Unveiling magnetic states in nanotubes: insights from remanent ferromagnetic resonance spectroscopy

Abstract Magnetic nanotubes have garnered immense attention for their potential in high-density magnetic memory, owing to their stable flux closure configuration and fast, reproducible reversal processes. However, characterizing their magnetic configuration through straightforward methodologies remains a challenge in both scope and detail. Here, we elucidate the magnetic state details using Remanence Field Ferromagnetic Resonance Spectroscopy (RFMR) for arrays of electrodeposited nanotubes. Micromagnetic simulations revealed distinct spin configurations while coming from saturation, including the edge vortex, onion, uniform and curling states, with chirality variations depending on the preparation field direction. We identified individual spin configurations, as depicted in our micromagnetic simulations, through careful measurements of the RFMR spectra starting from both positive and negative saturation. The Observations revealed opposite RFMR spectra, indicating opposite magnetic spin configurations after removing the positive and negative saturating fields when the magnetic field was applied along <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:mo stretchy="false">)</mml:mo> </mml:math> and perpendicular <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mn>90</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> to the nanotube axis. We observed a mixture of the non-uniform curling states with the end vortex state (onion-like curling state) at the end of the nanotubes for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msup> <mml:mspace width="0.5em"/> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow> <mml:mn>90</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> and uniform magnetization states in the middle of the nanotubes for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msup> </mml:math> configuration. Dynamic measurements in presence of the bias field, coupled with RFMR spectra analysis, provided insights into the evolution of individual modes. Additionally, our FMR analysis indicates nucleation within the edge vortex state, which was further corroborated by micromagnetic analysis and substantiated with First Order Reversal Curve (FORC) measurements.