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We report the dynamic characterization of the spin-torque-driven in-plane precession modes of a spin-torque nano-oscillator based on two different synthetic ferrimagnets: a pinned one characterized by a strong RKKY interaction which is exchange coupled to an antiferromagnetic layer; and a second one, non-pinned characterized by weak RKKY coupling. The microwave properties associated with the steady-state precession of both SyFs are characterized by high spectral purity and power spectral density. However, frequency dispersion diagrams of the damped and spin transfer torque modes reveal drastically different dynamical behavior and microwave emission properties in both SyFs. In particular, the weak coupling between the magnetic layers of the non-pinned SyF raises discontinuous dispersion diagrams suggesting a strong influence of mode crossing. An interpretation of the different dynamical features observed in the damped and spin torque modes of both SyF systems was obtained by solving simultaneously, in a macrospin approach, a linearized version of the Landau-Lifshitz-Gilbert equation including the spin transfer torque term., Comment: 16 pages, 8 figures

We investigate the dynamics of an injection locked in-plane uniform spin torque oscillator for several forcing configurations at large driving amplitudes. For the analysis, the spin wave amplitude equation is used to reduce the dynamics to a general oscillator equation in which the forcing is a complex valued function $F(p,{\psi})\propto{\epsilon}_1 (p)cos({\psi})+i{\epsilon}_2 (p)sin({\psi})$. Assuming that the oscillator is strongly nonisochronous and/or forced by a power forcing $(|{\nu}{\epsilon}_1/{\epsilon}_2 |\gg 1)$, we show that the parameters ${\epsilon}_{1,2} (p)$ govern the main bifurcation features of the Arnold tongue diagram : (i) the locking range asymmetry is mainly controlled by $d{\epsilon}_1 (p)/dp$, (ii) the Taken-Bogdanov bifurcation occurs for a power threshold depending on ${\epsilon}_{1,2} (p)$ and (iii) the frequency hysteretic range is related to the transient regime through the resonant frequency at zero mismatch frequency. Then, the model is compared with the macrospin simulation for driving amplitudes as large as $10^0-10^3 A/m$ for the magnetic field and $10^{10}-10^{12} A/m^2$ for the current density. As predicted by the model, the forcing configuration (nature of the driving signal, applied direction, the harmonic orders) affects substantially the oscillator dynamic. However, some discrepancies are observed. In particular, the prediction of the frequency and power locking range boundaries may be misestimated if the hysteretic boundaries are of same magnitude order. Moreover, the misestimation can be of two different types according if the bifurcation is Saddle node or Taken Bogdanov. These effects are a further manifestation of the complexity of the dynamics in nonisochronous auto-oscillators., Comment: 15 pages, 11 figures

In antiferromagnets, the efficient propagation of spin-waves has until now only been observed in the insulating antiferromagnet hematite, where circularly (or a superposition of pairs of linearly) polarized spin-waves propagate over long distances. Here, we report long-distance spin-transport in the antiferromagnetic orthoferrite YFeO$_3$, where a different transport mechanism is enabled by the combined presence of the Dzyaloshinskii-Moriya interaction and externally applied fields. The magnon decay length is shown to exceed hundreds of nano-meters, in line with resonance measurements that highlight the low magnetic damping. We observe a strong anisotropy in the magnon decay lengths that we can attribute to the role of the magnon group velocity in the propagation of spin-waves in antiferromagnets. This unique mode of transport identified in YFeO$_3$ opens up the possibility of a large and technologically relevant class of materials, i.e., canted antiferromagnets, for long-distance spin transport., Comment: Manuscript - 24 pages and 4 figures, Supplementary - 22 pages and 10 figures

Spintronic rf detectors were demonstrated, recently, for energy harvesting and wireless communication at low input power. Here we report on the optimization of the rectified output dc voltage using magnetic tunnel junctions (MTJ) with strong perpendicular anisotropy (PMA) of both the polarizing and the free layer. The magnetization of the polarizing layer is fixed out of plane, while the free layer thickness is adjusted so that its magnetization orientation changes from in plane to out of plane. The rectification dc output voltage lies in the mV range for moderate rf powers, with a signal to noise ratio of 10 to 100 for Prf = -25dBm. It shows a strong dependence on the dimensions of the MTJ: it increases by a factor of 5 to 6 when reducing the diameter from 150nm to 20nm. This enhancement can be doubled when reducing the FL thickness from 1.8nm to 1.6nm. This dimensional enhancement is attributed to the change of the effective anisotropy of the excited free layer, and the MTJ resistance. The results are of interest for the design of spintronic based rf detectors with optimized sensitivity.

An array of spin torque nano-oscillators (STNOs), coupled by dipolar interaction and arranged on a ring, has been studied numerically and analytically. The phase patterns and locking ranges are extracted as a function of the number $N$, their separation, and the current density mismatch between selected subgroups of STNOs. If $N\geq 6$ for identical current densities through all STNOs, two degenerated modes are identified an in-phase mode (all STNOs have the same phase) and an out-of-phase mode (the phase makes a 2$\pi$ turn along the ring). When inducing a current density mismatch between two subgroups, additional phase shifts occur. The locking range (maximum current density mismatch) of the in-phase mode is larger than the one for the out-of-phase mode and depends on the number $N$ of STNOs on the ring as well as on the separation. These results can be used for the development of magnetic devices that are based on STNO arrays.

It is demonstrated experimentally that a spin-torque nano-oscillator (STNO) rapidly sweep-tuned by a bias voltage can be used for time-resolved spectrum analysis of frequency-manipulated microwave signals with complicated multi-tone spectra. The critical reduction in the time of spectrum analysis comes from the naturally small time constants of a nano-sized STNO (1-100 ns). The demonstration is performed on a vortex-state STNO generating in a frequency range around 300 MHz, with frequency down-conversion and matched filtering used for signal processing. It is shown that this STNO-based spectrum analyzer can perform analysis of multi-tone signals, and signals with rapidly changing frequency components with time resolution on a $\mu$s time scale and frequency resolution limited only by the 'bandwidth' theorem. The proposed concept of rapid time-resolved spectrum analysis can be implemented with any type of micro and nano-scale frequency-swept oscillators having low time constants and high oscillation frequency.

Spin torque nano-oscillators (STNO) are nanoscale devices with wide band frequency tunability. Their multifunctional RF properties are well suited to define novel schemes for wireless communications that use basic protocols for data transmission such as amplitude, frequency and phase shift keying (ASK, FSK, PSK). In contrast to ASK and FSK, implementation of PSK is more challenging for STNOs because of their relatively high phase noise. Here we introduce a special PSK technique by combining their modulation and injection locking functionality. The concept is validated using magnetic tunnel junction based vortex STNOs for injection locking at 2f and f/2 showing phase shifts up to 2.1rad and data transmission rates up to 4Mbit/s. Quadrature phase shift keying and analog phase modulation are also implemented, where the latter is employed for voice transmission over a distance of 10 meters. This demonstrates that STNO phase noise and output power meet the requested performances for operation in existing communication schemes., Comment: to be submitted

In the field of spintronics, ferromagnetic/non-magnetic metallic multilayers are core building blocks for emerging technologies. Resonance experiments using stripline transducers are commonly used to characterize and engineer these stacks for applications. Up to now in these experiments, the influence of eddy currents on the excitation of the dynamics of ferromagnetic magnetization below the skin-depth limit was most often neglected. Here, using a coplanar stripline transducer, we experimentally investigated the broadband ferromagnetic resonance response of NiFe/Cu bilayers a few nanometers thick in the sub-skin-depth regime. Asymmetry in the absorption spectrum gradually built up as the excitation frequency and Cu-layer thickness increased. Most significantly, the sign of the asymmetry depended on the stacking order. Experimental data were consistent with a quantitative analysis considering eddy currents generated in the Cu layers and the subsequent phaseshift of the feedback magnetic field generated by the eddy currents. These results extend our understanding of the impact of eddy currents below the microwave magnetic skin-depth and explain the lineshape asymmetry and phase lags reported in stripline experiments.

Spin torque nano-oscillators are nanoscopic microwave frequency generators which excel due to their large frequency tuning range and agility for amplitude and frequency modulation. Due to their compactness, they are regarded as suitable candidates for applications in wireless communications, where cost-effective and CMOS-compatible standalone devices are required. In this work, we study the ability of a magnetic-tunnel-junction (MTJ) based spin torque nano-oscillator to respond to a binary input sequence encoded in a square-shaped current pulse for its application as a frequency-shift-keying (FSK) based emitter. We demonstrate that below the limit imposed by the spin torque nano-oscillators intrinsic relaxation frequency, an agile variation between discrete oscillator states is possible. For this kind of devices, we demonstrate FSK up to data rates of 400 Mbps which is well suited for the application of such scillators in wireless networks.

Experiments, numerical simulations and an analytic model were developed to elucidate the effects of noise in the synchronized state of a tunnel junction based spin torque nano oscillator (STNO). It is demonstrated that in the in plane magnetized structure, while the frequency is locked, much higher reference currents are needed to reduce the noise by phase locking. Our analysis shows that it is possible to control the phase noise by the reference microwave current (IRF) and that it can be further reduced by increasing the bias current (IDC) of the oscillator, keeping the reference current in feasible limits for applications.

The influence of dynamic interlayer interactions on the spin torque driven and damped excitations are illustrated for a three layer macrospin model system that corresponds to a standard spin-torque oscillator. The free layer and a synthetic antiferromagnetic (SyF) pinned layer of the spin-torque oscillator are in-plane magnetized. In order to understand experimental results, numerical simulations have been performed considering three types of interlayer interactions: exchange interaction between the two magnetic layers of the SyF, mutual spin torque between the top layer of the SyF and the free layer and dipolar interaction between all three magnetic layers. It will be shown that the dynamic dipolar coupling plays a predominant role. First, it leads to a hybridization of the free layer and the SyF linear modes and through this gives rise to a strong field dependence of the critical current. In particular, there is a field range of enhanced damping in which much higher current is required to drive the modes into steady state. This results in a gap in the excitation spectrum. Second, the dynamic dipolar interaction is also responsible for the non-linear interaction between the current driven steady state mode and the damped modes of the system. Here one can distinguish: (i) a resonant interaction that leads to a kink in the frequency-field and frequency-current dispersions accompanied by a small hysteresis and a reduction of the linewidth of the steady state mode and (ii) a non-resonant interaction that leads to a strong frequency redshift of the damped mode. The results underline the strong impact of interlayer coupling on the excitation spectra of spin-torque oscillators and illustrate in a simple three mode model system how in the non-linear regime the steady state and damped modes influence each other.

We report on the excitation and detection of short-waved spin waves with wave vectors up to about $40\,\mathrm{rad}\,\mu\mathrm{m}^{-1}$ in spin-wave waveguides made from ultrathin, in-plane magnetized Co$_{8}$Fe$_{72}$B$_{20}$ (CoFeB). The CoFeB is incorporated in a layer stack of Ta/CoFeB/Mgo, a layer system featuring large spin orbit torques and a large perpendicular magnetic anisotropy constant. The short-waved spin waves are excited by nanometric coplanar waveguides and are detected via spin rectification and microfocussed Brillouin light scattering spectroscopy. We show that the large perpendicular magnetic anisotropy benefits the spin-wave lifetime greatly, resulting in a lifetime comparable to bulk systems without interfacial damping. The presented results pave the way for the successful extension of magnonics to ultrathin asymmetric layer stacks featuring large spin orbit torques.

We investigate how the ability of the vortex oscillation mode of a spin-torque nano-oscillator to lock to an external microwave signal is modified when it is coupled to another oscillator. We show experimentally that mutual electrical coupling can lead to locking range enhancements of a factor 1.64. Furthermore, we analyze the evolution of the locking range as a function of the coupling strength through experiments and numerical simulations. By uncovering the mechanisms at stake in the locking range enhancement, our results will be useful for designing spin-torque nano-oscillators arrays with high sensitivities to external microwave stimuli.

In this manuscript the general concepts of spin wave theory are adapted to the dynamics of a self-polarized system based on two layers coupled via interlayer exchange (conservative coupling) and mutual spin torque (dissipative coupling). An analytical description of the non-linear dynamics is proposed and validated through numerical simulations. In contrast to the single layer model, the phase equation of the coupled system has a contribution coming from the dissipative part of the LLGS equation. It is shown that this is a major contribution to the frequency mandatory to describe well the most basic features of the dynamics of coupled systems. Using the proposed model a specific feature of coupled dynamics is addressed: the redshift to blueshift transition observed in the frequency current dependence of this kind of exchange coupled systems upon increasing the applied field. It is found that the blueshift regime can only occur in a region of field where the two linear eigenmodes contribute equally to the steady state mode (i.e. high mode hybridization). Finally, a general perturbed Hamiltonian equation for the coupled system is proposed., Comment: 16 pages, 7 figues

We study in-plane magnetic tunnel junctions with additional perpendicular polarizer for subnanosecond-current-induced switching memories. The spin-transfer-torque switching dynamics was studied as a function of the cell aspect ratio both experimentally and by numerical simulations using the macrospin model. We show that the anisotropy field plays a significant role in the dynamics, along with the relative amplitude of the two spin-torque contributions. This was confirmed by micromagnetic simulations. Real-time measurements of the reversal were performed with samples of low and high aspect ratio. For low aspect ratios, a precessional motion of the magnetization was observed and the effect of temperature on the precession coherence was studied. For high aspect ratios, we observed magnetization reversals in less than 1 ns for high enough current densities, the final state being controlled by the current direction in the magnetic tunnel junction cell., Comment: 6 pages, 7 figures

We investigated the spin pumping damping contributed by paramagnetic layers (Pd, Pt) in both direct and indirect contact with ferromagnetic Ni$_{81}$Fe$_{19}$ films. We find a nearly linear dependence of the interface-related Gilbert damping enhancement $\Delta\alpha$ on the heavy-metal spin-sink layer thicknesses t$_\textrm{N}$ in direct-contact Ni$_{81}$Fe$_{19}$/(Pd, Pt) junctions, whereas an exponential dependence is observed when Ni$_{81}$Fe$_{19}$ and (Pd, Pt) are separated by \unit[3]{nm} Cu. We attribute the quasi-linear thickness dependence to the presence of induced moments in Pt, Pd near the interface with Ni$_{81}$Fe$_{19}$, quantified using X-ray magnetic circular dichroism (XMCD) measurements. Our results show that the scattering of pure spin current is configuration-dependent in these systems and cannot be described by a single characteristic length.

We report on room temperature magnetoresistance and low frequency noise in sub-100nm elliptic CoFeB/MgO/CoFeB magnetic tunnel junctions with ultrathin (0.9nm) barriers. For magnetic fields applied along the hard axis, we observe current induced magnetization switching between the antiparallel and parallel alignments at DC current densities as low as 4*106A/cm2. We attribute the low value of the critical current to the influence of localized reductions in the tunnel barrier, which affects the current distribution. The analysis of random telegraph noise, which appears in the field interval near a magnetization switch, provides an estimate to the dimension of the pseudo pinholes that trigger the magnetization switching via local spin torque. Micromagnetic simulations qualitatively and quantitatively reproduce the main experimental observations.

We show that very large paramagnetic moments are created in ultrathin Pd layers through indirect interlayer exchange coupling. Pd $L$-edge x-ray magnetic circular dichroism measurements show Pd moments in [Pd(2.5nm)/Cu(3nm)/Ni$_{81}$Fe$_{19}$(5nm)/Cu(3nm)]$_{20}$ superlattices which are ferromagnetically aligned with the applied field and nearly 3% the size of Pd moments created in directly exchange coupled [Pd(2.5nm)/Ni$_{81}$Fe$_{19}$(5nm)]$_{20}$ superlattices. The induced moment is two orders of magnitude larger than that expected from RKKY exchange acting on the bulk paramagnetic susceptibility of Pd., Comment: 5 pages, 3 figures, to appear in Phys. Rev. B

Spin transfer driven excitations in magnetic nanostructures are characterized by a relatively large microwave emission linewidth (10 -100 MHz). Here we investigate the role of thermal fluctuations as well as of the non-linear amplitude-phase coupling parameter and the amplitude relaxation rate to explain the linewidth broadening of in-plane precession modes induced in planar nanostructures. Experiments on the linewidth broadening performed on MgO based magnetic tunnel junctions are compared to the linewidth obtained from macrospin simulations and from evaluation of the phase variance. In all cases we find that the linewidth varies linearly with temperature when the amplitude relaxation rate is of the same order as the linewidth and when the amplitude-phase coupling parameter is relatively small. The small amplitude-phase coupling parameter means that the linewidth is dominated by direct phase fluctuations and not by amplitude fluctuations, explaining thus its linear dependence as a function of temperature.

We have measured the size effect in nonlocal Gilbert relaxation rate in FM(t$_{FM}$) / Cu (5nm) [/ Pt (2nm)] / Al(2nm) heterostructures, FM = \{ Ni$_{81}$Fe$_{19}$, Co$_{60}$Fe$_{20}$B$_{20}$, pure Co\}. Common behavior is observed for three FM layers, where the additional relaxation obeys both a strict inverse power law dependence $\Delta G =K \:t^{n}$, $n=-\textrm{1.04}\pm\textrm{0.06}$ and a similar magnitude $K=\textrm{224}\pm\textrm{40 Mhz}\cdot\textrm{nm}$. As the tested FM layers span an order of magnitude in spin diffusion length $\lambda_{SDL}$, the results are in support of spin diffusion, rather than nonlocal resistivity, as the origin of the effect.