# Discriminating the physical impacts of various laser pulses on the magnetic structure of oriented electrical steels

O. Maloberti, M. Nesser, J. Dupuy, P. Dassonvalle, J. Fortin, C. Pineau, J.P. Birat

► To cite this version:

O. Maloberti, M. Nesser, J. Dupuy, P. Dassonvalle, J. Fortin, et al. Discriminating the physical impacts of various laser pulses on the magnetic structure of oriented electrical steels. Journal of Magnetism and Magnetic Materials, 2023, 566, pp.170248. 10.1016/j.jmmm.2022.170248. hal-03930003

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Submitted on 24 Oct 2023

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# Discriminating the physical impacts of various laser pulses on the magnetic structure of oriented electrical steels

O. Maloberti<sup>a,b,1</sup>, M. Nesser<sup>b</sup>, J. Dupuy<sup>c</sup>, P. Dassonvalle<sup>a,d</sup>, J. Fortin<sup>a,b</sup>, C. Pineau<sup>c</sup>, J.P. Birat<sup>f</sup>

<sup>a</sup>SYMADE-UNILASALLE Amiens, 14 quai de la Somme, Amiens, 80080, France; <sup>b</sup>Laboratoire LTI, IUT d'Amiens
Avenue des Facultés - Le Bailly, Amiens, 80025, France; <sup>c</sup>Multitel a.s.b.l., 2 Rue Pierre et Marie Curie Parc
Initialis, Mons, 7000, Belgique; <sup>d</sup>Laboratoire MIS, UPJV, 14 quai de la Somme, Amiens, 80080, France; <sup>e</sup>IRT-M2P,
4 rue Augustin Fresnel, Metz, 57070, France; <sup>f</sup>IF Steelman, 5 rue du Gate-Chaux, 57280, Semecourt, France

Pulsed laser technologies with Long (LPL) **Irradiation), Short (SPL) **Scribing) and Ultra-Short (USPL) **Ablation) pulse duration can be used on SiFe **Grain Oriented Electrical Steels (GOES) to refine the domains and reduce the power loss. The corresponding physics related to the magnetic structure is still a subject of research. This paper identifies separate characteristics responsible for the domains structure and the magnetization properties in a GOES sheet processed with the three laser pulses. Magnetic domains based properties are identified thanks to an average dynamic **μ-νc-Λ model**, the **Tensor Magnetic Phase Theory (TMPT)**, magnetic measurements/observations with the **Single Sheet Tester (SST)** and the **Magneto-Optical Indicator Film (MOIF)** technique.

**Keywords:** electrical steels, GOES, pulsed laser, irradiation, scribing, ablation, magnetic structure, magnetization dynamics.

## 1. Introduction, Context and State of the Art

First studies on 180° domain refinement were carried out using a mechanical scratching method [1] to reduce energy losses in GOES. Then different techniques have been proposed: plasma irradiation [2], spark ablation [3] ... Surface laser treatment, first with Long Pulsed Lasers (LPL ≥ 10 ns) or continuous Wave Lasers (CWL), appeared as an elegant non-contact method [4, 6]. Finally, different kinds of lasers in various pulse regimes were used more or less successfully [5, 6]. Recent research investigated advanced Short Pulsed (SPL < 10 ns) and Ultra-Short Pulsed Lasers (USPL < 10 ps) rather than LPL. It led to first comparisons of different pulse durations and its impacts on magnetic behaviors (permeability and losses) [7, 8], while defining a new terminology (see Fig. 1). Observations shew that the LPL process, called **Irradiation**, induces thermal stresses σ<sub>T</sub> in a Heat Affected Zone (HAZ α δ'p') through the coating without removing it. The latter modifies the magnetoelastic energy state of magnetic domains. Thus, for energy minimization reason, misoriented closure domains are locally generated and the 180° domains are refined. The SPL process, called **Scribing**, generates small grooves by melting and removal of the coating and superficial metal particles. In parallel, the process duration leads to a HAZ and thermal stresses σ<sub>M</sub>. In this case, the domains refinement can be induced either by magnetic poles or closure domains at the laser spots. The USPL process, called **Ablation**, generates deep grooves (or Material Removal Zone, MRZ) by vaporization and removal of the coating and metal particles by minimizing the HAZ. Physical interpretations and correlations between the process parameters and impacts and some magnetic properties have been partially studied [9, 10]. Reference [9] focused on the impacts of LPL and SPL on static and dynamic properties. Reference [10] identified the LPL, SPL and USPL impacts on the Bertotti separated loss coefficients [11]. Distinct physical justifications can be completed with the help of investigation model(s) based on the microscopic domains structure [12, 13]. Distinct physical justifications for the magnetic improvements shall be found with the help of a behavioral and loss model, based on a description of the microscopic magnetic structure with domains and walls. First, the average dynamic μ-νc-Λ model [12] will be used to identify the impact of pulsed laser processes on the separated properties μ, ν<sub>c</sub> and Λ related to the static internal permeability, coercive field strength and dynamic losses respectively. There, magnetization reversal mechanisms are described with an averaged domains and walls property Λ, lumping the walls' surface S, density n and mobility η. Thus, there is no distinction between the magnetic structure at the sheet surface and the one within the thickness. Hence, the Tensor Magnetic Phase Theory (TMPT) will be used to statistically describe the domains' structure and phases in the mass of the material [13]. Four original material characteristics have to be identified: a stress dependent and anisotropic exchange characteristic κ, a coercive reluctivity v<sub>c</sub> related to the grain boundaries and defects, the surface magnetic structure topological and dynamical properties lumped in a tensor variable [Λv<sub>c</sub><sup>2</sup>] and finally a dynamic damping characteristic τ, due to the damping magnetization reversal mechanisms, and certainly dependent on the walls mobility. Finally, microscopic observation of the magnetic structure thanks to the MOIF technique will inform about the shape and average size <w> of domains at the surface, which makes it possible to value the impact of a pulsed laser separately on both the refinement effect and the walls mobility effect depending on the pulse duration.

## 2. Description of the experiments

### 2.1. Laser treatments – process parameters

Three pulsed laser processes performed with a fixed spot size and scanning speed will be looked at (Fig. 1):

* The Long Pulsed Laser process (LPL)* induces thermal stresses σ<sub>T</sub> in the Heat Affected Zone (HAZ α δ'p') through the coating without removing it. This configuration will also be called **Irradiation**.

<footnote n="1">¹ Corresponding author: olivie.maloberti@gmail.com</footnote>
* The Short Pulsed Laser process (SPL)* generates a groove by melting and removal of the coating and superficial metal particles. In parallel, the process duration leads to a HAZ and thermal stresses $\sigma_M$. This configuration will be called Scribing.

* The Ultra Short Pulsed Laser process (USPL)** generates a deep groove (or Material Removal Zone, MRZ) by vaporization and removal of the coating and metal particles by minimizing the HAZ but generating a plasma and a Laser Induced Shock Wave. This configuration will be called Ablation.

<figure><img src="image_2.png" /><figcaption>Fig. 1: The three Pulsed Laser Processes selected.</figcaption></figure>

*LPL and SPL were performed with an IPG pulsed Ytterbium fiber laser with a wavelength of 1.064 µm. It delivers pulse duration between 4 and 200 ns. **USPL was performed with an Ytterbium Amplitude Laser at a wavelength of 1.03 µm with an adjustable pulse width between a few hundreds of fs and 10 ps.

References [7-10] provide optimal parameters to maximize the loss reduction factor up to 20% @ 1.7T 50Hz and minimize the J800 reduction by a factor of 5%. Each configuration corresponds to the optimal amount of energy without damaging the coating for LPL, inducing critical droplets for SPL and avoiding any recast and sheet deformation for USPL. Table 1 gives relative comparisons between pulse durations $\Delta t$ (µs), repetition frequencies $f_r$ (kHz), pulse energy densities $e_{pulse}$ (J.cm$^{-2}$), cumulative energy densities $e_{cum}$ (J.cm$^{-2}$) and pulse peak power densities $p_{peak}$ (MW.cm$^{-2}$) of the 3 selected laser processes (the reference values being the LPL ones).

<table><caption>Table 1: Main laser configurations</caption><thead><tr><th></th><th>Δt</th><th>f<sub>r</sub></th><th>e<sub>pulse</sub></th><th>e<sub>cum</sub></th><th>p<sub>peak</sub></th></tr></thead><tbody><tr><td>LPL (I)</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>SPL (S)</td><td>0.04</td><td>2.5</td><td>0.4</td><td>1</td><td>10</td></tr><tr><td>USPL (A)</td><td>0.000005</td><td>0.25</td><td>4.08</td><td>1.43</td><td>816327</td></tr></tbody></table>

## 2.2. Specimens: grades and dimensions

Two conventional grades of Si$_{0.03}$Fe$_{0.97}$ GOES with thicknesses 0.23 and 0.27 mm will be investigated: grades 23MXX® (specific losses < 1 W/kg @1.7T&50Hz, J800 > 1.7 T) and RXXX27® (specific losses < 1.2 W/kg @1.7T&50Hz, J800 > 1.8 T). Specimens used are squares with size 150*150 mm$^2$, laser treated either on one or two sides. 7 samples per grade are considered to analyse single pass laser configurations applied on one side (I11, S11, A11) or two sides (I12, S12, A12) in addition to the two passes laser ablation process (USPL 2) on the single-sided sample A21 (Table 2).

<table><caption>Table 2: List of specimens</caption><thead><tr><th>SAMPLE</th><th>THICKNESS</th><th>LASER PROCESS</th></tr></thead><tbody><tr><td>23I11, 23I12</td><td>0.23 mm</td><td>LPL IRRADIATION, 1/2 sides</td></tr><tr><td>27I11, 27I12</td><td>0.27 mm</td><td>LPL IRRADIATION, 1/2 sides</td></tr><tr><td>23S11, 23S12</td><td>0.23 mm</td><td>SPL SCRIBING, 1/2 sides</td></tr><tr><td>27S11, 27S12</td><td>0.27 mm</td><td>SPL SCRIBING, 1/2 sides</td></tr><tr><td>23A11, 23A12</td><td>0.23 mm</td><td>USPL ABLATION 1, 1/2 sides</td></tr><tr><td>27A11, 27A12</td><td>0.27 mm</td><td>USPL ABLATION 1, 1/2 sides</td></tr><tr><td>23A21</td><td>0.23 mm</td><td>USPL ABLATION 2, 1 side</td></tr><tr><td>27A21</td><td>0.27 mm</td><td>USPL ABLATION 2, 1 side</td></tr></tbody></table>
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 2: Loss reduction properties for LPL (I), SPL (S) and USPL (A) processes on grade 23MXX.</figcaption></figure>
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3 : Loss reduction properties for LPL (I), SPL (S) and USPL (A) processes on grade RXXX27.</figcaption></figure>

## 2.1. Magnetic measurements – Single Sheet Tester

The magnetic behaviour and losses of the whole specimens are measured thanks to a Single Sheet Tester (SST 150), providing an accuracy better than 0.5% at high induction and 3% at low induction. Laser treated sheets with thickness 0.23 mm are compared to an average of 16 standard sheets. Laser treated sheets with thickness 0.27 mm are compared before and after the process on same samples.
Fig. 2 and Fig. 3 give the results for both grades 23MXX and RXXX27 respectively as a function of the flux density B. Quasi-static hysteresis losses P_s (W/kg) are measured at very low frequency 3-5 Hz (skin depth is more than 3 to 5 times the sheet thickness) and the dynamic losses P_d (W/kg) correspond to the whole classical and excess losses that lead to the total losses at usual frequency f= 50 Hz. For both grades, the three different pulsed laser processes provide more or less the same loss reduction factor at high induction (1.5 – 1.7 T), the USPL process is the one that shows the highest improvements at low and intermediate induction levels B (0 – 1.5 T), especially with two passes or two sides treatment. In case of single pass and single sided processes, the LPL process is the one that improves the static losses the best. On the contrary, the SPL and USPL are the best options for dynamic losses whatever the number of sides and passes. For the grade RXXX27 with higher thickness, double sided LPL and SPL processes didn’t allow any improvement in front of the single sided process, probably due to too much thermal effect required to see any significant impact on such a thickness (up to +6% damage for LPL and +8% damage for SPL). In the next section, we address the questions: which characteristic is the most sensitive to a pulsed laser treatment and what are the origins of the specificity of each pulse duration ? Magnetic measurements will be used to identify the separated properties of two domains based models.

### 3. Loss models and magnetic properties

#### 3.1. The $\mu$-$\nu_c$-$\Lambda$ model

In this average dynamic $\mu$-$\nu_c$-$\Lambda$ model [12], the total magnetic field H inside the material is separated in three contributions: the static non-dissipative an-hysteretic magnetic field $\mu^{-1}B$ at equilibrium, the quasi-static coercive field strength $j\nu_cB$ mainly due to jumps of walls at defects and grains boundaries and the dynamic damping magnetic field $j\omega\sigma\Lambda^2B$ due to magnetization reversal mechanisms damped by microscopic eddy currents ($\omega = 2\pi f$ is the angle velocity and $\sigma$ the electrical conductivity). The property $\nu_c$ is the coercive reluctivity responsible for the quasi-static losses ($\pi\nu_c = K_h$, with $K_h$ the Bertotti coefficient) and is identified with $P_s = \nu_c \frac{B^2\omega}{2\pi\gamma}$ ($\gamma$ is the mass density). $\mu$ is defined as the static internal permeability related to the magnetization curve slope. $\Lambda$ ($\mu m$) lumps the walls' surface S, density n and mobility $\eta$ averaged within the thickness. The field diffusion-like equation is then derived from the dynamic field behavior $H = \mu^{-1}B + j\omega\sigma\Lambda^2B$, the Ohm law and the Maxwell formulae. The field solution of the $\mu$-$\nu_c$-$\Lambda$ model, detailed in [11], provides the apparent permeability $\mu_{app}$ (1a) and the dynamic losses $P_d$ (1b) effectively measured, which can be used to identify the impact of pulsed laser processes on the separated properties $\mu$ and $\Lambda$ respectively.

$$ \mu_{app} = \frac{B}{H_0} = \frac{\mu_{mag}}{\cos(-\varphi_{mag})} \quad \text{with} \quad \mu_{mag} e^{j\varphi_{mag}} = \frac{2\mu \tanh((k_+ + i k_-)\zeta/2)}{\zeta(1 + i\sigma\Lambda^2\mu\omega)(k_+ + i k_-)} \quad (1a) $$

$$ P_d = \frac{\zeta B^2 \omega}{4\mu\gamma} \left( \frac{\cosh(\zeta k_+) + \cos(\zeta k_-)}{\sinh^2(\zeta k_+) + \sin^2(\zeta k_-)} \right) \left( \frac{(\sigma\Lambda^2\mu\omega k_+ + k_-) \sinh(\zeta k_+) +}{(\sigma\Lambda^2\mu\omega - k_+) \sin(\zeta k_-)} \right) \quad (1b) $$

$H_0$ is the magnetic field applied at the surface, $\zeta$ the sheet thickness, $k_\pm$ are the diffusion wave vectors given by (1c) [12]:

$$ k_{\pm} = \sqrt{\frac{1}{2} \left( \frac{\sigma \mu \omega}{1 + (\sigma \Lambda^2 \mu \omega)^2} \right) \sqrt{\pm \sigma \Lambda^2 \mu \omega + \sqrt{1 + (\sigma \Lambda^2 \mu \omega)^2}}} \quad (1c) $$

#### 3.2. The "Tensor Magnetic Phase Theory" (TMPT)

The investigated TMPT model [13] is put to the test to statistically describe the natural magnetic structuring in the mass of the material with phases and space variations. The domains' structure is represented by a new tensor state variable $[\Lambda^2]$, which stem from a competition between several energy terms at the mesoscopic scale: the magnetic exchange, the magnetic anisotropy, the self-magnetostriction or/and stress induced anisotropy, the dipolar demagnetizing energy (dependent on the boundary condition $[\Lambda_0^2]$) and the dissipated microscopic eddy currents loss (driven by a time delay $\tau$). In case of GOES, $[\Lambda^2]$ is assumed to be diagonal; and a focus on the unknown $\Lambda = \Lambda_{RD}$, representative of the 180° domains in the Rolling Direction (RD), is relevant even if its space distribution is impacted by (closure) domains in other directions. Still using the same surface field behavior as previously, the total energy balance involves four material characteristics: the surface properties lumped in $\Lambda_0$, a coercive reluctivity $\nu_c$ still related to the grain boundaries and defects, a stress dependent and anisotropic exchange characteristic $\kappa$ (mm$^{-2}$) (ratio between anisotropy plus magneto-striction and magnetic exchange properties) and finally the dynamic damping characteristic $\tau$ ($\mu s$), certainly dependent on the walls mobility. The TMPT adds a coupling between the surface $\Lambda_0$ and the volume property $\Lambda$. Any domains refinement will act on $\Lambda_0$, laser induced stress on $\kappa$, induced pinning centers on $\nu_c$ and any walls nucleation, multiplication and mobility effect will be visible on $\tau$. The 1D solution [12] for $V=\Lambda^{-1}$ (2a), finally provides the mean magnetic polarization J (2b) apparent permeability $\mu_{app}$ (2c) the quasi static hysteresis losses $P_s$ (2d) and the dynamic ones $P_d$ (2e):
<figure><img src="image_7.png" /><figcaption>Fig. 4. Magnetic domains imaging for LPL (I), SPL (S) and USPL (A) on grade 23MXX after a double sided process (top) and on grade RXXX27 after a single sided process (bottom) with the MOIF technique.</figcaption></figure>
$$V^2(z) = \Lambda_0^{-2} \frac{\cosh(\sqrt{\kappa(1+j\tau\omega)}z)}{\cosh(\sqrt{\kappa(1+j\tau\omega)^2})} \quad (z: \text{coordinate // Normal Direction (ND)}) \quad (2a)$$

$$J = \frac{1}{\zeta} \left( \int_{-\frac{\zeta}{2}}^{\frac{\zeta}{2}} V^2(z) dz \right) \frac{\Lambda_0^2}{[1+j\sigma\Lambda_0^2\mu\omega]} \mu H_0 = \frac{\tanh(\sqrt{\kappa(1+j\tau\omega)^2})}{\sqrt{\kappa(1+j\tau\omega)^2(1+j\sigma\Lambda_0^2\mu\omega)}} \mu H_0 \quad (2b)$$

$$\mu_{app} = \frac{B}{H_0} \approx \frac{J}{H_0} = \frac{\tanh(\sqrt{\kappa(1+j\tau\omega)^2})}{\sqrt{\kappa(1+j\tau\omega)^2(1+j\sigma\Lambda_0^2\mu\omega)}} \mu \quad (2c)$$

$$P_s \approx \text{Real}_{\omega \to 0} \left( -j\omega \frac{\pi H_0 J^*}{\gamma} \right) = \nu_c \frac{\tanh(\sqrt{\kappa_2^2})}{\sqrt{\kappa_2^2}} \cdot \frac{B^2 \omega}{2\gamma} \quad (2d)$$

$$P_d \approx \text{Real} \left( \omega \frac{\pi \sigma \Lambda_0^2 \omega \cdot J_0^*}{\gamma} \right) = \sigma \Lambda_0^2 \cdot \text{Real} \left( \frac{(1+j\sigma\Lambda_0^2\mu\omega)\sqrt{\kappa(1+j\tau\omega)^2}}{\tanh(\sqrt{\kappa(1+j\tau\omega)^2})} \right) \cdot \frac{B^2\omega^2}{2\gamma} \quad (2e)$$

## 4. Magnetic structure

Surface magnetic domains shape, length and especially width $w$ are observed with the MOIF technique (Fig. 4). The observation of magnetic domains allows to estimate the statistical average of domains’ width $\langle w \rangle$ defined in equation (3). In fact, MOIF images of domains can be analyzed with the FFT technique in 2D (see Fig. 5 and Fig. 6). The geometrical parameter $\langle w \rangle$ is thus obtained thanks to the median value $\bar{k}$ of spatial frequency $k$ in the probability density spectra of the domains’ size in the transverse direction (TD).

$$\langle w \rangle = \frac{1}{n.S} = \frac{1}{2k} \quad (3)$$

Fig. 5 and Fig. 6 show that all the laser processes are able to refine the magnetic domains with low spatial frequencies $k$ by increasing the population of domains with higher spatial frequencies.

<table><caption>Table 3: Domains’ width refinement</caption><thead><tr><th></th><th>LPL<br>(%)</th><th>SPL<br>(%)</th><th>USPL 1<br>A12 (%)</th></tr></thead><tbody><tr><td>0,23</td><td>-21 %</td><td>-5 %</td><td>-22 %</td></tr><tr><td>0,27</td><td>-8 %</td><td>-6 %</td><td>-15 %</td></tr></tbody></table>

The increase of probability density with the highest $k$, leading to the most significant refinement effect, is obtained for the USPL process on two investigated conventional grades of Si<sub>w</sub>3.3%Fe<sub>w</sub>9.7% GOES with thicknesses 0.23 and 0.27 mm (23I12(-21%), 23S12(-5%), 23A12(-22%) and 27I11(-8%), 27S11(-6%), 27A12(-15%)) (Table 3). The connection between the identified property $\Lambda$, the width $w$ and the mobility $\eta$ is obtained with equation (4a). The change in mobility $d\eta$ can be expressed as a function of both variations $dw$ and $d\Lambda$ (4b).

$$\Lambda \propto \sqrt{\frac{w}{2\sigma J_s \eta}} \quad (4a)$$

$$d\eta \propto \left( \frac{dw}{2\sigma J_s \Lambda^2} - \frac{wd\Lambda}{\sigma J_s \Lambda^3} \right) \quad (4b)$$

$J_s$ is the saturation magnetic polarization.
<figure><img src="image_8.png" /><figcaption>Fig. 5: Domains refinement distribution of grade 23MXX (average of 8 images per process v.s. reference samples).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6: Domains refinement distribution of grade RXXX27 (comparisons on the same samples before and after).</figcaption></figure>

**5. Identifications and Cross Comparisons**

The different microscopic physical origins of loss reduction depending on the type of laser process used can be identified and clarified by looking at the results of Fig. 7 and Fig. 8, on top for grade 23MXX and at the bottom for grade RXXX27.

Any surface domains refinement will act on $\Lambda$ and $\Lambda_0$, laser induced stress on $\mu$ and $\kappa$, induced pinning centers on $\nu_c$ and $\nu_c$ and any walls nucleation, multiplication and mobility effect will be visible on $\eta$ and $\tau$. It seems to be not only a question of domains refinement!

A first result obtained whatever the model is that the use of LPL and SPL at both sides of the thicker material failed to reduce even more the losses like it is the case for the USPL. On low thicknesses (Fig. 2), a second side or a second pass is beneficial mainly for $P_d$ but detrimental for $P_s$. For higher thicknesses (Fig. 3), both USPL A12 and A21 are able to reduce both $P_s$ and $P_d$. The heat required to sufficiently stress the laser spots inside the entire thickness must be increased in the thick grade and this might enlarge the HAZ too much when applying the LPL or SPL process at both sides which is detrimental for the magnetic performances. One solution proposed is to create grooves either at both sides or with two passes without any heat generated thanks to the USPL ablation process. For the average $\mu-\nu_c-\Lambda$ model first in Fig. 7, it seems clear that there still cannot be any distinction between the different pulse durations at high induction levels (see **Erreur! Source du renvoi introuvable.** and Fig. 3 B>1.7T). At 1.7 T and above, the whole properties and therefore the loss reduction factors tend towards more or less the same values (Fig. 2, Fig. 3 and Table 4). An exception occurs for the impact of USPL ablation A12 and A21 processes on the quasi static internal permeability $\mu$ which can be more impacted than the others: at high induction level, the permeability $\mu$ is damaged, at low induction level $B$, the permeability $\mu$ is enhanced. The behavior is exacerbated for the USPL. Nevertheless, a clear distinction between the different pulse durations is identified for low and intermediate induction levels, below 1.5 T. The LPL irradiation process is able to reduce more the coercive reluctivity $\nu_c$ than the SPL scribing process that generates too much heat during the engraving process. The difference is more significant for the low thickness. USPL ablation A21 is the only one able to reduce even more $\nu_c$ for both thicknesses. Thanks to deep enough grooves without HAZ at both sides, the process A12 is a compromise between irradiation and scribing for the low thickness but works as well as A21 for the
thick sheet. On the contrary, the SPL scribing process is able to improve more the dynamical properties $A$ (reduction) and $\eta$ (increase) than the LPL irradiation process, probably due to the absence of magnetic poles in a groove and the presence of a residual stress still enforced by the coating. The improvements and differences are more significant for the low thickness. Again, USPL ablation A21 is the only one able to improve even more $A$ and $\eta$ for both thicknesses. Thanks to clean grooves at both sides, maximizing the magnetic poles induced refinement and the walls dynamics, the process A12 is a compromise between irradiation and scribing for the low thickness but works as well as and even better than A21 for the thick sheet.

For the average TMPT model then in Fig. 8, discriminating the different processes is possible for all the model parameters. In this model, the impact on the permeability is explained by the laser stress induced anisotropic exchange property $\kappa$ which is decreased at low $B$ and increased at high $B$, this phenomenon is exacerbated for low thicknesses and the USPL ablation processes. The deeper grooves generated by the USPL ablation processes would act at high $B$ like walls pinning spots that significantly increase the coercive reluctivity $v_c$ for both thicknesses. At low $B$, and for the thick sheet, ablation grooves can become either walls' activation or multiplication centers, similar to inclusions, which can reduce the coercive reluctivity $v_c$. more significantly than the other techniques. The USPL ablation process seems also able to reduce the dynamical properties $A_0$ and $\tau$ more than the LPL and the SPL processes, probably thanks to the presence of magnetic poles in a groove and the absence of any residual stress. The improvements and differences are larger for the low thickness. USPL ablation A21 is still the only one able to improve even more $A_0$ for both thicknesses. Thanks to deep grooves at one side, A21 is maximizing the magnetic poles induced refinement mainly at the sheet surface, which contributes to the significant decrease of property $A_0$. Thanks to clean grooves at both sides, A12 is optimizing the number of nucleation and multiplication centers at each side of the sheet; which helps the walls dynamics inside the volume and contributes to the most significant decrease of damping delay $\tau$.

## 6. Conclusion and Perspectives

Cross comparisons between the model, experiments and the observations allow to identify some discriminating physical principles behind the changes in magnetic structure due to different pulsed laser impacts. The method separates the quasi-static ($v_c$ or $v_c$), self-organizing ($\mu$ or $\kappa$), topological (domains size $A$ or $A_0$) and dynamical ($\eta$ or $\tau$) origins of the behavior and discriminates between different laser processes. This work also provides data for the field diffusion-like [12] and the boundary TMPT formulation [13] usable when integrating the electrical sheets in a magnetic core. The process optimization finally leads to the best performances for each laser configuration and both GOES grades with thicknesses 0.23 and 0.27 mm @1.7T50Hz given in Table 4.

<table><caption>Table 4: Loss reduction factors at 1.7 T and 50 Hz</caption><thead><tr><th>1,7T<br>50HZ</th><th>LPL<br>(%)</th><th>SPL<br>(%)</th><th>USPL 1<br>A12 (%)</th><th>USPL 2<br>A21 (%)</th></tr></thead><tbody><tr><td>0,23</td><td>-17,5 (I12)</td><td>-16,4 (S12)</td><td>-19,3</td><td>-13,4</td></tr><tr><td>0,27</td><td>-15,3 (I11)</td><td>-11 (S11)</td><td>-15,3</td><td>-15,4</td></tr></tbody></table>

However, it must be mentioned that no laser impact on the shape of hysteresis loops (including the coercive field) can be accurately determined as long as neither DC magnetic measurements or extrapolations nor non-linear hysteresis models are proposed within the TMPT. The complete faithful description, including the microscopic point of view, requires to analyse further the shape and dynamics of walls and domains at the vicinity of and in between the laser spots at the microscopic and nanoscopic scales [14]. Only properties in the Rolling Direction (RD) have been investigated. As a first perspective, the same cross comparisons have to be implemented in order to discriminate the different pulsed laser processes that are able to optimize the magnetic performances in the other directions, either in the Transverse Direction (TD) or in a flux direction that makes an arbitrary angle with the Rolling Direction (RD) [15].
<figure><img src="image_10.png" /><figcaption>Fig. 7: Impact of lasers on µ-Vc-A magnetic properties of grade 23MXX (left) and grade RXXX27 (right).</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 8: Impact of lasers on TMPT magnetic properties of grade 23MXX (left) and grade RXXX27 (right).</figcaption></figure>
## References

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## Acknowledgements

We thank APERAM Brazil and SEPSA for having given samples of GOES with thickness 0.27-0.28 mm and 0.23 mm. The project ESSIAL received funding from the European Research Council under the H2020-IND-CE-2016-17/H2020-FOF-2017 Program (Grant No. 766437).