# A Ti/Pt/Co Multilayer Stack for Transfer Function Based Magnetic Force Microscopy Calibrations

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{x}Ni

_{1−x}and Pt layers was introduced to compare the resolution of different MFM setups [21]. Other reference samples exploit intrinsic domain patterns in different stacks (Cu(200 nm) Ni/Cu/Si(001) [16] and Co/Pt multilayer [22,23]) or rely on a pattern written on a hard disk [24].

## 2. Results

#### 2.1. Fabrication of the Multilayer Stack

_{20}on a naturally oxidized Si(111) wafer. This sample will be referred to as Ti/Pt/Co or ‘tpc’ in the remainder of this paper. The Ti, Pt, and Co layers were deposited by using pulsed DC, DC, and RF power sources, respectively. The deposition chamber’s base pressure was $3\times {10}^{-9}\mathrm{mbar}$. The substrates were annealed prior to the deposition to clean it from residual surface contaminations as carbon and oxygen. The purity of the substrate and the targets were checked by x-ray photoemission spectroscopy (XPS). The XPS system, mounted on the same UHV cluster as the deposition system, allows control of the quality of the deposition. The deposition rates were calibrated by using XPS prior to the deposition and monitored by a quartz crystal microbalance (QCM) during the deposition. The QCM is calibrated according to the calibration values obtained from XPS. The calibrated deposition rates are $0.018{\mathrm{nms}}^{-1}$, $0.019{\mathrm{nms}}^{-1}$, and $0.037{\mathrm{nms}}^{-1}$ for Ti, Pt, and Co, respectively. As a result, the layer thicknesses are traceably defined and very reproducible. Alongside the thickness calibration, XPS based monitoring of the fabrication allows reproduction of the sample interface and layer structure in further depositions with very high accuracy. Furthermore, as an advantage of the magnetron sputtering technique, samples can be prepared on substrates with radii up to 5 cm. This guarantees a high availability of the reference material. The detailed steps for the calibration of deposition and XPS control of the samples can be found in the Appendices (Appendix A).

#### 2.2. Magnetic and Geometric Characterization of the Ti/Pt/Co Sample

- The domain pattern comparison is used to prove a good understanding of the micromagnetics of the Ti/PtCo material.
- The tpc stray field comparison serves the purpose of demonstrating that the reference sample is well understood and thus calculable and that different approaches (micromagnetic simulations, discrimination + forward calculation, qMFM) give the same magnetic stray field.
- The IFW stray field comparison will show that the Ti/Pt/Co sample, when actually used as a reference sample, gives correct quantitative stray field data in calibrated measurements, as validated by a comparison of Ti/Pt/Co-calibrated qMFM data on the Co/Pt sample with the results from discrimination and forward calculation.
- Finally, the ICF comparison will show that, not merely a proper quantitative analysis of “unknown” samples is achieved, but also a very good agreement of the ICF and the thereof derived tip magnetic properties, compared to calibrations with another reference sample.

#### 2.3. Micromagnetic Simulations of the Ti/Pt/Co Sample’s Magnetization Structure

^{3}[41] over a $1024\times 1024\times 20$ cell grid with a cell size of $5\times 5\times 3.8{\mathrm{nm}}^{3}$, starting from a random magnetization distribution. The exchange stiffness, ${A}_{ex}$, is slightly varied throughout the simulations within the range of ${A}_{ex}$ values discussed in the literature for similar magnetic multilayers ($5{\mathrm{pJm}}^{-1}-15{\mathrm{pJm}}^{-1}$) [42,43]. Considering an optimum recovery of the experimentally observed domain width of $\langle {D}^{MFM}\rangle =345\mathrm{nm}$, a value for ${A}_{ex}=6{\mathrm{pJm}}^{-1}$ is derived. A long-range Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange coupling was incorporated into the simulations, which arises due to the Ti/Pt layers stacking. An effective RKKY exchange field, ${J}_{RKKY}$, was implemented to the simulations by scaling the exchange coupling between each layer. The scaling factor is defined by $\Delta S=\frac{\left({J}_{RKKY}\cdot \delta {c}_{z}\right)}{\left(2\langle {A}_{ex}\rangle \right)}$, where $\delta {c}_{z}$ and $\langle {A}_{ex}\rangle $ are the thickness of the single simulation cell and the average of ${A}_{ex}$ over the coupled layers [44]. Similar to what was done in the case of the exchange stiffness, ${J}_{RKKY}$ was varied throughout the simulations, and the optimum value was found to be ${J}_{RKKY}=0.07{\mathrm{mJm}}^{-2}$. The simulation results for optimized parameters are summarized in Figure 3.

#### 2.4. Validation with qMFM and Stray Field Simulations

- (i)
- qMFM characterization of the Ti/Pt/Co sample

_{100}/Pt(2 nm). Similar to the Ti/Pt/Co sample, it shows a stripe domain pattern, at zero field with, however, a lower average domain size, $\langle {D}^{MFM,ref}\rangle =235\mathrm{nm}$. The magnetic parameters of the sample are summarized in Table 1. The MFM measurements were performed with a Nanoscope IIIa with a Dimension head using a NT-MDT Low Moment MFM tip, following the procedure discussed in [32]. The measurement heights were ${z}^{ref}=64\mathrm{nm}$ and ${z}^{tpc}=64\mathrm{nm}$ for calibration and validation measurements, respectively, with a pixel size of ${\delta}_{A}=10\times 10{\mathrm{nm}}^{2}$ on a $512\times 512$ spatial pixel grid. The quality factor, $Q=250$, was determined by fitting the resonance curve of the tip with a Lorentzian function. The full width of the resonance curve at $0.707$ of the maximum was used as the $Q$ [32]. The cantilever stiffness, $c=3\mathrm{N}/\mathrm{m}$, was provided by the manufacturer. The $IC{F}^{ref}$ will be further discussed below. The $TT{F}^{ref}$, i.e., the z-component of the stray field gradient, ${\mu}_{0}\frac{d{H}_{z}^{tip}}{dz}$, of the tip at the sample surface, calculated from the $IC{F}^{ref}$ using Equation (1). Before the calibrated measurement, i.e., the deconvolution as described in Equation (3), the ${\mu}_{0}\frac{d{H}_{z}^{tip}}{dz}$ distribution is circularly averaged around the center in order to eliminate artefacts arising from fast Fourier transforms (FFT).

- (ii)
- MFM domain pattern-based simulations

- (iii)
- Micromagnetic simulations

#### 2.5. Cross Validation of the Co/Pt Reference Sample by Ti/Pt/Co Calibrated qMFM

_{100}sample stray field data that result from applying the $TT{F}^{tpc}$ to the MFM phase shift data (Figure 5a) shown in Figure 5b–d show the magnetization distribution from the discrimination of the phase shift data and the thereof calculated stray field data, respectively. Line plots of both stray field data distributions, taken along the dashed lines and plotted together with their uncertainty bands, are compared in Figure 5f. The Ti/Pt/Co-calibrated qMFM data show excellent agreement with the simulations, mostly within the uncertainty margins. Again, small discrepancies can be explained by imperfections in the real sample that were not regarded in the uncertainty calculations.

#### 2.6. Feature Size Spectra

## 3. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. XPS Study and Calibration of Deposition

**Figure A1.**X-ray photoemission spectra of Au4f and Ag3d used for calibration of Co (

**a**), Pt (

**b**), and Ti (

**c**) depositions. Thickness-deposition time graph and deposition rates for Co, Pt, and Ti targets (

**d**).

**Figure A2.**X-ray photoemission spectra of tpc sample recorded from the top of first Co layer. The survey spectrum is used to detect any contamination on the sample and check the general structure of the sample (

**a**). High resolution windows of each layers and substrate is used to check the consistency of the photoemission cross section and the change in the chemical state of any layer (or substrate) (

**b**–

**g**).

## Appendix B. A Self-Correlation-Based Analysis of Domain Wall Widths

**Figure A3.**Plotlines through (

**a**,

**c**,

**e**) the self-correlation transforms for the Co/Pt reference sample (ref) (

**b**), the tpc reference sample (TPC (dec)) (

**d**), and the simulated MFM image of the micromagnetic simulation results (TPC (sim)) (

**f**).

## Appendix C. Determination of the Ti/Pt/Co Sample’s Uniaxial Anisotropy Constant, K_{u}, from the VSM Data

**Figure A4.**VSM measured M-H curves of the Ti/Pt/Co reference sample: (

**a**) shows a zoomed-in version of (

**b**). The red line shows the fit to the low-field linear part of the curve; (

**b**) also shows the construction of the μ

_{0}H

_{sat}value from the intersection of the fit with M = M

_{sat}.

## Appendix D. Domain Wall Kernel

## Appendix E. Uncertainties Used in Uncertainty Calculations

Parameter | Uncertainty |
---|---|

MFM phase shift Δ | $u\_\Delta \phi ={0.2}^{\xb0}$ |

regularization parameter, $\mathit{\alpha}$ | $u\_\alpha $: 1% |

stack thickness tpc sample, ${\mathit{d}}^{\mathit{t}\mathit{p}\mathit{c}}$ | $u\_d$ = 2 nm |

stack thickness ref sample, ${\mathit{d}}^{\mathit{r}\mathit{e}\mathit{f}}$ | $u\_d$ = 4 nm |

saturation magnetization tpc sample, ${\mathit{M}}_{\mathit{S}}^{\mathit{r}\mathit{e}\mathit{f}}$ | $u\_{M}_{S}^{ref}$: 6% |

saturation magnetization Co/Pt sample, ${\mathit{M}}_{\mathit{S}}^{\mathit{t}\mathit{p}\mathit{c}}$ | $u\_{M}_{S}^{tpc}$: 6% |

measurement height, $\mathit{h}$ | $u\_h:10\%$ |

## Appendix F. Estimation of Accessible Spatial Frequency Range

_{x}= sigma

_{x}= 50 nm).

**Figure A5.**Estimation of accessible wave vector range after calibration; tip mediated sensitivity, $\frac{d{B}_{z}^{}}{dz}$, and circularly averaged sample, ${\sigma}_{eff}^{}$, distribution in Fourier space for the Ti/Pt/Co (

**a**) and the Co/Pt sample (

**b**). The inset shows the generic tips, $\frac{d{B}_{z}^{}}{dz}$, in real space; (

**c**,

**d**) show the phase shift distribution of a simulated reference sample measurement using the generic tip for the Ti/Pt/Co and the Co/Pt sample, respectively. The horizontal lines show the noise floor for white Gaussian noise with 0.2° (black) and 0.02° (green) standard deviation.

**Table A2.**Cut-off wave vector and corresponding wavelength data for the Ti/Pt/Co and the Co/Pt sample for two different noise levels.

Δϕ | Low Cut-Off | High Cut-Off | ||
---|---|---|---|---|

Frequency | Wavelength | Frequency | Wavelength | |

Ti/Pt/Co multilayer Stack (tpc) | ||||

0.02° | <1.22 µm^{−1} | >5.12 µm | 42.256 µm^{−1} | 149 nm |

0.2° | <1.22 µm^{−1} | >5.12 µm | 56.295 µm^{−1} | 112 nm |

Co/Pt Stack (ref) | ||||

0.02° | <1.22 µm^{−1} | >5.12 µm | 50.726 µm^{−1} | 124 nm |

0.2° | <1.22 µm^{−1} | >5.12 µm | 63.231 µm^{−1} | 99 nm |

## Appendix G. Estimation of the Ti/Pt/Co Sample Surface Roughness

**Figure A6.**Surface roughness analysis: AFM topography image of the Ti/Pt/Co sample (

**a**) and histogram plot of the height distribution (

**b**).

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**Figure 1.**M-H hysteresis loop of the Ti/Pt/Co sample. (

**a**) the easy axis and hard axis hysteresis loops recorded by external field applied in plane, parallel to the sample surface (‖, blue) and out of plane, perpendicular to the sample surface ⊥, red). Measurements were performed by using VSM at room temperature (295 K). (

**b**) Zoomed-in plot of the out-of-plane measurement shown in (

**a**). The inset in (

**b**) shows an MFM image of the sample.

**Figure 2.**Flowchart of the validation process. The flowchart shows the different simulation and measurement steps used to validate the Ti/Pt/Co sample’s micromagnetic parameters. The comparisons that were performed based on the measurement results are marked as grey shaded boxes.

**Figure 3.**Results of the MuMax3 micromagnetic simulations of the Ti/Pt/Co sample: The relaxed magnetization pattern averaged over the stack thickness together with a zoomed in view (

**a**). Perpendicular magnetization component of the top layer in a transition between two domains together with a calculated transition using the standard Bloch wall model (

**b**). Cross section of a cutout of the magnetization of the Ti/Pt/Co sample showing all 20 layers (

**c**). The magnetization in the domains is homogeneous and independent of the layer number. The overall magnetization of the domains is depicted by the arrows. The dashed line shows the angle of the magnetization that follows a Bloch-like course of the domain wall transition. The dotted lines mark the domain wall width calculated using the Lilley formula.

**Figure 4.**Comparison of simulated and experimental Ti/Pt/Co sample data: (

**a**) measured MFM phase shift data and (

**b**) perpendicular stray field components B

_{z}data calculated using the Co/Pt sample calibrated qMFM; (

**c**) z component of the magnetization calculated from a discrimination of the MFM phase shift data from (

**a**); (

**d**) the thereof calculated perpendicular stray field components B

_{z}data using the Ti/Pt/Co micromagnetic material parameters; (

**e**) z-component of the magnetization from the micromagnetic simulation and (

**f**) the perpendicular stray field components B

_{z}data calculated thereof using a layer by layer approach; (

**g**) the stray field data with uncertainty bands from the data marked by the dashed lines in the stray field images in (

**b**,

**d**,

**f**).

**Figure 5.**(

**a**) MFM phase shift data of the [Pt/Co]

_{100}sample and (

**b**) quantitative perpendicular stray field components, B

_{z}, data, calculated thereof using Ti/Pt/Co calibrated qMFM; (

**c**) sample magnetization pattern from discrimination of the phase shift data followed by a convolution with a domain wall kernel and (

**d**) perpendicular stray field components, B

_{z}, data, calculated thereof by forward simulation using the known micromagnetic material parameters; (

**e**) plotlines of the perpendicular stray field components, B

_{z}, taken along the dashed lines of the stray field images together with uncertainty bands.

**Figure 6.**Comparison of ICFs and reference sample spectra: (

**a**,

**b**) show the ICFs calculated from calibration measurements using the Co/Pt (ICF

^{ref}) and the Ti/Pt/Co (ICF

^{tpc}) reference sample, respectively; (

**c**) shows plotlines through the maxima of the TTFs for both calibrations, TTF

^{ref}(red) and TTF

^{tpc}(blue) for a distance of 64 nm from the tip apex; (

**d**) shows plotlines through the Fourier spectra of the effective surface charge density of the Co/Pt reference sample (red) and Ti/Pt/Co sample. Dotted line marks the area of k-values accessible after calibration with the respective reference sample (see text).

**Table 1.**Sample parameters required for the calculation of the effective magnetic charge density of the Ti/Pt/Co sample and the Co/Pt reference sample.

Ti/Pt/Co Multilayer Stack | Co/Pt Stack | |
---|---|---|

Saturation Magnetization M_{s} | 201 kA/m | 500 kA/m |

Stack Thickness t | 20 × 3.8 nm | 100 × 1.3 nm |

Domain Wall Width ${\delta}_{DW}^{tpc}$ | 27 nm | 16 nm |

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## Share and Cite

**MDPI and ACS Style**

Sakar, B.; Sievers, S.; Fernández Scarioni, A.; Garcia-Sanchez, F.; Öztoprak, İ.; Schumacher, H.W.; Öztürk, O.
A Ti/Pt/Co Multilayer Stack for Transfer Function Based Magnetic Force Microscopy Calibrations. *Magnetochemistry* **2021**, *7*, 78.
https://doi.org/10.3390/magnetochemistry7060078

**AMA Style**

Sakar B, Sievers S, Fernández Scarioni A, Garcia-Sanchez F, Öztoprak İ, Schumacher HW, Öztürk O.
A Ti/Pt/Co Multilayer Stack for Transfer Function Based Magnetic Force Microscopy Calibrations. *Magnetochemistry*. 2021; 7(6):78.
https://doi.org/10.3390/magnetochemistry7060078

**Chicago/Turabian Style**

Sakar, Baha, Sibylle Sievers, Alexander Fernández Scarioni, Felipe Garcia-Sanchez, İlker Öztoprak, Hans Werner Schumacher, and Osman Öztürk.
2021. "A Ti/Pt/Co Multilayer Stack for Transfer Function Based Magnetic Force Microscopy Calibrations" *Magnetochemistry* 7, no. 6: 78.
https://doi.org/10.3390/magnetochemistry7060078