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Magnetic skyrmions are fascinating topological particle-like textures promoted by a trade-off among interfacial properties (perpendicular anisotropy and Dzyaloshinskii-Moriya interaction (DMI)) and dipolar interactions. Depending on the dominant interaction, complex spin textures, including pure N\'eel and hybrid skyrmions have been observed in multilayer heterostructures. A quantification of these different spin textures typically requires a depth-reoslved magnetic imaging or scattering techniques. In the present work, we will show qualitatively different collapsing dynamics for pure N\'eel and hybrid skyrmions induced by a perpendicular magnetic field in two representative systems, [Pt/Co/Ir]15 and [Ta/CoFeB/MgO]15 multilayers. Skyrmions in the former stack undergo two morphological transitions, upon reversing the perpendicular field direction. Skyrmions in [Ta/CoFeB/MgO]15 multilayers exhibit a continuous transition, which is mainly linked to a reversible change of the skyrmion size. A full micromagnetic phase diagram is presented to identify these two collapsing mechanisms as a function of material parameters. Since the two distinct collapsing dynamics rely on the detailed layer-dependent spin structures of skyrmions, they could be used as potential fingerprints for identifying the skyrmion type in magnetic multilayers. Our work suggests the employment of pure and hybrid skyrmions for specific applications, due to the strong correlation between the skyrmion dynamics and 3-dimentional spin profiles., Comment: 16 pages, 8 figures

A concept of an electrically tunable resonance detector of THz-frequency signals based on antiferromagnetic/heavy metal (AFM/HM) hetero-structure is proposed. The conversion of a THz-frequency input signal into DC voltage is done using the inverse spin Hall effect in an (AFM/HM) bilayer. An additional bias DC current in the HM layer can be used to vary the effective anisotropy of the AFM, and, therefore, to tune the AFMR frequency. The proposed AFM/HM hetero-structure works as a resonance-type quadratic detector which can be tuned by the bias current in the range of at least 10 percent of the AFMR frequency and our estimations show that the sensitivity of this detector could be comparable to that of modern detectors based on the Schottky, Gunn or graphene-based diodes.

Spin-diodes are usually resonant in nature (GHz frequency) and tuneable by magnetic field and bias current with performances, in terms of sensitivity and minimum detectable power, overcoming the semiconductor counterpart, i.e. Schottky diodes. Recently, spin diodes characterized by a low frequency detection (MHz frequency) have been proposed. Here, we show a strategy to design low frequency detectors based on magnetic tunnel junctions having the interfacial perpendicular anisotropy of the same order of the demagnetizing field out-of-plane component. Micromagnetic calculations show that to reach this detection regime a threshold input power has to be overcome and the phase shift between the oscillation magnetoresistive signal and the input radiofrequency current plays the key role in determining the value of the rectification voltage.

This paper introduces the concept of spin-orbit-torque-MRAM (SOT-MRAM) based physical unclonable function (PUF). The secret of the PUF is stored into a random state of a matrix of perpendicular SOT-MRAMs. Here, we show experimentally and with micromagnetic simulations that this random state is driven by the intrinsic nonlinear dynamics of the free layer of the memory excited by the SOT. In detail, a large enough current drives the magnetization along an in-plane direction. Once the current is removed, the in-plane magnetic state becomes unstable evolving towards one of the two perpendicular stable configurations randomly. In addition, an hybrid CMOS/spintronics model is used to evaluate the electrical characteristics of a PUF realized with an array of 16x16 SOT-MRAM cells. Beyond robustness against voltage and temperature variations, hardware authentication based on this PUF scheme has additional advantages over other PUF technologies such as non-volatility (no power consumption in standby mode), reconfigurability (the secret can be rewritten), and scalability. We believe that this work is a step forward the design of spintronic devices for application in security., Comment: 18 pages, 7 figures

The study of thermodynamics of topological defects is an important challenge to understand their underlying physics. Among them, magnetic skyrmions have a leading role for their physical properties and potential applications in storage and neuromorphic computing. In this paper, the thermodynamic statistics of magnetic skyrmions is derived. It is shown that the skyrmion free energy can be modelled via a parabolic function and the diameters statistics obeys the Maxwell-Boltzmann distribution. This allows for making an analogy between the behavior of the distribution of skyrmion diameters statistics and the diluted gas Maxwell-Boltzmann molecules distribution at thermodynamical equilibrium. The calculation of the skyrmion configurational entropy, due to thermally-induced changes of size and shape of the skyrmion, is essential for the determination of thermal fluctuations of the skyrmion energy around its average value. These results can be employed to advance the field of skyrmionics., Comment: Main text 26 pages and 6 figures. Supplementary Information 4 pages

A two-dimensional analytical model for the description of the excitation of nonreciprocal spin waves by spin current in spin-Hall oscillators in the presence of the interfacial Dzyaloshinskii-Moriya interaction (i-DMI) is developed. The theory allows one to calculate the threshold current for the excitation of spin waves, as well as the frequencies and spatial profiles of the excited spin wave modes. It is found, that the frequency of the excited spin waves exhibits a quadratic red shift with the i-DMI strength. At the same time, in the range of small and moderate values of the i-DMI constant, the averaged wave number of the excited spin waves is almost independent of the i-DMI, which results in a rather weak dependence on the i-DMI of the threshold current of the spin wave excitation. The obtained analytical results are confirmed by the results of micromagnetic simulations., Comment: 23 pages,5 figures

Understanding the physical properties of magnetic skyrmions is important for fundamental research with the aim to develop new spintronic device paradigms where both logic and memory can be integrated at the same level. Here, we show a universal model based on the micromagnetic formalism that can be used to study skyrmion stability as a function of magnetic field and temperature. We consider ultrathin, circular ferromagnetic magnetic dots. Our results show that magnetic skyrmions with a small radius compared to the dot radius are always metastable, while large radius skyrmions form a stable ground state. The change of energy profile determines the weak (strong) size dependence of the metastable (stable) skyrmion as a function of temperature and/or field. These results can open a path toward the design of optimal materials for skyrmion based devices.

A storage scheme based on racetrack memory, where the information can be coded in a domain or a skyrmion, seems to be an alternative to conventional hard disk drive for high density storage. Here, we perform a full micromagnetic study of the performance of synthetic antiferromagnetic (SAF) racetrack memory in terms of velocity and sensitivity to defects by using experimental parameters. We find that to stabilize a SAF skyrmion, the Dzyaloshinskii-Moriya Interaction in the top and the bottom ferromagnet should have an opposite sign. The velocity of SAF skyrmion and SAF Neel domain wall are of the same order and can reach values larger than 1200 m/s if a spin-orbit torque from the spin-Hall effect with opposite sign is applied to both ferromagnets.

Spin-Hall oscillators are promising sources of spin-wave signals for magnonics applications, and can serve as building blocks for magnonic logic in ultralow power computation devices. Here, we analytically and micromagnetically study magnetization dynamics excited in a Spin-Hall oscillator with oblique magnetization when the spin-Hall effect and interfacial Dzyaloshinskii-Moriya interaction act simultaneously. Our key results are (i) excitation of nonreciprocal spin-waves propagating perpendicularly to the in-plane projection of the static magnetization, (ii) skyrmions generation by pure spin-current, (iii) excitation of a new spin-wave mode with a spiral spatial profile originating from a gyrotropic rotation of a dynamical skyrmion. These results demonstrate that Spin-Hall oscillators can be used as generators of magnetic skyrmions and different types of propagating spin-waves for magnetic data storage and signal processing applications.

Solitons are very promising for the design of next generation of ultralow power devices for storage and computation. The key ingredient to achieve this goal is the fundamental understanding of their stabilization and manipulation. Here, we show how the interfacial Dzyaloshinskii Moriya Interaction (i DMI) is able to lift the energy degeneracy of a magnetic vortex state by stabilizing a topological soliton with radial chirality, hereafter called radial vortex. It has a non-integer skyrmion number S (0.5<|S|<1) due to both the vortex core polarity and the magnetization tilting induced by the i DMI boundary conditions. Micromagnetic simulations predict that a magnetoresistive memory based on the radial vortex state in both free and polarizer layers can be efficiently switched by a threshold current density smaller than 106 A/cm2. The switching processes occur via the nucleation of topologically connected vortices and vortex antivortex pairs, followed by spin wave emissions due to vortex antivortex annihilations.

Magnetic skyrmions are topologically protected states that are very promising for the design of the next generation of ultralow-power electronic devices. In this letter, we propose a magnetic tunnel junction based spin-transfer torque diode with a magnetic skyrmion as ground state and a perpendicular polarizer patterned as nanocontact for a local injection of the current. The key result is the possibility to achieve sensitivities (i.e. detection voltage over input microwave power) larger than 2000V/W for optimized contact diameters. Our results can be very useful for the identification of a new class of spin-torque diodes with a non-uniform ground state., Comment: 10 pages, 5 figures

We employed micro-focused Brillouin light scattering to study the amplification of the thermal spin wave eigenmodes by means of a pure spin current, generated by the spin-Hall effect, in a transversely magnetized Pt(4nm)/NiFe(4nm)/SiO2(5nm) layered nanowire with lateral dimensions 500x2750 nm2. The frequency and the cross section of both the center (fundamental) and the edge spin wave modes have been measured as a function of the intensity of the injected dc electric current. The frequency of both modes exhibits a clear redshift while their cross section is greatly enhanced on increasing the intensity of the injected dc. A threshold-like behavior is observed for a value of the injected dc of 2.8 mA. Interestingly an additional mode, localized in the central part of the nanowire, appears at higher frequency on increasing the intensity of the injected dc above the threshold value. Micromagnetic simulations were used to quantitatively reproduce the experimental results and to investigate the complex non-linear dynamics induced by the spin-Hall effect, including the modification of the spatial profile of the spin wave modes and the appearance of the extra mode above the threshold., Comment: 13 pages, 4 figures in journal of applied physics 2015

Magnetic Tunnel Junction devices find use in several applications based on the exploitation of the Spin-Transfer Torque phenomenon. The Ferromagnetic Resonance curve is a key characteristic of any Magnetic Tunnel Junctions. It is usually characterized both experimentally and numerically by performing a lot of measurements of the magnetic response to a sinusoidal field or current. Here we propose the use of a chirp signal as excitation signal to reconstruct the Ferromagnetic resonance curve with a single measurement/simulation. A micromagnetic comparison of the proposed method with the traditional one is shown.

Perpendicular MgO-based Magnetic Tunnel Junctions are optimal candidates as building block of Spin Transfer Torque (STT) magnetoresistive memories. However, up to now, the only STT is not enough to achieve switching current density below 106 A/cm2. A recent work [Wang et al., Nature Mater., vol. 11, pp 64-68, Jan. 2012] has experimentally demonstrated the possibility to perform magnetization switching assisted by an electric-field at ultra-low current density. Theoretically, this switching has been studied by using a macrospin approach only. Here, we show a full micromagnetic study. We found that the switching occurs via a complex nucleation process including the nucleation of magnetic vortexes.

Vortices and antivortices are typical non uniform magnetization configurations that can be achieved in spin-torque oscillators with in-plane materials. Dynamics of a vortex-antivortex pair, namely vortex dipole, were predicted and already observed. In this paper, we present a systematic micromagnetic study on that kind of dynamics in different spin-valves where the current is injected through a nano-aperture. Rotation and translation of vortex dipoles and rotation of vortex quadrupoles are shown depending on the shape and the size of the spin-valve. The origin of the different behaviors is explained within a micromagnetic framework., Comment: 4 pages, 4 figures

Magnetic storage based on racetrack memory is very promising for the design of ultra-dense, low-cost and low-power storage technology. Information can be coded in a magnetic region between two domain walls or, as predicted recently, in topological magnetic objects known as skyrmions. Here, we show the technological advantages and limitations of using Bloch and Neel skyrmions manipulated by spin current generated within the ferromagnet or via the spin-Hall effect arising from a non-magnetic heavy metal underlayer. We found that the Neel skyrmion moved by the spin-Hall effect is a very promising strategy for technological implementation of the next generation of skyrmion racetrack memories (zero field, high thermal stability, and ultra-dense storage). We employed micromagnetics reinforced with an analytical formulation of skyrmion dynamics that we developed from the Thiele equation. We identified that the excitation, at high currents, of a breathing mode of the skyrmion limits the maximal velocity of the memory.

This letter studies the dynamical behavior of spin-Hall nanoscillators from a micromagnetic point of view. The model parameters have been identified by reproducing recent experimental data quantitatively. Our results indicate that a strongly localized mode is observed for in-plane bias fields such as in the experiments, while predict the excitation of an asymmetric propagating mode for large enough out-of plane bias field similarly to what observed in spin-torque nanocontact oscillators. Our findings show that spin-Hall nanoscillators can find application as spin-wave emitters for magnonic applications where spin waves are used for transmission and processing information on nanoscale., Comment: 14 pages

This paper predicts the effect of the Dzyaloshinskii-Moriya interaction (DMI) and spin Hall effect in the spin-torque diode response of a Magnetic Tunnel Junction built over a Tantalum strip. Our results indicate that, for a microwave current large enough, the DMI can change qualitatively the resonant response by splitting the ferromagnetic resonance peak. We also find out that the two modes have a non-uniform spatial distribution.

This letter introduces a micromagnetic model able to characterize the magnetization dynamics in three terminal magnetic tunnel junctions, where the effects of spin-transfer torque and spin-orbit torque are taken into account. Our results predict that the possibility to separate electrically those two torque sources is very promising from a technological point of view for both next generation of nanoscale spintronic oscillators and microwave detectors. A scalable synchronization scheme based on the parallel connection of those three terminal devices is also proposed., Comment: Accepted to Applied Physics Letters

The magnetization switching of a thin ferromagnetic layer placed on top of a heavy metal (such as Pt, Ta or W) driven by an in-plane current has been observed in recent experiments. The magnetization dynamics of these processes is studied in a full micromagnetic framework which takes into account the transfer-torque from spin Hall effect due to the spin-orbit coupling. Simulations indicate that the reversal occurs via nucleation of complex magnetization patterns. In particular, magnetic bubbles appear during the reversal of the magnetization in the perpendicular configuration while for the in-plane configuration, nucleation of vortexes are observed.

The non-autonomous dynamics of spin-torque oscillators in presence of both microwave current and field at the same frequency can exhibit complex non-isochronous effects. A non-stationary mode hopping between quasi-periodic mode (frequency pulling) and periodic mode (phase locking), and a deterministic phase slip characterized by an oscillatory synchronization transient (non-Adlerian phase slip) after the phase jump of have been predicted. In the latter effect, a wavelet based analysis reveals that in the positive and negative phase jump the synchronization transient occurs at the frequency of the higher and lower sideband frequency respectively. The non-Adlerian phase slip effect, even if discovered in STOs, is a general property of non-autonomous behavior valid to any non-isochronous auto-oscillator in regime of moderate and large force locking., Comment: 12 page, 4 figures