# Controlling magnetic configuration in soft-hard bilayers probed by polarized neutron reflectometry

Nan Tang, Jung-Wei Liao, Siu-Tat Chui, Timothy Ziman, Alexander J.

Grutter, Kai Liu, Chih-Huang Lai, Brian J. Kirby, Dustin A. Gilbert

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Nan Tang, Jung-Wei Liao, Siu-Tat Chui, Timothy Ziman, Alexander J. Grutter, et al.. Control-
ling magnetic configuration in soft-hard bilayers probed by polarized neutron reflectometry. APL
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# Controlling magnetic configuration in soft-hard bilayers probed by polarized neutron reflectometry EP

Nan Tang; Jung-Wei Liao; Siu-Tat Chui 📉; Timothy Ziman 📉; Alexander J. Grutter; Kai Liu 📉;
Chih-Huang Lai 📉; Brian J. Kirby 📉; Dustin A. Gilbert 📉

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APL Mater. 10, 011107 (2022)

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# Controlling magnetic configuration in soft-hard bilayers probed by polarized neutron reflectometry EP

Cite as: APL Mater. 10, 011107 (2022); doi: 10.1063/5.0072812

Submitted: 24 September 2021 • Accepted: 19 November 2021 •

Published Online: 13 January 2022

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Nan Tang,<fnref n="1" /> Jung-Wei Liao,<fnref n="2" /> Siu-Tat Chui,<fnref n="3" /> and Timothy Ziman,<fnref n="4" />,<fnref n="5" />

Chih-Huang Lai,<fnref n="8" /> and Brian J. Kirby,<fnref n="8" /> and Dustin A. Gilbert<fnref n="1" />,<fnref n="9" />,α

## AFFILIATIONS

## ABSTRACT

Hard/soft magnetic bilayer thin films have been widely used in data storage technologies and permanent magnet applications. The magnetic configuration and response to temperatures and magnetic fields in these heterostructures are considered to be highly dependent on the interfacial coupling. However, the intrinsic properties of each of the layers, such as the saturation magnetization and layer thickness, also strongly influence the magnetic configuration. Changing these parameters provides an effective method to tailor magnetic properties in composite magnets. Here, we use polarized neutron reflectometry (PNR) to experimentally probe the interfacial magnetic configurations in the hard/soft bilayer thin films: $L_{10}$-FePt/A1-FePt, [Co/Pd]/CoPd, [Co/Pt]/FeNi, and $L_{10}$-FePt/Fe, all of which have a perpendicular magnetic anisotropy in the hard layer. These films were designed with different soft and hard layer thicknesses ($t_{soft}$ and $t_{hard}$) and saturation magnetization ($M_s^{soft}$ and $M_s^{hard}$). The influences of an in-plane magnetic field ($H_{ip}$) and temperature ($T$) are also studied using a $L_{10}$-FePt/A1-FePt bilayer sample. Comparing the PNR results to the micromagnetic simulations reveals that the interfacial magnetic configuration is highly dependent on $t_{soft}$, $M_s^{soft}$, and the external factors ($H_{ip}$ and $T$) and has a relatively weak dependence on $t_{hard}$ and $M_s^{hard}$. Key among these results, for thin $t_{soft}$, the hard and soft layers are rigidly coupled in the out-of-plane direction and then undergo a transition to relax in-plane. This transition can be delayed to larger $t_{soft}$ by decreasing $M_s^{soft}$. Understanding the influence of these parameters on the magnetic configuration is critical to designing functional composite magnets for applications.

© 2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0072812

## INTRODUCTION

Heterostructures of coupled, magnetically hard/soft composites<fnref n="1" />⁻<fnref n="5" /> have played a critical role in many modern data

storage<fnref n="6" />⁻¹⁷ and permanent magnet<fnref n="1" />,¹⁸⁻²⁰ technologies. In magnetic recording media, the high-anisotropy (magnetically hard) layer is frequently coupled to a magnetically soft layer, which aids in the data writing process.²¹⁻²³ In these exchange coupled composite

<footnote n="1">¹Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA</footnote>

<footnote n="2">²Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom</footnote>

<footnote n="3">³Bartol Research Institute, University of Delaware, Newark, Delaware 19716, USA</footnote>

<footnote n="4">⁴Institut Laue-Langevin, BP 156, 41 Avenue des Martyrs, 38042 Grenoble Cedex 9, France</footnote>

<footnote n="5">⁵LPMMC (UMR 5493), Université de Grenobles-Alpes and CNRS, Maison des Magistères, BP 166, 38042 Grenoble Cedex 9, France</footnote>

<footnote n="6">⁶NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Dr., Gaithersburg, Maryland 20899, USA</footnote>

<footnote n="7">⁷Department of Physics, Georgetown University, Washington, DC 20057, USA</footnote>

<footnote n="8">⁸Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 300044, Taiwan</footnote>

<footnote n="9">⁹Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA</footnote>

<footnote>a) Author to whom correspondence should be addressed: dagilbert@utk.edu</footnote>
(ECC) systems, the soft layer nucleates a domain wall that is easily pushed into the hard layer, reducing the writing field. As the anisotropy of the hard layer has been increased to allow for smaller grains, and, thus, higher recording densities,<sup>16,24–26</sup> the writability provided by the soft layer has become indispensable.<sup>27,28</sup> In another example, high-anisotropy magnetic materials are coupled to high moment materials to develop a composite magnetic structure with a large maximum energy product for permanent magnet applications.<sup>1,29</sup> The magnetic configuration in composite magnets, thus, reflects intrinsic properties of each layer, propagated across the interface by the interface exchange and dipolar fields. Since the interfaces are highly imperfect—rich in dislocations and vacancies, becoming a virtual grain boundary—the resultant properties are an enigmatic mixture of each material’s properties and can be challenging to predict. Understanding the full range of interactions within hard/soft coupled systems is critical for composite applications. Magnetic hard/soft bilayers can provide a model system to gain critical understanding of the magnetic interactions and their impacts on technological applications.<sup>30,31</sup>

In hard/soft bilayers with a perpendicularly magnetized hard layer, the magnetic interactions are highly dependent on the thickness of the soft layer, $t_{soft}$.<sup>32,33</sup> For the case of a thin soft layer with a thickness less than the classical exchange length ($l_{ex}$), it is typically accepted that the magnetic moments are rigidly coupled to the hard layer by the exchange interaction. Furthermore, as $t_{soft}$ increases, it is expected that the magnetic moment relaxes in-plane, especially away from the hard/soft interface, resulting in exchange spring-like behavior.<sup>34</sup> In addition to $t_{soft}$, the magnetic configuration is also influenced by the material properties including the saturation magnetization ($M_s^{hard}$ and $M_s^{soft}$), exchange stiffness ($A_{hard}$ and $A_{soft}$), the hard layer magnetocrystalline anisotropy ($K_u$), and the hard/soft interfacial coupling stiffness ($A_{int}$).<sup>30,31,35</sup> While some of these magnetic material parameters have predictable relationships with the magnetic configuration, e.g., $K_u$ and $A_{hard}$ can be used to determine the exchange length ($\approx\pi\sqrt{A_{hard}/K_u}$) in hard magnets, the dependence on $M_s^{hard}$ and $M_s^{soft}$ or the film thickness is not as straightforward. For modern applications in heat-assisted magnetic recording (HAMR) technologies, understanding the temperature dependence of these properties and its effect on the magnetic configuration is critical to device functionality.<sup>36–40</sup> This quality is manifested in HAMR devices where high temperatures are used to reduce $K_u$ but simultaneously also reduce $M_s^{hard}$ and $M_s^{soft}$, establishing an optimization problem to achieve the ideal writability. Finally, the applied magnetic field also strongly influences the magnetic configuration; while most of the magnetic energy terms are uniaxial, the field-dependent Zeeman energy is unidirectional and establishes a new balance between various energy terms. Therefore, to better design and control hard/soft magnetic heterostructures, it is important to understand the roles of sample geometry ($t_{soft}$), materials properties ($M_s^{hard}$ and $M_s^{soft}$), and external influences (applied in-plane magnetic field, $H_{ip}$, and temperature, $T$) in determining the magnetic configuration.

In this work, we use polarized neutron reflectometry (PNR) to investigate the magnetic configuration in hard/soft bilayer thin films. Comparing with previous magnetometry-based studies,<sup>2,30</sup> PNR reveals the magnetic depth profile within the film, which is

determined by the magnetic interactions. A series of bilayer samples with a hard magnetic underlayer (having perpendicular magnetic anisotropy) and a soft top layer is investigated, including $L_{10}$-FePt (hard)/A1-FePt (soft), [Co/Pd] (hard)/CoPd (soft), [Co/Pt] (hard)/FeNi (soft), and $L_{10}$-FePt (hard)/Fe (soft). By designing $M_s^{hard}$, $M_s^{soft}$, and $t_{soft}$, the magnetic interactions and the resultant magnetic configuration are systematically varied. Micromagnetic simulations are performed to support the experimental results and reflect similar magnetic behavior. The simulations also reveal the influence of $M_s^{hard}$ and hard layer thickness ($t_{hard}$) in determining the magnetic configuration. In addition to the intrinsic properties and sample structure, the influence of temperature ($T$) and magnetic field ($H$) on the magnetic configuration is also studied by PNR. Polarized neutron reflectometry measurements, together with micromagnetic simulations, provide a comprehensive understanding of the influence of the sample structure and external control variables on the magnetic configuration of hard/soft bilayer composite magnets. These results provide insight into the underlying physics correlating bilayer film structure with the magnetic configuration.

## METHODS

Four series of samples covering a range of $M_s^{soft}$, $M_s^{hard}$, and $t_{soft}$ are synthesized by magnetron sputtering, and the details can be found elsewhere:<sup>32,41–43</sup> (1) the Si/SiO<sub>2</sub> (200 nm)/$L_{10}$-FePt (4 nm)/A1-FePt ($t_{soft}$)/Ti (4 nm) samples were prepared in a vacuum system with a base pressure of $8 \times 10^{-8}$ Torr. The oriented $L_{10}$-FePt was prepared by rapid thermal annealing, as described previously.<sup>26,32,44</sup> Without breaking vacuum, the A1-FePt soft layer (2 nm or 5 nm) was deposited on $L_{10}$-FePt by co-sputtering of elemental targets, followed by a Ti capping layer. (2) The preparation process of Si/SiO<sub>2</sub> (200 nm)/$L_{10}$-FePt (4 nm)/Fe (9 nm)/Pt (2 nm) is similar to the Si/SiO<sub>2</sub> (200 nm)/$L_{10}$-FePt (4 nm)/A1-FePt ($t_{soft}$)/Ti (4 nm) samples but sputtering 9 nm Fe and 2 nm Pt as the soft and capping layers, respectively. (3) For the Si/SiO<sub>2</sub>/[Co (0.4 nm)/Pt (0.7 nm)]<sub>4</sub>/FeNi ($t_{soft}$)/Pd (2 nm) samples, four repeats of Co (0.4 nm)/Pt (0.7 nm) multilayer stack were first sputtered on a Si/SiO<sub>2</sub> substrate. Four different thicknesses of soft Fe<sub>0.2</sub>Ni<sub>0.8</sub> (0, 1, 3, and 7) nm layers are then deposited, followed by a 2 nm Pd capping layer. (4) The Si/Pd (20 nm)/[Co (0.3 nm)/Pd (0.9 nm)]<sub>25</sub>/CoPd ($t_{soft}$)/Pd (5 nm) samples were magnetron sputtered in an ultrahigh vacuum chamber with a base pressure of $9 \times 10^{-9}$ Torr. Magnetically hard [Co (0.3 nm)/Pd (0.9 nm)]<sub>25</sub> multilayers were sputtered onto the Si substrates with a 20 nm Pd buffer layer. Different thicknesses of $t_{soft}$ (2, 5, and 9) nm were then deposited, followed by a 5 nm Pd capping layer. For all the samples, the underlayer films ($L_{10}$-FePt, Co/Pt, and Co/Pd multilayers) have a strong perpendicular magnetic anisotropy (PMA).

Polarized neutron reflectometry was performed at the NIST Center for Neutron Research on both the Polarized Beam Reflec- tometer (PBR) and Multiple Angle Grazing Incidence K (MAGIK) reflectometer instruments, which uses 4.75 Å and 5.00 Å wavelength neutrons, respectively. For the $L_{10}$-FePt/A1-FePt samples to study the influence of $t_{soft}$ on the magnetic configuration, the film was rotated into a grazing incidence with the neutron beam. The films were first saturated with a magnetic field (700 mT) parallel to the film
normal direction, and then, the field was reduced to 50 mT. Then, the film was rotated such that the 50 mT field is applied along the film normal direction; this field is insufficient to significantly change the magnetic configuration and acts to preserve the orientation of the neutrons, i.e., as a guide field. The out-of-plane guide field sets the orientation of the neutron spin moment always along the out-of- or into-the-plane direction. The PNR measurement is executed by performing a coupled theta-2theta specular scan with control and sensitivity to the incident and scattered neutron spin. The non-spin-flip PNR cross sections [R<sup>++</sup> and R<sup>--</sup>, where R is the reflection intensity with the superscript indicating the spin configuration of the incident and reflected neutrons, +(-) indicting the spin-up (spin-down) geometries] typically provide sensitivity to the nuclear structure and the magnetization parallel to the neutron spin moment. However, the neutron scattering rules prohibit scattering from magnetization parallel to the momentum transfer vector, which for PNR is in the out-of-plane direction. PNR is sensitive only to the in-plane magnetization, and with an out-of-plane guide field, the non-spin-flip cross section encodes only the nuclear structure. Using an out-of-plane guide field, any net in-plane magnetization is orthogonal to the neutron spin and thus contributes to the spin-flip (R<sup>+</sup> and R<sup>-</sup>) cross section. In this geometry, sensitivity to the orientation of the in-plane magnetization is lost; however, the signal is increased by including all of the magnetic signal into the spin-flip cross section.45,46 For all other PNR measurements, the samples were saturated in the out-of-plane direction, then returned to remanence, and measured in a small in-plane guide field (1 mT). In this configuration, R<sup>++</sup> and R<sup>--</sup> provide sensitivity to both the nuclear depth profile and the depth profile of the net in-plane magnetization component parallel to the applied field. Spin-flip scattering for this configuration is not considered here. All the experimental data are then model fitted by the REFLID software.45

Three dimensional micromagnetic simulations are performed using the object oriented micromagnetic framework (OOMMF) platform⁴⁷ with a simulation volume of 200 nm × 1 nm × (t<sub>hard</sub> + t<sub>soft</sub>) and a mesh of 0.5 nm × 0.5 nm × 0.2 nm. The exchange stiffness for the hard magnet (A<sub>h</sub>), hard/soft interface (A<sub>int</sub>), and soft magnet (A<sub>s</sub>) is A<sub>h</sub> = A<sub>s</sub> = A<sub>int</sub> = 1.15 × 10<sup>-11</sup> J/m. The uniaxial anisotropy for the hard magnet (K<sub>u</sub>) is chosen to be 1 × 10<sup>6</sup> J/m<sup>3</sup>, while the anisotropy for the soft magnet (K<sub>s</sub>) is 0.

# EXPERIMENTAL RESULTS

## Effects of soft layer thickness

With the above experimental preparations, the first set of measurements were performed to study the influence of t<sub>soft</sub> on the magnetic configuration. Using an out-of-plane guide field, reflectometry data for the L1₀-FePt (4 nm)/A1-FePt (t<sub>soft</sub>) bilayer films with t<sub>soft</sub> = 2 nm and 5 nm are shown in Figs. 1(a) and 1(b), respectively. Data on the same sample but taken at a different time were shown in Ref. 32 and reflects a similar profile; differences in the capping layer structure are captured in this work, likely due to the higher q-range measured. For the t<sub>soft</sub> = 2 nm film, the experimental non-spin-flip R<sup>++</sup> and R<sup>--</sup> are essentially identical, and the spin-flip R<sup>+</sup> and R<sup>-</sup> are virtually zero. This indicates that there is little net in-plane magnetization anywhere in the film. In comparison, for the t<sub>soft</sub> = 5 nm film, the R<sup>++</sup> and R<sup>--</sup> are still overlapping, but R<sup>+</sup> and R<sup>-</sup> are now nonzero, indicating the presence of appreciable in-plane magnetization. These interpretations are confirmed by model fitting [solid lines in Figs. 1(a) and 1(b)] that yields the scattering length density (SLD)⁴⁸ depth profiles for the two films, as shown in Figs. 1(c) and 1(d). The profiles have a nuclear component (NSLD) indicative of the nuclear composition and a magnetic component (MSLD) proportional to the in-plane magnetization. Notably, the MSLD is approximately zero for t<sub>soft</sub> = 2 nm and nonzero for t<sub>soft</sub> = 5 nm. These results confirm that t<sub>soft</sub> can influence the magnetic configuration in the soft layer. Interestingly, this influence extends all the way to the interface; while both the hard and soft layers in the 2 nm sample are oriented out-of-plane, the soft layer in the 5 nm sample is almost entirely in-plane.

## Effects of saturation magnetization

Besides t<sub>soft</sub>, M<sub>s</sub><sup>hard</sup> and M<sub>s</sub><sup>soft</sup> are expected to influence the magnetic configurations in these bilayer films. PNR measurements are also performed on a series of samples with M<sub>s</sub><sup>hard</sup> << M<sub>s</sub><sup>soft</sup>, M<sub>s</sub><sup>hard</sup> < M<sub>s</sub><sup>soft</sup>, and M<sub>s</sub><sup>hard</sup> > M<sub>s</sub><sup>soft</sup>, including L1₀-FePt (4 nm)/Fe (9 nm), [Co (0.3 nm)/Pd (0.9 nm)]<sub>25</sub>/CoPd (9 nm), and [Co (0.4 nm)/Pt (0.7 nm)]<sub>4</sub>/FeNi (7 nm), respectively. For the case of M<sub>s</sub><sup>hard</sup> << M<sub>s</sub><sup>soft</sup> shown in Fig. 2(a), the experimental R<sup>++</sup> and R<sup>--</sup> curves are significantly separated, which indicates a net in-plane magnetization. The corresponding magnetic depth profiles, in Fig. 2(b), show a large MSLD in the soft layer (the Fe region). Using the MSLD for the bulk iron (4.85 × 10<sup>-4</sup> nm<sup>-2</sup>),⁴⁸ the soft Fe layer is confirmed to be almost entirely in-plane throughout its thickness. For M<sub>s</sub><sup>hard</sup> < M<sub>s</sub><sup>soft</sup> and M<sub>s</sub><sup>hard</sup> > M<sub>s</sub><sup>soft</sup>, the experimental R<sup>++</sup> and R<sup>--</sup> curves are strongly overlapping, as shown in Figs. 2(c) and 2(e), respectively. The corresponding magnetic depth profiles show almost no MSLD in Figs. 2(d) and 2(f), respectively. These results suggest that in both the [Co (0.3 nm)/Pd (0.9 nm)]<sub>25</sub>/CoPd (9 nm) and [Co (0.4 nm)/Pt (0.7 nm)]<sub>4</sub>/FeNi (7 nm) films, even at these relatively larger thicknesses, the soft-layer magnetization remains mostly in the out-of-plane direction. The PNR measurements are also performed on another five [Co (0.3 nm)/Pd (0.9 nm)]<sub>25</sub>/CoPd and [Co (0.4 nm)/Pt (0.7 nm)]<sub>4</sub>/FeNi samples with thinner soft layer thickness, as shown in S1. These films also show very little in-plane magnetization.

## Effects of in-plane field and temperature

The results above implicate a complex competition within these systems to define the soft-layer orientation, which depends on both M<sub>s</sub><sup>soft</sup> and t<sub>soft</sub>. Besides these intrinsic material parameters, the interfacial magnetic configuration is also dependent on the external variables (H<sub>ip</sub> and T). Six PNR measurements were performed on the L1₀-FePt/A1-FePt (2 nm) bilayer sample with μ₀H<sub>ip</sub> from 100 mT to 700 mT at T = 295 K and T = 500 K, as shown in Figs. 3(a) and 3(b), respectively. For each in-plane magnetic field, the corresponding R<sup>++</sup> and R<sup>--</sup> curves are separated, which indicates a net in-plane magnetization. This result can be alternatively confirmed by the spin asymmetry (SA) shown in Figs. 3(c) and 3(d) for T = 295 K and T = 500 K, respectively. SA is a quantity expressed as R<sup>++</sup>/R<sup>--</sup>, which highlights magnetic contributions to the scattering. Both Figs. 3(c) and 3(d) show a nonzero SA
<figure><img src="image_11.png" /><figcaption>FIG. 1. Model-fitted PNR data of L1₀-FePt (4 nm)/A1-FePt for (a) $t_{soft} = 2$ nm and (b) $t_{soft} = 5$ nm and the associated scattering length density profiles for (c) $t_{soft} = 2$ nm and (d) $t_{soft} = 5$ nm. The red, green, blue, and yellow regions correspond to the depth profile of SiO₂, L1₀-FePt, A1-FePt, and capping Ti layers, respectively.</figcaption></figure>

feature at all $H_{ip}$ and $T$, indicating the presence of a net in-plane magnetization for all the measurements. Fitted by REFL1D, the nuclear and magnetic depth profiles determined from model fitting are shown in Figs. 3(e) and 3(f), respectively. The fitting constrained the nuclear depth profiles to be the same for all the measurements since the nuclear structure was not expected to change with $T$ and $H_{ip}$. The magnetic depth profiles here are presented using both MSLD (left axis) and the converted in-plane magnetization (right axis). All the PNR measurements show an appreciable in-plane component of the magnetization. This relaxation follows a power law falloff from the maximal magnetization in the soft layer ($M^{top}$) to the in-plane component of the magnetization of the hard underlayer ($M^{bot}$). As an example, the position of $M^{top}$ and $M^{bot}$ for $\mu_0H_{ip} = 100$ mT and $T = 295$ K is demonstrated (blue dotted line). At both $T = 295$ K and $T = 500$ K, increasing $H_{ip}$ results in an overall increase in the in-plane magnetization,

including $M^{top}$ and $M^{bot}$, which can be attributed to the increase in the in-plane Zeeman energy.

An alternative analysis of the magnetic relaxation is performed by normalizing the magnetic depth profiles by their respective $M^{top}$, as shown in Fig. 3(g). For each $H_{ip}$, the maximum normalized magnetization ($M/M^{top} = 1$) appears at almost the same position in the soft layer about 5.8 nm away from the SiO₂ interface. Notably, increasing $H_{ip}$ causes an increase in the interfacial domain wall width, $l_{int}$,⁴⁹ particularly by extending further into the hard layer. The $H_{ip}$ presents an important role in determining the interfacial magnetic configurations by inducing an external Zeeman energy, while increasing $T$ enhances thermal fluctuations in the bilayer, reducing the anisotropy and competing with the exchange coupling. At each $H_{ip}$, increasing the temperature results in an overall reduction in the total magnetization including $M^{top}$ and $M^{bot}$. For $\mu_0H_{ip} = 100$ mT, $M^{top}$ changes from 320 kA/m at 295 K to 180 kA/m
<figure><img src="image_12.png" /><figcaption>**FIG. 2.** L1₀-FePt/Fe (a) fitted R<sup>++</sup> and R<sup>--</sup> and (b) the corresponding nuclear (black) and magnetic (red) SLD profiles, where the pink, green, blue, and yellow regions are the SiO₂, L1₀-FePt, Fe, and Pt capping layers, respectively. [Co/Pd]-multilayers/CoPd (c) fitted R<sup>++</sup> and R<sup>--</sup> and (d) nuclear (black) and magnetic (red) SLD profiles, where the pink, green, blue, yellow, and orange regions correspond to the Si, Pd seed layer, [Co/Pd] multilayers, CoPd soft layer, and Pd capping layer, respectively. [Co/Pt]-multilayers/FeNi (e) fitted R<sup>++</sup> and R<sup>--</sup> and corresponding nuclear (black) and magnetic (red) SLD profiles with SiO₂ (pink), Pt buffer layer (green), [Co/Pt] multilayers (blue), FeNi (yellow), and Pd capping layer (orange).</figcaption></figure>

at 500 K, which is more than 40% reduction. This temperature driven reduction in *M*¹⁰⁰p decreases with increasing *H*ᵢₚ, becoming 30% for *µ*₀*H*ᵢₚ = 300 mT and only 16% for *µ*₀*H*ᵢₚ = 700 mT. These results indicate that increasing *H*ᵢₚ can compensate the thermal

fluctuations, therefore increasing the in-plane soft-layer magnetiza-
tion. The normalized magnetic depth profiles for each *H*ᵢₚ show that
the interfacial magnetic configuration at 500 K is similar to the con-
figuration at 295 K, indicating that there is almost no change in *l*ᵢₘt or
<figure><img src="image_13.png" /><figcaption>FIG. 3. Polarized neutron reflectivity for L1₀-FePt (4 nm)/A1-FePt (2 nm) with in-plane magnetic fields of 100 mT, 300 mT, and 700 mT at (a) 295 K and (b) 500 K. The spin asymmetry for each field at (c) 295 K and (d) 500 K. The fitted (e) nuclear and (f) magnetic depth profiles and (g) the normalized magnetic depth profile. M^top corresponds to the maximal in-plane magnetization of the soft layer, and M^bot is the magnetization of the hard layer.</figcaption></figure>

the normalized relaxation rate with the temperature between 295 K and 500 K. These PNR experimental results reveal the influence of $M_s^{so ft}$, $t_{soft}$, $H_{ip}$, and $T$ on the interfacial magnetic configuration, as summarized in Table I.

Discussion and micromagnetic simulation

The PNR results provide a direct measurement of the magnetic relaxation within the bilayer system; the simulated magnetic depth profiles suggest that this relaxation follows a power law from $M^{top}$ to $M^{bot}$. PNR measurements show that this magnetic relaxation is dependent on sample geometry ($t_{soft}$), material properties ($M_s^{so ft}$), and external factors ($H_{ip}$ and $T$). For $t_{soft}$ larger than the critical thickness, the magnetic configuration changes from a rigid coupling, in which the soft layer has an out-of-plane orientation reflecting the hard underlayer to an in-plane relaxation, in which the soft layer rotates from out-of-plane to in-plane moving from the interface; this critical soft layer thickness increases with decreasing $M_s^{so ft}$. Increasing $H_{ip}$ is shown to increase the overall in-plane magnetization and $l_{int}$, while increasing $T$ from room temperature to 500 K results in a reduction in the in-plane magnetization, but $l_{int}$ remains almost unchanged. In a simplified model, the in-plane relaxation can be considered as a balance among the magnetostatic energy of the soft layer, perpendicular anisotropy of the hard layer, the interfacial exchange coupling between the soft and hard layers, and the Zeeman interaction. The increase in $t_{soft}$ or $M_s^{so ft}$ results in the increase in the total demagnetization energy and the decrease in the energy gap between the ground state and the excited magnon state.⁵⁰,⁵¹ When the thermal energy ($k_B T$) is high enough to overcome this energy gap, it will cause the transition from rigid coupling to the underlayer, which favors an in-plane orientation for the soft-layer magnetization. As a result, the interfacial magnetic configuration relaxes in-plane. For increasing $H_{ip}$, the Zeeman energy favors an in-plane orientation parallel to $H_{ip}$, which increases $M^{top}$ and $M^{bot}$. However, while increasing $H_{ip}$, the in-plane magnetic component of the soft layer increases more than the hard layer due to the much larger saturation magnetization and the absence of a perpendicular anisotropy. The angle between the magnetization vector of the bottom hard layer and that of the top of the soft layer increases. This increased angle causes the interfacial exchange coupling energy to increase commensurately. To compensate this increase in energy, $l_{int}$ extends further into the hard layer. Increasing $T$ to 500 K, the thermal fluctuations are enhanced, which decreases $M_s^{so ft}$, $M_s^{hard}$, and $K_u$. The reduction in $M_s^{so ft}$ decreases $l_{int}$, while the reduced $K_u$ should increase $l_{int}$; these two factors can compensate each other, resulting in an almost unchanged $l_{int}$. Indeed, in the experimental results, $l_{int}$ is almost unchanged. Ideally, increasing $l_{int}$ improves writability in HAMR media,⁵² suggesting that in this bilayer system, reducing the temperature dependence of $M_s^{so ft}$ by, e.g., increasing the Curie temperature would be a promising direction for improvement. The PNR measurements reveal the important roles of $t_{soft}$, $M_s^{so ft}$, $H_{ip}$, and $T$ in determining the configuration of the magnetic bilayer. The following simulations reinforce these observations and provide a more complete picture, which must also include $t_{hard}$ and $M_s^{hard}$.
<table><caption>TABLE I. Summary of PNR experimental results.</caption><thead><tr><th>Sample</th><th>T<sub>soft</sub> (nm)</th><th>Soft-layer<br>MSLD (×10<sup>-4</sup> nm<sup>-2</sup>)</th><th>Guide field (mT)</th><th>Temperature (K)</th></tr></thead><tbody><tr><td rowspan="8">L1<sub>0</sub>-FePt/A1-FePt</td><td>2</td><td>0.07</td><td>50 (out-of-plane)</td><td>295</td></tr><tr><td>5</td><td>1.46</td><td>50 (out-of-plane)</td><td>295</td></tr><tr><td>2</td><td>0.93</td><td>100</td><td>295</td></tr><tr><td>2</td><td>1.41</td><td>300</td><td>295</td></tr><tr><td>2</td><td>1.77</td><td>700</td><td>295</td></tr><tr><td>2</td><td>0.49</td><td>1</td><td>500</td></tr><tr><td>2</td><td>0.99</td><td>1</td><td>500</td></tr><tr><td>2</td><td>1.44</td><td>1</td><td>500</td></tr><tr><td rowspan="3">[Co/Pd]/CoPd</td><td>2</td><td>0.01</td><td>1</td><td>295</td></tr><tr><td>5</td><td>0.04</td><td>1</td><td>295</td></tr><tr><td>9</td><td>0.08</td><td>1</td><td>295</td></tr><tr><td rowspan="3">[Co/Pt]/FeNi</td><td>1</td><td>0.37</td><td>1</td><td>295</td></tr><tr><td>3</td><td>0.22</td><td>1</td><td>295</td></tr><tr><td>7</td><td>0.19</td><td>1</td><td>295</td></tr><tr><td>L1<sub>0</sub>-FePt/Fe</td><td>9</td><td>4.82</td><td>1</td><td>295</td></tr></tbody></table>

<figure><img src="image_14.png" /><figcaption>FIG. 4. OOMMF simulation for the out-of-plane magnetization for (a) $M_s^{hard} = 900$ kA/m and $M_s^{soft} = 300$ kA/m and $t_{hard} = 4$ nm with $t_{soft} = (2, 5, 9, 20, \text{and } 30)$ nm, (b) $M_s^{hard} = 700$ kA/m and $M_s^{soft} = 700$ kA/m and $t_{soft} = 9$ nm with $t_{hard} = (4, 9, 15, 20, \text{and } 30)$ nm, (c) $M_s^{hard} = 700$ kA/m and $M_s^{soft} = (300, 500, 700, 1000, \text{and } 1700)$ kA/m, and (d) $M_s^{soft} = 500$ kA/m and $M_s^{hard} = (300, 500, 700, 1000, \text{and } 1300)$ kA/m, where $t_{hard} = 4$ nm and $t_{soft} = 9$ nm.</figcaption></figure>
The first set of simulations that are presented explores the case of $M_s^{soft}$ (300 kA/m) < $M_s^{hard}$ (900 kA/m) over a range of $t_{soft}$ similar to our experiments with [Co/Pt]/NiFe, as shown in Fig. 4(a). For thin $t_{soft}$ (2 and 5) nm, the magnetic moments in the soft layer are strictly orientated in the out-of-plane direction. This magnetic configuration can be understood by the classical exchange length, $l_{ex}$: for $t_{soft} < l_{ex}$, the interfacial exchange coupling dominates the energy landscape and rigidly couples the hard and soft layers. Increasing $t_{soft}$ to 9 nm, the in-plane magnetic component of the soft layer begins to increase. Interestingly, the relaxation in the soft layer extends all the way to the interface, challenging the initial idea that the hard/soft exchange coupling is dominant in the interfacial region. Further increasing $t_{soft}$ to 20 nm and 30 nm, the relaxation rate of the magnetic configuration in the soft layer decreases, e.g., the soft layer recovers an out-of-plane orientation at the hard/soft interface. These results show a complex and nonmonotonic dependence of the soft-layer orientation on $t_{soft}$. For completeness, the dependence of the magnetic relaxation on $t_{hard}$ was also investigated in the case of $M_s^{soft} = M_s^{hard} = 700$ kA/m, as shown in Fig. 4(b). Increasing $t_{hard}$ does not significantly impact the magnetic configuration in the soft layer, indicating that the interfacial exchange interaction dominates the interaction between the hard and soft layers.

These results show a $t_{soft}$-dependent and non-$t_{hard}$-related magnetic relaxation: for $t_{soft} < l_{ex}$, the hard and soft layers are rigidly exchange coupled, while for thicker $t_{soft}$, the soft layer relaxes in-plane with a relaxation rate that decreases with increasing $t_{soft}$. The next set of simulations explore the role of $M_s^{soft}$ and $M_s^{hard}$ in determining the magnetic bilayer configuration while fixing $t_{soft}$ and $t_{hard}$. For a fixed $M_s^{hard} = 700$ kA/m, $M_s^{soft}$ is varied between 300 and 1700 kA/m, and the out-of-plane magnetization is shown in Fig. 4(c). Increasing $M_s^{soft}$ significantly accelerates the in-plane relaxation of the magnetic soft layer. This acceleration can be seen by evaluating the distance from the hard/soft interface at which the soft layer relaxes in-plane. For $M_s^{soft} = 300$ kA/m, this distance is >30 nm, while for $M_s^{soft} = 1700$ kA/m, this distance is only 2 nm. In contrast, models with a fixed $M_s^{soft}$ and variable $M_s^{hard}$ between 300 and 1300 kA/m, as shown in Fig. 4(d), show comparably little change. The bilayer simulations show generally that increasing $M_s^{hard}$ causes the in-plane relaxation to occur over a larger thickness, e.g., the out-of-plane component of the soft-layer magnetization extends further from the hard/soft interface.

These simulations agree with the experimental results. For example, in the FePt/Fe (9 nm) sample, the soft layer was almost fully in-plane, in strong contrast with the [Co/Pd]/CoPd (9 nm) sample, which was fully out-of-plane. The simulations would suggest that the differences in the hard layer have a little effect, while the $M_s^{soft}$ dominates the magnetic configuration. Indeed, with a much larger $M_s^{soft}$, Fe ($M_s^{soft} = 1700$ kA/m) is expected to be in-plane, while CoPd ($M_s^{soft} \approx 750$ kA/m) could remain out-of-plane.

## CONCLUSION

In summary, we have investigated magnetic configurations in perpendicularly coupled hard/soft bilayer films as a function of their geometric structure ($t_{soft}$), material properties ($M_s^{soft}$ and $M_s^{hard}$),

and external influences ($H_{ip}$ and $T$). Using polarized neutron reflectometry, the depth profiles for these coupled systems are experimentally determined and compared to micromagnetic simulations. For a very thin $t_{soft}$, on the order of $l_{ex}$, the magnetic moments in the soft layer are rigidly coupled to the hard layer throughout their entire thickness, while for thicker $t_{soft}$, the magnetic moments in the soft layer tend to relax in-plane. Surprisingly, the in-plane relaxation extends into the regions that were oriented in the out-of-plane direction for smaller $t_{soft}$, indicating that the relaxation is not simply progressive with increasing $t_{soft}$. The in-plane relaxation is also shown to be dependent on $M_s^{soft}$ with increasing $M_s^{soft}$ significantly increasing its rate. These results are directly demonstrated in [Co/Pd]/CoPd, [Co/Pt]/FeNi, $L_{10}$-FePt/Fe, and $L_{10}$-FePt/A1-FePt bilayer films using PNR and then confirmed by micromagnetic simulations. Moreover, the simulation results suggest that increasing $M_s^{hard}$ decreases the relaxation rate in the soft layer, while changes in $t_{hard}$ may not significantly influence the magnetic configuration. PNR experiments also reveal the importance of $H_{ip}$ and $T$ on the magnetic configuration. Specifically, for the $L_{10}$-FePt/A1-FePt system, increasing $H_{ip}$ or decreasing $T$ results in an overall increase in the in-plane magnetization. This result corresponds to the temperature-dependent balance of the magnetocrystalline anisotropy and the magnetostatic energy. Meanwhile, increasing $H_{ip}$ causes the measured $l_{int}$ to increase, while increasing $T$ leaves $l_{int}$ almost unchanged. The PNR and simulation results together show that the magnetic configuration in the bilayer samples can be modulated by varying $t_{soft}$, $M_s^{hard}$ and $M_s^{soft}$, and $H_{ip}$ and $T$. Understanding the impact of these parameters is critical for the design of hard/soft bilayer devices.

## SUPPLEMENTARY MATERIAL

See the supplementary material for the PNR measurements performed on [Co/Pd]-multilayers/CoPd with $t_{soft} = 2$ and 5 nm. The samples are first saturated with a 500 mT magnetic field along the film normal direction and then reduced to 0. An in-plane guide field 1 mT was applied while measuring. The reflectivity of $R^{++}$ and $R^{--}$ is largely overlapped with each other for $t_{soft} = 2$ [Figs. S1(a) and S1(b)], which indicates that there is no net in-plane magnetization. This is then proved by the converged magnetic depth profiles that no net MSLD can be probed. This non-in-plane magnetic behavior is also probed in $t_{soft} = 5$ nm [Figs. S1(c) and S1(d)]. With the same experimental setup as the above, PNR measurements and the model fitting on [Co/Pt]/FeNi with $t_{soft} = 0, 1$, and 3 nm are shown in Figs. S2(a)-S2(f). For each $t_{soft}$, $R^{++}$ and $R^{--}$ are largely converged with each other, and the corresponding magnetic depth profile presents no MSLD. These results indicate that the magnetization in the soft layer is along the perpendicular anisotropy orientation.

## ACKNOWLEDGMENTS

This study was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences Energy Early Career Research Program, under Award No. DE-SC0021344. Work at G.U. was supported by the NSF (Grant No. ECCS-1933527).
## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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