Search

Synthetic antiferromagnets host spin waves that are highly tunable. It is of practical interest to analyze the symmetry of their coupling to surface acoustic waves with the design of hybrid devices in view. For this we calculate the layer-resolved susceptibility tensor of a synthetic antiferromagnet, the effective magneto-elastic and magneto-rotation fields associated to a travelling elastic wave, and the power irreversibly transferred by the elastic wave to the magnetic layers. We consider Rayleigh-type surface acoustic waves: (a) that travel in an elastically isotropic, non-piezoelectric substrate, or (b) that propagate along the X direction at the surface of a Z-cut LiNbO$_3$ substrate, or (c) that are guided in a thin Z-cut LiNbO$_3$ film grown on a sapphire substrate. In particular, we show that the complementary angular dependencies of the acoustic and optical spin wave modes in synthetic antiferromagnets makes it possible to excite spin waves for any relative orientation of magnetization and acoustic wavevector. In addition, we discuss the symmetries of the driving fields and of the energy transferred to the magnetic degree of freedom. We evidence new interaction channels coupling the magnetization eigenmodes when elastic anisotropy and piezoelectricity of the substrate are considered.

We study the frequency non-reciprocity of the spin waves in symmetric CoFeB/Ru/CoFeB synthetic antiferromagnets stacks set in the scissors state by in-plane applied fields. Using a combination of Brillouin Light Scattering and propagating spin wave spectroscopy experiments, we show that the acoustical spin waves in synthetic antiferromagnets possess a unique feature if their wavevector is parallel to the applied field: the frequency non-reciprocity due to layer-to-layer dipolar interactions can be so large that the acoustical spin waves transfer energy in a unidirectional manner for a wide and bipolar interval of wavevectors. Analytical modeling and full micromagnetic calculations are conducted to account for the dispersion relations of the optical and acoustical spin waves for arbitrary field orientations. Our formalism provides a simple and direct method to understand and design devices harnessing unidirectional propagation of spin waves in synthetic antiferromagnets.

The interlayer exchange coupling confers specific properties to Synthetic Antiferromagnets that make them suitable for several applications of spintronics. The efficient use of this magnetic configuration requires an in-depth understanding of the magnetic properties and their correlation with the material structure. Here we establish a reliable procedure to quantify the interlayer exchange coupling and the intralayer exchange stiffness in synthetic antiferromagnets; we apply it to the ultrasmooth and amorphous Co$_{40}$Fe$_{40}$B$_{20}$ (5-40 nm)/Ru/ Co$_{40}$Fe$_{40}$B$_{20}$ material platform. The complex interplay between the two exchange interactions results in a gradient of the magnetization orientation across the thickness of the stack which alters the hysteresis and the spin wave eigenmodes of the stack in a non trivial way. We measured the field-dependence of the frequencies of the first four spin waves confined within the thickness of the stack. We modeled these frequencies and the corresponding thickness profiles of these spin waves using micromagnetic simulations. The comparison with the experimental results allows to deduce the magnetic parameters that best account for the sample behavior. The exchange stiffness is established to be 16 $\pm$ 2 pJ/m, independently of the Co$_{40}$Fe$_{40}$B$_{20}$ thickness. The interlayer exchange coupling starts from -1.7 mJ/m$^2$ for the thinnest layers and it can be maintained above -1.3 mJ/m$^2$ for CoFeB layers as thick as 40 nm. The comparison of our method with earlier characterizations using the sole saturation fields argues for a need to revisit the tabulated values of interlayer exchange coupling in thick synthetic antiferromagnets.

We study how a population of spin waves can be characterized from the analysis of the electrical microwave noise delivered by an inductive antenna placed in its vicinity. The measurements are conducted on a synthetic antiferromagnetic thin stripe covered by a micron-sized antenna that feeds a spectrum analyser after amplification. The antenna noise contains two contributions. The population of incoherent spin waves generates a fluctuating field that is sensed by the antenna: this is the "magnon noise". The antenna noise also contains the contribution of the electronic fluctuations: the Johnson-Nyquist noise. The latter depends on all impedances within the measurement circuit, which includes the antenna self-inductance. As a result, the electronic noise contains information about the magnetic susceptibility of the stripe, though it does not inform on the absolute amplitude of the magnetic fluctuations. For micrometer-sized systems at thermal equilibrium, the electronic noise dominates and the pure magnon noise cannot be determined. If in contrast the spinwave bath is not at thermal equilibrium with the measurement circuit, and if the spin wave population can be changed then one could measure a mode-resolved effective magnon temperature provided specific precautions are implemented., Comment: to appear in Phys. Rev. B. The authors acknowledge financial support from the French National Research Agency (ANR) under Contract No. ANR-20-CE24-0025 (MAXSAW). M.S.N. and J.L. acknowledge in addition the FETOPEN-01-2016-2017 [FET-Open research and innovation actions (CHIRON project: Grant Agreement ID: 801055)]

We develop a generic all-inductive procedure to measure the band structure of spin waves in a magnetic thin stripe. In contrast to existing techniques, our method works even if several spin wave branches coexist in the investigated frequency interval, provided that the branches possess sufficiently different group velocities. We first measure the microwave scattering matrix of a network composed of distant antennas inductively coupled to the spin wave bath of the magnetic film. After a mathematical transformation to the time-domain to get the transmission impulse response, the different spin wave branches are viewed as wavepackets that reach successively the receiving antenna after different travel times. In analogy with time-of flight spectroscopy, the wavepackets are then separated by time-gating. The time-gated responses are used to recalculate the contribution of each spin wave branch to the frequency domain scattering matrix. The dispersion relation of each branch stems from the absolute phase of the time-gated transmission parameter. The spin wave wavevector can be determined unambiguously if the results for several propagation distances are combined, so as to get the dispersion relations., Comment: Submitted to the PRB. This work was funded through the FETOPEN-01-2016-2017-FET-Open research and innovation actions (CHIRON project: Grant Agreement No. 801055) and was partly supported by the French RENATECH network. This work is also supported by a public grant overseen by ANR as part of the "Investissements d'avenir" program (Labex NanoSaclay, reference: ANR-10-LABX-0035)

We present an experimental study of spin-torque driven vortex self-oscillations in magnetic nanocontacts. We find that above a certain threshold in applied currents, the vortex gyration around the nanocontact is modulated by relaxation oscillations, which involve periodic reversals of the vortex core. This modulation leads to the appearance of commensurate but also more interestingly here, incommensurate states, which are characterized by devil's staircases in the modulation frequency. We use frequency- and time-domain measurements together with advanced time-series analyses to provide experimental evidence of chaos in incommensurate states of vortex oscillations, in agreement with theoretical predictions., Comment: 5 pages, 4 figures

Spin transfer torque magnetic random access memory (STT-MRAM) is considered as one of the most promising candidates to build up a true universal memory thanks to its fast write/read speed, infinite endurance and non-volatility. However the conventional access architecture based on 1 transistor + 1 memory cell limits its storage density as the selection transistor should be large enough to ensure the write current higher than the critical current for the STT operation. This paper describes a design of cross-point architecture for STT-MRAM. The mean area per word corresponds to only two transistors, which are shared by a number of bits (e.g. 64). This leads to significant improvement of data density (e.g. 1.75 F2/bit). Special techniques are also presented to address the sneak currents and low speed issues of conventional cross-point architecture, which are difficult to surmount and few efficient design solutions have been reported in the literature. By using a STT-MRAM SPICE model including precise experimental parameters and STMicroelectronics 65 nm technology, some chip characteristic results such as cell area, data access speed and power have been calculated or simulated to demonstrate the expected performances of this new memory architecture.

Power dissipation is one of the most important factors limiting the future miniaturisation of integrated circuits. The capability of controlling magnetic states with a low voltage through magnetoelectric coupling in magnetostrictive/piezoelectric systems may pave the way toward ultra low-power electronics. Although the former effect has been demon-strated in several multiferroic heterostructures, the incorporation of such complex geometries into practical magnetic memory and logic nanodevices has been lacking. Here, we demonstrate the room temperature control of a domain wall gate with an electric field in a nanowire consisting of a laterally polarized piezoelectric bar inducing a giant strain in a ferromagnetic spin-valve. We propose to use such novel domain wall gate as an elementary brick to generate a complete set of boolean logic functions or stabilize domain walls in high density memory applications., Comment: 16 pages, 4 figures

Vortex-based spin-torque oscillators can be made from extended spin valves connected to an electrical nanocontact. We study the implementation of frequency shift keying modulation in these oscillators. Upon a square modulation of the current in the 10 MHz range, the vortex frequency follows the current command, with easy identification of the two swapping frequencies in the spectral measurements. The frequency distribution of the output power can be accounted for by convolution transformations of the dc current vortex waveform, and the current modulation. Modeling indicates that the frequency transitions are phase coherent and last less than 25 ns. Complementing the multi-octave tunability and first-class agility, the capability of frequency shift keying modulation is an additional milestone for the implementation of vortex-based oscillators in RF circuit., Comment: 6 pages, 5 figures

We study spin-torque induced oscillations of MgO magnetic tunnel junctions in the time domain. By using the Hilbert transform on the time traces, we obtain for the first time a direct experimental measure of the coupling between the power and the phase fluctuations. We deduce the power restoration rate and we obtain low values for the coupling strength, which is consistent with the weak frequency dependence on the applied voltage., Comment: 3 pages, 3 figures

We study the agility of current-tunable oscillators based on a magnetic vortex orbiting around a point contact in spin-valves. Theory predicts frequency-tuning by currents occurs at constant orbital radius, so an exceptional agility is anticipated. To test this, we have inserted an oscillator in a microwave interferometer to apply abrupt current variations while time resolving its emission. Using frequency shift keying, we show that the oscillator can switch between two stabilized frequencies differing by 25% in less than ten periods. With a wide frequency tunability and a good agility, such oscillators possess desirable figures of merit for modulation-based rf applications., Comment: 3 pages, 3 figures

We present an experimental and theoretical study of the magnetic field dependence of the mode frequency of thermally excited spin waves in rectangular shaped nanopillars of lateral sizes 60x100, 75x150, and 105x190 nm2, patterned from MgO-based magnetic tunnel junctions. The spin wave frequencies were measured using spectrally resolved electrical noise measurements. In all spectra, several independent quantized spin wave modes have been observed and could be identified as eigenexcitations of the free layer and of the synthetic antiferromagnet of the junction. Using a theoretical approach based on the diagonalization of the dynamical matrix of a system of three coupled, spatially confined magnetic layers, we have modeled the spectra for the smallest pillar and have extracted its material parameters. The magnetization and exchange stiffness constant of the CoFeB free layer are thereby found to be substantially reduced compared to the corresponding thin film values. Moreover, we could infer that the pinning of the magnetization at the lateral boundaries must be weak. Finally, the interlayer dipolar coupling between the free layer and the synthetic antiferromagnet causes mode anticrossings with gap openings up to 2 GHz. At low fields and in the larger pillars, there is clear evidence for strong non-uniformities of the layer magnetizations. In particular, at zero field the lowest mode is not the fundamental mode, but a mode most likely localized near the layer edges., Comment: 16 pages, 4 figures, (re)submitted to PRB

We present an experimental and theoretical study of the low-field dynamics of current-driven vortex oscillations in nanocontacts based on spin-valve multilayers. These oscillations appear as low-frequency (250-500 MHz) excitations in the electrical power spectrum which arise from to variations in the giant-magnetoresistance. We show that the vortex oscillations, once nucleated at large fields applied perpendicular to the film plane, persist at zero applied magnetic fields. Some training effects on the oscillation frequency and linewidth also observed for small in-plane magnetic fields., Comment: 6 pages, 7 figures

We present an experimental study of the power spectrum of current-driven magnetization oscillations in MgO tunnel junctions under low bias. We find the existence of narrow spectral lines, down to 8 MHz in width at a frequency of 10.7 GHz, for small applied fields with clear evidence of an auto-oscillation threshold. Micromagnetics simulations indicate that the excited mode corresponds to an edge mode of the synthetic antiferromagnet.

We demonstrate spin torque induced auto-oscillation in MgO-based magnetic tunnel junctions. At the generation threshold, we observe a strong line narrowing down to 6 MHz at 300K and a dramatic increase in oscillator power, yielding spectrally pure oscillations free of flicker noise. Setting the synthetic antiferromagnet into autooscillation requires the same current polarity as the one needed to switch the free layer magnetization. The induced auto-oscillations are observed even at zero applied field, which is believed to be the acoustic mode of the synthetic antiferromagnet. While the phase coherence of the auto-oscillation is of the order of microseconds, the power autocorrelation time is of the order of milliseconds and can be strongly influenced by the free layer dynamics.

We present experimental evidence of sub-GHz spin-transfer oscillations in metallic nano-contacts that are due to the translational motion of a magnetic vortex. The vortex is shown to execute large-amplitude orbital motion outside the contact region. Good agreement with analytical theory and micromagnetics simulations is found., Comment: 4 pages, 3 figures

The lineshape in an auto-oscillator with a large nonlinear frequency shift in the presence of thermal noise is calculated. Near the generation threshold, this lineshape becomes strongly non-Lorentzian, broadened, and asymmetric. A Lorentzian lineshape is recovered far below and far above threshold, which suggests that lineshape distortions provide a signature of the generation threshold. The theory developed adequately describes the observed behavior of a strongly nonlinear spin-torque nano-oscillator., Comment: 4 pages, 3 figures

We analyze the statistical distribution of switching durations in spin-transfer switching induced by current steps, and discuss biasing strategies to enhance the reproducibility of switching durations. We use a macrospin approximation and model the effect of finite temperature as a Boltzmann distribution of initial magnetization states (adiabatic limit). We compare three model spin-valves: a spin-valve with a free layer whose easy axis is parallel to the pinned layer magnetization (standard geometry), a pinned layer with magnetization tilted with respect to the free layer easy axis (pinned layer biasing), and a free layer whose magnetization is pulled away from easy axis by a hard axis bias (free layer biasing). In the conventional geometry, the switching durations follow a broad regular distribution, with an extended long tail comprising very long switching events. For the two biasing strategies, the switching durations follow a multiply-stepped distribution, reflecting the precessional nature of the switching, and the statistical number of precession cycles needed for reversal. We derive analytical criteria to avoid switching events lasting much longer than the average switching duration, in order to achieve the highest reproducibilities. Depending on the current amplitude and the biasing strength, the width of the switching time distribution can be substantially reduced, the best reproducibility being achieved for free layer biasing at overdrive current of a few times unity., Comment: submitted to Phys Rev. B

We study the distribution of switching times in spin-transfer switching induced by sub-ns current pulses in pillar-shaped spin-valves. The pulse durations leading to switching follow a comb-like distribution, multiply-peaked at a few most probable, regularly spaced switching durations. These durations reflect the precessional nature of the switching, which occurs through a fluctuating integer number of precession cycles. This can be modeled considering the thermal variance of the initial magnetization orientations and the occurrence of vanishing total torque in the possible magnetization trajectories. Biasing the spin-valve with a hard axis field prevents some of these occurrences, and can provide an almost perfect reproducibility of the switching duration., Comment: submitted to PRB

We study the current and temperature dependences of the microwave voltage emission of spin-valve nanopillars subjected to an in-plane magnetic field and a perpendicular-to-plane current. Despite the complex multilayer geometry, clear microwave emission is shown to be possible and spectral lines as narrow as 3.8 MHz (at 150 K) are observed., Comment: To appear in Applied Physics Letters

We study analytically the precessional switching of the magnetization of a thin macrospin. We analyze its response when subjected to an external field along its in-plane hard axis. We derive the exact trajectories of the magnetization. The switching versus non switching behavior is delimited by a bifurcation trajectory, for applied fields equal to half of the effective anisotropy field. A magnetization going through this bifurcation trajectory passes exactly along the hard axis and exhibits a vanishing characteristic frequency at that unstable point, which makes the trajectory noise sensitive. Attempting to approach the related minimal cost in applied field makes the magnetization final state unpredictable. We add finite damping in the model as a perturbative, energy dissipation factor. For a large applied field, the system switches several times back and forth. Several trajectories can be gone through before the system has dissipated enough energy to converge to one attracting equilibrium state. For some moderate fields, the system switches only once by a relaxation dominated precessional switching. We show that the associated switching field increases linearly with the damping parameter. The slope scales with the square root of the effective anisotropy. Our simple concluding expressions are useful to assess the potential application of precessional switching in magnetic random access memories.

We study how a magnetic field step triggers the precessional switching of the magnetization in an isotropic thin film . Using a variational approach, we estimate analytically the switching frequency and compare it to the results obtained numerically by direct integration of the equations of motion. We show that the periodic motions of the three magnetization components can be described satisfactorily with truncated Fourier expansions, indicating a relatively high spectral purity of the magnetic response. Our analytical expressions are simple enough to be physically transparent at first sight, in contrast to the results of the more elaborate models that treat also anisotropy.

Combining He ion irradiation and thermal mobility below 600K, we both trigger and control the transformation from chemical disorder to order in thin films of an intermetallic ferromagnet (FePd). Kinetic Monte Carlo simulations show how the initial directional short range order determines order propagation. Magnetic ordering perpendicular to the film plane was achieved, promoting the initially weak magnetic anisotropy to the highest values known for FePd films. This post-growth treatment should find applications in ultrahigh density magnetic recording., Comment: 7 pages, 3 Figures

We demonstrate a quasi ballistic switching of the magnetization in a microscopic mag-neto resistive memory cell. By means of time resolved magneto transport we follow the large angle precession of the free layer magnetization of a spin valve cell upon applica-tion of transverse magnetic field pulses. Stopping the field pulse after a 180 degree precession rotation leads to magnetization reversal with reversal times as short as 165 ps. This switching mode represents the fundamental ultra fast limit of field induced magnetization reversal., Comment: 16 pages, 4 figures, experimental. submitted to Phys. Rev. Lett

We study the precessional switching of the magnetization in microscopic spin valve cells induced by ultra short in-plane hard axis magnetic field pulses. Stable and highly efficient switching is monitored following pulses as short as 140 ps with energies down to 15 pJ. Multiple application of identical pulses reversibly toggles the cell's magnetization be-tween the two easy directions. Variations of pulse duration and amplitude reveal alter-nating regimes of switching and non-switching corresponding to transitions from in-phase to out-of-phase excitations of the magnetic precession by the field pulse. In the low field limit damping becomes predominant and a relaxational reversal is found allowing switching by hard axis fields below the in-plane anisotropy field threshold., Comment: 17 pages, 4 figures