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Thiophene oligomers are an important class of organic materials for photovoltaic applications, owing to their unique optoelectronic properties. Recently it was suggested that incorporation of furan units to the thiophene chains, maintaining the chain structure, namely thienylfuran linear oligomers, can bring improvements to the final material. In this work, we present a theoretical study of thiophene, furan and thienylfuran short chains, up to 4 units. Structural and electronic properties were obtained using Hartree-Fock (HF) and Density Functional Theory (DFT) calculations plus beyond mean-field methodologies, specifically Second-order M\"oller-Plesset perturbation theory on HF (HF-MP2) and many-body perturbation theory by the G0W0 approximation on DFT (G0W0@DFT). The optical properties were calculated on top of G0W0@DFT data using the Bethe-Salpeter Equation. We investigate properties from the monomers T and F to tetramers with different sequencing of units TT, TF or FF, always bonded through the usual carbon atoms. As well known for the uniform oligothiophene chains, also here for any TT sequencing we find a torsion angle of $150^{\circ}$, while all other sequencing of units result planar, which can be relevant for film producing. Also we find that the first optical transitions for the oligomers reach a promising threshold of $\sim 3$ eV at the tetramer length, combined with ionization potentials around $\sim 7$ eV, which confirms the relevance of these organic compounds for photovoltaic applications., Comment: 11 pages, 3 figures

Motivated by the importance of magnetization dynamics in nanomagnets for the development and optimization of magnetic devices and sensors, we measured and modeled spin wave spectra in patterned elliptical nanomagnets. Ferromagnetic resonance spectra for multiple nanomagnets of Ni80Fe20 , fabricated by electron-beam lithography to have nominal short-axes of 200 nm or 100 nm, were measured by use of heterodyne magneto-optical microwave microscopy. Scanning electron microscope images taken of the same nanomagnets were used to define element shapes for micromagnetic simulations. Measured spectra show significant differences between nominally identical nanomagnets, which could be only partially attributed to uncontrolled shape variations in the patterning process, as evidence by the limited agreement between the measured and simulated spectra. Agreement between measurements and simulations was improved by including a zone of reduced magnetization and exchange at the edges of the nanomagnets in the simulations. Our results show that the reduction of shape variations between individual magnetic random-access memory elements can potentially improve their performance. However, unambiguous determination of materials parameters in nanomagnets based on analysis and modeling of spin wave spectra remains problematic.

Ultrafast optical pumping of spatially nonuniform magnetic textures is known to induce far-from-equilibrium spin transport effects. Here, we use ultrafast x-ray diffraction with unprecedented dynamic range to study the laser-induced dynamics of labyrinth domain networks in ferromagnetic CoFe/Ni multilayers. We detected azimuthally isotropic, odd order, magnetic diffraction rings up to 5th order. The amplitudes of all three diffraction rings quench to different degrees within 1.6 ps. In addition, all three of the detected diffraction rings both broaden by 15% and radially contract by 6% during the quench process. We are able to rigorously quantify a 31% ultrafast broadening of the domain walls via Fourier analysis of the order-dependent quenching of the three detected diffraction rings. The broadening of the diffraction rings is interpreted as a reduction in the domain coherence length, but the shift in the ring radius, while unambiguous in its occurrence, remains unexplained. In particular, we demonstrate that a radial shift explained by domain wall broadening can be ruled out. With the unprecedented dynamic range of our data, our results provide convincing evidence that labyrinth domain structures are spatially perturbed at ultrafast speeds under far-from-equilibrium conditions, albeit the mechanism inducing the perturbations remains yet to be clarified.

We report a large spin Hall effect in the 3$d$ transition metal alloy Ni$_x$Cu$_{1-x}$ for $x\in\left\{ 0.3,0.75\right\} $, detected via the ferromagnetic resonance of a Permalloy (Py = Ni$_{80}$Fe$_{20}$) film deposited in a bilayer with the alloy. A thickness series at $x$ = 0.6, for which the alloy is paramagnetic at room temperature, allows us to determine the spin Hall ratio $\theta_{\rm{SH}}\approx1$, spin diffusion length $\lambda_{\rm{s}}$, spin mixing conductance $G_{\uparrow\downarrow}$, and damping $\alpha_{\rm{SML}}$ due to spin memory loss . We compare our results with similar experiments on Py/Pt bilayers measured using the same method. Ab initio band structure calculations with disorder and spin-orbit coupling suggest an intrinsic spin Hall effect in Ni$_x$Cu$_{1-x}$ alloys, although the experiments here cannot distinguish between extrinsic and intrinsic mechanisms., Comment: New ab initio calculations of Ni-Cu alloy band structure added; new author; new fig in main text and new appendix describing calculations

Spin-orbit interaction (SOI) couples charge and spin transport, enabling electrical control of magnetization. A quintessential example of SOI-induced transport is the anomalous Hall effect (AHE), first observed in 1880, in which an electric current perpendicular to the magnetization in a magnetic film generates charge accumulation on the surfaces. Here we report the observation of a counterpart of the AHE that we term the anomalous spin-orbit torque (ASOT), wherein an electric current parallel to the magnetization generates opposite spin-orbit torques on the surfaces of the magnetic film. We interpret the ASOT as due to a spin-Hall-like current generated with an efficiency of 0.053+/-0.003 in Ni80Fe20, comparable to the spin Hall angle of Pt. Similar effects are also observed in other common ferromagnetic metals, including Co, Ni, and Fe. First principles calculations corroborate the order of magnitude of the measured values. This work suggests that a strong spin current with spin polarization transverse to magnetization can exist in a ferromagnet, despite spin dephasing. It challenges the current understanding of spin-orbit torque in magnetic/nonmagnetic bilayers, in which the charge-spin conversion in the magnetic layer has been largely neglected., Comment: 23 pages, 3 figures and 1 table

Ni$_{0.8}$Fe$_{0.2}$ (Py) and Py alloyed with Cu exhibit intriguing ultrafast demagnetization behavior, where the Ni magnetic moment shows a delayed response relative to the Fe, an effect which is strongly enhanced by Cu alloying. We have studied a broad range of Cu concentrations to elucidate the effects of Cu alloying in Py. The orbital/spin magnetic moment ratios are largely unaffected by Cu alloying, signifying that Cu-induced changes in the ultrafast demagnetization are not related to spin-orbit interactions. We show that magnon diffusion can explain the delayed Ni response, which we attribute to an enhanced magnon generation rate in the Fe sublattice relative to the Ni sublattice. Furthermore, Py exhibits prominent RKKY-like exchange interactions, which are strongly enhanced between Fe atoms and diminished between Ni atoms by Cu alloying. An increased Fe magnon scattering rate is expected to occur concurrently with this increased Fe-Fe exchange interaction, supporting the results obtained from the magnon diffusion model.

Sub-picosecond magnetisation manipulation via femtosecond optical pumping has attracted wide attention ever since its original discovery in 1996. However, the spatial evolution of the magnetisation is not yet well understood, in part due to the difficulty in experimentally probing such rapid dynamics. Here, we find evidence of rapid magnetic order recovery in materials with perpendicular magnetic anisotropy via nonlinear magnon processes. We identify both localisation and coalescence regimes, whereby localised magnetic textures nucleate and subsequently evolve in accordance with a power law formalism. Coalescence is observed for optical excitations both above and below the switching threshold. Simulations indicate that the ultrafast generation of noncollinear magnetisation via optical pumping establishes exchange-mediated spin currents with an equivalent 100% spin polarised charge current density of $10^8$ A/cm$^2$. Such large spin currents precipitate rapid recovery of magnetic order after optical pumping. These processes suggest an ultrafast optical route for the stabilization of desired meta-stable states, e.g., isolated skyrmions.

Understanding the evolution of spin-orbit torque (SOT) with increasing heavy-metal thickness in ferromagnet/normal metal (FM/NM) bilayers is critical for the development of magnetic memory based on SOT. However, several experiments have revealed an apparent discrepancy between damping enhancement and damping-like SOT regarding their dependence on NM thickness. Here, using linewidth and phase-resolved amplitude analysis of vector network analyzer ferromagnetic resonance (VNA-FMR) measurements, we simultaneously extract damping enhancement and both field-like and damping-like inverse SOT in Ni$_{80}$Fe$_{20}$/Pt bilayers as a function of Pt thickness. By enforcing an interpretation of the data which satisfies Onsager reciprocity, we find that both the damping enhancement and damping-like inverse SOT can be described by a single spin diffusion length ($\approx$ 4 nm), and that we can separate the spin pumping and spin memory loss (SML) contributions to the total damping. This analysis indicates that less than 40% of the angular momentum pumped by FMR through the Ni$_{80}$Fe$_{20}$/Pt interface is transported as spin current into the Pt. On account of the SML and corresponding reduction in total spin current available for spin-charge transduction in the Pt, we determine the Pt spin Hall conductivity ($\sigma_\mathrm{SH} = (2.36 \pm 0.04)\times10^6 \Omega^{-1} \mathrm{m}^{-1}$) and bulk spin Hall angle ($\theta_\mathrm{SH}=0.387 \pm0.008$) to be larger than commonly-cited values. These results suggest that Pt can be an extremely useful source of SOT if the FM/NM interface can be engineered to minimize SML. Lastly, we find that self-consistent fitting of the damping and SOT data is best achieved by a model with Elliott-Yafet spin relaxation and extrinsic inverse spin Hall effect, such that both the spin diffusion length and spin Hall conductivity are proportional to the Pt charge conductivity.

Planar ferromagnetic channels have been shown to theoretically support a long-range ordered and coherently precessing state where the balance between local spin injection at one edge and damping along the channel establishes a dissipative exchange flow, sometimes referred to as a spin superfluid. However, realistic materials exhibit in-plane anisotropy, which breaks the axial symmetry assumed in current theoretical models. Here, we study dissipative exchange flows in a ferromagnet with in-plane anisotropy from a dispersive hydrodynamic perspective. Through the analysis of a boundary value problem for a damped sine-Gordon equation, dissipative exchange flows in a ferromagnetic channel can be excited above a spin current threshold that depends on material parameters and the length of the channel. Symmetry-broken dissipative exchange flows display harmonic overtones that redshift the fundamental precessional frequency and lead to a reduced spin pumping efficiency when compared to their symmetric counterpart. Micromagnetic simulations are used to verify that the analytical results are qualitatively accurate, even in the presence of nonlocal dipole fields. Simulations also confirm that dissipative exchange flows can be driven by spin transfer torque in a finite-sized region. These results delineate the important material parameters that must be optimized for the excitation of dissipative exchange flows in realistic systems., Comment: 20 pages, 5 figures

The spin-orbit interaction enables interconversion between a charge current and a spin current. It is usually believed that in a nonmagnetic metal (NM) or at a NM/ferromagnetic metal (FM) bilayer interface, the symmetry of spin-orbit effects (SOE) requires that the spin current, charge current and spin orientation are all orthogonal to each other. Here we show the observation of a SOE near the NM/FM interface that exhibits a very different symmetry from the conventional spin Hall effect, insofar as the spin polarization is further rotated about the magnetization. These results imply that a perpendicularly polarized spin current can be generated with an in-plane charge current simply by use of a FM/NM bilayer with magnetization collinear to the charge current. The ability to generate a spin current with arbitrary polarization using typical magnetic materials will greatly benefit the development of magnetic memories.

A systematic experimental study of Gilbert damping is performed via ferromagnetic resonance for the disordered crystalline binary 3d transition metal alloys Ni-Co, Ni-Fe and Co-Fe over the full range of alloy compositions. After accounting for inhomogeneous linewidth broadening, the damping shows clear evidence of both interfacial damping enhancement (by spin pumping) and radiative damping. We quantify these two extrinsic contributions and thereby determine the intrinsic damping. The comparison of the intrinsic damping to multiple theoretical calculations yields good qualitative and quantitative agreement in most cases. Furthermore, the values of the damping obtained in this study are in good agreement with a wide range of published experimental and theoretical values. Additionally, we find a compositional dependence of the spin mixing conductance.

The structure and static magnetic properties - saturation magnetization, perpendicular anisotropy, spectroscopic g-factor, and orbital magnetization - of thin-film 3d transition metal alloys are determined over the full range of alloy compositions via X-ray diffraction, magnetometry, and ferromagnetic resonance measurements. We determine the interfacial perpendicular magnetic anisotropy by use of samples sets with varying thickness for specific alloy concentrations. The results agree with prior published data and theoretical predictions. They provide a comprehensive compilation of the magnetic properties of thin-film Ni-Co, Ni-Fe and Co-Fe alloys that goes well beyond the often-cited Slater-Pauling dependence of magnetic moment on alloy concentration.

Microwave magnetodynamics in ferromagnets are often studied in the small-amplitude or weakly nonlinear regime corresponding to modulations of a well-defined magnetic state. However, strongly nonlinear regimes, where the aforementioned approximations are not applicable, have become experimentally accessible. By re-interpreting the governing Landau-Lifshitz equation of motion, we derive an exact set of equations of dispersive hydrodynamic form that are amenable to analytical study even when full nonlinearity and exchange dispersion are included. The resulting equations are shown to, in general, break Galilean invariance. A magnetic Mach number is obtained as a function of static and moving reference frames. The simplest class of solutions are termed uniform hydrodynamic states (UHSs), which exhibit fluid-like behavior including laminar flow at subsonic speeds and the formation of a Mach cone and wave-fronts at supersonic speeds. A regime of modulational instability is also possible, where the UHS is violently unstable. The hydrodynamic interpr, Comment: 20 pages, 5 figures

The phenomenology of magnetic damping is of critical importance for devices that seek to exploit the electronic spin degree of freedom since damping strongly affects the energy required and speed at which a device can operate. However, theory has struggled to quantitatively predict the damping, even in common ferromagnetic materials. This presents a challenge for a broad range of applications in spintronics and spin-orbitronics that depend on materials and structures with ultra-low damping. Such systems enable many experimental investigations that further our theoretical understanding of numerous magnetic phenomena such as damping and spin-transport mediated by chirality and the Rashba effect. Despite this requirement, it is believed that achieving ultra-low damping in metallic ferromagnets is limited due to the scattering of magnons by the conduction electrons. However, we report on a binary alloy of Co and Fe that overcomes this obstacle and exhibits a damping parameter approaching 0.0001, which is comparable to values reported only for ferrimagnetic insulators. We explain this phenomenon by a unique feature of the bandstructure in this system: The density of states exhibits a sharp minimum at the Fermi level at the same alloy concentration at which the minimum in the magnetic damping is found. This discovery provides both a significant fundamental understanding of damping mechanisms as well as a test of theoretical predictions.

Ni$_{80}$Fe$_{20}$ (Py) and Py-Cu exhibit intriguing ultrafast demagnetization behavior, where the Ni magnetic moment shows a delayed response relative to the Fe [S. Mathias et al., PNAS {\bf 109}, 4792 (2012)]. To unravel the mechanism responsible for this behavior, we have studied Py-Cu alloys for a wide range of Cu concentrations using X-ray magnetic circular dichroism (XMCD). The magnetic moments of Fe and Ni are found to respond very differently to Cu alloying: Fe becomes a strong ferromagnet in Py, with the magnetic moment largely unaffected by Cu alloying. In contrast, the Ni magnetic moment decreases continuously with increasing Cu concentration. Our results are corroborated by ab-initio calculations of the electronic structure, which we discuss in the framework of virtual bound states (VBSs). For high Cu concentrations, Ni exhibits VBSs below the Fermi level, which are likely responsible for an increased orbital/spin magnetic ratio at high Cu concentrations. Fe exhibits VBSs in the minority band, approximately 1 eV above the Fermi level in pure Py, that move closer to the Fermi level upon Cu alloying. A strong interaction between the VBSs and excited electrons above the Fermi level enhances the formation of localized magnons at Fe sites, which explains the different behavior between Fe and Ni during ultrafast demagnetization.

We discuss the phases of QCD in the parameter space spanned by the number of light flavours and the temperature with respect to the realisation of chiral and conformal symmetries. The intriguing interplay of these symmetries is best studied by means of lattice simulations, and some selected results from our recent work are presented here., Comment: 10 pages, proceedings of the 9th International Workshop on Critical Point and Onset of Deconfinement, 17-21 November, 2014, ZiF, Bielefeld, Germany

We discuss our results on QCD with a number of fundamental fermions ranging from zero to sixteen. These theories exhibit a wide array of fascinating phenomena which have been under close scrutiny, especially in recent years, first and foremost is the approach to conformality. To keep this review focused, we have chosen scale generation, or lack thereof as a guiding theme, however the discussion will be set in the general framework of the analysis of the phases and phase transitions of strong interactions at zero and nonzero temperature., Comment: 15 pages, prepared for IJMPA Special Issue 'Recent Nonperturbative Developments in QCD-like Theories'

We study the SU(3) gauge theory with twelve flavours of fermions in the fundamental representation as a prototype of non-Abelian gauge theories inside the conformal window. Guided by the pattern of underlying symmetries, chiral and conformal, we analyze the two-point functions theoretically and on the lattice, and determine the finite size scaling and the infinite volume fermion mass dependence of the would-be hadron masses. We show that the spectrum in the Coulomb phase of the system can be described in the context of a universal scaling analysis and we provide the nonperturbative determination of the fermion mass anomalous dimension gamma*=0.235(46) at the infrared fixed point. We comment on the agreement with the four-loop perturbative prediction for this quantity and we provide a unified description of all existing lattice results for the spectrum of this system, them being in the Coulomb phase or the asymptotically free phase. Our results corroborate the view that the fixed point we are studying is not associated to a physical singularity along the bare coupling line and estimates of physical observables can be attempted on either side of the fixed point. Finally, we observe the restoration of the U(1) axial symmetry in the two-point functions., Comment: 40 pages, 22 figures

We determined the spin-transport properties of Pd and Pt thin films by measuring the increase in ferromagnetic resonance damping due to spin-pumping in ferromagnetic (FM)-nonferromagnetic metal (NM) multilayers with varying NM thicknesses. The increase in damping with NM thickness depends strongly on both the spin- and charge-transport properties of the NM, as modeled by diffusion equations that include both momentum- and spin-scattering parameters. We use the analytical solution to the spin-diffusion equations to obtain spin-diffusion lengths for Pt and Pd. By measuring the dependence of conductivity on NM thickness, we correlate the charge- and spin-transport parameters, and validate the applicability of various models for momentum-scattering and spin-scattering rates in these systems: constant, inverse-proportional (Dyakanov-Perel), and linear-proportional (Elliot-Yafet). We confirm previous reports that the spin-scattering time can be shorter than the momentum scattering time in Pt, and the Dyakanov-Perel-like model is the best fit to the data.

We demonstrate that the spectroscopic g-factor can be determined with high precision and accuracy by broadband ferromagnetic resonance measurements and applying an asymptotic analysis to the data. Spectroscopic data used to determine the g-factor is always obtained over a finite range of frequencies, which can result in significant errors in the fitted values of the spectroscopic g-factor. We show that by applying an asymptotic analysis to broadband datasets, precise values of the intrinsic g-factor can be determined with errors well below 1 %, even when the exact form of the Kittel equation (which describes the relationship between the frequency and resonance field) is unknown. We demonstrate this methodology with measured data obtained for sputtered Ni80Fe20 ("Permalloy") thin films of varied thicknesses, where we determine the bulk g-factor value to be 2.109 +/- 0.003. Such an approach is further validated by application to simulated data that includes both noise and an anisotropy that is not included in the Kittel equation that was used in the analysis. Finally, we show a correlation of thickness and interface structure to the magnitude of the asymptotic behavior, which provide insight into additional mechanisms that may induce deviations from the Kittel equation., Comment: Submitted to Journal of Applied Physics

We use broadband ferromagnetic resonance spectroscopy and x-ray diffraction to investigate the fundamental origin of perpendicular anisotropy in Co90Fe10/Ni multilayers. By careful evaluation of the spectroscopic g-factor, we determine the orbital moment along the out-of-plane and in-plane directions. For the multilayers, we find a direct relationship between the orbital moment asymmetry and the perpendicular anisotropy, consistent with the theory of Bruno [P.Bruno, Phys. Rev. B, 39, 865 (1989)]. A systematic x-ray diffraction study revealed the presence of a trigonal strain as high as 0.7 % in some samples. However, we found no direct correlation between the strain and the anisotropy, indicating that the anisotropy is not dominated by magnetoelastic effects. In order to further study the interface structure on the anisotropy, we prepared a set of equivalent alloy samples. The strain in the alloy samples was comparable to that of the multilayer samples; however the orbital moment asymmetry in the alloy samples showed a very different trend allowing us to isolate the effect of the interfaces in the multilayers., Comment: In press at Physical Review B

We measured spin transport in nonferromagnetic (NM) metallic multilayers from the contribution to damping due to spin pumping from a ferromagnetic Co90Fe10 thin film. The multilayer stack consisted of NM1/NM2/Co90Fe10(2 nm)/NM2/NM3 with varying NM materials and thicknesses. Using conventional theory for one dimensional diffusive spin transport in metals, we show that the effective damping due to spin pumping can be strongly affected by the spin transport properties of each NM in the multilayer, which permits the use of damping measurements to accurately determine the spin transport properties of the various NM layers in the full five-layer stack. We find that due to its high electrical resistivity, amorphous Ta is a poor spin conductor, in spite of a short spin-diffusion length of 1.0 nm, and that Pt is an excellent spin conductor by virtue of its low electrical resistivity and a spin diffusion length of only 0.5 nm. Spin Hall effect measurements may have underestimated the spin Hall angle in Pt by assuming a much longer spin diffusion length., Comment: Submitted to Phys. Rev. B

We demonstrate a strong dependence of the effective damping on the nanomagnet size and the particular spin-wave mode that can be explained by the theory of intralayer transverse-spin-pumping. The effective Landau-Lifshitz damping is measured optically in individual, isolated nanomagnets as small as 100 nm. The measurements are accomplished by use of a novel heterodyne magneto-optical microwave microscope with unprecedented sensitivity. Experimental data reveal multiple standing spin-wave modes that we identify by use of micromagnetic modeling as having either localized or delocalized character, described generically as end- and center-modes. The damping parameter of the two modes depends on both the size of the nanomagnet as well as the particular spin-wave mode that is excited, with values that are enhanced by as much as 40% relative to that measured for an extended film. Contrary to expectations based on the ad hoc consideration of lithography-induced edge damage, the damping for the end-mode decreases as the size of the nanomagnet decreases. The data agree with the theory for damping caused by the flow of intralayer transverse spin-currents driven by the magnetization curvature. These results have serious implications for the performance of nanoscale spintronic devices such as spin-torque-transfer magnetic random access memory., Comment: The manuscript is published in Physical Review Letters. We revised the manuscript to meet the length requirement

The propagation and controlled manipulation of strongly nonlinear, two-dimensional solitonic states in a thin, anisotropic ferromagnet are theoretically demonstrated. It has been recently proposed that spin-polarized currents in a nanocontact device could be used to nucleate a stationary dissipative droplet soliton. Here, an external magnetic field is introduced to accelerate and control the propagation of the soliton in a lossy medium. Soliton perturbation theory corroborated by two-dimensional micromagnetic simulations predicts several intriguing physical effects, including the acceleration of a stationary soliton by a magnetic field gradient, the stabilization of a stationary droplet by a uniform control field in the absence of spin torque, and the ability to control the soliton's speed by use of a time-varying, spatially uniform external field. Soliton propagation distances approach 10 $\mu$m in low loss media, suggesting that droplet solitons could be viable information carriers in future spintronic applications, analogous to optical solitons in fiber optic communications., Comment: 7 pages, 6 figures

A novel type of solitary wave is predicted to form in spin torque oscillators when the free layer has a sufficiently large perpendicular anisotropy. In this structure, which is a dissipative version of the conservative droplet soliton originally studied in 1977 by Ivanov and Kosevich, spin torque counteracts the damping that would otherwise destroy the mode. Asymptotic methods are used to derive conditions on perpendicular anisotropy strength and applied current under which a dissipative droplet can be nucleated and sustained. Numerical methods are used to confirm the stability of the droplet against various perturbations that are likely in experiments, including tilting of the applied field, non-zero spin torque asymmetry, and non-trivial Oersted fields. Under certain conditions, the droplet experiences a drift instability in which it propagates away from the nanocontact and is then destroyed by damping., Comment: 15 pages, 12 figures

We measure the power spectral density of frequency fluctuations in nanocontact spin torque oscillators over time scales up to 50 ms. We use a mixer to convert oscillator signals ranging from 10 GHz to 40 GHz into a band near 70 MHz before digitizing the time domain waveform. We analyze the waveform using both zero crossing time stamps and a sliding Fourier transform, discuss the different limitations and advantages of these two methods, and combine them to obtain a frequency noise spectrum spanning more than five decades of Fourier frequency $f$. For devices having a free layer consisting of either a single Ni$_{\text{}80}$Fe$_{\text{}20}$ layer or a Co/Ni multilayer we find a frequency noise spectrum that is white at large $f$ and varies as \emph{$1/f$} at small $f$. The crossover frequency ranges from $\approx\unit[10^{4}]{Hz}$ to $\approx\unit[10^{6}]{Hz}$ and the $1/f$ component is stronger in the multilayer devices. Through actual and simulated spectrum analyzer measurements, we show that $1/f$ frequency noise causes both broadening and a change in shape of the oscillator's spectral line as measurement time increases. Our results indicate that the long term stability of spin torque oscillators cannot be accurately predicted from models based on thermal (white) noise sources.

We studied the microwave assisted magnetic reversal of 65 nm by 71 nm elliptical Ni80Fe20 nanomagnets. Hysteresis curves were measured by magneto-optical Kerr effect for a range of microwave frequencies and amplitudes. The coercive field Hc was reduced by 26% for an rf field of 0.08Hc when the microwave frequency coincided with the minimum of the experimentally determined ferromagnetic resonance frequency with varying dc field. The experimental results for the fractional reduction in Hc with rf field amplitude are in good agreement with numerical simulations for an array of interacting macrospins with a physically realistic shape anisotropy distribution

We measure oscillator phase from the zero crossings of the voltage vs. time waveform of a spin torque nanocontact oscillating in a vortex mode. The power spectrum of the phase noise varies with Fourier frequency $f$ as $1/f^2$, consistent with frequency fluctuations driven by a thermal source. The linewidth implied by phase noise alone is about 70 % of that measured using a spectrum analyzer. A phase-locked loop reduces the phase noise for frequencies within its 3 MHz bandwidth., Comment: 6 pages, 5 figures, supplementary material. Submitted to {Appl. Phys. Lett.}

A model of spin torque induced magnetization dynamics based upon semi-classical spin diffusion theory for a single layer nanocontact is presented. The model incorporates effects due to the current induced Oersted field and predicts the generation of a variety of spatially dependent, coherent, precessional magnetic wave structures. Directionally controllable collimated spin wave beams, vortex spiral waves, and localized standing waves are found to be excited by the interplay of the Oersted field and the orientation of an applied field. These fields act as a spin wave ``corral'' around the nanocontact that controls the propagation of spin waves in certain directions., Comment: 19 pages, 8 figures; added content, figure, and more references

A nonlinear model of spin-wave excitation involving a point contact in a thin ferromagnetic film that includes the Oersted magnetic field contribution is presented. We consider the case of an external dc field applied perpendicular to the film plane. The two-dimensional vectorial model reduces to an exact one-dimensional equation of motion. Large-amplitude vortex modes are computed, which represent a fundamental shift in the geometrical understanding of spin transfer nano-oscillators. Odd symmetry forces the magnetization to be pinned in the center of the point contact. Using the spin transfer efficiency as a single fitting parameter, the calculated dependence of frequency on current and contact size is in good agreement with recent experimental data. These vortex states are geometrically very different from previously computed cylindrical modes that exhibit even symmetry when the Oersted field is ignored., Comment: The authors have withdrawn this manuscript because the highly symmetric vortex mode has been found to be numerically unstable to 2D perturbations

A nonlinear model of spin wave excitation using a point contact in a thin ferromagnetic film is introduced. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the fully nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm. Simulations also predict a saturation and red shift of the frequency at currents large enough to invert the magnetization under the point contact. The theory is approximated by a cubic complex Ginzburg-Landau type equation. The mode's nonlinear frequency shift is found by use of perturbation techniques, whose results agree with those of direct numerical simulations., Comment: 5 pages, 4 figures, submitted to PRL

A time-resolved ferromagnetic resonance technique was used to investigate the magnetization dynamics of a 10 nm thin Permalloy film. The experiment consisted of a sequence of magnetic field pulses at a repetition rate equal to the magnetic systems resonance frequency. We compared data obtained by this technique with conventional pulsed inductive microwave magnetometry. The results for damping and frequency response obtained by these two different methods coincide in the limit of a small angle excitation. However, when applying large amplitude field pulses, the magnetization had a non-linear response. We speculate that one possible cause of the nonlinearity is related to self-amplification of incoherence, known as the Suhl instabilities., Comment: 23 pages, 8 figures, submitted to PRB

Spin-polarized dc electric current flowing into a magnetic layer can induce precession of the magnetization at a frequency that depends on current. We show that addition of an ac current to this dc bias current results in a frequency modulated (FM) spectral output, generating sidebands spaced at the modulation frequency. The sideband amplitudes and shift of the center frequency with drive amplitude are in good agreement with a nonlinear FM model that takes into account the nonlinear frequency-current relation generally induced by spin transfer. Single-domain simulations show that ac current modulates the cone angle of the magnetization precession, in turn modulating the frequency via the demagnetizing field. These results are promising for communications and signal processing applications of spin-transfer oscillators., Comment: 13 pages, 3 Figures

We have measured microwave frequency, current-driven magnetization dynamics in point contacts made to Co90Fe10/Cu/ Ni80Fe20 spin valves as a function of applied field strength and angle relative to the film plane. As the field direction is varied from parallel to nearly perpendicular, the device power output increases by roughly two orders of magnitude while the frequencies of the excitations decrease. For intermediate angles the excited frequency does not monotonically vary with applied current and also exhibits abrupt, current-dependent jumps. For certain ranges of current, and applied field strength and direction, the excitation linewidths decrease to a few megahertz, leading to quality factors over 18,000.

We have directly measured coherent high-frequency magnetization dynamics in ferromagnet films induced by a spin-polarized DC current. The precession frequency can be tuned over a range of several gigahertz, by varying the applied current. The frequencies of excitation also vary with applied field, resulting in a microwave oscillator that can be tuned from below 5 GHz to above 40 GHz. This novel method of inducing high-frequency dynamics yields oscillations having quality factors from 200 to 800. We compare our results with those from single-domain simulations of current-induced dynamics.

We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson linear model, but only within a distance s. If the local minimum is out from this distance, the particle evaporates through a refuse mechanism similar to the Kim-Kosterlitz nonlinear model. In d=1, the growth exponent beta, measured from the temporal behavior of roughness, indicates that in the coarse-grained limit, the linear term of the Kardar-Parisi-Zhang equation dominates in short times (low-roughness) and, in asymptotic times, the nonlinear term prevails. The crossover between linear and nonlinear behaviors occurs in a characteristic time t_c which only depends on the magnitude of the parameter s, related to the nonlinear term. In d=2, we find indications of a similar crossover, that is, logarithmic temporal behavior of roughness in short times and power law behavior in asymptotic times.

We introduce a model that simulates a kinetic roughening process with two kinds of particles: one follows the ballistic deposition (BD) kinetic and, the other, the restricted solid-on-solid (KK) kinetic. Both of these kinetics are in the universality class of the nonlinear KPZ equation, but the BD kinetic has a positive nonlinear constant while the KK kinetic has a negative one. In our model, called BD-KK model, we assign the probabilities p and (1-p) to the KK and BD kinetics, respectively. For a specific value of p, the system behaves as a quasi linear model and the up-down symmetry is recuperated. We show that nonlinearities of odd-order are relevant in these low nonlinear limit., Comment: 10 pages; 4 figures