D. Grundler - Academia.edu (original) (raw)

Papers by D. Grundler

The quantum oscillatory magnetization M of a two-dimensional electron system in a magnetic field ... more The quantum oscillatory magnetization M of a two-dimensional electron system in a magnetic field B is found to provide quantitative information on both the Rashba-and Dresselhaus spin-orbit interaction (SOI). This is shown by first numerically solving the model Hamiltonian including the linear Rashba-and Dresselhaus SOI and the Zeeman term in an in particular doubly tilted magnetic field and second evaluating the intrinsically anisotropic magnetization for different directions of the in-plane magnetic field component. The amplitude of specific magnetic quantum oscillations in M (B) is found to be a direct measure of the SOI strength at fields B where SOI-induced Landau level anticrossings occur. The anisotropic M allows one to quantify the magnitude of both contributions as well as their relative sign. The influence of cubic Dresselhaus SOI on the results is discussed. We use realistic sample parameters and show that recently reported experimental techniques provide a sensitivity which allows for the detection of the predicted phenomena.

Applied Physics Letters, 2014

Nanotechnology, Jan 18, 2017

We show that chemical fixation enables top-down micro-machining of large periodic 3D arrays of pr... more We show that chemical fixation enables top-down micro-machining of large periodic 3D arrays of protein-encapsulated magnetic nanoparticles (NPs) without loss of order. We machined 3D micro-cubes containing a superlattice of NPs by means of focused ion beam etching, integrated an individual micro-cube to a thin-film coplanar waveguide and measured the resonant microwave response. Our work represents a major step towards well-defined magnonic metamaterials created from the self-assembly of magnetic nanoparticles.

Nature Communications, 2016

Seven decades after the discovery of collective spin excitations in microwave-irradiated ferromag... more Seven decades after the discovery of collective spin excitations in microwave-irradiated ferromagnets, there has been a rebirth of magnonics. However, magnetic nanodevices will enable smart GHz-to-THz devices at low power consumption only, if such spin waves (magnons) are generated and manipulated on the sub-100 nm scale. Here we show how magnons with a wavelength of a few 10 nm are exploited by combining the functionality of insulating yttrium iron garnet and nanodisks from different ferromagnets. We demonstrate magnonic devices at wavelengths of 88 nm written/read by conventional coplanar waveguides. Our microwave-to-magnon transducers are reconfigurable and thereby provide additional functionalities. The results pave the way for a multi-functional GHz technology with unprecedented miniaturization exploiting nanoscale wavelengths that are otherwise relevant for soft X-rays. Nanomagnonics integrated with broadband microwave circuitry offer applications that are wide ranging, from n...

Physical Review B, 2002

We present studies on the low-temperature magnetization of a two-dimensional electron system ͑2DE... more We present studies on the low-temperature magnetization of a two-dimensional electron system ͑2DES͒ in the integer quantum Hall-effect regime. The 2DES was formed in a modulation-doped AlGaAs/GaAs heterojunction. Using molecular-beam epitaxy it has been integrated into a highly sensitive micromechanical cantilever magnetometer. We observe de Haas-van Alphen oscillations at even filling factors up to ϭ40 which for р20 are almost perfectly sawtoothlike. Oscillations at odd filling factors ϭ3,5,7, and 9 are due to the spin splitting of Landau levels. For a quantitative analysis of our data, calculations of the magnetization based on a model density of states ͑DOS͒ have been performed. We describe the DOS by narrow Gaussian broadened Landau levels with an energy-independent background. In particular we find that this background DOS increases linearly with. This behavior is qualitatively explained using the concept of edge channels. From our data we evaluate the level broadening and, at odd filling factors, the exchange-energy contribution to the spin splitting of Landau levels.

Sci. Rep., 2014

Wave control in the solid state has opened new avenues in modern information technology. Surface-... more Wave control in the solid state has opened new avenues in modern information technology. Surface-acoustic-wave-based devices are found as mass market products in 100 millions of cellular phones. Spin waves (magnons) would offer a boost in today's data handling and security implementations, i.e., image processing and speech recognition. However, nanomagnonic devices realized so far suffer from the relatively short damping length in the metallic ferromagnets amounting to a few 10 micrometers typically. Here we demonstrate that nm-thick YIG films overcome the damping chasm. Using a conventional coplanar waveguide we excite a large series of short-wavelength spin waves (SWs). From the data we estimate a macroscopic of damping length of about 600 micrometers. The intrinsic damping parameter suggests even a record value about 1 mm allowing for magnonics-based nanotechnology with ultra-low damping. In addition, SWs at large wave vector are found to exhibit the non-reciprocal properties relevant for new concepts in nanoscale SW-based logics. We expect our results to provide the basis for coherent data processing with SWs at GHz rates and in large arrays of cellular magnetic arrays, thereby boosting the envisioned image processing and speech recognition.

Physical Review B, 2012

We report spin wave excitations in a nanopatterned antidot lattice fabricated from a 30-nm thick ... more We report spin wave excitations in a nanopatterned antidot lattice fabricated from a 30-nm thick Ni 80 Fe 20 film. The 250-nm-wide circular holes are arranged in a rhombic unit cell with a lattice constant of 400 nm. By Brillouin light scattering, we find that quantized spin wave modes transform to propagating ones and vice versa by changing the in-plane orientation of the applied magnetic field H by 30 •. Spin waves of either negative or positive group velocity are found. In the latter case, they propagate in narrow channels exhibiting a width of below 100 nm. We use the plane wave method to calculate the spin wave dispersions for the two relevant orientations of H. The theory allows us to explain the wave-vector-dependent characteristics of the prominent modes. Allowed minibands are formed for selected modes only for specific orientations of H and wave vector. The results are important for applications such as spin wave filters and interconnected waveguides in the emerging field of magnonics where the control of spin wave propagation on the nanoscale is key.

Solid State Communications, 2014

Spin dynamics controlled by magnetoelastic coupling and applied electric fields might play a vita... more Spin dynamics controlled by magnetoelastic coupling and applied electric fields might play a vital role in future developments of magnonics, i.e., the exploitation of spin waves for the transmission and processing of information. We have performed broadband spin-wave spectroscopy on a magnetostrictive CoFeB alloy grown on a ferrolectric BaTiO 3 substrate causing elastic strain with a quasi-periodic modulation. We find characteristic eigenfrequencies and spin-wave modes with large group velocities and small damping. These results suggest bright perspectives for electric-field control of reprogrammable magnonics.

Physical Review Letters, 2006

We have studied the spin excitations of ferromagnetic rings and observed a distinct series of qua... more We have studied the spin excitations of ferromagnetic rings and observed a distinct series of quantized modes in the vortex state. We attribute them to spin waves that circulate around the ring and interfere constructively. They form azimuthal eigenmodes of a magnetic ring resonator which we resolve up to the fourth order. The eigenfrequencies are calculated semianalytically and classified as a function of magnetic field by a quantization rule which takes into account a periodic boundary condition. Strikingly each mode exists only below a characteristic field.

Physical Review Letters, 2012

The spin-wave band structure of a two-dimensional bicomponent magnonic crystal, consisting of Co ... more The spin-wave band structure of a two-dimensional bicomponent magnonic crystal, consisting of Co nanodisks partially embedded in a Permalloy thin film, is experimentally investigated along a highsymmetry direction by Brillouin light scattering. The eigenfrequencies and scattering cross sections are interpreted using plane wave method calculations and micromagnetic simulations. At the boundary of both the first and the second Brillouin zones, we measure a forbidden frequency gap whose width depends on the magnetic contrast between the constituent materials. The modes above and below the gap exhibit resonant spin-precession amplitudes in the complementary regions of periodically varying magnetic parameters. Our findings are key to advance both the physics and the technology of band gap engineering in magnonics.

Physical Review B, 2013

With the direct measurement of the quantum oscillatory magnetization M of a two-dimensional elect... more With the direct measurement of the quantum oscillatory magnetization M of a two-dimensional electron system (2DES) in an InGaAs/InP asymmetric quantum well we discover a frequency anomaly of the de Haas-van Alphen effect which is not consistent with existing theories on spin-orbit interaction (SOI). Strikingly, the oscillatory magnetoresistance of the same heterostructure, that is, the Shubnikov-de Haas effect conventionally used to explore SOI, does not show the frequency anomaly. This explains why our finding has not been reported for almost three decades. The understanding of the ground state energy of a 2DES is evidenced to be incomplete when SOI is present.

Physical Review B, 2005

We present de Haas-van Alphen ͑dHvA͒ measurements on high-mobility two-dimensional electron syste... more We present de Haas-van Alphen ͑dHvA͒ measurements on high-mobility two-dimensional electron systems formed in modulation-doped Si/ SiGe ͑100͒ quantum wells and demonstrate directly the manifestation of the valley splitting in the magnetization. We resolve sawtoothlike magnetization oscillations at even filling factors which reflect the Landau quantization and the spin splitting of Landau levels in the electronic energy spectrum. At odd filling factors we observe the lifting of the valley degeneracy in Si at high magnetic field. The magnetization is a thermodynamic quantity that at low temperature reflects the ground-state energy of the interacting electron system. We can thus determine quantitatively the energetic splitting of the two occupied conduction-band valleys directly from the oscillation amplitude. Both valley and spin splitting are found to be enhanced by electron-electron interactions. The energy gap due to valley splitting is found to be ജ0.8 meV at high perpendicular field B Ќ. From studies in tilted magnetic fields we find that the valley splitting is governed solely by B Ќ. From the spin splitting we recalculate an enhanced g factor g * = 2.9 at = 2 including the influence of disorder. This is significantly larger than the band-structure g factor of 2 in Si. We have successfully applied the coincidence technique for the dHvA effect and thus obtained a complementary means to determine the g factor. It yields a constant value g * Х 3.2 for filling factors ജ 10. A detailed analysis of the magnetization traces enabled us also to determine quantitatively the residual level broadening ⌫ in this highmobility Si/ SiGe system. We obtain a small value of ⌫ = 0.15 meVϫ B Ќ ͓T͔ 1/2 for the Si/ SiGe heterostructure of 200 000 cm 2 / ͑V s͒ mobility at 0.3 K.

Physical Review B, 2008

Spin-wave modes in Ni 80 Fe 20 thin-film antidot lattices are investigated using micromagnetic si... more Spin-wave modes in Ni 80 Fe 20 thin-film antidot lattices are investigated using micromagnetic simulations and a semianalytical theoretical approach. The simulations reveal a rich eigenmode spectrum consisting of edge and center modes. We find both spatially localized and spin waves extending over many unit cells. To classify the different types of modes and to analyze the microscopic properties, we adapt a semianalytical approach. We show how to reduce the two-dimensional problem of the antidot lattice to a one-dimensional problem if certain high-symmetry axes are considered. For lattices of unit-cell lengths ranging from 200 to 1100 nm, we find that the characteristic mode eigenfrequencies can be correlated with both local inhomogeneities of the demagnetization field and specific wave vectors caused by geometry-imposed mode quantization conditions. We compare our results with recently published experimental data and discuss the crossover from dipolar to exchangedominated spin waves. Moreover, we simulate propagation of spin waves and find a preferred axis of propagation perpendicular to the external magnetic field.

Physical Review B, 2012

We report on the formation of a complete band gap for spin waves in a two-dimensional magnonic cr... more We report on the formation of a complete band gap for spin waves in a two-dimensional magnonic crystal consisting of a periodic hole lattice. We go beyond the partial band gaps observed so far in that we apply a magnetic field perpendicular to the permalloy thin film. We explore the relevant geometrical parameters using micromagnetic simulations. In nanopatterned devices we obtain complete band gaps of up to 1.4 GHz. The magnetostatic forward volume waves addressed here overcome in particular spin-wave localization effects. These effects have led to complicated and highly anisotropic miniband formation or Bragg reflection in in-plane fields for a long time. We demonstrate how direct band-gap tailoring via geometrical lattice symmetries becomes possible in nanostructured magnetic antidot lattices.

Physical Review B, 2011

We study the spin dynamics in arrays of densely packed submicron Ni 80 Fe 20 wires which form one... more We study the spin dynamics in arrays of densely packed submicron Ni 80 Fe 20 wires which form one-dimensional magnonic crystals. They are subject to an in-plane magnetic field H being collinear with the wires. In the case when neighboring wires are magnetized antiparallel, broadband spin-wave spectroscopy reveals a mode repulsion behavior around a certain field H mr. We attribute this to dipolar coupling and avoided crossing of resonant modes of individual wires. The modes are found to hybridize across the array and form acoustic and optical modes. When an array of alternating-width wires is considered, H mr is found to vary characteristically as a function of the width difference w of neighboring wires. Interestingly, the sign of H mr reflects the orientation of the wires' magnetization. For our devices we find experimentally frequency splittings δf on the order of 1 GHz between the acoustic and optical mode. We use micromagnetic modeling to analyze spin precession profiles and investigate the hybridization of modes. The simulated splitting is larger than the observed one. We attribute the discrepancy to a reduced dipolar coupling in the real samples. Using a theoretical model which considers the reduced dipolar coupling we analyze δf for different geometrical parameters such as the edge-to-edge separation a and the width difference w. Though relevant for H mr , w is not decisive for δf. Instead, a is key for the frequency splitting. The results are relevant in order to tailor the dynamic response and band structure of magnonic crystals.

Physical Review B, 2014

Torque magnetometry at low temperature and in high magnetic fields B is performed on a MgZnO/ZnO ... more Torque magnetometry at low temperature and in high magnetic fields B is performed on a MgZnO/ZnO heterostructure incorporating a high-mobility two-dimensional electron system. We find a sawtooth-like quantum oscillatory magnetization M (B), i.e., the de Haas-van Alphen (dHvA) effect. At the same time, unexpected spike-like overshoots in M and non-equilibrium currents are observed which allow us to identify the microscopic nature and density of the residual disorder. The acceptor-like scatterers give rise to a magnetic thaw down effect which enhances the dHvA amplitude beyond the electron-electron interaction effects being present in the MgZnO/ZnO heterostructure.

Physical Review B, 2011

All-electrical spin-wave spectroscopy and frequency-resolved magneto-optical Kerr-effect measurem... more All-electrical spin-wave spectroscopy and frequency-resolved magneto-optical Kerr-effect measurements are combined to study spin waves propagating through a magnetic antidot lattice nanopatterned from a Ni 80 Fe 20 thin film. Spin waves are injected from a plain film into the antidot lattice and the transmission across the interface is explored in detail for different wavelengths. We find that spin waves with a wavelength much greater than the lattice periodicity are not described well by recently discussed approaches. Instead the spin-wave dispersion is consistent with an effective magnetization smaller than the saturation magnetization measured on the unstructured ferromagnetic material. Consistently, we find that the transmission coefficients are modeled well by assuming an effectively continuous metamaterial for spin waves characterized by the reduced magnetization. The experimental data and interpretation are substantiated theoretically using the plane-wave method and micromagnetic modeling. The results are interesting for the development of frequency-selective mirrors in magnonics through lateral nanopatterning.

Physical Review B, 2013

We report a combined experimental and theoretical study of the quasistatic hysteresis and dynamic... more We report a combined experimental and theoretical study of the quasistatic hysteresis and dynamic excitations in large-area arrays of NiFe nanodisks forming a hexagonal lattice with the lattice constant of 390 nm. Arrays were fabricated by patterning a 20-nm-thick NiFe film using the etched nanosphere lithography. We have studied a close-packed (edge-to-edge separation between disks d cp = 65 nm) and an ultraclosed packed (d ucp = 20 nm) array. Hysteresis loops for both arrays were qualitatively similar and nearly isotropic, i.e., independent on the in-plane external field orientation. The shape of these loops revealed that magnetization reversal is governed by the formation and expulsion of vortices inside the nanodisks. When we assumed that the nanodisks' magnetization significantly decreases near their edges, micromagnetic simulations with material parameters determined independently from continuous film measurements could satisfactorily reproduce the hysteresis. Despite the isotropic hysteresis, significant in-plane anisotropy of the dynamic response of the ultraclose-packed array was found experimentally by the all-electrical spin-wave spectroscopy and Brillouin light scattering. Dynamical simulations could successfully reproduce the difference between excitation spectra for fields directed along the two main symmetry axes of the hexagonal lattice. Simulations revealed that this difference is caused by the magnetodipolar interaction between nanodisks, which leads to a strong variation of the spatial distribution of the oscillation power both for bulk and edge modes as a function of the bias field orientation. Comparison of simulated and measured frequencies enabled the unambiguous identification of experimentally observed modes. Results of this systematic research are relevant both for fundamental studies of spin-wave modes in patterned magnetic structures and for the design of magnonic crystals for potential applications as, e.g., spin-wave guides and filters.

Physical Review B, 2007

We present a combined experimental, computational, and semianalytical study of the magnetization ... more We present a combined experimental, computational, and semianalytical study of the magnetization dynamics of permalloy disks and nanostructured rings with a systematically varied ring width. We investigate the dynamics of the quasisaturated state. In the case of wide rings the spin wave mode spectrum is similar to that of a disk. The small inner hole can be viewed as a weak perturbation. When the central hole increases, its influence becomes more important and two characteristic modes form gradually. They become localized at different positions in the ring. We explain the localization by the increasing inhomogeneity of the internal magnetic field and the formation of domain wall regions as the rings grow more narrow. In narrow rings one of the modes is clearly confined to the two segments where the internal field H int is at a maximum and the other to the domain wall region where H int is small. Dynamic magnetic simulations agree well with the measured spectra and confirm this interpretation. We also applied a semianalytical model, which confirms that the mode localization is driven by the internal field inhomogeneity.

IEEE Transactions on Magnetics, 2010

We present a combined experimental investigation of magnetic normal modes in an antidot lattice u... more We present a combined experimental investigation of magnetic normal modes in an antidot lattice using both Brillouin light scattering and broadband ferromagnetic resonance. It was fabricated on a silicon substrate using optical ultraviolet lithography. The sample consisted of a 30-nm-thick Ni 80 Fe 20 squared antidot array with circular holes whose diameter and edge-to-edge spacing are 250 and 150 nm, respectively. Experiments were performed as a function of the applied magnetic field 0 H ext in the range from 100 to 100 mT, with H ext applied along both the square lattice axis and its diagonal. Several peaks were observed in both the Brillouin light scattering and ferromagnetic resonance spectra, and their evolution with the intensity and the direction of the applied field H ext was measured. Micromagnetic simulations enabled us to identify the modes in terms of their symmetry obtaining a good quantitative agreement with the measured frequencies. In addition, we show how the inhomogeneity of the internal field affected the properties of the magnetic eigenmodes and their localization in different regions of the antidot lattice.

The quantum oscillatory magnetization M of a two-dimensional electron system in a magnetic field ... more The quantum oscillatory magnetization M of a two-dimensional electron system in a magnetic field B is found to provide quantitative information on both the Rashba-and Dresselhaus spin-orbit interaction (SOI). This is shown by first numerically solving the model Hamiltonian including the linear Rashba-and Dresselhaus SOI and the Zeeman term in an in particular doubly tilted magnetic field and second evaluating the intrinsically anisotropic magnetization for different directions of the in-plane magnetic field component. The amplitude of specific magnetic quantum oscillations in M (B) is found to be a direct measure of the SOI strength at fields B where SOI-induced Landau level anticrossings occur. The anisotropic M allows one to quantify the magnitude of both contributions as well as their relative sign. The influence of cubic Dresselhaus SOI on the results is discussed. We use realistic sample parameters and show that recently reported experimental techniques provide a sensitivity which allows for the detection of the predicted phenomena.

Applied Physics Letters, 2014

Nanotechnology, Jan 18, 2017

We show that chemical fixation enables top-down micro-machining of large periodic 3D arrays of pr... more We show that chemical fixation enables top-down micro-machining of large periodic 3D arrays of protein-encapsulated magnetic nanoparticles (NPs) without loss of order. We machined 3D micro-cubes containing a superlattice of NPs by means of focused ion beam etching, integrated an individual micro-cube to a thin-film coplanar waveguide and measured the resonant microwave response. Our work represents a major step towards well-defined magnonic metamaterials created from the self-assembly of magnetic nanoparticles.

Nature Communications, 2016

Seven decades after the discovery of collective spin excitations in microwave-irradiated ferromag... more Seven decades after the discovery of collective spin excitations in microwave-irradiated ferromagnets, there has been a rebirth of magnonics. However, magnetic nanodevices will enable smart GHz-to-THz devices at low power consumption only, if such spin waves (magnons) are generated and manipulated on the sub-100 nm scale. Here we show how magnons with a wavelength of a few 10 nm are exploited by combining the functionality of insulating yttrium iron garnet and nanodisks from different ferromagnets. We demonstrate magnonic devices at wavelengths of 88 nm written/read by conventional coplanar waveguides. Our microwave-to-magnon transducers are reconfigurable and thereby provide additional functionalities. The results pave the way for a multi-functional GHz technology with unprecedented miniaturization exploiting nanoscale wavelengths that are otherwise relevant for soft X-rays. Nanomagnonics integrated with broadband microwave circuitry offer applications that are wide ranging, from n...

Physical Review B, 2002

We present studies on the low-temperature magnetization of a two-dimensional electron system ͑2DE... more We present studies on the low-temperature magnetization of a two-dimensional electron system ͑2DES͒ in the integer quantum Hall-effect regime. The 2DES was formed in a modulation-doped AlGaAs/GaAs heterojunction. Using molecular-beam epitaxy it has been integrated into a highly sensitive micromechanical cantilever magnetometer. We observe de Haas-van Alphen oscillations at even filling factors up to ϭ40 which for р20 are almost perfectly sawtoothlike. Oscillations at odd filling factors ϭ3,5,7, and 9 are due to the spin splitting of Landau levels. For a quantitative analysis of our data, calculations of the magnetization based on a model density of states ͑DOS͒ have been performed. We describe the DOS by narrow Gaussian broadened Landau levels with an energy-independent background. In particular we find that this background DOS increases linearly with. This behavior is qualitatively explained using the concept of edge channels. From our data we evaluate the level broadening and, at odd filling factors, the exchange-energy contribution to the spin splitting of Landau levels.

Sci. Rep., 2014

Wave control in the solid state has opened new avenues in modern information technology. Surface-... more Wave control in the solid state has opened new avenues in modern information technology. Surface-acoustic-wave-based devices are found as mass market products in 100 millions of cellular phones. Spin waves (magnons) would offer a boost in today's data handling and security implementations, i.e., image processing and speech recognition. However, nanomagnonic devices realized so far suffer from the relatively short damping length in the metallic ferromagnets amounting to a few 10 micrometers typically. Here we demonstrate that nm-thick YIG films overcome the damping chasm. Using a conventional coplanar waveguide we excite a large series of short-wavelength spin waves (SWs). From the data we estimate a macroscopic of damping length of about 600 micrometers. The intrinsic damping parameter suggests even a record value about 1 mm allowing for magnonics-based nanotechnology with ultra-low damping. In addition, SWs at large wave vector are found to exhibit the non-reciprocal properties relevant for new concepts in nanoscale SW-based logics. We expect our results to provide the basis for coherent data processing with SWs at GHz rates and in large arrays of cellular magnetic arrays, thereby boosting the envisioned image processing and speech recognition.

Physical Review B, 2012

We report spin wave excitations in a nanopatterned antidot lattice fabricated from a 30-nm thick ... more We report spin wave excitations in a nanopatterned antidot lattice fabricated from a 30-nm thick Ni 80 Fe 20 film. The 250-nm-wide circular holes are arranged in a rhombic unit cell with a lattice constant of 400 nm. By Brillouin light scattering, we find that quantized spin wave modes transform to propagating ones and vice versa by changing the in-plane orientation of the applied magnetic field H by 30 •. Spin waves of either negative or positive group velocity are found. In the latter case, they propagate in narrow channels exhibiting a width of below 100 nm. We use the plane wave method to calculate the spin wave dispersions for the two relevant orientations of H. The theory allows us to explain the wave-vector-dependent characteristics of the prominent modes. Allowed minibands are formed for selected modes only for specific orientations of H and wave vector. The results are important for applications such as spin wave filters and interconnected waveguides in the emerging field of magnonics where the control of spin wave propagation on the nanoscale is key.

Solid State Communications, 2014

Spin dynamics controlled by magnetoelastic coupling and applied electric fields might play a vita... more Spin dynamics controlled by magnetoelastic coupling and applied electric fields might play a vital role in future developments of magnonics, i.e., the exploitation of spin waves for the transmission and processing of information. We have performed broadband spin-wave spectroscopy on a magnetostrictive CoFeB alloy grown on a ferrolectric BaTiO 3 substrate causing elastic strain with a quasi-periodic modulation. We find characteristic eigenfrequencies and spin-wave modes with large group velocities and small damping. These results suggest bright perspectives for electric-field control of reprogrammable magnonics.

Physical Review Letters, 2006

We have studied the spin excitations of ferromagnetic rings and observed a distinct series of qua... more We have studied the spin excitations of ferromagnetic rings and observed a distinct series of quantized modes in the vortex state. We attribute them to spin waves that circulate around the ring and interfere constructively. They form azimuthal eigenmodes of a magnetic ring resonator which we resolve up to the fourth order. The eigenfrequencies are calculated semianalytically and classified as a function of magnetic field by a quantization rule which takes into account a periodic boundary condition. Strikingly each mode exists only below a characteristic field.

Physical Review Letters, 2012

The spin-wave band structure of a two-dimensional bicomponent magnonic crystal, consisting of Co ... more The spin-wave band structure of a two-dimensional bicomponent magnonic crystal, consisting of Co nanodisks partially embedded in a Permalloy thin film, is experimentally investigated along a highsymmetry direction by Brillouin light scattering. The eigenfrequencies and scattering cross sections are interpreted using plane wave method calculations and micromagnetic simulations. At the boundary of both the first and the second Brillouin zones, we measure a forbidden frequency gap whose width depends on the magnetic contrast between the constituent materials. The modes above and below the gap exhibit resonant spin-precession amplitudes in the complementary regions of periodically varying magnetic parameters. Our findings are key to advance both the physics and the technology of band gap engineering in magnonics.

Physical Review B, 2013

With the direct measurement of the quantum oscillatory magnetization M of a two-dimensional elect... more With the direct measurement of the quantum oscillatory magnetization M of a two-dimensional electron system (2DES) in an InGaAs/InP asymmetric quantum well we discover a frequency anomaly of the de Haas-van Alphen effect which is not consistent with existing theories on spin-orbit interaction (SOI). Strikingly, the oscillatory magnetoresistance of the same heterostructure, that is, the Shubnikov-de Haas effect conventionally used to explore SOI, does not show the frequency anomaly. This explains why our finding has not been reported for almost three decades. The understanding of the ground state energy of a 2DES is evidenced to be incomplete when SOI is present.

Physical Review B, 2005

We present de Haas-van Alphen ͑dHvA͒ measurements on high-mobility two-dimensional electron syste... more We present de Haas-van Alphen ͑dHvA͒ measurements on high-mobility two-dimensional electron systems formed in modulation-doped Si/ SiGe ͑100͒ quantum wells and demonstrate directly the manifestation of the valley splitting in the magnetization. We resolve sawtoothlike magnetization oscillations at even filling factors which reflect the Landau quantization and the spin splitting of Landau levels in the electronic energy spectrum. At odd filling factors we observe the lifting of the valley degeneracy in Si at high magnetic field. The magnetization is a thermodynamic quantity that at low temperature reflects the ground-state energy of the interacting electron system. We can thus determine quantitatively the energetic splitting of the two occupied conduction-band valleys directly from the oscillation amplitude. Both valley and spin splitting are found to be enhanced by electron-electron interactions. The energy gap due to valley splitting is found to be ജ0.8 meV at high perpendicular field B Ќ. From studies in tilted magnetic fields we find that the valley splitting is governed solely by B Ќ. From the spin splitting we recalculate an enhanced g factor g * = 2.9 at = 2 including the influence of disorder. This is significantly larger than the band-structure g factor of 2 in Si. We have successfully applied the coincidence technique for the dHvA effect and thus obtained a complementary means to determine the g factor. It yields a constant value g * Х 3.2 for filling factors ജ 10. A detailed analysis of the magnetization traces enabled us also to determine quantitatively the residual level broadening ⌫ in this highmobility Si/ SiGe system. We obtain a small value of ⌫ = 0.15 meVϫ B Ќ ͓T͔ 1/2 for the Si/ SiGe heterostructure of 200 000 cm 2 / ͑V s͒ mobility at 0.3 K.

Physical Review B, 2008

Spin-wave modes in Ni 80 Fe 20 thin-film antidot lattices are investigated using micromagnetic si... more Spin-wave modes in Ni 80 Fe 20 thin-film antidot lattices are investigated using micromagnetic simulations and a semianalytical theoretical approach. The simulations reveal a rich eigenmode spectrum consisting of edge and center modes. We find both spatially localized and spin waves extending over many unit cells. To classify the different types of modes and to analyze the microscopic properties, we adapt a semianalytical approach. We show how to reduce the two-dimensional problem of the antidot lattice to a one-dimensional problem if certain high-symmetry axes are considered. For lattices of unit-cell lengths ranging from 200 to 1100 nm, we find that the characteristic mode eigenfrequencies can be correlated with both local inhomogeneities of the demagnetization field and specific wave vectors caused by geometry-imposed mode quantization conditions. We compare our results with recently published experimental data and discuss the crossover from dipolar to exchangedominated spin waves. Moreover, we simulate propagation of spin waves and find a preferred axis of propagation perpendicular to the external magnetic field.

Physical Review B, 2012

We report on the formation of a complete band gap for spin waves in a two-dimensional magnonic cr... more We report on the formation of a complete band gap for spin waves in a two-dimensional magnonic crystal consisting of a periodic hole lattice. We go beyond the partial band gaps observed so far in that we apply a magnetic field perpendicular to the permalloy thin film. We explore the relevant geometrical parameters using micromagnetic simulations. In nanopatterned devices we obtain complete band gaps of up to 1.4 GHz. The magnetostatic forward volume waves addressed here overcome in particular spin-wave localization effects. These effects have led to complicated and highly anisotropic miniband formation or Bragg reflection in in-plane fields for a long time. We demonstrate how direct band-gap tailoring via geometrical lattice symmetries becomes possible in nanostructured magnetic antidot lattices.

Physical Review B, 2011

We study the spin dynamics in arrays of densely packed submicron Ni 80 Fe 20 wires which form one... more We study the spin dynamics in arrays of densely packed submicron Ni 80 Fe 20 wires which form one-dimensional magnonic crystals. They are subject to an in-plane magnetic field H being collinear with the wires. In the case when neighboring wires are magnetized antiparallel, broadband spin-wave spectroscopy reveals a mode repulsion behavior around a certain field H mr. We attribute this to dipolar coupling and avoided crossing of resonant modes of individual wires. The modes are found to hybridize across the array and form acoustic and optical modes. When an array of alternating-width wires is considered, H mr is found to vary characteristically as a function of the width difference w of neighboring wires. Interestingly, the sign of H mr reflects the orientation of the wires' magnetization. For our devices we find experimentally frequency splittings δf on the order of 1 GHz between the acoustic and optical mode. We use micromagnetic modeling to analyze spin precession profiles and investigate the hybridization of modes. The simulated splitting is larger than the observed one. We attribute the discrepancy to a reduced dipolar coupling in the real samples. Using a theoretical model which considers the reduced dipolar coupling we analyze δf for different geometrical parameters such as the edge-to-edge separation a and the width difference w. Though relevant for H mr , w is not decisive for δf. Instead, a is key for the frequency splitting. The results are relevant in order to tailor the dynamic response and band structure of magnonic crystals.

Physical Review B, 2014

Torque magnetometry at low temperature and in high magnetic fields B is performed on a MgZnO/ZnO ... more Torque magnetometry at low temperature and in high magnetic fields B is performed on a MgZnO/ZnO heterostructure incorporating a high-mobility two-dimensional electron system. We find a sawtooth-like quantum oscillatory magnetization M (B), i.e., the de Haas-van Alphen (dHvA) effect. At the same time, unexpected spike-like overshoots in M and non-equilibrium currents are observed which allow us to identify the microscopic nature and density of the residual disorder. The acceptor-like scatterers give rise to a magnetic thaw down effect which enhances the dHvA amplitude beyond the electron-electron interaction effects being present in the MgZnO/ZnO heterostructure.

Physical Review B, 2011

All-electrical spin-wave spectroscopy and frequency-resolved magneto-optical Kerr-effect measurem... more All-electrical spin-wave spectroscopy and frequency-resolved magneto-optical Kerr-effect measurements are combined to study spin waves propagating through a magnetic antidot lattice nanopatterned from a Ni 80 Fe 20 thin film. Spin waves are injected from a plain film into the antidot lattice and the transmission across the interface is explored in detail for different wavelengths. We find that spin waves with a wavelength much greater than the lattice periodicity are not described well by recently discussed approaches. Instead the spin-wave dispersion is consistent with an effective magnetization smaller than the saturation magnetization measured on the unstructured ferromagnetic material. Consistently, we find that the transmission coefficients are modeled well by assuming an effectively continuous metamaterial for spin waves characterized by the reduced magnetization. The experimental data and interpretation are substantiated theoretically using the plane-wave method and micromagnetic modeling. The results are interesting for the development of frequency-selective mirrors in magnonics through lateral nanopatterning.

Physical Review B, 2013

We report a combined experimental and theoretical study of the quasistatic hysteresis and dynamic... more We report a combined experimental and theoretical study of the quasistatic hysteresis and dynamic excitations in large-area arrays of NiFe nanodisks forming a hexagonal lattice with the lattice constant of 390 nm. Arrays were fabricated by patterning a 20-nm-thick NiFe film using the etched nanosphere lithography. We have studied a close-packed (edge-to-edge separation between disks d cp = 65 nm) and an ultraclosed packed (d ucp = 20 nm) array. Hysteresis loops for both arrays were qualitatively similar and nearly isotropic, i.e., independent on the in-plane external field orientation. The shape of these loops revealed that magnetization reversal is governed by the formation and expulsion of vortices inside the nanodisks. When we assumed that the nanodisks' magnetization significantly decreases near their edges, micromagnetic simulations with material parameters determined independently from continuous film measurements could satisfactorily reproduce the hysteresis. Despite the isotropic hysteresis, significant in-plane anisotropy of the dynamic response of the ultraclose-packed array was found experimentally by the all-electrical spin-wave spectroscopy and Brillouin light scattering. Dynamical simulations could successfully reproduce the difference between excitation spectra for fields directed along the two main symmetry axes of the hexagonal lattice. Simulations revealed that this difference is caused by the magnetodipolar interaction between nanodisks, which leads to a strong variation of the spatial distribution of the oscillation power both for bulk and edge modes as a function of the bias field orientation. Comparison of simulated and measured frequencies enabled the unambiguous identification of experimentally observed modes. Results of this systematic research are relevant both for fundamental studies of spin-wave modes in patterned magnetic structures and for the design of magnonic crystals for potential applications as, e.g., spin-wave guides and filters.

Physical Review B, 2007

We present a combined experimental, computational, and semianalytical study of the magnetization ... more We present a combined experimental, computational, and semianalytical study of the magnetization dynamics of permalloy disks and nanostructured rings with a systematically varied ring width. We investigate the dynamics of the quasisaturated state. In the case of wide rings the spin wave mode spectrum is similar to that of a disk. The small inner hole can be viewed as a weak perturbation. When the central hole increases, its influence becomes more important and two characteristic modes form gradually. They become localized at different positions in the ring. We explain the localization by the increasing inhomogeneity of the internal magnetic field and the formation of domain wall regions as the rings grow more narrow. In narrow rings one of the modes is clearly confined to the two segments where the internal field H int is at a maximum and the other to the domain wall region where H int is small. Dynamic magnetic simulations agree well with the measured spectra and confirm this interpretation. We also applied a semianalytical model, which confirms that the mode localization is driven by the internal field inhomogeneity.

IEEE Transactions on Magnetics, 2010

We present a combined experimental investigation of magnetic normal modes in an antidot lattice u... more We present a combined experimental investigation of magnetic normal modes in an antidot lattice using both Brillouin light scattering and broadband ferromagnetic resonance. It was fabricated on a silicon substrate using optical ultraviolet lithography. The sample consisted of a 30-nm-thick Ni 80 Fe 20 squared antidot array with circular holes whose diameter and edge-to-edge spacing are 250 and 150 nm, respectively. Experiments were performed as a function of the applied magnetic field 0 H ext in the range from 100 to 100 mT, with H ext applied along both the square lattice axis and its diagonal. Several peaks were observed in both the Brillouin light scattering and ferromagnetic resonance spectra, and their evolution with the intensity and the direction of the applied field H ext was measured. Micromagnetic simulations enabled us to identify the modes in terms of their symmetry obtaining a good quantitative agreement with the measured frequencies. In addition, we show how the inhomogeneity of the internal field affected the properties of the magnetic eigenmodes and their localization in different regions of the antidot lattice.