We report the results of a set of simulations of small arrays of submicron ferromagnetic particles. The actions of dipolar and exchange interactions were qualitatively investigated by analysing the ferromagnetic resonance spectra at 9.37 GHz resulting from the magnetization response of con- nected and unconnected particles in the array as a function of the applied dc magnetic field. We find that the magnetization precession movement (at resonance) observed in individual particles in the array presents a distinctive behaviour (an amplitude mismatch) in comparison to isolated, one-particle reference simulations, a result that we attribute to the action of interparticle dipolar couplings. Exchange interactions appear to have an important role in modifying the spectra of connected particles, even through a small contact surface.
Nanostructured Fe dots were prepared on antiferromagnetic FeF2 thin films and investigated by magneto-optical Kerr effect (MOKE). We studied the influence of dot sizes on the magnetic hysteresis and compared the result with both continuous thin film bilayers and nanostructured Fe/FeF2 pillars. Hysteresis loops were measured at temperatures below and above (10 and 90 K, respectively) the Neel temperature of the antiferromagnet. A vortex state is found for dots of 300 nm diameter, where the exchange bias field is reduced compared to larger dot system and the continuous bilayer. Micromagnetic sim…
In this work, a self-consistent thermodynamic approach to micromagnetism is presented. The magnetic degrees of freedom are modeled using the Landau-Lifshitz-Baryakhtar theory, that separates the different contributions to the magnetic damping, and thereby allows them to be coupled to the electron and phonon systems in a self-consistent way. We show that this model can quantitatively reproduce ultrafast magnetization dynamics in Nickel.
We explore the behavior of periodic arrays of magnetic nanowires by micromagnetic simulations using the Nmag modeling package. A large number of modeling studies on such arrays of nanowires have been performed using finite size models. We show that these finite size micromagnetic descriptions can only be used in specific situations. We perform a systematic study of more or less dense 1D and 2D arrays of nanowires using either finite size or infinite size models and we show that finite size models fail to capture some of the features of real infinite systems. We show that that the mean field mo…
In our present publication we will continue studying the effects of the magnetostatic energy on the magnetization behavior of FMSMAs recently started in some our publications. Our method is based on the direct minimization of our new micromagnetic free energy model of FMSMAs taking into account both the magnetic anisotropy energy and the magnetostatic energy contributions associated with the laminated two-variant twin microstructure. Here, our special interest is to investigate a distribution of local magnetizations within both twin variants, their orientation and their dependence on the exter…
We investigate the magnetic thermal noise in magnetic nanowires with and without a domain wall by employing micromagnetic simulations. The magnetic thermal noise due to random thermal fluctuation fields gives important physical quantities related with the magnetic susceptibility. We find that the resonance frequency of a domain wall is distinguishable from one of a magnetic domain itself. For the single domain without a domain wall, the resonance frequency is well described by the Kittel's formula considering a ferromagnetic specimen as a simple ellipsoid with demagnetizing factors for various…
A three-dimensional phase-field model is proposed for simulating the magnetic martensitic phase transformation. The model considers a paramagnetic cubic austenite to ferromagnetic tetragonal martensite transition, as it occurs in magnetic Heusler alloys like Ni2 MnGa, and is based on a Landau 2-3-4 polynomial with temperature dependent coefficients. The paramagnetic-ferromagnetic transition is recaptured by interpolating the micromagnetic energy as a function of the order parameter for the ferroelastic domains. The model is numerically implemented in real space by finite element (FE) method. F…
We report on the determination of micromagnetic parameters of epilayers of the ferromagnetic semiconductor (Ga,Mn)As, which has easy axis in the sample plane, and (Ga,Mn)(As,P) which has easy axis perpendicular to the sample plane. We use an optical analog of ferromagnetic resonance where the laser-pulse-induced precession of magnetization is measured directly in the time domain. By the analysis of a single set of pump-and-probe magneto-optical data we determined the magnetic anisotropy fields, the spin stiffness and the Gilbert damping constant in these two materials. We show that incorporati…
(Ga,Mn)As is at the forefront of research exploring the synergy of magnetism with the physics and technology of semiconductors, and has led to discoveries of new spin-dependent phenomena and functionalities applicable to a wide range of material systems. Its recognition and utility as an ideal model material for spintronics research has been undermined by the large scatter in reported semiconducting doping trends and micromagnetic parameters. In this paper we establish these basic material characteristics by individually optimizing the highly non-equilibrium synthesis for each Mn-doping level …
Ferri-/ferromagnetic exchange coupled composites are promising candidates for bit patterned media because of the ability to control the magnetic properties of the ferrimagnet by its composition. A micromagnetic model for the bilayer system is presented where we also incorporate the microstructural features of both layers. Micromagnetic finite element simulations are performed to investigate the magnetization reversal behaviour of such media. By adding the exchange coupled ferrimagnet to the ferromagnet, the switching field could be reduced by up to $40\,\%$ and also the switching field distrib…
The magnetic domain structure and magnetic properties of a ferromagnetic (Ga,Mn)As epilayer with perpendicular magnetic easy-axis are investigated. We show that, despite strong hysteresis, domain theory at thermodynamical equilibrium can be used to determine the micromagnetic parameters. Combining magneto-optical Kerr microscopy, magnetometry and ferromagnetic resonance measurements, we obtain the characteristic parameter for magnetic domains $λ_c$, the domain wall width and specific energy, and the spin stiffness constant as a function of temperature. The nucleation barrier for magnetization …
Spin relaxation in the ultrathin metallic films of stacked microelectronic devices is investigated on the basis of a modified Landau-Lifshitz equation of micromagnetic dynamics in which the damping torque is treated as originating from the coupling between precessing magnetization-vector and the introduced stress-tensors of intrinsic and extrinsic magnetic anisotropy. Particular attention is given to the time of exponential relaxation and ferromagnetic resonance linewidth which are derived in analytic form from the equation of magnetization energy loss and Gabor uncertainty relation between th…
We use the continuum micromagnetic framework to derive the formulas for compact skyrmion lifetime due to thermal noise in ultrathin ferromagnetic films with relatively weak interfacial Dzyaloshinskii-Moriya interaction. In the absence of a saddle point connecting the skyrmion solution to the ferromagnetic state, we interpret the skyrmion collapse event as ``capture by an absorber'' at microscale. This yields an explicit Arrhenius collapse rate with both the barrier height and the prefactor as functions of all the material parameters, as well as the dynamical paths to collapse.
The magnetic properties of ferromagnetic thin films down to the nanoscale are ruled by the exchange stiffness, anisotropies and the effects of magnetic fields. As surfaces break inversion symmetry, an additional effective chiral exchange is omnipresent in any magnetic nanostructure. These so-called Dzyaloshinskii-Moriya interactions (DMI) affect all inhomogeneous magnetic states either subtly or spectacularly. E.g., DMIs cause a chirality selection of the rotation sense and can fix the local rotation axis for the magnetization in domain walls (DW). But, they can stabilize also entirely differe…
We have studied current-driven domain wall motion in modified Ga_0.95Mn_0.05As Hall bar structures with perpendicular anisotropy by using spatially resolved Polar Magneto-Optical Kerr Effect Microscopy and micromagnetic simulation. Regardless of the initial magnetic configuration, the domain wall propagates in the opposite direction to the current with critical current of 1~2x10^5A/cm^2. Considering the spin transfer torque term as well as various effective magnetic field terms, the micromagnetic simulation results are consistent with the experimental results. Our simulated and experimental re…
The attainability of modification of the apparent magnetic anisotropy in (III,Mn)V ferromagnetic semiconductors is probed by means of the finite-elements-based modelling. The most representative case of (Ga,Mn)As and its in-plane uniaxial anisotropy is investigated. The hysteresis loops of the continuous films of a ferromagnetic semiconductor as well as films structured with the elliptic antidots are modelled for various eccentricity, orientation, and separation of the anti dots. The effect of anti-dots on the magnetic anisotropy is confirmed but overall is found to be very weak. The subsequen…
We study the dynamics of flat circular permalloy nanomagnets for 1.) magnetic vortex and 2.) single-domain configurations, using micromagnetic simulation. Dynamical studies for isolated vortex structures show that both the vorticity and the central polarity of the out-of-plane component can be switched fast (50-100 ps) and independently. Micromagnetic simulations of the switching process in thin cylindrical Permalloy (Py) nanoparticles with an initial stable single-domain state show nearly homogeneous single-domain behaviour followed by excitation of spin waves.
We present a micromagnetic approach to exchange bias (EB) in ferromagnetic (FM)/antiferromagnetic (AFM) thin film systems with a small number of irreversible interfacial magnetic moments. We express the exchange bias field $H_{EB}$ in terms of fundamental micromagnetic length scale---the exchange length $l_{ex}$. The benefit from this approach is a better separation of a term related to FM layer from a term related to FM/AFM coupling at interfaces. Using this approach we estimate the highest limit of $H_{EB}$ in real FM/AFM systems.
We report a time resolved imaging and micromagnetic simulation study of the relaxation dynamics of a magnetic vortex in the non-linear regime. We use time-resolved photoemission electron microscopy and micromagnetic calculations to examine the emergence of non-linear vortex dynamics in patterned Ni80Fe20 disks in the limit of long field pulses. We show for core shifts beyond ~20-25% of the disk radius, the initial motion is characterized by distortions of the vortex, a transient cross-tie wall state, and instabilities in the core polarization that influence the core trajectories.
We present a new approach to infer the surface density of magnetic moments $I_s$ in ultrathin ferromagnetic films with perpendicular anisotropy. It relies on quantitative stray field measurements with an atomic-size magnetometer based on the nitrogen-vacancy center in diamond. The method is applied to microstructures patterned in a 1-nm-thick film of CoFeB. We report measurements of $I_s$ with a few percent uncertainty and a spatial resolution in the range of $(100$ nm)$^2$, an improvement by several orders of magnitude over existing methods. As an example of application, we measure the modifi…
This paper presents the results of simulations of the magnetization field {\it ac} response (at $2$ to $12$ GHz) of various submicron ferrite particles (cylindrical dots). The ferrites in the present simulations have the spinel structure, expressed here by M$_{1-n}$Zn$_{n}$Fe$_2$O$_4$ (where M stands for a divalent metal), and the parameters chosen were the following: (a) for $n=0$: M = \{ Fe, Mn, Co, Ni, Mg, Cu \}; (b) for $n=0.1$: M = \{ Fe, Mg \} (mixed ferrites). These runs represent full 3D micromagnetic (one-particle) ferrite simulations. We find evidences of confined spin waves in all s…
We present a comprehensive theoretical and experimental study of voltage-controlled standing spin waves resonance (SSWR) in PMN-PT/NiFe multiferroic heterostructures patterned into microstrips. A spin-diode technique was used to observe ferromagnetic resonance (FMR) mode and SSWR in NiFe strip mechanically coupled with a piezoelectric substrate. Application of an electric field to a PMNPT creates a strain in permalloy and thus shifts the FMR and SSWR fields due to the magnetostriction effect. The experimental results are compared with micromagnetic simulations and a good agreement between them…
Further development of a previously introduced method for numerically simulating magnetic spin waves is presented. Together with significant improvements in speed, the method now allows one to calculate the energy absorbed by the various modes excited by a position- and time-dependent H1 field in a ferromagnetic body of arbitrary shape in the presence of a (uniform or non uniform) static H0 field as well as the internal exchange and anisotropy fields. The method is applied to the case of the single vortex state in a thin disc, a ring, and various square slabs, for which the absorption spectra …
By means of micromagnetic spin dynamics calculations, a quantitative calculation is carried out to explore the mechanism of exchange bias (EB) in ferromagnetic (FM)/compensated antiferromagnetic (AFM) bilayers. The antiferromagnets with low and high Neel temperatures have been both considered, and the crossover from negative to positive EB is found only in the case with low Neel temperature. We propose that the mechanism of EB in FM/compensated AFM bilayers is due to the symmetry broken of AFM that yields some net ferromagnetic components.
We investigate the spin dynamics including Gilbert damping in the ferromagnetic nanowire arrays. We have measured the ferromagnetic resonance of ferromagnetic nanowire arrays using vector-network analyzer ferromagnetic resonance (VNA-FMR) and analyzed the results with the micromagnetic simulations. We find excellent agreement between the experimental VNA-FMR spectra and micromagnetic simulations result for various applied magnetic fields. We find that the demagnetization factor for longitudinal conditions, Nz (Ny) increases (decreases) as decreasing the nanowire width in the micromagnetic simu…
We report the experimental observation of magnetic skyrmion-like states in patterned ferromagnetic nanostructures consisting of perpendicular magnetized Co/Pt multilayer film exchange coupled with Co nanodisks in vortex state. The magnetic force microscopy and micromagnetic simulations show that depending on the magnitude of Co/Pt perpendicular anisotropy in these systems two different modes of skyrmion formation are realized.
We present a microscopic theory of the long-wavelength magnetic properties of the ferromagnetic diluted magnetic semiconductor (Ga,Mn)As. Details of the host semiconductor band structure, described by a six-band Kohn-Luttinger Hamiltonian, are taken into account. We relate our quantum-mechanical calculation to the classical micromagnetic energy functional and determine anisotropy energies and exchange constants. We find that the exchange constant is substantially enhanced compared to the case of a parabolic heavy-hole-band model.
The current-induced motion of a domain wall in a semicircle nanowire with applied Zeeman field is investigated. Starting from a micromagnetic model we derive an analytical solution which characterizes the domain-wall motion as a harmonic oscillation. This solution relates the micromagnetic material parameters with the dynamical characteristics of a harmonic oscillator, i.e., domain-wall mass, resonance frequency, damping constant, and force acting on the wall. For wires with strong curvature the dipole moment of the wall as well as its geometry influence the eigenmodes of the oscillator. Based…
We derive an equilibrium statistical theory for the macroscopic description of a ferromagnetic material at positive finite temperatures. Our formulation describes the most-probable equilibrium macrostates that yield a coherent deterministic large-scale picture varying at the size of the domain, as well as it captures the effect of random spin fluctuations caused by the thermal noise. We discuss connections of the proposed formulation to the Landau-Lifschitz theory and to the studies of domain formation based on Monte Carlo lattice simulations.
The anisotropic magnetoresistance (AMR) in thin permalloy strips was calculated at each steps during magnetization by the finite element method. The magnetization at equilibrium under different external fields was obtained by micromagnetic simulations, while the resistance with different magnetization was obtained by solving the Poisson equations iteratively until self-consistence. We find that the relation between magnetization and AMR deviates from the Stoner-Wohlfarth prediction when the magnetization is reduced from saturation. The reason is that the demagnetization is not necessarily from…
Recently a significant interest in ferromagnetic curved thin films has appeared. In particular, thin spherical shells are currently of great interest due to their capability to support skyrmion solutions which can be stabilized by curvature effects only, in contrast to the planar case where the Dzyaloshinskii-Moriya interaction is required. This paper aims to a $Γ$-asymptotic analysis of the micromagnetic energy functional, when the shell is generated, like in the case of a sphere, by a bounded, convex and smooth surface.
This paper is devoted to numerical simulations of the magnetization dynamics driven by a spin-polarized current in extended ferromagnetic multilayers when a point-contact setup is used. We present (i) detailed analysis of methodological problems arising by such simulations and (ii) physical results obtained on a system similar to that studied in Rippard et al., Phys. Rev. Lett., v. 92, 027201 (2004). We demonstrate that the usage of a standard Slonczewski formalism for the phenomenological treatment of a spin-induced torque leads to a qualitative disagreement between simulation results and exp…
The motion of skyrmions along ferromagnetic strips driven by current pulses is theoretically analyzed by means of micromagnetic simulations. Analytical expressions describing the skyrmion dynamics during and after the current pulse are obtained from an extended rigid skyrmion model, and its predictions are compared with full micromagnetic simulations for perfect samples with a remarkable agreement. The dynamics along realistic samples with random disorder is also studied by both models. Our analysis describes the relevant ingredients behind the current-driven skyrmion dynamics, and it is expec…
We report the results of micromagnetic simulations of domain wall (DW) nucleation and pinning/depinning processes in ferromagnetic planar structure consisting of nanowire (NW) with perpendicular anisotropy and special V-shaped nanoparticle (NP) with in-plane anisotropy located on top of NW. The magnetization reversal features of this system in an external magnetic field are investigated depending on the direction of particle magnetic moment. Possible variants of magnetic logic cells (LCs) based on such system are discussed.
In this study, the magnetic reversal process of exchange-coupled bilayer systems, consisting of a ferrimagnetic TbFeCo alloy layer and a ferromagnetic [Co/Ni/Pt]N multilayer, was investigated. In particular, minor loop studies, probing solely the reversal characteristics of the softer ferromagnetic layer, reveal two distinct reversal mechanisms, which depend strongly on the thickness of the ferromagnetic layer. For thick layers, irreversible switching of the macroscopic minor loop is observed. The underlying microscopic origin of this reversal process was studied in detail by high-resolution m…
The large curvature effects on micromagnetic energy of a thin ferromagnetic film with nonlocal dipolar energy are considered. We predict that the dipolar interaction and surface curvature can produce perpendicular anisotropy which can be controlled by engineering a special type of periodic surface shape structure. Similar effects can be achieved by a significant surface roughness in the film. We show that in general the anisotropy can point in an arbitrary direction depending on the surface curvature. We provide simple examples of these periodic surface structures to demonstrate how to enginee…
We investigate the switching field distribution and the resulting bit error rate of exchange coupled ferri-/ferromagnetic bilayer island arrays by micromagnetic simulations. Using islands with varying microstructure and anisotropic properties, the intrinsic switching field distribution is computed. The dipolar contribution to the switching field distribution is obtained separately by using a model of a triangular patterned island array resembling $1.4\,\mathrm{Tb/in}^2$ bit patterned media. Both contributions are computed for different thickness of the soft exchange coupled ferrimagnet and als…
