[Paper Review] Dynamics of Current and Field Driven Domain Wall Motion under the Influence of Transverse Magnetic Field

R. Arun, P. Sabareesan+1 more|arXiv (Cornell University)|Mar 16, 2015

Magnetic properties of thin films3 citations

TL;DR

This study analytically and numerically investigates current- and field-driven transverse Néel domain wall motion in ferromagnetic nanostrips under a transverse magnetic field, using the Landau-Lifshitz-Gilbert equation with spin-transfer torques. The key finding is that the transverse magnetic field significantly enhances the saturated velocity in field-driven cases—increasing from 857 m/s to 2666 m/s as the field rises from 0 to 400 Oe—while having negligible effect in current-driven scenarios.

ABSTRACT

The dynamics of transverse Neel domain wall in a ferromagnetic nanostrip in the presence of driving field, current and transverse magnetic field is investigated by the Landau-Lifshitz-Gilbert(LLG) equation with the adiabatic and non-adiabatic spin-transfer torques both analytically and numerically. The analytical expressions for the velocity, width, excitation angle and displacement for the domain wall are obtained by using small angle approximation along with Walkers trial function. The results show that the initial velocity of the domain wall can be controlled by the adiabatic spin-transfer torque and the saturated velocity can be controlled by the non-adiabatic spin-transfer torque and driving field. The large increase in the saturated velocity of the domain wall driven by current and field due to the transverse magnetic field is identified through the presence of driving field. There is no impact in the saturated velocity of the domain wall driven by current from the transverse magnetic field. For the domain wall driven by the current in the presence of the transverse magnetic field, the saturated velocity remains constant. The transverse magnetic field along with current and driving field is more advantageous that the transverse magnetic field along with current for increasing the saturated velocity of the domain wall. The numerical results showed that the saturated velocity is increased by the transverse magnetic field with the irrespective of the directions of the driving field and current further it is higher and lower when the directions of driving field and current are antiparallel and parallel respectively. The obtained analytical solutions are closely coincided with the computed numerical results.

Motivation & Objective

• To understand the dynamics of transverse Néel domain walls in ferromagnetic nanostrips under combined current, driving field, and transverse magnetic field.
• To address the lack of systematic analytical studies on current- and field-driven domain wall motion in the presence of transverse magnetic fields.
• To derive analytical expressions for domain wall parameters such as velocity, width, excitation angle, and displacement using small-angle approximation and Walker’s trial function.
• To validate analytical results against numerical simulations and assess the influence of transverse magnetic field on saturated velocity in different driving regimes.

Proposed method

• Formulated the Landau-Lifshitz-Gilbert (LLG) equation in spherical coordinates for a ferromagnetic nanostrip with adiabatic and non-adiabatic spin-transfer torques.
• Applied Walker’s trial function and small-angle approximation to reduce the dynamical equation for the domain wall’s excitation angle to a Riccati-type equation.
• Solved the Riccati equation analytically to derive expressions for velocity, width, excitation angle, and displacement of the domain wall.
• Performed numerical simulations using the LLG equation to validate analytical predictions across varying current, driving field, and transverse magnetic field strengths.
• Systematically compared analytical and numerical results for different configurations of current and driving field directions (parallel vs. antiparallel).
• Investigated the role of transverse magnetic field in modifying domain wall width, velocity, and stability under both current- and field-driven conditions.

Experimental results

Research questions

• RQ1 How does the transverse magnetic field affect the saturated velocity of a current-driven transverse Néel domain wall?
• RQ2 What is the influence of the transverse magnetic field on the saturated velocity of a field-driven transverse Néel domain wall?
• RQ3 How do the directions of the current and driving field (parallel vs. antiparallel) affect the saturated velocity in the presence of a transverse magnetic field?
• RQ4 To what extent do analytical solutions based on small-angle approximation and Walker’s trial function accurately predict the domain wall dynamics compared to numerical simulations?
• RQ5 How does the transverse magnetic field alter the domain wall width and excitation angle in the presence of spin-transfer torques and external fields?

Key findings

• The transverse magnetic field increases the saturated velocity of field-driven domain walls by up to 2.1 times, rising from 857 m/s to 2666 m/s when the transverse field increases from 0 Oe to 400 Oe.
• For current-driven domain walls, the saturated velocity remains largely unchanged with increasing transverse magnetic field, indicating no significant enhancement in this regime.
• The initial velocity of the domain wall can be controlled by the adiabatic spin-transfer torque, while the saturated velocity is governed by the non-adiabatic spin-transfer torque and the driving field.
• The analytical solutions for excitation angle, velocity, width, and displacement closely match the numerical results, validating the small-angle approximation and Walker’s trial function approach.
• When the driving field and current are antiparallel, the saturated velocity is higher than when they are parallel, regardless of the transverse magnetic field strength.
• The transverse magnetic field increases the domain wall width and induces asymmetry and twisting, particularly in field-driven scenarios, without altering the saturated velocity in current-driven cases.