# High-entropy effect at rare-earth site in DyNi

Yuito Nakamura  Department of Electrical Engineering, Faculty of Engineering,
Fukuoka Institute of Technology, 3-30-1 Wajiro-higashi, Higashi-ku, Fukuoka
811-0295, Japan  Koshin Takeshita  Department of Electrical Engineering,
Faculty of Engineering, Fukuoka Institute of Technology, 3-30-1 Wajiro-
higashi, Higashi-ku, Fukuoka 811-0295, Japan  Terukazu Nishizaki  Department
of Electrical Engineering, Faculty of Science and Engineering, Kyushu Sangyo
University, 2-3-1 Matsukadai, Higashi-ku, Fukuoka, 813-8503, Japan  Jiro
Kitagawa<EMAIL_ADDRESS>Department of Electrical Engineering, Faculty
of Engineering, Fukuoka Institute of Technology, 3-30-1 Wajiro-higashi,
Higashi-ku, Fukuoka 811-0295, Japan

###### Abstract

We report the structural and magnetic properties of RNi (R=Dy,
Tb1/3Dy1/3Ho1/3, and Gd1/5Tb1/5Dy1/5Ho1/5Er1/5) to investigate the high-
entropy effect at the rare-earth site. The lattice parameters are almost
unchanged by the increase of configurational entropy, which is due to the
successive partial substitution of Dy by pair of rare earth elements located
on both sides of Dy in the periodic table. All compounds exhibit ferromagnetic
ground states. The replacement of Dy with Tb+Ho, which does not have magnetic
interactions in competition with Dy, does not affect the magnetic ordering
temperature. Although (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni shows the Curie
temperature close to that of DyNi, an additional magnetic anomaly, which would
be a spin reorientation, is observed probably due to the introduction of
competing magnetic interactions between R=Gd and Er compounds and R=Tb, Dy,
and Ho ones. We have also assessed the magnetocaloric effect, and the
configurational entropy dependence of the magnetic entropy change reflects
that of the temperature derivative of the magnetic susceptibility. Our
analysis suggests the possibility of enhancing magnetocaloric properties by
designing the anisotropy of rare-earth magnetic moments in the high-entropy
state.

##  I Introduction

High-entropy alloys (HEAs) are unique systems composed of multiple elements
with near equimolar ratios. They offer a vast compositional space and are a
promising platform for studying novel phenomenaZherebtsov:Int2020 ;
Kitagawa:APLMater2022 ; Baba:Materials2021 . Additionally, they have attracted
considerable attention due to their rich functionalities, such as high
strength, energy storage, radiation protection, magnetism, superconductivity,
and biocompatibilitySathiyamoorthi:PMS2022 ; Chang:AM2020 ; Wang:JMCA2021 ;
Marques:EES2021 ; Pickering:Entropy2021 ; Chaudhary:MT2021 ; Kitagawa:JMMM2022
; Kitagawa:Metals2020 ; Castro:Metals2021 . HEA concept is now introduced into
intermetallic compounds (high-entropy intermetallic compounds).

Table 1: Lattice parameters ($a$, $b$, and $c$), and magnetic ordering temperature $T_{\mathrm{C}}$ of each sample. sample |  $a$ (Å) |  $b$ (Å) |  $c$ (Å) |  $T_{\mathrm{C}}$ (K)
---|---|---|---|---
DyNi | 7.026(4) | 4.176(2) | 5.444(3) | 59
(Tb1/3Dy1/3Ho1/3)Ni | 7.029(5) | 4.171(3) | 5.439(3) | 63
(Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni | 7.044(6) | 4.168(3) | 5.447(4) | 63

Numerous rare-earth intermetallic compounds exhibit magnetic moments solely
attributed to the rare-earth elements. However, the influence of a high-
entropy state at the rare-earth site on the magnetic ordering temperatures of
such systems remains insufficiently explored. We are primarily concerned with
the robustness of the magnetic ordering of rare-earth atoms in the presence of
the high-entropy state. In this study, we focus on the well-defined RNi
(R:rare-earth) system, wherein magnetic ordering temperatures and magnetic
structures are elucidated. The highest magnetic ordering
temperatureRajivgandhi:JMMM2017  is 71 K in GdNi. The ordering temperature is
moderately lower compared to R2In or R6CoTe2 series, where Gd2In and Gd6CoTe2
show the highest magnetic ordering temperatures of 190 K and 220 K,
respectivelyFranco:PMS2018 . Hence, we anticipate the possible destruction of
magnetic orderings within all RNi compounds by increasing atomic disorder.

Additionally, we are concerned with the potential modulation of magnetocaloric
effects by introducing a high-entropy state. Certain RNi compounds demonstrate
a significant magnetocaloric effect in proximity to the temperature of liquid
hydrogenRajivgandhi:JMMM2017 ; Zhao:JMST2021 . This observation holds promise
for magnetic refrigeration-based hydrogen liquefaction and is significant in
realizing a hydrogen society. The magnetocaloric effects of HEAs have garnered
considerable attentionChaudhary:MT2021 ; Perrin:JOM2017 ; Law:APLMater2021 ;
Perrin:Enc2022 ; Law:JMR2023 . Notably, the equimolar quinary alloy GdTbDyHoEr
exhibits a remarkable magnetocaloric effectYuan:AM2017 . A recent
investigation into the configurational entropy dependence of magnetocaloric
effects in rare-earth HEAs has revealed that magnetic properties depend on the
intrinsic magnetic characteristics of rare-earth elementsLu:JALCOM2021 .
Another studyLaw:JMR2023  suggests a reduction in the peak value of magnetic
entropy change with an increase in configurational entropy in HEAs containing
Dy. Transition-metal-based HEAs, such as FeMnNiGeSi, have emerged as a novel
material class enabling the manipulation of magnetocaloric effects by
introducing magneto-structural transformationsLaw:AM2021 . To the best of our
knowledge, reports on the magnetocaloric effects of crystalline high-entropy
rare-earth intermetallic compounds are rare, while there are many reports for
amorphous HEAs containing rare-earth and transition-metal elementsLaw:JMR2023
.

It is well-established that the lattice parameters and the number of 4$f$
electrons significantly impact the magnetic properties in rare-earth
intermetallic compounds. So, we examined the configurational entropy
dependence of the magnetic properties of DyNi through a successive replacement
of Dy with a pair of rare-earth elements located on both sides of Dy in the
periodic table: partial replacement by Tb+Ho or Gd+Tb+Ho+Er. Within our
replacement sequence, we can maintain the lattice constants and the average
number of 4$f$ electrons. Consequently, we could explore the high-entropy
effect at the rare-earth site while preserving the electronic state of DyNi
intact. In RNi compounds, GdNi and (Dy, Ho, or Er)Ni crystallize into the
orthorhombic CrB-type and the orthorhombic FeB-type structure,
respectivelyRajivgandhi:JMMM2017 ; Paudyal:PRB2008 ; Sato:JMMM1986 . The
crystal structure of TbNi might be controversial: a monoclinic structure with
the space group P21m or an orthorhombic with the space group
PnmaRajivgandhi:JMMM2017 . All RNi (R=Gd to Er) compounds are ferromagnets
with the Curie temperature $T_{\mathrm{C}}$=71 K for R=Gd, 67 K for R=Tb, 62 K
for R=Dy, 37 K for R=Ho, and 13 K for R=Er, respectivelyGignoux:JMMM1976 ;
Rajivgandhi:JMMM2017 . Despite the changes in crystal structure that occur
upon going from R=Gd to R=Tb and from R=Tb to R=Dy, we synthesized DyNi,
(Tb1/3Dy1/3Ho1/3)Ni, and (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni, which are
predominantly composed of the FeB-type structure components.

In this paper, we report on the structural and magnetic properties of RNi
(R=Dy, Tb1/3Dy1/3Ho1/3, and Gd1/5Tb1/5Dy1/5Ho1/5Er1/5). Our findings confirm
that ferromagnetic ordering is robust, and that $T_{\mathrm{C}}$ is relatively
unaffected by the increase of configurational entropy at the rare-earth site.
(Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni shows an additional magnetic anomaly below
$T_{\mathrm{C}}$, which suggests a possible spin reorientation. We evaluated
the configurational entropy dependence of the magnetocaloric effect, which is
discussed along with the anisotropy of rare-earth magnetic moments.

Figure 1:  XRD patterns of DyNi, (Tb1/3Dy1/3Ho1/3)Ni, and
(Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni. The origin of each pattern is shifted by a
value for clarity.

##  II Materials and Methods

Polycrystalline samples were prepared using a homemade arc furnace as detailed
in Table 1. The materials used were rare earth (Gd, Tb, Dy, Ho, and Er) (99.9
%) and Ni (99.9 %). The constituent elements with the stoichiometric ratio
were melted on a water-cooled Cu hearth under an Ar atmosphere. The button-
shaped samples were remelted several times and flipped each time to ensure
homogeneity. Each as-cast sample was then annealed in an evacuated quartz tube
at 800 ∘C for four days. Room temperature X-ray diffraction (XRD) patterns of
powdered samples were obtained using an X-ray diffractometer (XRD-7000L,
Shimadzu) with Cu-K$\alpha$ radiation.

The temperature dependence of dc magnetization $\chi_{\mathrm{dc}}$ ($T$)
between 50 K and 300 K was measured using VSM (vibrating sample magnetometer)
option of VersaLab (Quantum Design). The isothermal magnetization curves
between 50 K and 110 K were also taken using the VersaLab.

##  III Results and Discussion

Figure 1 displays the XRD patterns of DyNi, (Tb1/3Dy1/3Ho1/3)Ni, and
(Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni, along with the simulation pattern of DyNi with
the FeB-type structure taken from the ICSD database (Coll Code: 103332). All
experimental patterns match the simulation pattern. As mentioned in the
Introduction, GdNi or TbNi crystallizes into a structure different from the
FeB-type of RNi (R=Dy, Ho, and Er). However, the FeB-type structure is
stabilized when dominant elements of Dy, Ho, and Er are present. We note that
the extra diffraction peaks assigned as the R2O3 (R=Dy, Tb+Dy+Ho, or
Gd+Tb+Dy+Ho+Er) phase are detected (see * in Fig. 1). Table 1 lists the
lattice parameters determined with the help of Rietveld refinement
programIzumi:SSP2007 ; Tsubota:SR2017 . While the $c$-axis length is almost
independent of configurational entropy change at the rare-earth site, the
$a$-axis (the $b$-axis) exhibits a slight expansion (contraction) with
increasing configurational entropy.

Figure 2:  Temperature dependences of $\chi_{\mathrm{dc}}$ of RNi system. The
external field is 100 Oe. The inset is the temperature derivative of
$\chi_{\mathrm{dc}}$ for each sample. Figure 3:  Isothermal magnetization
curves around $T_{\mathrm{C}}$ for (a) DyNi, (b) (Tb1/3Dy1/3Ho1/3)Ni, and (c)
(Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni , respectively. (d) Comparison of magnetization
curves among three RNi compounds at 50 K, 70 K, 90 K, and 110 K.

Figure 2 depicts $\chi_{\mathrm{dc}}$ ($T$) under an external field of 100 Oe
for the RNi system. Each sample exhibits a steep increase in
$\chi_{\mathrm{dc}}$ below approximately 70 K, which is indicative of
ferromagnetic ordering. $T_{\mathrm{C}}$ is defined by the minimum point of
the temperature derivative of $\chi_{\mathrm{dc}}$ (see the inset of Fig.2 and
Table 1). This is one of the effective ways to obtain $T_{\mathrm{C}}$ of
ferromagnetsOikawa:APL2001 ; Miyahara:JSNM2018 . DyNi undergoes a
ferromagnetic transition at $T_{\mathrm{C}}$=59 K, which is consistent with
the literature dataGignoux:JMMM1976 . (Tb1/3Dy1/3Ho1/3)Ni possesses
$T_{\mathrm{C}}$=63 K, slightly enhanced compared to DyNi, and the
$T_{\mathrm{C}}$ value remains unchanged in (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni. We
note that the $\chi_{\mathrm{dc}}$ ($T$) of (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni
shows a small anomaly around 57 K, which is discussed later. The results of
$\chi_{\mathrm{dc}}$ ($T$) indicate that ferromagnetic ordering is resistant
to atomic disorder at the rare-earth site.

DyNi, HoNi, and ErNi, which possess the orthorhombic FeB-type structure,
exhibit a non-collinear magnetic structure at $T_{\mathrm{C}}$ = 62 K, 37 K,
and 13 K, respectivelyRajivgandhi:JMMM2017 ; Gignoux:JMMM1976 . In these
compounds, rare-earth magnetic moments have a ferromagnetic arrangement
parallel to the $a$-axis and an antiferromagnetic arrangement parallel to the
$c$-axis. The angle between the rare-earth moment and the $a$-axis is 29∘ for
DyNi, 25∘ for HoNi, or 61∘ for ErNiRajivgandhi:JMMM2017 ; Gignoux:JMMM1976 .
Although the crystal structures of GdNi and TbNi differ from the FeB-type
(GdNi: CrB-type, TbNi: monoclinic or orthorhombic)Rajivgandhi:JMMM2017 , they
are also ferromagnets with $T_{\mathrm{C}}$ = 69 K and 67 K,
respectivelyRajivgandhi:JMMM2017 . The magnetic ordering temperatures of RNi
(=Dy, Ho, and Er) compounds follow the de Gennes scaling, which suggests a
weak effect of energy-level splitting of the $J$-multiplet due to the
crystalline-electric-field effectBucher:PRB1975 ; Kitagawa:JALCOM1997  at
$T_{\mathrm{C}}$. In such a case, the 4$f$ electron distribution of a single
rare-earth ion would be responsible for the magnetic
structureRinehart:ChemSci2011 ; Kitagawa:RP2019 . The 4$f$ electron
distribution of a single R3+ ion (R=Dy or Ho) is oblate, and the direction of
the rare-earth magnetic moment is perpendicular to the equatorially expanded
4$f$-electron charge cloudRinehart:ChemSci2011 . On the other hand, the 4$f$
electron distribution of a single Er3+ ion is prolateRinehart:ChemSci2011 ,
causing the magnetic moment of Er ion to be perpendicular to that of the R3+
ion (R=Dy or Ho). In fact, the magnetic moments of DyNi and HoNi are nearly
parallel to the $a$-axis and the direction of the Er3+ moment tilts toward the
$c$-axis. The 4$f$ electron distribution of a single Tb3+ ion is oblate, which
is the same as Dy3+ or Ho3+. Therefore, the magnetic structure of
(Tb1/3Dy1/3Ho1/3)Ni would not be significantly different from that of DyNi.
However, in (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni, competition between easy
magnetization axes might occur, potentially leading to a spin reorientation as
observed in (Gd0.38Tb0.27Dy0.20Ho0.15)Mn6Sn6Min:CP2022 . As shown in Fig. 2,
$\chi_{\mathrm{dc}}$ ($T$) of (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni shows a small
anomaly around 57 K, which is clearly detected by d$\chi$/d$T$ with a double-
dip structure (see the inset of Fig. 2). We speculate that the anomaly at a
lower temperature of 57 K suggests a change of magnetic structure like a spin
reorientation.

The isothermal magnetization curves ($M$: magnetization and $H$: external
field) measured around $T_{\mathrm{C}}$ are shown in Fig.3(a) for DyNi, Fig.
3(b) for (Tb1/3Dy1/3Ho1/3)Ni, and Fig.3(c) for (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni,
respectively. In each sample, the pronounced steep increase of magnetization
at lower external fields below approximately $T_{\mathrm{C}}$ supports the
ferromagnetic ground state. We note that the noticeable irreversibility is not
observed in any of the samples. Figure 3(d) provides a comparison of the
magnetization curves among the three compounds at temperatures of 50 K, 70 K,
90 K, and 110 K. With decreasing temperature, the $M$-$H$ curve of
(Tb1/3Dy1/3Ho1/3)Ni deviates from the other curves, albeit displaying a
resemblance to that of (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni. As illustrated in Fig.
2, $\chi_{\mathrm{dc}}$ ($T$) of (Tb1/3Dy1/3Ho1/3)Ni is smaller compared to
the other two compounds at low temperatures, indicating a relatively weaker
magnetic response in (Tb1/3Dy1/3Ho1/3)Ni. Consequently, this might lead to the
lowest $M$ for (Tb1/3Dy1/3Ho1/3)Ni at a fixed $T$ (temperature) and $H$. It
should be noted that the variation in magnetic moment associated with each
sample is another contributing factor to the differences in $M$ at fixed $T$
and $H$. Further investigation is required to elucidate the individual
element’s specific contribution. Moreover, Fig. 3(d) reveals the intersection
of magnetization curves between DyNi and (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni at 50 K
or 70 K. Such phenomena may be attributed to changes in magnetic anisotropy
energy and saturation magnetic moment.

Figure 4:  (a) Temperature dependences of -$\Delta S_{\mathrm{mag}}$ at
$H_{\mathrm{max}}$=10 kOe, 20 kOe, and 30 kOe for RNi system. (b) Temperature
dependences of $-\mathrm{d}\chi_{\mathrm{dc}}/\mathrm{d}T$ for RNi system.

The magnetic entropy change $\Delta S_{\mathrm{mag}}$ ($T$,$H$) is obtained by
using the Maxwell’s relation as follows:

$\Delta S_{\mathrm{mag}}(T,H)=\int_{0}^{H_{\mathrm{max}}}\left[\frac{\partial
M(T,H)}{\partial T}\right]_{H}dH$ (1)

, where $H_{\mathrm{max}}$ is the maximum external field. The temperature
dependences of -$\Delta S_{\mathrm{mag}}$ ($T$) at $H_{\mathrm{max}}$=10 kOe,
20 kOe, and 30 kOe for the RNi system are summarized in Fig.4 (a). All samples
show a maximum of -$\Delta S_{\mathrm{mag}}$ ($T$) at approximately
$T_{\mathrm{C}}$. According to Eq. (1), $\Delta S_{\mathrm{mag}}$ ($T$) is
influenced by $[\frac{\partial M(T,H)}{\partial T}]_{H}$. This implies that a
significant change in $M$ with decreasing temperature at a fixed $H$ is
necessary to enhance $\Delta S_{\mathrm{mag}}$ ($T$). Therefore, it is
worthwhile to compare -$\Delta S_{\mathrm{mag}}$ ($T$) with
$-\mathrm{d}\chi_{\mathrm{dc}}/\mathrm{d}T$ (refer to Figs.4 (a) and 4 (b)),
as the latter represents the change in the initial slope of the $M$-$H$ curve
resulting from the temperature variations. A larger value of
$-\mathrm{d}\chi_{\mathrm{dc}}/\mathrm{d}T$ has the potential to contribute to
a more significant change in $M$ when the temperature changes. The dependence
of $-\mathrm{d}\chi_{\mathrm{dc}}/\mathrm{d}T$ on configurational entropy
resembles that of -$\Delta S_{\mathrm{mag}}$ ($T$), particularly at
$H_{\mathrm{max}}$=10 kOe. At each $H_{\mathrm{max}}$, while the peak value of
-$\Delta S_{\mathrm{mag}}$ for (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni diminishes
compared to DyNi, the temperature dependence of -$\Delta S_{\mathrm{mag}}$
becomes broader. This broadening is advantageous for magnetic refrigeration
applications. The presence of a spin reorientation below $T_{\mathrm{C}}$
contributes to this advantage, as the modification in magnetic structure gives
rise to an additional $-\mathrm{d}\chi_{\mathrm{dc}}/\mathrm{d}T$. As
mentioned earlier, this spin reorientation likely arises from the interaction
between rare-earth elements with distinct magnetic anisotropy. Consequently,
the present study suggests the potential enhancement of magnetocaloric
properties by manipulating rare-earth magnetic moment anisotropy in the high-
entropy state.

In this discussion, we aim to compare the magnetocaloric effect between RNi
and rare-earth HEAs. Specifically, we examine the peak value of -$\Delta
S_{\mathrm{mag}}$, denoted as -$\Delta S^{\mathrm{peak}}_{\mathrm{mag}}$. In
the RNi system, the configurational entropy dependence of -$\Delta
S^{\mathrm{peak}}_{\mathrm{mag}}$ exhibits a non-systematic trend. -$\Delta
S^{\mathrm{peak}}_{\mathrm{mag}}$ decreases on going from DyNi,
(Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni to (Tb1/3Dy1/3Ho1/3)Ni. In certain rare-earth
HEAsLaw:JMR2023 , -$\Delta S^{\mathrm{peak}}_{\mathrm{mag}}$ decreases in the
order of GdTbDy, GdTbDyHo, GdTb, and GdTbDyHoEr (GdTbHoEr). In these rare-
earth HEAs, changes occur in the average number of 4$f$ electrons and lattice
constants, resulting in varying magnetic ordering temperatures ranging from
184 K to 258 KLaw:JMR2023 . In contrast, our RNi system maintains a nearly
constant $T_{\mathrm{C}}$, likely due to minimal alterations in lattice
parameters and the average number of 4$f$ electrons. However, both RNi and
rare-earth HEAs exhibit a non-systematic configurational entropy dependence of
-$\Delta S^{\mathrm{peak}}_{\mathrm{mag}}$. Therefore, it appears that factors
other than configurational entropy may influence the control of -$\Delta
S^{\mathrm{peak}}_{\mathrm{mag}}$. Here we comment on the -$\Delta
S^{\mathrm{peak}}_{\mathrm{mag}}$ value of (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni. It
is widely acknowledged that -$\Delta S^{\mathrm{peak}}_{\mathrm{mag}}$ follows
a power law dependence on the magnetic fieldFranco:IJR2010 , represented as
-$\Delta S^{\mathrm{peak}}_{\mathrm{mag}}$$\propto$$H^{n}$. By applying this
relation to (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni (see also Fig.4 (a)) and deducing
the exponent $n$ to be 0.89, we can estimate -$\Delta
S^{\mathrm{peak}}_{\mathrm{mag}}$ value at $H_{\mathrm{max}}$=50 kOe to be
10.6 J/kg$\cdot$K. This value is larger compared to equimolar quinary rare-
earth HEAs such as GdTbDyHoEr and GdTbHoErPr, which exhibit -$\Delta
S^{\mathrm{peak}}_{\mathrm{mag}}$ values of 8.6 J/kg$\cdot$K and 6.92
J/kg$\cdot$K, respectively, at $H_{\mathrm{max}}$=50 kOeYuan:AM2017 ;
Lu:JALCOM2021 .

##  IV Summary

We have studied the effect of configurational entropy on the structural and
magnetic properties of DyNi by successively replacing Dy with pair of R
elements located on both sides of Dy in the periodic table. This elemental
substitution of Dy preserves the lattice parameters and average number of 4$f$
electrons. Although the crystal structures of GdNi and TbNi differ from the
FeB-type of RNi (R=Dy, Ho, and Er), all RNi (R=Dy, Tb1/3Dy1/3Ho1/3, and
Gd1/5Tb1/5Dy1/5Ho1/5Er1/5) samples crystallize into the FeB-type structure.
$T_{\mathrm{C}}$ of DyNi is almost unchanged by increasing the configurational
entropy at the rare-earth site, and the ferromagnetic ordering is robust under
the high-entropy state. In (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni, the additional
magnetic anomaly is observed, which would be attributed to a spin
reorientation resulting from the introduction of Gd+Er and the emergence of
competing magnetic interactions. The competition does not disrupt the
ferromagnetic ordering, even in the high-entropy state, but rather leads to a
spin reorientation transition. Furthermore, we assessed the magnetocaloric
effect of the RNi system. Although the peak value of -$\Delta
S_{\mathrm{mag}}$ of (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni is reduced compared to
DyNi, the temperature dependence of -$\Delta S_{\mathrm{mag}}$ becomes
broader. Additionally, we observed a strong correlation between the
configurational entropy dependence of -$\Delta S_{\mathrm{mag}}$ ($T$) and
that of -$\mathrm{d}\chi_{\mathrm{dc}}/\mathrm{d}T$. Hence, the broadening of
-$\Delta S_{\mathrm{mag}}$ ($T$) in (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni can be
attributed to the spin reorientation arising from the mixing of rare-earth
elements with distinct magnetic anisotropy. Consequently, our study suggests
the potential for enhancing the magnetocaloric properties by designing the
anisotropy of rare-earth magnetic moments in the high-entropy state.

## ACKNOWLEDGMENTS

J.K. is grateful for the support provided by the Comprehensive Research
Organization of Fukuoka Institute of Technology.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

Yuito Nakamura: Investigation, Formal analysis. Koshin Takeshita:
Investigation, Formal analysis. Terukazu Nishizaki: Investigation, Formal
analysis, Writing - reviewing & editing. Jiro Kitagawa: Supervision, Formal
analysis, Writing - original draft, Writing - reviewing & editing.

### DATA AVAILABILITY

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

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