Barkhausen Noise from Precessional Domain Wall Motion

Abstract

The jerky dynamics of domain walls driven by applied magnetic fields in disordered ferromagnets -the Barkhausen effect -is a paradigmatic example of crackling noise. We study Barkhausen noise in disordered Pt/Co/Pt thin films due to precessional motion of domain walls using full micromagnetic simulations, allowing for a detailed description of the domain wall internal structure. In this regime the domain walls contain topological defects known as Bloch lines which repeatedly nucleate, propagate and annihilate within the domain wall during the Barkhausen jumps. In addition to bursts of domain wall propagation, the in-plane Bloch line dynamics within the domain wall exhibits crackling noise, and constitutes the majority of the overall spin rotation activity.Understanding the bursty crackling noise response of elastic objects in random media -domain walls (DWs) [1], cracks [2], fluids fronts invading porous media [3], et cetera -to slowly varying external forces is one of the main problems of statistical physics of materials. An important example is given by the magnetic field driven dynamics of DWs in disordered ferromagnets, where they respond to a slowly changing external magnetic field by exhibiting a sequence of discrete jumps with a power-law size distribution [1,4]. This phenomenon, known as the Barkhausen effect [5], has been studied extensively, and a fairly well-established picture of the possible universality classes of the avalanche dynamics, using the language of critical phenomena, is emerging [1,4].Magnetic DWs constitute a unique system exhibiting crackling noise since the driving field may, in addition to pushing the wall forward, excite internal degrees of freedom within the DW [6]. This effect is well-known especially in the nanowire geometry -important for the proposed spintronics devices such as the racetrack memory [7] -where the onset of precession of the DW magnetization above a threshold field leads to an abrupt drop in the DW propagation velocity (the Walker breakdown [8]), and hence to a non-monotonic driving field vs DW velocity relation [9]; these features are well-captured by the so-called 1d models [10].In wider strips or thin films, the excitations of the DW internal magnetization accompanying the velocity drop cannot be described by precession of an individual magnetic moment. Instead, one needs to consider the nucleation, propagation and annihilation of topological defects known as Bloch lines (BLs) within the DW [11][12][13]. BLs, i.e., transition regions separating different chiralities of the DW, have been studied in the context of bubble materials already in the 1970's [13]. Their role in the physics of the Barkhausen effect needs to be studied. The typical models of Barkhausen noise, such as elastic interfaces in random media [4,14], scalar field models [15] or the random field Ising model (RFIM) [16][17][18], exclude BLs by construction.Here, we focus on understanding the consequences of the presence of BLs within DWs on the jerky DW motion through a disordered thin ferromagne...

Depinning exponents of thin film domain walls depend on disorder strength

“…1a) for different σ is the timeaverage over the second half of the simulation time. For σ = 0, V (B ext ) exhibits a linear increase with B ext up to a Walker field B W ≈ 2.7 mT (in excellent agreement with both the prediction B W = α 2 µ 0 M s N n ≈ 2.6 mT using N n = ∆ πD ln 2 [22], and micromagnetic simulations [21]), at which point V abruptly drops due to the onset of precession of φ. We note that due to weak numerical noise in our implementation, some BLs are present even for σ = 0, and hence the σ = 0 curve shown in Fig.…”

“…The motion of BLs, separating regions of different chiralities of the Bloch DW, mediates largescale precession of the DW magnetization in an analogous manner to dislocation motion mediating plastic flow in crystals. Such effects were recently studied by full micromagnetic simulations of Barkhausen noise [21]. However, micromagnetic simulations describing the magnetization dynamics everywhere in the system are limited to small system sizes, resulting in significant finite size effects.…”

“…In this Letter, we study the depinning dynamics of thin film DWs in large systems (up to two orders of magnitude larger than in recent micromagnetic simulations [21]) by developing a reduced model able to describe BL dynamics inside the DW while including only the degrees of freedom of the line-like DW itself. Strikingly, and contrary to what one observes in simple elastic line models of DWs neglecting the internal degrees of freedom, we find that the depinning exponents evolve with the disorder strength.…”

Degradation of domains with sequential field application

“…For example, it was recently shown that scaling exponents describing Barkhausen jumps in thin ferromagnetic films of Pt/Co/Pt obtained by full micromagnetic simulations cannot be distinguished from those expected for the much simpler quenched EW equation. Thus, commonly used simple models based on describing domain walls as elastic lines correctly capture the large-scale critical dynamics of the system [32]. On the other hand, this approach is computationally expensive, thus limiting the system sizes that can be studied in reasonable times.…”

Magnetic domain dynamics in an insulating quantum ferromagnet

“…Analogous behavior has been observed in plastic deformation of sheared materials, where local pinning sites similarly can distort the free energy landscape and allow for seemingly "uphill" motion. [37,38] Numerical simulations of domain-wall motion in disordered perpendicular-anisotropy thin films [39] likewise have observed a small fraction of reversepolarity events. The occurrence probability of these precursor events is strongly temperature dependent, with approximately 5% of the 80 mK events showing a precursor, decreasing to 1% at 250 mK and less than 0.1% at 500 mK and above where thermal fluctuations dominate.…”