The Experts below are selected from a list of 276 Experts worldwide ranked by ideXlab platform
Radu Ignat - One of the best experts on this subject based on the ideXlab platform.
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Asymmetric Domain Walls of Small Angle in Soft Ferromagnetic Films
Archive for Rational Mechanics and Analysis, 2016Co-Authors: Lukas Döring, Radu IgnatAbstract:We focus on a special type of domain walls appearing in the Landau-Lifshitz theory for soft Ferromagnetic Films. These domain walls are divergence-free $S^2$-valued transition layers that connect two directions in $S^2$ (differing by an angle $2\theta$) and minimize the Dirichlet energy. Our main result is the rigorous derivation of the asymptotic structure and energy of such "asymmetric" domain walls in the limit $\theta \to 0$. As an application, we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model.
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Asymmetric Domain Walls of Small Angle in Soft Ferromagnetic Films
Archive for Rational Mechanics and Analysis, 2016Co-Authors: Lukas Döring, Radu IgnatAbstract:We focus on a special type of domain wall appearing in the Landau–Lifshitz theory for soft Ferromagnetic Films. These domain walls are divergence-free $${\mathbb{S}^2}$$ S 2 -valued transition layers that connect two directions $${m_\theta^\pm \in \mathbb{S}^2}$$ m θ ± ∈ S 2 (differing by an angle $${2\theta}$$ 2 θ ) and minimize the Dirichlet energy. Our main result is the rigorous derivation of the asymptotic structure and energy of such “asymmetric” domain walls in the limit $${\theta \downarrow 0}$$ θ ↓ 0 . As an application, we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model.
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a reduced model for domain walls in soft Ferromagnetic Films at the cross over from symmetric to asymmetric wall types
Journal of the European Mathematical Society, 2014Co-Authors: Lukas Döring, Radu Ignat, Felix OttoAbstract:We study the Landau-Lifshitz model for the energy of multi-scale transition layers – called “domain walls” – in soft Ferromagnetic Films. Domain walls separate domains of constant magnetization vectors m α ∈ S that differ by an angle 2α. Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The minimal energy splits into a contribution from an asymmetric, divergence-free core which performs a partial rotation in S by an angle 2θ, and a contribution from two symmetric, logarithmically decaying tails, each of which completes the rotation from angle θ to α in S. The angle θ is chosen such that the total energy is minimal. The contribution from the symmetric tails is known explicitly, while the contribution from the asymmetric core is analyzed in [7]. Our reduced model is the starting point for the analysis of a bifurcation phenomenon from symmetric to asymmetric domain walls. Moreover, it allows for capturing asymmetric domain walls including their extended tails (which were previously inaccessible to brute-force numerical simulation).
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A reduced model for domain walls in soft Ferromagnetic Films at the cross-over from symmetric to asymmetric wall types
J. Eur. Math. Soc. (JEMS) 6, 2014Co-Authors: Lukas Döring, Radu Ignat, Felix OttoAbstract:We study the Landau-Lifshitz model for the energy of multi-scale transition layers -- called "domain walls" -- in soft Ferromagnetic Films. Domain walls separate domains of constant magnetization vectors $m^\pm \in \mathbb{S}^2$ that differ by an angle $2\alpha$. Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The minimal energy splits into a contribution from an asymmetric, divergence-free core which performs a partial rotation in $\mathbb{S}^2$ by an angle $2\theta$, and a contribution from two symmetric, logarithmically decaying tails, each of which completes the rotation from angle $\theta$ to $\alpha$ in $\mathbb{S}^1$. The angle $\theta$ is chosen such that the total energy is minimal. The contribution from the symmetric tails is known explicitly, while the contribution from the asymmetric core is analyzed in [7]. Our reduced model is the starting point for the analysis of a bifurcation phenomenon from symmetric to asymmetric domain walls. Moreover, it allows for capturing asymmetric domain walls including their extended tails (which were previously inaccessible to brute-force numerical simulation).
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a compactness result in thin film micromagnetics and the optimality of the neel wall
Journal of the European Mathematical Society, 2008Co-Authors: Radu Ignat, Felix OttoAbstract:We study a model for the magnetization in thin Ferromagnetic Films. It comes as a vari- ational problem forS 1 -valued mapsm 0 (the magnetization) of two variablesx 0 :
Lukas Döring - One of the best experts on this subject based on the ideXlab platform.
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Asymmetric Domain Walls of Small Angle in Soft Ferromagnetic Films
Archive for Rational Mechanics and Analysis, 2016Co-Authors: Lukas Döring, Radu IgnatAbstract:We focus on a special type of domain walls appearing in the Landau-Lifshitz theory for soft Ferromagnetic Films. These domain walls are divergence-free $S^2$-valued transition layers that connect two directions in $S^2$ (differing by an angle $2\theta$) and minimize the Dirichlet energy. Our main result is the rigorous derivation of the asymptotic structure and energy of such "asymmetric" domain walls in the limit $\theta \to 0$. As an application, we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model.
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Asymmetric Domain Walls of Small Angle in Soft Ferromagnetic Films
Archive for Rational Mechanics and Analysis, 2016Co-Authors: Lukas Döring, Radu IgnatAbstract:We focus on a special type of domain wall appearing in the Landau–Lifshitz theory for soft Ferromagnetic Films. These domain walls are divergence-free $${\mathbb{S}^2}$$ S 2 -valued transition layers that connect two directions $${m_\theta^\pm \in \mathbb{S}^2}$$ m θ ± ∈ S 2 (differing by an angle $${2\theta}$$ 2 θ ) and minimize the Dirichlet energy. Our main result is the rigorous derivation of the asymptotic structure and energy of such “asymmetric” domain walls in the limit $${\theta \downarrow 0}$$ θ ↓ 0 . As an application, we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model.
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a reduced model for domain walls in soft Ferromagnetic Films at the cross over from symmetric to asymmetric wall types
Journal of the European Mathematical Society, 2014Co-Authors: Lukas Döring, Radu Ignat, Felix OttoAbstract:We study the Landau-Lifshitz model for the energy of multi-scale transition layers – called “domain walls” – in soft Ferromagnetic Films. Domain walls separate domains of constant magnetization vectors m α ∈ S that differ by an angle 2α. Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The minimal energy splits into a contribution from an asymmetric, divergence-free core which performs a partial rotation in S by an angle 2θ, and a contribution from two symmetric, logarithmically decaying tails, each of which completes the rotation from angle θ to α in S. The angle θ is chosen such that the total energy is minimal. The contribution from the symmetric tails is known explicitly, while the contribution from the asymmetric core is analyzed in [7]. Our reduced model is the starting point for the analysis of a bifurcation phenomenon from symmetric to asymmetric domain walls. Moreover, it allows for capturing asymmetric domain walls including their extended tails (which were previously inaccessible to brute-force numerical simulation).
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A reduced model for domain walls in soft Ferromagnetic Films at the cross-over from symmetric to asymmetric wall types
J. Eur. Math. Soc. (JEMS) 6, 2014Co-Authors: Lukas Döring, Radu Ignat, Felix OttoAbstract:We study the Landau-Lifshitz model for the energy of multi-scale transition layers -- called "domain walls" -- in soft Ferromagnetic Films. Domain walls separate domains of constant magnetization vectors $m^\pm \in \mathbb{S}^2$ that differ by an angle $2\alpha$. Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The minimal energy splits into a contribution from an asymmetric, divergence-free core which performs a partial rotation in $\mathbb{S}^2$ by an angle $2\theta$, and a contribution from two symmetric, logarithmically decaying tails, each of which completes the rotation from angle $\theta$ to $\alpha$ in $\mathbb{S}^1$. The angle $\theta$ is chosen such that the total energy is minimal. The contribution from the symmetric tails is known explicitly, while the contribution from the asymmetric core is analyzed in [7]. Our reduced model is the starting point for the analysis of a bifurcation phenomenon from symmetric to asymmetric domain walls. Moreover, it allows for capturing asymmetric domain walls including their extended tails (which were previously inaccessible to brute-force numerical simulation).
Francisco A Tamarit - One of the best experts on this subject based on the ideXlab platform.
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spin reorientation transition and phase diagram of ultrathin Ferromagnetic Films
Physical Review B, 2008Co-Authors: Marianela Carubelli, Orlando V Billoni, Santiago Alberto Pighin, Sergio A Cannas, Daniel A Stariolo, Francisco A TamaritAbstract:We show results from Monte Carlo simulations of a two dimensional Heisenberg model for ultrathin Films with perpendicular anisotropy. A complete phase diagram is obtained as a function of anisotropy and temperature, spanning a wide range of behavior. We discuss our results in relation with experimental findings in different ultrathin Films. We observe and characterize a line of Spin Reorientation Transitions . This transition from out of plane stripe order to in plane Ferromagnetic order presents a paramagnetic gap in between in a finite region in parameter space, as reported in experiments. For large anisotropies direct transitions from a low temperature stripe phase to a paramagnetic or tetragonal phase with dominant perpendicular magnetization is observed, also in agreement with experiments. We also show the phase diagram for a system without exchange, i.e. with pure dipolar and anisotropy interactions. It shows a similar behavior to the Ferromagnetic case with antiFerromagnetic instead of stripe phases at low temperatures. A Spin Reorientation Transition is also found in this case.
Cyrill B Muratov - One of the best experts on this subject based on the ideXlab platform.
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A Quantitative Description of Skyrmions in Ultrathin Ferromagnetic Films and Rigidity of Degree $$\pm \,1$$ ±
Archive for Rational Mechanics and Analysis, 2021Co-Authors: Anne Bernand-mantel, Cyrill B Muratov, Theresa M. SimonAbstract:We characterize skyrmions in ultrathin Ferromagnetic Films as local minimizers of a reduced micromagnetic energy appropriate for quasi two-dimensional materials with perpendicular magnetic anisotropy and interfacial Dzyaloshinskii–Moriya interaction. The minimization is carried out in a suitable class of two-dimensional magnetization configurations that prevents the energy from going to negative infinity, while not imposing any restrictions on the spatial scale of the configuration. We first demonstrate the existence of minimizers for an explicit range of the model parameters when the energy is dominated by the exchange energy. We then investigate the conformal limit, in which only the exchange energy survives and identify the asymptotic profiles of the skyrmions as degree 1 harmonic maps from the plane to the sphere, together with their radii, angles and energies. A byproduct of our analysis is a quantitative rigidity result for degree $$\pm \,1$$ ± 1 harmonic maps from the two-dimensional sphere to itself.
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A quantitative description of skyrmions in ultrathin Ferromagnetic Films and rigidity of degree $\pm1$ harmonic maps from $\mathbb{R}^2$ to $\mathbb{S}^2$
Archive for Rational Mechanics and Analysis, 2020Co-Authors: Anne Bernand-mantel, Cyrill B Muratov, Theresa M. SimonAbstract:We characterize skyrmions in ultrathin Ferromagnetic Films as local minimizers of a reduced micromagnetic energy appropriate for quasi two-dimensional materials with perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction. The minimization is carried out in a suitable class of two-dimensional magnetization configurations that prevents the energy from going to negative infinity, while not imposing any restrictions on the spatial scale of the configuration. We first demonstrate existence of minimizers for an explicit range of the model parameters when the energy is dominated by the exchange energy. We then investigate the conformal limit, in which only the exchange energy survives and identify the asymptotic profiles of the skyrmions as degree 1 harmonic maps from the plane to the sphere, together with their radii, angles and energies. A byproduct of our analysis is a quantitative rigidity result for degree $\pm 1$ harmonic maps from the two-dimensional sphere to itself.
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A Quantitative Description of Skyrmions in Ultrathin Ferromagnetic Films and Rigidity of Degree $$\pm \,1$$ ± 1
Archive for Rational Mechanics and Analysis, 2020Co-Authors: Anne Bernand-mantel, Cyrill B Muratov, Theresa M. SimonAbstract:We characterize skyrmions in ultrathin Ferromagnetic Films as local minimizers of a reduced micromagnetic energy appropriate for quasi two-dimensional materials with perpendicular magnetic anisotropy and interfacial Dzyaloshinskii–Moriya interaction. The minimization is carried out in a suitable class of two-dimensional magnetization configurations that prevents the energy from going to negative infinity, while not imposing any restrictions on the spatial scale of the configuration. We first demonstrate the existence of minimizers for an explicit range of the model parameters when the energy is dominated by the exchange energy. We then investigate the conformal limit, in which only the exchange energy survives and identify the asymptotic profiles of the skyrmions as degree 1 harmonic maps from the plane to the sphere, together with their radii, angles and energies. A byproduct of our analysis is a quantitative rigidity result for degree $$\pm \,1$$ ± 1 harmonic maps from the two-dimensional sphere to itself.
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Magnetic Domains in Thin Ferromagnetic Films with Strong Perpendicular Anisotropy
Archive for Rational Mechanics and Analysis, 2019Co-Authors: Hans Knupfer, Cyrill B Muratov, Florian NolteAbstract:We investigate the scaling of the ground state energy and optimal domain patterns in thin Ferromagnetic Films with strong uniaxial anisotropy and the easy axis perpendicular to the film plane. Starting from the full three-dimensional micromagnetic model, we identify the critical scaling for which the transition from single domain to multidomain ground states such as bubble or maze patterns occurs as the film thickness goes to zero and the lateral extent goes to infinity. Furthermore, we analyze the asymptotic behavior of the energy in these two asymptotic regimes. In the single domain regime, the energy Γ -converges towards a much simpler two-dimensional and local model. In the multidomain regime, we derive the scaling of the minimal energy and deduce a scaling law for the typical domain size.
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magnetic domains in thin Ferromagnetic Films with strong perpendicular anisotropy
arXiv: Analysis of PDEs, 2017Co-Authors: Hans Knupfer, Cyrill B Muratov, Florian NolteAbstract:We investigate the scaling of the ground state energy and optimal domain patterns in thin Ferromagnetic Films with strong uniaxial anisotropy and the easy axis perpendicular to the film plane. Starting from the full three-dimensional micromagnetic model, we identify the critical scaling where the transition from single domain to multidomain ground states such as bubble or maze patterns occurs. Furthermore, we analyze the asymptotic behavior of the energy in two regimes separated by a transition. In the single domain regime, the energy $\Gamma$-converges towards a much simpler two-dimensional and local model. In the second regime, we derive the scaling of the minimal energy and deduce a scaling law for the typical domain size.
Joan Kirschner - One of the best experts on this subject based on the ideXlab platform.
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magnons in ultrathin Ferromagnetic Films with a large perpendicular magnetic anisotropy
Physical Review B, 2013Co-Authors: Kh Zakeri, Joan Kirschner, T H Chuang, Y Meng, Y.j. Chen, A. ErnstAbstract:We report on an experimental observation of high-energy magnon excitations in ultrathin Ferromagnetic Films with a perpendicular easy axis. We demonstrate that a transversally spin-polarized beam can be used to excite and probe the high-energy magnons within spin-polarized electron energy-loss spectroscopy experiments. The magnon dispersion relation and lifetime are probed over the entire surface Brillouin zone for a set of body-centered tetragonal FeCo Films with a large perpendicular magnetic anisotropy. First-principles calculations reveal that in addition to the tetragonal distortion, which is the origin of the large perpendicular magnetic anisotropy, the interfacial electronic hybridization also has a considerable impact on the properties of magnons.
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spin polarized electron energy loss spectroscopy of high energy large wave vector spin waves in ultrathin fcc co Films on cu 001
Physical Review Letters, 2003Co-Authors: R Vollmer, Markus Etzkorn, P S Kumar, H Ibach, Joan KirschnerAbstract:The realm of high energy, large wave vector spin waves in ultrathin Films and at surfaces is unexplored because a suitable method was not available up to now. We present experimental data for an 8 ML thick Co film deposited on Cu(001) which show that spin-polarized electron energy loss spectroscopy can be used to measure spin-wave dispersion curves of ultrathin Ferromagnetic Films up to the surface Brillouin zone boundary.