We show that the coupling between two ferromagnetic layers separated by a nonmagnetic spacer can be used to control the depinning of domain walls and induce unidirectional domain wall propagation. We investigated CoFeB/Ti/CoFeB trilayers where the easy axis of the magnetization of the top CoFeB layer is out-of-plane and that of the bottom layer is in-plane. Using Magneto-optic Kerr effect microscopy, we find that the depinning of a domain wall in the perpendicularly magnetized CoFeB layer is influenced by the orientation of the magnetization of the in-plane layer, which gives rise to a field-driven asymmetric domain expansion. This effect occurs due to the magnetic coupling between the internal magnetization of the domain wall and the magnetization of the in-plane CoFeB layer, which breaks the symmetry of up-down and down-up homochiral Néel domain walls in the perpendicular CoFeB layer. Micromagnetic simulations support these findings by showing that the interlayer coupling either opposes or favors the Dzyaloshinskii-Moriya interaction in the domain wall, thereby generating an imbalance in the depinning fields. This effect also allows for artificially controlling the chirality and dynamics of domain walls in magnetic layers lacking a strong Dzyaloshinskii-Moriya interaction.
In ferromagnetic trilayers, a spin-orbit-induced spin current can have a spin polarization of which direction is deviated from that for the spin Hall effect. Recently, magnetization switching in ferromagnetic trilayers has been proposed and confirmed by the experiments. In this work, we theoretically and numerically investigate the switching current required for perpendicular magnetization switching in ferromagnetic trilayers. We confirm that the tilted spin polarization enables field-free deterministic switching at a lower current than conventional spin-orbit torque or spin-transfer torque sw…
Magnetic proximity effect between topological insulator (TI) and ferromagnetic insulator (FMI) is considered to have great potential in spintronics. However, a complete determination of interfacial magnetic structure has been highly challenging. We theoretically investigate the interlayer exchange coupling of two FMIs separated by a TI thin film, and show that the particular electronic states of the TI contributing to the proximity effect can be directly identified through the coupling behavior between two FMIs, together with a tunability of coupling constant. Such FMI/TI/FMI structure not onl…
We represent the results of micromagnetic modeling and experimental magnetic force microscopy investigations of domain wall (DW) pinning-depinning effects in the hybrid systems consisting of ferromagnetic nanowire (NW) and two ferromagnetic nanoparticles (NPs). It was demonstrated that the special NW-NPs configuration including the NW with DW nucleating bulb at one end and two-NP gate enables the realization of controlled DW pinning-depinning based on switching of magnetization in NPs subsystem. The algorithm of external driving field manipulation and independent NPs switching, which allow one…
The domain wall depinning from a notch in a Permalloy nanostrip on top of a ${\rm SiO_2/Si}$ substrate is studied theoretically under application of static magnetic fields and the injection of short current pulses. The influence of Joule heating on current-induced domain wall depinning is explored self-consistently by coupling the magnetization dynamics in the ferromagnetic strip to the heat transport throughout the system. Our results indicate that Joule heating plays a remarkable role in these processes, resulting in a reduction in the critical depinning field and/or in a temporary destructi…
We study the Josephson current through a ferromagnetic trilayer, both in the diffusive and clean limits. For colinear (parallel or antiparallel) magnetizations in the layers, the Josephson current is small due to short range proximity effect in superconductor/ferromagnet structures. For non colinear magnetizations, we determine the conditions for the Josephson current to be dominated by another contribution originating from long range triplet proximity effect.
The demagnetization and associated magnetocaloric effect in strong-weak-strong ferromagnetic trilayers, upon a reorientation of the strong ferromagnets from parallel to antiparallel magnetization, is simulated using atomistic spin dynamics. The simulations yield non-trivial spin distributions in the antiparallel state, which in turn allows entropy to be calculated directly. Empirical functional forms are obtained for the magnetization distribution in the spacer, differing significantly from some of the commonly used models. Finally, we find that the magnetocaloric effect in the system can be s…
In this article we study the ferromagnetic behavior of ABC-stacked trilayer graphene. This is done using a nearest-neighbor tight-binding model, in the presence of long-range Coulomb interactions. For a given electron-electron interaction g and doping level n, we determine whether the total energy is minimized for a paramagnetic or ferromagnetic configuration of our variational parameters. The g versus n phase diagram is first calculated for the unscreened case. We then include the effects of screening using a simplified expression for the fermion bubble diagram. We show that ferromagnetism in…
The spin-orbit torque, a torque induced by a charge current flowing through the heavy-metal conducting layer with strong spin-orbit interactions, provides an efficient way to control the magnetization direction in heavy-metal/ferromagnet nanostructures, required for applications in the emergent magnetic technologies like random access memories, high-frequency nano oscillators, or bio-inspired neuromorphic computations. We study the interface properties, magnetization dynamics, magnetostatic features and spin-orbit interactions within the multilayer system Ti(2)/Co(1)/Pt(0-4)/Co(1)/MgO(2)/Ti(2)…
There is an increasing interest in the electronic properties of few layer graphene as it offers a platform to study electronic interactions because the dispersion of bands can be tuned with number and stacking of layers in combination with electric field. However, electronic interaction becomes important only in very clean devices and so far the trilayer graphene experiments are understood within non-interacting electron picture. Here, we report evidence of strong electronic interactions and quantum Hall ferromagnetism (QHF) seen in ABA trilayer graphene (ABA-TLG). Due to high mobility $\sim$5…
We consider analytically current-driven dynamics of magnetic Néel walls in heavy metal/ferromagnetic metal/oxide trilayers where strong spin-orbit coupling and interfacial Dzyaloshinskii-Moriya interaction (i-DMI) coexist. We show that field-like spin-orbit torque (FL-SOT) with effective field along $\mathbf{n}\times\hat{\mathbf{J}}$ ($\mathbf{n}$ being the interface normal and $\hat{\mathbf{J}}$ being the charge current direction) and i-DMI induced torque can both lead to Walker breakdown suppression meanwhile leaving the wall mobility (velocity versus current density) unchanged. However, i-D…
We consider a microscopic theory of F/S/F trilayers with metallic or insulating ferromagnets. The trilayer with metallic ferromagnets is controlled by the formation of non local pair correlations among the two ferromagnets which do not exist with insulating ferromagnets. The difference between the insulating and ferromagnetic models can be understood from lowest order diagrams. Metallic ferromagnets are controlled by non local pair correlations and the superconducting gap is larger if the ferromagnetic electrodes have a parallel spin orientation. Insulating ferromagnets are controlled by pair …
We present a quantitative investigation of magnetic domain wall pinning in thin magnets with perpendicular anisotropy. A self-consistent description exploiting the universal features of the depinning and thermally activated sub-threshold creep regimes observed in the field driven domain wall velocity, is used to determine the effective pinning parameters controlling the domain wall dynamics: the effective height of pinning barriers, the depinning threshold, and the velocity at depinning. Within this framework, the analysis of results published in the literature allows for a quantitative compar…
We study the depinning of domain walls by pure diffusive spin currents in a nonlocal spin valve structure based on two ferromagnetic permalloy elements with copper as the nonmagnetic spin conduit. The injected spin current is absorbed by the second permalloy structure with a domain wall and from the dependence of the wall depinning field on the spin current density we find an efficiency of 6*10^{-14}T/(A/m^2), which is more than an order of magnitude larger than for conventional current induced domain wall motion. Theoretically we reproduce this high efficiency, which arises from the surface t…
A novel approach to tune the ferromagnetic resonance frequency of a soft magnetic Ni$_{80}$Fe$_{20}$ (Permalloy = Py) film with in-plane magnetic anisotropy (IMA) based on the controlled coupling to a hard magnetic NdCo$_\text{x}$ film with perpendicular magnetic anisotropy (PMA) through a non-magnetic Al spacer is studied. Using transverse magneto-optical Kerr effect (TMOKE), alternating gradient magnetometry (AGM) as well as vector network analyzer ferromagnetic resonance (VNA-FMR) spectroscopy, the influence of both Co concentration and Al spacer thickness on the static and dynamic magnetic…
The magnetic properties of thin-film Pd/Fe/Pd trilayers in which an embedded ~1.5 A-thick ultrathin layer of Fe induces ferromagnetism in the surrounding Pd have been investigated. The thickness of the ferromagnetic trilayer is controlled by varying the thickness of the top Pd layer over a range from 8 A to 56 A. As the thickness of the top Pd layer decreases, or equivalently as the embedded Fe layer moves closer to the top surface, the saturated magnetization normalized to area and the Curie temperature decrease whereas the coercivity increases. These thickness-dependent observations for prox…
We revisit the non-collinear exchange coupling across the trilayer magnetic junction mediated by the diluted-magnetic-semiconductor thin film. By numerical approaches, we investigate the spiral angle between the ferromagnetic layers extensively in the parameter space. In contrast to previous study, we discovered the important role of spin relaxation, which tends to favor spiral exchange over the oscillatory Ruderman-Kittel-Kasuya-Yosida interaction. Finally, we discuss the physics origins of these two types of magnetic interactions.
The pinning and depinning of antiferromagnetic (AFM) domain wall is certainly the core issue of AFM spintronics. In this work, we study theoretically the Néel-type domain wall pinning and depinning at a notch in an antiferromagnetic (AFM) nano-ribbon. The depinning field depending on the notch dimension and intrinsic physical parameters are deduced and also numerically calculated. Contrary to conventional conception, it is revealed that the depinning field is remarkably dependent of the damping constant and the time-dependent oscillation of the domain wall position in the weakly damping regime…
When two Landau levels are brought to a close coincidence between them and with the chemical potential in the Integer Quantum Hall regime, the two Landau levels can just cross or collapse while the external or pseudospin field that induces the alignment changes. In this work, all possible crossings are analyzed theoretically for the particular case of semiconductor trilayer systems, using a variational Hartree-Fock approximation. The model includes tunneling between neighboring layers, bias, intra-layer and inter-layer Coulomb interaction among the electrons. We have found that the general pse…
We present a detailed numerical simulation study of the effects caused by the magnetodipolar interaction between ferromagnetic (FM) layers of a trilayer magnetic nanoelement on its magnetization dynamics. As an example we use a Co/Cu/Ni80Fe20 element with a square lateral shape where the magnetization of FM layers forms a closed Landau-like domain pattern. First we show that when the thickness of the non-magnetic (NM) spacer is in the technology relevant region h ~ 10 nm, magnetodipolar interaction between 90o Neel domain walls in FM layers qualitatively changes the equilibrium magnetization s…
Josephson junctions containing ferromagnetic materials exhibit interesting physics and show promise as circuit elements for superconducting logic and memory. For memory applications, the properties of the junction should be controllable by changing the magnetic configuration inside the junction. To achieve good magnetic switching properties, one should choose a soft magnetic material such as NiFe (permalloy); however, NiFe exhibits poor supercurrent transmission in Josephson junctions. In this work we put thin layers of Ni on either side of the NiFe and characterize the magnetic behavior and s…
We investigate the non-collinear exchange coupling across the trilayer magnetic junction composed of an intermediate layer with Rashba interaction and two sandwiching ferromagnetic ones. To compute the mediated exchange coupling, one needs to go beyond the single-particle argument and integrate over the contributions from the whole Fermi surface. Surprisingly, we find that the topology of the Fermi surface plays a crucial role in determining whether the oscillatory RKKY or the spiral interactions would dominate. At the end, we discuss the connection of our numerical results to experiments and …
We report on the electrical transport properties of Nb based Josephson junctions with Pt/Co$_{68}$B$_{32}$/Pt ferromagnetic barriers. The barriers exhibit perpendicular magnetic anisotropy, which has the main advantage for potential applications over magnetisation in-plane systems of not affecting the Fraunhofer response of the junction. In addition, we report that there is no magnetic dead layer at the Pt/Co$_{68}$B$_{32}$ interfaces, allowing us to study barriers with ultra-thin Co$_{68}$B$_{32}$. In the junctions, we observe that the magnitude of the critical current oscillates with increas…
We demonstrate optical manipulation of the position of a domain wall in a dilute magnetic semiconductor, GaMnAsP. Two main contributions are identified. Firstly, photocarrier spin exerts a spin transfer torque on the magnetization via the exchange interaction. The direction of the domain wall motion can be controlled using the helicity of the laser. Secondly, the domain wall is attracted to the hot-spot generated by the focused laser. Unlike magnetic field driven domain wall depinning, these mechanisms directly drive domain wall motion, providing an optical tweezer like ability to position and…
Recent advances on the stabilization and manipulation of chiral magnetization configurations in systems consisting in alternating atomic layers of ferromagnetic and non-magnetic materials hold promise of innovation in spintronics technology. The low dimensionality of the systems promotes spin orbit driven interfacial effects like antisymmetric Dzyaloshinskii-Moriya interactions (DMI) and surface magnetic anisotropy, whose relative strengths may be tuned to achieve stable nanometer sized magnetic objects with fixed chirality. While in most of the cases this is obtained by engineering complex mu…
The vortex state, characterized by an in-plane closed flux domain structure and an out-of-plane magnetization at its centre (the vortex core), is one of the magnetic equilibria of thin soft ferromagnetic micron-size dots. In the last two decades many groups have been working on the dynamics of the magnetic moment in nanomagnetic materials at low temperatures, it giving rise to the observation of quantum relaxations and quantum hysteresis cycles. For the first time, we report experimental evidence of quantum dynamics of the vortex core of micron-size permalloy (Fe$_{19}$Ni$_{81}$) disks induced…
We investigate the proximity spin-orbit and exchange couplings in ABA and ABC trilayer graphene encapsulated within monolayers of semiconducting transition-metal dichalcogenides and the ferromagnetic semiconductor Cr$_2$Ge$_2$Te$_6$. Employing first-principles calculations we obtain the electronic structures of the multilayer stacks and extract the relevant proximity-induced orbital and spin interaction parameters by fitting the low-energy bands to model Hamiltonians. We also demonstrate the tunability of the proximity effects by a transverse electric field. Using the model Hamiltonians we als…
We investigate the influence of Meissner screening and trapped magnetic flux on magnetization dynamics for a Ni80Fe20 film sandwiched between two thick Nb layers (100 nm) using broadband (5-20 GHz) ferromagnetic resonance (FMR) spectroscopy. Below the superconducting transition Tc of Nb, significant zero-frequency line broadening (5-6 mT) and DC resonance field shift (50 mT) to a low field are both observed if the Nb thickness is comparable to the London penetration depth of Nb films (>= 100 nm). We attribute the observed peculiar behaviors to the increased incoherent precession near the Ni80F…
In magnetic trilayer systems, spin pumping is generally addressed as a reciprocal mechanism characterized by one unique spin mixing conductance common to both interfaces. However, this assumption is questionable in cases where different types of interfaces are present in the material. Here, we present a general theory for analyzing spin pumping in cases with more than one unique interface. The theory is applied to analyze layer-resolved ferromagnetic resonance experiments on the trilayer system Ni$_{20}$Fe$_{80}$/Ru/Fe$_{49}$Co$_{49}$V$_2$ where the Ru spacer thickness is varied to tune the in…
In magnetic trilayer structures, a contribution to the Gilbert damping of ferromagnetic resonance arises from spin currents pumped from one layer to another. This contribution has been demonstrated for layers with weakly coupled, separated resonances, where magnetization dynamics are excited predominantly in one layer and the other layer acts as a spin sink. Here we show that trilayer structures in which magnetizations are excited simultaneously, antisymmetrically, show a spin-pumping effect roughly twice as large. The antisymmetric (optical) mode of antiferromagnetically coupled Ni$_{79}$Fe$_…
Spin transport analysis for a spin pseudovalve-type L_l/SC/L_r trilayer for L = {FeCr, Fe, Co, NiFe, Ni} and SC = {GaSb, InSb, InAs, GaAs, ZnSe}
Instituto de Física La Plata IFLP-CONICET, CCT La Plata. Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata UNLP（拉普拉塔物理研究所 (IFLP-CONICET)、拉普拉塔中央科学技术区、拉普拉塔国立大学理学院）；Grupo de Ciencia y Tecnología de Materiales Cerámicos CYTEMAC, Departamento de Física, Facultad de Ciencias Naturales, Exactas y de la Educación, Universidad del Cauca UNICAUCA（考卡大学自然科学、精确与教育学院物理系陶瓷材料科学与技术小组）
We investigated the dependence of the seed [Ta/Pt, Ta/Au] and capping [Pt/Ta, Au/Ta] layers on spin pumping effect in the ferromagnetic 3 nm thick Co thin film using ferromagnetic resonance spectroscopy. The data is fitted with Kittel equation to evaluate damping constant and g-factor. A strong dependence of seed and capping layers on spin pumping has been discussed. The value of damping constant {alpha} is found to be relatively large i.e. 0.0326 for the Ta{3}/Pt{3}/Co{3}/Pt{3}/Ta{3} {nm} multi-layer structure, while it is 0.0104 for Ta{3}/Co{3}/Ta{3} {nm}. Increase in {alpha} is observed due…
Magnetic thin films at ferromagnetic resonance (FMR) leak angular momentum, which may be absorbed by adjacent layers. This phenomenon, known as spin pumping, is manifested by an increase in the resonance linewidth ($ΔH$), and the closely related Gilbert damping. Another effect of this transfer of spin currents is a dynamical and long-range coupling that can drive two magnetic layers into a collective precession when their FMR frequencies coincide. A collective behavior is also found in magnetic trilayers with interlayer exchange coupling (IEC). In this study we investigate the interplay betwee…
We demonstrate spin-valve magnetoresistance with a current-in-plane (CIP) configuration in (Ga,Fe)Sb / InAs (thickness $t_\mathrm{InAs}$ nm) / (Ga,Fe)Sb trilayer heterostructures, where (Ga,Fe)Sb is a ferromagnetic semiconductor (FMS) with high Curie temperature ($T_\mathrm{C}$). An MR curve with an open minor loop is clearly observed at 3.7 K in a sample with $t_\mathrm{InAs}$ = 3 nm, which originates from the parallel - antiparallel magnetization switching of the (Ga,Fe)Sb layers and spin-dependent scattering at the (Ga,Fe)Sb / InAs interfaces. The MR ratio increases (from 0.03 to 1.6%) with…
X ray resonant magnetic scattering (XRMS) was used to characterize the magnetization of 2D arrays of trilayer submicron magnets. The interpretation of the data required the understanding of the morphology of the magnets which was also deduced from the scattered intensity. The magnets consisted of two magnetostatically coupled ferromagnetic layers separated by a non-magnetic spacer. The scattered intensity from the disks resulted to be dependent on the disks surface curvature. This made the collected intensity at each Bragg reflection (BR) to be correlated to the reflected light from locations …
We use the high spatial sensitivity of the anomalous Hall effect in the ferromagnetic semiconductor Ga1-xMnxAs, combined with the magneto-optical Kerr effect, to probe the nanoscale elastic flexing behavior of a single magnetic domain wall in a ferromagnetic thin film. Our technique allows position sensitive characterization of the pinning site density, which we estimate to be around 10^14 cm^{-3}. Analysis of single site depinning events and their temperature dependence yields estimates of pinning site forces (10 pN range) as well as the thermal deactivation energy. Finally, our data hints at…
We report a comparative study of magnetic field driven domain wall motion in thin films made of different magnetic materials for a wide range of field and temperature. The full thermally activated creep motion, observed below the depinning threshold, is shown to be described by a unique universal energy barrier function. Our findings should be relevant for other systems whose dynamics can be modeled by elastic interfaces moving on disordered energy landscapes.
A nonlinear magnetoresistance - called unidirectional spin-Hall magnetoresistance - is recently experimentally discovered in metallic bilayers consisting of a heavy metal and a ferromagnetic metal. To study the fundamental mechanism of the USMR, both ferromagnetic and heavy metallic layer thickness dependence of the USMR are presented in a Pt/Co/AlOx trilayer at room temperature. To avoid ambiguities, second harmonic Hall measurements are used for separating spin-Hall and thermal contributions to the non-linear magnetoresistance. The experimental results are fitted by using a drift-diffusion t…
We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or "magnetization noise", in an archetypal ferromagnetic film that can be smoothly tuned through a spin reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin Pt/Co/Pt trilayer, from the perpendicular to in-plane direction, via graded Ar$^+$ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise, $S(ν)$, exhibits a remarkably robust $ν^{-3/2}$ power law over freq…
We describe a theory of Mn local-moment magnetization relaxation due to p-d kinetic-exchange coupling with the itinerant-spin subsystem in the ferromagnetic semiconductor (Ga,Mn)As alloy. The theoretical Gilbert damping coefficient implied by this mechanism is calculated as a function of Mn moment density, hole concentration, and quasiparticle lifetime. Comparison with experimental ferromagnetic resonance data suggests that in annealed strongly metallic samples, p-d coupling contributes significantly to the damping rate of the magnetization precession at low temperatures. By combining the theo…
We develop theory of proximity effect in a superconductor - GMR alloy - superconductor trilayers, which takes into account strong spin dependence of electron scattering of compositional disorder in a diluted ferromagnetic alloy. We show that in such a system the critical current oscillations as the function of the thickness of the ferromagnetic layer, with the period of $v_{F}/2I$, decay exponentially with the characteristic length of the order of the mean free path.
We have studied the effect of He$^+$ irradiation on the dynamics of chiral domain walls in Pt/Co/AlOx trilayers in the creep regime. The irradiation leads to a strong decrease of the depinning field and a non-monotonous change of the effective pinning barriers. The variations of domain wall dynamics result essentially from the strong decrease of the effective anisotropy constant, which increases the domain wall width. The latter is found to present a perfect scaling with the length-scale of the interaction between domain wall and disorder, $ξ$. On the other hand, the strength of the domain wal…
We consider a Josephson junction with ${\rm F_1 F_2 F_3}$ ferromagnetic trilayers in the ballistic regime, where the magnetization in each ferromagnet ${\rm F}_i (i=1,2,3)$, can have arbitrary orientations and magnetization strengths. The trilayers are sandwiched between two $s$-wave superconductors with a macroscopic phase difference $Δφ$. A broad range of magnetization strengths of the central $\rm F_2$ layer are considered, from an unpolarized normal metal (N) to a half-metallic phase, supporting only one spin species. Our results reveal that when the magnetization configuration in ${\rm F_…
We theoretically study the magnetization inside a normal metal induced in an s-wave superconductor/ferromagnetic metal/normal metal/ferromagnetic metal/s-wave superconductor (S/F1/N/F2/S) Josephson junction. Using quasiclassical Green's function method, we show that the magnetization becomes finite inside N. The origin of this magnetization is due to odd-frequency spin-triplet Cooper pairs formed by electrons of equal and opposite spins, which are induced by proximity effect in the S/F1/N/F2/S junction. We find that the magnetization M(d,q) in N can be decomposed into two parts, M(d,q)=MI(d)+M…
