We measure the spin-charge interconversion by the spin Hall effect in ferromagnetic/Pt nanodevices. The extracted effective spin Hall angles (SHAs) of Pt evolve drastically with the ferromagnetic (FM) materials (CoFe, Co, and NiFe), when assuming transparent interfaces and a bulk origin of the spin injection/detection by the FM elements. By carefully measuring the interface resistance, we show that it is quite large and cannot be neglected. We then evidence that the spin injection/detection at the FM/Pt interfaces are dominated by the spin polarization of the interfaces. We show that interfacial asymmetric spin scattering becomes the driving mechanism of the spin injection in our samples.
Current-voltage characteristics and $P-E$ loops are simulated in SrRuO$_{3}$/BaTiO$_{3}$/Pt tunneling junctions with interfacial dead layer. The unswitchable interfacial polarization is coupled with the screen charge and the barrier polarization self-consistently within the Thomas-Fermi model and the Landau-Devonshire theory. The shift of P-E loop from the center position and the unequal values of the positive coercive field and the negative coercive field are found, which are induced by the asymmetricity of interface dipoles. A complete J-V curve of the junction is shown for different barrier…
We investigate the effect of capping layer (CAP) on the interfacial magnetic anisotropy energy density (K_S), magnetic damping (α), and spin-orbit torques (SOTs) in heavy-metal (Pt) / ferromagnet (Co or Py) / CAP (MgO/Ta, HfOx, or TaN). At room temperature (RT) the CAP materials influence the effective magnitude of K_S, which is associated with a formation of interfacial magnetic oxides. The dynamical dissipation parameters of Co are considerably influenced by the CAP (especially MgO) while those of Py are not. This is possibly due to an extra magnetic damping via spin-pumping process across t…
The thickness dependence of spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers is studied using the first-principles non-equilibrium Green's function formalism combined with the Anderson disorder model. A systematic expansion in orthogonal vector spherical harmonics is used for the angular dependence of the torque. The damping-like torque in Co/Pt and Co/Au bilayers can be described as a sum of the spin-Hall contribution, which increases with thickness in agreement with the spin-diffusion model, and a comparable interfacial contribution. The magnetoconductance in the p…
Thin films of Topological insulators (TIs) coupled with ferromagnets (FMs) are excellent candidates for energy-efficient spintronics devices. Here, the effect of crystalline structural disorder of TI on interfacial and magnetic properties of sputter-deposited TI/FM, Bi2Te3/Ni80Fe20, heterostructures is reported. Ni and a smaller amount of Fe from Py was found to diffuse across the interface and react with Bi2Te3. For highly crystalline c-axis oriented Bi2Te3 films, a giant enhancement in Gilbert damping is observed, accompanied by an effective out-of-plane magnetic anisotropy and enhanced damp…
In ferromagnetic thin films, broken inversion symmetry and spin-orbit coupling give rise to interfacial Dzyaloshinskii-Moriya interactions. Analytic expressions for spin-wave properties show that the interfacial Dzyaloshinskii-Moriya interaction leads to non-reciprocal spin-wave propagation, i.e. different properties for spin waves propagating in opposite directions. In favorable situations, it can increase the spin-wave attenuation length. Comparing measured spin wave properties in ferromagnet$|$normal metal bilayers and other artificial layered structures with these calculations can provide …
Due to its low intrinsic damping, Y$_3$Fe$_5$O$_{12}$ and its substituted variations are often used for ferromagnetic layer at spin pumping experiment. Spin pumping is an interfacial spin current generation in the interface of ferromagnet and non-magnetic metal, governed by spin mixing conductance parameter $G^{\uparrow\downarrow}$. $G^{\uparrow\downarrow}$ has been shown to enhance the damping of the ferromagnetic layer. The theory suggested that the effect of $G^{\uparrow\downarrow}$ on gyromagnetic ratio only come from its negligible imaginary part. In this article, we show that the differe…
The interfacial Dzyaloshinskii-Moriya interaction (DMI) is intimately related to the prospect of superior domain-wall dynamics and the formation of magnetic skyrmions. Although some experimental efforts have been recently proposed to quantify these interactions and the underlying physics, it is still far from trivial to address the interfacial DMI. Inspired by the reported tilt of the magnetization of the side edge of a thin film structure, we here present a quasi-static, straightforward measurement tool. By using laterally asymmetric triangular-shaped microstructures, it is demonstrated that …
Charge transfer is of particular importance in manipulating the interface physics in transition-metal oxide heterostructures. In this work, we have fabricated epitaxial bilayers composed of polar 3d LaMnO3 and nonpolar 5d SrIrO3. Systematic magnetic measurements reveal an unexpectedly large exchange bias effect in the bilayer, together with a dramatic enhancement of the coercivity of LaMnO3. Based on first-principles calculations and x-ray absorption spectroscopy measurements, such a strong interfacial magnetic coupling is found closely associated with the polar nature of LaMnO3 and the strong…
We investigate thermoelectric properties of a ferromagnet-superconductor hybrid structure with Rashba spin-orbit interaction and delta function potential barrier at the interfacial layer. The exponential rise of thermal conductance with temperature manifests a cross-over temperature scale separating two opposite behaviors of it with the change of polarization in the ferromagnet whereas the inclusion of interfacial Rashba spin-orbit field results in a non-monotonic behavior of it with the strength of Rashba field. We employ scattering matrix approach to determine the amplitudes of all the scatt…
Using spin waves we directly probe the interface of an exchange biased Ni$_{80}$Fe$_{20}$/Ir$_{25}$Mn$_{75}$ film which has been modified by the presence of an Au dusting layer. Combining this experimental data with a discretised simulation model, parameters relating to interface exchange coupling and modification of interface magnetisation are determined. Exchange coupling is found to be relatively uniform as gold thickness is increased, and undergoes a sudden drop at 1.5$\textrmÅ$ of gold. Interface magnetisation decreases as a function of the gold dusting thickness. Antiparallel alignment o…
Combined measurements of normal and inverted Hanle effects in CoFe/MgO/semiconductor (SC) contacts reveal the effect of spin relaxation rate on the interfacial spin depolarization (ISD) from local magnetic fields. Despite the similar ferromagnetic electrode and interfacial roughness in both CoFe/MgO/Si and CoFe/MgO/Ge contacts, we have observed clearly different features of the ISD depending on the host SC. The precession and relaxation of spins in different SCs exposed to the local fields from more or less the same ferromagnets give rise to a notably different ratio of the inverted Hanle sign…
Effective interfacial Dzyaloshinskii-Moriya interaction and skyrmion stabilization in ferromagnet/paramagnet and ferromagnet/superconductor hybrid systems
At the interface between a nonmagnetic metal (NM) and a ferromagnetic insulator (FI) spin current can interact with the magnetization, leading to a modulation of the spin current. The interfacial exchange field at these FI-NM interfaces can be probed by placing the interface in contact with the spin transport channel of a lateral spin valve (LSV) device and observing additional spin relaxation processes. We study interfacial exchange field in lateral spin valve devices where Cu spin transport channel is in proximity with ferromagnetic insulator EuS (EuS-LSV) and yttrium iron garnet Y$_3$Fe$_5$…
Spin-dependent transport at heavy metal/magnetic insulator interfaces is at the origin of many phenomena at the forefront of spintronics research. A proper quantification of the different interfacial spin conductances is crucial for many applications. Here, we report the first measurement of the spin Hall magnetoresistance (SMR) of Pt on a purely ferromagnetic insulator (EuS). We perform SMR measurements in a wide range of temperatures and fit the results by using a microscopic model. From this fitting procedure we obtain the temperature dependence of the spin conductances ($G_s$, $G_r$ and $G…
Finding efficient ways of manipulating magnetic bits is one of the core goals in spintronic research. Electrically-generated spin-orbit torques (SOTs) are good candidates for this and the search for materials capable of generating highly-efficient SOTs has gained a lot of traction in the recent years. While antiferromagnet/ferromagnet bilayer structures have been employed extensively for passive applications, e.g. by using exchange bias fields, their active properties are not yet widely employed. Here we show the presence of large interfacial SOTs in bilayer of a ferromagnet and the two-dimens…
We investigate the magnetization dynamics through the magnetoimpedance effect in ferromagnetic NiFe/Cu/Co films. We observe that the magnetoimpedance response is dependent on the thickness of the non-magnetic Cu spacer material, a fact associated to the kind of the magnetic interaction between the ferromagnetic layers. Thus, we present an experimental study on asymmetric magnetoimpedance in ferromagnetic films with biphase magnetic behavior and explore the possibility of tuning the linear region of the magnetoimpedance curves around zero magnetic field by varying the thickness of the non-magne…
Different models have been used to evaluate the interfacial Dzyaloshinskii-Moriya interaction (DMI) from the asymmetric bubble expansion method using magneto-optics. Here we investigate the most promising candidates over a range of different magnetic multilayers with perpendicular anisotropy. Models based on the standard creep hypothesis are not able to reproduce the domain wall (DW) velocity profile when the DW roughness is high. Our results demonstrate that the DW roughness and the interface roughness of the sample layers are correlated. Furthermore, we give guidance on how to obtain reliabl…
We report that current-induced spin-orbit torques (SOTs) in heavy-metal/ferromagnetic-metal bilayers are strongly altered by the oxidation of the ferromagnetic layer near the interface. We measured damping-like (DL) and field-like (FL) SOTs for Pt/Co and Pt/Ni$_{81}$Fe$_{19}$ (Pt/Py) films using spin-torque ferromagnetic resonance. In the Pt/Co film, we found that the oxidation of the Co layer near the interface enhances both DL and FL SOTs in spite of the insulating nature of the CoO$_x$ layer. The enhancement of the SOTs disappears by inserting a thin Ti layer at the Pt/CoO$_x$ interface, in…
In bilayer nanowires consisting of a ferromagnetic layer and a non-magnetic layer with strong spin-orbit coupling, currents create torques on the magnetization beyond those found in simple ferromagnetic nanowires. The resulting magnetic dynamics appear to require torques that can be separated into two terms, damping-like and field-like. The damping-like torque is typically derived from models describing the bulk spin Hall effect and the spin transfer torque, and the field-like torque is typically derived from a Rashba model describing interfacial spin-orbit coupling. We derive a model based on…
Current induced spin-orbit magnetic fields (iSOFs), arising either in single-crystalline ferromagnets with broken inversion symmetry1,2 or in non-magnetic metal/ferromagnetic metal bilayers3,4, can produce spin-orbit torques which act on a ferromagnet's magnetization,thus offering an efficient way for its manipulation.To further reduce power consumption in spin-orbit torque devices, it is highly desirable to control iSOFs by the field-effect, where power consumption is determined by charging/discharging a capacitor5,6. In particular, efficient electric-field control of iSOFs acting on ferromag…
We experimentally investigate the origin of the two-magnon scattering (TMS) in heavy-metal (HM)/ferromagnet (FM)/oxide heterostructures (FM = Co, Ni81Fe19, or Fe60Co20B20) by varying the materials located above and below the FM layers. We show that strong TMS in HM/FM/oxide systems arises primarily at the HM/FM interface and increases with the strength of interfacial spin-orbit coupling and magnetic roughness at this interface. TMS at the FM/oxide interface is relatively weak, even in systems where spin-orbit coupling at this interface generates strong interfacial magnetic anisotropy. We also …
We study the role of thermal magnons in the spin and heat transport across a normal-metal/insulating-ferromagnet interface, which is beyond an elastic electronic spin transfer. Using an interfacial exchange Hamiltonian, which couples spins of itinerant and localized orbitals, we calculate spin and energy currents for an arbitrary interfacial temperature difference and misalignment of spin accumulation in the normal metal relative to the ferromagnetic order. The magnonic contribution to spin current leads to a temperature-dependent torque on the magnetic order parameter; reciprocally, the coher…
We use a perturbative approach to study the effects of interfacial spin-orbit coupling in magnetic multilayers by treating the two-dimensional Rashba model in a fully three-dimensional description of electron transport near an interface. This formalism provides a compact analytic expression for current-induced spin-orbit torques in terms of unperturbed scattering coefficients, allowing computation of spin-orbit torques for various contexts, by simply substituting scattering coefficients into the formulas. It applies to calculations of spin-orbit torques for magnetic bilayers with bulk magnetis…
Chiral spin textures at the interface between ferromagnetic and heavy nonmagnetic metals, such as Neel-type domain walls and skyrmions, have been studied intensively because of their great potential for future nanomagnetic devices. The Dyzaloshinskii-Moriya interaction (DMI) is an essential phenomenon for the formation of such chiral spin textures. In spite of recent theoretical progress aiming at understanding the microscopic origin of the DMI, an experimental investigation unravelling the physics at stake is still required. Here, we experimentally demonstrate the close correlation of the DMI…
We study the relation between tunnel magnetoresistance (TMR) and interfacial electronic states modified by magnetic impurities introduced at the interface of the ferromagnetic tunnel junctions, by making use of the periodic Anderson model and the linear response theory. It is indicated that the TMR ratio is strongly reduced depending on the position of the $d$-levels of impurities, based on reduction in the spin-dependent $s$-electron tunneling in the majority spin state. The results are compared with experimental results for Cr-dusted ferromagnetic tunnel junctions, and also with results for …
We report that spin current transport across Pt-ferromagnet (FM) interfaces is strongly dependent on the type and the thickness of the FM layer and on post-deposition processing protocols. By employing both harmonic voltage measurements and spin-torque ferromagnetic resonance measurements, we find that the efficiency of the Pt spin Hall effect in exerting a damping-like spin torque on the FM ranges from < 0.05 to > 0.10 under different interfacial conditions. We also show that the temperature dependence of the spin torque efficiencies for both the damping-like torque and field-like torque is d…
Using ab-initio methods we calculate thermoelectric and spin thermoelectric properties of silicene nanoribbons with bare, mono-hydrogenated and di-hydrogenated edges. Asymmetric structures, in which one edge is either bare or di-hydrogenated while the other edge is mono-hydrogenated (0H-1H and 2H-1H nanoribbons) have ferromagnetic ground state and display remarkable conventional and spin thermoelectric properties. Strong enhancement of the thermoelectric efficiency, both conventional and spin ones, results from a very specific band structure of such nanoribbons, where one spin channel is block…
Controlled spin transport in magnetic stacks is required to realize pure spin current-driven logic and memory devices. The control over the generation and detection of the pure spin current is achieved by tuning the spin to charge conversion efficiency of the heavy metal interfacing with ferromagnets. Here, we demonstrate the direct tunability of spin angular momentum transfer and thereby spin pumping, in CoFeB/Pt stack, with interfacial magnetic anisotropy. The ultra-low thickness of CoFeB thin film tilts the magnetic easy axis from in-plane to out-of-plane due to surface anisotropy. The Ferr…
Room temperature ferromagnetic materials composed only by light elements like carbon, hydrogen and/or nitrogen, so called carbon magnet, are very attractive for creating new material categories both in science and industry. Recently several experiments suggest ferromagnetic features at a room temperature, especially in graphite base materials. This paper reveals a mechanism of such ferromagnetic features by modeling nanometer size asymmetric graphene molecule by using both a semi-empirical molecular orbital method and a first principle density function theory. Asymmetrically dihydrogenated zig…
The Andreev reflection of narrow ferromagnet/superconductor point contacts is theoretically studied. We show that the conductance quantization depends on whether the contact region is superconducting or ferromagnetic as well as on the strength of the exchange field in the ferromagnet. The Andreev reflection of the ferromagnetic contact is more suppressed than that of the superconducting contact. We also show that the conductance-voltage curve has a bump at zero bias-voltage if there is no interfacial-scattering. On the contrary, the conductance-voltage curve shows a dip if the system has an in…
We predict a magnetoresistance induced by the interfacial Rashba spin-orbit coupling in normal metal|ferromagnetic insulator bilayer. It depends on the angle between current and magnetization directions identically to the "spin Hall magnetoresistance" mechanism caused by a combined action of spin Hall and inverse spin Hall effects. Due to the identical phenomenology it is not obvious whether the magnetoresistance reported by Nakayama et al. is a bulk metal or interface effect. The interfacial Rashba induced magnetoresistance may be distinguished from the bulk metal spin Hall magnetoresistance …
Combining the first-principles noncollinear calculations of scattering matrices with Andreev approximation, we investigated the spin-triplet Andreev reflection (AR) spectra for the interface between half-metallic ferromagnet Co$_{2}$MnSi and \emph{s}-wave BCS superconductor Al with and without interfacial roughness, where the orientations of magnetic moments near the interface are randomly distributed. The calculated results show that the AR spectra have peak structures near zero bias for the clean interface with relative weak magnetic disorder. With increasing the degree of interfacial roughn…
Ultrathin ferromagnets with frustrated exchange and the Dzyaloshinskii-Moriya interaction can support topological solitons such as skyrmions and antiskyrmions, which are metastable and can be considered particle-antiparticle counterparts. When spin-orbit torques are applied, the motion of an isolated antiskyrmion driven beyond its Walker limit can generate skyrmion-antiskyrmion pairs. Here, we use atomistic spin dynamics simulations to shed light on the scattering processes involved in this pair generation. Under certain conditions a proliferation of these particles and antiparticles can appea…
After one decade of the intensive theoretical and experimental explorations, whether interfacial spin-orbit coupling (ISOC) at metallic magnetic interfaces can effectively generate a spin current has remained in dispute. Here, utilizing the Ti/FeCoB bilayers that are unique for the negligible bulk spin Hall effect and the strong tunable ISOC, we establish that there is no significant charge-to-spin conversion at magnetic interfaces via spin-orbit filtering effect or Rashba-Edelstein(-like) effect even when the ISOC is stronger than that of a typical Pt/ferromagnet interface and can promote str…
Voltage control effects provide an energy-efficient means of tailoring material properties, especially in highly integrated nanoscale devices. However, only insulating and semiconducting systems can be controlled so far. In metallic systems, there is no electric field due to electron screening effects and thus no such control effect exists. Here we demonstrate that metallic systems can also be controlled electrically through ionic not electronic effects. In a Pt/Co structure, the control of the metallic Pt/Co interface can lead to unprecedented control effects on the magnetic properties of the…
Switchable Exchange Bias Resulting from Correlated Domain Structures in Orthogonally Coupled Antiferromagnet/Ferromagnet van der Waals Heterostructures
Ultrafast THz radiation generation from ferromagnetic/nonmagnetic bilayer heterostructure-based spintronic emitters generally exploits the conversion from spin- to charge-current within the nonmagnetic layer and its interface with the ferromagnetic layer. Various possible sub-contributions to the underlying mechanism of inverse spin Hall effect for the THz emission from such structures, need to be exploited for not only investigating the intricacies at the fundamental level in the material properties themselves but also for improving their performance for broadband and high-power THz emission.…
Recent studies rediscovered the crucial role of field-like spin orbit torque (SOT) in nanosecond-timescale SOT dynamics. However, there is not yet an effective way to control its relative amplitude. Here, we experimentally modulate the field-like SOT in W/CoFeB/MgO trilayers through tuning the interfacial spin accumulation. By performing spin Hall magnetoresistance measurement, we find that the CoFeB with enhanced spin dephasing, either generated from larger layer thickness or from proper annealing, can distinctly boost the spin absorption and enhance the interfacial spin mixing conductance G_…
Transition metal dichalcogenides (TMDs) are promising materials for efficient generation of current-induced spin-orbit torques on an adjacent ferromagnetic layer. Numerous effects, both interfacial and bulk, have been put forward to explain the different torques previously observed. Thus far, however, there is no clear consensus on the microscopic origin underlying the spin-orbit torques observed in these TMD/ferromagnet bilayers. To shine light on the microscopic mechanisms at play, here we perform thickness dependent spin-orbit torque measurements on the semiconducting WSe$_{2}$/permalloy bi…
Topological Hall Effect Induced by Chiral Spin Textures at the Ferroelectric/Ferromagnetic Interface
National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University（南京大学物理学院固态微结构国家重点实验室，先进微结构协同创新中心）；Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所，北京凝聚态物理国家研究中心）
The antisymmetric Dzyaloshinskii-Moriya interaction (DMI) in noncentrosymmetric systems leads to various nonuniform chiral magnetic textures. Polarized neutron scattering is a powerful method for investigation such chiral distributions. The most used technique is a small-angle neutrons scattering (SANS). Multilayered magnetic films with the interface induced DMI (iDMI) can't be investigated by SANS because of their small volume. The appropriate technique is a polarized neutron reflectometry. Within the framework of the continuum theory of micromagnetics, we explore the impact of the iDMI on th…
Symmetry Breaking by Interfacial Dead Layers: Observation of Forbidden Self-Induced Spin-Orbit Torque in Symmetric Ferromagnets
Indian Institute of Technology Ropar（印度理工学院罗帕尔分校）；Virginia Commonwealth University（弗吉尼亚联邦大学）；Jaypee Institute of Information Technology（贾伊皮信息技术学院）；Université de Lorraine（洛林大学）；Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza（阿拉贡纳米科学与材料研究所 (INMA)，西班牙科学研究中心-萨拉戈萨大学）；Indian Institute of Technology Bhubaneswar（印度理工学院布巴内斯瓦尔分校）；Carnegie Mellon University（卡内基梅隆大学）
We show that the coupling between two ferromagnetic layers separated by a nonmagnetic spacer can be used to control the depinning of domain walls and induce unidirectional domain wall propagation. We investigated CoFeB/Ti/CoFeB trilayers where the easy axis of the magnetization of the top CoFeB layer is out-of-plane and that of the bottom layer is in-plane. Using Magneto-optic Kerr effect microscopy, we find that the depinning of a domain wall in the perpendicularly magnetized CoFeB layer is influenced by the orientation of the magnetization of the in-plane layer, which gives rise to a field-d…
Andreev reflection spectroscopy of ferromagnet/superconductor (FS) junctions is an important probe of spin polarization. We theoretically investigate spin-polarized transport in FS junctions in the presence of Rashba and Dresselhaus interfacial spin-orbit fields and show that Andreev reflection can be controlled by changing the magnetization orientation. We predict a giant in- and out-of-plane magnetoanisotropy of the junction conductance. If the ferromagnet is highly spin polarized---in the half-metal limit---the magnetoanisotropic Andreev reflection depends universally on the spin-orbit fiel…
We establish a general formulation for spin current pumped by magnons at the interface between a normal metal and a magnetic insulator, valid for any non-collinear magnetic configuration in the linear spin wave regime. This current is generated by driving the system in a non-equilibrium state, covering setups such as thermal spin injection (spin Seebeck effect) or spin voltage by irradiation of the insulator (spin pumping). We illustrate the formula in the special case of a honeycomb topological ferromagnet, for simplicity, and cover both the spin Seebeck and spin-pumping setups. We show how t…
Probing Interfacial Spin Dynamics and Temperature Dependent Asymmetry in Spin Pumping Across Ni80Fe20/Cu/Cr1.12Te2 Interfaces
Department of Physics, Indian Institute of Technology Kanpur（印度坎普尔理工学院物理系）；Natural Sciences and Science Education, National Institute of Education, Nanyang Technological University（南洋理工大学国立教育学院自然科学与科学教育）
We study the magnetic anisotropy which arises at the interface between a thin film ferromagnet and a 3-d Rashba material. The 3-d Rashba material is characterized by the spin-orbit strength $α$ and the direction of broken bulk inversion symmetry $\hat n$. We find an in-plane uniaxial anisotropy in the $\hat{z}\times\hat{n}$ direction, where $\hat z$ is the interface normal. For realistic values of $α$, the uniaxial anisotropy is of a similar order of magnitude as the bulk magnetocrystalline anisotropy. Evaluating the uniaxial anisotropy for a simplified model in 1-d shows that for small band f…
A spin current through a ferromagnet/heavy-metal interface may shrink due to the spin-flip at the interface, resulting in the spin-memory loss. Here we propose a mechanism of the spin-memory loss. In contrast to other mechanisms based on interfacial spin-orbit coupling, our mechanism is based on the bulk spin-orbit coupling in a heavy-metal. We demonstrate that the bulk spin-orbit coupling induces the entanglement between the spin and orbital degrees of freedom and this spin-orbital entanglement can give rise to sizable spin-flip at the interface even when the interfacial spin-orbit coupling i…
Spin-orbit torques offer a promising mechanism for electrically controlling magnetization dynamics in nanoscale heterostructures. While spin-orbit torques occur predominately at interfaces, the physical mechanisms underlying these torques can originate in both the bulk layers and at interfaces. Classifying spin-orbit torques based on the region that they originate in provides clues as to how to optimize the effect. While most bulk spin-orbit torque contributions are well studied, many of the interfacial contributions allowed by symmetry have yet to be fully explored theoretically and experimen…
