analysis of the covalent Pb-O bonding structure, which plays a central role in determining ferroelectricity in ${\text{PbTiO}}_{3}$, revealed that the closure domain structure consists of the $180\ifmmode^\circ\else\textdegree\fi{}$ as well as $90\ifmmode^\circ\else\textdegree\fi{}$ domain walls.

The polarization response such as ferroelectric and ferroelastic switching in ferroelectrics is the important feature for ferroelectric and electromechanical applications. In polycrystalline form ferroelectrics, effects of the microstructural parameters such as texture, grain size, and residual stress are there and have not fully been understood. Among these effects, (1) the origin of grain size effects on ferroelastic switching, (2) mechanical stress effects on polarization switching, and (3) ferroelectric switching kinetics and the relationship to grain boundaries are investigated.Firstly, the microscopic origin of ferroelastic switching suppression in smaller grains is discovered using a microscopic probing technique (piezoresponse force microscopy). It is demonstrated that there is no independent grain size effect on ferroelastic switching; the grain size affects the domain structure in a grain, and the domain structure plays an important role in the ferroelastic switching suppression. This result suggests that the grain size is not an independent critical parameter for the electromechanical property degradation in a grain < 1 m as the ferroelastic switching is a dominant component for the electromechanical property.The study about the mechanical stress effects on the electric field induced polarization switching rationalizes the emergence of the electric field induced low-symmetry phases observed in tetragonal Pb(Zr,Ti)O3 and BaTiO3 ceramics after poling. It is demonstrated that a shear stress plays an important role in stabilizing the monoclinic phase in Pb(Zr,Ti)O3 whereas a normal stress along the polarization axis is a key for the monoclinic phase in BaTiO3 with a thermodynamic approach. It is suggested that the fraction of the low-symmetry phase, which is important for the large electromechanical property, can be engineered by applying an appropriate stress.For the work about ferroelectric switching kinetics, the first direct Barkhausen noise associated with ferroelectric switching is measured. The domain switching time is quantified by the frequency of the Barkhausen noise. It is discovered that the dominant domain wall pinning site is grain boundaries based on the domain wall jump distance between pinning sites calculated from the switching time. This result suggests that the technique is a good tool for understanding the relationship between microstructure – domain wall kinetics.In sum, the mechanisms of the polarization switching suppression due to domain structure and grain boundaries, and the emergence of the low symmetry phases due to stresses are revealed. These discoveries facilitate further improvements of the device performances with engineering the domain structure, grain boundaries and residual stress.

Recent progresses in transmission electron microscopy studies of two-dimensional ferroelectrics

The ability of high damping capacity iron-chromium based coatings to absorb mechanical vibrations has been investigated over a wide range of frequencies varying between ∫= 10Hz to 10 kHz, and deformation amplitude between ϵ = 10-6to 10-3. The magnetomechanical hysteresis loss (Q-1) was determined based on the modal analysis technique of a flat beam and was found to be very sensitive to internal stress in the samples. Heat treatments usually enhanced the loss capability, but only high-temperature annealing of coatings restored the whole damping capacity to be comparable to that of cast alloys of same chemical composition. The variation of Q-1 versus vibration amplitude first increased rapidly, passed through a maximum, and then declined relatively slowly to its initial values. The position of the maximum damping was shifted towards lower strains with annealing time and temperature. In contrast to the strain amplitude, the vibration frequency did not influence damping behavior significantly, as expected in ferromagnetic materials. The structure of magnetic domains was observed using the magnetooptical Kerr effect Modification of structure following heat treatments was associated with different values of the damping capacity. Accordingly, the beneficial effect of annealing on damping capacity arises on the one hand from improved mobility of unpinned domain walls and on the other hand from growth of 90 deg domains, leading rather to equiaxed domain configurations. The irreversible movement of domain walls upon application of an external stress in general occurred suddenly and abruptly between two pinned positions.

In ferroelectric ceramics every grain has an average polarization arising from the spontaneous polarization of all domains. Since the domain configuration is known in fine grained as well as in coarse grained perovskite ceramics the average polarization can be easily determined. An electric field can invert the average polarization by 180° if it exceeds a critical field strength E2crit. At fields above E2crit a new 90° domain wall being perpendicular to the regular 90° domain walls nucleates at the boundary of the grain. It traverses the grain driven by the external field and disappears at the opposite grain boundary where its energy is dissipated. This transient domain wall is highly mobile, because, on its passage through the grain it does not change the gross shape of the grain. The calculated values of the critical electric field and its temperature dependence are in good agreement with observations. In addition, the new domain wall is the origin of dielectric nonlinearities in ferroelectric ceramics for large signal ac-fields or for dc-biased fields. The very high permittivity which is observed in fine grained ceramics can also be ascribed to the presence of these easily movable walls. Internal depolarization fields in this case cause the generation of the new walls. The electric hysteresis curve P(E) is described by a progress parameter δ such that P(δ) and E(δ) are separate hysteresis curves. A model for the determination of P(δ) and E(δ) is presented. The final hysteresis curve results from the elimination of δ.

The loss of centrosymmetry via oxygen octahedral rotations is demonstrated in the n = 2 Dion–Jacobson family of layered oxide perovskites, A′LaB2O7 (A′ = Rb, Cs; B = Nb, Ta). Ab initio density functional theory calculations predict that all four materials should adopt polar space groups, in contrast to the results of previous experimental studies that have assigned these materials to the centrosymmetric P4/mmm space group. Optical second harmonic generation experiments confirm the presence of a noncentrosymmetric phase at ambient temperature. Piezoresponse force microscopy experiments also show that this phase is piezoelectric. To elucidate the symmetry‐breaking and assign the appropriate space groups, the crystal structure of CsLaNb2O7 is refined as a function of temperature from synchrotron X‐ray diffraction data. Above 550 K, CsLaNb2O7 adopts the previously determined centrosymmetric P4/mmm space group. Between 550 and 350 K, the symmetry is lowered to the noncentrosymmetric space group Amm2. Below 350 K, additional symmetry lowering is observed as peak splitting, but the space group cannot be unambiguously identified.

Technologically important properties of ferroic materials are determined by their intricate response to external stimuli. This response is driven by distortions of the crystal structure and/or by domain wall motion. Experimental separation of these two mechanisms is a challenging problem which has not been solved so far. Here, we apply X-ray photon correlation spectroscopy (XPCS) to extract the contribution of domain wall dynamics to the overall response. Furthermore, we show how to distinguish the dynamics related to the passing of domain walls through the periodic (Peierls) potential of the crystal lattice and through the random potential caused by lattice defects (pinning centers). The approach involves the statistical analysis of correlations between X-ray speckle patterns produced by the interference of coherent synchrotron X-rays scattered from different nanosize volumes of the crystal and identification of Poisson-type contribution to the statistics. We find such a contribution in the thermally driven response of the monoclinic phase of a ferroelectric PbZr0.55Ti0.45O3 crystal and calculate the number of domain wall jumps in the studied microvolume.