Magnetic interactions and spin-wave stiffness constant of In-substituted yttrium iron garnets

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Original Article

Magnetic interactions and spin-wave stiffness constant of

In-substituted yttrium iron garnets

Vu Thi Hoai Huong

a

, Dao Thi Thuy Nguyet

a,*

, Nguyen Phuc Duong

a

, To Thanh Loan

a

,

Siriwat Soontaranon

b

, Le Duc Anh

c

a_{International Training Institute for Materials Science (ITIMS), Hanoi University of Science and Technology, 1 Dai Co Viet Road, Hanoi, 10000, Viet Nam}
b_{Synchrotron Light Research Institute, University Avenue 111, Nakhon Ratchasima, 30000, Thailand}

c_{Department of Electronic Engineering and Information System, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8654, Japan}

a r t i c l e i n f o

Article history:

Received 29 December 2019
Received in revised form
22 February 2020
Accepted 24 February 2020
Available online xxx
Keywords:

In-substituted yttrium iron garnets
Magnetization

Curie temperature
Molecularfield coefficients
Spin-wave stiffness constant

a b s t r a c t

Indium-substituted yttrium iron garnet samples, Y3Fe5
xInxO12(x¼ 0e0.7, step 0.1), were prepared using

a citrate solgel method. Synchrotron X-ray diffraction (SXRD) measurements combined with the Rietveld
refinement technique were used to investigate the crystallization, structure parameters and lattice
distortion in the samples. Magnetization and Curie temperature of the samples were measured with the
SQUID and VSM equipments. The non-magnetic indium ions were found to reside at the octahedral sites,
leading to an increase of the total magnetization and a decrease in the Curie temperature. Molecularfield
coefficients Naa, Nddand Nadwere determined byfitting the experimental thermomagnetization curves in

the framework of a two-sublattice ferrimagnetic model. The stiffness constant of the spin waves, D, in
these samples was calculated based on the exchange interaction constants, Jij, and its temperature

dependence was derived for the sublattice magetizations. The calculated results for D(T) are in good
agreement with the experimentally measured data and are significantly large around room temperature.
© 2020 The Authors. Publishing services by Elsevier B.V. on behalf of Vietnam National University, Hanoi.
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1. Introduction

Yttrium iron garnet (YIG) belongs to a cubic ferrite family with
the space group Oh10eIa3d [1]. Considering one formula unit,

Y3Fe5O12, three Y atoms occupy the 24c (dodecahedral) sites, two Fe

atoms occupy the 16a (octahedral) sites and three Fe atoms occupy
the 24d (tetragonal) sites which are formed by the surrounding O2

ions. Since Y ions have no magnetic moment, there are only two
magnetic sublattices formed by Fe ions at the 16a and 24d sites,

which couple antiparallel to each other with the net magnetization,
Mtot¼ Md
Ma, in accordance with the N
eel model [1]. With the

existence of differently sized crystallographic sites, YIG can be used
for substituting a wide variety of ionic radii and valence states,
which provide a wide range of control of magnetization and Curie
temperature. At substitution of nonmagnetic ions for Fe in
mod-erate concentrations, the decrease in the number of nearest
mag-netic iron neighbors leads to a canting of magmag-netic moments.
Hence, the pair exchange constants Jij(where i and j are a or d)

between an iron ion and its remaining surrounding magnetic ions
also decrease [2]. Our recent study on the magnetic properties of
the co-substituted Y_3
2xCa2xFe5
xVxO12series, revealed that a

se-vere local structure distortion, along with the magnetic dilution
effect, can reduce the overlap between the 3d orbitals of Fe and the
2p orbitals of O, leading to another cause of reduction for Jij[3].

Within a molecularfield model, the temperature dependence of the
spontaneous magnetization (Ms) and the Curie temperature (TC)

can be calculated on the basis of molecularfield coefficients, which
characterize the interactions in each sublattice (Naa, Ndd) and those

between sublattices (Nad). Studies on magnetically diluted YIG

samples have shown that appropriate sets of coefficients can
effectively reproduce the experimental MseT curves.

Studies on magnonics have been explored for YIG because it is a
ferrimagnetic insulator with a low magnetization damping [4e8]
and a long spin-wave propagation lifetime [9,10]. Spin waves can be
manipulated for various applications, including logic operations
[6e8,11e13], data buffering elements [7], and magnon transistors
[8]. Hence, YIG shows the potential for application in computing
technology.

This study discusses the magnetic properties of the solid solution
systems of Y3Fe5
xInxO12, where In atoms favorably occupy the a

sites that form the weak magnetization sublattice. The solubility of
these solid solutions has not fully been studied, and their magnetic

* Corresponding author.

E-mail addresses:,(D.T. Thuy
Nguyet).

Peer review under responsibility of Vietnam National University, Hanoi.

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properties have not been comprehensively investigated. Previous

studies showed that the total magnetization is enhanced in a certain
concentration range of nonmagnetic elements, although magnetic
dilution in the a sublattice causes spin canting in the oppositely
magnetized d sublattice. However, the d sublattice becomes
anti-ferromagnetically ordered in case the number of magnetic neighbors
at the a sites surrounding a magnetic ion in the d sublattice exceeds a
concentration threshold value close to zero, at which the total
magnetization drastically decreases [2]. Gilleo and Geller [14,15]
investigated the magnetic moments of YIG samples substituted with
nonmagnetic ions, i.e., Rẳ Sc3ỵ, Zr3ỵ, and In3ỵat the a sublattice
with the following general formula: Y3[Fe2
xRx]Fe3O12. The results

show that the samples are ordered ferrimagnetically in the
con-centration region 0 x  ~0.7, and that their net magnetic moment
increases proportionally with x. The increase rate is similar to that of
the series of the samples substituted with different R species.
Nevertheless, the increase rate is lower than the expected value of
the collinear N
eel configuration because of the spin canting in the
d sublattice. As the concentration increases beyond ~0.7, the degree
of canting abruptly changes and, consequently, the
antiferromag-netic phase dominates with the net moment decreasing to zero at
x¼ 1. This work focuses on the ferrimagnetic phases of Y3Fe3
xInxO12

with 0 x  0.7. The saturation magnetizations in a wide
temper-ature range (minimum value of 5 K) and the Curie tempertemper-atures of
these compositions are collected. Their spin wave stiffness constants
are evaluated on the basis of exchange constants and sublattice
magnetizations derived from the molecularfield theory.

2. Experimental

2.1. Sample preparation

Y3Fe5
xInxO12particle samples (x¼ 0e0.7, step 0.1) were

pre-pared using the solegel method in accordance with a previous study
[3]. The starting materials for the preparation of the samples were
high-purity Fe(NO3)3, Y2O3, and In2O3(99.99%, Sigma-Aldrich). The

oxides were dissolved in 1 M HNO3to form nitrate solutions. The

Fig. 1. SXRD patterns of the Y3Fe5
xInxO12samples (x¼ 0, 0.3, 0.6). The inset shows the highest intensity peaks (420).

Table 1

Structural parameters of the YFe5
xInxO12series estimated from Rietveld

refine-ment: lattice constant (A), average interatomic distances (ddeO, daeO, dceO) and
microstrain (ε).

x A (Å) ddeO(Å) daeO(Å) dceO(Å) <dSXRD> (Å) ε (%)

0 12.369 1.8568 1.9814 2.3804 20 0.345
0.1 12.397 1.8610 1.9859 2.3858 21 0.376
0.2 12.412 1.8639 1.9882 2.3886 25 0.388
0.3 12.414 1.8634 1.9884 2.3840 21 0.413
0.4 12.416 1.8639 1.9889 2.3894 22 0.420
0.5 12.429 1.8658 1.9910 2.3919 21 0.430
0.6 12.433 1.8664 1.9916 2.3927 21 0.448
0.7 12.466 1.8714 1.9969 2.3990 20 0.455
Fig. 2. SXRD pattern and Rietveld refinement data of the sample Y3Fe4.7In0.3O12. The

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metal nitrate solutions were mixed with the required amount of
metal ions at a stoichiometric ratio of [Y]:[Fe]:[In]¼ 3:(5
x):x. An
aqueous citric acid solution was added to the solution with a total
cation/citric acid molar ratio of 1/3. The mixtures were stirred at
400 rpm and slowly evaporated at 80C to form gels. The gels were
dried at 95C for more than 12 h to form xerogels. Particle samples
were obtained after the xerogels were burned at 400C for 2 h and
annealed at Tan¼ 900C for 5 h.

2.2. Characterization

Synchrotron X-ray powder diffraction (SXRD) experiments were
carried out at the beamline SAXS of the Synchrotron Light Research
Institute in Thailand (

l

¼ 1.54 Å) to identify the crystal structure of
the samples. Data were analyzed using the Rietveld method and the
FullProf program [16]. Diffraction peaks were modeled using a
pseudo-Voigt function. LaB6was used as the standard to determine

the instrumental broadening.

Field emission scanning electron microscopy (FESEM; JEOL
JSM-7600 F) was adopted to examine particle sizes and morphological
characteristics.

Magnetization curves in the temperature range from 5 K to
room temperature were measured using a superconducting
quan-tum interference device (Quanquan-tum Design) with magneticfields of
up to 10 kOe. The magnetic characteristics were also studied with a

vibrating sample magnetometer (ADE Technology-DMS 5000) at
80e600 K. In both facilities, the maximum applied magnetic field
was 10 kOe.

3. Results and discussion

3.1. Crystal structure and morphological characteristics

The SXRD measurements of the sample series show that the
diffraction peaks of all samples can be indexed within the standard
diffraction pattern of YIG without any indication of foreign phases.
For demonstration, the SXRD patterns of three compositions (x¼ 0,
0.3, and 0.6) are shown inFig. 1. The inset shows a shift of the (420)
lines toward small Bragg angles, indicating that the lattice constant
increases as the indium concentration increases. Structural
pa-rameters, including the lattice constant A and the average bond
lengths between cations in d, a, and c sites and oxygen (ddeO, daeO,
and dceO), were determined via the Rietveld refinement. The
in-crease in lattice constant can be ascribed to the larger atomic radius
of In compared to Fe. In the octahedral a sites, the radius of Fe3ỵ
(rFe3ỵẳ 0.785 ) is smaller than that of In3ỵ(rIn3ỵẳ 0.94 ) [17]. In

accordance with the lattice expansion effect, ddeO, daeO, and dceO
also increase with x. The average size of the coherent scattering
region <dSXRD> and the average lattice microstrain <ε> ¼

D

A/A

were determined through the analysis of the peak that broadened
after the Rietveld method application by using the FullProf program
with the instrumental resolution function identified via the SXRD
analysis of LaB6. All the obtained structure parameters are listed in

Table 1. The mean crystallite sizes are in the range of 20e25 nm. The
increase in the average microstrain with increasing x can be
un-derstood in terms of lattice unit cell distortion caused by the In
substitution.

The microstructure of the samples was characterized through
FESEM. The micrographs of the samples are shown inFig. 3. The
grain sizes of the sample with the lowest In content at x¼ 0.1 are
considerably increased compared with those of the pure sample
possibly because of the low melting point of the In component. It
has been shown that the melting temperature of indium oxide
(In2O3) in powder form is as low as 850C [18]. For Tan¼ 900C,

the indium component can be in a melting state and this molten
part can draw the surrounding materials to form big grains. The
grain sizes reach the micron scale as the indium concentration
further increases. The micrographs of the substituted samples
indicate that small grains melt and merge to form larger ones
during crystallization. The grain sizes are much larger than the
crystallite sizes <dSXRD> as determined via the SXRD line

broadening.

Fig. 3. FESEM images of the samples x¼ 0, 0.1, 0.3, 0.7.

Fig. 4. Magnetization curves measured at 5 K and 290 K of the Y3Fe5
xInxO12samples (x¼ 0e0.7).

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3.2. Magnetic properties

The magnetization curves MeH of the investigated samples
were measured at different temperatures. For demonstration, the
MeH curves recorded at T ¼ 5 K and 290 K are displayed inFig. 4. A
general behavior is that the magnetization approaches technical
saturation above ~2.5 kOe. As the magneticfield further increases,
the saturation state is attained with negligible magnetic
suscepti-bility. The magnetization loops of the samples show small magnetic
hysteresis behavior. The coercivity for the pure YIG nanoparticle
sample was discussed in detail in [19]. The values of the saturation
magnetization Mswere determined on the basis of theflat part of

the curves in the highfield region. As such, the saturation magnetic
moments mexp_{were calculated in Bohr magneton per formula unit.}

The saturation magnetic moments of the samples at 5 K as a
function of indium concentration are presented inFig. 5, and the
values are listed inTable 2. The saturation magnetization
monot-onously increases as the substitution level increases, indicating that
In atoms mostly reside in a sites, which belong to the weak
magnetization sublattice.Fig. 5also shows the plot of the linear
behavior of the saturation magnetic moment m(x) of the samples
prepared via a solid-state reaction versus the concentration of
nonmagnetic atoms (Sc3ỵ, Zr3ỵ, In3ỵ) reported by Geller [14] and
Gilleo [15]. m(x) versus x dependence follows the expression

m(x)ẳ 5 ỵ 4.05*x. (1)

m(x) in Eq.(1)is lower than that in the collinear N
eel configuration,
i.e., m(x)¼ 5 þ 5*x, because of the spin canting in the d sublattice.
The magnetic moments of the samples agree with those derived

using Eq.(1), although their values are slightly lower (<4%) than the
expected values for some of the samples. This deviation can be
attributed to a small amount of nonmagnetic impurity in these
samples, or to a fraction of In atoms (<0.03 atoms per formula unit)

Fig. 5. Magnetic moment, mexp_{, at 5 K of the samples as a function of the In}

concen-tration, x. The solid line represents the calculated values according to Eq.(1).

Table 2

Curie temperature (TC), experimental magnetic moment at 5 K (m(5)exp) and

calculated magnetic moment at 0 K (m(0)cal_{), and estimated indium contents at the a}

sites and d sites of the Y3Fe5
xInxO12series.

x TC(K) M (5 K)exp

(mB/f.u.)

In3ỵat a sites In3ỵat d sites

0 564 4.9 0 0

0.1 540 5.4 0.1 0

0.2 522 5.8 0.2 0

0.3 510 5.97 0.273 0.027

0.4 484 6.35 0.37 0.03
0.5 466 6.84 0.48 0.02
0.6 450 7.3 0.586 0.014
0.7 433 7.65 0.68 0.02

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that occupy the a sites. Thus, the cation distribution in this sample
series can be approximately expressed as {Y3}[Fe2
xInx](Fe3)O12. To

justify this derivation, we reproduced the corresponding SXRD
patterns by using the FullProf program. In the calculations, the
cation distribution model was constructed with the following
atomic coordinations: Y is in the dodecahedral site 24c (1/8,0,1/4),
Fe/In in the octahedral 16a (0,0,0) and tetrahedral 24d (3/8,0,1/4)
sites, and O in the 96h position (x, y, z). The O position parameters
were fixed at the values determined on the basis of neutron
diffraction data [1]. The calculated results agree with the
experi-mentalfindings with a goodness of fit (

c

2_{) in the range of 1.13}_e1.68

and the weighted profile R-factor (Rwp) in the range of 8.43%e11.3%.

For demonstration, the SXRD pattern and the Rietveld refinement
of the sample x¼ 0.3 are shown inFig. 2.

The Curie temperature was determined (Table 2) on the basis
of Msexpressed in emu per gram as shown inFig. 6for the

sam-ples x¼ 0, 0.2, 0.5 and 0.7. The thermomagnetic measurements in
the low field (H ¼ 100 Oe) were also determined (Fig. 7). TC

extracted from the curves agrees with those determined using Ms

versus T curves. Gilleo [15] predicted the evolution of the Curie
temperature for magnetically diluted YIG series by using a
simplified model based on the number of magnetic interactions
pairs. A comparison between the experimental and calculated
values is shown inFig. 8. An agreement between the two sets of TC

values is observed showing the dominance of the intersublattice
magnetic interaction Jad over the intrasublattice interactions Jaa

and Jddin establishing the magnitude of the magnetic ordering

temperature.

3.3. Molecularfield calculations

Dionne [2] calculated the Ms versus T curve of YIG and its

nonmagnetic substituted derivatives through a molecular field
approximation. The intrasublattice and intersublattice interactions
between the magnetic moments in the a and d sublattices are
characterized by Naa, Ndd, and Nad, respectively. Dionne [2]

exam-ined the magnetization curves of various compositions with the
general formula Y3[Fe2
uRu](Fe3
wQw), where the results for

nonmagnetic elements R and Q are Sc4ỵ, Sn4ỵ, Zr4ỵ, In3ỵ, Al3ỵand
Ga3ỵ; revealed linear relations of the exchange parameters with the
nonmagnetic ion concentrations of the a and d sublattices for
u 0.70 and w  1.95 (for further details, see [2]). In a random

distribution assumption, the average microscopic exchange
in-tegrals <Jij> are related to the molecular field coefficient Nij as

follows [20]:

< Jij> ¼

4

p

njgigj

m

2B

2Z_ij
1
4

p

A3_N
A

8
!

Nij; (2)

where njand gjare the number of Fe ions and spectroscopic

split-ting factor in the j sublattice, respectively; zij is the nearest

neighbor; A is the lattice constant; and NAis Avogadro's number.

Molecular field calculations were performed for the sample
series to further investigate the influence of In substitution in the
magnetic interactions. According to the derived cation distribution,

the In concentration at the d sublattice is set to zero (w¼ 0). In the
calculations, the effect of spin canting in the d sublattice was

Fig. 7. Temperature dependence of magnetization measured in an applied field,

H¼ 100 Oe, for the Y3Fe5
xInxO12samples (x¼ 0e0.7). Fig. 8. Curie temperatures TCof the Y3Fe5
xInxO12samples (x¼ 0e0.7). Solid square:

experiment; line: calculated results (see text).

Fig. 9. Intra- (a) and intersublattice (b) molecularfield coefficients, Nddand Nad,

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considered. The sublattice magnetizations per mole at 0 K, Ma(0),

and Md(0) are determined as

Ma(0)ẳ Sag

m

BNA(2
x),

Md(0)ẳ Ma(0)ỵ (5 ỵ 4.05*x)NA, (3)

where Md(0) is derived from Eq.(1), Sais the spin number of the

magnetic ions in the a sublattice (S¼ 5/2 for Fe), g is the
spectro-scopic splitting factor (g¼ 2 for Fe), and NAis Avogadro's number. In

garnet structures, octahedra are far apart and do not share the
oxy-gen corner [14]. Therefore, magnetic dilution in this sublattice only
reduces the magnetization but does not affect the average interaction
within the sublattice <Jaa>. In the calculations, Naa is fixed

at _{30.4 mol/m}3 [2]. Spin canting in the d sublattice caused by

magnetic dilution in the a sublattice reduces the average
intra-sublattice and interintra-sublattice interactions<Jdd> and <Jad>,

respec-tively. Considering that an octahedron shares oxygen corners with

the six surrounding tetrahedra, the distortions of the octahedra
containing In3ỵ with a large radius modify the hybridization
be-tween the 3d wavefunctions of Fe3ỵand those of the 2p type of O2
,
which may be another cause of the decrease in the interactions of
Fe3ỵin tetrahedral sites [3]. The experimental MseT curves are fitted

by decreasing values for Nddand Nad as the In concentration

in-creases.Fig. 6illustrates the plot of the bestfit results, along with the
experimental data.Fig. 9presents the corresponding coefficients as a
function of the concentration x and those calculated by Dionne [2].
The results calculated in this study agree with the previously
calcu-lated results. The average exchange integrals Jijcalculated from the

molecularfield coefficients Nijby using Eq.(2)are listed inTable 3.

With respect to the propagation of spin waves in these garnet
materials, the precession of the net magnetization vector in the
effective magneticfield is described using the LandaueLifshitz and
Gilbert equations [21]. In the case of a zero appliedfield (Happ¼ 0)

and a negligible anisotropyfield compared to the exchange field,
precession mainly depends on the exchangefield Hex. According to

spin-wave theory, the energy of the spin wave is proportional to the

stiffness constant D as follows [22]:

ħ

u

¼ Dk2_, ₍₄₎

where

u

is the angular frequency, and k is the wave vector. D
rep-resents the strength of the exchange interactions that keep the net
magnetization vectors of the united cells parallel to each other.

According to Douglas [22], D at 0 K is related to Jij by the

following equation:

D(0)¼ (5/16) (5Jad
8Jaa
3Jdd)A2, (5)

Table 3

Molecular-field coefficients, Nij, and exchange integrals, Jij, of the Y3Fe5
xInxO12

series.
x Naa

(mol/cm3₎ N_(mol/cmdd 3₎ N_(mol/cmad 3₎ ₍₁₀Jaa
15_erg) J₍₁₀dd
15_erg) Jad(10

15_erg)

0
65
30.4 97.0
2.3
2.4 4.90
0.1
65
29.0 95.5
2.3
2.3 4.83
0.2
65
28.0 94.5
2.3
2.2 4.78
0.3
65
26.5 93.0
2.3
2.1 4.70
0.4
65
25.5 92.0
2.3
2.0 4.65
0.5
65
24.5 91.0
2.3
1.9 4.60

0.6
65
23.0 90.0
2.3
1.8 4.55
0.7
65
21.5 88.0
2.3
1.7 4.45

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where A is the lattice constant. D calculated from Jijaccording to Eq.

(5)[23e25] is lower than that obtained from experimental
tech-niques, such as specific heat, microwave [25e29], and Brillouin
scattering [30]. Using the sets of the exchange integral values
derived by Dionne for YIG [2], a negative D is obtained using Eq.(5).
However, previous works reported that D calculated using Jad

agrees well with the experimental results if Jaaand Jddare set to

zero [31,32]. This phenomenon occurs because the spins in the
sublattices a and d remain parallel to each other, while the
sub-lattice magnetizations Maand Mddeviate as the spin wave

propa-gates in the presence of the Weiss molecularfield. Hence, only Jad

contributes to D [32]. When Jadis equal to 4.9 10
15erg for the

pure YIG sample (Table 3), then D¼ 1.17  10
28erg cm2. D agrees
with the results derived from microwave and Brillouin methods in
which it can be expressed as D¼ (1 ± 0.1)  10
28_{erg cm}2_[26_e28_].

Fig. 10a shows the calculated D(0) values that are proportional to Jad

for the sample series.

Using the Green function method and assuming that only Jad

governs the magnitude of D, Srivastava et al. [32] showed that the
temperature dependence of D can be expressed in terms of
sub-lattice magnetizations as follows:

DTị
D0ịẳ

MaTị=Ma0ịMdTị=Md0ịịị

MdTị
MaTị=Md0ị
Ma0ịịị; (6)

On the basis of the calculated sublattice magnetizations at
different temperatures, we calculated the temperature
depen-dence of D(T)/D(0) for YIG by using Eq.(6).Fig. 10b illustrates the
results, together with the experimental data obtained from
mi-crowave measurements reported by Le Craw and Walker [26] and
Bahgar et al. [29]. The obtained calculations agree well with the
experimental results, particularly with the data provided by
Bahgar et al. [29]. D(T) slightly increases with temperature and
drastically decreases as temperature reaches the Curie point. The
maximal difference, (D(T)
D(0))/D(0), of 6.5% is obtained at
T¼ 300 K. This calculation reveals that D should approach zero at
TC. Similarly, D(T) was calculated for the substituted compositions.

The results for several compositions (x¼ 0, 0.3, 0.5, and 0.7) are
provided inFig. 10c for illustration. After the In substitution, the
stiffness constant is strongly enhanced within the temperature
range of 50e300 K. D(T)/D(0) increases as x increases, and the
maximal difference reaches 12% at 250 K for the sample with

x¼ 0.7. The significant increase in D for the In-substituted samples
in the moderate temperature range is related to the strong
decrease in the net magnetization, which is the denominator in
Eq.(6), because of the reduction of the Curie temperature.
4. Conclusions

In this study, single-phase YFe_5
xInxO12samples (x¼ 0e0.7) are

synthesized using the citrate solegel route with subsequent
annealing at 900 C in air. In the samples, almost all In atoms
occupy octahedral sites, thereby causing an increase in saturation
magnetization and a decrease in Curie temperature. TCis

propor-tional to the number of magnetic interaction pairs between Fe3ỵin
the two sublattices, indicating that Jadis crucial for the magnitude

of the magnetic ordering temperature. Nddand Naddecrease almost

linearly as the In substitution level increases. This result confirms
the universal rules reported by Dionne [2] for magnetically diluted
YIG compounds. D(0) is estimated from Jijin accordance with spin

wave theory. The calculated D(0) of pure YIG matches the
experi-mental result only in case Jadis used. The temperature dependence

of D(T)/D(0) is calculated on the basis of the sublattice
magneti-zation data derived from molecularfield theory. For pure YIG, the
calculated and experimental D(T)/D(0) agree with each other. These

results show that the YFe_5
xInxO12 (x ¼ 0e0.7) samples with

enhanced magnetization and sizable stiffness constant at room
temperature can serve as media for spin wave control and
manipulation.

Declaration of competing interest
We have no con_{flict of interest.}
Acknowledgment

This research was funded by the Vietnam National Foundation
for Science and Technology Development under grant number
103.02-2016.05.

References

[1] M.A. Gilleo, Ferromagnetic insulators: garnets, in: E. P Wohlfarth (Ed.),
Handbook of Magnetic Materials, 2, North-Holland Publishing Company,
1980, pp. 1e54.

[2] G.F. Dionne, Molecularfield coefficients of substituted yttrium iron garnets,
J. Appl. Phys. 41 (1970) 4874.

[3] V.T.H. Huong, N.P. Duong, D.T.T. Nguyet, S. Soontaranon, T.T. Loan, Local
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