Offset fields in perpendicularly magnetized tunnel junctions

We study the offset fields affecting the free layer of perpendicularly magnetized tunnel junctions. In extended films, the free layer offset field results from interlayer exchange coupling with the reference layer through the MgO tunnel oxide. The free layer offset field is thus accompanied with a shift of the free layer and reference layer ferromagnetic resonance frequencies. The shifts depend on the mutual orientation of the two magnetizations. The offset field decreases with the resistance area product of the tunnel oxide. Patterning the tunnel junction into an STT-MRAM disk-shaped cell changes substantially the offset field, as the reduction of the lateral dimension comes with the generation of stray fields by the reference and the hard layer. The experimental offset field compares best with the spatial average of the sum of these stray fields, thereby providing guidelines for the offset field engineering.Comment: Special issue of J. Phys. D: Appl. Phys (2019) on STT-MRA

Exchange stiffness in ultrathin perpendicularly-magnetized CoFeB layers determined using spin wave spectroscopy

We measure the frequencies of spin waves in nm-thick perpendicularly magnetized FeCoB systems, and model the frequencies to deduce the exchange stiffness of this material in the ultrathin limit. For this, we embody the layers in magnetic tunnel junctions patterned into circular nanopillars of diameters ranging from 100 to 300 nm and we use magneto-resistance to determine which rf-current frequencies are efficient in populating the spin wave modes. Micromagnetic calculations indicate that the ultrathin nature of the layer and the large wave vectors used ensure that the spin wave frequencies are predominantly determined by the exchange stiffness, such that the number of modes in a given frequency window can be used to estimate the exchange. For 1 nm layers the experimental data are consistent with an exchange stiffness A= 20 pJ/m, which is slightly lower that its bulk counterpart. The thickness dependence of the exchange stiffness has strong implications for the numerous situations that involve ultrathin films hosting strong magnetization gradients, and the micromagnetic description thereof.Comment: 5 pages, 4 figures, submitted to PR

Dynamical influence of vortex-antivortex pairs in magnetic vortex oscillators

We study the magnetization dynamics in a nanocontact magnetic vortex oscillators as function of temperature. Low temperature experiments reveal that the dynamics at low and high currents differ qualitatively. At low currents, we excite a temperature independent standard oscillation mode, consisting in the gyrotropic motion of a free layer vortex about the nanocontact. Above a critical current, a sudden jump of the frequency is observed, concomitant with a substantial increase of the frequency versus current slope factor. Using micromagnetic simulation and analytical modeling, we associate this new regime to the creation of a vortex-antivortex pair in the pinned layer of the spin valve. The vortex-antivortex distance depends on the Oersted field which favors a separation, and on the exchange bias field, which favors pair merging. The pair in the pinned layer provides an additional spin torque altering the dynamics of the free layer vortex, which can be quantitatively accounted for by an analytical model

Frequency shift keying in vortex-based spin torque oscillators

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 figure

Quantized spin wave modes in magnetic tunnel junction nanopillars

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 PR

Probing the Dzyaloshinskii-Moriya interaction in CoFeB ultrathin films using domain wall creep and Brillouin light spectroscopy

We have characterized the strength of the interfacial Dyzaloshinskii-Moriya interaction (DMI) in ultrathin perpendicularly magnetized CoFeB/MgO films, grown on different underlayers of W, TaN, and Hf, using two experimental methods. First, we determined the effective DMI field from measurements of field-driven domain wall motion in the creep regime, where applied in-plane magnetic fields induce an anisotropy in the wall propagation that is correlated with the DMI strength. Second, Brillouin light spectroscopy was employed to quantify the frequency non-reciprocity of spin waves in the CoFeB layers, which yielded an independent measurement of the DMI. By combining these results, we show that DMI estimates from the different techniques only yield qualitative agreement, which suggests that open questions remain on the underlying models used to interpret these results.Comment: 8 page

Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality constraints. A number of optimization problems in applications can be stated in this form, examples being the entropy-linear programming, the ridge regression, the elastic net, the regularized optimal transport, etc. We extend the Fast Gradient Method applied to the dual problem in order to make it primal-dual so that it allows not only to solve the dual problem, but also to construct nearly optimal and nearly feasible solution of the primal problem. We also prove a theorem about the convergence rate for the proposed algorithm in terms of the objective function and the linear constraints infeasibility.Comment: Submitted for DOOR 201

Modulating spin transfer torque switching dynamics with two orthogonal spin-polarizers by varying the cell aspect ratio

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 figure

Inducing or suppressing the anisotropy in multilayers based on CoFeB

Controlling the uniaxial magnetic anisotropy is of practical interest to a wide variety of applications. We study Co$_{40}$Fe$_{40}$B$_{20}$ single films grown on various crystalline orientations of LiNbO$_3$ substrates and on oxidized silicon. We identify the annealing conditions that are appropriate to induce or suppress uniaxial anisotropy. Anisotropy fields can be increased by annealing up to 11 mT when using substrates with anisotropic surfaces. They can be decreased to below 1 mT when using isotropic surfaces. In the first case, the observed increase of the anisotropy originates from the biaxial strain in the film caused by the anisotropic thermal contraction of the substrate when back at room temperature after strain relaxation during annealing. In the second case, anisotropy is progressively removed by applying successive orthogonal fields that are assumed to progressively suppress any chemical ordering within the magnetic film. The method can be applied to CoFeB/Ru/CoFeB synthetic antiferromagnets but the tuning of the anisotropy comes with a decrease of the interlayer exchange coupling and a drastic change of the exchange stiffness