We study how a bias voltage changes magnetic exchange interactions. We derive a general expression for magnetic exchange interactions for systems coupled to reservoirs under a bias potential, and apply it to spin valves. We find that for metallic systems, the interlayer exchange coupling shows a weak, oscillatory dependence on the bias potential. For tunneling systems, we find a quadratic dependence on the bias potential, and derive an approximate expression for this bias dependence for a toy model. We give general conditions for when the interlayer exchange coupling is a quadratic function of bias potential.
We study the magnetic damping in the simplest of synthetic antiferromagnets, i.e. antiferromagnetically exchange-coupled spin valves in which applied magnetic fields tune the magnetic configuration to become noncollinear. We formulate the dynamic exchange of spin currents in a noncollinear texture based on the spindiffusion theory with quantum mechanical boundary conditions at the ferrromagnet|normal-metal interfaces and derive the Landau-Lifshitz-Gilbert equations coupled by the static interlayer non-local and the dynamic exchange interactions. We predict non-collinearity-induced additional d…
Magnetization dynamic response of coupled and uncoupled spin valves with structure NiFe(20 nm)/Cu(t_Cu)/NiFe(20 nm)/IrMn(10nm) were probed using broadband ferromagnetic resonance absorption measurements. By varying the Cu thickness t_Cu we were able to tailor the coupling intensity between the free and pinned layers. Broadband spectra show two resonant modes for each measured field. It is noticed that the coupling among NiFe layers modifies the amplitude of the absorption peaks and, moreover, the dispersion relations of the modes, which are distorted specially at the anti-parallel state. A num…
We study electron transport through single-electron spin-valve transistors in the presence of non-local exchange between the ferromagnetic leads and the central normal-metal island. The Coulomb interaction is described with the orthodox model for Coulomb blockade and we allow for noncollinear lead magnetization directions. Two distinct exchange mechanisms that have been discussed in the literature are shown to be of comparable strength and are taken into account on equal footing. We present results for the linear conductance as a function of gate voltage and magnetic configuration, and discuss…
We demonstrate first measurements of successful spin generation in crystalline Co$_2$FeSi/MgO/GaAs hybrid structures grown by molecular-beam epitaxy (MBE), with different MgO interlayer thicknesses. Using non-local spin valve and non-local Hanle measurement configurations, we determine spin lifetimes of ${τ\approx 100}$~ns and spin diffusion lengths of ${λ\approx 5.6}$~$μ$m for different MgO layer thicknesses proving the high quality of the GaAs transport channel. For an optimized MgO layer thickness, the bias dependence of the spin valve signals indicates the verification of the half-metallic…
Current-induced dynamics in spin valves including composite free layer with antiferromagnetic interlayer exchange coupling is studied theoretically within the diffusive transport regime. We show that current-induced dynamics of a synthetic antiferromagnet is significantly different from dynamics of a synthetic ferrimagnet. From macrospin simulations we obtain conditions for switching the composite free layer, as well as for appearance of various self-sustained dynamical modes. Numerical simulations are compared with simple analytical models of critical current based on linearized Landau-Lifshi…
We investigate heat and charge transport through a diffusive SIF1F2N tunnel junction, where N (S) is a normal (superconducting) electrode, I is an insulator layer and F1,2 are two ferromagnets with arbitrary direction of magnetization. The flow of an electric current in such structures at subgap bias is accompanied by a heat transfer from the normal metal into the superconductor, which enables refrigeration of electrons in the normal metal. We demonstrate that the refrigeration efficiency depends on the strength of the ferromagnetic exchange field h and the angle α between the magnetizations o…
We study the electronic transport through a noncollinear single-electron spin-valve transistor. It consists of a small metallic island weakly coupled to two ferromagnetic leads with noncollinear magnetization directions. The electric current is influenced by Coulomb charging and by spin accumulation. Furthermore, the interplay of Coulomb interaction and tunnel coupling to spin-polarized leads yields a many-body exchange field, in which the accumulated island spin precesses. We analyze the effects of this exchange field in both the linear and nonlinear transport regime. In particular, we find t…
Current-driven spin torques in metallic spin-valves composed of antiferromagnets are theoretically studied using the non-equilibrium Green's function method implemented on a tight-binding model. We focus our attention on G-type and L-type antiferromagnets in both clean and disordered regimes. In such structures, spin torques can either rotate the magnetic order parameter coherently (coherent torque) or compete with the internal antiferromagnetic exchange (exchange torque). We show that, depending on the symmetry of the spin-valve, the coherent and exchange torques can be either in the plane, α…
We examined dipolar field effects on the microwave generation in the domain wall spin-valve by solving simultaneously the Landau-Lifshitz-Gilbert and Zhang-Levy-Fert diffusion equations. By numerically analyzing dipolar field dependence, we showed that the microwave generation needs the dipole-dipole interaction for a 180$^\circ$ domain wall and the amplitude of the microwave voltage signal depends strongly on the exchange length. In order to design a microwave generator using the domain wall spin-valve with high efficiency, we propose that the materials with short exchange length are preferre…
According to the recent experiment by the Fert group, the velocity of domain wall motion in the spin valve ferromagnetic nanowires was almost doubly enhanced compared to the old value. In this work, we propose an additional torque model, arising from the interlayer exchange interaction, which can enhance or suppress the domain wall velocity depending on the sign of the exchange constant or the wall motion direction relative to the magnetization orientation of the fixed layer.
We study the concept of spin heat accumulation in excited spin valves, more precisely the effective electron temperature that may become spin dependent, both in linear response and far from equilibrium. A temperature or voltage gradient create non-equilibrium energy distributions of the two spin ensembles in the normal metal spacer, which approach Fermi-Dirac functions through energy relaxation mediated by electron-electron and electron-phonon coupling. Both mechanisms also exchange energy between the spin subsystems. This inter-spin energy exchange may strongly affect thermoelectric propertie…
Nonlinear current-voltage characteristics and magnetoresistance of point contacts between a normal metal (N) and films of amorphous ferromagnet (F) Co40Fe40B20 of different thickness, exchange-biased by antiferromagnetic Mn80Ir20 are studied. A surface spin valve effect in the conductance of such F-N contacts is observed. The effect of exchange bias is found to be inversely proportional to the Co40Fe40B20 film thickness. This behavior as well as other magneto-transport effects we observe on single exchange-pinned ferromagnetic films are similar in nature to those found in conventional three-la…
We study interlayer exchange interaction in magnetic tunnel junctions with ferroelectric barrier. We focus on the influence of image forces on the voltage dependence of the interlayer magnetic interaction (magneto-electric effect). The influence of the image forces is twofold: 1) they significantly enforce magneto-electric effect occurring due to the surface charges at the interface between ferroelectric and ferromagnets; 2) in combination with voltage dependent dielectric constant of the ferroelectric barrier image forces cause an additional contribution to the magneto-electric effect in magn…
Electrons in a quantum-dot spin valve, consisting of a single-level quantum dot coupled to two ferromagnetic leads with magnetizations pointing in arbitrary directions, experience an exchange field that is induced on the dot by the interplay of Coulomb interaction and quantum fluctuations. We show that a third, superconducting lead with large superconducting gap attached to the dot probes this exchange field very sensitively. In particular, we find striking signatures of the exchange field in the symmetric component of the supercurrent with respect to the bias voltage applied between the ferro…
The magnetic behaviour of ultrathin ferromagnetic films deposited on substrates is strongly affected by the properties of the substrate. We investigate the spin pumping rate, interlayer exchange coupling and dynamic exchange coupling between ultrathin ferromagnetic films through palladium, a non-magnetic substrate that displays strong Stoner enhancement. We find that the interlayer exchange coupling, both in the static and dynamic versions, is qualitatively affected by the substrate's Stoner enhancement. For instance, the oscillatory behavior that is a hallmark property of the RKKY exchange co…
Fluctuations of the magnetization in spin valves are shown to cause resistance noise that strongly depends on the magnetic configuration. Due to the applied external field and the dynamic exchange interaction through the normal metal spacer, the electrical noise level of the antiparallel configuration can exceed that of the parallel one by an order of magnitude, in agreement with recent experimental results.
We address the interplay between stacking and interlayer exchange for ferromagnetically ordered CrI$_3$, both for bilayers and bulk. Whereas bulk CrI$_3$ is ferromagnetic, both magneto-optical and transport experiments show that interlayer exchange for CrI$_3$ bilayers is antiferromagnetic. Bulk CrI$_3$ is known to assume two crystal structures, rhombohedral and monoclinic, that differ mostly in the stacking between monolayers. Below 210-220 Kelvin, bulk CrI$_3$ orders in a rhombohedral phase. Our density functional theory calculations show a very strong dependence of interlayer exchange and s…
We investigate transport through a single-level quantum dot coupled to noncollinearly magnetized ferromagnets in the presence of localized spins in either the tunnel barrier or on the quantum dot. For a spin embedded in the tunnel barrier, we find an interplay between current-induced switching of the spin, spin-dependent tunneling through the barrier and spin accumulation on the dot resulting in characteristic signals in the current. We, furthermore, find huge Fano factors due to random telegraph noise. For noncollinear geometries, an exchange field that depends on the impurity spin state lead…
Ion bombardment has been shown to be capable of enhancing the interlayer exchange coupling in a trilayer system that exhibits giant magnetoresistance. We demonstrate that this phenomenon can be derived from the phase coherence among scattered paths within the two rough interfaces when their topographies are correlated. In the case of mild corrugations, our method reproduces the predictions by the proximity force approximation which does not consider the interference. When the characteristic Fourier conjugate of the tomography becomes large and comparable to the Fermi momentum, interesting new …
We study the spin thermalization, i.e., the inter-spin energy relaxation mediated by electron-electron scattering in small spin valves. When one or two of the dimensions of the spin valve spacer are smaller than the thermal coherence length, the direct spin energy exchange rate diverges and needs to be regularized by the sample dimensions. Here we consider two model systems: a long quasi-1D wire and a thin quasi-2D sheet.
Spin valves consisting of heterostructures of single-layer hexagonal crystal on an antiferromagnetic substrate or of bilayer hexagonal crystal intercalated between two (anti)ferromagnetic insulators, with the current-in-plane geometry, are proposed. The two-dimensional hexagonal crystals such as graphene, silicene, germanene, and stanene are modeled by the tight binding model of honeycomb lattice. The magnetization orientation of the antiferromagnetic substrate(s) controls the band gap and topological properties of bulk, which in turn control the transport of three types of spin valve geometri…
The FMR linewidth and its anisotropy in F$_1$/f/F$_2$/AF multilayers, where spacer f has a low Curie point compared to the strongly ferromagnetic F$_1$ and F$_2$, is investigated. The role of the interlayer exchange coupling in magnetization relaxation is determined experimentally by varying the thickness of the spacer. It is shown that stronger interlayer coupling via thinner spacers enhances the microwave energy exchange between the outer ferromagnetic layers, with the magnetization of F$_2$ exchange-dragged by the resonance precession in F$_1$. A weaker mirror effect is also observed: the m…
Magnetic domain walls can be moved by spin-polarized currents due to spin-transfer torques. This opens the possibility to use them in spintronic memory devices as, e.g., in racetrack storage. Naturally, in miniaturized devices domain walls can get very close to each other and affect each others dynamics. In this work we consider two separated domain walls in different layers which interact via an interlayer exchange coupling. One of these walls is moved by a spin-polarized current. Depending on several parameters as the current density, the interlayer coupling or the pinning potential, the com…
Chiral magnetism, wherein there is a preferred sense of rotation of the magnetization, has become a key aspect for future spintronic applications. It determines the chiral nature of magnetic textures, such as skyrmions, domain walls or spin spirals, and a specific magnetic chirality is often required for spintronic applications. Current research focuses on identifying and controlling the interactions that define the magnetic chirality. The influence of the interfacial Dzyaloshinskii-Moriya interaction (iDMI) and, recently, the dipolar interactions have previously been reported. Here, we experi…
The dynamics of the magnetic order parameters of ferromagnet/normal-metal/ferromagnet spin valves and isolated ferromagnets may be very different. We investigate the role of the nonequilibrium spin-current exchange between the ferromagnets in the magnetization precession and switching. We find a (low-temperature) critical current bias for a coherent current-induced magnetization excitation in spin valves, which unifies and generalizes previous ideas of Slonczewski and Berger. In the absence of an applied bias, the effect of the spin transfer can be expressed as magnetic--configuration-dependen…
We study interaction effects on transport through a small metallic cluster connected to two ferromagnetic leads (a single-electron spin-valve transistor) in the "orthodox model" for the Coulomb blockade. The non-local exchange between the spin accumulation on the island and the ferromagnetic leads is shown to affect the transport properties such as the electric current and spin-transfer torque as a function of the magnetic configuration, gate voltage, and applied magnetic field.
Two ferromagnetic layers magnetically decoupled by a thick normal metal spacer layer can be, nevertheless, dynamically coupled via spin currents emitted by the spin-pump and absorbed through the spin-torque effects at the neighboring interfaces. A decrease of damping in both layers due to a partial compensation of the angular momentum leakage in each layer was previously observed at the coincidence of the two ferromagnetic resonances. In case of non-zero magnetic coupling, such a dynamic exchange will depend on the mutual precession of the magnetic moments in the layers. A difference in the li…
It is shown that the coupling between magnetic layers separated by non-magnetic metallic superlattices can decay exponentially as a function of the spacer thickness $N$, as opposed to the usual $N^{-2}$ decay. This effect is due to the lack of constructive contributions to the coupling from extended states across the spacer. The exponential behavior is obtained by properly choosing the distinct metals and the superlattice unit cell composition.
Recently it has been predicted that a spin-polarized electrical current perpendicular-to-plane (CPP) directly flowing through a magnetic element can induce magnetization switching through spin-momentum transfer. In this letter, the first observation of current-induced magnetization switching (CIMS) in exchange-biased spin-valves (ESPVs) at room temperature is reported. The ESPVs show the CIMS behavior under a sweeping dc current with a very high critical current density. It is demonstrated that a thin Ruthenium (Ru) layer inserted between a free layer and a top electrode effectively reduces th…
We perform 3D micromagnetic simulations of current-driven magnetization dynamics in nanoscale exchange biased spin-valves that take account of (i) back action of spin-transfer torque on the pinned layer, (ii) non-linear damping and (iii) random thermal torques. Our simulations demonstrate that all these factors significantly impact the current-driven dynamics and lead to a better agreement between theoretical predictions and experimental results. In particular, we observe that, at a non-zero temperature and a sub-critical current, the magnetization dynamics exhibits nonstationary behaviour in …
To study spin flipping within the antiferromagnet IrMn, we extended prior Current-Perpendicular-to-Plane (CPP) Giant Magnetoresistance (GMR) studies of Py-based exchange-biased-spin-valves containing IrMn inserts to thicker IrMn layers-5 nm less than or equal to t(IrMn) less than or equal to 30 nm. Unexpectedly, AΔR = A[R(AP) - R(P)]--the difference in specific resistance between the anti-parallel (AP) and parallel (P) magnetic states of the two Py layers-did not decrease with increasing t(IrMn), for t(IrMn) greater than 5 nm, but rather became constant to within our measuring uncertainty. Thi…
The bulk Rashba semiconductors BiTeX (X=I, Cl and Br) with intrinsically enhanced Rashba spin-orbit coupling provide a new platform for investigation of spintronic and magnetic phenomena in materials. We theoretically investigate the interlayer exchange interaction between two ferromagnets deposited on opposite surfaces of a bulk Rashba semiconductor BiTeI in its trivial and topological insulator phases. In the trivial phase BiTeI, we find that for ferromagnets with a magnetization orthogonal to the interface, the exchange coupling is reminiscent of that of a conventional three-dimensional met…
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$_5$…
We report a study of interlayer exchange interaction in multilayer CoPt/Co structures consisting of periodic CoPt multilayer film with an "easy axis" anisotropy and thick Co layer with an "easy plane" anisotropy separated by Pt spacer with variable thickness. The magnetooptical Kerr effect (MOKE) and ferromagnetic resonance (FMR) measurements show up the essentially non-collinear state of magnetic moments of the layers and strong exchange coupling between CoPt and Co subsystems. The estimation of effective anisotropy and exchange coupling in a simple model based on the Landau-Lifshitz-Gilbert …
This paper contains the notes of lectures on the theory of interlayer exchange coupling presented at the 30-th Ferienschule of the Institut fuer Festkoerperforschung, Forschungszentrum Juelich, March 1999.
The oscillatory interlayer exchange interaction between two magnetic layers separated by a metallic spacer is one of the few coherent quantum phenomena that persist 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 anti-ferromagnetic (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 int…
We study the combined effects of spin transfer torque, voltage modulation of interlayer exchange coupling and magnetic anisotropy on the switching behavior of perpendicular magnetic tunnel junctions (p-MTJs). In asymmetric p-MTJs, a linear-in-voltage dependence of interlayer exchange coupling enables the effective perpendicular anisotropy barrier to be lowered for both voltage polarities. This mechanism is shown to reduce the critical switching current and effective activation energy. Finally, we analyze the possibility of having switching via interlayer exchange coupling only.
We theoretically investigate the finite-frequency as well as the zero-frequency charge-current fluctuations through a noncollinear single-electron spin-valve transistor in the limit of sequential tunneling. The system under consideration consists of two tunnel junctions that connect a small central metallic island to two ferromagnetic leads with noncollinear magnetization. Due to the spin-dependent tunnel coupling and the electron-electron interaction on the central electrode an exchange field that acts on the accumulated island spin is present. We analyze how this many-particle interaction ef…
We theoretically investigate the interlayer dipolar and exchange couplings for an array of metallic magnetic nanowires grown on top of an extended ultrathin yttrium iron garnet film. The calculated interlayer dipolar coupling agrees with observed anticrossings [Chen \emph{et al.}, Phys. Rev. Lett. \textbf{120}, 217202 (2018)], concluding that the interlayer exchange coupling is suppressed by a spacer layer between the nanowires and film. The Kittel mode in the nanowire array couples chirally to spin waves in the film, even though Damon-Eshbach surface modes do not exist. The chirality is suppr…
Influence of Ferromagnetic Interlayer Exchange Coupling on Current-induced Magnetization Switching and Dzyaloshinskii-Moriya Interaction in Co/Pt/Co Multilayer System
We study sharp peaks in the conductance-voltage characteristics of a double quantum dot and a quantum dot spin-valve that are located around zero bias. The peaks share similarities with a Kondo peak but can be clearly distinguished, in particular as they occur at high temperatures. The underlying physical mechanism is a strong current suppression that is quenched in bias-voltage dependent ways by exchange interactions. Our theoretical results are based on the quantum master equation methodology, including the Born-Markov approximation and a numerically exact, hierarchical scheme, which we exte…
Aiming to clarify the mechanisms governing the interlayer magnetic coupling, we have investigated the stacking energy and interlayer magnetism of bilayer CrBr$_3$ systemically. The magnetic ground states of bilayer CrBr$_3$ with different R-type and H-type stacking orders are established, which is found to be in good agreement with recent experiment (Science $\mathbf{366}$,983(2019)).Further analyses indicate that the stacking energy is mainly determined by the Coulomb interaction between the interlayer nearest-neighbor Br-Br atoms. While interlayer magnetism can be understood by a competition…
In the asymptotic limit, the interlayer exchange coupling decays as $D^{-2}$, where $D$ is the spacer thickness. A systematic procedure for calculating the preasymptotic corrections, i.e., the terms of order $D^{-n}$ with $n \ge 3$, is presented. The temperature dependence of the preasymptotic corrections is calculated. The results are used to discuss the preasymptotic corrections for the Co/Cu/Co(001) system.
We propose an electric-field-controlled mechanism for magnetization switching assisted solely by the interlayer-exchange coupling (IEC) between the fixed and the free magnets, which are separated by two oxide barriers sandwiching a spacer material known for exhibiting large IEC. The basic idea relies on the formation of a quantum-well (QW) within the spacer material and controlling the transmission coefficient across the structure with an electric-field via the resonant tunneling phenomena. Using non-equilibrium Green's function (NEGF) method, we show that the structure can exhibit a bias-depe…
This paper presents a review of the phenomenon of interlayer exchange coupling in magnetic multilayers. The emphasis is put on a pedagogical presentation of the mechanism of the phenomenon, which has been successfully explained in terms of a spin-dependent quantum confinement effect. The theoretical predictions are discussed in connection with corresponding experimental investigations.
We study the influence of spin waves on transport through a single-level quantum dot weakly coupled to ferromagnetic electrodes with noncollinear magnetizations. Side peaks appear in the differential conductance due to emission and absorption of spin waves. We, furthermore, investigate the nonequilibrium magnon distributions generated in the source and drain lead. In addition, we show how magnon-assisted tunneling can generate a fullly spin-polarized current without an applied transport voltage. We discuss the influence of spin waves on the current noise. Finally, we show how the magnonic cont…
We study frequency-dependent current noise through a single-level quantum dot connected to ferromagnetic leads with non-collinear magnetization. We propose to use the frequency-dependent Fano factor as a tool to detect single-spin dynamics in the quantum dot. Spin precession due to an external magnetic and/or a many-body exchange field affects the Fano factor of the system in two ways. First, the tendency towards spin-selective bunching of the transmitted electrons is suppressed, which gives rise to a reduction of the low-frequency noise. Second, the noise spectrum displays a resonance at the …
We propose a heat valve based on the interplay between thermal transport and proximity-induced exchange splitting in Josephson tunnel junctions. We demonstrate that the junction heat conductance strongly depends on the relative alignment of the exchange fields induced in the superconductors. Colossal magneto-heat resistance ratios as large as 10^7% are predicted to occur under proper temperature and phase conditions, as well as suitable ferromagnet-superconductor combinations. Moreover, the quantum phase tailoring, intrinsic to the Josephson coupling, offers an additional degree of freedom for…
