## Final Report Summary - MAGNONICS (Mastering magnons in magnetic metamaterials)

Executive summary:

Nanostructured magnetic (magnonic) metamaterials with GHz and THz dynamics and / or with negative electromagnetic properties.

Nanomanufacturing techniques:

- protein based colloidal crystallisation (bottom-up), electron beam and photo lithography;

- focused ion beam etching;

- etched nanosphere lithography;

- precision electrodeposition; atomic layer deposition;

- various conventional sputtering and evaporation techniques.

Dynamical characterisation techniques:

- all-electrical spin wave spectroscopy (AESWS);

- conventional and microfocus Brillouin light scattering (BLS) spectroscopy;

- time resolved scanning Kerr microscopy (TRSKM);

- THz spectroscopy.

Theoretical methods:

- electromagnetic and spin dynamics models for band gap and effectively continuous properties describing excitations in magnonic metamaterials, including micromagnetics (all aspects);

- Plane wave method (PWM) (magnonic dispersions), Dynamical matrix method (DMM) (magnonic spectra and dispersions), numerical and semi-analytical discrete dipole models (static and dynamics of arrays of magnetic nanoparticles produced by the protein based colloidal crystallisation);

- MatLab based Finite-difference time domain (FDTD) solution of full Maxwell equations with account of Ferromagnetic resonance (FMR) phenomena (electromagnetic response of magnonic metamaterials), and mixing rules (effective permeability of magnonic metamaterials consisting of arrays of magnetic elements).

Achievements:

- establishment of new types of magnonic metamaterials, in particular including three-dimensional (3D) magnonic arrays produced by the protein based colloidal crystallisation and 2D all-ferromagnetic binary magnonic metamaterials, and of functional magnonic architectures (including that enabled by designer coupling between long wavelength electromagnetic and short wavelength spin waves);

- establishing of theoretical methods by which to calculate the effectively continuous (including electromagnetic) properties of magnonic metamaterials and of concepts of design of the metamaterial responses.

Potential applications:

- electromagnetic antennas (e.g. patch antennas);

- signal conditioning devices (e.g. microwave filters); and

- magnonic devices and logic architectures, including magnonic filters, logic gates, programmable gate arrays etc.

Project context and objectives:

MAGNONICS consortium combines nanofabrication, dynamical characterisation, and theoretical modelling within a multinational collaboration that has strived to explore novel nano-structured magnetic metamaterials that exhibit high-frequency responses artificially tailored at the nanoscale. These so-called magnonic nanomaterials form a new class of metamaterials with collective magnonic and associated electromagnetic responses giving rise to new complex but potentially very rewarding functionalities. At the same time, they provide an added value to existing magnetic devices and conventional metamaterials. The study of magnonic metamaterials forms a sub-field of a wider field of research called magnonics.

The main goal of the MAGNONICS project has been to realise, on the one hand, new nanotechnologies and, on the other hand, this new class of metamaterials, i.e. magnetic metamaterials, and hence to prove the concept of magnonics.

MAGNONICS project has explored several key aspects of magnonics and magnonic metamaterials, ultimately required to make magnonics a pervasive technology. Firstly, the project has adopted existing and developed novel nanomanufacturing technologies for the specific tasks of magnonics. Secondly, the project has used some state-of-the-art existing and newly developed novel dynamic characterisation techniques to perform seminal experiments that will guide the development of magnonics and magnonic metamaterial for the decades ahead. Thirdly, the project has developed theoretical methods as required for the description and predicting of outcomes of the dynamical testing of magnonic metamaterials. Finally, the project has brought to the table a few novel concept of devices and architectures in which magnonic metamaterials could be used providing functional benefits.

As a result, the project has strived to achieve its technical objectives of:

1. using new nanotechnologies to fabricate novel macroscale periodic magnetic structures with nanoscale features and to characterise their structural and static properties;

2. characterising and understanding dynamic magnetic properties of the fabricated periodic magnetic structures, and revealing their inherent novel collective dynamic properties at high frequencies, thereby demonstrating that they form magnetic metamaterials;

3. incorporating the created magnetic metamaterials into working miniature devices in place of continuous materials, thereby demonstrating various ways of exploitation of their useful functionalities.

The findings of MAGNONICS project provide a major contribution to reforming current and underpin future applications of magnetic materials in high-tech data communication, processing, and storage devices, forming the Information technology (IT) spine of the new European knowledge driven economy. In longer term, the uncovered basic understandings of the magnonic phenomena will underpin the competitiveness of European high-tech industry on the international hi-tech knowledge-rich functional materials with impacts ranging from high speed magnetic data storage to data communication technologies.

Project results:

MAGNONICS consortium has explored several key aspects of magnonics and magnonic metamaterials, addressing their nanomanufacturing, dynamic characterisation, theoretical modelling, and design of devices. As a result of this research, several important breakthroughs have been achieved either crossing the different work directions, or sometimes limited to particular ones. The three most significant breakthroughs are described first.

Perhaps, the most innovative and ground-breaking achievement of the project is the exploration of the protein based 3D arrays of magnetic nanoparticles as magnonic metamaterials. This achievement has become a result of the extensive development of the bottom-up fabrication of such structures using the protein based colloidal crystallisation process and then adaptation of the more conventional top-down nano-patterning techniques to place the structures enabling their state-of-the-art cryogenic measurements using the AESWS at GHz frequencies. The sensitivity of the cryogenic AESWS measurements had to be improved remarkably, while a set of advanced theoretical tools has also to be developed to facilitate understanding of the measured signal. As a result, evidence of the propagation of the magnonic signal through such 3D magnonic metamaterials was produced at the very end of the project. Unfortunately, the success could not be extended to the THz domain, albeit the excellent prospects for refinement of the THz spectroscopy as a technique for studies in magnonics suggest that such measurements could prove successful in future.

The next in significance achievement came from the advancement of the top-down nonmanufacturing techniques that enables fabrication of arrays of magnetic nanoelements embedded within a matrix of another magnetic material. In a number of publications, a detailed understanding of their magnonic (both band gap and effectively continuous) properties has been delivered, which has facilitated by the remarkable development in both the sensitivity of the dynamical measurement techniques (including the BLS, TRSKM, and the aforementioned AESWS) and theoretical modelling (including PWM and the micromagnetic simulations). The measurements have been bench-marked against those of single-constituent magnonic metamaterials (i.e. arrays of magnetic elements and antidots), culminating in the complete mapping of the 2D magnonic band structure by BLS. The latter has been enabled by the further advancement of the DMM. Finally, the project has witnessed a remarkable success in exploration of applied aspects of magnonics and magnonic metamaterials. Theoretical evidence of the negative effective permeability at frequencies reaching some hundreds GHz has been delivered. The developed concepts and recipes for the permeability calculation could now be applied to a range of designer magnonic metamaterials. In additional, a novel (and unforeseen at the time of proposal submission) concept of magnonic data architectures driven by free space microwaves has been developed and experimentally demonstrated as a result of overcoming the bottle-neck of coupling between long wavelength electromagnetic and short wave wavelength spin waves.

Here we provide a list of further science and technology (S&T) achievements of smaller scale but high importance for the fields of magnonics, magnonic meta-materials and technologies, and also more generally for magnetics research: Comprehensive theoretical understanding of the band gap and effectively continuous properties of the created magnonic metamaterials has been achieved.

The PWM has been extended to the calculation of magnonic band structure of thin slabs of 1D and 2D magnonic crystals and validated via comparison with experimental results.

The PWM has been developed to the calculation of magnonic spectra of antidot lattices and successfully used to interpret experimental data acquired using the AESWS and BLS.

The PWM has been also extended to the calculations of the magnonic band structure in planar magnonic crystals for an arbitrary chosen direction of the external magnetic field. The method has been successfully used for the interpretation of the data in the rhombic antidot lattices measured by BLS.

The PWM has been developed for calculations of magnonic spectra in the re-programmable magnonic crystal, i.e. in the ferromagnetic and antiferromagnetic ordered Py stripes. Then it has been validated by comparing numerical results with the experimental data obtained with broadband microwave spectroscopy.

The nearly free magnon model (an analogue of the nearly free electron model) has been defined and used to describe analytically the magnonic band gap width in 2D bi-component Co / Py magnonic crystals. The results have been successfully used for the interpretation experimental data obtained with BLS.

The negative effective permeability in meta-material based on 1D planar magnonic crystals has been predicted based on the PWM calculations. The figure of merit for a negative refraction has been estimated and its value has been found to be promising for the future development.

The Goos-Haenchen shift for spin waves in the exchange limit has been predicted. It has been found that the Goos-Heanchen shift critically depends on the exchange coupling between two ferromagnetic materials.

The finite element method has been developed in the frequency domain for the calculations of the magnonic band structure in 1D planar magnonic crystals with nonuniform composition across the thickness. The developed method opens the prospects for the calculations of the magnonic band structure in 3D magnonic crystals of finite thickness. Based on the PWM calculations the materials composition of the 3D bi-component magnonic crystals based on the protein-based colloidal magnonic arrays have been determined to have absolute magnonic band gap in 3D.

The DMM has been developed to deal with dipole-coupled particles and arrays of antidots and to evaluate the BLS cross section, and applied to systems experimentally investigated within the project: chains and 2D arrays of magnetic dots, square arrays of antidots.

Thermally excited spin waves in planar one- and two-dimensional magnonic crystals have been studied using both conventional (k-vector resolved) and micro-focused (spatial resolved) BLS measurements in arrays of dense magnetic elements (dots and stripes) and antidots (periodic arrangement of holes embedded into a continuous magnetic film), and the results have been compared with calculations performed by micromagnetic simulations, the PWM, and the DMM.

In addition, microfocused BLS technique has been applied to reveal the propagating spin waves emitted by a nanocontact by spin-transfer torque effect. The generation of spin waves by using a dc spin polarised current is important to inject spin waves into magnonic crystal and devices in alternative to conventional microwave antennas.

The 3D version of the Fast Fourier technique (FFT) for calculating the magneto-dipolar interaction field in continuous ferromagnetic structures has been implemented, so that large-scale simulations of 3D micromagnetic problems have become possible.

The combined Ewald-FFT method for the calculation of the magneto-dipole interaction field in ordered and disordered systems of fine magnetic particles has been developed. In particular, this method enables highly efficient numerical simulations of magnetisation processes in magnetoferritin-based crystals. Basing on this method, two software packages capable of extracting the key magnetic parameters of a single magnetoferritin particle, which serves as the building block for corresponding crystals, have been developed. These tools allow one to precisely determine the magnetic moment of a single MF particle and its uniaxial and cubic magnetic anisotropy constants.

Numerical simulations of quasistatic magnetisation processes measured by MOKE in 2D hexagonal arrays of magnetic nanodisks have been performed. Such simulations, combined with BLS experiments on the unpatterned magnetic film used for the production of the 2D nanodisk array, allow the exact determination of magnetic parameters of the film material (magnetisation, exchange stiffness constant and the surface anisotropy constant), which is the mandatory prerequisite for studying the system dynamics.

Time-domain micromagnetic simulations of spin-wave excitations observed by FMR, BLS, and TRSKM techniques in 2D arrays of magnetic nanodisks has allowed to unambiguously identify the experimentally observed modes, and to find out the spatial structure of corresponding magnons in the nanodot arrays under study.

A concept for a spin wave filter based on the antidot lattice cut out into a thin magnetic film has been proposed and verified by numerical simulations. It has been shown, that such a filter exhibits large frequency gaps in the transmitted magnon spectrum. Positions and widths of these gaps can be controlled not only by changing the lattice geometry (number of antidot columns, antidots lattice constants, antidot diameter), but also by simply varying the external magnetic field.

A concept for focusing spin waves in thin magnetic films has been suggested, basing on the usage of the Fresnel-like 'zone plate', consisting of slits with predefined lengths, which are cut out in such a thin film. Using numerical simulations, we have shown, that a column of these slits is able to increase the power of magnetisation oscillations at a given point up to 5 times due to the constructive interference of spin waves transmitted through such a 'zone plate'. The position of the focus point can be controlled by the sizes of slits and the external magnetic field.

The method for 'bending' the wave front of an initially plane spin wave, employing the site-dependent damping has been proposed. The spatially varying damping leads to a bending of magnon 'rays' due to the corresponding change of the magnon refraction index. Using a site-dependent damping which increases towards the edges of a thin magnetic stripe, we could show that this method allows to achieve, e.g. the effective focusing of spin waves for the wave propagating along such a stripe. The degree of focusing and the position of the region where the magnetisation oscillation power is strongly enhanced may be controlled separately by varying the spatial profile of the damping constant by using, e.g. the ion irradiation with the site-dependent intensity.

A list of 11 potentially exploitable results is also supplied within 'The final plan for the use and dissemination of foreground'.

Potential impact:

The MAGNONICS project has produced basic scientific understanding and knowledge that underpin the development of a novel technology while its side results will have many technological applications on other areas of science and technology.

The project results have an immense potential for new applications in electronics and microwave communications. The main benefits from use of magnetic materials and specifically magnonic metamaterials in electronics and telecommunications devices are controllability by external magnetic fields, non-volatility, and re-configurability, all of which have been demonstrated within MAGNONICS. The exploitation of propagating spin waves rather than spin polarised currents and localised spins will make it possible to reduce the energy consumption of magneto-electronic devices. The broad frequency spectrum of magnons means that such devices will have enough head-room to easily adapt to the continuous increase in data rates.

There are two different ways how magnetic crystals could be used. In the first of them, the wavelength of the excitation of interest (e.g. EM radiation) is much greater than the period and patterned features of the magnonic crystal. Thus, the latter behaves as an effectively continuous metamaterial with a frequency response determined by the folded band spectrum of magnons. These entirely new electromagnetic materials could be utilised in a variety of applications where tuning the transmission, absorption and reflection of electromagnetic radiation is crucial, e.g. as in microwave telecommunications. In the second approach, magnons themselves are used as carriers of information in magnonic circuits with features comparable in size to the magnonic wavelength. This gives rise to strong interference and diffraction of magnons, in turn leading e.g. to formation of the output in logic devices or the band spectrum of magnons in magnonic crystals.

Within the first approach, the main useful functionality of magnonic metamaterials is the opportunity to tailor their electromagnetic response by modifying their magnonic spectrum via nanopatterning or by applying external magnetic field. The interaction between constituent elements of magnonic crystals is strong enough to support collective magnonic excitations, and so magnonic crystals behave as a quasi-continuous metamaterial. MAGNONICS has yielded new recipes for tailoring collective magnonic responses of such metamaterials. Their electromagnetic response reflects their tailored magnonic responses, thus potentially leading to novel commercially exploitable material properties. As far as the second approach (based on the use magnons as carriers of information) is concerned, the main useful functionality of magnonic crystals is their frequency and wavelength selectivity, which directly results from their periodicity and the associated magnonic band spectrum. MAGNONICS has actively pursued the strategic aim of the Nanosciences, nanotechnologies, materials and new production technologies (NMP) work programme to develop 'added value materials with higher knowledge content, new functionalities and improved performance'. The major factor determining the selection of the nanofabrication techniques exploited and further developed within this project has been the need to fabricate large-area samples with perfectly periodic structure on the nanometre scale. This need is common within the family of metamaterials, and so the design and processing know-how generated in this project will be of direct and strong impact upon the metamaterials research in its most general meaning. Further impact is expected in the area of nano-fabrication of bit patterned data storage media and arrays of phase locked spin transfer torque nano-oscillators, in which the addressability of individual data bits and the phase locking of the nano-oscillators respectively both rely upon their perfect ordering over large areas.

Project website: http://www.magnonics.org/

Nanostructured magnetic (magnonic) metamaterials with GHz and THz dynamics and / or with negative electromagnetic properties.

Nanomanufacturing techniques:

- protein based colloidal crystallisation (bottom-up), electron beam and photo lithography;

- focused ion beam etching;

- etched nanosphere lithography;

- precision electrodeposition; atomic layer deposition;

- various conventional sputtering and evaporation techniques.

Dynamical characterisation techniques:

- all-electrical spin wave spectroscopy (AESWS);

- conventional and microfocus Brillouin light scattering (BLS) spectroscopy;

- time resolved scanning Kerr microscopy (TRSKM);

- THz spectroscopy.

Theoretical methods:

- electromagnetic and spin dynamics models for band gap and effectively continuous properties describing excitations in magnonic metamaterials, including micromagnetics (all aspects);

- Plane wave method (PWM) (magnonic dispersions), Dynamical matrix method (DMM) (magnonic spectra and dispersions), numerical and semi-analytical discrete dipole models (static and dynamics of arrays of magnetic nanoparticles produced by the protein based colloidal crystallisation);

- MatLab based Finite-difference time domain (FDTD) solution of full Maxwell equations with account of Ferromagnetic resonance (FMR) phenomena (electromagnetic response of magnonic metamaterials), and mixing rules (effective permeability of magnonic metamaterials consisting of arrays of magnetic elements).

Achievements:

- establishment of new types of magnonic metamaterials, in particular including three-dimensional (3D) magnonic arrays produced by the protein based colloidal crystallisation and 2D all-ferromagnetic binary magnonic metamaterials, and of functional magnonic architectures (including that enabled by designer coupling between long wavelength electromagnetic and short wavelength spin waves);

- establishing of theoretical methods by which to calculate the effectively continuous (including electromagnetic) properties of magnonic metamaterials and of concepts of design of the metamaterial responses.

Potential applications:

- electromagnetic antennas (e.g. patch antennas);

- signal conditioning devices (e.g. microwave filters); and

- magnonic devices and logic architectures, including magnonic filters, logic gates, programmable gate arrays etc.

Project context and objectives:

MAGNONICS consortium combines nanofabrication, dynamical characterisation, and theoretical modelling within a multinational collaboration that has strived to explore novel nano-structured magnetic metamaterials that exhibit high-frequency responses artificially tailored at the nanoscale. These so-called magnonic nanomaterials form a new class of metamaterials with collective magnonic and associated electromagnetic responses giving rise to new complex but potentially very rewarding functionalities. At the same time, they provide an added value to existing magnetic devices and conventional metamaterials. The study of magnonic metamaterials forms a sub-field of a wider field of research called magnonics.

The main goal of the MAGNONICS project has been to realise, on the one hand, new nanotechnologies and, on the other hand, this new class of metamaterials, i.e. magnetic metamaterials, and hence to prove the concept of magnonics.

MAGNONICS project has explored several key aspects of magnonics and magnonic metamaterials, ultimately required to make magnonics a pervasive technology. Firstly, the project has adopted existing and developed novel nanomanufacturing technologies for the specific tasks of magnonics. Secondly, the project has used some state-of-the-art existing and newly developed novel dynamic characterisation techniques to perform seminal experiments that will guide the development of magnonics and magnonic metamaterial for the decades ahead. Thirdly, the project has developed theoretical methods as required for the description and predicting of outcomes of the dynamical testing of magnonic metamaterials. Finally, the project has brought to the table a few novel concept of devices and architectures in which magnonic metamaterials could be used providing functional benefits.

As a result, the project has strived to achieve its technical objectives of:

1. using new nanotechnologies to fabricate novel macroscale periodic magnetic structures with nanoscale features and to characterise their structural and static properties;

2. characterising and understanding dynamic magnetic properties of the fabricated periodic magnetic structures, and revealing their inherent novel collective dynamic properties at high frequencies, thereby demonstrating that they form magnetic metamaterials;

3. incorporating the created magnetic metamaterials into working miniature devices in place of continuous materials, thereby demonstrating various ways of exploitation of their useful functionalities.

The findings of MAGNONICS project provide a major contribution to reforming current and underpin future applications of magnetic materials in high-tech data communication, processing, and storage devices, forming the Information technology (IT) spine of the new European knowledge driven economy. In longer term, the uncovered basic understandings of the magnonic phenomena will underpin the competitiveness of European high-tech industry on the international hi-tech knowledge-rich functional materials with impacts ranging from high speed magnetic data storage to data communication technologies.

Project results:

MAGNONICS consortium has explored several key aspects of magnonics and magnonic metamaterials, addressing their nanomanufacturing, dynamic characterisation, theoretical modelling, and design of devices. As a result of this research, several important breakthroughs have been achieved either crossing the different work directions, or sometimes limited to particular ones. The three most significant breakthroughs are described first.

Perhaps, the most innovative and ground-breaking achievement of the project is the exploration of the protein based 3D arrays of magnetic nanoparticles as magnonic metamaterials. This achievement has become a result of the extensive development of the bottom-up fabrication of such structures using the protein based colloidal crystallisation process and then adaptation of the more conventional top-down nano-patterning techniques to place the structures enabling their state-of-the-art cryogenic measurements using the AESWS at GHz frequencies. The sensitivity of the cryogenic AESWS measurements had to be improved remarkably, while a set of advanced theoretical tools has also to be developed to facilitate understanding of the measured signal. As a result, evidence of the propagation of the magnonic signal through such 3D magnonic metamaterials was produced at the very end of the project. Unfortunately, the success could not be extended to the THz domain, albeit the excellent prospects for refinement of the THz spectroscopy as a technique for studies in magnonics suggest that such measurements could prove successful in future.

The next in significance achievement came from the advancement of the top-down nonmanufacturing techniques that enables fabrication of arrays of magnetic nanoelements embedded within a matrix of another magnetic material. In a number of publications, a detailed understanding of their magnonic (both band gap and effectively continuous) properties has been delivered, which has facilitated by the remarkable development in both the sensitivity of the dynamical measurement techniques (including the BLS, TRSKM, and the aforementioned AESWS) and theoretical modelling (including PWM and the micromagnetic simulations). The measurements have been bench-marked against those of single-constituent magnonic metamaterials (i.e. arrays of magnetic elements and antidots), culminating in the complete mapping of the 2D magnonic band structure by BLS. The latter has been enabled by the further advancement of the DMM. Finally, the project has witnessed a remarkable success in exploration of applied aspects of magnonics and magnonic metamaterials. Theoretical evidence of the negative effective permeability at frequencies reaching some hundreds GHz has been delivered. The developed concepts and recipes for the permeability calculation could now be applied to a range of designer magnonic metamaterials. In additional, a novel (and unforeseen at the time of proposal submission) concept of magnonic data architectures driven by free space microwaves has been developed and experimentally demonstrated as a result of overcoming the bottle-neck of coupling between long wavelength electromagnetic and short wave wavelength spin waves.

Here we provide a list of further science and technology (S&T) achievements of smaller scale but high importance for the fields of magnonics, magnonic meta-materials and technologies, and also more generally for magnetics research: Comprehensive theoretical understanding of the band gap and effectively continuous properties of the created magnonic metamaterials has been achieved.

The PWM has been extended to the calculation of magnonic band structure of thin slabs of 1D and 2D magnonic crystals and validated via comparison with experimental results.

The PWM has been developed to the calculation of magnonic spectra of antidot lattices and successfully used to interpret experimental data acquired using the AESWS and BLS.

The PWM has been also extended to the calculations of the magnonic band structure in planar magnonic crystals for an arbitrary chosen direction of the external magnetic field. The method has been successfully used for the interpretation of the data in the rhombic antidot lattices measured by BLS.

The PWM has been developed for calculations of magnonic spectra in the re-programmable magnonic crystal, i.e. in the ferromagnetic and antiferromagnetic ordered Py stripes. Then it has been validated by comparing numerical results with the experimental data obtained with broadband microwave spectroscopy.

The nearly free magnon model (an analogue of the nearly free electron model) has been defined and used to describe analytically the magnonic band gap width in 2D bi-component Co / Py magnonic crystals. The results have been successfully used for the interpretation experimental data obtained with BLS.

The negative effective permeability in meta-material based on 1D planar magnonic crystals has been predicted based on the PWM calculations. The figure of merit for a negative refraction has been estimated and its value has been found to be promising for the future development.

The Goos-Haenchen shift for spin waves in the exchange limit has been predicted. It has been found that the Goos-Heanchen shift critically depends on the exchange coupling between two ferromagnetic materials.

The finite element method has been developed in the frequency domain for the calculations of the magnonic band structure in 1D planar magnonic crystals with nonuniform composition across the thickness. The developed method opens the prospects for the calculations of the magnonic band structure in 3D magnonic crystals of finite thickness. Based on the PWM calculations the materials composition of the 3D bi-component magnonic crystals based on the protein-based colloidal magnonic arrays have been determined to have absolute magnonic band gap in 3D.

The DMM has been developed to deal with dipole-coupled particles and arrays of antidots and to evaluate the BLS cross section, and applied to systems experimentally investigated within the project: chains and 2D arrays of magnetic dots, square arrays of antidots.

Thermally excited spin waves in planar one- and two-dimensional magnonic crystals have been studied using both conventional (k-vector resolved) and micro-focused (spatial resolved) BLS measurements in arrays of dense magnetic elements (dots and stripes) and antidots (periodic arrangement of holes embedded into a continuous magnetic film), and the results have been compared with calculations performed by micromagnetic simulations, the PWM, and the DMM.

In addition, microfocused BLS technique has been applied to reveal the propagating spin waves emitted by a nanocontact by spin-transfer torque effect. The generation of spin waves by using a dc spin polarised current is important to inject spin waves into magnonic crystal and devices in alternative to conventional microwave antennas.

The 3D version of the Fast Fourier technique (FFT) for calculating the magneto-dipolar interaction field in continuous ferromagnetic structures has been implemented, so that large-scale simulations of 3D micromagnetic problems have become possible.

The combined Ewald-FFT method for the calculation of the magneto-dipole interaction field in ordered and disordered systems of fine magnetic particles has been developed. In particular, this method enables highly efficient numerical simulations of magnetisation processes in magnetoferritin-based crystals. Basing on this method, two software packages capable of extracting the key magnetic parameters of a single magnetoferritin particle, which serves as the building block for corresponding crystals, have been developed. These tools allow one to precisely determine the magnetic moment of a single MF particle and its uniaxial and cubic magnetic anisotropy constants.

Numerical simulations of quasistatic magnetisation processes measured by MOKE in 2D hexagonal arrays of magnetic nanodisks have been performed. Such simulations, combined with BLS experiments on the unpatterned magnetic film used for the production of the 2D nanodisk array, allow the exact determination of magnetic parameters of the film material (magnetisation, exchange stiffness constant and the surface anisotropy constant), which is the mandatory prerequisite for studying the system dynamics.

Time-domain micromagnetic simulations of spin-wave excitations observed by FMR, BLS, and TRSKM techniques in 2D arrays of magnetic nanodisks has allowed to unambiguously identify the experimentally observed modes, and to find out the spatial structure of corresponding magnons in the nanodot arrays under study.

A concept for a spin wave filter based on the antidot lattice cut out into a thin magnetic film has been proposed and verified by numerical simulations. It has been shown, that such a filter exhibits large frequency gaps in the transmitted magnon spectrum. Positions and widths of these gaps can be controlled not only by changing the lattice geometry (number of antidot columns, antidots lattice constants, antidot diameter), but also by simply varying the external magnetic field.

A concept for focusing spin waves in thin magnetic films has been suggested, basing on the usage of the Fresnel-like 'zone plate', consisting of slits with predefined lengths, which are cut out in such a thin film. Using numerical simulations, we have shown, that a column of these slits is able to increase the power of magnetisation oscillations at a given point up to 5 times due to the constructive interference of spin waves transmitted through such a 'zone plate'. The position of the focus point can be controlled by the sizes of slits and the external magnetic field.

The method for 'bending' the wave front of an initially plane spin wave, employing the site-dependent damping has been proposed. The spatially varying damping leads to a bending of magnon 'rays' due to the corresponding change of the magnon refraction index. Using a site-dependent damping which increases towards the edges of a thin magnetic stripe, we could show that this method allows to achieve, e.g. the effective focusing of spin waves for the wave propagating along such a stripe. The degree of focusing and the position of the region where the magnetisation oscillation power is strongly enhanced may be controlled separately by varying the spatial profile of the damping constant by using, e.g. the ion irradiation with the site-dependent intensity.

A list of 11 potentially exploitable results is also supplied within 'The final plan for the use and dissemination of foreground'.

Potential impact:

The MAGNONICS project has produced basic scientific understanding and knowledge that underpin the development of a novel technology while its side results will have many technological applications on other areas of science and technology.

The project results have an immense potential for new applications in electronics and microwave communications. The main benefits from use of magnetic materials and specifically magnonic metamaterials in electronics and telecommunications devices are controllability by external magnetic fields, non-volatility, and re-configurability, all of which have been demonstrated within MAGNONICS. The exploitation of propagating spin waves rather than spin polarised currents and localised spins will make it possible to reduce the energy consumption of magneto-electronic devices. The broad frequency spectrum of magnons means that such devices will have enough head-room to easily adapt to the continuous increase in data rates.

There are two different ways how magnetic crystals could be used. In the first of them, the wavelength of the excitation of interest (e.g. EM radiation) is much greater than the period and patterned features of the magnonic crystal. Thus, the latter behaves as an effectively continuous metamaterial with a frequency response determined by the folded band spectrum of magnons. These entirely new electromagnetic materials could be utilised in a variety of applications where tuning the transmission, absorption and reflection of electromagnetic radiation is crucial, e.g. as in microwave telecommunications. In the second approach, magnons themselves are used as carriers of information in magnonic circuits with features comparable in size to the magnonic wavelength. This gives rise to strong interference and diffraction of magnons, in turn leading e.g. to formation of the output in logic devices or the band spectrum of magnons in magnonic crystals.

Within the first approach, the main useful functionality of magnonic metamaterials is the opportunity to tailor their electromagnetic response by modifying their magnonic spectrum via nanopatterning or by applying external magnetic field. The interaction between constituent elements of magnonic crystals is strong enough to support collective magnonic excitations, and so magnonic crystals behave as a quasi-continuous metamaterial. MAGNONICS has yielded new recipes for tailoring collective magnonic responses of such metamaterials. Their electromagnetic response reflects their tailored magnonic responses, thus potentially leading to novel commercially exploitable material properties. As far as the second approach (based on the use magnons as carriers of information) is concerned, the main useful functionality of magnonic crystals is their frequency and wavelength selectivity, which directly results from their periodicity and the associated magnonic band spectrum. MAGNONICS has actively pursued the strategic aim of the Nanosciences, nanotechnologies, materials and new production technologies (NMP) work programme to develop 'added value materials with higher knowledge content, new functionalities and improved performance'. The major factor determining the selection of the nanofabrication techniques exploited and further developed within this project has been the need to fabricate large-area samples with perfectly periodic structure on the nanometre scale. This need is common within the family of metamaterials, and so the design and processing know-how generated in this project will be of direct and strong impact upon the metamaterials research in its most general meaning. Further impact is expected in the area of nano-fabrication of bit patterned data storage media and arrays of phase locked spin transfer torque nano-oscillators, in which the addressability of individual data bits and the phase locking of the nano-oscillators respectively both rely upon their perfect ordering over large areas.

Project website: http://www.magnonics.org/