# Pervasive beyond room-temperature ferromagnetism in a doped van der Waals
magnet

Xiang Chen<EMAIL_ADDRESS>Materials Sciences Division, Lawrence
Berkeley National Lab, Berkeley, California 94720, USA  Physics Department,
University of California, Berkeley, California 94720, USA  Yu-Tsun Shao
School of Applied and Engineering Physics, Cornell University, Ithaca, New
York 14853, USA  Rui Chen  Department of Materials Science and Engineering,
University of California, Berkeley, California 94720, USA  Materials Sciences
Division, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
Sandhya Susarla  Department of Materials Science and Engineering, University
of California, Berkeley, California 94720, USA  Materials Sciences Division,
Lawrence Berkeley National Lab, Berkeley, California 94720, USA  Tom Hogan
Quantum Design, Inc., San Diego, CA 92121, USA  Yu He  Department of Applied
Physics, Yale University, New Haven, Connecticut, 06511, USA  Physics
Department, University of California, Berkeley, California 94720, USA
Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley,
California 94720, USA  Hongrui Zhang  Department of Materials Science and
Engineering, University of California, Berkeley, California 94720, USA  Siqi
Wang  NSF Nanoscale Science and Engineering Center (NSEC), 3112 Etcheverry
Hall, University of California, Berkeley, California 94720, USA  Jie Yao
Department of Materials Science and Engineering, University of California,
Berkeley, California 94720, USA  Materials Sciences Division, Lawrence
Berkeley National Lab, Berkeley, California 94720, USA  Peter Ercius  The
Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720,
USA  David A. Muller  School of Applied and Engineering Physics, Cornell
University, Ithaca, New York 14853, USA  Kavli Institute at Cornell for
Nanoscale Science, Cornell University, Ithaca, New York 14853, USA
Ramamoorthy Ramesh  Department of Materials Science and Engineering,
University of California, Berkeley, California 94720, USA  Materials Sciences
Division, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
Physics Department, University of California, Berkeley, California 94720, USA
Robert J. Birgeneau<EMAIL_ADDRESS>Physics Department, University of
California, Berkeley, California 94720, USA  Materials Sciences Division,
Lawrence Berkeley National Lab, Berkeley, California 94720, USA  Department of
Materials Science and Engineering, University of California, Berkeley,
California 94720, USA

###### Abstract

The existence of long range magnetic order in low dimensional magnetic
systems, such as the quasi-two-dimensional (2D) van der Waals (vdW) magnets,
has attracted intensive studies of new physical phenomena. The vdW FeNGeTe2
($N$ = 3, 4, 5; FGT) family is exceptional owing to its vast tunability of
magnetic properties. In particular, a ferromagnetic ordering temperature
($T_{\text{C}}$) above room temperature at $N$ = 5 (F5GT) is observed. Here,
our study shows that, by nickel (Ni) substitution of iron (Fe) in F5GT, a
record high $T_{\text{C}}$ = 478(6) K is achieved. Importantly, pervasive,
beyond-room-temperature ferromagnetism exists in almost the entire doping
range of the phase diagram of Ni-F5GT. We argue that this striking observation
in Ni-F5GT can be possibly due to several contributing factors, including
increased 3D magnetic couplings due to the structural alterations.

##  I Introduction

Spontaneous symmetry breaking is forbidden at non-zero temperatures in
isotropic spin systems with dimensions $d$ $\leq$ 2 [1, 2]. Long range
magnetic order in materials with reduced dimensionality can still be
stabilized via both magnetic anisotropy and weak three-dimensional (3D)
magnetic couplings [3, 4, 5]. In quasi-two-dimensional (quasi-2D) Heisenberg
magnets, such as the van der Waals (vdW) bonded materials, the ordering
process typically occurs as follows [6, 7, 8]. At the highest temperature, the
system is expected to exhibit 2D, classical isotropic magnetic correlations.
As the temperature $T$ is lowered, the correlation length grows exponentially
with $1/T$ and at sufficiently large length scales there is inevitably a
crossover from 2D Heisenberg to 3D Ising or XY behavior followed by a phase
transition to the 3D long range magnetic order. The details of the crossover
depend on the strength of the 3D magnetic interactions and the symmetry and
strength of the magnetic anisotropy. Van der Waals materials represent
exciting realizations of these phenomena plus they contain the broad prospect
of important technological applications [9, 10, 11, 12, 13, 14, 15].

Among the prominent bulk vdW materials for studying quasi-2D magnetism, such
as Cr2Ge2Te6 [16, 17], CrI3 [18, 19], Fe3GeTe2 (F3GT) [20, 21, 22, 23, 24, 25]
and CrTe2 [26, 27], the F3GT system is exceptional owing to the coupling
between the electronic and magnetic degrees of freedom and its remarkable
tunability. The bulk form of F3GT has a ferromagnetic (FM) transition
temperature $T_{\text{C}}$ $\sim$ 230 K, which can be readily enhanced up to
room temperature (RT), by either patterning the microstructure or applying
ionic gating [28, 29]. By intercalating more iron (Fe) into F3GT, $i.e.$,
FeNGeTe2 ($N$=4 for F4GT or 5 for F5GT) [30, 31, 32], the marked effects are
the elevated $T_{\text{C}}$ up to RT and enhanced magnetization while only
moderately increasing the magnetic moment size [30, 32, 33]. The F5GT compound
is particularly interesting because of its advantageous characteristics for
potential RT spintronic applications, including a $T_{\text{C}}$ above RT
($\sim$315 K), large magnetization ($\sim$700 kA/m), strong spin lattice
coupling [32, 33] and exotic magnetic textures [34, 35].

To achieve practical applications of the quasi-2D magnetic materials, one
common theme is to strengthen the FM and enhance the $T_{\text{C}}$ of the vdW
magnets. Some proven avenues to dramatically raise the $T_{\text{C}}$ include
gating [28, 37], applying pressure or strain [38], ion intercalation or
carrier doping [39, 40]. By cobalt (Co) substitution of F5GT, $i.e.$
$({\text{Fe}}_{1-x}{\text{Co}}_{x})_{5+\delta}{\text{GeTe}}_{2}$ (Co-F5GT),
the magnetic ordering temperature is further increased to $\sim$ 360 K, along
with the evolution of the magnetic ground state [41, 42, 36,
Zhang_2022_FCGT_sciadv]. More strikingly, at $x$ = 0.5 of Co-F5GT, a novel
wurtzite-type polar magnetic metal was discovered, along with the
N$\acute{\text{e}}$el-type skyrmion lattice at RT [36,
Zhang_2022_FCGT_sciadv]. The aforementioned discoveries of the F5GT system
highlight its immense tunability and capacity for applications in next-
generation spintronics.

In this letter, we report pervasive, well-beyond-room-temperature FM in the
F5GT vdW magnet with nickel (Ni) substitution, $i.e.$,
$({\text{Fe}}_{1-x}{\text{Ni}}_{x})_{5+\delta}{\text{GeTe}}_{2}$ (Ni-F5GT).
Strikingly, a record high $T_{\text{C}}$ = 478(6) K is reached at a Ni doping
level of $x=0.36(2)$. In addition, the FM order persists robustly against Ni
replacement until $x$ $\sim$ 0.86(1), beyond which only weak paramagnetism
exists. Several factors might be relevant for the dramatic enhancement of the
FM in Ni-F5GT.

Figure 1: (Color online) (a) Illustration of the AA-stacking order of both the
Fe-rich and Ni-rich domains in Ni doped Fe5GeTe2 (Ni-F5GT) (Green symbols: Fe;
Orange: Ni; Purple: Te; Blue: Ge) [43]. (b) The (0 0 L) type of peaks of
Ni-F5GT at select Ni doping levels $x$. (c) Effective layer spacing $d$ as a
function of Ni doping (colored symbols) or Co doping (gray symbols, [36]) in
Fe5+δGeTe2. Vertical dashed lines indicate different regions in Ni-F5GT.

The Ni-F5GT single crystals were grown by the chemical vapor transfer method
[32, 33, 43]. The exact Ni doping level $x$ and total cation count per formula
unit ($f.u.$) $5+\delta$ were verified by energy-dispersive X-ray spectroscopy
(EDX/EDS) (Fig. S1). The lattice and atomic structure of Ni-F5GT were
investigated by a combination of techniques, including powder and/or single
crystal x-ray diffraction (XRD) and high-angle annular dark-field scanning
transmission electron microscopy (HAADF-STEM). Magnetization measurements were
performed via a commercial Quantum Design MPMS3.

Figure 2: (Color online) Nanoscale phase separation of Ni-F5GT at $x$ =
0.36(2). (a) Energy-dispersive X-ray spectroscopy map showing both the Fe-rich
(green) and Ni-rich (red) regions. (b)-(d) Atomic resolution HAADF-STEM image
demonstrating the two types of domains. The enlarged (c) Fe-rich and (d) Ni-
rich domains show flat and rumpled atomic planes, respectively. The Te-Te
planes in (b) are color-coded based on the number and the rumpling of the
atomic layers. Scale bars in (c)-(d), 5 Å.

The unit cell of F5GT is composed of three identical layers (stacks) with the
rhombohedral layer stacking (space group R$\bar{3}$m), labelled as ABC-
stacking [32]. Upon introducing Ni into F5GT, such as at $x$ = 0.19(1), the
crystal structure undergoes a transition from ABC-stacking to AA-stacking
(space group P$\bar{3}$m1, illustrated in Fig. 1(a)), as confirmed by single
crystal XRD (Fig. S2). The AA-stacking order is also verified by HAADF-STEM
images at other doping levels (Fig. 2 and Fig. S5). When viewed along the [1 1
0] direction, the identical layers stack exactly on top of each other along
the $c$ direction and are separated by a vdW spatial gap. Within each layer
(stack), the center germanium (Ge, blue symbols) atom is surrounded by three
different sites of iron (Fe1, Fe2 and Fe3, green) atoms which are further
protected by the outer Te (purple) atoms, $i.e.$, forming a Te-Fe1-Fe3-Fe2-Ge-
Fe2-Fe3-Fe1-Te plane-like (labelled as TGT-$plane$) structure.

With increasing Ni doping in Ni-F5GT, the excess cation count $\delta$
gradually increases from $\delta\sim$ 0 at $x$ = 0 to $\delta$ $\sim$ 0.5 at
$x$ $\sim$ 0.3 (labelled as region (I) with 0 $\leq$ $x$ $\leq$ 0.3), and
saturates when $x$ $>$ 0.3 (Fig. S1). Interestingly, in the intermediate
doping range 0.36(2) $\leq$ $x$ $\leq$ 0.86(1) (region (II)), although the
sample still maintains the AA-stacking, two types of domains coexist, as
evidenced from the splitting of the (0 0 $L$) peaks from the XRD measurements
(Fig. 1(b)), the direct atomic visualization from the HAADF-STEM images (Fig.
2 and Fig. S5) and the STEM-EDX maps (Fig. 2 and Fig. S4). As an example at
$x$ = 0.36(2) (Fig. 2 and illustrated in Fig. 1(a)), the two types of domains
correspond to Fe-rich domains (Fig. 2(c)) and Ni-rich domains (Fig. 2(d)),
respectively. In the Fe-rich domains, the TGT-$planes$ are almost flat and
more extended in space; while the TGT-$planes$ are rumpled in the Ni-rich
domains. Because of the contrasting local atomic arrangements of the Fe and Ni
atoms within the TGT-$planes$, the effective layer spacing $d$ of either the
Fe-rich or Ni-rich domain shows a strong deviation from the value at $x$ = 0
(Fig. 1(c)). This strong alteration may have a dramatic impact on the
electronic and/or magnetic properties of Ni-F5GT.

While the Ni-F5GT samples are still metallic (Fig. S6), the magnetic
properties are strongly influenced by Ni substitution (Fig. 3 and Fig. S7).
With moderate Ni replacement, the $T_{C}$ of Ni-F5GT is already considerably
enhanced (Figs. 3(a)-3(b)). For instance, at $x$ = 0.19(1), the experimentally
determined $T_{C}$ = 395(6) K already approaches 400 K (Fig. 3(a)). Meanwhile,
the Ising spin moment switches to the in-plane direction and seems to remain
so until $x$ $\sim$ 0.86(1) (Fig. 3(e) and Fig. S7). Upon further increasing
the Ni content, a record high $T_{C}$ $=$ 478(6) K is achieved at $x$ =
0.36(2), together with the maximum in-plane ($H_{C}^{ab}$ $\approx$ 500 Oe)
and out-of-plane ($H_{C}^{c}$ $\approx$ 1600 Oe) coercive fields (Figs. 3(c),
3(f) and Fig. S7). After reaching the maximum $T_{C}$ in Ni-F5GT, the FM order
is only gradually weakened by further Ni doping. Strikingly, even at $x$ =
0.86(1), the as-grown sample of Ni-F5GT maintains an above-room-temperature
$T_{C}$ $\approx$ 380 K, which is only lowered and stabilized at 220 K or 150
K, depending on how the sample is thermally cycled above its original $T_{C}$
(Fig. S8). Only beyond this point of further Ni replacement (0.86(1) $<$ $x$
$\leq$ 1, region (III)), the FM order of Ni-F5GT is completely suppressed,
rendering the weak paramagnetism, accompanied by the adoption of a different,
layered tetragonal structure (space group I4/mmm) as Ni5.5GeTe2 [44].

The saturation magnetic moment per $f.u.$ of Ni-F5GT at 2 K decreases
approximately linearly with increasing Ni content (Figs. 3(c),(e) and Fig.
S7), from $\sim$10 $\mu_{B}$/$f.u.$ at $x$ = 0 to nearly zero (weakly
paramagnetic) at $x$ = 1. This implies that the Ni dopants are not magnetic
and only dilute the FM in Ni-F5GT. Surprisingly, the magnetic ordering
temperature $T_{C}$ does not follow this expected trend (Fig. 4). Instead,
pervasive, above-room-temperature FM exists almost over the entire range of
the phase diagram (0 $\leq$ $x$ $\leq$ 0.79(1)). Particularly, in region (I)
of the phase diagram of Ni-F5GT, the $T_{C}$ shows a strong, positive
deviation from the Vegard’s Law behavior ($i.e.$, a dilution of the magnetic
component), thus suggesting additional factors might be present for the
unusual evolution of $T_{C}$. Our study demonstrates the remarkable Ni
enhanced FM in Ni-F5GT, as summarized in Fig. 4, where three different regions
are categorized based on the structural and magnetic characterization.

Figure 3: (Color online) Magnetization data of Ni-F5GT at select Ni doping
level $x$. (a)-(b) Temperature dependent magnetization of Ni-F5GT (external
in-plane magnetic field is 50 Oe). For clarity, the magnetization data at $x$
= 0.97(1) and $x$ = 1 are multiplied by 200 and 2000, respectively. (c)-(d)
In-plane isothermal magnetization at $T$ = 2 K (c) and $T$ = 400 K (d),
respectively. (e) Saturation moment per formula unit at 2 K under the magnetic
field of 7 T. (f) Coercive fields extracted from the isothermal magnetization
at $T$ = 2 K. In (e)-(f), the magnetic field is applied along the $ab$-plane
(red symbols) or $c$-direction (green symbols).

The unique feature of Ni-F5GT is the immense impact on the lattice and
magnetism by Ni substitution, including the radical change of the layer
spacing $d$ (Fig. 1(c)) and the local atomic arrangements (Fig. 1(a), Fig. 2,
Figs. S2-S5), as compared to F5GT or Co-F5GT [32, 36]. It is evident that the
change of the layer spacing $d$ in Ni-F5GT is significantly more pronounced
than its evolution in Co-F5GT. Importantly, the layer spacing $d$ of the Fe-
rich domains (green symbols in Fig. 1(c)) closely tracks the evolution of
$T_{\text{C}}$ in Ni-F5GT at 0 $\leq$ $x$ $\leq$ 0.86(1) (Fig. 4). This is
supported by the experimental observation that the Fe-rich domains maintain
the AA-stacking order with the straight-and-flat TGT-$planes$ over a broad Ni
doping range 0 $<$ $x$ $\leq$ 0.86(1) and thus may be mainly responsible for
the robust FM in Ni-F5GT. The Ni dopants are also indispensable for donating
electrons to the system and forming the Ni-rich domains in region (II), which
help preserve the Fe-rich domains. This phase separation in region (II)
naturally explains the domain pinning enhanced coercive fields (Fig. 3(f)).
Meanwhile, the preserved Fe-rich domains maintain the robust $T_{C}$ of
Ni-F5GT in this region.

Our work on Ni-F5GT reveals a complicated yet intriguing system, in which the
lattice, electronic and magnetic degrees of freedom are closely intertwined.
To understand the enhancement of FM in Ni-F5GT, especially the region (I)
(Fig. 4), it is necessary to consider the possible effects of both electron
doping and structural alteration by Ni replacement. Carrier doping is often
seen to be detrimental to the correlation induced long range magnetic order,
as recognized in the unconventional superconductors, such as the cuprates and
iron pnictides [45, 46]. For the itinerant FM, charge doping can, in some
cases, help meet the Stoner criterion and actually promote magnetic order
[47]. The related F3GT system, which may also apply to F5GT, has both
itinerant and localized spin moment contributions to the magnetism [21, 23,
28, 24, 25, 48, 49]. Hence, the ordering temperature of F3GT can be elevated
by electrostatic gating of its thin layer form [28, 37]. In Ni-F5GT, the
electrons provided by the Ni dopants may greatly influence the electronic band
structure and the density of states (DOS) near the Fermi level
($E_{\text{F}}$). Alternatively, the magnetic exchange coupling $J_{i,j}$
between spins $\boldsymbol{S}_{i}$ and $\boldsymbol{S}_{j}$ on sites $i$ and
$j$, might also be altered via the Ruderman–Kittel–Kasuya–Yosida (RKKY)
exchange since the electronic structure is likely altered substantially by Ni-
doping [28, 25, 50, 51]. All together, the itinerant FM might also be enhanced
by electron doping in Ni-F5GT.

Now focusing on the localized spin moments and considering a simple Heisenberg
model with a weak magnetic anisotropy, in which the magnetic contributions
from the itinerant FM can also be effectively mapped into the Hamiltonian [52,
28]:

$H=\sum_{\begin{subarray}{c}i<j\end{subarray}}J_{i,j}\boldsymbol{S}_{i}\cdot\boldsymbol{S}_{j}-\sum_{\begin{subarray}{c}i\end{subarray}}A(S_{i}^{z})^{2}$
(1)

Here, $A$ is the single-ion anisotropy ($A$ $>$ 0 for Ising spin moment).
Since $A$ is small and close to zero in Ni-F5GT [33], a mean-field treatment
results in the magnetic transition temperature [28, 12]:

$T_{C}=\frac{S(S+1)}{3k_{B}}({z_{nn}}J_{nn}+...)$ (2)

where $z_{nn}$ is the coordination number of the nearest neighbouring sites,
$S$ is the magnetic spin quantum number and $J_{nn}$ the nearest-neighbour
exchange coupling. On the mean-field level, a larger $z_{nn}$ or $J_{nn}$
promises a larger $T_{C}$. Perhaps, this is why the ordering temperature in
FeNGeTe2 is quickly increased from $T_{C}$ $\sim$ 230 K at $N$ = 3 to $T_{C}$
$\sim$ 317 K at $N$ = 5 [20, 21, 30, 32, 33]. In Ni-F5GT, since the average
magnetic moment per Fe is almost unchanged and the in-plane FM indicates a
small yet negative $A$ (Fig. 3(e) and Fig. S7), hence neither $S$ nor $A$ is
responsible for the enhancement of the FM. However, the structural alterations
may affect both $z_{nn}$ and $J_{i,j}$, and therefore are strong candidates
for explaining the further enhanced $T_{C}$.

Firstly, a small increment of $\delta$ is observed for lightly Ni doped F5GT
(region (I) in Fig. 4 and Fig. S1). One direct consequence is the larger site
occupancy of the Fe1 site, which is up to $\sim$75$\%$ at $x$ $\sim$ 0.3 as
compared to a maximum of $\sim$50$\%$ at $x$ = 0. Considering that the Fe1-Fe3
bond length is the shortest among all of the direct Fe-Fe bonds (Fig. S3), the
Fe1 site might be critical for determining the $T_{C}$ in Ni-F5GT. Therefore,
a larger $\delta$, which implies a greater $z_{nn}$ of the Fe1 site, might
promote a higher $T_{C}$ (Eqn. (2)). Secondly, with more Ni substitution in
region (I), the explicit effect is that the TGT-$planes$ of the Fe-rich
domains are becoming more flat and extended in space (Fig. 2(c), Fig. S3,
Figs. S5(c),(e)). Microscopically, other than the small spatial re-
arrangements of the Fe2 and Fe3 sites, it is the Fe1 site that is becoming
increasingly distant from the Fe3 site along the $c$ direction while keeping
the Fe-Fe bond lengths nearly unchanged (Fig. S3). This explains the
enlargement of the layer spacing $d$ (Fig. 1(c)), which positively correlates
with the $T_{C}$ in Ni-F5GT. Understandably, the intralayer and interlayer
exchange coupling, especially these related to the Fe1 site, might be
effectively strengthened, which render the 3D magnetic interactions stronger
and eventually lead to the enhancement of $T_{C}$ in Ni-F5GT.

Figure 4: (Color online) Ni doping level $x$ dependent $T_{C}$ in Ni-F5GT.
Empty symbols: $T_{C}$ for as-grown samples; solid symbols: $T_{C}$ after
thermal cycling. Vertical dashed lines indicate different regions in Ni-F5GT.

In summary, our work reveals a new arena for studying the vdW magnetic metals
with strong room temperature ferromagnetism. A record high ferromagnetic order
with a $T_{C}$ $=$ 478(6) K is realized in Ni-F5GT at $x$ = 0.36(2). Albeit
with the non-magnetic dilution, several factors are speculated to assist the
pervasive, well-above-room-temperature FM in Ni-F5GT. Candidate contributors
include the increased site occupancy, structural modifications altered
magnetic exchange couplings and the electron doping effect. Clearly, as
stated, these ideas are purely speculative and require much more thorough
investigation. Although further research is needed to understand fully the
mechanism of the enhanced magnetism, our study highlights that the Ni-F5GT
system is an extremely rare example of strongly enhanced ferromagnetism, in
spite of the detrimental factors such as the non-magnetic dilution and
electron doping effects introduced by Ni dopants. In addition, Ni-F5GT offers
unique or alternative avenues towards enhanced coercivity, varying length
scale of phase separation, thermal cycling influenced $T_{C}$ and potential
relevance to skyrmionics in F5GT and other related vdW magnets [41, 42, 36,
Zhang_2022_FCGT_sciadv].

X.C. wishes to thank Nicholas S. Settineri and Weiwei Xie for some single
crystal XRD measurement and acknowledge the Applications Group at Quantum
Design for their contribution of high temperature (300-600 K) magnetization
measurements to this work. Work at Lawrence Berkeley National Laboratory was
funded by the U.S. Department of Energy, Office of Science, Office of Basic
Energy Sciences, Materials Sciences and Engineering Division under Contract
No. DE-AC02-05-CH11231 within the Quantum Materials Program (KC2202). Y.T.S.,
H.Z. and D.A.M acknowledge financial support from the Department of Defense,
Air Force Office of Scientific Research under award FA9550-18-1-0480. R.C. and
J.Y. acknowledge the support by Intel Corporation under an award titled
Valleytronics center. The electron microscopy studies were performed at the
Cornell Center for Materials Research, a National Science Foundation (NSF)
Materials Research Science and Engineering Centers program (DMR 1719875). The
microscopy work at Cornell was supported by the NSF PARADIM DMR-2039380, with
additional support from Cornell University, the Weill Institute and the Kavli
Institute at Cornell. S.S. acknowledges the help from Dr. Rohan Dhall and is
supported by the Quantum Materials Program under the Basic Energy Sciences,
Department of Energy. The microscopy work was performed at Molecular Foundry
that is supported by the Office of Science, Office of Basic Energy Sciences,
of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The
devices for transport measurements were fabricated in the UC Berkeley Marvell
Nanofabrication Laboratory.

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