{"id":{"repo_id":"exeter","oai_identifier":"oai:figshare.com:article/31448926"},"canonical_url":"https://search.dev.ndltd.org/etd/exeter/oai:figshare.com:article/31448926","repository":{"repo_id":"exeter","name":"University of Exeter","base_url":"https://api.figshare.com/v2/oai"},"display":{"title":"Current Induced Magnetisation Dynamics in Ferromagnetic Nanowires","abstract":"Ferromagnetic nanowires are functional and integral constituents in a variety of advanced technologies, including tuneable microwave devices, magnetic storage, spintronics, electromagnetic wave absorbers, noise suppressors, and biomedical applications. Their significance and popularity stem from the ability to tune both their static and dynamic magnetic responses through their geometry, dimensions, lattice parameters, material composition, magnetic anisotropy, and external fields. Arrays of magnetic nanowires can also be synthesised with high degree of uniformity and with controlled anisotropy using template assisted electrodeposition methods making them more accessible. Furthermore, metallic ferromagnetic nanowires are compatible with semiconductor fabrication techniques for integration into, for example, magnonic nanostructures and devices. Understanding the magnetisation dynamics and spin wave modes in individual and arrays of magnetic nanowires and their dependence on the nanowire and lattice material and geometrical parameters is critical for the design and tuning of magnetic devices, composites and metamaterials employing magnetic nanowires. Fabricated arrays with nanowire diameters of few nanometres or tens of nanometers support high frequency operations but are difficult to characterise and observe experimentally, which make modelling and simulation essential tools for the design and development of associated materials and devices. Modelling the magnetisation dynamics in magnetic nanowires is complex due to the rich micromagnetic energy landscape and supported resonance modes. This is made more challenging in metallic magnetic nanowires (in microwave devices and absorbers for example) which require consideration of applied and induced currents, and of electromagnetic wave interaction that produce non-uniform electromagnetic fields with different skin depths (both non-magnetic and magnetic) that control the resonance mechanism and spin-wave modes in the magnetic nanowires. Available analytical models of the magnetisation dynamics and resonance in magnetic nanowires simplify the Landau-Lifshitz-Gilbert (LLG) equation of magnetisation to arrive at closed-form solutions that limits their applicability (for example operate in the magnetostatic or exchange limits and apply to simple geometries). Numerical models offer more detail but often focus on the micromagnetic or the electromagnetic responses separately. Thus, there is a need for a numerical approach that can solve both the electromagnetic (Maxwell’s equations) and micromagnetic (LLG equation) coupled system and accurately simulate the magnetisation dynamics and fields in magnetic nanowires and arrays. Cobalt exhibits strong saturation magnetisation and pronounced magnetocrystalline anisotropy (MCA) making it a favourable material or constituent for high frequency applications. Crystallographic measurements and fabrication studies indicated that the MCA in cobalt nanowires is predominantly perpendicular to the nanowire axis, and the potential for controlling the angle of anisotropy. This control provides an additional and interesting mechanism of tuning the resonance frequency and spin-wave modes in cobalt nanowires. The effect of different angles of MCA on the dynamic response in magnetic nanowires and on resonance modes is not well understood which, again, is important for the design and tuning of microwave devices, absorbers and biomedical applications. Arrays of metallic ferromagnetic nanowires embedded in dielectric matrices, exhibit a tuneable effective electromagnetic response through external fields that is affected by the resonance properties of individual nanowires and the dipolar coupling between them. When excited by electromagnetic waves, electric fields couple with metallic magnetic nanowires and induce currents and skin effects that spatially and temporally affect the magnetisation distributions and hence resonance modes in the nanowires and arrays. There is currently lack of understanding of the effective dynamic response of arrays of metallic ferromagnetic nanowires and their effective properties arising from the complexity and scale of the problem. Current approaches focus on simplified semi-analytical models that ignore exchange or solved separately using either micromagnetics or electromagnetics (assuming a frequency dependent permeability as input). Hence there is a need for a numerical model that addresses the above challenges to model and understand the dynamic permeability in magnetic nanowire arrays to design and tune devices and metamaterials. This research and thesis establish a comprehensive transient electromagnetic - micromagnetic numerical model in finite-elements within COMSOL Multiphysics that couples the solution of Maxwell’s and LLG equations to model and simulate the magnetisation dynamics and resonance in individual and arrays of magnetic nanowires, excited by applied (axial) currents and electromagnetic plane waves. This model includes the contributions of exchange, magnetocrystalline anisotropy, magnetostatic fields and induced currents (eddy currents). This model was used to study and understand the current-induced resonance in individual, semi-infinite, two-dimensional circular cobalt nanowires with diameters in the range 10-100 nm and at different angles of uniaxial magnetocrystalline anisotropy. The individual nanowires are excited by a 70 GHz Gaussian electric current pulse applied parallel to the nanowire axis. The calculated transient magnetisation distributions and power absorption spectra indicate predominately curling mode resonance for nanowire diameters ≥ 20 nm with symmetrical radial spin-wave modes when the magnetocrystalline is parallel to the nanowire axis. The resonance frequencies and their size dependence agree with Aharoni’s exchange curling theory. Increasing the out of plane MCA angle breaks the circular symmetry and produces elliptical curling magnetisation accompanied by significant reduction in the resonance frequencies (for example from 50 GHz fundamental mode frequency in a 100 nm diameter nanowire with MCA parallel to the nanowire axis, to 15 GHz for perpendicular anisotropy). These results demonstrate the significant impact of MCA angle on resonance in ferromagnetic nanowires and the promising potential of using this anisotropy to tune the frequency response of magnetic nanowires. The finite-element electromagnetic-micromagnetic model was further applied to investigate the complex electromagnetic wave response and effective dynamic permeability of periodic, two-dimensional arrays of cobalt nanowires with diameters in the range 10-200 nm and packing fractions of 0.1, 0.3 and 0.6. The 70 GHz Gaussian electromagnetic wave source wavelength in the simulation is larger than the nanowire diameters and lattice constants and thus operating in the metamaterial limit. This enabled the extraction of the effective dynamic permeability of the array from the simulated scattering parameters. With the MCA parallel to the nanowire axis, the simulated peak frequencies in the imaginary permeability correspond approximately to a uniform mode ferromagnetic frequency for an interacting nanowire array. The imaginary permeability peaks also exhibited slight shift towards lower frequencies with increase in the magnitude of the permeability with increased packing fractions due to dipolar interactions and collective precession. The simulations also showed that the peak resonance frequencies in the permeability spectra for each packing fraction have negligible sensitivity to nanowire diameters, particularly for diameters greater than 100 nm. This is be attributed to the ≈ 50 nm magnetic skin depth in cobalt which confines the response to the circumferential region of the nanowire. Increasing the deviation of the MCA angle from the nanowire axis causes significant shift in the resonance frequencies in the simulated permeability spectra to lower frequencies with increased magnitude of the permeability, similar to the behaviour of individual nanowires. For the case of perpendicular anisotropy, two distinct frequency peaks appear in the permeability spectra. Analysis of the total power absorbed in the nanowire array revealed that the lower frequency peak corresponds to the fundamental resonance mode in the individual nanowires while the second higher frequency peak corresponds to the dipolar field contribution. Increasing the packing fraction shifts the two peaks closer to each other due to the increased dipolar coupling. The outcomes of this research provide a more detailed understanding of the dynamic response of individual and arrays of metallic ferromagnetic nanowires and establish their potential as tuneable building blocks for high-frequency metamaterial and device applications. Moreover, the numerical method here can be easily extended to three-dimensions and enable the modelling and simulation of a wide range of magnetic materials and devices.<p></p>","abstract_html":"Ferromagnetic nanowires are functional and integral constituents in a variety of advanced technologies, including tuneable microwave devices, magnetic storage, spintronics, electromagnetic wave absorbers, noise suppressors, and biomedical applications. Their significance and popularity stem from the ability to tune both their static and dynamic magnetic responses through their geometry, dimensions, lattice parameters, material composition, magnetic anisotropy, and external fields. Arrays of magnetic nanowires can also be synthesised with high degree of uniformity and with controlled anisotropy using template assisted electrodeposition methods making them more accessible. Furthermore, metallic ferromagnetic nanowires are compatible with semiconductor fabrication techniques for integration into, for example, magnonic nanostructures and devices. Understanding the magnetisation dynamics and spin wave modes in individual and arrays of magnetic nanowires and their dependence on the nanowire and lattice material and geometrical parameters is critical for the design and tuning of magnetic devices, composites and metamaterials employing magnetic nanowires. Fabricated arrays with nanowire diameters of few nanometres or tens of nanometers support high frequency operations but are difficult to characterise and observe experimentally, which make modelling and simulation essential tools for the design and development of associated materials and devices. Modelling the magnetisation dynamics in magnetic nanowires is complex due to the rich micromagnetic energy landscape and supported resonance modes. This is made more challenging in metallic magnetic nanowires (in microwave devices and absorbers for example) which require consideration of applied and induced currents, and of electromagnetic wave interaction that produce non-uniform electromagnetic fields with different skin depths (both non-magnetic and magnetic) that control the resonance mechanism and spin-wave modes in the magnetic nanowires. Available analytical models of the magnetisation dynamics and resonance in magnetic nanowires simplify the Landau-Lifshitz-Gilbert (LLG) equation of magnetisation to arrive at closed-form solutions that limits their applicability (for example operate in the magnetostatic or exchange limits and apply to simple geometries). Numerical models offer more detail but often focus on the micromagnetic or the electromagnetic responses separately. Thus, there is a need for a numerical approach that can solve both the electromagnetic (Maxwell’s equations) and micromagnetic (LLG equation) coupled system and accurately simulate the magnetisation dynamics and fields in magnetic nanowires and arrays. Cobalt exhibits strong saturation magnetisation and pronounced magnetocrystalline anisotropy (MCA) making it a favourable material or constituent for high frequency applications. Crystallographic measurements and fabrication studies indicated that the MCA in cobalt nanowires is predominantly perpendicular to the nanowire axis, and the potential for controlling the angle of anisotropy. This control provides an additional and interesting mechanism of tuning the resonance frequency and spin-wave modes in cobalt nanowires. The effect of different angles of MCA on the dynamic response in magnetic nanowires and on resonance modes is not well understood which, again, is important for the design and tuning of microwave devices, absorbers and biomedical applications. Arrays of metallic ferromagnetic nanowires embedded in dielectric matrices, exhibit a tuneable effective electromagnetic response through external fields that is affected by the resonance properties of individual nanowires and the dipolar coupling between them. When excited by electromagnetic waves, electric fields couple with metallic magnetic nanowires and induce currents and skin effects that spatially and temporally affect the magnetisation distributions and hence resonance modes in the nanowires and arrays. There is currently lack of understanding of the effective dynamic response of arrays of metallic ferromagnetic nanowires and their effective properties arising from the complexity and scale of the problem. Current approaches focus on simplified semi-analytical models that ignore exchange or solved separately using either micromagnetics or electromagnetics (assuming a frequency dependent permeability as input). Hence there is a need for a numerical model that addresses the above challenges to model and understand the dynamic permeability in magnetic nanowire arrays to design and tune devices and metamaterials. This research and thesis establish a comprehensive transient electromagnetic - micromagnetic numerical model in finite-elements within COMSOL Multiphysics that couples the solution of Maxwell’s and LLG equations to model and simulate the magnetisation dynamics and resonance in individual and arrays of magnetic nanowires, excited by applied (axial) currents and electromagnetic plane waves. This model includes the contributions of exchange, magnetocrystalline anisotropy, magnetostatic fields and induced currents (eddy currents). This model was used to study and understand the current-induced resonance in individual, semi-infinite, two-dimensional circular cobalt nanowires with diameters in the range 10-100 nm and at different angles of uniaxial magnetocrystalline anisotropy. The individual nanowires are excited by a 70 GHz Gaussian electric current pulse applied parallel to the nanowire axis. The calculated transient magnetisation distributions and power absorption spectra indicate predominately curling mode resonance for nanowire diameters ≥ 20 nm with symmetrical radial spin-wave modes when the magnetocrystalline is parallel to the nanowire axis. The resonance frequencies and their size dependence agree with Aharoni’s exchange curling theory. Increasing the out of plane MCA angle breaks the circular symmetry and produces elliptical curling magnetisation accompanied by significant reduction in the resonance frequencies (for example from 50 GHz fundamental mode frequency in a 100 nm diameter nanowire with MCA parallel to the nanowire axis, to 15 GHz for perpendicular anisotropy). These results demonstrate the significant impact of MCA angle on resonance in ferromagnetic nanowires and the promising potential of using this anisotropy to tune the frequency response of magnetic nanowires. The finite-element electromagnetic-micromagnetic model was further applied to investigate the complex electromagnetic wave response and effective dynamic permeability of periodic, two-dimensional arrays of cobalt nanowires with diameters in the range 10-200 nm and packing fractions of 0.1, 0.3 and 0.6. The 70 GHz Gaussian electromagnetic wave source wavelength in the simulation is larger than the nanowire diameters and lattice constants and thus operating in the metamaterial limit. This enabled the extraction of the effective dynamic permeability of the array from the simulated scattering parameters. With the MCA parallel to the nanowire axis, the simulated peak frequencies in the imaginary permeability correspond approximately to a uniform mode ferromagnetic frequency for an interacting nanowire array. The imaginary permeability peaks also exhibited slight shift towards lower frequencies with increase in the magnitude of the permeability with increased packing fractions due to dipolar interactions and collective precession. The simulations also showed that the peak resonance frequencies in the permeability spectra for each packing fraction have negligible sensitivity to nanowire diameters, particularly for diameters greater than 100 nm. This is be attributed to the ≈ 50 nm magnetic skin depth in cobalt which confines the response to the circumferential region of the nanowire. Increasing the deviation of the MCA angle from the nanowire axis causes significant shift in the resonance frequencies in the simulated permeability spectra to lower frequencies with increased magnitude of the permeability, similar to the behaviour of individual nanowires. For the case of perpendicular anisotropy, two distinct frequency peaks appear in the permeability spectra. Analysis of the total power absorbed in the nanowire array revealed that the lower frequency peak corresponds to the fundamental resonance mode in the individual nanowires while the second higher frequency peak corresponds to the dipolar field contribution. Increasing the packing fraction shifts the two peaks closer to each other due to the increased dipolar coupling. The outcomes of this research provide a more detailed understanding of the dynamic response of individual and arrays of metallic ferromagnetic nanowires and establish their potential as tuneable building blocks for high-frequency metamaterial and device applications. Moreover, the numerical method here can be easily extended to three-dimensions and enable the modelling and simulation of a wide range of magnetic materials and devices.&lt;p&gt;&lt;/p&gt;","abstract_has_math":false,"creators":["Mohammad Alneari (21039101)"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026-03-02T00:00:00Z","date_published":"2026-03-02T00:00:00Z","updated_at":"2026-07-27T19:34:10Z","subjects":["Micromagnetics","Ferromagnetic resonance","Cobalt nanowires","Finite element method","Magnetisation dynamics"],"languages":[],"rights":["All rights reserved","Open Access after 2027-09-09"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10779/exe.31448926.v1"],"render_values":[{"text":"10779/exe.31448926.v1","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Mohammad Alneari (21039101)"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2026-03-02T00:00:00Z"]},{"key":"dc:relation","label":"Dc Relation","values":["https://figshare.com/articles/thesis/Current_Induced_Magnetisation_Dynamics_in_Ferromagnetic_Nanowires/31448926"]},{"key":"dc:type","label":"Dc Type","values":["Text","Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Micromagnetics","Ferromagnetic resonance","Cobalt nanowires","Finite element method","Magnetisation dynamics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["All rights reserved","Open Access after 2027-09-09"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10779/exe.31448926.v1"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ferromagnetic nanowires are functional and integral constituents in a variety of advanced technologies, including tuneable microwave devices, magnetic storage, spintronics, electromagnetic wave absorbers, noise suppressors, and biomedical applications. Their significance and popularity stem from the ability to tune both their static and dynamic magnetic responses through their geometry, dimensions, lattice parameters, material composition, magnetic anisotropy, and external fields. Arrays of magnetic nanowires can also be synthesised with high degree of uniformity and with controlled anisotropy using template assisted electrodeposition methods making them more accessible. Furthermore, metallic ferromagnetic nanowires are compatible with semiconductor fabrication techniques for integration into, for example, magnonic nanostructures and devices. Understanding the magnetisation dynamics and spin wave modes in individual and arrays of magnetic nanowires and their dependence on the nanowire and lattice material and geometrical parameters is critical for the design and tuning of magnetic devices, composites and metamaterials employing magnetic nanowires. Fabricated arrays with nanowire diameters of few nanometres or tens of nanometers support high frequency operations but are difficult to characterise and observe experimentally, which make modelling and simulation essential tools for the design and development of associated materials and devices. Modelling the magnetisation dynamics in magnetic nanowires is complex due to the rich micromagnetic energy landscape and supported resonance modes. This is made more challenging in metallic magnetic nanowires (in microwave devices and absorbers for example) which require consideration of applied and induced currents, and of electromagnetic wave interaction that produce non-uniform electromagnetic fields with different skin depths (both non-magnetic and magnetic) that control the resonance mechanism and spin-wave modes in the magnetic nanowires. Available analytical models of the magnetisation dynamics and resonance in magnetic nanowires simplify the Landau-Lifshitz-Gilbert (LLG) equation of magnetisation to arrive at closed-form solutions that limits their applicability (for example operate in the magnetostatic or exchange limits and apply to simple geometries). Numerical models offer more detail but often focus on the micromagnetic or the electromagnetic responses separately. Thus, there is a need for a numerical approach that can solve both the electromagnetic (Maxwell’s equations) and micromagnetic (LLG equation) coupled system and accurately simulate the magnetisation dynamics and fields in magnetic nanowires and arrays. Cobalt exhibits strong saturation magnetisation and pronounced magnetocrystalline anisotropy (MCA) making it a favourable material or constituent for high frequency applications. Crystallographic measurements and fabrication studies indicated that the MCA in cobalt nanowires is predominantly perpendicular to the nanowire axis, and the potential for controlling the angle of anisotropy. This control provides an additional and interesting mechanism of tuning the resonance frequency and spin-wave modes in cobalt nanowires. The effect of different angles of MCA on the dynamic response in magnetic nanowires and on resonance modes is not well understood which, again, is important for the design and tuning of microwave devices, absorbers and biomedical applications. Arrays of metallic ferromagnetic nanowires embedded in dielectric matrices, exhibit a tuneable effective electromagnetic response through external fields that is affected by the resonance properties of individual nanowires and the dipolar coupling between them. When excited by electromagnetic waves, electric fields couple with metallic magnetic nanowires and induce currents and skin effects that spatially and temporally affect the magnetisation distributions and hence resonance modes in the nanowires and arrays. There is currently lack of understanding of the effective dynamic response of arrays of metallic ferromagnetic nanowires and their effective properties arising from the complexity and scale of the problem. Current approaches focus on simplified semi-analytical models that ignore exchange or solved separately using either micromagnetics or electromagnetics (assuming a frequency dependent permeability as input). Hence there is a need for a numerical model that addresses the above challenges to model and understand the dynamic permeability in magnetic nanowire arrays to design and tune devices and metamaterials. This research and thesis establish a comprehensive transient electromagnetic - micromagnetic numerical model in finite-elements within COMSOL Multiphysics that couples the solution of Maxwell’s and LLG equations to model and simulate the magnetisation dynamics and resonance in individual and arrays of magnetic nanowires, excited by applied (axial) currents and electromagnetic plane waves. This model includes the contributions of exchange, magnetocrystalline anisotropy, magnetostatic fields and induced currents (eddy currents). This model was used to study and understand the current-induced resonance in individual, semi-infinite, two-dimensional circular cobalt nanowires with diameters in the range 10-100 nm and at different angles of uniaxial magnetocrystalline anisotropy. The individual nanowires are excited by a 70 GHz Gaussian electric current pulse applied parallel to the nanowire axis. The calculated transient magnetisation distributions and power absorption spectra indicate predominately curling mode resonance for nanowire diameters ≥ 20 nm with symmetrical radial spin-wave modes when the magnetocrystalline is parallel to the nanowire axis. The resonance frequencies and their size dependence agree with Aharoni’s exchange curling theory. Increasing the out of plane MCA angle breaks the circular symmetry and produces elliptical curling magnetisation accompanied by significant reduction in the resonance frequencies (for example from 50 GHz fundamental mode frequency in a 100 nm diameter nanowire with MCA parallel to the nanowire axis, to 15 GHz for perpendicular anisotropy). These results demonstrate the significant impact of MCA angle on resonance in ferromagnetic nanowires and the promising potential of using this anisotropy to tune the frequency response of magnetic nanowires. The finite-element electromagnetic-micromagnetic model was further applied to investigate the complex electromagnetic wave response and effective dynamic permeability of periodic, two-dimensional arrays of cobalt nanowires with diameters in the range 10-200 nm and packing fractions of 0.1, 0.3 and 0.6. The 70 GHz Gaussian electromagnetic wave source wavelength in the simulation is larger than the nanowire diameters and lattice constants and thus operating in the metamaterial limit. This enabled the extraction of the effective dynamic permeability of the array from the simulated scattering parameters. With the MCA parallel to the nanowire axis, the simulated peak frequencies in the imaginary permeability correspond approximately to a uniform mode ferromagnetic frequency for an interacting nanowire array. The imaginary permeability peaks also exhibited slight shift towards lower frequencies with increase in the magnitude of the permeability with increased packing fractions due to dipolar interactions and collective precession. The simulations also showed that the peak resonance frequencies in the permeability spectra for each packing fraction have negligible sensitivity to nanowire diameters, particularly for diameters greater than 100 nm. This is be attributed to the ≈ 50 nm magnetic skin depth in cobalt which confines the response to the circumferential region of the nanowire. Increasing the deviation of the MCA angle from the nanowire axis causes significant shift in the resonance frequencies in the simulated permeability spectra to lower frequencies with increased magnitude of the permeability, similar to the behaviour of individual nanowires. For the case of perpendicular anisotropy, two distinct frequency peaks appear in the permeability spectra. Analysis of the total power absorbed in the nanowire array revealed that the lower frequency peak corresponds to the fundamental resonance mode in the individual nanowires while the second higher frequency peak corresponds to the dipolar field contribution. Increasing the packing fraction shifts the two peaks closer to each other due to the increased dipolar coupling. The outcomes of this research provide a more detailed understanding of the dynamic response of individual and arrays of metallic ferromagnetic nanowires and establish their potential as tuneable building blocks for high-frequency metamaterial and device applications. Moreover, the numerical method here can be easily extended to three-dimensions and enable the modelling and simulation of a wide range of magnetic materials and devices.<p></p>"]},{"key":"dc:title","label":"Title","values":["Current Induced Magnetisation Dynamics in Ferromagnetic Nanowires"]}]}],"canonical_facts":{"dc:creator":["Mohammad Alneari (21039101)"],"dc:date":["2026-03-02T00:00:00Z"],"dc:description":["Ferromagnetic nanowires are functional and integral constituents in a variety of advanced technologies, including tuneable microwave devices, magnetic storage, spintronics, electromagnetic wave absorbers, noise suppressors, and biomedical applications. Their significance and popularity stem from the ability to tune both their static and dynamic magnetic responses through their geometry, dimensions, lattice parameters, material composition, magnetic anisotropy, and external fields. Arrays of magnetic nanowires can also be synthesised with high degree of uniformity and with controlled anisotropy using template assisted electrodeposition methods making them more accessible. Furthermore, metallic ferromagnetic nanowires are compatible with semiconductor fabrication techniques for integration into, for example, magnonic nanostructures and devices. Understanding the magnetisation dynamics and spin wave modes in individual and arrays of magnetic nanowires and their dependence on the nanowire and lattice material and geometrical parameters is critical for the design and tuning of magnetic devices, composites and metamaterials employing magnetic nanowires. Fabricated arrays with nanowire diameters of few nanometres or tens of nanometers support high frequency operations but are difficult to characterise and observe experimentally, which make modelling and simulation essential tools for the design and development of associated materials and devices. Modelling the magnetisation dynamics in magnetic nanowires is complex due to the rich micromagnetic energy landscape and supported resonance modes. This is made more challenging in metallic magnetic nanowires (in microwave devices and absorbers for example) which require consideration of applied and induced currents, and of electromagnetic wave interaction that produce non-uniform electromagnetic fields with different skin depths (both non-magnetic and magnetic) that control the resonance mechanism and spin-wave modes in the magnetic nanowires. Available analytical models of the magnetisation dynamics and resonance in magnetic nanowires simplify the Landau-Lifshitz-Gilbert (LLG) equation of magnetisation to arrive at closed-form solutions that limits their applicability (for example operate in the magnetostatic or exchange limits and apply to simple geometries). Numerical models offer more detail but often focus on the micromagnetic or the electromagnetic responses separately. Thus, there is a need for a numerical approach that can solve both the electromagnetic (Maxwell’s equations) and micromagnetic (LLG equation) coupled system and accurately simulate the magnetisation dynamics and fields in magnetic nanowires and arrays. Cobalt exhibits strong saturation magnetisation and pronounced magnetocrystalline anisotropy (MCA) making it a favourable material or constituent for high frequency applications. Crystallographic measurements and fabrication studies indicated that the MCA in cobalt nanowires is predominantly perpendicular to the nanowire axis, and the potential for controlling the angle of anisotropy. This control provides an additional and interesting mechanism of tuning the resonance frequency and spin-wave modes in cobalt nanowires. The effect of different angles of MCA on the dynamic response in magnetic nanowires and on resonance modes is not well understood which, again, is important for the design and tuning of microwave devices, absorbers and biomedical applications. Arrays of metallic ferromagnetic nanowires embedded in dielectric matrices, exhibit a tuneable effective electromagnetic response through external fields that is affected by the resonance properties of individual nanowires and the dipolar coupling between them. When excited by electromagnetic waves, electric fields couple with metallic magnetic nanowires and induce currents and skin effects that spatially and temporally affect the magnetisation distributions and hence resonance modes in the nanowires and arrays. There is currently lack of understanding of the effective dynamic response of arrays of metallic ferromagnetic nanowires and their effective properties arising from the complexity and scale of the problem. Current approaches focus on simplified semi-analytical models that ignore exchange or solved separately using either micromagnetics or electromagnetics (assuming a frequency dependent permeability as input). Hence there is a need for a numerical model that addresses the above challenges to model and understand the dynamic permeability in magnetic nanowire arrays to design and tune devices and metamaterials. This research and thesis establish a comprehensive transient electromagnetic - micromagnetic numerical model in finite-elements within COMSOL Multiphysics that couples the solution of Maxwell’s and LLG equations to model and simulate the magnetisation dynamics and resonance in individual and arrays of magnetic nanowires, excited by applied (axial) currents and electromagnetic plane waves. This model includes the contributions of exchange, magnetocrystalline anisotropy, magnetostatic fields and induced currents (eddy currents). This model was used to study and understand the current-induced resonance in individual, semi-infinite, two-dimensional circular cobalt nanowires with diameters in the range 10-100 nm and at different angles of uniaxial magnetocrystalline anisotropy. The individual nanowires are excited by a 70 GHz Gaussian electric current pulse applied parallel to the nanowire axis. The calculated transient magnetisation distributions and power absorption spectra indicate predominately curling mode resonance for nanowire diameters ≥ 20 nm with symmetrical radial spin-wave modes when the magnetocrystalline is parallel to the nanowire axis. The resonance frequencies and their size dependence agree with Aharoni’s exchange curling theory. Increasing the out of plane MCA angle breaks the circular symmetry and produces elliptical curling magnetisation accompanied by significant reduction in the resonance frequencies (for example from 50 GHz fundamental mode frequency in a 100 nm diameter nanowire with MCA parallel to the nanowire axis, to 15 GHz for perpendicular anisotropy). These results demonstrate the significant impact of MCA angle on resonance in ferromagnetic nanowires and the promising potential of using this anisotropy to tune the frequency response of magnetic nanowires. The finite-element electromagnetic-micromagnetic model was further applied to investigate the complex electromagnetic wave response and effective dynamic permeability of periodic, two-dimensional arrays of cobalt nanowires with diameters in the range 10-200 nm and packing fractions of 0.1, 0.3 and 0.6. The 70 GHz Gaussian electromagnetic wave source wavelength in the simulation is larger than the nanowire diameters and lattice constants and thus operating in the metamaterial limit. This enabled the extraction of the effective dynamic permeability of the array from the simulated scattering parameters. With the MCA parallel to the nanowire axis, the simulated peak frequencies in the imaginary permeability correspond approximately to a uniform mode ferromagnetic frequency for an interacting nanowire array. The imaginary permeability peaks also exhibited slight shift towards lower frequencies with increase in the magnitude of the permeability with increased packing fractions due to dipolar interactions and collective precession. The simulations also showed that the peak resonance frequencies in the permeability spectra for each packing fraction have negligible sensitivity to nanowire diameters, particularly for diameters greater than 100 nm. This is be attributed to the ≈ 50 nm magnetic skin depth in cobalt which confines the response to the circumferential region of the nanowire. Increasing the deviation of the MCA angle from the nanowire axis causes significant shift in the resonance frequencies in the simulated permeability spectra to lower frequencies with increased magnitude of the permeability, similar to the behaviour of individual nanowires. For the case of perpendicular anisotropy, two distinct frequency peaks appear in the permeability spectra. Analysis of the total power absorbed in the nanowire array revealed that the lower frequency peak corresponds to the fundamental resonance mode in the individual nanowires while the second higher frequency peak corresponds to the dipolar field contribution. Increasing the packing fraction shifts the two peaks closer to each other due to the increased dipolar coupling. The outcomes of this research provide a more detailed understanding of the dynamic response of individual and arrays of metallic ferromagnetic nanowires and establish their potential as tuneable building blocks for high-frequency metamaterial and device applications. Moreover, the numerical method here can be easily extended to three-dimensions and enable the modelling and simulation of a wide range of magnetic materials and devices.<p></p>"],"dc:identifier":["10779/exe.31448926.v1"],"dc:relation":["https://figshare.com/articles/thesis/Current_Induced_Magnetisation_Dynamics_in_Ferromagnetic_Nanowires/31448926"],"dc:rights":["All rights reserved","Open Access after 2027-09-09"],"dc:subject":["Micromagnetics","Ferromagnetic resonance","Cobalt nanowires","Finite element method","Magnetisation dynamics"],"dc:title":["Current Induced Magnetisation Dynamics in Ferromagnetic Nanowires"],"dc:type":["Text","Thesis"]},"updated_at":"2026-07-27T19:34:10Z"}