arXiv subjects

Jürgen Lindner

Publications and source records attributed to Jürgen Lindner.

At least 37 records · Page 2Linked to original sources

arXiv2022

Finite-element dynamic-matrix approach for propagating spin waves: Extension to mono- and multilayers of arbitrary spacing and thickness

In our recent work [AIP Adv. 11, 095006], we presented an efficient numerical method to compute dispersions and spatial mode profiles of spin waves propagating in waveguides with translationally invariant equilibrium magnetization. Using a finite-element method (FEM) allowed to model two-dimensional waveguide cross sections of arbitrary shape but only finite size. Here, we extend our FEM propagating-wave dynamic-matrix approach from finite waveguides to the important practical cases of infinitely-extended mono- and multilayers of arbitrary spacing and thickness. To obtain the mode profiles and frequencies, the linearized equation of motion of magnetization is solved as an eigenvalue problem only on a one-dimensional line-trace mesh, defined along the normal direction of the layers. Being an important contribution in multilayer systems, we introduce interlayer-exchange interaction into our FEM approach. With the calculation of dynamic dipolar fields being the main focus of this paper, we also extend the previously presented plane-wave Fredkin-Koehler method to calculate the dipolar potential of spin waves in infinite layers. The major benefit of this method is that it avoids the discretization of any non-magnetic material, such as non-magnetic spacers in multilayers. Therefore, the computational effort becomes completely independent on the spacer thicknesses. Furthermore, it keeps the resulting discretized eigenvalue problem sparse, which therefore, inherits a comparably low arithmetic complexity. As a validation of our method (implemented into the open-source finite-element micromagnetic package TetraX), we present results for various systems and compare them with theoretical predictions as well as with established finite-difference numerical methods. We believe this method offers an efficient and versatile tool to calculate spin-wave dispersions in layered magnetic systems.

cond-mat.mes-hall↗

arXiv2022

Curvilinear spin-wave dynamics beyond the thin-shell approximation: Magnetic nanotubes as a case study

Surface curvature of magnetic systems can lead to many static and dynamic effects which are not present in flat systems of the same material. These emergent magnetochiral effects can lead to frequency nonreciprocity of spin waves, which has been shown to be a bulk effect of dipolar origin and is related to a curvature-induced symmetry breaking in the magnetic volume charges. So far, such effects have been investigated theoretically mostly for thin shells, where the spatial profiles of the spin waves can be assumed to be homogeneous along the thickness. Here, using a finite-element dynamic-matrix approach, we investigate the transition of the spin-wave spectrum from thin to thick curvilinear shells, at the example of magnetic nanotubes in the vortex state. With increasing thickness, we observe the appearance of higher-order radial modes which are strongly hybridized and resemble the perpendicular-standing-waves (PSSWs) in flat films. Along with an increasing dispersion asymmetry, we uncover the curvature-induced non-reciprocity of the mode profiles. This is explained in a very simple picture general for thick curvilinear shells, considering the inhomogeneity of the emergent geometric volume charges along the thickness of the shell. Such curvature-induced mode-profile asymmetry also leads to non-reciprocal hybridization which can facilitate unidirectional spin-wave propagation. With that, we also show how curvature allows for nonlinear three-wave splitting of a higher-order radial mode into secondary modes which can also propagate unidirectionally. We believe that our study provides a significant contribution to the understanding of the spin-wave dynamics in curvilinear magnetic systems, but also advertises these for novel magnonic applications.

cond-mat.mes-hall↗

arXiv2022

Control and tunability of magnetic bubble states in multilayers with strong perpendicular magnetic anisotropy at ambient conditions

The reversal of magnetic bubble helicity through topologically trivial transient states provides an additional degree of freedom that promises the development of multidimensional magnetic memories. A key requirement for this concept is the stabilization of bubble states at ambient conditions on application-compatible substrates. In the present work we demonstrate a stabilization routine for remanent bubble states in high perpendicular magnetic anisotropy [(Co(0.44\,nm)/Pt(0.7\,nm)]$_X$, X = 48, 100, 150 multilayers on Si/SiO$_2$ substrates by exploring the effect of external magnetic fields ($H_\mathrm{m}$) of different strength and angles ($θ$) with respect to the film surface normal. By systematic variation of these two parameters, we demonstrate that remanent bubble density and mean bubble diameter can be carefully tuned and optimized for each sample. Our protocol based on magnetometry only reveals the densest remanent bubble states at $H_\mathrm{m} = 0.87 H_\mathrm{s}$ ($H_\mathrm{s}$ is the magnetic saturation field) and $θ=60^\circ - 75^\circ$ for all $X$ with a maximum of 3736 domains/100 $μ$m$^2$ for the X = 48 sample. The experimental observations are supported by micromagnetic simulations taking into account the nanoscale lateral grain structure of multilayers synthesized by magnetron sputter deposition, and thus helping understand the different density of the bubble states found in these systems.

cond-mat.mtrl-sci↗

arXiv2021

Symmetry- and curvature effects on spin waves in vortex-state hexagonal nanotubes

Analytic and numerical studies on curved magnetic nano-objects predict numerous exciting effects that can be referred to as magneto-chiral effects, which do not originate from intrinsic Dzyaloshinskii-Moriya interaction or interface-induced anisotropies. In constrast, these chiral effects stem from isotropic exchange or dipole-dipole interaction, present in all magnetic materials, which acquire asymmetric contributions in case of curved geometry of the specimen. As a result, for example, the spin-wave dispersion in round magnetic nanotubes becomes asymmetric, namely spin waves of the same frequency propagating in opposite directions along the nanotube exhibit different wavelenghts. Here, using time-resolved scanning transmission X-ray microscopy experiments, standard micromagntic simulations and a dynamic-matrix approach, we show that the spin-wave spectrum undergoes additional drastic changes when transitioning from a continuous to a discrete rotational symmetry, i.e. from round to hexagonal nanotubes, which are much easier to fabricate. The polygonal shape introduces localization of the modes both to the sharp, highly curved corners and flat edges. Moreover, due to the discrete rotational symmetry, the degenerate nature of the modes with azimuthal wave vectors known from round tubes is partly lifted, resulting in singlet and duplet modes. For comparison with our experiments, we calculate the microwave absorption from the numerically obtained mode profiles which shows that a dedicated antenna design is paramount for magnonic applications in 3D nano-structures. To our knowledge these are the first experiments directly showing real space spin-wave propagation in 3D nano objects.

cond-mat.mes-hall↗

arXiv2021

Control of stripe domain wall magnetization in perpendicular anisotropy multilayers

We report on the controlled switching of domain wall (DW) magnetization in aligned stripe domain structures, stabilized in [Co (0.44 nm)/Pt (0.7 nm)]$_X$ ($X = 48$, 100, 150) multilayers with perpendicular magnetic anisotropy. The switching process, induced by an external magnetic field, is monitored by measuring the evolution of the in-plane magnetization. % We show that the remanent in-plane magnetization originates from the polarization of the Bloch-type DWs. With micromagnetic simulations, we reveal that the reversal of the DW polarization is the result of the emergence and collapse of horizontal Bloch lines within the DWs at particular strengths of the external magnetic field, applied opposite to the DW polarization. Our findings are relevant for DW-based magnonics and bubble skyrmion applications in magnetic multilayers.

physics.app-ph↗

arXiv2020

Dimensional crossover in spin Hall oscillators

Auto-oscillations of magnetization driven by direct spin current have been previously observed in multiple quasi-zero-dimensional (0D) ferromagnetic systems such as nanomagnets and nanocontacts. Recently, it was shown that pure spin Hall current can excite coherent auto-oscillatory dynamics in quasi-one-dimensional (1D) ferromagnetic nanowires but not in quasi-two-dimensional (2D) ferromagnetic films. Here we study the 1D to 2D dimensional crossover of current-driven magnetization dynamics in wire-based Pt/$\mathrm{Ni}_{80}\mathrm{Fe}_{20}$ bilayer spin Hall oscillators via varying the wire width. We find that increasing the wire width results in an increase of the number of excited auto-oscillatory modes accompanied by a decrease of the amplitude and coherence of each mode. We also observe a crossover from a hard to a soft onset of the auto-oscillations with increasing the wire width. The amplitude of auto-oscillations rapidly decreases with increasing temperature suggesting that interactions of the phase-coherent auto-oscillatory modes with incoherent thermal magnons plays an important role in suppression of the auto-oscillatory dynamics. Our measurements set the upper limit on the dimensions of an individual spin Hall oscillator and elucidate the mechanisms leading to suppression of coherent auto-oscillations with increasing oscillator size.

cond-mat.mes-hall↗

arXiv2020

Helium Ion Microscopy for Reduced Spin Orbit Torque Switching Currents

Spin orbit torque driven switching is a favourable way to manipulate nanoscale magnetic objects for both memory and wireless communication devices. The critical current required to switch from one magnetic state to another depends on the geometry and the intrinsic properties of the materials used, which are difficult to control locally. Here we demonstrate how focused helium ion beam irradiation can modulate the local magnetic anisotropy of a Co thin film at the microscopic scale. Real-time in-situ characterisation using the anomalous Hall effect showed up to an order of magnitude reduction of the magnetic anisotropy under irradiation, and using this, multi-level switching is demonstrated. The result is that spin-switching current densities, down to 800 kA cm$^{-2}$, can be achieved on predetermined areas of the film, without the need for lithography. The ability to vary critical currents spatially has implications not only for storage elements, but also neuromorphic and probabilistic computing.

cond-mat.mes-hall↗

arXiv2020

Experimental observation of the curvature-induced asymmetric spin-wave dispersion in hexagonal nanotubes

Theoretical and numerical studies on curved magnetic nano-objects predict numerous exciting effects that can be referred to as magneto-chiral effects, which do not originate from the intrinsic Dzyaloshinskii-Moriya interaction or surface-induced anisotropies. The origin of these chiral effects is the isotropic exchange or the dipole-dipole interaction present in all magnetic materials but renormalized by the curvature. Here, we demonstrate experimentally that curvature induced effects originating from the dipole-dipole interaction are directly observable by measuring spin-wave propagation in magnetic nanotubes with hexagonal cross section using time resolved scanning transmission X-ray microscopy. We show that the dispersion relation is asymmetric upon reversal of the wave vector when the propagation direction is perpendicular to the static magnetization. Therefore counter-propagating spin waves of the same frequency exhibit different wavelenghts. Hexagonal nanotubes have a complex dispersion, resulting from spin-wave modes localised to the flat facets or to the extremely curved regions between the facets. The dispersion relations obtained experimentally and from micromagnetic simulations are in good agreement. %The asymmetric spin-wave transport is present for all modes, promoting hexagonal nanotubes for magnonic applications. These results show that spin-wave transport is possible in 3D, and that the dipole-dipole induced magneto-chiral effects are significant.

cond-mat.mes-hall↗

arXiv2020

Ion-Irradiation-Induced Cobalt/Cobalt Oxide Heterostructures: Printing 3D Interfaces

Interfaces separating ferromagnetic (FM) layers from non-ferromagnetic layers offer unique properties due to spin-orbit coupling and symmetry breaking, yielding effects such as exchange bias, perpendicular magnetic anisotropy, spin-pumping, spin-transfer torques, conversion between charge and spin currents and vice-versa. These interfacial phenomena play crucial roles for magnetic data storage and transfer applications, which require forming FM nano-structures embedded in non-ferromagnetic matrices. Here, we investigate the possiblity of creating such nano-structures by ion-irradiation. We study the effect of lateral confinement on the ion-irradiation-induced reduction of non-magnetic metal oxides (e.g., antiferro- or paramagnetic) to form ferromagnetic metals. Our findings are later exploited to form 3-dimensional magnetic interfaces between Co, CoO and Pt by spatially-selective irradiation of CoO/Pt multilayers. We demonstrate that the mechanical displacement of the O atoms plays a crucial role during the reduction from insulating, non-ferromagnetic cobalt oxides to metallic cobalt. Metallic cobalt yields both perpendicular magnetic anisotropy in the generated Co/Pt nano-structures, and, at low temperatures, exchange bias at vertical interfaces between Co and CoO. If pushed to the limit of ion-irradiation technology, this approach could, in principle, enable the creation of densely-packed, atomic scale ferromagnetic point-contact spin-torque oscillator (STO) networks, or conductive channels for current-confined-path based current perpendicular-to-plane giant magnetoresistance read-heads.

cond-mat.mtrl-sci↗

arXiv2019

Magnetic response of FeRh to static and dynamic disorder

Changes of the magnetic and crystal structure on the microscopic scale in 40 nm FeRh thin films have been applied to investigate the phenomena of a disorder induced ferromagnetism at room temperature initiated through light ion-irradiation with fluences up to 0.125 Ne$^+$/nm$^{-2}$. Magnetometry shows an increase of magnetic ordering at low temperatures and a decrease of the transition temperature combined with a broadening of the hysteresis with rising ion fluence. $^{57}$Fe Mössbauer spectroscopy reveals the occurrence of an additional magnetic contributions with an hyperfine splitting of 27.2 T - identical to that of ferromagnetic B2-FeRh. The appearance of an anti-site Fe-contribution can be assumed to be lower than 0.6 Fe-at%, indicating that no change of the chemical composition is evident. The investigation of the local structure shows an increase of the static mean square relative displacement determined by X-ray absorption fine structure spectroscopy, while an increase of the defect-concentration has been determined by positron annihilation spectroscopy. From the changes of the microscopic magnetic structure a similarity between the temperature induced and the structural disorder induced ferromagnetic phase can be observed. These findings emphasize the relationship between magnetic ordering and the microscopic defect structure in FeRh.

cond-mat.mtrl-sci↗

arXiv2019

Magneto-structural correlations in a systematically disordered B2 lattice

Ferromagnetism in certain B2 ordered alloys such as Fe$_{60}$Al$_{40}$ can be switched on, and tuned, via antisite disordering of the atomic arrangement. The disordering is accompanied by a $\sim$1 % increase in the lattice parameter. Here we performed a systematic disordering of B2 Fe$_{60}$Al$_{40}$ thin films, and obtained correlations between the order parameter ($S$), lattice parameter ($a_0$), and the induced saturation magnetization ($M_{s}$). As the lattice is gradually disordered, a critical point occurs at 1-$S$=0.6 and $a_0$=291 pm, where a sharp increase of the $M_{s}$ is observed. DFT calculations suggest that below the critical point the system magnetically behaves as it would still be fully ordered, whereas above, it is largely the increase of $a_0$ in the disordered state that determines the $M_{s}$. The insights obtained here can be useful for achieving tailored magnetic properties in alloys through disordering.

cond-mat.mtrl-sci↗

arXiv2019

Thermally driven two-magnet nano-oscillator with large spin-charge conversion

Next-generation spintronic applications require material properties that can be hardly met by one material candidate. Here we demonstrate that by combining insulating and metallic magnets, enhanced spin-charge conversion and energy-efficient thermal spin currents can be realized. We develop a nanowire device consisting of an yttrium iron garnet and permalloy bi-layer. An interfacial temperature gradient drives the nanowire magnetization into auto-oscillations at gigahertz frequencies. Interfacial spin coupling and magnetoresistance of the permalloy layer translate spin dynamics into sizable microwave signals. The results show prospect for energy-efficient spintronic devices and present an experimental realization of magnon condensation in a heterogeneous magnetic system.

cond-mat.mes-hall↗

arXiv2019

Spin-transfer dynamics in MgO-based magnetic tunnel junctions with an out-of-plane magnetized free layer and an in-plane polarizer

Here, we present an analytical and numerical model describing the magnetization dynamics in MgO-based spin-torque nano-oscillators with an in-plane magnetized polarizer and an out-of-plane free layer. We introduce the spin-transfer torque asymmetry by considering the cosine angular dependence of the resistance between the two magnetic layers in the stack. For the analytical solution, dynamics are determined by assuming a circular precession trajectory around the direction perpendicular to the plane, as set by the effective field, and calculating the energy integral over a single precession period. In a more realistic approach, we include the bias dependence of the tunnel magnetoresistance, which is assumed empirically to be a piecewise linear function of the applied voltage. The dynamical states are found by solving the stability condition for the Jacobian matrix for out-of-plane static states. We find that the bias dependence of the tunnel magnetoresistance, which is an inseparable effect in every tunnel junction, exhibits drastic impact on the spin-torque nano-oscillator phase diagram, mainly by increasing the critical current for dynamics and quenching the oscillations at high currents. The results are in good agreement with our experimental data published elsewhere.

cond-mat.mes-hall↗

arXiv2018

Spin-Wave Modes in Transition from a Thin Film to a Full Magnonic Crystal

Spin-wave modes are studied under the gradual transition from a flat thin film to a 'full' (one-dimensional) magnonic crystal. For this purpose, the surface of a pre-patterned 36.8 nm thin permalloy film was sequentially ion milled resulting in magnonic hybrid structures, referred to as surface-modulated magnonic crystals, with increasing modulation depth. After each etching step, ferromagnetic resonance measurements were performed yielding the spin-wave resonance modes in backward-volume and Damon-Eshbach geometry. The spin-wave spectra of these hybrid systems reveal an even larger variety of spin-wave states compared to the 'full' magnonic crystal. The measurements are corroborated by quasi-analytical theory and micromagnetic simulations in order to study the changing spin-wave mode character employing spin-wave mode profiles. In backward-volume geometry, a gradual transition from the uniform mode in the film limit to a fundamental mode in the thin part of the magnonic crystal was observed. Equivalently, the first and the second film modes are transform into a center and an edge mode of the thick part of the magnonic crystal. Simple transition rules from the $n^{\mathrm{th}}$ film mode to the $m^{\mathrm{th}}$ mode in the 'full' magnonic crystal are formulated unraveling the complex mode structure particularly in the backward-volume geometry. An analogous analysis was performed in the Damon-Eshbach geometry.

cond-mat.mes-hall↗

arXiv2018

Symmetry and localization properties of defect modes in magnonic superlattices

Symmetry and localization properties of defect modes of a one-dimensional bi-component magnonic superlattice are theoretically studied. The magnonic superlattice can be seen as a periodic array of nanostripes, where stripes with different width, termed as defect stripes, are periodically introduced. By controlling the geometry of the defect stripes, a transition from dispersive to practically flat spin-wave defect modes can be observed inside the magnonic band gaps. It is shown that the spin-wave profile of the defect modes can be either symmetric or antisymmetric, depending on the geometry of the defect. Due to the localized character of the defect modes, a particular magnonic superlattice is proposed, wherein the excitation of either symmetric or antisymmetric flat magnonic modes is enabled at the same time. Also, it is demonstrated that the relative frequency position of the antisymmetric mode inside the band gap does not significantly change with the application of an external field, while the symmetric modes move to the edges of the frequency band gaps. The results are complemented by numerical simulations, where an excellent agreement is observed between both methods. The proposed theory allows exploring different ways to control the dynamic properties of the defect modes in metamaterial magnonic superlattices, which can be useful for applications on multifunctional microwave devices operating over a broad frequency range.

cond-mat.mes-hall↗

arXiv2018

Zero-field dynamics stabilized by in-plane shape anisotropy in MgO-based spin-torque oscillators

Here we demonstrate numerically that shape anisotropy in MgO-based spin-torque nano-oscillators consisting of an out-of-plane magnetized free layer and an in-plane polarizer is necessary to stabilize out-of-plane magnetization precession without the need of external magnetic fields. As the in-plane anisotropy is increased, a gradual tilting of the magnetization towards the in-plane easy direction is introduced, favouring zero-field dynamics over static in-plane states. Above a critical value, zero-field dynamics are no longer observed. The optimum ratio of in-plane shape to out-of-plane uniaxial anisotropy, for which large angle out-of-plane zero-field dynamics occur within the widest current range, is reported.

cond-mat.mtrl-sci↗

arXiv2018

Magnetocrystalline anisotropy and exchange probed by high-field anomalous Hall effect in fully-compensated half-metallic Mn2RuxGa thin films

Magnetotransport is investigated in thin films of the half-metallic ferrimagnet Mn$_2$Ru$_x$Ga in pulsed magnetic fields of up to 58 T. A non-vanishing Hall signal is observed over a broad temperature range, spanning the compensation temperature 155 K, where the net magnetic moment is strictly zero, the anomalous Hall conductivity is 6673 $Ω^{-1}.m^{-1}$ and the coercivity exceeds 9 T. Molecular field modelling is used to determine the intra- and inter-sublattice exchange constants and from the spin-flop transition we infer the anisotropy of the electrically active sublattice to be 216 kJ/m$^3$ and predict the magnetic resonances frequencies. Exchange and anisotropy are comparable and hard-axis applied magnetic fields result in a tilting of the magnetic moments from their collinear ground state. Our analysis is applicable to collinear ferrimagnetic half-metal systems.

cond-mat.mtrl-sci↗

arXiv2018

Injection locking of multiple auto-oscillation modes in a tapered nanowire spin Hall oscillator

Spin Hall oscillators (SHO) are promising candidates for the generation, detection and amplification of high frequency signals, that are tunable through a wide range of operating frequencies. They offer to be read out electrically, magnetically and optically in combination with a simple bilayer design. Here, we experimentally study the spatial dependence and spectral properties of auto-oscillations in SHO devices based on Pt(7 nm)/\ Ni$_{\mathrm{80}}$Fe$_{\mathrm{20}}$(5 nm) tapered nanowires. Using Brillouin light scattering microscopy, we observe two individual self-localized spin-wave bullets that oscillate at two distinct frequencies (5.2 GHz and 5.45 GHz) and are localized at different positions separated by about 750 nm within the SHO. This state of a tapered SHO has been predicted by a Ginzburg-Landau auto-oscillator model, but not yet been directly confirmed experimentally. We demonstrate that the observed bullets can be individually synchronized to external microwave signals, leading to a frequency entrainment, linewidth reduction and increase in oscillation amplitude for the bullet that is selected by the microwave frequency. At the same time, the amplitude of other parasitic modes decreases, which promotes the single-mode operation of the SHO. Finally, the synchronization of the spin-wave bullets is studied as a function of the microwave power. We believe that our findings promote the realization of extended spin Hall oscillators accomodating several distinct spin-wave bullets, that jointly cover an extended range of tunability.

cond-mat.mes-hall↗