Theory of interlayer magnetic coupling

Real-time dynamics of angular momentum transfer from spin to acoustic chiral phonon in oxide heterostructures

Chiral phonons have recently been explored as a novel degree of freedom in quantum materials. The angular momentum carried by these quasiparticles is generated by the breaking of chiral degeneracy of phonons, owing to the chiral lattice structure or the rotational motion of ions of the material. In ferromagnets, a mechanism for generating non-equilibrium chiral phonons has been suggested, but their temporal evolution, which obeys Bose-Einstein statistics, remains unclear. Here we report the real-time dynamics of thermalized chiral phonons in an artificial superlattice composed of ferromagnetic metallic SrRuO3 and non-magnetic insulating SrTiO3. Following the photo-induced ultrafast demagnetization in the SrRuO3 layer, we observed the appearance of a magneto-optic signal in the superlattice, which is absent in the SrRuO3 single films. This magneto-optic signal exhibits thermally driven dynamic properties and a clear correlation with the thickness of the non-magnetic SrTiO3 layer, implying that it originates from thermalized chiral phonons. We use numerical calculations considering the magneto-elastic coupling in SrRuO3 to validate our experimental observations and the angular momentum transfer mechanism between the lattice and spin systems in ferromagnetic systems and also to the non-magnetic system.

Interlayer engineering of Fe3GeTe2: From 3D superlattice to 2D monolayer

The discoveries of ferromagnetism down to the atomically thin limit in van der Waals (vdW) crystals by mechanical exfoliation have enriched the family of magnetic thin films [C. Gong et al., Nature 546, 265-269 (2017) and B. Huang et al., Nature 546, 270-273 (2017)]. However, compared to the study of traditional magnetic thin films by physical deposition methods, the toolbox of the vdW crystals based on mechanical exfoliation and transfer suffers from low yield and ambient corrosion problem and now is facing new challenges to study magnetism. For example, the formation of magnetic superlattice is difficult in vdW crystals, which limits the study of the interlayer interaction in vdW crystals [M. Gibertini, M. Koperski, A. F. Morpurgo, K. S. Novoselov, Nat. Nanotechnol. 14, 408-419 (2019)]. Here, we report a strategy of interlayer engineering of the magnetic vdW crystal Fe3GeTe2 (FGT) by intercalating quaternary ammonium cations into the vdW spacing. Both three-dimensional (3D) vdW superlattice and two-dimensional (2D) vdW monolayer can be formed by using this method based on the amount of intercalant. On the one hand, the FGT superlattice shows a strong 3D critical behavior with a decreased coercivity and increased domain wall size, attributed to the co-engineering of the anisotropy, exchange interaction, and electron doping by intercalation. On the other hand, the 2D vdW few layers obtained by over-intercalation are capped with organic molecules from the bulk crystal, which not only enhances the ferromagnetic transition temperature (TC), but also substantially protects the thin samples from degradation, thus allowing the preparation of large-scale FGT ink in ambient environment.

Antiferromagnetic interlayer exchange coupled Co68B32/Ir/Pt multilayers

Synthetic antiferromagnetic structures can exhibit the advantages of high velocity similarly to antiferromagnets with the additional benefit of being imaged and read-out through techniques applied to ferromagnets. Here, we explore the potential and limits of synthetic antiferromagnets to uncover ways to harness their valuable properties for applications. Two synthetic antiferromagnetic systems have been engineered and systematically investigated to provide an informed basis for creating devices with maximum potential for data storage, logic devices, and skyrmion racetrack memories. The two systems considered are (system 1) CoB/Ir/Pt of N repetitions with Ir inducing the negative coupling between the ferromagnetic layers and (system 2) two ferromagnetically coupled multilayers of CoB/Ir/Pt, coupled together antiferromagnetically with an Ir layer. From the hysteresis, it is found that system 1 shows stable antiferromagnetic interlayer exchange coupling between each magnetic layer up to N = 7. Using Kerr imaging, the two ferromagnetic multilayers in system 2 are shown to undergo separate maze-like switches during hysteresis. Both systems are also studied as a function of temperature and show different behaviors. Micromagnetic simulations predict that in both systems the skyrmion Hall angle is suppressed with the skyrmion velocity five times higher in system 1 than system 2.

Controlling Dzyaloshinskii-Moriya interaction in a centrosymmetric nonsymmorphic crystal

Presence of the Dzyaloshinskii-Moriya (DM) interaction in limited noncentrosymmetric materials leads to novel spin textures and exotic chiral physics. The emergence of DM interaction in centrosymmetric crystals could greatly enrich material realization. Here we show that an itinerant centrosymmetric crystal respecting a nonsymmorphic space group is a new platform for the DM interaction. Taking P4/nmm space group as an example, we demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction induces the DM interactions, in addition to the Heisenberg exchange and the Kaplan-Shekhtman-Entin-wohlman-Aharony (KSEA) interaction. The direction of DM vector depends on the positions of magnetic atoms in the real space, and the amplitude depends on the location of the Fermi surface in the reciprocal space. The diversity stems from the position-dependent site groups and the momentum-dependent electronic structures guaranteed by the nonsymmorphic symmetries. Our study unveils the role of the nonsymmorphic symmetries in affecting magnetism, and suggests that the nonsymmorphic crystals can be promising platforms to design magnetic interactions.

Time-dependent exchange creates the time-frustrated state of matter

Magnetic systems governed by exchange interactions between magnetic moments harbor frustration that leads to ground state degeneracy and results in the new topological state often referred to as a frustrated state of matter (FSM). The frustration in the commonly discussed magnetic systems has a spatial origin. Here we demonstrate that an array of nanomagnets coupled by the real retarded exchange interactions develops a new state of matter, time frustrated matter (TFM). In a spin system with the time-dependent retarded exchange interaction, a single spin-flip influences other spins not instantly but after some delay. This implies that the sign of the exchange interaction changes, leading to either ferro- or antiferromagnetic interaction, depends on time. As a result, the system’s temporal evolution is essentially non-Markovian. The emerging competition between different magnetic orders leads to a new kind of time-core frustration. To establish this paradigmatic shift, we focus on the exemplary system, a granular multiferroic, where the exchange transferring medium has a pronounced frequency dispersion and hence develops the TFM.

Temperature- and Field-Induced Transformation of the Magnetic State in Co2.5Ge0.5BO5

A tetravalent-substituted cobalt ludwigite Co_2.5Ge_0.5BO₅ has been synthesized using the flux method. The compound undergoes two magnetic transitions: a long-range antiferromagnetic transition at T_N1 = 84 K and a metamagnetic one at T_N2 = 36 K. The sample-oriented magnetization measurements revealed a fully compensated magnetic moment along the a- and c-axes and an uncompensated one along the b-axis leading to high uniaxial anisotropy. A field-induced enhancement of the ferromagnetic correlations at T_N2 is observed in specific heat measurements. The DFT+GGA calculation predicts the spin configuration of (↑↓↓↑) as a ground state with a magnetic moment of 1.37 μ_B/f.u. The strong hybridization of Ge(4s, 4p) with O (2p) orbitals resulting from the high electronegativity of Ge⁴⁺ is assumed to cause an increase in the interlayer interaction, contributing to the long-range magnetic order. The effect of two super-superexchange pathways Co²⁺-O-B-O-Co²⁺ and Co²⁺-O-M4-O-Co²⁺ on the magnetic state is discussed.

Magnetoresistive effect in a quantum heterostructure with helical spacer: interplay between helicity and external electric field

Giant magnetoresistive effect in a multi-layered structure not only depends on the properties of magnetic systems, it also strongly depends on the type of non-magnetic spacer that is clamped between magnetic layers. In this work, we critically investigate the role of a helical spacer in presence of a transverse electric field. Two kinds of helical geometries, possessing short-range (SRH) and long-range hopping (LRH) of electrons, are taken into account mimicking single-stranded DNA and protein molecules respectively. Sandwiching the magnetic-non-magnetic-magnetic quantum heterostructure between source and drain contact electrodes, we investigate the properties of giant magnetoresistance (GMR) following the Green's function formalism within a tight-binding framework. The interplay between SRHs and LRHs of electrons provides several nontrivial signatures in GMR, especially in the presence of transverse electric field, as it makes the system a deterministic disordered one, similar to the well-known Aubry-Andre-Harper from. The famous gapped nature of energy band structure in presence of cosine modulation leads to high degree of magnetoresistance at multiple Fermi energies, compared to the traditional spacers. The magnetoresistive effect can be monitored selectively by adjusting the electric field strength and its direction. Comparing the results between the SRH and LRH cases, we find that the later one is more superior. Finally, to make the system more realistic we include the effect of dephasing. Our analysis may provide some fundamental aspects of designing electronic and spintronic devices based on magnetoresistive effect.

Unconventional interlayer exchange coupling via chiral phonons in synthetic magnetic oxide heterostructures

Chiral symmetry breaking of phonons plays an essential role in emergent quantum phenomena owing to its strong coupling to spin degree of freedom. However, direct experimental evidence of the chiral phonon-spin coupling is lacking. In this study, we report a chiral phonon-mediated interlayer exchange interaction in atomically controlled ferromagnetic metal (SrRuO₃)-nonmagnetic insulator (SrTiO₃) heterostructures. Owing to the unconventional interlayer exchange interaction, we have observed rotation of spins as a function of nonmagnetic insulating spacer thickness, resulting in a spin spiral state. The chiral phonon-spin coupling is further confirmed by phonon Zeeman effect. The existence of the chiral phonons and their interplay with spins along with our atomic-scale heterostructure approach unveil the crucial roles of chiral phonons in magnetic materials.

Bipolar Electric-Field Switching of Perpendicular Magnetic Tunnel Junctions through Voltage-Controlled Exchange Coupling

Perpendicular magnetic tunnel junctions (p-MTJs) switched utilizing bipolar electric fields have extensive applications in energy-efficient memory and logic devices. Voltage-controlled magnetic anisotropy linearly lowers the energy barrier of the ferromagnetic layer via the electric field effect and efficiently switches p-MTJs only with a unipolar behavior. Here, we demonstrate a bipolar electric field effect switching of 100 nm p-MTJs with a synthetic antiferromagnetic free layer through voltage-controlled exchange coupling (VCEC). The switching current density, ∼1.1 × 10⁵ A/cm², is 1 order of magnitude lower than that of the best-reported spin-transfer torque devices. Theoretical results suggest that the electric field induces a ferromagnetic-antiferromagnetic exchange coupling transition of the synthetic antiferromagnetic free layer and generates a fieldlike interlayer exchange coupling torque, which causes the bidirectional magnetization switching of p-MTJs. These results could eliminate the major obstacle in the development of spin memory devices beyond their embedded applications.

Chiral Coupling between Magnetic Layers with Orthogonal Magnetization

We report on the occurrence of strong interlayer Dzyaloshinskii-Moriya interaction (DMI) between an in-plane magnetized Co layer and a perpendicularly magnetized TbFe layer through a Pt spacer. The DMI causes a chiral coupling that favors one-handed orthogonal magnetic configurations of Co and TbFe, which we reveal through Hall effect and magnetoresistance measurements. The DMI coupling mediated by Pt causes effective magnetic fields on either layer of up to 10-15 mT, which decrease monotonically with increasing Pt thickness. Ru, Ta, and Ti spacers mediate a significantly smaller coupling compared to Pt, highlighting the essential role of Pt in inducing the interlayer DMI. These results are relevant to understand and maximize the interlayer coupling induced by the DMI as well as to design spintronic devices with chiral spin textures.

Contactless Mechanical Power Transmission Through the High-T c Superconducting Pinning Effect

Mechanical power transmission (MPT) components are almost indispensable for every engineering equipment with motions. In order to satisfy some rigorous requirements, such as contamination free and zero leakage in the mixing process of biomedical solutions, a contactless MPT mode was proposed in this study based on the high-T _c superconducting flux pinning mechanism. It makes the stirring container with the driven part inside that can be totally isolated from the external environment. The physical principle of superconducting flux pinning effect was discussed firstly to explore a feasible structural scheme, which can completely restrain all the six degrees of freedom (DOFs) by the linkage of magnetic flux lines. Then, a measurement device was established to verify and investigate the proposed contactless MPT mode. The motion can be transferred synchronously from the superconducting driving part to the permanent magnet driven part since they are unified as an integrity through the pinned flux lines. The influence of driving speed, cooling clearance, and magnet arrangement on the transmitted torque was analyzed. The verified contactless MPT mode also has the advantages of self-stability and overload protection, which can avoid the drawbacks of traditional permanent magnetic transmission mode.

High thermal durability of Ru-based synthetic antiferromagnet by interfacial engineering with Re insertion

Synthetic antiferromagnets (SAFs), composed of Ru spacer with a Re insertion layer, reveal superior thermal stability up to 450 °C annealing, making the back-end of line process a wider manufacturing window and tolerance to integrate the perpendicular magnetic tunneling junctions (P-MTJs) into CMOS process. The coupling strength decays significantly for SAFs with single Ru spacer after annealing above 400 °C. Due to the characteristics of refractory metals, Re can behave as a diffusion barrier during annealing. Furthermore, the Re spacer can still keep reasonable RKKY coupling strength. Therefore, the SAFs with Ru/Re composite spacers exhibit higher RKKY coupling strength than Ru spacers after 450 °C annealing. In addition, we discovered the different enhancements for the upper and lower interfacial Re insertion, which was attributed to the varied defect formation at interfaces. The stacking fault was formed at the upper Ru/Co interface in as-deposited state. When Re was inserted at the upper interface, the diffusion between Co and Ru was significantly suppressed and the stacking fault can be eliminated during annealing, leading to enhanced interlayer coupling. Through the interfacial engineering, we may have more degrees of freedom to tune the SAF performance and thus enhance process compatibility of P-MTJ to the CMOS process.

Interlayer exchange couple based reliable and robust 3-input adder design methodology

In this paper, a novel inter-layer exchange coupled (IEC) based 3-input full adder design methodology is proposed and subsequently the architecture has been implemented on the widely accepted micromagnetic OOMMF platform. The impact of temperature on the IEC coupled full-adder design has been analyzed up to Curie temperature. It was observed that even up to Curie temperature the IEC based adder design was able to operate at sub-50 nm as contrast to dipole coupled adder design which failed at 5 K for sub 50 nm. Simulation results obtained from OOMMF micromagnetic simulator shows, the IEC based adder design was at a lower energy state as compared to the dipole coupled adder indicating a more stable system and as the temperature of the design was increased, the total energy increased resulting in reduced stability. Potential explanation for the thermodynamic stability of IEC model lies in its energetically favored architecture, such that the total energy was lower than its dipole coupled counterparts. IEC architecture demonstrates supremacy in reliability and strength enabling NML to march towards beyond CMOS devices.

Scattering modes of skyrmions in a bilayer system with ferromagnetic coupling

Magnetic skyrmions are quasiparticle-like textures that are topologically different from a single domain magnetization state. Their topological protection, combined with the low current density needed to move them, make these objects relevant to be used as information storage structures. In such a context, the analysis of the interactions between skyrmions is interesting and relevant for future applications. In this work, through micromagnetic simulations and numerical calculations, we studied the interaction between two skyrmions living on different parallel ferromagnetic racetracks connected by an exchange-like interaction. The upper and lower racetracks are separated by a height offset and the interaction between the upper and the lower skyrmion is analyzed in terms of the magnetic and geometrical parameters. Three states are predicted, as a function of these parameters: scattered or free skyrmions, bound skymions, and annihilated skyrmions. Our results, presented in a phase diagram, demonstrate that even in the case here called free skyrmions, there is a small and brief interaction when both are close enough, but the skyrmion in the top layer does not drag the skyrmion in the bottom layer. For bound skyrmions, both keep linked during larger times. In the latter case, there are strong changes in the velocity of the skyrmions induced by the effect of a higher effective mass when both are coupled.

The impact of number of repeats N on the interlayer exchange in [Formula: see text](001) superlattices

The strength of the interlayer exchange coupling in [Fe/MgO][Formula: see text](001) superlattices with 2 ≤ N ≤ 10 depends on the number of bilayer repeats (N). The exchange coupling is antiferromagnetic for all the investigated thicknesses while being nine times larger in a sample with N = 4 as compared to N = 2. The sequence of the magnetic switching in two of the samples (N = 4, N = 8) is determined using polarized neutron reflectometry. The outermost layers are shown to respond at the lowest fields, consistent with having the weakest interlayer exchange coupling. The results are consistent with the existence of quantum well states defined by the thickness of the Fe and the MgO layers as well as the number of repeats (N) in [Fe/MgO][Formula: see text](001)superlattices.

Magnetoresistive Sensor in Two-Dimension on a 25 μm Thick Silicon Substrate for In Vivo Neuronal Measurements

Neuronal electrical activity is widely studied in vivo, and the ability to measure its magnetic equivalent to obtain an undisturbed signal with both amplitude and direction information leading to neuronal signal mapping would be a promising tool for neuroscience. To provide such a tool, a probe with spin-electronics-based magnetic sensors with orthogonal axes of sensitivity for two directions of measurement is realized, thanks to a local magnetization re-orientation technique induced by Joule heating. This probe is tested under in vivo measurement conditions in the brain of an anesthetized rat. To be as close as possible to neurons and to create minimal damage during the probe's insertion, the tip thickness has been drastically decreased using a silicon-on-insulator substrate. Our probes provide the ability to perform in vivo magnetic measurements on two orthogonal axes on a 25 μm thick silicon tip with a sensitivity of 1.7%/mT along one axis and 0.9%/mT along the perpendicular axis in the sensor plane, for a limit of detection at 1 kHz of 1.0 and 1.3 nT, respectively. These probes have been tested through a phantom study and during an in vivo experiment. The robustness and stability over one year are demonstrated.

Magnetic Chirality Controlled by the Interlayer Exchange Interaction

Chiral magnetism, wherein there is a preferred sense of rotation of the magnetization, determines the chiral nature of magnetic textures such as skyrmions, domain walls, or spin spirals. Current research focuses on identifying and controlling the interactions that define the magnetic chirality in thin film multilayers. The influence of the interfacial Dzyaloshinskii-Moriya interaction (IDMI) and, recently, the dipolar interactions have been reported. Here, we experimentally demonstrate that an indirect interlayer exchange interaction can be used as an additional tool to effectively manipulate the magnetic chirality. We image the chirality of magnetic domain walls in a coupled bilayer system using scanning electron microscopy with polarization analysis. Upon increasing the interlayer exchange coupling, we induce a transition of the magnetic chirality from clockwise rotating Néel walls to degenerate Bloch-Néel domain walls and we confirm our findings with micromagnetic simulations. In multilayered systems relevant for skyrmion research, a uniform magnetic chirality across the magnetic layers is often desired. Additional simulations show that this can be achieved for reduced IDMI values (up to 30%) when exploiting the interlayer exchange interaction. This work opens up new ways to control and tailor the magnetic chirality by the interlayer exchange interaction.

Spin transfer torque and exchange coupling in Josephson junctions with ferromagnetic superconductor reservoirs

In this paper, the spin transfer torque (STT) and the exchange coupling of the Josephson junctions containing the interesting cases of diffusive/ballistic-triplet/singlet ferromagnetic superconductor (FS) materials are investigated. First, the diffusive FS₁/F _c /FS₂ structures with F _c being a junction consisting of ferromagnetic and normal metal parts as well as insulating barriers are investigated. Secondly, the ballistic Josephson junction containing the triplet chiral p/wave FS reservoirs is studied. Using the Nazarov quantum circuit theory for the diffusive structures, it is found that the antiparallel/parallel or vice versa parallel/antiparallel transition of the favorable exchange coupling takes place due to the appearance of the only out-of-plane STT. Furthermore, the analyze of the phase difference interval in which an interlayer length-induced antiparallel/parallel transition can be occurred, is performed. Afterward, the mentioned ballistic structure is dealt with solving the 16 [Formula: see text] 16 Bogoliubov-de-Gennes equation. It is found that although the exchange fields of the FS are laid in the z and y  direction, the STT interestingly exists in all three directions of x, y  and z. This exciting finding suggests that the favorable equilibrium configuration concerning the least exchange coupling occurs in the relative exchange field direction different from 0 or [Formula: see text].

Guidelines for Selecting Interlayer Spacers in Synthetic 2D-Based Antiferromagnets from First-Principles Simulations

Following the recent synthesis of graphene-based antiferromagnetic ultrathin heterostructures made of Co and Fe, we analyse the effect of the spacer between both ferromagnetic materials. Using density functional calculations, we carried out an exhaustive study of the geometric, electronic and magnetic properties for intercalated single Co MLs on top of Ir(111) coupled to monolayered Fe through n graphene layers (n = 1, 2, 3) or monolayered h-BN. Different local atomic arrangements have been considered to model the Moiré patterns expected in these heterostructures. The magnetic exchange interactions between both ferromagnets ( J C o - F e ) are computed from explicit calculations of parallel and anti-parallel Fe/Co inter-layer alignments, and discussed in the context of recent experiments. Our analysis confirms that the robust antiferromagnetic superexchange-coupling between Fe and Co layers is mediated by the graphene spacer through the hybridization of C's p z orbitals with Fe and Co's 3d states. The hybridization is substantially suppressed for multilayered graphene spacers, for which the magnetic coupling between ferromagnets is critically reduced, suggesting the need for ultrathin (monolayer) spacers in the design of synthetic graphene-based antiferromagnets. In the case of h-BN, p z orbitals also mediate d(Fe/Co) coupling. However, there is a larger contribution of local ferromagnetic interactions. Magnetic anisotropy energies were also calculated using a fully relativistic description, and show out-of-plane easy axis for all the configurations, with remarkable net values in the range from 1 to 4 meV.

Tuning Magnetic Chirality by Dipolar Interactions

The stabilization of chiral magnetic domain walls and skyrmions has been attributed to the actively investigated Dzyaloshinskii-Moriya interaction. Recently, however, predictions were made that suggest dipolar interactions can also stabilize chiral domain walls and skyrmions, but direct experimental evidence has been lacking. Here we show that dipolar interactions can indeed stabilize chiral domain walls by directly imaging the magnetic domain walls using scanning electron microscopy with polarization analysis in archetype Pt/CoB/Ir thin film multilayers. We further demonstrate the competition between the Dzyaloshinskii-Moriya and dipolar interactions by imaging a reversal of the domain wall chirality as a function of the magnetic layer thickness. Finally, we suggest that this competition can be tailored by a Ruderman-Kittel-Kasuya-Yosida interaction. Our work therefore reveals that dipolar interactions play a key role in the stabilization of chiral spin textures. This insight will open up new routes towards balancing interactions for the stabilization of chiral magnetism.

Engineering magnetoresistance: a new perspective

A new proposal is given to achieve high degree of magnetoresistance (MR) in a magnetic quantum device where two magnetic layers are separated by a non-magnetic (NM) quasiperiodic layer that acts as a spacer. The NM spacer is chosen in the form of well-known Aubry-André or Harper (AAH) model which essentially gives the non-trivial features in MR due to its gaped spectrum and yields the opportunities of controlling MR selectively by tuning the AAH phase externally. We also explore the role of dephasing on magnetotransport to make the model more realistic. Finally, we illustrate the experimental possibilities of our proposed quantum system.

Interlayer exchange coupling in ferromagnetic semiconductor trilayers with out-of-plane magnetic anisotropy

We report the observation of ferromagnetic (FM) and antiferromagnetic (AFM) interlayer exchange coupling (IEC) in GaMnAsP-based trilayer structures with out-of-plane magnetic anisotropy. Magnetization and anomalous Hall effect (AHE) measurements show well-resolved magnetization transitions corresponding to the two GaMnAsP layers. Minor loop measurements reveal a characteristic shift caused by IEC in all trilayer samples investigated. Interestingly, the FM IEC changes to AFM IEC for a trilayer with the thinnest (7 nm) top GaMnAsP layer as the temperature increases. The observation of temperature-induced transition of FM and AFM IEC in the same sample suggests the possibility of device applications by controlling the type of IEC in such GaMnAsP-based multilayers.

Interlayer Couplings Mediated by Antiferromagnetic Magnons

Collinear antiferromagnets (AFs) support two degenerate magnon excitations carrying opposite spin polarizations, by which magnons can function as electrons in various spin-related phenomena. In an insulating ferromagnet(F)/AF/F trilayer, we explore the magnon-mediated interlayer coupling by calculating the magnon thermal energy in the AF as a function of the orientations of the Fs. The effect manifests as an interlayer exchange interaction and a perpendicular magnetic anisotropy; they both depend on temperature and the AF thickness. In particular, the exchange interaction turns out to be antiferromagnetic at low temperatures and ferromagnetic at high temperatures, whose magnitude can be 10-100  μeV for nanoscale separations, allowing experimental verification.

Interface Engineering and Emergent Phenomena in Oxide Heterostructures

Complex oxide interfaces have mesmerized the scientific community in the last decade due to the possibility of creating tunable novel multifunctionalities, which are possible owing to the strong interaction among charge, spin, orbital, and structural degrees of freedom. Artificial interfacial modifications, which include defects, formal polarization, structural symmetry breaking, and interlayer interaction, have led to novel properties in various complex oxide heterostructures. These emergent phenomena not only serve as a platform for investigating strong electronic correlations in low-dimensional systems but also provide potentials for exploring next-generation electronic devices with high functionality. Herein, some recently developed strategies in engineering functional oxide interfaces and their emergent properties are reviewed.

Magnetic Hysteresis in Nanostructures with Thermally Controlled RKKY Coupling

Mechanisms of the recently demonstrated ex-situ thermal control of the indirect exchange coupling in magnetic multilayer are discussed for different designs of the spacer layer. Temperature-induced changes in the hysteresis of magnetization are shown to be associated with different types of competing interlayer exchange interactions. Theoretical analysis indicates that the measured step-like shape and hysteresis of the magnetization loops is due to local in-plane magnetic anisotropy of nano-crystallites within the strongly ferromagnetic films. Comparison of the experiment and theory is used to contrast the mechanisms of the magnetization switching based on the competition of (i) indirect (RKKY) and direct (non-RKKY) interlayer exchange interactions as well as (ii) indirect ferromagnetic and indirect antiferromagnetic (both of RKKY type) interlayer exchange. These results, detailing the rich magnetic phase space of the system, should help enable the practical use of RKKY for thermally switching the magnetization in magnetic multilayers.

Anomalous optical nonreciprocity in magnetic nanoisland arrays

We study the phenomenon of optical nonreciprocity in multilayer systems of magnetic nanoislands [FeNi-Al₂O₃] _N . An anomalously large optical nonreciprocity was observed in these systems. The effect was manifested in nonequivalence of polarization plane rotation of reflected light for the sample in an initial position and rotated by [Formula: see text]. We assume that the super-vortex magnetization in the FeNi layers is responsible for the optical nonreciprocity effect. It was found that the value of nonreciprocity effect depends on the effective thickness of FeNi island layer and reaches a maximum with the super-vortex magnetization formation. The nonreciprocity magnitude is significantly higher than the values observed recently in systems of specially formed magnetic nanoparticles. Nonreciprocity magnitude is strongly dependent on interlayer interaction between nanoisland layers at large distances.

Synthetic Antiferromagnetic Spintronics

Spintronic and nanomagnetic devices often derive their functionality from layers of different materials and the interfaces between them. This is especially true for synthetic antiferromagnets - two or more ferromagnetic layers that are separated by metallic spacers or tunnel barriers and which have antiparallel magnetizations. Here, we discuss the new opportunities that arise from synthetic antiferromagnets, as compared to crystal antiferromagnets or ferromagnets.

Structural and magnetic characteristics of the Co/Cu/Co thin-film systems

The results on investigation of structural and magnetic characteristics of Co/Cu/Co thin-film systems obtained by magnetron sputtering on glass substrates are presented. The thickness of Co layers in all samples is equal to 5 nm and the Cu layer is varied from 0.5 to 4 nm. It is found that the saturation field, HS, oscillates in magnitude with increasing Cu layer thickness with the period of the order of 1 nm. The maximum values of HS are observed for tCu = 1.4, 2.2 and 3.2 nm. The hysteresis loops measured for these samples in a magnetic field applied along the easy magnetization axis have a two-step form, and for other tCu – rectangular one. The obtained results are explained by the presence of exchange coupling between the ferromagnetic layers through a Co spacer and its oscillating behavior with changing tCu.

Optically Tunable Magnetoresistance Effect: From Mechanism to Novel Device Application

The magnetoresistance effect in sandwiched structure describes the appreciable magnetoresistance effect of a device with a stacking of two ferromagnetic layers separated by a non-magnetic layer (i.e., a sandwiched structure). The development of this effect has led to the revolution of memory applications during the past decades. In this review, we revisited the magnetoresistance effect and the interlayer exchange coupling (IEC) effect in magnetic sandwiched structures with a spacer layer of non-magnetic metal, semiconductor or organic thin film. We then discussed the optical modulation of this effect via different methods. Finally, we discuss various applications of these effects and present a perspective to realize ultralow-power, high-speed data writing and inter-chip connection based on this tunable magnetoresistance effect.

Spin-transfer torque in multiferroic tunnel junctions with composite dielectric/ferroelectric barriers

Using model calculations, we demonstrate a very high level of control of the spin-transfer torque (STT) by electric field in multiferroic tunnel junctions with composite dielectric/ferroelectric barriers. We find that, for particular device parameters, toggling the polarization direction can switch the voltage-induced part of STT between a finite value and a value close to zero, i.e. quench and release the torque. Additionally, we demonstrate that under certain conditions the zero-voltage STT, i.e. the interlayer exchange coupling, can switch sign with polarization reversal, which is equivalent to reversing the magnetic ground state of the tunnel junction. This bias- and polarization-tunability of the STT could be exploited to engineer novel functionalities such as softening/hardening of the bit or increasing the signal-to-noise ratio in magnetic sensors, which can have important implications for magnetic random access memories or for combined memory and logic devices.

Voltage-controlled interlayer coupling in perpendicularly magnetized magnetic tunnel junctions

Magnetic interlayer coupling is one of the central phenomena in spintronics. It has been predicted that the sign of interlayer coupling can be manipulated by electric fields, instead of electric currents, thereby offering a promising low energy magnetization switching mechanism. Here we present the experimental demonstration of voltage-controlled interlayer coupling in a new perpendicular magnetic tunnel junction system with a GdO_x tunnel barrier, where a large perpendicular magnetic anisotropy and a sizable tunnelling magnetoresistance have been achieved at room temperature. Owing to the interfacial nature of the magnetism, the ability to move oxygen vacancies within the barrier, and a large proximity-induced magnetization of GdO_x, both the magnitude and the sign of the interlayer coupling in these junctions can be directly controlled by voltage. These results pave a new path towards achieving energy-efficient magnetization switching by controlling interlayer coupling.

Exploring electric field controlled magnetism enables high efficiency and low energy consumption spintronic devices. Here, by manipulating oxygen vacancies and magnetic moment, the authors achieve voltage control of magnetic interlayer coupling in GdO_x based magnetic tunnel junctions.

Microscopic theory of the Coulomb based exchange coupling in magnetic tunnel junctions

We study interlayer exchange coupling based on the many-body Coulomb interaction between conduction electrons in magnetic tunnel junction. This mechanism complements the known interaction between magnetic layers based on virtual electron hopping (or spin currents). We find that these two mechanisms have different behavior on system parameters. The Coulomb based coupling may exceed the hopping based exchange. We show that the Coulomb based exchange interaction, in contrast to the hopping based coupling, depends strongly on the dielectric constant of the insulating layer. The dependence of the interlayer exchange interaction on the dielectric properties of the insulating layer in magnetic tunnel junction is similar to magneto-electric effect where electric and magnetic degrees of freedom are coupled. We calculate the interlayer coupling as a function of temperature and electric field for magnetic tunnel junction with ferroelectric layer and show that the exchange interaction between magnetic leads has a sharp decrease in the vicinity of the ferroelectric phase transition and varies strongly with external electric field.

Influence of the Coulomb interaction on the exchange coupling in granular magnets

We develop a theory of the exchange interaction between ferromagnetic (FM) metallic grains embedded into insulating matrix by taking into account the Coulomb blockade effects. For bulk ferromagnets separated by the insulating layer the exchange interaction strongly depends on the height and thickness of the tunneling barrier created by the insulator. We show that for FM grains embedded into insulating matrix the exchange coupling additionally depends on the dielectric properties of this matrix due to the Coulomb blockade effects. In particular, the FM coupling decreases with decreasing the dielectric permittivity of insulating matrix. We find that the change in the exchange interaction due to the Coulomb blockade effects can be a few tens of percent. Also, we study dependence of the intergrain exchange interaction on the grain size and other parameters of the system.

Control of the Oscillatory Interlayer Exchange Interaction with Terahertz Radiation

The oscillatory interlayer exchange interaction between two magnetic layers separated by a metallic spacer is one of the few coherent quantum phenomena that persists at room temperature. Here, we show that this interaction can be controlled dynamically by illuminating the sample (e.g., a spin valve) with radiation in the 10-100 THz range. We predict that the exchange interaction can be changed from ferromagnetic to antiferromagnetic (and vice versa) by tuning the amplitude and/or the frequency of the radiation. Our chief theoretical result is an expression that relates the dynamical exchange interaction to the static one that has already been extensively measured.

Controlling the magnetism of adsorbed metal-organic molecules

Gaining control on the size or the direction of the magnetic moment of adsorbed metal-organic molecules constitutes an important step towards the realization of a surface-mounted molecular spin electronics. Such control can be gained by taking advantage of interactions of the molecule's magnetic moment with the environment. The paramagnetic moments of adsorbed metal-organic molecules, for example, can be controlled by the interaction with magnetically ordered substrates. Metalloporphyrins and -phthalocyanines display a quasi-planar geometry, allowing the central metal ion to interact with substrate electronic states. This can lead to magnetic coupling with a ferromagnetic or even antiferromagnetic substrate. The molecule-substrate coupling can be mediated and controlled by insertion layers such as oxygen atoms, graphene, or nonmagnetic metal layers. Control on the magnetic properties of adsorbed metalloporphyrins or -phthalocyanines can also be gained by on-surface chemical modification of the molecules. The magnetic moment or the magnetic coupling to ferromagnetic substrates can be changed by adsorption and thermal desorption of small molecules that interact with the fourfold-coordinated metal center via the remaining axial coordination site. Spin-crossover molecules, which possess a metastable spin state that can be switched by external stimuli such as temperature or light, are another promising class of candidates for control of magnetic properties. However, the immobilization of such molecules on a solid surface often results in a quench of the spin transition due to the interaction with the substrate. We present examples of Fe(II) spin-crossover complexes in direct contact with a solid surface that undergo a reversible spin-crossover transition as a function of temperature, by illumination with visible light, or can be switched by the tip of a scanning tunneling microscope.

Interlayer Exchange Coupling: A General Scheme Turning Chiral Magnets into Magnetic Multilayers Carrying Atomic-Scale Skyrmions

We report on a general principle using interlayer exchange coupling to extend the regime of chiral magnetic films in which stable or metastable magnetic Skyrmions can appear at a zero magnetic field. We verify this concept on the basis of a first-principles model for a Mn monolayer on a W(001) substrate, a prototype chiral magnet for which the atomic-scale magnetic texture is determined by the frustration of exchange interactions, impossible to unwind by laboratory magnetic fields. By means of ab initio calculations for the Mn/W_{m}/Co_{n}/Pt/W(001) multilayer system we show that for certain thicknesses m of the W spacer and n of the Co reference layer, the effective field of the reference layer fully substitutes the required magnetic field for Skyrmion formation.

Interlayer coupling through a dimensionality-induced magnetic state

Dimensionality is known to play an important role in many compounds for which ultrathin layers can behave very differently from the bulk. This is especially true for the paramagnetic metal LaNiO₃, which can become insulating and magnetic when only a few monolayers thick. We show here that an induced antiferromagnetic order can be stabilized in the [111] direction by interfacial coupling to the insulating ferromagnet LaMnO₃, and used to generate interlayer magnetic coupling of a nature that depends on the exact number of LaNiO₃ monolayers. For 7-monolayer-thick LaNiO₃/LaMnO₃ superlattices, negative and positive exchange bias, as well as antiferromagnetic interlayer coupling are observed in different temperature windows. All three behaviours are explained based on the emergence of a (¼,¼,¼)-wavevector antiferromagnetic structure in LaNiO₃ and the presence of interface asymmetry with LaMnO₃. This dimensionality-induced magnetic order can be used to tailor a broad range of magnetic properties in well-designed superlattice-based devices.

Oxide materials can be combined to create heterostructures exhibiting complex properties not found in either substance individually. Here, the authors observe antiferromagnetic interlayer exchange coupling between ferromagnetic lanthanum manganite and nominally paramagnetic lanthanum nickel oxide.

Systematic layer-by-layer characterization of multilayers for three-dimensional data storage and logic

Magnetic kink solitons are used as a probe to experimentally measure the layer-by-layer coercivity and interlayer coupling strength of an antiferromagnetically coupled perpendicularly magnetized Co multilayer. The magnetic response is well described by a nearest neighbor Ising macrospin model. By controlling the position of one, two or three solitons in the stack using globally applied magnetic fields, we successfully probe the switching of individual buried layers under different neighboring configurations, allowing us to access individual layer's characteristic parameters. We found the coercivity to increase dramatically up the multilayer, while the interlayer coupling strength decreased slightly. We corroborate these findings with scanning transmission electron microscopy images where a degrading quality of the multilayer is observed. This method provides a very powerful tool to characterize the quality of individual layers in complex multilayers, without the need for depth-sensitive magnetic characterization equipment.

Long-range magnetic coupling across a polar insulating layer

Magnetic interactions in solids are normally mediated by short-range exchange or weak dipole fields. Here we report a magnetic interaction that can propagate over long distances (∼10 nm) across a polar insulating oxide spacer. Evidence includes oscillations of magnetization, coercivity and field-cooled loop shift with the thickness of LaAlO₃ in La_0.67Sr_0.33MnO₃/LaAlO₃/SrTiO₃ heterostructures. Similar modifications of the hysteresis loop appear when two coupled films of La_0.67Sr_0.33MnO₃ are separated by LaAlO₃, or another polar insulator, but they are absent when the oxide spacer layer is nonpolar. The loop shift is attributed to strong spin–orbit coupling and Dzyaloshinskii–Moriya interaction at the interfaces. There is evidence from inelastic light scattering that the polar spacer mediates long-range transmission of orbital magnetization. This coupling mechanism is expected to apply for any conducting ferromagnetic oxide with mixed valence; in view of electron hopping frequency involved, it raises the prospect of terahertz tunability of magnetic coupling.

Magnetic interactions in solids are usually short-range or else they involve itinerant electrons. Here, the authors evidence a long-range magnetic coupling mediated by orbital moments in a polar spacer layer of nonmagnetic insulating oxide, with a sign which oscillates with spacer thickness.

Thermally robust perpendicular Co/Pd-based synthetic antiferromagnetic coupling enabled by a W capping or buffer layer

Perpendicularly magnetized tunnel junctions (p-MTJs) that contain synthetic antiferromagnetic (SAF) frames show promise as reliable building blocks to meet the demands of perpendicular magnetic anisotropy (PMA)-based spintronic devices. In particular, Co/Pd multilayer-based SAFs have been widely employed due to their outstanding PMA features. However, the widespread utilization of Co/Pd multilayer SAFs coupled with an adjacent CoFeB reference layer (RL) is still a challenge due to the structural discontinuity or intermixing that occurs during high temperature annealing. Thus, we address the thermally robust characteristics of Co/Pd multilayer SAFs by controlling a W layer as a potential buffer or capping layer. The W-capped Co/Pd multilayer SAF, which acts as a pinning layer, exhibited a wide-range plateau with sharp spin-flip and near-zero remanence at the zero field. Structural analysis of the W-capped multilayer SAF exhibited single-crystal-like c-axis oriented crystalline features after annealing at 400 °C, thereby demonstrating the applicability of these frames. In addition, when the W layer serving as a buffer layer in the Co/Pd multilayer SAF was coupled with a conventional CoFeB RL, higher annealing stability up to 425 °C and prominent antiferromagnetic coupling behavior were obtained.

Engineering the interlayer exchange coupling in magnetic trilayers

When the thickness of metal film approaches the nanoscale, itinerant carriers resonate between its boundaries and form quantum well states (QWSs), which are crucial to account for the film’s electrical, transport and magnetic properties. Besides the classic origin of particle-in-a-box, the QWSs are also susceptible to the crystal structures that affect the quantum resonance. Here we investigate the QWSs and the magnetic interlayer exchange coupling (IEC) in the Fe/Ag/Fe (001) trilayer from first-principles calculations. We find that the carriers at the Brillouin-zone center (belly) and edge (neck) separately form electron- and hole-like QWSs that give rise to an oscillatory feature for the IEC as a function of the Ag-layer thickness with long and short periods. Since the QWS formation sensitively depends on boundary conditions, one can switch between these two IEC periods by changing the Fe-layer thickness. These features, which also occur in the magnetic trilayers with other noble-metal spacers, open a new degree of freedom to engineer the IEC in magnetoresistance devices.

Fluctuation theorem for a small engine and magnetization switching by spin torque

We consider a reversal of the magnetic moment of a nanomagnet by a fluctuating spin torque induced by a nonequilibrium current of electron spins. This is an example of the problem of the escape of a particle from a metastable state subjected to a fluctuating nonconservative force. Spin torque is a nonconservative force, and its fluctuations are beyond the description of the fluctuation-dissipation theorem. We estimate the joint probability distribution of work done by the spin torque and the Joule heat generated by the current, which satisfies the fluctuation theorem for a small engine. We predict a threshold voltage above which the spin-torque shot noise induces probabilistic switching events and below which such events are blocked. We adopt the theory of full-counting statistics under the adiabatic pumping of spin angular momentum. This enables us to account for the backaction effect, which is crucial to maintain consistency with the fluctuation theorem.

Multi-bit operations in vertical spintronic shift registers

Spintronic devices have in general demonstrated the feasibility of non-volatile memory storage and simple Boolean logic operations. Modern microprocessors have one further frequently used digital operation: bit-wise operations on multiple bits simultaneously. Such operations are important for binary multiplication and division and in efficient microprocessor architectures such as reduced instruction set computing (RISC). In this paper we show a four-stage vertical serial shift register made from RKKY coupled ultrathin (0.9 nm) perpendicularly magnetised layers into which a 3-bit data word is injected. The entire four stage shift register occupies a total length (thickness) of only 16 nm. We show how under the action of an externally applied magnetic field bits can be shifted together as a word and then manipulated individually, including being brought together to perform logic operations. This is one of the highest level demonstrations of logic operation ever performed on data in the magnetic state and brings closer the possibility of ultrahigh density all-magnetic microprocessors.

Magnetization states of all-oxide spin valves controlled by charge-orbital ordering of coupled ferromagnets

Charge-orbital ordering is commonly present in complex transition metal oxides and offers interesting opportunities for novel electronic devices. In this work, we demonstrate for the first time that the magnetization states of the spin valve can be directly manipulated by charge-orbital ordering. We investigate the interlayer exchange coupling (IEC) between two epitaxial magnetite layers separated by a nonmagnetic epitaxial MgO dielectric. We find that the state of the charge-orbital ordering in magnetite defines the strength, and even the sign of the IEC. First-principles calculations further show that the charge-orbital ordering modifies the spin polarized electronic states at the Fe₃O₄/MgO interfaces and results in a sufficiently large phase shift of wave function which are responsible for the observed IEC sign change across Verwey temperature. Our findings may open new interesting avenues for the electric field control of the magnetization states of spin valves via charge-orbital ordering driven IEC sign change.

Spin configuration of magnetic multi-layers: effect of exchange, dipolar and Dzyalozhinski-Moriya interactions

We investigate the effect of coupling (intensity and nature), applied field, and anisotropy on the spin dynamics of a multi-layer system composed of a hard magnetic layer coupled to a soft magnetic layer through a nonmagnetic spacer. The soft layer is modeled as a stack of several atomic planes while the hard layer, of a different material, is either considered as a pinned macroscopic magnetic moment or again as a stack of atomic planes. We compute the magnetization profile and hysteresis loop of the whole multi-layer system by solving the Landau-Lifshitz equations for the net magnetic moment of each (atomic) plane. We study the competition between the intra-layer anisotropy and exchange interaction, applied magnetic field, and the interface exchange, dipolar or Dzyalozhinski-Moriya interaction. Compared with the exchange coupling, the latter two couplings present peculiar features in the magnetization profile and hysteresis loop that may help identify the nature of the interface coupling in multi-layer magnetic systems.

Electron-mediated ferromagnetic behavior in CoO/ZnO multilayers

CoO/Al-doped ZnO (AZO) multilayers exhibit ferromagnetism up to ~300 K. The magnetic behavior oscillates with odd vs even number of Co layers in the insulating antiferromagnetic CoO and (separately) with the thickness of the AZO layers and vanishes if AZO is replaced by intrinsic ZnO. Magnetization is due to uncompensated (111) ferromagnetic planes of insulating CoO for odd numbers of atomic planes per layer that are coupled together via RKKY exchange mediated by electron carriers in the nonmagnetic AZO layers. The period of the oscillation with AZO thickness qualitatively matches the Fermi wave vector calculated from the carrier concentration measured by ordinary Hall effect. Magnetic polarization of the AZO carriers is confirmed via an anomalous Hall effect that is proportional to the magnetization.

Spin-transfer and exchange torques in ferromagnetic superconductors

We consider how superconducting correlations influence spin-transfer torques in ferromagnetic superconductors. It is demonstrated that there is a novel torque arising from particle-hole interference that depends on the U(1) phase associated with the superconducting order parameter. We also show that there is an equilibrium exchange torque between two ferromagnetic superconductors in contact via a normal metal mediated by Andreev states. The latter equilibrium magnetic torque is also sensitive to spin-resolved phase differences in the superconducting order parameters as well as to an externally applied phase difference.

Switching magnetization by 180° with an electric field

Magnetoelectric coupling allows for manipulating the magnetization by an external electric field or the electrical polarization by an external magnetic field. Here, we propose a mechanism to electrically induce 180° magnetization switching combining two effects: the magnetoelectric coupling at a multiferroic interface and magnetic interlayer exchange coupling. By means of first-principles methods, we investigate a ferroelectric layer in contact with a Fe/Au/Fe trilayer. The calculations show that the interface magnetism is strongly coupled to the ferroelectric layer. Furthermore, under certain conditions a reversal of polarization causes a sign reversal of the interlayer exchange coupling which is results in a 180° switching of the free layer magnetization. We argue that this magnetoelectric coupling mechanism is very robust and can find applications in magnetic data storage.