PHYSICAL REVIEW B
110
, 144419 (2024)
Pressure induced Invar effect in Fe
55
Ni
45
: An experimental study with nuclear resonant scattering
P. Guzman
,
*
S. H. Lohaus
, C. M. Bernal-Choban
, and B. Fultz
California Institute of Technology
, Pasadena, California 91125, USA
J. Y. Zhao, G. Shen, M. Y. Hu
, and E. E. Alp
Advanced Photon Source
, Argonne National Laboratory, Argonne, Illinois 60439, USA
B. Lavina
Center for Advanced Radiation Sources, The
University of Chicago
, Chicago, Illinois 60637, USA
and
Advanced Photon Source
, Argonne National Laboratory, Argonne, Illinois 60439, USA
(Received 1 March 2024; revised 9 September 2024; accepted 20 September 2024; published 11 October 2024)
Pressure-dependent synchrotron x-ray diffraction (XRD), nuclear resonant inelastic x-ray scattering (NRIXS),
and nuclear forward scattering (NFS) measurements were made on
57
Fe
55
Ni
45
. XRD measurements were at 298
and 392 K at pressures up to 20 GPa, confirming a pressure-induced Invar effect between 7 and 13 GPa. A
decrease of the
57
Fe magnetic moment was found in NFS measurements under pressure, showing an increase in
magnetic entropy. The
57
Fe phonon density of states (DOS) was obtained from NRIXS measurements. The low
thermal expansion in the high-pressure Invar region originates from a competition between the thermal expansion
from spins and phonons as calculated from Maxwell relations. The longitudinal phonon modes changed their
pressure dependence near the Curie transition, which is evidence for a spin-phonon interaction.
DOI:
10.1103/PhysRevB.110.144419
I. INTRODUCTION
A. Invar effect
ThefccalloyFe
64
Ni
36
exhibits the classic Invar effect,
where its thermal expansion is nearly zero at ambient con-
ditions. In 1920, Charles-Édouard Guillaume was awarded
the Nobel Prize “in recognition of the service he has ren-
dered to precision measurements in Physics by his discovery
of anomalies in nickel steel alloys” [
1
–
3
]. Invar alloys of
Fe
64
Ni
36
have long been used for precision instruments and
devices that maintain their dimensional stability over a range
of temperatures [
4
].
Guillaume found that the Invar effect was lost for nonmag-
netic states of the material, and understood that there was a
role for magnetism in thermal expansion to counteract the
expected positive thermal expansion of the alloy. Recently,
the phonon and magnetic contributions to thermal expansion
in Invar were isolated, and shown to cancel [
5
]. Furthermore,
interactions between spins and phonons were shown to extend
the range of pressures for near-zero thermal expansion in
Fe
65
Ni
35
from 0 to 3 GPa (the Curie pressure was reported
to be 4.6 GPa). Invar behavior has been reported in other sys-
tems such as Fe-Pt, Fe-Co, Ni-Mn, and hcp Gd [
6
–
14
]. Many
amorphous materials containing iron show Invar anomalies at
ambient pressure. References [
4
,
15
–
19
] provide a thorough
review of experimental and theoretical work on the Invar
problem.
Both lattice dynamics and magnetism are changed with
pressure. Under pressure, it was reported that Invar behavior
*
Contact author: pgguzman@caltech.edu
develops in Fe
55
Ni
45
,Fe
20
Ni
80
, and Pd
3
Fe [
20
–
22
], and ef-
fects of pressure on materials with the ambient Invar effect
have been investigated in numerous previous studies [
23
–
40
].
Here we present a study of the pressure-induced Invar
effect in Fe
55
Ni
45
, first reported in 2001 [
20
]. By comparing
x-ray lattice parameters from samples in a diamond-anvil cell
at two temperatures, we found an anomalous thermal expan-
sion occurring at pressures between 7 and 13 GPa. Nuclear
forward scattering (NFS) showed that a Curie transition in
Fe
55
Ni
45
occurs at 13 GPa in pressure, so there should be
an increase in spin disorder and magnetic entropy just below
this pressure. From [
41
] it is known that the Curie temper-
ature of Fe
55
Ni
45
is 700 K. Nuclear resonant inelastic x-ray
scattering (NRIXS) was used to measure the partial phonon
density of states (DOS) of
57
Fe atoms. The NRIXS spec-
tra showed an arrest in the increase of longitudinal phonon
modes between 7 and 13 GPa, but the average phonon en-
tropy decreased as the frequencies of other phonons increased
with pressure. The decrease of phonon entropy counteracted
precisely the pressure-dependence of the magnetic entropy,
which increased from spin disorder as the Curie transition
was approached. A Maxwell relation shows that magnetism
and phonons therefore have canceling contributions to ther-
mal expansion near 10 GPa. The behavior is similar to
what was observed below the Curie pressure in Fe
65
Ni
35
[
5
] at pressures up to 3 GPa. The arrest of the longitudinal
phonon frequencies is interpreted as evidence of spin-phonon
interactions.
Finally, the alloy Fe
55
Ni
45
is known as “Elinvar” because
it has no change of its elastic constants at temperatures near
ambient. We show in the Supplemental Material [
42
] that the
Elinvar behavior occurs at low pressures, but the NRIXS and
2469-9950/2024/110(14)/144419(8)
144419-1
©2024 American Physical Society
P. GUZMAN
et al.
PHYSICAL REVIEW B
110
, 144419 (2024)
NFS measurements were not sufficiently precise to pinpoint
its thermodynamic origins.
B. Thermophysics of thermal expansion
The fractional change in volume
V
with temperature
T
is
the volume coefficient of thermal expansion,
β
:
β
=
1
V
(
∂
V
∂
T
)
P
.
(1)
The phonon and spin contributions to the thermal expansion
can be found experimentally by use of a thermodynamic
Maxwell relation [
5
]
(
∂
V
∂
T
)
P
=−
(
∂
S
∂
P
)
T
,
(2)
so
β
can expressed as
β
=−
1
V
(
∂
S
∂
P
)
T
.
(3)
The entropy is dominated by vibrational and magnetic degrees
of freedom (the pressure dependence of the electronic contri-
bution was found to be negligible [
5
]):
β
=−
1
V
[(
∂
S
ph
∂
P
)
T
+
(
∂
S
mag
∂
P
)
T
]
.
(4)
The contribution of phonons is measured through nuclear
resonant inelastic x-ray scattering (NRIXS), while the con-
tribution of spins is measured through nuclear forward
scattering (NFS).
II. EXPERIMENT
A. Sample preparation
The Fe
55
Ni
45
alloy was prepared by arc melting high-
purity Ni (99
.
99%) and enriched 95
.
73%
57
Fe (from Isoflex)
under an argon atmosphere. (The intensities of NRIXS and
NFS spectra are increased by enriching with the
57
Fe isotope,
which has a natural abundance of only 2
.
2%.) Foil samples
of 15–20 μm thickness were prepared by cold rolling the
arc-melted ingots, and subsequently annealing at 600
◦
Cfor
12 h in vacuum-sealed quartz ampoules. X-ray diffractom-
etry (XRD) was used to confirm the fcc crystal structure
of Fe
55
Ni
45
.
Pieces of approximately 50
×
50 μm square were cut from
the samples and loaded into diamond anvil cells (DACs) for
in situ
experiments with NRIXS, NFS, and XRD. The DACs,
symmetric-type and panoramic cells, were loaded with pres-
sure transmitting helium using the COMPRES-GSECARS
gas loading system [
43
] as the pressure medium to better
ensure hydrostatic pressures at the sample. Beryllium gaskets
were used for NRIXS and NFS to minimize the absorption of
x-ray and
γ
-ray signals emitted from the samples. Holes were
drilled in the Be gaskets by laser micromachining system to
create a sample chamber, using facilities at sector 16 (High-
Pressure Collaborative Access Team) of the Advanced Photon
Source (APS) [
44
]. To determine the pressure inside the sam-
ple chamber, two ruby spheres were placed near the sample,
and a Raman spectrometer was used to measure and analyze
their optical fluorescence spectra. The pressure reported is the
average of the two ruby spheres.
B. Synchrotron measurements
The small size of the x-ray beam at the APS allows for
measurements on small samples under controlled pressures in
DACs. XRD patterns at multiple pressures were measured at
beamline 16-BMD (HPCAT) of the APS. The symmetric-type
DACs with samples loaded were placed directly in the beam
path for measurements at room temperature (RT
295 K)
and in a heating block for measurements at 392 K. Lattice
parameters were determined from the (111) diffraction peaks,
which gave the strongest intensities and most consistent peak
shapes. Peak centers were determined by fitting these peaks to
Gaussian functions. Fe
55
Ni
45
has a cubic structure, so the unit
cell volume was obtained from the lattice parameter cubed.
Peak centers were used to quantify how the unit cell volume
changed with pressure, and how the material expanded with
an increase in temperature of 97 K.
The partial phonon densities of states (DOS) of
57
Fe were
obtained by NRIXS measurements at beamline 3 ID-B of
the APS at Argonne National Laboratory. The NRIXS spec-
tra were collected with three avalanche photodiode detectors
positioned at the side openings of the panoramic DACs, per-
pendicular to the incident x-ray beam. The NRIXS spectra
were acquired by scanning the energy of the incident beam
across the nuclear resonance of
57
Fe at 14.41 keV [
45
].
The energy resolution of the inelastic spectra was approx-
imately 1.1 meV with the high-resolution monochromator.
The
PHOENIX
software package [
46
] was used to remove
the resonant elastic peak at 14.41 keV, subtract the back-
ground, and correct for multiphonon scattering to get the
DOS of
57
Fe.
The pressure dependence of the
57
Fe hyperfine magnetic
field (HMF) of
57
Fe
55
Ni
45
was obtained by NFS measure-
ments, also performed at beamline 3 ID-B of the APS. NFS
measures the time beats that arise from interferences between
γ
-ray emissions of different
57
Fe nuclei during their transi-
tions from excited to ground states [
45
]. These time beats are
superimposed on an exponential decay from the lifetime of
the excited state. The
CONUSS
software package [
46
] was used
to analyze the beat patterns by fitting with two asymmetrized
Gaussians. The mean HMF at each pressure was determined
as the average of this model HMF distribution.
III. RESULTS
A. X-ray lattice parameter, NRIXS, and NFS
Figure
1
shows the unit cell volume from x-ray lattice
parameter data as a function of pressure and temperature.
At pressures below 3 GPa, the curvatures of the unit cell
volume as a function of pressure, which is inversely related
to the bulk modulus, are similar between RT and 392 K. An
analysis on the curvature of the unit cell volume as a function
of pressure is discussed in the Supplemental Material [
42
]. At
pressures between 7 and 13 GPa, the unit cell volume shows
no detectable thermal expansion between RT and 392 K.
At pressures below 7 GPa and above 13 GPa, however, the
volume increases with temperature, becoming a more typical
144419-2
PRESSURE INDUCED INVAR EFFECT IN ...
PHYSICAL REVIEW B
110
, 144419 (2024)
FIG. 1. Pressure dependence of the unit cell volume of
Fe-45%Ni at RT (filled circles) and 392 K (open circles). Inset:
Pressure dependence of the coefficient of thermal expansion (CTE)
measured by XRD. A pressure induced Invar effect is observed
between 7 and 13 GPa (shaded area).
β
=
3
×
10
−
5
K
−
1
. Figure
1
inset shows the coefficient of
thermal expansion calculated with Eq. (
1
) between RT and
392 K. A spline interpolation was used to determine the
difference between the unit cell volumes as a function of
pressure at RT and 392 K.
The NRIXS and NFS spectra were collected consecutively
under the same experimental conditions from the same sam-
ple. Figure
2
shows phonon DOS curves measured by NRIXS
at pressures up to 24 GPa. These spectra show a general in-
crease in energy with increasing pressure. The vertical dashed
line is a reference that shows how there is little change in the
center of the peak from longitudinal phonon modes between
7.2 and 12.8 GPa. Pairs of DOS curves, shown in the Supple-
mental Material [
42
], show this same trend.
Figure
3
shows the NFS spectra at different pressures.
Clear magnetic beat patterns are seen at pressures below
14.9 GPa. The beats spread apart in time as the HMF is
reduced by increased pressure. Values of the HMF were ob-
tained from the
CONUSS
fits shown as the solid lines in Fig.
3
.
This trend is caused by a reduction in HMF with pressure,
which is shown in Fig.
4
.
B. Phonon entropy
The NRIXS method is an incoherent scattering that pro-
vides the phonon spectrum of the solid projected onto the
resonant
57
Fe nuclei. Contributions from the other atoms in
an alloy are not directly measured in an NRIXS spectrum,
and this might be a concern in obtaining a thermodynamic
vibrational entropy from an alloy if the other elements differed
in their vibrational spectra. Fortunately, a prior study com-
pared the inelastic spectra from NRIXS to inelastic neutron
scattering spectra of Fe-Ni alloys showed that the phonon
partial DOS of Ni and Fe have the same shape [
47
]. For
Fe
55
Ni
45
, the total phonon DOS is therefore the same as that
obtained by NRIXS. This was also confirmed in recent report
[
5
] by comparing spectra from inelastic neutron scattering
FIG. 2. Pressure dependence of the
57
Fe DOS of Fe-45%Ni
obtained by
PHOENIX
software from NRIXS measurements at RT.
The black vertical line is fixed at the average of the peak posi-
tion of the longitudinal modes from the 9.2 and 11.1 GPa DOS
curves. The maximum of the longitudinal mode for each DOS curve
is shown by the blue vertical dashed line. Error bars are shown
in black.
and NRIXS for Fe
64
Ni
36
. The phonon entropy,
S
ph
, is then
determined from the phonon DOS,
g
(
), as [
48
]
S
ph
=
3
k
B
∫
∞
0
g
(
)[(1
+
n
,
T
)ln(1
+
n
,
T
)
−
n
,
T
ln
n
,
T
]
d
,
(5)
where
is the phonon energy, and
n
,
T
=
1
/
[exp(
/
k
B
T
)
−
1] is the Planck distribution for phonon occupancy. Figure
5
shows the pressure dependence of the
S
ph
(
P
) obtained from
Eq. (
5
) with the phonon DOS data of Fig.
2
. The curve of
S
ph
(
P
)vs
P
is nearly linear. Subtle deviations from linearity
are observed in the range of 7 to 13 GPa, corresponding to the
range of the pressure-induced Invar effect.
C. Magnetic entropy
Figure
4
shows the average
57
Fe HMF as a function of
pressure, obtained from
CONUSS
fits to the NFS spectra. The
HMF is proportional to the magnetic moment of Fe atoms
[
49
], so Fig.
4
shows that pressure causes the magnetization to
decrease, and magnetization is lost above the Curie pressure
144419-3
P. GUZMAN
et al.
PHYSICAL REVIEW B
110
, 144419 (2024)
FIG. 3. Pressure dependence of the time signal of Fe
55
Ni
45
mea-
sured with NFS at RT, with
CONUSS
fits (blue solid curves) to the beat
patterns.
of 13 GPa. The magnetization
M
(
P
) and the magnetic entropy
S
mag
were determined from the data of Fig.
4
as in [
50
],
which used a mean-field model with spin disordering that
FIG. 4. Pressure dependence of the HMF in Fe
55
Ni
45
quantified
from NFS with
CONUSS
measured at RT.
FIG. 5. Pressure dependence of the vibrational entropy (squares),
magnetic entropy (triangles), and their sum (circles) obtained from
NRIXS and NFS measured at RT. The shading marks the pressure
induced Invar region. The dashed vertical line marks the Curie pres-
sure.
S
mag
and
S
sum
was determined with
S
T
mag
from [
41
]. The
S
∗
mag
and
S
∗
sum
were determined with
S
T
mag
from [
5
].
corresponds to the decreasing magnetization
M
(
P
):
S
mag
(
P
)
=−
S
T
mag
2ln2
[
[1
+
M
(
P
)] ln
(
1
+
M
(
P
)
2
)
+
[1
−
M
(
P
)] ln
(
1
−
M
(
P
)
2
)
]
.
(6)
This model does not include magnetic short-range order, and
is therefore valid only below the Curie temperature (
T
C
). The
change in magnetic entropy from RT to
T
C
(
S
T
mag
) is obtained
from the magnetic heat capacity, and is used to calibrate the
change in entropy below the Curie pressure in Eq. (
6
). It was
found in previous experimental studies on fcc Fe-Ni alloys
that, for concentrations greater than 44.7% Ni, a significant
and inseparable contribution to the specific heat is caused by
heat evolution from chemical short-range ordering [
41
]. It was
suggested that it is impractical to extract the magnetic heat
capacity from the specific heat for Fe-Ni alloys with Ni con-
centrations of 44.7% or greater due to chemical short-range
ordering. To obtain
S
T
mag
for Fe
55
Ni
45
, we averaged the specific
heat data for Fe
61.1
Ni
38.9
and Fe
66.2
Ni
33.8
from [
41
] because
their heat capacities were not influenced by atomic ordering.
S
T
mag
=
0
.
128
k
B
/
atom was obtained for
S
T
mag
by averaging
the specific heats of 38.9% Ni and 33.8% Ni and reducing
the average in proportion to the reduced amount of iron in
our material. This 0.128
k
B
/
atom result is comparable to the
value of
S
T
mag
=
0
.
086
k
B
/
atom reported in [
5
], again after
scaling their reported value for the iron concentration. The
change in entropy below the Curie pressure resulting from
the decrease in magnetization as determined from Eq. (
6
)is
shown in Fig.
5
, for both values of
S
T
mag
.
It is known from [
5
,
51
,
52
] that the magnetic structure in
Fe rich fcc Fe-Ni alloys is dominated by the Fe atoms, with
only a minor contribution from Ni. From [
52
,
53
] we know
that pressure has a minor influence on the alignment of the Ni
144419-4
PRESSURE INDUCED INVAR EFFECT IN ...
PHYSICAL REVIEW B
110
, 144419 (2024)
FIG. 6. Pressure dependence of the coefficient of thermal expan-
sion (CTE) from the individual contributions of phonons (squares),
magnetism (triangles), and their sum (circles) to Eq. (
4
). The shaded
area represents the range of the pressure induced Invar effect. The
dashed vertical line marks the Curie pressure.
β
mag
and
β
sum
were
determined with
S
T
mag
from [
41
].
β
∗
mag
and
β
∗
sum
were determined with
S
T
mag
from [
5
].
magnetic moments, and contributes minimally to the magnetic
entropy. Therefore, the change in magnetic entropy under
pressure
S
mag
(
P
)ofFig.
5
from NFS accounts for nearly
all the change in magnetism in Fe
55
Ni
45
.
IV. DISCUSSION
Figure
5
shows the phonon entropy
S
ph
(
P
), the change
in magnetic entropy
S
mag
(
P
), and their sum,
S
sum
(
P
). Be-
tween the pressures of 7 and 13 GPa,
S
sum
(
P
) is a nearly
constant. This pressure range is the region of low thermal ex-
pansion observed by synchrotron XRD under pressure (Fig.
1
inset). The separate contributions to thermal expansion (
β
)
from phonons, spins, and their sum are shown in Fig.
6
.
Below 7 GPa,
β
ph
(
P
) is approximately
+
3
×
10
−
5
K
−
1
and
β
mag
(
P
) is negligible. This is again the case for pressures
greater than 13 GPa. From 7 to 13 GPa, the magnitude of
β
ph
(
P
) remains approximately constant, but
β
mag
(
P
) increases
to
−
3
×
10
−
5
K
−
1
. This cancellation of
β
ph
(
P
) from phonons
and
β
mag
(
P
) from magnetism accounts for the low thermal ex-
pansion in the range of the pressure-induced Invar effect. The
magnetic entropy changes most rapidly with pressure just be-
low the Curie pressure, contributing to the thermal expansion
by Eq. (
4
). At pressures above the Curie transition, and well
below, phonons are the main source of thermal expansion.
Figure
7
shows the coefficient of thermal expansion (CTE)
from synchrotron XRD measurements under pressure, com-
pared to the CTE derived from the contributions of phonons
and magnetism from Eq. (
4
). The agreement between the
two independent methods for determining the pressure de-
pendence of thermal expansion is good, with the largest
discrepancy being caused by uncertainty in the magnetic en-
tropy of the Curie transition.
The phonon entropy of Fig.
5
,
S
ph
, is nearly monotonic
with pressure. Figure
2
shows there is an overall stiffening of
FIG. 7. Pressure dependence of the coefficient of thermal ex-
pansion (CTE) from the individual contributions of phonons and
magnetism (circles) compared to the measured CTE by synchrotron
XRD (diamonds) Shading marks the region of the pressure-induced
Invar effect. The dashed vertical line marks the Curie pres-
sure.
β
NRIXS
+
NFS
was determined with
S
T
mag
values from [
41
]and
β
∗
NRIXS
+
NFS
was determined with
S
T
mag
values from [
5
].
the phonon DOS at all pressures. Through the Curie transition,
the lower-energy transverse modes continue to stiffen with
pressure, although these changes are small. Changes in the
phonon DOS near the Curie pressure, when the magnetization
is changing rapidly, are an indication of a spin-phonon inter-
action. Specifically, in the pressure range of 7.2 to 12.8 GPa,
the position of the peak from the longitudinal modes remains
nearly constant and does not increase with pressure. This peak
is marked with the vertical dashed line in Fig.
2
, and Fig. S4 in
the Supplemental Material [
42
] shows this by comparing pairs
of phonon DOS spectra with differences of 2 GPa in pressure.
A similar behavior of the longitudinal peak was found in
Fe
65
Ni
35
Invar below the Curie pressure, and computational
research showed that a spin-phonon interaction was needed
to account for it [
5
]. A definitive proof of a spin-phonon
interaction in Fe
55
Ni
45
cannot be made solely with the present
experimental results, however.
Ab initio
calculations of spin-
phonon interactions in alloys are challenging [
5
,
54
,
55
]but
they are emerging.
A comparison between the present data on Fe
55
Ni
45
and
the prior results on Fe
65
Ni
35
Invar [
5
] highlights interesting
features of Invar behavior in Fe-Ni. The pressure-induced In-
var behavior in Fe
55
Ni
45
has a lower bound in pressure, unlike
the case for Fe
65
Ni
35
Invar, which begins at ambient pressure.
Perhaps the key difference between the two materials is that
the Curie pressure,
P
C
,of13GPainFe
55
Ni
45
is higher than the
P
C
of 4.6 GPa in Fe
65
Ni
35
by nearly a factor of 3. With total
magnetic entropies that are similar, the change of magnetic
entropy with pressure is spread over a range in pressure that
is approximately three times wider, so the magnetic contri-
bution to thermal expansion should be smaller in Fe
55
Ni
45
than in Fe
65
Ni
35
.
With pressure, the more gradually changing
∂
S
mag
/∂
P
for
Fe
55
Ni
45
is expected to be competitive with the
∂
S
vib
/∂
P
144419-5
P. GUZMAN
et al.
PHYSICAL REVIEW B
110
, 144419 (2024)
at pressures approaching
P
C
where
M
(
P
) changes more
rapidly. Indeed, the region of anomalous thermal expansion
in Fe
55
Ni
45
extends from 7.5 GPa to nearly the
P
C
of 13 GPa,
a range of 5.5 GPa. In contrast, the region of Invar behavior in
Fe
65
Ni
35
is approximately 0 to 3 GPa, about half this range.
The Invar behavior in Fe
65
Ni
35
does not extend to
P
C
because
its
∂
S
mag
/∂
P
and
∂
S
vib
/∂
P
both become large between 3
and 4.6 GPa. Although they retain their opposite signs, the
cancellation of their large magnitudes is not sufficiently pre-
cise. The magnetization decreases rapidly in a small pressure
range near
P
C
in Fe
65
Ni
35
Invar. Curiously, there is also a
significant change in
∂
S
vib
/∂
P
from spin-phonon interactions
in this same range of magnetic disordering. The evidence for
spin-phonon coupling in Fe
55
Ni
45
is less distinct because the
spins become disordered over a broader range of pressure, and
the change in spin-phonon coupling is, therefore, more grad-
ual. It is not clear if the spin-phonon interaction in Fe
55
Ni
45
differs significantly from that in Fe
65
Ni
35
, but its change with
pressure is less obvious.
V. CONCLUSION
A pressure-induced Invar effect in Fe
55
Ni
45
was confirmed
by synchrotron XRD measurements at RT and 392 K, where
a low thermal expansion was observed from 7 to 13 GPa. The
contributions of phonons and magnetism to the thermal ex-
pansion of Fe
55
Ni
45
were determined by obtaining entropies
of phonons and spins from NRIXS and NFS measurements.
From 7 to 13 GPa, a rapid change in magnetic entropy from
the disordering of spins was observed, giving a thermal expan-
sion that opposed the more monotonic contribution of thermal
expansion from phonons. The pressure-induced Invar effect
in Fe
55
Ni
45
is a consequence of this cancellation of the ther-
modynamic contributions to thermal expansion from phonons
and spins. The phonon DOS of Fe
55
Ni
45
showed an arrest of
the stiffening with pressure of the longitudinal phonon modes,
indicative of a spin-phonon coupling.
ACKNOWLEDGMENTS
This work was supported by the National Science Foun-
dation under Grant No. 1904714 (P.G., S.H.L., C.M.B-
C., and B.F.). P.G. acknowledges support of the NSF
Graduate Research Fellowship DGE-1745301. This research
used resources of the APS, a U.S. DOE Office of Science
User Facility operated for the DOE Office of Science by
Argonne National Laboratory under Contract No. DE-AC02-
06CH11357 (P.G., S.H.L., C.M.B-C., and B.F.). HPCAT
operations are supported by DOE-NNSA’s Office of Ex-
perimental Sciences. Use of the COMPRES-GSECARS
gas-loading system was supported by COMPRES under NSF
Cooperative Agreement EAR 1606856 and by GSECARS
through NSF Grant No. EAR-1634415 and DOE Grant No.
DE-FG02-94ER14466. We thank C. Li for assistance with
the pressure cells and E. Priesen Reis for assistance with
magnetization measurements.
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