Mapping the Landscape of Domain-Wall Pinning in Ferromagnetic Films Using Differential Magneto-Optical Microscopy

Abstract

The propagation of domain walls in a ferromagnetic film is largely determined by domain wall pinning at defects in the material. In this letter we map the effective potential landscape for domain wall pinning in Permalloy films by raster scanning a single ferromagnetic vortex and monitoring the hysteretic vortex displacement vs. applied magnetic field. The measurement is carried out using a differential magneto-optical microscopy technique which yields spatial sensitivity ∼ 10 nm. We present a simple algorithm for extracting an effective pinning potential from the measurement of vortex displacement vs. applied field. The resulting maps of the pinning potential reveal distinct types of pinning sites, which we attribute to quasi-zero-, one-, and two-dimensional defects in the Permalloy film.Studying the pinning of domain walls by defects in ferromagnetic films is critical for understanding and optimizing domain wall motion and magnetization switching. Pinning occurs when the domain wall, which is a quasi-linear region of high magnetostatic, exchange, and/or anisotropy energy density, encounters a defect which gives rise to a local minimum of the total energy[1-3]. Here we study a simpler situation -the pinning of a ferromagnetic vortex core. The ground state configuration of a thin, micron-scale ferromagnetic disk with negligible magnetocrystalline anisotropy is a vortex. This state is characterized by a curl of in-plane magnetization circulating about a central core [4][5][6]. The vortex core, with half-width ∼ 10 nm and magnetization oriented largely out of plane [7], is a point-like region of high energy density. As it is scanned across the sample via an applied magnetic field, the vortex core acts like a nanoscale probe for imaging the pinning potential [6,8]. The pinning effects studied here in ferromagnetic disks are likely similar to those in vortex domain walls in ferromagnetic nanowires [9], with proposed applications in spintronic memory [10]. More generally, the vortex pinning maps that we obtain give insight into how pinning of extended domain walls would arise in these films, as the effects rely on similar energetic considerations.

Probing the pinning strength of magnetic vortex cores with sub-nanometer resolution

“…Moreover, intentional defect configurations can enable reliable positioning of textures in future devices such as race-track memories 1,3,4 , i.e., adequate defect configurations could avoid interactions with edges that might annihilate the texture or could locally pin the texture for readout 8,9 . However, previous experiments probing the interaction between texture and defects were either limited in terms of controlled positioning of the texture 10,11 or in terms of spatial resolution [12][13][14][15][16][17][18][19] , such that novel methods are urgently needed. In detail, previous experiments probed domain walls 12,14,18 , magnetic vortices 13,15,17,19,20 or skyrmions 10 embedded in stripes 14,18 , rings 16 , islands 13,15,17,19,20 or thin films [10][11][12] revealing pinning at large, artificial structures (size: 10-100 nm), such as notches 16 , holes 15,20 or locally thinned areas of the film 13,14 as well as at intrinsic irregularities, e.g., due to surface roughness 21 or dislocations 11 .…”

Stochastic Dynamics of a Ferromagnetic Vortex Revealed by Single-Spin Magnetometry

“…1(c) we can construct an effective one-dimensional pinning potential u p (x) (see Ref. 20 ), shown in Fig. 1(d).…”

“…1(c) are within a bistable region produced by the two large pinning sites labeled I and II. These pinning sites likely arise from ∼ 10-nm-high bumps on the underlying gold 20 . Smaller pinning sites arising from intrinsic defects in the permalloy are less likely to show clear bistability.…”

“…Pinning sites are included in the model by introducing a pinning potential U p (x) = − n w n (x − x n ) as a sum of peaked functions w n at positions x n . The total energy U = U 0 + U p then yields the equilibrium position of the vortex core as it traverses across the disk 17,20 .…”

“…Optical or x-ray techniques can both provide time resolution much faster than the typical ∼ns scale dynamics here, and diffraction-limited imaging resolution (∼ 100 nm and ∼ 10 nm respectively). In a differential measurement, changes in displacement of the vortex core can be measured below the diffraction limit as the core translates within the probe spot, with resolution typically observed down to ∼ 10 nm in optical measurements 20 . However, a common feature of these measurements is the need to average many repetitions of the measurement, confounding measurements where the dynamics are not identical in every repetition.…”