# Transition from ferromagnetic to noncollinear to paramagnetic state with
increasing Ru concentration in FeRu films

Juliana Lisik<EMAIL_ADDRESS>Manuel Rojas<EMAIL_ADDRESS>Spencer Myrtle
Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V5A
1S6, Canada  Dominic H. Ryan<EMAIL_ADDRESS>Physics Department and
Centre for the Physics of Materials, McGill University, 3600 University
Street, Montreal, Quebec, H3A 2T8, Canada  René Hübner  Institute of Ion Beam
Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner
Landstraße 400, 01328 Dresden, Germany  Pavlo Omelchenko  Simon Fraser
University, 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada
Claas Abert  Amil Ducevic  Dieter Suess  Physics of Functional Materials,
Faculty of Physics, University of Vienna, Kolingasse 14–16, 1090 Vienna,
Austria  Ivan Soldatov  Rudolf Schaefer  Leibniz-Institut für Festkörper- und
Werkstoffforschung Dresden, Germany  Johannes Seyd  Manfred Albrecht
Institute of Physics, University of Augsburg, 86135 Augsburg, Germany  Erol
Girt<EMAIL_ADDRESS>Simon Fraser University, 8888 University Drive, Burnaby,
British Columbia V5A 1S6, Canada

###### Abstract

The structural and magnetic properties of sputter-deposited Fe100-xRux films
were studied for $x\leq 50$. The crystal structure of Fe100-xRux is shown to
be predominantly body-centered cubic for $x<13$ and to undergo a gradual
transition to hexagonal close-packed in the concentration range $13\lesssim
x\lesssim 20$. Magnetic measurements indicate that the addition of Ru induces
a noncollinear magnetic order in the body-centered cubic FeRu alloys, while
the hexagonal close-packed FeRu alloys exhibit paramagnetic behavior.
Increasing the Ru concentration in body-centered cubic FeRu alloys decreases
the size of magnetic domains, approaching the size of magnetic grains. A
simple atomistic model was used to show that antiferromagnetic coupling of Fe
atoms across Ru atoms can be responsible for inducing noncollinear order in
the FeRu cubic structures. Magnetic multilayer structures used in thin-film
magnetic devices make extensive use of both Fe and Ru layers. Our results
reveal that the presence of even a small amount of Ru in Fe influences the
magnetic order of Fe, which could impact the performance of these devices.

##  I Introduction

Iron is the most abundant element in the Earth by mass, composing about 80% of
Earth’s core; furthermore, it is the fourth most abundant element in Earth’s
crust [1]. The structural, electrical, and magnetic properties of iron and its
alloys are at the root of many applications. Of the three elements that have
ferromagnetic alignment above room temperature (iron, cobalt, and nickel),
iron has the largest saturation magnetization, making iron alloys a crucial
component of magnetic devices (e.g. hard and soft magnets, magnetic sensors,
and recording media). However, despite centuries of research, understanding
the phase diagram and magnetic properties of iron alloys remains an active
research topic.

The unary phase diagram of Fe consists of three crystal structures that meet
at a triple point located at approximately
$477\text{\,}\mathrm{\SIUnitSymbolDegree}\mathrm{C}$ and
$11\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$. At standard temperature and
pressure, Fe is body-centered cubic (bcc), which is known as $\alpha$-Fe, and
has well-known ferromagnetic order. The crystal structure transitions from bcc
to face-centered cubic (fcc) at high temperatures. At pressures above
$11\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$, the crystal structure of Fe
transitions from bcc to hexagonal close-packed (hcp), which is known as
$\epsilon$-Fe. The hcp Fe phase is stable for pressures and temperatures
corresponding to the conditions of Earth’s core [2]. At the transition from
bcc to hcp Fe, there is a rapid decrease in magnetic moment [3]. However,
unlike bcc Fe, the magnetic state of hcp Fe is not well understood. Some
experimental studies find that hcp Fe does not appear to have any long-range
magnetic order, as determined from low-temperature Mössbauer measurements [4,
5], X-ray magnetic circular dichroism (XMCD) [3], and neutron powder
diffraction [6]. X-ray emission spectroscopy, on the other hand, detects a
localized magnetic moment for hcp Fe between about 12 and
$40\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$ [7, 6] with a magnitude of
$0.74\mu_{\text{B}}$ at $20\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$ [6]. More
recently, a ground state of alternating antiferromagnetic and nonmagnetic
atomic layers was used to explain the conflicting experimental observations
discussed above [6].

Thin-film magnetic devices make extensive use of not only Fe but also Ru
layers [8, 9, 10]. Thus, it is important to study how the presence of Ru in
Fe, which can occur during deposition or annealing, affects the magnetic
properties of Fe. When Fe is alloyed with Ru, not only the bcc phase but also
the hcp phase can be stabilized at standard temperature and pressure. The bcc
phase of FeRu has been seen for up to $4\text{\,}\mathrm{at.\,\%}$ of Ru in Fe
[11]. Recent studies suggest that FeRu is ferromagnetic in this phase [12], as
is pure Fe. Additionally, Mössbauer studies of bulk bcc FeRu argue for the
presence of spin and charge density waves in the vicinity of the Ru impurity
in Fe [13]. As more Ru is added, the hcp phase appears: it has been seen above
$23\text{\,}\mathrm{at.\,\%}$ of Ru in the equilibrium phase diagram [11].
There are many parallels between high-pressure hcp Fe and hcp FeRu; however,
theoretical and experimental studies of FeRu are scarce. Similar to high-
pressure Fe studies, during the transition from bcc to hcp, the magnetization
of FeRu collapses. The magnetic structure of the hcp FeRu alloy remains a
debated topic. Early Mössbauer studies did not observe any hyperfine
structure, but the existence of an antiferromagnetic phase with a magnetic
moment of about $0.1\mu_{\text{B}}$ was estimated [14, 15]. More recent
Mössbauer studies suggest that hcp FeRu is paramagnetic [12]. Finally, neutron
diffraction studies of bulk hcp Fe71Ru29 reported an incommensurate
antiferromagnetic state with a Néel temperature of $124\text{\,}\mathrm{K}$
and a low-temperature Fe magnetic moment of about $\mu_{\text{B}}$ [16].
Theoretical work on the ground state of Fe50Ru50 identifies a type-II
antiferromagnetic phase as the lowest energy state [17].

More recently, thin-film FeRu has been shown to mediate a large noncollinear
magnetic coupling between two ferromagnetic layers [18]. The coupling angle
and strength was controlled by the concentration of Ru within the FeRu alloy.
Controlling the coupling angle is important for the design of magnetic thin-
film devices, as the optimal structure almost always requires noncollinear
alignment between at least two adjacent ferromagnetic films [19, 20, 21, 22].
At present, it is not clear what role the bcc and hcp structures within the
FeRu alloy play in the observed noncollinear coupling.

In this paper, we investigate the structural and magnetic properties of FeRu
films over a composition range from 0 to $50\text{\,}\mathrm{at.\,\%}$ of Ru
in Fe. The emphasis is on the range of Ru concentrations from 0 and
$20\text{\,}\mathrm{at.\,\%}$, within which the transition from bcc to hcp
crystal structure occurs. Structural properties are explored with X-ray
diffraction and transmission electron microscopy, and magnetic properties are
explored with Mössbauer spectroscopy, vibrating sample magnetometry, magneto-
optical Kerr effect microscopy, and Lorentz transmission electron microscopy.
Our results show that, as Ru is added to ferromagnetic Fe films, the magnetic
behaviour of the films transitions to noncollinear and then to paramagnetic.
Furthermore, we argue that noncollinear coupling is a result of the
competition between ferromagnetic Fe-Fe coupling and antiferromagnetic
coupling between Fe atoms separated by Ru atoms.

##  II Experimental Details

The studied films, Ta(3.5)$|$Ru(3.5)$|$Fe100-xRux($d$)$|$ Ru(3.5), were
deposited with radio-frequency magnetron sputtering on (100) Si, Si3N4
membranes, and Kapton substrates at room temperature and an argon pressure
below $2\text{\,}\mathrm{m}\mathrm{T}\mathrm{o}\mathrm{r}\mathrm{r}$. In these
films, the numbers in parentheses indicate the layer thicknesses in nm, $x$ is
the atomic concentration of Ru in Fe100-xRux, and $d=20$ or
$100\text{\,}\mathrm{n}\mathrm{m}$ is the thickness of the FeRu layer. Si
substrates were used for all studies except for transmission Mössbauer
spectroscopy, which requires Kapton substrates to maximize the signal.
Throughout this paper, we will refer to
Ta(3.5)$|$Ru(3.5)$|$Ru100-xFex($d$)$|$Ru(3.5) films as
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(d)|\mathrm{Ru}$,
as the thicknesses of the seed and capping layers were kept the same for all
samples. The Ta seed layer is deposited to induce the $\langle$0001$\rangle$
growth orientation of the bottom Ru layer, and the top Ru film is used to
protect the Ru100-xFex layer from oxidation. Selected films were annealed at
$400\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for 1 hour to study the thermal
stability of the phase structure.

Prior to deposition, (100) Si substrates were cleaned with the standard RCA
SC-1 process to remove particles and organic contaminants. Kapton substrates
were cleaned with isopropyl alcohol and ethanol. The substrates were
subsequently rinsed in deionized water and dried. Clean substrates were first
placed in a load lock chamber, which is evacuated to about 5$\times 10^{-7}$
Torr, and then transferred, without breaking the vacuum, to a process chamber
with base pressure below 5$\times 10^{-8}$ Torr for deposition. The films were
deposited from three elemental $5.08\text{\,}\mathrm{c}\mathrm{m}$
($2\text{\,}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{h}$) diameter targets of Ta,
Ru, and Fe. The target-to-substrate distance is approximately
$20\text{\,}\mathrm{c}\mathrm{m}$. The substrate holder rotates during
deposition to ensure thickness and composition uniformity of the deposited
films across the substrate surface. The entire sputter process is computer-
controlled. For the Ta and pure Ru layers, the sputtering rates were 0.26 and
$0.22\text{\,}\mathrm{\SIUnitSymbolAngstrom}\mathrm{/}\mathrm{s}$,
respectively. To deposit the Fe100-xRux layer, the sputtering rate for Fe was
varied from $0.30\text{\,}\mathrm{\SIUnitSymbolAngstrom}\mathrm{/}\mathrm{s}$
($x=50$) to $0.59\text{\,}\mathrm{\SIUnitSymbolAngstrom}\mathrm{/}\mathrm{s}$
($x=4$), and the sputtering rate for Ru was varied from
$0.35\text{\,}\mathrm{\SIUnitSymbolAngstrom}\mathrm{/}\mathrm{s}$ ($x=50$) to
$0.03\text{\,}\mathrm{\SIUnitSymbolAngstrom}\mathrm{/}\mathrm{s}$ ($x=4$). The
pure Fe layer was sputtered with a rate of
$0.36\text{\,}\mathrm{\SIUnitSymbolAngstrom}\mathrm{/}\mathrm{s}$. The
sputtering rates were inferred from X-ray diffraction (XRD) measurements
performed using CuKα radiation. Low-angle out-of-plane $\theta$-$2\theta$
(reflectivity) measurements of single layers of each material or of
Ru(2)$|$X$|$Ru(2) multilayers (X = Ta, Fe, and FeRu) were fit with X′PERT
reflectivity software from Panalytical.

Structural characterization of the deposited layers was carried out by XRD
using out-of-plane $\theta$-$2\theta$, in-plane $\theta$-$2\theta$, and
rocking curve measurements. For the out-of-plane and in-plane
$\theta$-$2\theta$ measurements, the angle between the incident X-ray beam and
the film surface, $\theta_{1}$, is the same as the angle between the reflected
X-ray beam and the film surface, $\theta_{2}$, i.e.,
$\theta_{1}=\theta_{2}=\theta$. For the rocking curve measurement,
$\theta_{1}+\theta_{2}$ is kept constant and the sample is rocked by angle
$\omega$ so that $\theta_{1}$ varies from $\theta-\omega/2$ to
$\theta+\omega/2$. The scattering wave vector is perpendicular to the film
surface for the out-of-plane $\theta$-$2\theta$ measurement and varies around
the perpendicular direction for the rocking curve measurement. For the in-
plane $\theta$-$2\theta$ measurement, however, the scattering wave vector is
almost parallel to the film surface, at an angle of $0.5\degree$.

To further characterize the film microstructure, bright-field and high-
resolution transmission electron microscopy (HRTEM) imaging were performed on
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(20)|\mathrm{Ru}$
($x=13$ and 17) and Ta$|$Ru$|$Fe(100)$|$Ru films on an
image-C${}_{\text{s}}$-corrected Titan 80-300 microscope (FEI) operated at an
accelerating voltage of $300\text{\,}\mathrm{k}\mathrm{V}$. Scanning
transmission electron microscopy (STEM) coupled with spectrum imaging analysis
based on energy-dispersive X-ray spectroscopy (EDXS) was performed at
$200\text{\,}\mathrm{k}\mathrm{V}$ with a Talos F200X microscope equipped with
a Super-X EDX detector system (FEI). The HRTEM images were further examined by
fast Fourier transform (FFT) analysis to detect the spatial distribution of
different lattice structures. Prior to TEM analysis, the specimen, mounted in
a high-visibility low-background holder, was placed into a Model 1020 Plasma
Cleaner (Fischione) for $10\text{\,}\mathrm{s}$ to remove possible organic
contamination.

The 57Fe Mössbauer spectroscopy measurements were carried out on
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
($0\leq x\leq 50$), Ta$|$Fe(100)$|$Ta, and Fe(100) films. For each film, one
deposition was performed, sputtering on Kapton film taped to an
$8\text{\,}\mathrm{i}\mathrm{n}$-diameter Si substrate for Mössbauer
measurements and simultaneously sputtering on
$1\text{\,}\mathrm{i}\mathrm{n}$-diameter Si substrates for magnetometry
measurements, which are discussed in the next paragraph. For conversion
electron Mössbauer spectroscopy (CEMS) measurements,
$\sim$$50\text{\,}\mathrm{m}\mathrm{m}$-diameter Kapton film samples were used
(removed from the Si substrate), and for transmission Mössbauer spectroscopy
(TMS) measurements, stacks of fifteen $15\text{\,}\mathrm{m}\mathrm{m}$ square
Kapton film samples (also removed from the Si substrate) were made. This is
because TMS measurements require thicker samples in order to obtain a useful
signal-to-noise ratio. Mössbauer measurements were performed using a
$1.8\text{\,}\mathrm{G}\mathrm{B}\mathrm{q}$ 57CoRh source driven in constant
acceleration mode and calibrated using a thin bcc Fe foil. Isomer shifts are
quoted relative to the centroid of the bcc Fe spectrum. Room-temperature CEMS
measurements were collected using a conventional homemade detector. The
$\sim$$50\text{\,}\mathrm{m}\mathrm{m}$-diameter Kapton film sample is mounted
inside the detector with a flowing 90% He + 10% CH4 gas mixture used to detect
the backscattered electrons. All films were measured at room temperature, but
the
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
($x=18.5$) film was also measured with TMS at $9.7\text{\,}\mathrm{K}$. Low
temperatures were obtained by mounting the stacked samples in a vibration-
isolated closed-cycle helium refrigerator. All films were measured at zero
external magnetic field, but Fe(100) and
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
($x=4$ and $8$) were also measured in a $0.166\text{\,}\mathrm{T}$ magnetic
field created by permanent magnets to remove magnetic domains. The magnetic
components of the spectra were fitted using an assumed Gaussian distribution
of hyperfine fields with independent widths to the high and low sides of the
peak of the distribution. This form is needed to fit the clearly asymmetric
magnetic patterns observed. The paramagnetic components were fitted variously
as: symmetric doublets with a small, unresolved, quadrupole splitting; a
Gaussian distribution of quadrupole splittings; and, where the two lines in
the doublet are clearly of unequal intensity, two independent lines.

The field dependence of the magnetization, $M(H)$, of
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(d)|\mathrm{Ru}$
($d=20$ and $100\text{\,}\mathrm{n}\mathrm{m}$), Ta$|$Fe(100)$|$Ta, and
Fe(100) films was measured using a vibration sample magnetometer (VSM) and
superconducting quantum interference device (SQUID) VSM in magnetic fields of
up to $7\text{\,}\mathrm{T}$ and at temperatures of 295 and
$5\text{\,}\mathrm{K}$. Measurements were performed with the magnetic field
applied parallel as well as perpendicular to the film surface.

A wide-field magneto-optical Kerr microscope was used to image magnetic domain
structure in the Ta$|$Ru$|$Fe96Ru${}_{4}(100)$$|$Ru film. An external magnetic
field was applied parallel to the film plane and the magnetic domain structure
was observed, utilizing the longitudinal magneto-optical Kerr effect (MOKE)
with two complementary sensitivity directions: along and transverse to the
applied field.

The magnetic domain morphology of Ta$|$Ru$|$Fe92Ru8(20)$|$Ru was imaged by
Lorentz transmission electron microscopy (LTEM) at room temperature using a
JEOL NEOARM-200F system operated at
$200\text{\,}\mathrm{k}\mathrm{e}\mathrm{V}$ beam energy in the Fresnel mode
with an underfocus of $-1\text{\,}\mathrm{m}\mathrm{m}$. Magnetic fields up to
$2\text{\,}\mathrm{T}$ can be applied along the electron beam direction, which
is typically perpendicular to the film plane. In order to apply an in-plane
magnetic field in addition to the out-of-plane magnetic field, the sample must
be tilted by a tilt angle $\theta$ with respect to the film normal. The sample
for LTEM was prepared by magnetron sputter deposition on a
$30\text{\,}\mathrm{n}\mathrm{m}$-thick Si3N4 membrane, and images were
acquired with a Gatan OneView camera.

##  III Film Microstructure

###  III.1 X-ray diffraction

Figure 1: (a) Out-of-plane and (b) in-plane $\theta$-$2\theta$ measurements of
as-deposited Ta(3.5)$|$Ru(3.5)$|$Fe100-xRux(100)$|$Ru(3.5) for $x=0$, 13, 23,
and 50. The inset plots in (a) represent the rocking curve measurements of
these samples and include the full-width-at-half-maximum. Dashed lines are
placed at the expected positions of diffraction peaks. Those labelled Fe and
Ru correspond to bcc Fe and hcp Ru, respectively, and those labelled hcp and
bcc correspond to hcp Fe100-xRux ($x=23$ or 50) and bcc Fe87Ru13,
respectively. The Si {200} and {400} diffraction peaks in (a) are from the Si
substrate.

XRD measurements were performed on
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}($d$)|\mathrm{Ru}$
films for $d=20$ and $100\text{\,}\mathrm{n}\mathrm{m}$. The out-of-plane and
in-plane $\theta$-$2\theta$ measurements of as-deposited
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
for $x=0$, 13, 23, and 50 in Fig. 1 reveal that the Ru layers have hcp lattice
structure, while the lattice structure of Fe100-xRux depends on the Ru
concentration, $x$. For $x=23$ and 50, Fe100-xRux has hcp lattice structure,
and for $x=13$, Fe100-xRux has bcc lattice structure with no hcp lattice
structure visible at the precision of our XRD measurements. We obtained this
information by comparing the positions of the measured diffraction peaks with
the expected positions of hcp and bcc diffraction peaks (represented by the
dashed lines in Fig. 1) from previous XRD data as well as our own. Previous
XRD data on hcp Ru and Fe50Ru50 [23] were used to determine the positions of
the hcp Ru lines, the hcp Fe50Ru50 lines (in Fig. 1(b) only), and the hcp
Fe77Ru23 lines (by extrapolation). Our out-of-plane and in-plane XRD data on
bcc Fe and Fe96Ru4 (Fig. 3), which will be discussed later, were used to
determine the positions of the bcc Fe line (in Fig. 1(a) only) and the bcc
Fe87Ru13 lines (by extrapolation).

From the out-of-plane $\theta$-$2\theta$ measurements in Fig. 1(a) for $x=0$,
13 and 23, it is apparent that hcp Ru and Fe77Ru23 have a {002} texture and
that bcc Fe and Fe87Ru13 have a {110} texture. The diffraction pattern of hcp
Fe77Ru23 also reveals a {101} diffraction peak with an intensity two orders of
magnitude smaller than the {002} diffraction peak. The quality of the texture
of the three films plotted in Fig. 1(a) is determined by rocking curve
measurements, which are displayed in the inset plots above the spectrum of
each film. The {110} reflection was measured for bcc Fe and Fe87Ru13, while
the {002} reflection was measured for hcp Fe77Ru23. These plots indicate that
the full-width-at-half-maximum (FWHM) of the rocking curve is $2.6\degree$ for
the {110} reflection of Fe87Ru13 and for the {002} reflection of Fe77Ru23,
suggesting highly textured FeRu films. For Fe, the FWHM of the rocking curve
is $1.8\degree$ for the {110} reflection, indicating a stronger texture
compared to FeRu films. Figure 1(a) also shows Si {400} and a small trace of
Si {200} reflections from the substrate. Si {200} is forbidden and could be a
result of multiple diffraction of X-rays in the crystal [24].

Our films are polycrystalline with grains textured along the growth direction
and randomly oriented in the plane of the film. For this reason, in-plane
$\theta$-$2\theta$ measurements can be used to detect reflections from a range
of planes perpendicular to the film surface, while out-of-plane
$\theta$-$2\theta$ measurements can only detect the planes along which the
film is textured. For the in-plane X-ray measurements, the diffraction pattern
remains unaffected by the direction of the incident beam direction, owing to
the random in-plane orientation of the grains. In contrast, if the sample has
a single crystal structure, the incident beam must be precisely oriented with
respect to the crystal lattice to obtain the diffraction pattern for in-plane
measurements. Consequently, in-plane X-ray measurements allow one to
distinguish between textured polycrystalline and single crystal samples. The
in-plane $\theta$-$2\theta$ measurements for $x=13$, 23, and 50 are presented
in Fig. 1(b). These measurements show that, for hcp Ru, hcp Fe50Ru50, and hcp
Fe77Ru23, we observe reflections from the {100}, {110}, and {200} planes. For
each of these families of planes, the expected diffraction peak positions for
Ru, Fe50Ru50, and Fe77Ru23 are shown. For bcc Fe87Ru13, we observe reflections
from the {110}, {002}, and {112} planes. Since reflections are detected from
multiple planes—a consequence of the random in-plane orientation of the
grains—the in-plane $\theta$-$2\theta$ measurements are better suited to
detect the phase structure in our films than the out-of-plane measurements.
Figure 1(b) shows that, as the concentration of Ru in Fe100-xRux decreases
from 50 to $23\text{\,}\mathrm{at.\,\%}$, the {100}, {110}, and {200} hcp
diffraction peaks shift to higher angles, indicating a decrease in the lattice
parameters of the FeRu layer. This is expected, because Fe and Ru form a solid
solution in this composition range and Fe atoms are smaller than Ru atoms. Our
results indicate that Fe100-xRux transitions from hcp to bcc as the
concentration of Ru is further decreased from 23 to
$13\text{\,}\mathrm{at.\,\%}$. These observations are consistent with previous
structural FeRu studies [25, 26, 15].

Figure 2: (a) In-plane $\theta$-$2\theta$ measurements of as-deposited
Ta(3.5)$|$Ru(3.5)$|$Fe100-xRux(20)$|$Ru(3.5) for $x=13$, 17, 20, and 23. (b)
In-plane $\theta$-$2\theta$ measurements before and after annealing at
$400\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for $x=20$ and 13. Dashed lines
are placed at the expected positions of diffraction peaks. Those labelled Ru
correspond to hcp Ru, and those labelled hcp and bcc correspond to hcp
Fe77Ru23 and bcc Fe87Ru13, respectively.

In-plane $\theta$-$2\theta$ XRD measurements of
$20\text{\,}\mathrm{n}\mathrm{m}$-thick FeRu films,
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(20)|\mathrm{Ru}$,
are presented in Fig. 2(a) for $x=13$, 17, 20, and 23. The expected
diffraction peak positions are calculated in the same way as those in Fig. 1
and are again represented by dashed lines. The expected positions for bcc
Fe100-xRux ($x=13$ and 17) are very close together, as well as the positions
for hcp Fe100-xRux ($x=17$, 20, and 23). Consequently, we only included the
expected diffraction peak positions for bcc Fe87Ru13 and hcp Fe77Ru23 in Fig.
2, which are the same as those plotted in Fig. 1. As expected, the lattice
structure of the $20\text{\,}\mathrm{n}\mathrm{m}$-thick films (Fig. 2(a)) is
the same as that of the $100\text{\,}\mathrm{n}\mathrm{m}$-thick films (Fig.
1(b)). For both thicknesses, diffraction peaks corresponding only to the bcc
lattice structure can be detected for Fe87Ru13, and peaks corresponding only
to the hcp lattice structure can be detected for Fe77Ru23. For the first
intermediate composition in the $20\text{\,}\mathrm{n}\mathrm{m}$-thick
measurements, Fe83Ru17, both bcc and hcp reflections are visible, but for
Fe80Ru20, only hcp reflections are clearly visible.

One of the most promising applications of FeRu takes advantage of the
recently-discovered property that FeRu spacer layers can noncollinearly couple
two ferromagnetic layers; this allows for significant improvement in the
performance of spintronic devices such as spin-transfer-torque magnetic
random-access memory [18]. For these devices to be compatible with the modern
CMOS fabrication process, they need to be annealed at
$400\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Hence, in this paper, we explored
the structural properties of
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(20)|\mathrm{Ru}$
for $x=13$ and 20 before and after annealing at
$400\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for 1 hour. The in-plane
$\theta$-$2\theta$ measurements shown in Fig. 2(b) show that the as-deposited
and annealed films have the same lattice structure. For Fe87Ru13, annealing
causes a slight decrease in the bcc FeRu {110}, {002}, and {112} diffraction
peak intensities along with the emergence of a trace of hcp phase, which could
indicate that a small amount of the bcc phase transforms to the hcp phase as
the temperature is increased. In the equilibrium phase diagram of FeRu [11], a
mixture of the bcc and hcp phases is present for this Ru concentration at
$400\text{\,}\mathrm{\SIUnitSymbolCelsius}$. For Fe80Ru20, annealing causes an
increase in the hcp FeRu {100}, {110}, and {200} diffraction peak intensities,
which could indicate that annealing improves the texture of the hcp lattice
structure of FeRu. A small amount of the bcc phase could be present in the as-
deposited Fe80Ru20 film but not detectable by XRD, and as it transforms into
the hcp phase during annealing, the hcp diffraction peak intensities increase.
These annealing results are encouraging, as they show that hcp FeRu layers
annealed at temperatures of up to $400\text{\,}\mathrm{\SIUnitSymbolCelsius}$
will retain their lattice structure in the composition range of interest for
noncollinear coupling of Co$|$Fe100-xRu${}_{x}|$Co films, $x\geq 20$ [18].
This assumes that the diffusion of Co, Fe, and Ru across the Co$|$Fe100-xRux
interfaces is negligible at and below
$400\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

Figure 3: $2\theta$ value of the bcc {110} diffraction peak from in-plane and
out-of-plane $\theta$-$2\theta$ XRD measurements of as-deposited
Ta(3.5)$|$Ru(3.5)$|$Fe100-xRux(100)$|$Ru(3.5) ($x=0$, 4, and 8). The
corresponding lattice constants of the bcc structure are shown on the
secondary axis. The bcc Ru interpolation is a linear function using the
measured lattice constants of our Fe film and the lattice constant of a
hypothetical bcc unit cell of Ru atoms with radius
$0.1359\text{\,}\mathrm{nm}$ [27]. The Fe96Ru4 extrapolation is a linear
function using the measured lattice constants of our Fe and Fe96Ru4 films. The
size of the markers corresponds to the size of the error bars.

In the range from $x=0$ to 8, additional in-plane and out-of-plane
$\theta$-$2\theta$ measurements were performed on as-deposited
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$.
Figure 3 shows the $2\theta$ value of the bcc Fe or FeRu {110} diffraction
peak measured for these films and the corresponding lattice constant as a
function of $x$. Since Fe and Ru form a solid solution in this composition
range and Fe atoms are smaller than Ru atoms, an increase in Ru concentration
leads to an increase in lattice constant. By Bragg’s law, this translates to a
decrease in the angle $2\theta$ at which diffraction peaks are detected. As
mentioned above, this effect is also visible in Fig. 1(b) as the Ru
concentration increases from 23 to $50\text{\,}\mathrm{at.\,\%}$. Along with
the experimental $2\theta$ and lattice constant values in Fig. 3 are two
linear functions, both of which assume that
$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ remains bcc for $0\leq x\leq 8$. The bcc
Ru interpolation, represented by the solid green line, is a linear function
constructed from the following two points: the measured lattice constant of
our Fe film obtained from the average of the in-plane and out-of-plane
measurements ($x=0$) and the lattice constant of a hypothetical bcc unit cell
of Ru atoms with radius $0.134\text{\,}\mathrm{nm}$ ($x=100$). The Fe96Ru4
extrapolation, represented by the dashed yellow line, is a linear function
constructed from the average of the in-plane and out-of-plane measurements of
our Fe film ($x=0$) and our Fe96Ru4 film ($x=4$). We used these two points
because the equilibrium phase diagram shows that up to
$4\text{\,}\mathrm{at.\,\%}$ of Ru can be added to bcc Fe at elevated
temperatures before the hcp lattice structure begins to appear [11]. The
measured lattice constant at $x=8$ is larger than that expected from both
linear functions, indicating that Ru atoms are substituting Fe atoms in the
bcc lattice up to at least $8\text{\,}\mathrm{at.\,\%}$ of Ru in Fe. This is
not unexpected, as films deposited by sputtering are likely not in
equilibrium. Furthermore, the out-of-plane and in-plane measurements in Fig. 3
yield similar results, indicating little difference in the lattice spacing for
the two directions and suggesting that there is no distortion of the cubic
structure.

###  III.2 Transmission electron microscopy

Figure 4: (a) Bright-field TEM and (b) STEM-EDXS-based element distribution
images of Ta(3.5)$|$Ru(3.5)$|$Fe83Ru${}_{17}(20)|$Ru(3.5) with scale bar
below, and (c) fast Fourier transform (FFT) patterns of hcp FeRu and Ru along
the [110] zone axis and bcc FeRu along the [1$\bar{1}$1] and [100] zone axes.
Example high-resolution TEM images of
Ta(3.5)$|$Ru(3.5)$|$Fe100-xRu${}_{x}(20)|$Ru(3.5) for (d) $x=17$ and (e)
$x=13$ with scale bar in (d), including FFT patterns of various regions in the
Ru and FeRu layers.

Cross-sectional transmission electron microscopy (TEM) imaging was performed
on
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(20)|\mathrm{Ru}$
for $x=13$ and 17 to identify the distribution of the hcp and bcc phases in
FeRu. Fe83Ru17 was selected because it consists of a mixture of hcp and bcc
FeRu, as is evident from our X-ray diffraction (XRD) measurements in Fig.
2(a). Fe87Ru13 was selected because this alloy has the highest Ru
concentration for which hcp diffraction peaks are not clearly detected in the
XRD patterns.

Figure 4(a) and (b) show a representative bright-field TEM image and the
corresponding element distributions obtained by EDXS-based spectrum imaging
analysis for
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{83}\mathrm{Ru}_{17}(20)|\mathrm{Ru}$,
respectively. The EDXS measurements confirm that the distribution of Fe and Ru
in the FeRu film is homogeneous within measurement uncertainty. This suggests
that the coexistence of the hcp and bcc phases in the FeRu films is not due to
variation of the composition.

HRTEM images presented in Fig. 4(d) and (e) for
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{83}\mathrm{Ru}_{17}(20)|\mathrm{Ru}$ and
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{87}\mathrm{Ru}_{13}(20)|\mathrm{Ru}$,
respectively, are further analyzed by FFT analysis. The FFT patterns are
placed on the HRTEM images at the locations at which they are calculated.
Representative FFT patterns of hcp Ru and FeRu in [110] zone axis geometry and
bcc FeRu in [1$\bar{1}$1] and [100] zone axis geometry are displayed
separately in Fig. 4(c). In both films, the FFT patterns of Ru clearly show
that Ru has hcp lattice structure, which is in agreement with the XRD
measurements. FFT analysis also reveals that both FeRu films consist of grains
that have entirely hcp and entirely bcc crystal structure; furthermore, each
film has indications of individual grains showing both phases. Since hcp
diffraction peaks were not detectable in the XRD patterns of Fe87Ru13, it is
evident that TEM analysis is more precise than XRD in detecting the presence
of small amounts of a secondary phase.

We also performed cross-sectional TEM on Ta$|$Ru$|$Fe(100)$|$Ru to analyze the
diffusion of Ru into the pure Fe film. The bright-field TEM and superimposed
EDXS-based element distribution maps for a representative section of the
sample are shown in the Supplemental Material [28]. Quantifying the EDXS
signal from the whole Fe layer, a Ru content of $0.1\text{\,}\mathrm{at.\,\%}$
was determined. This could either be due to the diffusion of Ru into the Fe
layer during the sputtering process or due to the introduction of Ru into the
Fe layer during the TEM lamella preparation process.

##  IV Magnetic Properties

###  IV.1 Mössbauer spectroscopy

Film | IS | QS | $B_{\textbf{HF}}$ | $\Phi_{\text{MS}}$ | PM
---|---|---|---|---|---
($\text{\,}\mathrm{m}\mathrm{m}\mathrm{/}\mathrm{s}$) | ($\text{\,}\mathrm{m}\mathrm{m}\mathrm{/}\mathrm{s}$) | ($\text{\,}\mathrm{T}$) | ($\text{\,}\mathrm{\SIUnitSymbolDegree}$) | (%)
§Fe50Ru50 |  -0.047(2) |  0.219(3) |  |  | 100
§Fe77Ru23 |  -0.074(1) |  0.188(2) |  |  | 100
§Fe80.5Ru19.5 |  -0.07(1) | 0.14(2) |  |  | 100
| §Fe80.5Ru19.5*
---
(at $9.9\text{\,}\mathrm{K}$)
0.044(2) | 0.31(1) |  |  | 100
§Fe81.5Ru18.5 |  0.028(1) |  |  30.2(1) | 40(2) | 61(2)
-0.072(1) |  0.171(3) |  |
§Fe81.5Ru18.5* (at $9.7\text{\,}\mathrm{K}$) | 0.19(1) |  |  32.3(6) | 35(2) | 65(1)
-0.045(2) | 0.30(1) |  |
§Fe87Ru13 |  0.037(4) |  |  32.2(1) | 45(1) | 4(1)
-0.37(2) | 0.79(4) |  |
§Fe92Ru8* |  0.027(3) |  |  31.5(1) | 44(1) | 3.0(5)
| §Fe92Ru8*
---
(at $0.166\text{\,}\mathrm{T}$)
0.032(3) |  |  31.2(3) | 47(1) | 3.0(5)
§Fe96Ru4* |  0.019(3) |  |  31.9(1) | 51(1) | 2.5(7)
| §Fe96Ru4*
---
(at $0.166\text{\,}\mathrm{T}$)
0.018(5) |  |  32.9(3) | 55(1) | 2(1)
§Fe* |  0.000(4) |  |  32.83(3) | 68(2) | 0
| §Fe*
---
(at $0.166\text{\,}\mathrm{T}$)
0.003(5) |  |  32.61(4) | 67(2) | 0
Ta$|$Fe$|$Ta |  0.007(1) |  |  33.39(2) | 73(1) | 0
Fe |  -0.003(1) |  |  33.42(1) | 80(1) | 0
Fe* |  -0.002(1) |  |  33.13(1) | 82(1) | 0
| Fe*
---
(at $0.166\text{\,}\mathrm{T}$)
-0.001(1) |  |  32.38(1) | 85(2) | 0

Table 1: Isomer shift (IS), quadrupole splitting (QS), hyperfine magnetic
field ($B_{\text{HF}}$), angle between average magnetization and film normal
($\Phi_{\text{MS}}$), and amount of paramagnetic phase (PM) were extracted
from Mössbauer spectroscopy measurements of the films in the left column.
Films marked with § signify that the full structure is
Ta(3.5)$|$Ru(3.5)$|$Fe100-xRux(100)$|$Ru(3.5). Rows marked with * indicate
that the sample was measured via transmission Mössbauer spectroscopy, and rows
without * were measured via conversion electron Mössbauer spectroscopy. Unless
specified, each measurement is performed at zero external magnetic field.

Mössbauer measurements were used to study
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
films, with transmission Mössbauer spectroscopy (TMS) performed on samples
with $x=0$, 4, and 8 at room temperature and conversion electron Mössbauer
spectroscopy (CEMS) performed on samples with $x=13$, 18.5, 19.5, 23, and 50
at room temperature. Furthermore, CEMS was performed on Ta$|$Fe(100)$|$Ta, and
CEMS and TMS were both performed on a single Fe(100) layer, all at room
temperature. Additional TMS measurements of the single Fe(100) layer and of
the
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
samples with $x=0$, 4, and 8 were performed in the presence of a
$0.166\text{\,}\mathrm{T}$ in-plane magnetic field, and TMS measurements of
the samples with $x=18.5$ and 19.5 were performed at 9.7 and
$9.9\text{\,}\mathrm{K}$, respectively.

For all measured films, the Mössbauer spectra were fitted to determine the
isomer shift (IS), quadrupole splitting (QS), and hyperfine magnetic field
($B_{\text{HF}}$). Paramagnetic components of Mössbauer spectra have a
$B_{\text{HF}}$ of zero, and films with a cubic lattice structure have a QS of
zero. The angle between the gamma ray (perpendicular to the film plane) and
the average magnetization of the film, $\Phi_{\text{MS}}$, was determined by
comparing the peak intensities of the second and fifth lines with the other
lines in the spectra. The intensities of the second and fifth lines depend
only on the angle between the gamma ray (perpendicular to the film plane) and
hyperfine field and are not affected by the in-plane orientation of the
hyperfine field or the sign of the component of the hyperfine field along the
gamma ray (parallel and antiparallel are equivalent). As a result, Mössbauer
measurements yield the same angle if the out-of-plane magnetization components
of the film are all pointing in the same direction as the gamma ray, all
pointing in the opposite direction of the gamma ray, or any combination of the
two. In contrast, VSM measurements with the external magnetic field applied
perpendicular to the film normal treat these cases differently. In VSM
measurements, the projections onto the field direction of all the
magnetization components are summed, taking into account that projections in
the same direction as the external magnetic field are positive and projections
in the opposite direction are negative (see Sec. IV.2). The four above-
described parameters extracted from Mössbauer measurements—IS, QS,
$B_{\text{HF}}$, and $\Phi_{\text{MS}}$—as well as the amount of paramagnetic
phase in the film (PM), are tabulated in Table 1 for all films measured by
Mössbauer spectroscopy.

Figure 5: (a) Conversion electron Mössbauer spectroscopy (CEMS) measurements
at room temperature of Ta(3.5)$|$Ru(3.5)$|$Fe100-xRux(100)$|$Ru(3.5) for
$x=13$, 23, and 50 and (b) CEMS measurements at room temperature and
transmission Mössbauer spectroscopy (TMS) measurements at low temperature of
Ta(3.5)$|$Ru(3.5)$|$Fe100-xRux(100)$|$Ru(3.5) for $x=18.5$ and 19.5. All
measurements are performed at zero external magnetic field.

Table 1 shows that
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
is fully paramagnetic for $x\geq 19.5$, as indicated by PM being
$100\text{\,}\%$ and $B_{\text{HF}}$ being absent. This can be visualized in
the CEMS measurements in Fig. 5, which show one central peak for $x=19.5$, 23,
and 50. When compared with the X-ray diffraction (XRD) measurements, it
follows that hcp FeRu is paramagnetic at room temperature. When the Ru
concentration decreases from 19.5 to $18.5\text{\,}\mathrm{at.\,\%}$,
$B_{\text{HF}}$ appears and the amount of paramagnetic phase in the film drops
from 100 to $61\text{\,}\%$. The mixture of the paramagnetic and magnetic
phase in Fe81.5Ru18.5 can also be seen in the CEMS measurements in Fig. 5(b).
At this concentration, $B_{\text{HF}}$ is $30.2\pm 0.1\text{\,}\mathrm{T}$,
which is already about $90\%$ of the hyperfine field known for pure Fe,
$33\text{\,}\mathrm{T}$ [29]. As the Ru concentration in
$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ decreases further from $18.5$ to
$13\text{\,}\mathrm{at.\,\%}$, $B_{\text{HF}}$ increases to $32.2\pm
0.1\text{\,}\mathrm{T}$ and only $4\text{\,}\%$ of the film is paramagnetic.
The small amount of paramagnetic phase remaining in the film is indicated by
the small central peak in the CEMS measurements of Fe87Ru13 in Fig. 5(a).
Though the presence of the hcp phase in Fe87Ru13 was not detected by XRD, it
was detected by the more precise method, TEM, confirming that the paramagnetic
contribution observed by Mössbauer spectroscopy is due to the hcp FeRu phase.
Mössbauer spectroscopy also shows that films for which the magnetic phase is
detected, i.e., $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ with $x\leq 18.5$, also
have an average magnetization that is tilted out of the film plane. The
average magnetization angle from the film normal, $\Phi_{\text{MS}}$, does not
change significantly until the Ru concentration is less than
$8\text{\,}\mathrm{at.\,\%}$. For Fe81.5Ru18.5, CEMS measurements give an
$\Phi_{\text{MS}}=$40\pm 2\text{\,}\mathrm{\SIUnitSymbolDegree}$$ from the
film normal. For Fe87Ru13, CEMS measurements yield $\Phi_{\text{MS}}=$45\pm
1\text{\,}\mathrm{\SIUnitSymbolDegree}$$, and for Fe92Ru8, TMS measurements
give $\Phi_{\text{MS}}=$44\pm 1\text{\,}\mathrm{\SIUnitSymbolDegree}$$.

When Fe81.5Ru18.5 is cooled to $9.7\text{\,}\mathrm{K}$, $B_{\text{HF}}$ of
the magnetic phase increases from $30.2\pm 0.1\text{\,}\mathrm{T}$ to $32.3\pm
0.6\text{\,}\mathrm{T}$, but the amounts of the paramagnetic and magnetic
phases remain practically the same (see Table 1 and Fig. 5(b)). Additionally,
Table 1 and Fig. 5(b) show that Fe80.5Ru19.5 remains fully paramagnetic when
cooled to $9.9\text{\,}\mathrm{K}$. This indicates that Fe100-xRux is
paramagnetic above $9.9\text{\,}\mathrm{K}$ for $x\geq 19.5$, which differs
from previous neutron diffraction studies that reported an incommensurate
antiferromagnetic state of Fe71Ru29 with a Néel temperature of
$124\text{\,}\mathrm{K}$ [16].

Figure 6: (a) Transmission Mössbauer spectroscopy (TMS) measurements at room
temperature of Ta(3.5)$|$Ru(3.5)$|$Fe100-xRux(100)$|$Ru(3.5) for $x=0$, 4, and
8, and (b) conversion electron Mössbauer spectroscopy (CEMS) at room
temperature of Fe(100) (no surrounding layers) and
Ta(3.5)$|$Fe(100)$|$Ta(3.5). All measurements are performed at zero external
magnetic field.

The TMS measurements of
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
for $x=4$ and $8$ in Fig. 6(a) show that these films have only a trace of the
paramagnetic phase, which disappears for $x=0$. This is confirmed by the
amount of paramagnetic phase tabulated in Table 1. Comparing these results
with the XRD measurements, we can confirm that bcc Fe and FeRu are magnetic.
Since the magnetic phase has cubic structure (bcc), quadrupole splitting is
zero for $x\leq 8$. Table 1 shows that the hyperfine field increases as $x$
decreases from 8 to $0\text{\,}\mathrm{at.\,\%}$ of Ru in Fe and reaches
approximately $33\text{\,}\mathrm{T}$, the hyperfine field previously measured
for pure Fe [29]. In the same Ru concentration range, the average
magnetization direction moves towards the plane, as seen in Table 1. For
$x=8$, TMS measurements give an angle of $\Phi_{\text{MS}}=$44\pm
1\text{\,}\mathrm{\SIUnitSymbolDegree}$$ from the film normal. For $x=4$,
$\Phi_{\text{MS}}$ increases to $51\pm
1\text{\,}\mathrm{\SIUnitSymbolDegree}$, and for $x=0$, $\Phi_{\text{MS}}$
increases further to $68\pm 2\text{\,}\mathrm{\SIUnitSymbolDegree}$ from the
film normal. This result for Ta$|$Ru$|$Fe(100)$|$Ru is very unexpected. Due to
the relatively small magnetocrystalline anisotropy of bcc Fe as compared to
the large in-plane shape anisotropy of the studied Fe films, the magnetization
is expected to lie in the plane. The large shape anisotropy arises from the
large $M_{s}$ of the studied Fe films. One possible explanation of the out-of-
plane magnetization components measured in Ta$|$Ru$|$Fe(100)$|$Ru is the
presence of a very small amount of Ru in the Fe film. Quantification of the
STEM-EDXS analysis of this film (Supplemental Material [28]) indicated that
the Fe layer may contain up to $0.1\text{\,}\mathrm{at.\,\%}$ of Ru.

To eliminate any contribution from Ru in the Fe film, CEMS was performed on an
$100\text{\,}\mathrm{n}\mathrm{m}$-thick Fe film surrounded only by
$3.5\text{\,}\mathrm{n}\mathrm{m}$-thick Ta, and CEMS and TMS were both
performed on a single $100\text{\,}\mathrm{n}\mathrm{m}$-thick Fe layer. The
parameters of these three measurements are presented in Table 1, and the CEMS
measurements of both films are displayed in Fig. 6(b). The hyperfine fields
for both films are approximately $33\text{\,}\mathrm{T}$, in agreement with
the hyperfine field known for Fe [29]. However, the average magnetization
direction as compared to that of Ta$|$Ru$|$Fe$|$Ru moves closer to the plane
for Ta$|$Fe$|$Ta ($\Phi_{\text{MS}}=$73\pm
1\text{\,}\mathrm{\SIUnitSymbolDegree}$$ from the normal), and closer still
for the single Fe layer ($\Phi_{\text{MS}}=$80\pm
1\text{\,}\mathrm{\SIUnitSymbolDegree}$$ from CEMS and $82\pm
1\text{\,}\mathrm{\SIUnitSymbolDegree}$ from TMS). Since domain walls have
out-of-plane magnetization components that could be responsible for these
observations, an in-plane magnetic field of $0.166\text{\,}\mathrm{T}$ was
applied to the single Fe layer to expel all domains and TMS was again
performed. As a result of the application of the magnetic field,
$\Phi_{\text{MS}}$ of the single Fe layer only increased to $85\pm
2\text{\,}\mathrm{\SIUnitSymbolDegree}$ from the film normal, showing that the
presence of domain walls only changes the average magnetization direction by a
few degrees. For confirmation, we also measured
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
for $x=0$, 4, and 8 with TMS in the presence of the $0.166\text{\,}\mathrm{T}$
in-plane magnetic field and, as with the single Fe layer, the expelling of
magnetic domains only changed $\Phi_{\text{MS}}$ by a few degrees.
Micromagnetic simulations of an $100\text{\,}\mathrm{n}\mathrm{m}$-thick Fe
layer grown along the $\langle 110\rangle$ directions were performed to
determine whether the magnetization has an out-of-plane component and are
presented in the Supplemental Material [28]. In the absence of an external
magnetic field, the simulations yielded an average magnetization of $84\pm
10\text{\,}\mathrm{\SIUnitSymbolDegree}$ from the film normal. However, when a
$0.05\text{\,}\mathrm{T}$ in-plane magnetic field was applied in the
simulations, magnetic domains were expelled, and the film was fully saturated
along the field direction with no out-of-plane magnetization component.

###  IV.2 Vibrating sample magnetometry

Figure 7: $M(H)$ measurements with magnetic field applied parallel to the film
surface over (a) the full measured field range and (b) a zoomed-in field range
to highlight the hysteresis loops of as-deposited Fe(100),
§$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$(100) for $x=4$ and 8, and
§$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$(20) for $x=7$, 10, 13, 15, 17, 18.5, and
19.5, where § signifies that the full structure is
Ta(3.5)$|$Ru(3.5)$|$Fe100-xRu${}_{x}(d)|$Ru(3.5). $M_{s}$, $M_{r}$, and
$M_{r}/M_{s}$ from the $M(H)$ measurements in (a,b) are plotted at (c) 295 and
(d) $5\text{\,}\mathrm{K}$. $M(H)$ measurements with magnetic field applied
perpendicular to the film surface of as-deposited Fe(100) and
§$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$(20) for $x=7$, 13, 17, and 19.5 at (e)
295 and (f) $5\text{\,}\mathrm{K}$. The dashed lines in (e) represent the
calculated demagnetizing fields for Fe(100) and
§$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$(20) ($7\leq x\leq 17$) films.

Vibrating sample magnetometry (VSM) measurements were used to determine the
magnetization of
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(d)|\mathrm{Ru}$,
Ta$|$Fe(100)$|$Ta, and Fe(100) films as a function of an external magnetic
field applied either parallel or perpendicular to the film surface and at a
temperature of 5 or $295\text{\,}\mathrm{K}$. From the measurements, we
obtained the saturation magnetization, $M_{s}$, and the remanent magnetization
along the field direction, $M_{r}$. The remanent-to-saturation magnetization
ratio, $M_{r}/M_{s}$, allows us to infer information about the magnetic
structure of the $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ films. Additionally, for
selected structures, we found the external magnetic field above which the
magnetization is reversible, $H_{\text{rev}}$. Above this field, domains are
expelled from the film and do not contribute to the $M(H)$ measurements.

Figure 7(a,b) shows the $M(H)$ measurements at $295\text{\,}\mathrm{K}$ of
Fe(100),
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
for $x=4$ and 8, and
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(20)|\mathrm{Ru}$
for $x=$ 7, 10, 13, 15, 17, 18.5, and 19.5, with the magnetic field applied
parallel to the film surface (referred to as in-plane). $M_{r}$, $M_{s}$, and
the $M_{r}/M_{s}$ ratio for each film are plotted as a function of Ru
concentration in Fig. 7(c) and (d) at 295 and $5\text{\,}\mathrm{K}$,
respectively. When a very large in-plane magnetic field is applied, the
magnetic moments lie along the field direction, producing a net magnetization
of $M_{s}$ in the field direction. As the field is reduced to zero, the
magnetic moments may deviate from the field direction, resulting in a remanent
magnetization along the field direction of $M_{r}\leq M_{s}$. Therefore, the
ratio $M_{r}/M_{s}$ provides information on the distribution of magnetic
moments in the film in the absence of an external magnetic field.
$M_{r}/M_{s}=1$ means that the magnetic moments are fully aligned along the
field direction after the field is removed, and $M_{r}/M_{s}=0$ means that
there is no net magnetization along the field direction after the field is
removed. The observed $M_{r}/M_{s}$ values of the in-plane $M(H)$ measurements
will be discussed in Sec. V.1.

It can be seen in Fig. 7(c) that $M_{s}$ decreases with Ru concentration from
approximately $1710\text{\,}\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$ for the
single Fe layer to $61\text{\,}\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$ for
Fe80.5Ru19.5 at room temperature. Over the $0\leq x\leq 10$ composition range
of $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$, the slow decrease in $M_{s}$ is due
to Ru atoms substituting Fe atoms in the host bcc lattice. This agrees with
the small decrease in the hyperfine field measured by Mössbauer spectroscopy
over this composition range (Table 1). The sharp decrease in $M_{s}$ observed
in $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ for $13\leq x\leq 19.5$ is mainly due
to the increasing amount of paramagnetic hcp FeRu and decreasing amount of
magnetic bcc FeRu in the films. This is corroborated by our Mössbauer
measurements in this composition range (Table 1), which show a large increase
in the amount of paramagnetic phase in the film (from $4\%$ to $100\%$) and
only a small change in the hyperfine field.

The $M_{s}$ measurements at $5\text{\,}\mathrm{K}$ in Fig. 7(d) are slightly
higher than those at $295\text{\,}\mathrm{K}$ for all plotted Ru
concentrations, as is expected for ferromagnetic materials [30]. Fig. 7(d)
also shows that if the ambient temperature is decreased from 295 to
$5\text{\,}\mathrm{K}$, $M_{r}$ stays practically the same for the single Fe
layer but increases for all FeRu alloys. Consequently, the $M_{r}/M_{s}$ ratio
also increases as the ambient temperature is reduced to 5 K. The increase is
most significant for films with the highest Ru concentrations.

From Fig. 7(a,b), it is evident that the field required to saturate the FeRu
alloys is much higher than that required to saturate the pure Fe film. Large
saturation fields are observed even for very low concentrations of Ru in Fe.
To highlight the approach to saturation, Fig. 8(a) shows the normalized $M(H)$
curves for $H\geq 0$ of Fe(100) and of
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(100)|\mathrm{Ru}$
for $x=0$, 4, and 8. Even for Ta$|$Ru$|$Fe(100)$|$Ru, the field required to
saturate the magnetization is significantly larger than that required for the
single Fe layer with no surrounding layers. This could be due to Ru diffusing
into the Fe layer, which is suggested by the TEM-based analysis in the
Supplemental Material [28].

Figure 8: (a) $M(H)/M_{s}$ and (b) $M(H)$ measurements of as-deposited Fe(100)
and of Ta(3.5)$|$Ru(3.5)$|$Fe100-xRux(100)$|$Ru(3.5) for $x=0$, 4, and 8,
where the § in the legend signifies that the layer is grown on top of Ta$|$Ru
and capped with Ru. The magnified inset plot in (a) highlights the variation
in saturation field. The magnetic field ranges in (b) are chosen to highlight
the hysteresis loops of the samples. Cyan diamonds are placed at the lowest
field for which the hysteresis loop is reversible, indicating the removal of
magnetic domains.

Marked on each $M(H)$ curve in Fig. 8(a) with a cyan diamond is the point at
which the magnetization becomes reversible with the magnetic field,
$M(H_{\text{rev}})$, meaning that all the magnetic domains have been expelled
from the film. These points are also indicated in Fig. 8(b), which shows the
$M(H)$ loops of the same films in Fig. 8(a). As the Ru concentration in the
film increases, the field required to expel the domains increases; however, in
each case, the domains are expelled in fields lower than
$0.13\text{\,}\mathrm{T}$. Magneto-optical microscopy measurements, which will
be presented in Sec. IV.3, show that domains disappear at $\sim
0.030\text{\,}\mathrm{T}$ in Fe96Ru4, confirming that there are no domains
above the $H_{\text{rev}}$ fields marked in Fig. 8. Since domains are not
present in the reversible region, the presence of domains cannot explain the
large saturation fields seen in Fig. 8(a).

Figure 7(e) shows the $M(H)$ measurements of as-deposited Fe(100) and
$\mathrm{Ta}|\mathrm{Ru}|\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}(20)|\mathrm{Ru}$
for $x=7$, 13, 17, and 19.5 at $295\text{\,}\mathrm{K}$, with the magnetic
field applied perpendicular to the film plane (referred to as perpendicular-
to-plane). When a large magnetic field is applied, the magnetic moments are
saturated along the field direction. When the field is removed, Fe and all
FeRu alloys have an $M_{r}/M_{s}$ ratio of nearly zero, indicating that the
net projection of magnetic moments along the field direction is nearly zero.
Combining this information with the out-of-plane magnetization detected by
Mössbauer spectroscopy, we conclude that there are out-of-plane magnetization
components pointing both up and down along the film normal that almost fully
cancel each other out.

The field required to saturate the magnetization of the single Fe layer
perpendicular to the film plane is slightly larger than the shape anisotropy
or demagnetizing field, $\mu_{0}M_{s}=$2.15\text{\,}\mathrm{T}$$, which is
represented by the respective dashed line (purple) in Fig. 7(e). In addition
to shape anisotropy, Fe films have a much smaller magnetocrystalline
anisotropy which is oriented along the $\langle 100\rangle$ directions. The
magnetocrystalline anisotropy field also contributes to the field required to
saturate the sample. When 7 to $17\text{\,}\mathrm{at.\,\%}$ of Ru is added to
the Fe film, the saturation fields for the perpendicular-to-plane measurements
increase to above $6\text{\,}\mathrm{T}$, which is several times larger than
the demagnetizing fields of the films (represented by additional dashed lines
in Fig. 7(e)). The perpendicular-to-plane $M(H)$ measurements performed at
$5\text{\,}\mathrm{K}$, presented in Fig. 7(f), are very similar to those
performed at $295\text{\,}\mathrm{K}$.

###  IV.3 Magneto-optical Kerr effect microscopy

Magneto-optical Kerr effect (MOKE) microscopy measurements were performed on
Ta$|$Ru$|$Fe96Ru${}_{4}(100)$$|$Ru to observe how the domain structure of the
film evolves in an in-plane applied magnetic field. Initially, a magnetic
field of $-1.1\text{\,}\mathrm{T}$ was applied in the film plane, saturating
the magnetic moments along the field direction. The field was subsequently
removed and then swept up to $1.1\text{\,}\mathrm{T}$ while the domain
structure was observed. Fig. 9(a) presents the MOKE microscopy image of
Ta$|$Ru$|$Fe96Ru${}_{4}(100)$$|$Ru at an applied field of
$14.3\text{\,}\mathrm{mT}$. For reference, the $M(H)$ loop of the film, Fig.
9(c), is placed below the image. At $14.3\text{\,}\mathrm{mT}$, the coercive
field of the film, small domains textured along the field direction were
observed. When the magnetic field reached $30\text{\,}\mathrm{mT}$, the
domains were entirely expelled, as can be seen in Fig. 9(b). This field
coincides with the point marked by a diamond in Fig. 8 at which the $M(H)$
loop of the Fe96Ru4 sample becomes reversible. Therefore, the reversible parts
of our $M(H)$ loops are not affected by any out-of-plane magnetization
components or noncollinearity in domain walls. The texture of the domains
follows the direction of the applied magnetic field, suggesting that the film
is isotropic within the plane, i.e., there is no preferred magnetic anisotropy
direction in the plane. The observed pattern is neither purely stripe nor
ripple domain structure, but rather a domain structure typical for
polycrystalline magnetic films that have magnetocrystalline anisotropy
averaged out in the film plane.

Figure 9: MOKE microscopy image of the Ta$|$Ru$|$Fe96Ru${}_{4}(100)$$|$Ru film
surface with (a) $14.3\text{\,}\mathrm{mT}$ and (b) $30\text{\,}\mathrm{mT}$
applied parallel to the film surface. Small domains that are elongated along
the film direction are visible at $14.3\text{\,}\mathrm{mT}$, and no domains
are visible as $30\text{\,}\mathrm{mT}$. (c) $M(H)$ loop of
Ta$|$Ru$|$Fe96Ru${}_{4}(100)$$|$Ru, which is also plotted in Fig. 8(b). Dashed
lines are placed at the field values that correspond with (a) and (b).

###  IV.4 Lorentz transmission electron microscopy

Figure 10: (a–d) Lorentz transmission electron microscopy images taken at the
same location on a Ta(3.5)$|$Ru(3.5)$|$Fe92Ru8(20)$|$Ru(3.5) film, for
increasing applied magnetic field values, as labelled. (e,f) Corresponding
contrast differences showing all the switching events that occurred due to the
respective field increase. The scale bar at the bottom applies to all images.
All images are taken at room temperature with a defocus of
$-1\text{\,}\mathrm{m}\mathrm{m}$ and a tilting angle of
$+$40\text{\,}\mathrm{\SIUnitSymbolDegree}$$.

The magnetization reversal process of a Ta$|$Ru$|$Fe92Ru8(20)$|$Ru film was
investigated in more detail by Lorentz transmission electron microscopy
(LTEM), which is able to probe the in-plane magnetization orientation at the
nanoscale. The sample was tilted by a tilt angle of $\theta$ with respect to
the film normal, yielding an in-plane magnetic field of
$H_{\text{IP}}=H_{\text{appl}}\sin{\theta}$ and an out-of-plane magnetic field
of $H_{\text{OOP}}=H_{\text{appl}}\cos{\theta}$.

Prior to acquiring images, the sample was tilted by
$-40\text{\,}\mathrm{\SIUnitSymbolDegree}$ with respect to the film normal in
an applied magnetic field of about $2\text{\,}\mathrm{T}$ to align the in-
plane magnetization of the sample toward the negative direction. Subsequently,
$H_{\text{appl}}$ was increased to zero in order to bring the in-plane
magnetization to the negative remanence point. Images were then acquired at
room temperature with the sample tilted at
$\theta=+$40\text{\,}\mathrm{\SIUnitSymbolDegree}$$, beginning at the negative
remanence point and increasing $H_{\text{appl}}$ in steps up to
$2\text{\,}\mathrm{T}$. It is important to point out that, by tilting the
sample by $+$40\text{\,}\mathrm{\SIUnitSymbolDegree}$$, the LTEM contrast is
more enhanced than that of the zero tilt case (images not shown), which is
consistent with the average magnetization angle measured by Mössbauer
spectroscopy of about $45\text{\,}\mathrm{\SIUnitSymbolDegree}$ from the film
normal.

Figure 10(a) shows the magnetic domain structure at zero magnetic field,
revealing that the size of the magnetic features is similar to the grain size
(determined by the bright-field TEM images in Fig. 4(a)). By increasing the
applied magnetic field $H_{\text{appl}}$ from zero to
$144\text{\,}\mathrm{mT}$ (i.e.,
$H_{\text{IP}}=$92.6\text{\,}\mathrm{m}\mathrm{T}$$ and
$H_{\text{OOP}}=$110.3\text{\,}\mathrm{m}\mathrm{T}$$), individual switching
events can be seen (Fig. 10(a–d)). The switching events are more clear in the
corresponding difference images presented in Fig. 10(e,f). The small reversed
areas are most likely noncollinear spin clusters arising from the competing
ferromagnetic and antiferromagnetic interactions between the Fe atoms, as will
be discussed in Sec. V.2.

At higher magnetic fields, up to $2\text{\,}\mathrm{T}$, only a few individual
switching events are observed (images not shown). Furthermore, the overall
LTEM contrast is reduced, implying that the magnetization is predominantly
oriented along the applied magnetic field direction. This is consistent with
Fig. 7(b), which shows that the magnetization of Ta$|$Ru$|$Fe92Ru8(20)$|$Ru is
reversible at fields above about $0.1\text{\,}\mathrm{T}$. The individual
reversal events can be observed in the video provided in the Supplemental
Material [28], which was recorded via LTEM of a sample area as an external
magnetic field was increased from 96 to $112\text{\,}\mathrm{mT}$.

##  V Discussion

###  V.1 Experimental Results

The structural measurements, X-ray diffraction (XRD) and transmission electron
microscopy (TEM), show that the studied films are polycrystalline with grains
that are randomly oriented in the plane of the film. The grains with bcc
crystal structure are textured along the growth direction, $\langle
110\rangle$, and the grains with hcp crystal structure are textured along the
$\langle 001\rangle$ directions. For
Ta$|$Ru$|$$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$$|$Ru films with both bcc and
hcp $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$, rocking curve measurements show that
the full-width-at-half-maximum is $2.6\text{\,}\mathrm{\SIUnitSymbolDegree}$
or below.

The XRD and TEM measurements indicate that room-temperature
$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ transitions from bcc to hcp crystal
structure as $x$ increases from $\sim 13\text{\,}\mathrm{at.\,\%}$ to $\sim
20\text{\,}\mathrm{at.\,\%}$. From the TEM measurements, we also observed that
the Fe87Ru13 and Fe83Ru17 films consist of grains having entirely hcp or
entirely bcc lattice structure; furthermore, each film has indications of
individual grains showing both phases. STEM-EDXS analysis measurements of the
Ta$|$Ru$|$$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$$|$Ru structure reveal a uniform
distribution of Ru throughout the FeRu films.

XRD measurements show that the lattice expansion with the addition of Ru to Fe
is linear for up to $8\text{\,}\mathrm{at.\,\%}$ of Ru in Fe, indicating that
Ru atoms substitute Fe atoms in the bcc crystal structure. Out-of-plane and
in-plane measurements of $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ for $0\leq x\leq
8$ indicate no difference in the lattice spacing for the in-plane and out-of-
plane directions, suggesting that the cubic structure is not distorted by the
addition of Ru.

Our Mössbauer spectroscopy measurements show no magnetic order in
$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ films with $x\geq 19.5$, while films with
$x\leq 13$ contain more than $96\%$ of the magnetic phase. Combining these
measurements with the structural measurements suggests that hcp FeRu is
paramagnetic and bcc FeRu is magnetic. In the absence of an external magnetic
field, the angle of the average magnetization with respect to the film normal,
$\Phi_{\text{MS}}$, of Ta$|$Ru$|$$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$$|$Ru
increases from $40\pm 2\text{\,}\mathrm{\SIUnitSymbolDegree}$ for $x=18.5$, to
$51\pm 1\text{\,}\mathrm{\SIUnitSymbolDegree}$ for $x=4$, and to $68\pm
2\text{\,}\mathrm{\SIUnitSymbolDegree}$ for $x=0$. For a single layer of Fe,
$\Phi_{\text{MS}}$ increases to $82\pm
1\text{\,}\mathrm{\SIUnitSymbolDegree}$. Since domain walls have out-of-plane
magnetization components, the angle was also measured in the presence of a
$0.166\text{\,}\mathrm{T}$ external magnetic field to expel all magnetic
domains in the film. With the field applied, $\Phi_{\text{MS}}$ increased
slightly to $55\pm 1\text{\,}\mathrm{\SIUnitSymbolDegree}$ for $x=4$ and to
$85\pm 2\text{\,}\mathrm{\SIUnitSymbolDegree}$ for the single Fe layer.
Therefore, magnetization in domain walls does not contribute significantly to
the out-of-plane magnetization component observed. Micromagnetic simulations
presented in the Supplemental Material [28] support the presence of an out-of-
plane magnetization component in our $100\text{\,}\mathrm{n}\mathrm{m}$-thick
single Fe layer with domains expelled. The simulations give an average angle
between the magnetic moments in the film and the film normal of $84.4\pm
1.0\text{\,}\mathrm{\SIUnitSymbolDegree}$ in the presence of a
$0.05\text{\,}\mathrm{T}$ in-plane magnetic field.

The room-temperature $M(H)$ measurements of the
$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ films with the magnetic field applied
parallel to the film plane show that $M_{s}$ initially decreases slowly with
$x$ up to $10\text{\,}\mathrm{at.\,\%}$, which is predominantly due to Ru
atoms substituting Fe atoms in the host bcc lattice. For $13\leq x\leq 23$,
$M_{s}$ sharply decreases to 0, which is mainly due to the magnetic phase
transforming into the paramagnetic phase. On the other hand, the remanent
magnetization $M_{r}$ sharply decreases with $x$ up to
$8\text{\,}\mathrm{at.\,\%}$ and decreases at a lower rate for larger $x$; the
$M_{r}/M_{s}$ ratio follows the same trend as $M_{r}$. This trend correlates
with the increase in the out-of-plane magnetization component observed by
Mössbauer spectroscopy, i.e., the decrease in the angle $\Phi_{\text{MS}}$
with respect to the film normal. The $M_{r}/M_{s}$ measurements of the
$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ films at $5\text{\,}\mathrm{K}$ are
similar to those at room temperature except for $x\geq 17$, for which
$M_{r}/M_{s}$ increases due to the increase in the magnetic order of the
structure.

The $M(H)$ measurements of the $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ films with
the field applied perpendicular to the plane measured a very small
magnetization along the film normal at zero field for all measured
compositions. This reveals that the majority of the out-of-plane magnetization
components detected by Mössbauer spectroscopy for $x\leq 18.5$ at zero field
cancel each other out: the out-of-plane components must point in both
directions along the film normal. This is expected, as the demagnetizing field
in the film is minimized when the net magnetization along the film normal is
zero.

The MOKE microscopy measurements showed that magnetic domains are entirely
expelled in the reversible part of the $M(H)$ loop. The field at which the
$M(H)$ loop becomes reversible, $H_{\text{rev}}$, increases from
$0.0037\text{\,}\mathrm{T}$ for the single Fe layer to
$0.13\text{\,}\mathrm{T}$ for Ta$|$Ru$|$Fe92Ru8$|$Ru. The normalized
magnetization at these fields, $M(H_{\text{rev}})/M_{s}$, is about 0.96 for
the single Fe layer and 0.59 for Ta$|$Ru$|$Fe92Ru8$|$Ru. The MOKE measurements
also show that there is no stripe domain pattern present in our films to
contribute to the large out-of-plane magnetization component observed within
the film.

For ferromagnetic films with non-interacting magnetic grains whose easy axes
are randomly oriented in all directions, the $M_{r}/M_{s}$ ratio is 0.5 (see
Supplemental Material [28]). If the easy axes of the magnetic grains are
randomly oriented only in the plane of the film, with no out-of-plane
components due to large in-plane magnetic anisotropy, $M_{r}/M_{s}$ increases
to 0.64 (see Supplemental Material [28]). In cases where there is a strong
direct exchange interaction between the grains, as in our films, the magnetic
moments are pulled toward each other, significantly increasing $M_{r}/M_{s}$.
This is corroborated by our pure Fe films, for which $M_{r}/M_{s}$ is 0.94. On
the contrary, $M_{r}/M_{s}<0.5$ for our $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$
films with $x\geq 8$, suggesting that a reduced interaction between magnetic
grains cannot explain the low $M_{r}/M_{s}$ ratio in our RuFe films.

The field required to saturate the magnetic moments of ferromagnetic materials
along the direction of the external field, the saturation field, can be
calculated as $2K_{1}/M_{s}$, where $K_{1}$ is the first anisotropy constant
and $M_{s}$ is the saturation magnetization of the ferromagnetic material
[30]. Here, we assume $K_{2}=K_{3}=0$ and neglect the demagnetizing fields.
For pure Fe, $K_{1}=$48\text{\,}\mathrm{k}\mathrm{J}\mathrm{/}\mathrm{m}^{3}$$
[30], resulting in a saturation field of $0.056\text{\,}\mathrm{T}$. Since the
magnetic phase of FeRu has a cubic crystal structure (bcc) and no structural
distortion is observed for Fe100-xRux films with $x\leq 8$, $K_{1}$ is small,
resulting in a relatively small saturation field. The observed saturation
field in our FeRu films is two orders of magnitude larger than that of Fe,
suggesting that our films are not ferromagnetic (i.e., the magnetic
interactions do not cause the magnetic moments of Fe atoms to align in the
same direction).

Furthermore, our samples have a large $M_{s}$, exceeding
$1.5\text{\,}\mathrm{M}\mathrm{J}\mathrm{/}\mathrm{m}^{3}$ for
$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ with $x\leq 8$, which induces a large in-
plane shape anisotropy in our films. Due to the small magnetocrystalline
anisotropy of the magnetic phase of FeRu, it is expected that the shape
anisotropy will force the magnetization of the film to lie in the film plane.
On the contrary, the average magnetization is aligned at an angle between
$39\text{\,}\mathrm{\SIUnitSymbolDegree}$ and
$50\text{\,}\mathrm{\SIUnitSymbolDegree}$ out of the film plane (i.e.,
$\Phi_{\text{MS}}$ between $51\text{\,}\mathrm{\SIUnitSymbolDegree}$ and
$40\text{\,}\mathrm{\SIUnitSymbolDegree}$) for $x\geq 4$ at room temperature.
Even in the presence of an external magnetic field large enough to expel all
domains, the average magnetization was at an angle of at least
$35\text{\,}\mathrm{\SIUnitSymbolDegree}$ out of the film plane for $x\geq 4$.
This clearly shows that magnetization in domain walls is not responsible for
the observed out-of-plane magnetization component. Thus, the out-of-plane
magnetization component is another indication that our films are not
ferromagnetic films.

The low $M_{r}/M_{s}$, high saturation field, and presence of an out-of-plane
magnetization component observed in our FeRu films can be explained by
noncollinear coupling between magnetic Fe atoms within the films, which gives
rise to a nanogranular magnetic domain structure as observed by LTEM for a
$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ film with $x=8$. The noncollinear
coupling can arise from the competition between ferromagnetic coupling between
neighbouring Fe atoms and antiferromagnetic coupling between Fe atoms
separated by Ru atoms. This will be discussed in the following subsection.

###  V.2 Atomistic model

The recently-developed atomistic model [31] was successfully used to simulate
the magnetic coupling of Co layers across FeRu layers. In the model, the
crystal structure is simplified to simple cubic with a lattice constant of
$a=$0.25\text{\,}\mathrm{n}\mathrm{m}$$. Neighbouring Fe atoms couple
ferromagnetically due to Heisenberg exchange interactions, while two Fe atoms
separated by one or more Ru atoms couple antiferromagnetically. The model only
includes ferromagnetic and antiferromagnetic couplings between pairs of Fe
atoms along the three principal axes of the simple cubic unit cell. Further
details about the atomistic model can be found in Ref. [31] and Ref. [32].

We used the atomistic model to simulate $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$
films for $0\leq x\leq 10$, using a saturation magnetization of
$M_{s}=$1700\text{\,}\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$$ to obtain the
dipole moment of the Fe atoms and an exchange stiffness of
$A_{\text{ex}}=$21\text{\,}\mathrm{p}\mathrm{J}\mathrm{/}\mathrm{m}$$ to
obtain the Heisenberg exchange constant between the Fe atoms. The
antiferromagnetic coupling strengths of Fe across one, two, and three Ru atoms
are $-3.13\text{\times}{10}^{-21}\text{\,}\mathrm{,}$
$-1.14\text{\times}{10}^{-21}\text{\,}\mathrm{,}$ and
$-4.43\text{\times}{10}^{-22}\text{\,}\mathrm{J}$, respectively. To account
for the large shape anisotropy in our $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$
films, we introduced a demagnetizing field, with the easy-plane shape
anisotropy being $K_{\text{shape}}=-\mu_{0}M_{s}^{2}/2$. Figure 11(a) shows
the magnetic moment distribution in the Fe90Ru10 film after a large magnetic
field is applied along the $x$-axis, parallel to the film plane, and then
reduced to zero. The complex configuration is caused by the competition
between the ferromagnetic and antiferromagnetic couplings between the Fe
atoms. The vast majority of magnetic moments have a positive projection along
the magnetic field direction after the field is removed, and for this reason,
the colour of the magnetic moments with a negative projection is kept the same
in Fig. 11(a).

From the magnetic moment distribution of the Fe90Ru10 film, we calculated the
average projection of the normalized magnetic moments on the $x$-axis (the
field direction), the $y$-axis, and the $z$-axis (the film normal) as a
function of the external magnetic field, as shown in Fig. 11(b). Since the
magnetic field is applied along the $x$-axis, the magnetic moments
preferentially point in the positive $x$ direction, as expected; in fact,
$\overline{m_{x}}\geq 0.8$ for all fields greater than or equal to
$0.1\text{\,}\mathrm{T}$. However, the magnetic moments have no analogous
preferential direction along the $y$-axis or $z$-axis, causing the average
projection on these two axes to be zero. For this reason, we have plotted the
average of the absolute value of the normalized magnetic moment projections
along the $y$ and $z$ directions, $\overline{|m_{y}|}$ and
$\overline{|m_{z}|}$, respectively. The absolute value projection along the
$z$ direction is similar to the magnetization detected by Mössbauer
spectroscopy. Figure 11(a,b) show that there is a substantial magnetization
component in the $z$ direction, perpendicular to the film plane. This can
explain the out-of-plane magnetization component observed by Mössbauer
spectroscopy.

Figure 11: (a) Simulated magnetic moment distribution of an Fe90Ru10 film
after magnetic field along $x$-axis is removed. (b) For the same film, average
projection of normalized magnetic moments along $x$-axis (field direction) and
average absolute value projections along $y$-axis and $z$-axis (film normal)
as a function of applied magnetic field. (c) Simulated normalized $M(H)$
dependence of $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ films ($0\leq x\leq 10$).

In Fig. 11(c), the average projection of the normalized magnetic moments along
the field direction, $\overline{m_{x}}$, is plotted as a function of external
magnetic field for $100\text{\,}\mathrm{n}\mathrm{m}$-thick
$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ films in the concentration range $0\leq
x\leq 10$. These curves correspond with our normalized $M(H)$ curves measured
by VSM. Figure 11(c) shows a decreasing trend in $M_{r}/M_{s}$ with increasing
Ru concentration in Fe that agrees with our measurements in Figs. 7 and 8.
Additionally, Fig. 11(c) shows that a large field is required to fully
saturate the films, as shown in Fig. 8(a). However, the simulated decrease in
$M_{r}/M_{s}$ is much slower than the experimental decrease in $M_{r}/M_{s}$,
and the saturation fields are much larger.

##  VI Conclusion

In summary, we have studied the structural and magnetic properties of sputter-
deposited Fe and $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ films by means of X-ray
diffraction (XRD), transmission electron microscopy (TEM), Mössbauer
spectroscopy, vibrating sample magnetometry (VSM), magneto-optical Kerr effect
(MOKE) microscopy, and and Lorentz transmission electron microscopy (LTEM).
All studied films are polycrystalline, and the
$\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ films, which were grown on a Ta$|$Ru seed
layer, exhibit strong texture along the growth direction. The crystal
structure of the $\mathrm{Fe}_{100-x}\mathrm{Ru}_{x}$ films is predominantly
bcc for $x<13$ and undergoes a gradual transition to hcp in the concentration
range $13\lesssim x\lesssim 20$. Within this transitional range, the films
consist of grains that have fully hcp, fully bcc, and a mixture of hcp and bcc
lattice structures.

While Fe has ferromagnetic order, the addition of Ru introduces a noncollinear
magnetic coupling within bcc FeRu. The noncollinear coupling is attributed to
the competition between ferromagnetic and antiferromagnetic coupling in the
film: ferromagnetic coupling between neighbouring Fe atoms and
antiferromagnetic coupling between Fe atoms separated by Ru atoms. On the
other hand, hcp FeRu was found to be paramagnetic at room temperature.

Thin-film FeRu was recently shown to mediate a large noncollinear interlayer
coupling between two hcp ferromagnetic layers, for Ru concentrations from 20
to $38\text{\,}\mathrm{at.\,\%}$ [18]. Here we show that, for the FeRu
composition range of interest for noncollinear coupling, FeRu maintains hcp
crystal structure. This is important for the epitaxial growth of these
noncollinearly-coupled trilayer structures.

Magnetic multilayer structures used for applications, including magnetic
sensors and magnetic solid state memory, make extensive use of both Fe and Ru
layers. Here we showed that the presence of a small amount of Ru in Fe can
induce noncollinear magnetization alignment between Fe atoms. This can
strongly affect the performance of these devices.

##  VII Acknowledgement

The authors thank Sabri Koraltan for useful discussions, Romy Aniol for TEM
specimen preparation, Afan Terko for plotting Fig. 11, and Dr. Jan Rhensius
and Simon Josephy from QZabre for useful discussions. We acknowledge financial
support from the Natural Sciences and Engineering Research Council of Canada
(NSERC), Fonds Québécois de la Recherche sur la Nature et les Technologies
(FRQNT), and the Austrian Science Fund (FWF) P 34671. The use of the HZDR Ion
Beam Center TEM facilities and the funding of TEM Talos by the German Federal
Ministry of Education and Research (BMBF; Grant No. 03SF0451) in the framework
of HEMCP are also acknowledged.

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