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        論文出處        https://www.nature.com/articles/s41467-022-29340-2

                        https://imgur.com/mGaD73U







Magnetic refrigeration material operating at a full temperature range
required for hydrogen liquefaction

Xin Tang, H. Sepehri-Amin, N. Terada, A. Martin-Cid, I. Kurniawan, S.
Kobayashi, Y. Kotani, H. Takeya, J. Lai, Y. Matsushita, T. Ohkubo, Y. Miura,
T. Nakamura & K. Hono

Nature Communications volume 13, Article number: 1817 (2022) Cite this article

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Abstract

Magnetic refrigeration (MR) is a key technique for hydrogen liquefaction.
Although the MR has ideally higher performance than the conventional gas
compression technique around the hydrogen liquefaction temperature, the lack
of MR materials with high magnetic entropy change in a wide temperature range
required for the hydrogen liquefaction is a bottle-neck for practical
applications of MR cooling systems. Here, we show a series of materials with
a giant magnetocaloric effect (MCE) in magnetic entropy change (-m.2
mK) in the Er(Ho)Co2-based compounds, suitable for operation in
the full temperature range required for hydrogen liquefaction (20-77). We
also demonstrate that the giant MCE becomes reversible, enabling sustainable
use of the MR materials, by eliminating the magneto-structural phase
transition that leads to deterioration of the MCE. This discovery can lead to
the application of Er(Ho)Co2-based alloys for the hydrogen liquefaction using
MR cooling technology for the future green fuel society.

Introduction

Magnetic materials undergo isothermal magnetic entropy changes (ΔSm) or
adiabatic temperature changes (ΔTad) upon the application or removal of an
external magnetic field. This phenomenon is known as the magnetocaloric
effect (MCE)1. Magnetic refrigeration (MR) based on the MCE is considered to
be a promising energy-efficient and environmentally benign refrigeration
technology2. The concept of cooling by adiabatic demagnetisation at the
ultra-low temperatures was proposed independently by Debye3 and Giauque4
based on thermodynamic studies in the late 1920s. This concept was
experimentally demonstrated in the early 1930s by Giauque and MacDougall on
the adiabatic demagnetisation of Gd2(SO4)3.8H2O, leading to attainment of
temperatures below 1K5. The operation of MR can be also extended to room
temperature application using magnetic refrigerants, such as Gd5Si2Ge26,7,8,
(Mn,Fe)2P9, MnAs10,11, Ni-Mn-based Heusler alloy12,13 and
La(Fe,Si)13H14,15,16. Recently, the global demand for the reduction of CO2
emission has increased the attention devoted to the use of renewable energy
for which hydrogen plays an important role in the so-called decarbonised
hydrogen society17. In this context, magnetic refrigeration has been
demonstrated to be a potential candidate for hydrogen liquefaction and
avoidance of hydrogen boil-off during storage18. In this approach, hydrogen
gas is cooled to ~77 (boiling temperature of liquid nitrogen) followed by
a further decrease in temperature to its liquefaction temperature of 20.
Because the existing magnetic refrigerant materials cannot maintain a large
MCE over the wide temperature span of 77–20, a series of refrigerant
materials are used in an active magnetic regenerator (AMR) system (Fig. 1a).

Fig. 1: Magnetic refrigeration materials required for hydrogen liquefaction
using magnetic refrigeration.

figure 1

a Schematic of the active magnetic regenerator for hydrogen liquefaction. A
series of magnetic refrigerants with tailored transition temperatures at
external field (μ0Hext) are required to cover the large temperature range
from the boiling temperature of nitrogen (77) to the boiling temperature
of hydrogen (20). b Isothermal magnetic entropy change (Sm) as a
function of temperature. Second-order magnetic phase transition materials
illustrated by dashed blue curves, for example, HoB220, HoNi224, HoAl228, and
DyAl228 show no hysteresis, a giant MCE only at temperatures below 20 and
small MCE at temperatures above 30. First-order magnetic phase transition
materials indicated by black curves with symbols exhibit giant magnetocaloric
effects (MCEs) (large Sm) at a broad temperature range but with thermal
hysteresis near the transition temperature, resulting in irreversible giant
MCEs. Therefore, giant and reversible MCEs with broad operating temperature
window illustrated by gradient colour from red to blue corresponding to the
magnetic refrigerants with different transition in (a) from 77 to 20
are desirable for active magnetic regenerator.

Full size image
The isothermal magnetic entropy change (ΔSm) is given by

ΔSm=μ0∫0H(∂M∂T)HdH
(1)
and is used to characterise the magnetocaloric response of a magnetic
refrigerant, where μ0 is the permeability of free space, M is the
magnetisation, T is the temperature, and H is the external magnetic field.
The maximum value of ΔSm is achieved near the magnetic transition
temperature (Ttr) owing to the large value of ∂M∂T. HoAl2 compound is one
of the potential magnetic refrigerant materials for hydrogen liquefaction,
which has 猶m.16mKat temperature of 32 obtained from
a single crystal and is called as a material with a giant MCE1,19. To realise
an efficient AMR system for H2 liquefaction applications, a larger magnetic
entropy change of 猶m.2 J cmK covering a broad temperature
range of 20–77 for magnetic refrigerants is needed. Giant MCEs (猶m
.2JmK) have been realised in Ho-based compounds (Fig. 1b), such
as HoB220, HoN21,22, and HoNi223,24 at temperatures below 20. These
ferro/paramagnetic phase transitions without thermal hysteresis have been
classified as second-order magnetic phase transitions (SOPT). SOPT materials
without thermal hysteresis intrinsically lead to reversible MCE and
mechanical stability during cyclic performance25,26, and hence are desirable
for practical application. To meet the requirements of AMR, giant MCE must be
maintained at temperatures up to 77. However, the increase in Ttr of SOPT
materials has been found to be achieved at the expense of |△Sm|. For
example, |△Sm| values of 0.17mK and 0.15mK are
obtained at 30 for the (GdxHo1-x)B2 and HoAl2 compounds27,28,
respectively, and |△Sm| decreases to 0.10mK at 60 for the
DyAl2 compound28. Hence, there are very few refrigerant materials exhibiting
a giant MCE of |△Sm| > 0.2mK that do not show thermal hysteresis
at the temperatures of 30–77 required for H2 liquefaction in AMR systems.
By contrast, magnetic refrigerant materials with first-order magnetic phase
transition (FOPT) have giant MCEs induced by their magnetostructural phase
transitions. For example, in ErCo2, a transformation from the paramagnetic
phase (cubic) to the ferrimagnetic phase (rhombohedral) results in 猶m0.37mK at 37 (Fig. 1b)29. With Ho substitution for Er, Ttr can
be increased to 80 while maintaining a giant MCE (猶m 0.2 cmK1) in the (Ho1-xErx)Co2 compounds30. However, the (Ho1-xErx)Co2 compounds
undergoing FOPT suffer from thermal hysteresis resulting in an irreversible
MCE and mechanical instabilities25,26, hindering their application for AMR.

In this work, we demonstrate that for (Ho)ErCo2 compounds, the substitution
of Co by particular 3d metal elements, such as Fe or Fe + Ni, can eliminate
the hysteresis by avoiding the structural transformation, while maintaining a
giant MCE at the transition temperature. Different from the conventional
reports, the narrow operating temperature window is substantially expanded in
this work by developing a series of materials with hysteresis-free and
tailored transitions at the temperature range of 20–77 with△Sm|0.2mK. Thus, this discovery can directly lead to the realisation
of the AMR system as a great leap toward the application of magnetic cooling
technology for hydrogen liquefaction.

Results

Tuning the transition temperature and thermal hysteresis
Magnetisation as a function of temperature M(T) at a magnetic field of 1T is
plotted for ErCo2 and Er(Co,Fe,Ni)2-based alloys (Fig. 2a, b). The ErCo2
alloy itself undergoes the paramagnetic/ferrimagnetic transition at TC7
 that accompanies a magnetostructural phase transition that gives rise to
an abrupt change in the magnetisation, and correspondingly induces a giant
magnetic entropy change of 0.37mK (supplementary Fig. 1). This
comes at the cost of thermal hysteresis of 2 (Fig. 2a), hindering the
reversibility of MCE and the practical application of these materials. Figure
2a, b show that the partial substitution of Co with Fe or Fei solves
this problem. The elimination of the thermal hysteresis was successfully
achieved in the ErCo1.96Fe0.04 alloy with a broad transition temperature
span, showing the features of SOPT. Further increase of Fe substitution for
Co leads to less sharp transitions observed from the M-T curves and a
reduction of magnetic entropy changes, as shown in supplementary Fig. 1.
Tunable transition temperature is another requirement of magnetocaloric
materials for AMR systems. As observed from Fig. 2a, the transition
temperature increased from 37 to 62 when x increased to 0.07 in the
ErCo2Fex alloy while hysteresis was eliminated. The transition temperature
can also be tuned toward a lower temperature (28) when Ni is alloyed in
the ErCo1.96Fe0.04 alloy, while maintaining the hysteresis-free state, as
shown in Fig. 2b. Refrigeration capacity (RC), defined as the integrated area
under the -ΔSm(T) curve at the peak’s half value is another important
parameter that is a measure for the amount of heat transfer from the cold to
the hot reservoirs in a single ideal MR cycle. The RC is improved from 2.2
m for ErCo2 to 2.42m in the case of the ErCo1.96Fe0.04 alloy.
With a further increase in Fe content, a magnetic entropy change of 0.17cmK at 57 can be obtained for the ErCo1.95Fe0.05 alloy with an
enhanced RC of 2.95m. Although conventionally, a larger RC is
achieved at the expense of the peak value of -ΔSm, making the use of
magnetic refrigerants with SOPT less attractive, the |ΔSm| value for the
ErCo2-xFex (x.04) alloys developed in this study induces the largest
entropy change of 0.21mK within the temperature range of 30–77K compared to all known refrigerant materials without hysteresis reported to
date1,21,22,23,24,27,28,31,32, Arrott plots were employed (Fig. 2c, d) to
determine the order of the magnetic phase transitions. A negative slope and
reflection points near the transition temperature were observed for the ErCo2
alloy, revealing a typical FOPT based on the Banerjee criterion33. The
negative slope was strongly suppressed, and a characteristic of SOPT was
observed for the compositionally-modified ErCo1.95Fe0.05 alloy.

Fig. 2: Tuning the transition temperature, thermal hysteresis, and order of
magnetic phase transition in an ErCo2-based system.
figure 2

a, b The Magnetisation (M) is plotted versus temperature at an applied
magnetic field of 1T showing that the transition temperature can be tuned to
higher temperatures (a) and to lower temperatures (b), while eliminating the
hysteresis by substituting Co by Fe and Fei in the ErCo2-based system.
The colours of the curves in a, b correspond to the colour of listed alloy
compositions. c, d The Arrott plots measured from 27 to 69 at a
temperature step (△T) of 3 for c ErCo2 and d ErCo1.95Fe0.05 alloy show
the changes of the phase transition from first-order to second-order,
respectively.

Characterisation of phase transitions

Although the Arrott plots qualitatively show the nature of the magnetic phase
transition, the latter can be investigated further by tracking the change in
the crystal lattice during the phase transition. An unambiguous assessment of
the phase transition was carried out using in-situ XRD measurement under
cryogenic temperatures. The details of the determination of the phase
transition by XRD are shown in the supplementary note 1. The change in the
lattice spacing upon cooling from 100 to 5 is plotted in Fig. 3a. Because
the quantities 2–√ar and cr/3–√ of the lattice parameters for the
rhombohedral phase are equivalent to the ac of the cubic lattice,2–√ar and
cr/3–√ for the rhombohedral phase are plotted to compare directly with the
lattice parameter of the cubic phase. A step jump in the lattice spacing in
ErCo2 was observed near the transition temperature for the ErCo2 alloy. With
Fe substitution for Co in the ErCo1.96Fe0.04 alloy, the lattice constant
change was substantially reduced, even though a cubic/rhombohedral crystal
structure change was observed. This result clearly shows that the addition of
Fe can suppress the large volume change that occurs in the magnetostructural
phase transition in ErCo2 at Ttr. A further increase in Fe content in the
ErCo1.95Fe0.05 alloy leads to no changes in the lattice spacing or volume per
chemical formula caused by the structural transition near Ttr, indicating the
realisation of SOPT. In other words, this work demonstrates a concept that
the substitution of a 3d metal element, such as Fe for Co in the ErCo2-based
Laves phase eliminates the structural phase transition, thereby reducing the
thermal hysteresis to 0.

Fig. 3: Analysis of the lattice constant and crystal volume change around the
transition temperature range using cryogenic x-ray diffraction (XRD).

figure 3

a Temperature dependence of the lattice parameters for ErCo2-based alloys.
The lattice parameters are obtained from the Rietveld refinement. The lattice
parameters of the rhombohedral phase are plotted for 2–√ar (black) and cr/3
–√ (red) to compare directly with the lattice parameter of the cubic phase.
b Temperature-dependent volume per chemical formula for ErCo2 (black),
ErCo1.96Fe0.04 (purple) and ErCo1.95Fe0.05 (red) alloys, the crystal
structure change upon transition is also illustrated by a unit cell (red and
brown spheres represent Er and Co atoms, respectively, and red and brown
arrows represent the magnetic moments of the Er and Co atoms, respectively).

A further characterisation of the nature of the phase transitions in
Er(Co1-xFex)2 was performed by measuring the specific heat, C, using the
thermal relaxation method, the details of which are described in the
supplementary note 2. In Fig. 4a, the specific heat values given by three
measurements are the same in each temperature for the three samples (ErCo2,
ErCo1.96Fe0.04 and ErCo1.95Fe0.05 alloys), within the experimental accuracy,
apart from the temperatures close to the phase transition temperatures. Here,
we analysed the dependence of the time evolution of the sample temperature on
the phase transition temperatures for the three samples shown in Fig. 4b. For
ErCo2, a significant difference in T(t) was found at the phase transition
temperature of ~35, as indicated by arrow (I) in Fig. 4a. The temperature
rise during the first run is significantly suppressed by the existing latent
heat, compared to those in the second and third runs. The strong thermal
hysteretic behaviour observed in Fig. 2 for the phase transition of ErCo2
corresponds to the FOPT behaviour. For sample II (ErCo1.96Fe0.04), a similar
behaviour was observed (Fig. 4b), indicating that the phase transition is
still first-order. It is clear that the ΔTmax value in the first measurement
is lower than those in the second and third measurements. On the other hand,
the hysteretic behaviour was not observed within the experimental accuracy in
sample III (ErCo1.95Fe0.05) as shown in Fig. 4b. Thus, we conclude that the
phase transitions for ErCo2 and ErCo1.96Fe0.04 are FOPT, while the
ErCo1.95Fe0.05 sample does not show FOPT behaviour, which is consistent with
that observed by in-situ XRD shown in Fig. 3.

Fig. 4: Analysis of the latent heat involved with first-order phase
transition.

figure 4

a Temperature dependence of the specific heat measured by the thermal
relaxation method for ErCo2 (black), ErCo1.96Fe0.04 (blue) and ErCo1.95Fe0.05
(red) alloys. b Time evolution of the sample temperature obtained using the
relaxation method at the temperature where each sample shows a peak anomaly
indicated by arrows (I), (II), and (III) in a. The dashed lines denote heat
power for each measurement (1st (black), 2nd (blue) and 3rd (red)
measurements) in b.

Origin of large magnetocaloric effect

Figure 5a shows the results of the specific magnetometric measurements of Er
and Co probed by X-ray magnetic circular dichroism (XMCD). Note that the data
for the ErCo2 alloy were adopted from reference34. The Co magnetisation at
low temperatures (<10) remains opposite to the Er magnetisation after
alloying with Fe, thus revealing that the ferrimagnetic behaviour is not
changed by the substitution of Co with Fe. Unlike for ErCo2 alloy that
exhibits a sharp change in the magnetic moment of Er at Ttr, the change in
the magnetic moment of Er is more gradual around Ttr, which is consistent
with the M–T curves presented in Fig. 2. The evolution of the magnetic
moments of Er and Co can be directly seen from the XMCD signal shown in the
Supplementary Fig. 2. In the XMCD signal of the Co L2,3 edges, an inversion
of the edges appears at the temperatures above 56, corresponding to the
change in the sign of the magnetic moment of Co. For the Er M4,5 XMCD
spectra, the intensity of the signal decreases as the temperature increases.
In-situ Lorentz microscopy observation in the Fresnel mode was employed to
understand the evolution of magnetic domains during cooling. Figure 5b shows
the selected micrographs in the cooling process at four different
temperatures. These are also marked as i–iv and I–IV in Fig. 5a for ErCo2
and ErCo1.95Fe0.05 alloys, respectively. For both samples, there is no
contrast in the paramagnetic state. The XMCD result in Fig. 5a shows that the
magnetic moment of Er atoms increases upon cooling of the ErCo2 sample via
the magnetic momentum alignment, while the net magnetic moment of Co remains
almost zero. This results in the formation of fine and maze-like magnetic
domain structures, as shown in ii in Fig. 5b. Note that close to the Ttr of
ErCo2, a mountain-like contrast marked by red circles appears originating
from a large strain caused by the cubic/rhombohedral structural
transformation. The change in the magnetic domain structure upon cooling to 37
 is due to a substantial increase in the magnetic moment of Er by
formation of ferrimagnetic phase, as shown in Fig. 5a. Note that unlike the
ErCo2 sample, no distinct strain contours were observed in the ErCo1.95Fe0.05
sample because the cubic structure was preserved at the temperatures below 52
 in the latter case. The observed transition in the shape of the magnetic
domains from II to IV, i. e. fine maze-like domain patterns in II, strip-like
domain patterns in IV, and their mixture in III (indicated by black arrow
heads), are due to the gradual increase in the magnetic moment of Er upon a
decrease in temperature without existence of any strain contour. Note that
the ErCo1.95Fe0.05 phase is in its ferrimagnetic state at the temperature of
10.

Fig. 5: Magnetism and magnetic structure for ErCo2-based alloys.

figure 5

a Temperature-dependent magnetic moments for Er (red) and Co (blue) in
ErCo234, and ErCo1.95Fe0.05 alloys. b Magnetic domain evolution in
ErCo2-based alloys examined using cryogenic Lorentz microscopy in the Fresnel
mode. The black arrow heads show the magnetic domains and red circles
illustrate the mountain-like contrasts caused by strain; the crystal
structure change upon transition is also shown by a unit cell (red and brown
spheres for Er and Co atoms, respectively, and red and brown arrows for the
magnetic moments of Er and Co, respectively).

The giant MCE in the ErCo2 alloy originates from the magnetostructural phase
transition and itinerant electron metamagnetism (IEM). The latter was
proposed by Wohlfarth and Rhodes35. According to the proposed concept, the
creation of a magnetic moment in Co is a consequence of the IEM induced by
localised ferromagnetic ordering of Er moments that induces a large exchange
field at the transition temperature. This can be observed in Fig. 5a, wherein
Co has nearly zero magnetisation in the paramagnetic state, while it
antiferromagnetically couples with Er at temperatures below 37. In this
study, we found SOPT with the substitution of Fe for Co in the ErCo1.95Fe0.05
alloy, in which no structural transformation was observed, while a giant MCE
was induced. However, based on the XMCD results, the magnetic moment of Co at
temperatures below Ttr remains comparable in ErCo2 and ErCo1.95Fe0.05 alloys,
suggesting that IEM is preserved upon a small substitution of Fe for Co. In
addition to the structural transition, any change in the density of states at
the Fermi level between these two alloys influences the IEM in Fe-doped
alloys36,37. We calculated the density of states using density functional
theory (DFT) using experimental lattice constants (Supplementary Fig. 3).
Trace amounts of Fe substitution for Co have negligible influence on the
electronic structure around the Fermi level compared with the
cubic/rhombohedral ErCo2. This implies that the instability of the 3d
sublattice magnetism and IEM is preserved for the ErCo1.95Fe0.05 alloy, which
is consistent with the experimental data obtained by XMCD (Fig. 5a). This
observation is in contrast to the conventional belief that FOPT results from
IEM36,37. Here, we demonstrate that by eliminating the structural phase
transition, thermal hysteresis can be eliminated, while the giant MCE can
still be achieved due to the preserved IEM in the ErCo1.95Fe0.05 alloy.

Discussion

In practical applications, the surface/volume ratio of the magnetic
refrigerants should be increased to achieve better heat exchange between the
refrigerants and heat-exchanger fluid. Hence, spherical particles are
desired. We employed a gas atomisation method and obtained spherical
particles with an average particle diameter in the range of 210–350gm. An
example of spherical particles of the ErCo1.96Fe0.04 alloy is shown in the
inset of Fig. 6a. The optimal annealing of the gas-atomised powders
(supplementary Fig. 4) led to the realisation of a GSm value comparable to
that of the bulk sample (Fig. 6a). To develop magnetic refrigeration
materials suitable for a broad temperature range of 77–20, we further
investigated different 3d metal dopants to ErCo2 and HoCo2-based compounds.
We substituted Ni, Al, Fe, and their combinations for Co in Er(Ho)Co2 alloys.
Figure 6b shows that hysteresis can be eliminated in conventional FOPT-type
ErCo2 and HoCo2 alloys by the doping, and the transition temperature can be
tuned from 20 to 77. These changes enable the values of GSm.2JmK to be achieved in the range from 20 to 77 to cover the
required temperature range for hydrogen liquefaction (Fig. 6c). The magnetic
refrigerants developed in this study yielded significantly larger entropy
changes than those of HoNi224, HoAl228, REMn2X238,39,40, RECo2Mnx41 and
DyAl228 for cryogenic applications, particularly in the temperature range
from 30 to 77. For example, the GSm values for the
ErCo1.85Ni0.11Fe0.04 and HoCo1.8Ni0.15Al0.05 alloys are 55% and 93 % larger
than those of HoAl2 and DyAl2 at the same transition temperatures. Further
characterisation of ΔTad of magnetic refrigerants is depicted in Fig. 6d;
above 4, ΔTad can be achieved for the magnetic refrigerants developed in
this work that can cover the application temperature range from 20 to 77
for hydrogen liquefaction.

Fig. 6: Magnetocaloric effects in compositionally engineered (Ho)ErCo2-based
alloys.

figure 6

a Comparison of the temperature-dependent magnetic entropy change (GSm(T))
of a bulk sample (black) and gas-atomised (blue) ErCo1.96Fe0.04 particle. The
inset shows a scanning electron microscopy (SEM) image of a gas-atomised
sample. b Temperature-dependent magnetisation M(T) measurements of the
cooling and heating branches from 5 to 100 at 1 intervals (μ0H1T) for a series of magnetic refrigerants with tailored transition
temperatures, the spherical particles in AMR with different colours
correspond to different magnetic refrigerants with different transition
temperatures in b. c Temperature-dependent magnetic entropy change GSm(T)
curves of magnetic refrigerants with tailored transition temperatures
covering the large temperature window from 20 to 77. d Adiabatic
temperature change (ΔTad) at the field change (ΔH) of 5T of the selected
magnetic refrigerants developed in this work at their transition
temperatures. The selected colours of the curves in b–d correspond to the
colour of listed alloy compositions.

Hysteresis is a widespread phenomenon resulting from the nature of the
first-order phase transition in magnetic refrigerants that leads to the
irreversibility of the magnetocaloric response. Herein, we demonstrate that
the elimination of hysteresis can be realised by avoiding the crystal
structure change across the phase transition, specifically by alloying with
3d elements, while maintaining the giant magnetocaloric effect comparable to
that of a conventional FOPT Er(Ho)Co2 alloy. The role of Fe in suppressing
the structural transformation upon phase transition is due to the change from
FOPT to SOPT as revealed by in-situ XRD, latent heat measurement, and Lorentz
TEM for ErCo1.95Fe0.05. Moreover, the giant MCE was maintained for SOPT
because of the preservation of IEM as found by XMCD experiments and DFT
calculations. The Er(Ho)Co2-based alloys developed in this study have
numerous merits, such as significantly larger magnetic entropy changes
compared with those of known materials in the temperature range of 20–77,
a wide operating temperature window due to the stacking of the refrigerants
covering the range of application temperatures for hydrogen liquefaction,
easy fabrication, and stable magnetocaloric properties of gas-atomised
particles. This may lead to the application of Er(Ho)Co2-based alloys for
hydrogen liquefaction using an active magnetic regenerator. Moreover, the
approach for achieving giant reversible MCE in this study is also expected to
be applicable for eliminating the detrimental hysteresis of magnetic
refrigerants with FOPT for applications near room temperature, such as
Gd5Si2Ge26,7,8, (MnFe)2P9 and La(FeSi)13H14,15.

Methods
Sample preparation

Polycrystalline (Ho)ErCo2-based samples were prepared by arc melting pure
constituent elements in an Ar atmosphere, with 2–5 wt.% extra Er and Ho
added to compensate the evaporation during sample preparation. The ingots
were remelted four times after flipping over to achieve better homogeneity.
Thereafter, the ingots were sealed in quartz in an argon atmosphere and
annealed for 50 at 1273. The phase constituents and crystal structure
were examined by XRD (Rigaku SmartLab 9W) with Cu Kα1 radiation in the
temperature range of 5–300. Thermomagnetic measurements were conducted
using a superconducting quantum interference device magnetometer (SQUID-VSM).

Thermomagnetic measurements

To directly measure the adiabatic temperature change, a zirconium oxynitride
thin-film CernoxTM thermometer (CX-SD, Lake Shore Cryotronics) was placed on
the large surface of a cubic-shaped sample and fixed by thin copper wires.
The sample assembly was inserted into the quantum design physical property
measurement system (PPMS). The temperature and magnetic field were controlled
by PPMS. The sample space was pumped by a cryopump, and the pressure was
maintained below 10orr to reach adiabatic conditions. The thermal
relaxation method for latent heat measurements was implemented in the
physical properties measurement system (PPMS) manufactured by Quantum Design.
To evaluate the time evolution of sample temperature during measurement, the
raw data were extracted for each measurement.

Cryogenic microstructure characterisations

Cryogenic Lorentz microscopy was conducted using ultra-high-voltage (1.2 MV)
Hitachi-TEM instrument. The temperature of the TEM specimen was reduced to ~10
 in a cryostat TEM sample holder using liquid helium. The specimens for
the TEM analysis were prepared by an FEI Helios G4-UX dual-beam system using
the lift-out method. The soft XMCD spectra at the Er M4,5 and Co L2,3 edges
were recorded using the total electron yield method at the BL25SU beamline of
SPring-8. The XMCD signal (μm) was obtained as μm=(μlμr+)μl++μr), where μr and μl represent the X-ray absorption spectrum (XAS) for the
helicity plus (h+) and minus (h of soft X-rays, respectively, and μ+ and
μrespectively represent XAS for a positive and negative applied field
with intensity equal to 1.9. The degree of circular polarisation was
previously estimated as 0.96 at 400V42 and was expected to be similar or
larger in the energy region used in the present work. The angle between the
magnetic field and the incident X-ray beam was 10° (ref. 43). The rod-shaped
sample was fractured in the ultra-high vacuum chamber of the XMCD apparatus
with the vacuum level of <5터a to obtain a fresh surface for the
XMCD experiments. The samples were measured at different temperatures between
10 and 100. The magnetic moments were calculated using the magneto-optical
sum rule analysis for XMCD44,45,46 by taking into consideration the
spin-correction factor necessary to apply the sum rules for rare earths47.

First-principles calculations

Density functional theory (DFT) calculations were performed using the
full-potential linearised augmented plane wave (FLAPW) method as implemented
in the WIEN2K code48. The exchange-correlation interaction was approximated
using the Perdew–Burke–Ernzerhof (PBE)49 formulation based on the
generalised gradient approximation (GGA). The k-point sampling of the
Brillouin zone was performed using 11턱턱 k-mesh grids. The
spin-orbit coupling (SOC) was included in the calculations self-consistently.
The localised 4 electrons of Er were treated based on the implementation
of the Hubbard’s U parameter using the DFT method with U0V
and J.75V, including the orbital polarisation. The experimental
lattice constants for the rhombohedral and cubic structures were used, and Fe
doping in ErCo1.95Fe0.05 was simulated using the virtual crystal
approximation50. The ferrimagnetic behaviour and 6gB orbital moments for
Er were confirmed in all systems.



--
七魄興輪無上伊甸瑜珈雖然是以看來較為平和的方式以蟬蛻和生乳取代血肉等腥穢之物
作為密義源起供養；然而聚歛於上的是冥界的深冤與大樂奔瀉的淨慈，行者於閉關修持
之時若生起退失動搖之心，則神識旋即離散且肉身消殞；即便如此還是願意受灌頂嗎？
 https://imgur.com/cEVD0kE ---妖道七祖《攝一切魔根本瑜珈論/誓命問品第一》---
文章代碼(AID): #1K0Lp7VP (CFantasy) [ptt.cc] Re: [新聞] 湖南偏鄉驚曝百餘......
https://imgur.com/eRQKYMF           文章網址: https://tinyurl.com/56ervywe

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