More than 30 years ago, Malozemoff (Phys. Rev. B 35, 3679 (1987)) hypothesized that exchange interaction at the interface between a ferromagnet (F) and an antiferromagnet (AF) can act as an effective random field, which can profoundly affect the magnetic properties of the system. However, until now this hypothesis has not been directly experimentally tested. We utilize magnetoelectronic measurements to analyze the effective exchange fields at Permalloy/CoO interface. Our results cannot be explained in terms of quasi-uniform effective exchange fields, but are in agreement with the random-field hypothesis of Malozemoff. The presented approach opens a new route for the quantitative analysis of effective exchange fields and anisotropies in magnetic heterostructures for memory, sensing and computing applications.
We investigate the effect of eddy currents on ferromagnetic resonance (FMR) in ferromagnet-normal metal (FM/NM) bilayer structures. Eddy-current effects are usually neglected for NM layer thicknesses below the microwave (MW) skin depth (approx. 800 nm for Au at 10 GHz). However, we show that in much thinner NM layers (10-100 nm of Au or Cu) they induce a phase shift in the FMR excitation when the MW driving field has a component perpendicular to the sample plane. This results in a strong asymmetry of the measured absorption lines. In contrast to typical eddy-current effects, the asymmetry is l…
We predict the emergence of spin Hall magnetoresistance in a magnetic bilayer composed of a normal metal adjacent to an antiferromagnet. Based on a recently derived drift-diffusion equation, we show that the resistance of the bilayer depends on the relative angle between the direction transverse to the current flow and the Néel order parameter. Although this effect presents striking similarities with the spin Hall magnetoresistance recently reported in ferromagnetic bilayers, in the present case its physical origin is attributed to the anisotropic spin relaxation of itinerant spins in the anti…
The properties of antiferromagnetic ferromagnetic bilayer have been studied using self-consistent mean-field approximation for Heisenberg Hamiltonian. The perpendicular exchange coupling has been revealed in a bilayer with a compensated interface. For a uniform antiferromagnetic film a symmetrical hysteresis loop has been calculated, because the transverse instability develops within the antiferromagnetic film at certain critical value of external magnetic field. On the other hand, shifted hysteresis loop with a finite exchange bias field has been obtained for a non-uniform antiferromagnetic f…
The interlayer magnetic interaction in bilayer CrI$_3$ plays a crucial role for its device applications. In this work, we studied the interlayer magnetic interaction in $π/3$-twisted bilayer CrI$_3$ using first-principles calculations. Our calculations show that the interlayer coupling can be ferromagnetic or antiferromagnetic depending crucially on lateral shift. The strongest antiferromagnetic interlayer interaction appears in the $\bar{A}A$-stacking. The magnetic force theory calculations demonstrate that such an antiferromagnetic interaction is dominanted by the $e_g$-$e_g$ channel. Partic…
The interplay between electronic transport and antiferromagnetic order has attracted a surge of interest as recent studies have shown that a moderate change in the spin orientation of a collinear antiferromagnet may have a significant effect on the electronic band structure. Among numerous electrical probes to read out such magnetic order, unidirectional magnetoresistance (UMR), where the resistance changes under the reversal of the current direction, can provide rich insights into the transport properties of spin-orbit coupled systems. However, UMR has never been observed in antiferromagnets …
The effect of localized holes on the long-range antiferromagnetic order in bilayer cuprates is studied, by applying the renormalization group to the appropriate non-linear sigma model. The theory accounts quantitatively for the magnetic phase diagram of Ca doepd YBa_2Cu_3O_6.
The periodic deviations of ferromagnetic and antiferromagnetic spins from corresponding uniform configurations are shown to be energetically favorable close to a compensated interface of ferromagnetic antiferromagnetic bilayer. The amplitude of the deviations decreases exponentially into the film volumes as a function of a coordinate perpendicular to the interface. The interaction energy is found to be proportional to a square of a scalar product of unit ferromagnetic and antiferromagnetic vectors.
In epitaxial (111) oriented Ni$_{80}$Fe$_{20}$/Fe$_{50}$Mn$_{50}$ bilayers, we separate two distinct behaviors: unidirectional anisotropy (exchange bias) in thick Fe$_{50}$Mn$_{50}$, and enhanced coercivity in thin Fe$_{50}$Mn$_{50}$. By measuring the magnetization response to a rotating magnetic field, we quantitatively determine the relevant anisotropies, and demonstrate that the enhanced coercivity is related to the rotatable magnetic anisotropy of Fe$_{50}$Mn$_{50}$. We also demonstrate the consequences of the anisotropy changes with temperature.
By means of micromagnetic spin dynamics calculations, a quantitative calculation is carried out to explore the mechanism of exchange bias (EB) in ferromagnetic (FM)/compensated antiferromagnetic (AFM) bilayers. The antiferromagnets with low and high Neel temperatures have been both considered, and the crossover from negative to positive EB is found only in the case with low Neel temperature. We propose that the mechanism of EB in FM/compensated AFM bilayers is due to the symmetry broken of AFM that yields some net ferromagnetic components.
Twisting in bilayers introduces structural chirality with two enantiomers, i.e., left- and right-hand bilayers, depending on the oriented twist angle. The interplay between this global chirality and additional degrees of freedom, such as magnetic ordering and the local octahedral chirality arising from the geometry of the bonds, can yield striking phenomena. In this work, we focus on collinear antiferromagnetic CrI$_3$ twisted homo-bilayers, which are characterized by a staggered octahedral chirality in each monolayer. Using symmetry analysis, density functional theory and tight-binding model …
We propose an experimental scheme to determine the spin-transfer torque efficiency excited by the spin-orbit interaction in ferromagnetic bilayers from the measurement of the longitudinal magnetoresistace. Solving a diffusive spin-transport theory with appropriate boundary conditions gives an analytical formula of the longitudinal charge current density. The longitudinal charge current has a term that is proportional to the square of the spin-transfer torque efficiency and that also depends on the ratio of the film thickness to the spin diffusion length of the ferromagnet. Extracting this cont…
A theoretical formulation of magnetoresistance effect in a metallic ferromagnetic/nonmagnetic bilayer originated from the charge-spin conversion by the anomalous Hall effect is presented. Analytical expressions of the longitudinal and transverse resistivities in both nonmagnet and ferromagnet are obtained by solving the spin diffusion equation. The magnetoresistance generated from charge-spin conversion purely caused by the anomalous Hall effect in the ferromagnet is found to be proportional to the square of the spin polarizations in the ferromagnet and has fixed sign. We also find additional …
We report the magnetotransport properties of ferromagnet (FM)/antiferromagnet (AFM) Fe$_2$CrSi/Ru$_2$MnGe epitaxial bilayers using current-in-plane configurations. Above the critical thickness of the Ru$_2$MnGe layer to induce exchange bias, symmetric and asymmetric curves were observed in response to the direction of FM magnetocrystalline anisotropy. Because each magnetoresistance curve showed full and partial AFM rotation, the magnetoresistance curves imply the impact of the Fe$_2$CrSi magnetocrystalline anisotropy to govern the AFM rotation. The maximum magnitude of the angular-dependent re…
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…
The analytical theory for a ferromagnetic antiferromagnetic bilayer with a compensated interface has been developed using an explicit expression for the interfacial interaction energy density. A stability of a solution describing domain walls within ferromagnetic and antiferromagnetic films has been investigated. It is shown that even for high values of surface interaction strength a transverse instability originates within the antiferromagnetic film, because the deviation of the unit antiferromagnetic vector out of the interface plane becomes energetically favorable in large enough external m…
Current-induced spin-orbit torques in Co$_2$FeAl/Pt ultrathin bilayers are studied using a magnetoresistive harmonic response technique, which distinguishes the dampinglike and fieldlike contributions. The presence of a temperature-dependent magnetic proximity effect is observed through the anomalous Hall and anisotropic magnetoresistances, which are enhanced at low temperatures for thin platinum thicknesses. The fieldlike torque efficiency decreases steadily as the temperature is lowered for all Pt thicknesses studied, which we propose is related to the influence of the magnetic proximity eff…
We studied the magnetoresistance of normal metal (NM)/ferromagnet (FM) bilayers in the linear and nonlinear (current-dependent) regimes and compared it with the amplitude of the spin-orbit torques and thermally induced electric fields. Our experiments reveal that the magnetoresistance of the heavy NM/Co bilayers (NM = Ta, W, Pt) is phenomenologically similar to the spin Hall magnetoresistance (SMR) of YIG/Pt, but has a much larger anisotropy, of the order of 0.5%, which increases with the atomic number of the NM. This SMR-like behavior is absent in light NM/Co bilayers (NM = Ti, Cu), which pre…
Two-dimensional (2D) ferromagnets with high Curie temperature have long been the pursuit for electronic and spintronic applications. CrI3 is a rising star of intrinsic 2D ferromagnets, however, it suffers from weak exchange coupling. Here we propose a general strategy of self-intercalation to achieve enhanced ferromagnetism in bilayer CrI3. We showed that filling either Cr or I atoms into the van der Waals gap of stacked and twisted CrI3 bilayers can induce the double exchange effect and significantly strengthen the interlayer ferromagnetic coupling. According to our first-principles calculati…
We determine magnon spectra of an atomic bilayer magnet with ferromagnetic intra- and both ferro- and anti- ferromagnetic interlayer coupling. Analytic expressions for the full magnon band of the latter case reveal that both exchange interactions govern the fundamental magnon gap. The inter and intralayer magnetic ordering are not independent: the intralayer ferromagnetism stabilizes antiferromagnetic inter-layer order. The topology of these exchange-anisotropy spin models without spin-orbit interaction turns out to be trivial.
We carefully investigated the ferromagnetic coupling in the as-grown and annealed ferromagnetic semiconductor GaMnAs/AlGaMnAs bilayer devices. We observed that the magnetic interaction between the two layers strongly affects the magnetoresistance of the GaMnAs layer with applying out of plane magnetic field. After low temperature annealing, the magnetic easy axis of the AlGaMnAs layer switches from out of plane into in-plane and the interlayer coupling efficiency is reduced from up to 0.6 to less than 0.4. However, the magnetic coupling penetration depth for the annealed device is twice that o…
The spin Hall magnetoresistance (SMR) and anomalous Hall effect (AHE) are observed in a Cr2O3/Ta structure. The structural and surface morphology of Cr2O3/Ta bilayers have been investigated. Temperature dependence of longitudinal and transverse resistances measurements confirm the relationship between SMR and AHE signals in Cr2O3/Ta structure. By means of temperature dependent magnetoresistance measurements, the physical origin of SMR in the Cr2O3/Ta structure is revealed, and the contribution to the SMR from the spin current generated by AHE has been proved. The so-called boundary magnetizati…
For ferromagnet/antiferromagnet bilayers, rotation of the easy axis has been \textit{for the first time} observed during measurements of training effect and the recovery of exchange bias using FeNi/FeMn system. These salient phenomena strongly suggest irreversible motion of antiferromagnet spins during subsequent measurements of hysteresis loops. It is found that the rotation of the easy axis can partly account for the training effect and the recovery of the exchange bias.
We utilize anisotropic magnetoresistance to study temporal evolution of the magnetization state in epitaxial Ni$_{80}$Fe$_{20}$/Fe$_{50}$Mn$_{50}$ ferromagnet/antiferromagnet bilayers. The resistance exhibits power-law evolution over a wide range of temperatures and magnetic fields, indicating that aging is characterized by a wide range of activation time scales. We show that aging is a cooperative process, i.e. the magnetic system is not a superposition of weakly interacting subsystems characterized by simple Arrhenius activation. The observed effects are reminiscent of avalanches in granular…
Strong ferromagnetic interlayer exchange couplings $J$ in perpendicularly magnetized systems are becoming increasingly desirable for applications. We study whether ferromagnetic interlayer exchange couplings can be measured by a combination of broadband ferromagnetic resonance methods and magnetometry hysteresis loops. For this we model the switching and the eigenexcitations in bilayer systems comprising a soft layer coupled to a thicker harder layer that possesses higher perpendicular magnetic anisotropy. For large $J >0$ the switching fields are essentially independent of $J$ but the frequen…
In this work, IrMn$_{3}$/insulating-Y$_{3}$Fe$_{5}$O$_{12}$ exchange-biased bilayers are studied. The behavior of the net magnetic moment $Δm_{AFM}$ in the antiferromagnet is directly probed by anomalous and planar Hall effects, and anisotropic magnetoresistance. The $Δm_{AFM}$ is proved to come from the interfacial uncompensated magnetic moment. We demonstrate that the exchange bias and rotational hysteresis are induced by the irreversible switching of the $Δm_{AFM}$. In the training effect, the $Δm_{AFM}$ changes continuously. This work highlights the fundamental role of the $Δm_{AFM}$ in th…
We report magnetization and magetoresistance measurements in hybrid ferromagnetic metal/semiconductor heterostructures comprised of MnAs/(Ga,Mn)As bilayers. Our measurements show that the (metallic) MnAs and (semiconducting) (Ga,Mn)As layers are exchange coupled, re- sulting in an exchange biasing of the magnetically softer (Ga,Mn)As layer that weakens with layer thickness. Magnetoresistance measurements in the current-perpendicular-to-the-plane geometry show a spin valve effect in these self-exchange biased bilayers. Similar measurements in MnAs/p- GaAs/(Ga,Mn)As trilayers show that the excha…
We report broadband spectroscopy and numerical analysis by which we explore propagating spin waves in a magnetic bilayer consisting of a 23 nm thick permalloy film deposited on 130 nm thick $Y_{3}Fe_{5}O_{12}$. In the bilayer, we observe a characteristic mode that exhibits a considerably larger group velocity at small in-plane magnetic field than both the magnetostatic and perpendicular standing spin waves. Using the finite element method, we confirm the observations by simulating the mode profiles and dispersion relations. They illustrate the hybridization of spin wave modes due to exchange c…
The paper presents a computational study of the ground-state magnetic phases of a selected bilayer graphene nanoflake in external electric field and magnetic field. The electric field has parallel and perpendicular component while the magnetic field is oriented in plane. The system consists of two rectangular layers having armchair edges and zigzag terminations with Bernal stacking. The theoretical model is based on a tight binding Hamiltonian with Hubbard term. The magnetic phase diagram involving the total spin is constructed, showing the stability areas of phases with total spin values equa…
The evolution of information technology has been driven by the discovery of new forms of large magnetoresistance (MR), such as giant magnetoresistance (GMR) and tunnelling magnetoresistance (TMR) in magnetic multilayers. Recently, new types of MR have been observed in much simpler bilayers consisting of ferromagnetic (FM)/nonmagnetic (NM) thin films; however, the magnitude of MR in these materials is very small (0.01 ~ 1%). Here, we demonstrate that NM/FM bilayers consisting of a NM InAs quantum well conductive channel and an insulating FM (Ga,Fe)Sb layer exhibit giant proximity magnetoresista…
Heterostructures of two-dimensional (2D) layered materials with selective compositions play an important role in creating novel functionalities. Effective interface coupling between 2D ferromagnet and electronic materials would enable the generation of exotic physical phenomena caused by intrinsic symmetry breaking and proximity effect at interfaces. Here, epitaxial growth of bilayer Bi(110) on 2D ferromagnetic Fe3GeTe2 (FGT) with large magnetic anisotropy has been reported. Bilayer Bi(110) islands are found to extend along fixed lattice directions of FGT. The six preferred orientations could …
A drastic modification of electronic band structure is predicted in bilayer graphene when it is placed between two ferromagnetic insulators. Due to the exchange interaction with the proximate ferromagnet, the electronic energy dispersion in the graphene channel strongly depends on the magnetization orientation of two ferromagnetic layers, $\mathbf{M_{1}}$ and $\mathbf{M_{2}} $. While the parallel configuration $\mathbf{M_{1}}= \mathbf{M_{2}}$ leads to simple spin splitting of both conduction and valence bands, an energy gap is induced as soon as the angle $θ$ between $\mathbf{M_{1}}$ and $% \m…
The magnetic characteristics of polycrystalline exchange-biased antiferromagnet/ferromagnet-bilayers are determined by a complex interplay of parameters, describing structural and magnetic properties of the material system, including in particular the grain volume distribution of the antiferromagnet. An ideal characterization of such systems would be a non-destructive determination of the relevant parameters for each individual grain. This is in most cases not feasible, since typical characterization methods do average over larger areas. Here, we show that it is however possible to determine a…
Spin-orbit torque (SOT)-induced magnetization switching shows promise for realizing ultrafast and reliable spintronics devices. Bipolar switching of perpendicular magnetization via SOT is achieved under an in-plane magnetic field collinear with an applied current. Typical structures studied so far comprise a nonmagnet/ferromagnet (NM/FM) bilayer, where the spin Hall effect in the NM is responsible for the switching. Here we show that an antiferromagnet/ferromagnet (AFM/FM) bilayer system also exhibits a SOT large enough to switch the magnetization of FM. In this material system, thanks to the …
We have observed the evolution of phase diagram and vortex pinning using a single ferromagnet/superconductor bilayer of [Co/Pt]8/Nb through a special demagnetization procedure. It induces a continuous and reversible change of the domain width with equal positive/negative domains enabling the observation of the predicted tunable phase diagram. The tunable domain pattern also systematically affects vortex pinning. We have determined the dependence of the activation energy of vortex pinning on domain width, temperature, and magnetic field.
The continuum theory of domain structures in ferromagnetic/superconducting bilayers fails when the equilibrium domain size becomes comparable with effective penetration depth $Λ$. Instead, a lattice of discrete vortices must be considered. Here, we report our results on the discrete vortex lattices in stripe domain structures of ferromagnetic/superconducting bilayers. The vortices are assumed to be situated periodically on chains in stripe domains. We study the configurations containing up to three chains per domain, and calculate their equilibrium energies, equilibrium domain size and vortex …
Extraordinary electronic phases can form in artificial oxide heterostructures, which will provide a fertile ground for new physics and also give rise to novel device functions. Based on a systematic first-principles density functional theory study of the magnetic and electronic properties of the (111) superlattices (ABO3)2/(AB'O3)10 of 4d and 5d transition metal perovskite (B = Ru, Rh, Ag, Re, Os, Ir, Au; AB'O3 = LaAlO3, SrTiO3), we demonstrate that due to quantum confinement, bilayers (LaBO3)2 (B = Ru, Re, Os) and (SrBO3)2 (B = Rh, Os, Ir) are ferromagnetic with ordering temperatures up to ro…
Recently intrinsic ferromagnetism in two-dimensional(2D) van der Waals materials was discovered [1, 2, 3]. A monolayer of Chromiun triiodide(CrI3) is ferromagnetic while a bilayer structure was reported to be anti-ferro magnetic, moreover an external electric field changes its magnetic phase [4]. We have studied the two found in nature stackings of CrI3 bilayers and found that indeed the magnetic phase of one of them can be tuned by an external electric field while the other remains ferromagnetic. We simulate those results with ab initio calculations and explain them with a simple model based …
We studied the magnetic behavior of bilayers of multiferroic and nominally antiferromagnetic o-YMnO$_3$ (375~nm thick) and ferromagnetic La$_{0.7}$Sr$_{0.3}$MnO$_3$ and La$_{0.67}$Ca$_{0.33}$MnO$_3$ ($8 \ldots 225~$nm), in particular the vertical magnetization shift $M_E$ and exchange bias field $H_E$ for different thickness and magnetic dilution of the ferromagnetic layer at different temperatures and cooling fields. We have found very large $M_E$ shifts equivalent to up to 100\% of the saturation value of the o-YMO layer alone. The overall behavior indicates that the properties of the ferrom…
Epitaxial La0.67Sr0.33MnO3 (LSMO)/ SrRuO3 (SRO) ferromagnetic bilayers have been grown on (001) SrTiO3 (STO) substrates by pulsed laser deposition with atomic layer control. We observe a shift in the magnetic hysteresis loop of the LSMO layer in the same direction as the applied biasing field (positive exchange bias). The effect is not present above the Curie temperature of the SRO layer (), and its magnitude increases rapidly as the temperature is lowered below . The direction of the shift is consistent with an antiferromagnetic exchange coupling between the ferromagnetic LSMO layer and the f…
We have performed magnetic measurements like temperature (T), cooling field (HFC) dependence of exchange bias (EB) and training effect to investigate the magnetic nature of the interface of the Fe/Ir20Mn80 systems. Thin film bilayer samples of different thicknesses of Ir20Mn80 have been prepared by dc magnetron sputtering at room temperature. The variation of exchange bias field (HEB) with the increase in thickness of Ir20Mn80 predicts the antiferromagnet (AFM) bulk spins contribution to EB. Exponential decay of HEB and coercive field (HC) with temperature reveals the presence of spin glass (S…
The discrete vortex lattices in a ferromagnet/superconductor bilayer are studied when the ferromagnet has periodic stripe domains with an out-of-plane magnetization. The vortices are assumed to be situated periodically on chains in the stripe domains. Only up to two vortex chains per domain configurations are considered. When the domain period is fixed, the threshold magnetization is calculated at which the transition from the Meissner state to the mixed state occurs. When the domain period is not fixed, the equilibrium domain size and vortex positions are calculated, depending on the domain's…
We present a comprehensive study of the exchange bias effect in a model system. Through numerical analysis of the exchange bias and coercive fields as a function of the antiferromagnetic layer thickness we deduce the absolute value of the averaged anisotropy constant of the antiferromagnet. We show that the anisotropy of IrMn exhibits a finite size effect as a function of thickness. The interfacial spin disorder involved in the data analysis is further supported by the observation of the dual behavior of the interfacial uncompensated spins. Utilizing soft x-ray resonant magnetic reflectometry …
Spin angular momentum transfer in magnetic bilayers offers the possibility of ultrafast and low-loss operation for next-generation spintronic devices. We report the field- and temperature- dependent measurements on the magnetization precessions in Co$_2$FeAl/(Ga,Mn)As by time-resolved magneto-optical Kerr effect (TRMOKE). Analysis of the effective Gilbert damping and phase shift indicates a clear signature of an enhanced dynamic exchange coupling between the two ferromagnetic (FM) layers due to the reinforced spin pumping at resonance. The temperature dependence of the dynamic exchange-couplin…
