Received: 3 July 2023
Revised: 5 December 2023
Accepted: 5 December 2023
DOI: 10.1111/jace.19663
RESEARCH ARTICLE
Manifestation of chemical pressure: Magnetism and
magnetostriction in nanoscale RFeO3 (R = Sm, Dy, Ho,
and Lu)
Smita Chaturvedi1,2,3
1 Department
2 Physics
Priyank Shyam4
Ying Liu2,5
Gopalan Srinivasan2
of Physics, Interdisciplinary School of Science, Savitribai Phule Pune University, Pune, India
Department, Oakland University, Rochester, Michigan, USA
3 Department
of Physics, Indian Institute of Science Education and Research, Pune, India
4 Interdisciplinary
5 Department
Nanoscience Centre, Aarhus University, Aarhus, Denmark
of Materials Science and Engineering, Hubei University, Wuhan, China
Correspondence
Smita Chaturvedi, Department of Physics,
Interdisciplinary School of Science,
Savitribai Phule Pune University,
Ganeshkhind, Pune 411007, India.
Email: smita.chaturvedi24@gmail.com
Abstract
The effect of ionic radii sizes on magnetostriction is studied in relation to structural and magnetic properties. To explore the effect of the chemical pressure,
nanoparticles of rare-earth (RE) orthoferrites, SmFeO3 , DyFeO3 , HoFeO3 , and
Priyank Shyam, Interdisciplinary
Nanoscience Centre, Aarhus University,
Aarhus, Denmark.
Email: priyank.shyam@gmail.com
LuFeO3 are studied using X-ray diffraction, field emission scanning electron
microscopy, and Raman spectroscopy. Magnetic and magnetostriction measure-
Funding information
Department of Science and Technology,
Science and Engineering Research Board
India, Grant/Award Number:
TAR/2022/000621; Fulbright Fellowship,
Grant/Award Number: 2372/F-N APE
FLEX/2018; National Science Foundation,
Grant/Award Numbers: ECCS-1923732,
ECCS-EAGER-2236879, DMR-1808892; Air
Force Office of Scientific Research
(AFOSR), Grant/Award Number:
FA9550-20-1-0114
directly influences the structural parameters. The distortion of FeO6 octahedra is
observed as a result of changing chemical pressure within the lattice. The different magnitudes of magnetostriction in RE orthoferrites can be attributed to the
ments are also performed. In these orthoferrites, the coordination of the RE
ion is eightfold, whereas the RE ionic radii are significantly different, which
different degrees of distortion of FeO6 octahedra, R–O dynamics, and spin–orbit
interactions in the system. The maximum value of magnetostriction (∼ 19 ppm)
and magnetization at 2 K (30.64 emu/g) is demonstrated by HoFeO3 . Comparison of structural parameters of the samples to their respective bulk counterparts
indicated relative structural distortion in nanoparticles.
KEYWORDS
magnetostriction, nanomaterial, structure–property relation
1
INTRODUCTION
With the emerging era of IoT (Internet of Things), materials possessing magnetostriction are of great significance
owing to their significant applications in various types of
magnetic sensors and actuators, which are the nervous
system of IoT. Materials exhibiting high values of magne-
J Am Ceram Soc. 2024;1–12.
tostriction, like Terfenol-D, SmFe2 , rare-earth (RE)-iron
compounds and composites, have potential application
in various fields such as sound generator, contactors,
vibration control in aerospace and translation devices
in automobile industries, magnetostrictive filters, and
so on.1–3 Materials at nanoscale have certain unique
advantages in terms of their physical properties. The high
wileyonlinelibrary.com/journal/jace
© 2024 The American Ceramic Society.
1
2
concentration of interfaces in nanoparticles provides the
ground for existence and interplay of rich magnetic phases
for better magnetic coupling, for example, ferrimagnetic–
antiferromagnetic, ferromagnetic–antiferrromagnetic.4
Due to finite size effects, such as high surface-to-volume
ratio and different crystal structures, magnetic nanoparticles are found to exhibit interesting and considerably
different magnetic properties than those found in their
bulk counterpart. The optimization of the nanoparticles’
size, morphology, agglomeration, and shapes to tune their
unique magnetic properties is exciting and rewarding.5
Perovskite oxides RFeO3 with space group Pnma (also
reported as the symmetry Pbnm in literature) are gaining significance as potential multiferroic materials.6–8
Featuring high temperature spin reorientation and possibility of spin canting/exchange-striction induced ferromagnetism/ferroelectricity, these ferrites are emerging
as potential multifunctional materials for energy-efficient
sensors and actuators.
Studying single crystals of various RE RFeO3 orthoferrites, Marezio et al. suggested that the structural arrangements, indicating the iron octahedra distortion, are very
small when replacing the RE ion R from Pr to Lu. Although
the same distortion for Lu to Sm is almost constant,
the position/size of oxygen polyhedra around the RE
ions varies appreciably across the series.9 The dynamics of structural parameters, such as bond lengths, bond
angles, and rotation/tilt of FeO6 octahedra, play a crucial
role in determining the physical properties of these RE
orthoferrites.10 These structural parameters were reported
to be directly influenced by chemical pressure (ionic radii)
using ab initio calculations.7 The effect of change in chemical pressure on the structure of nanoscale RE orthoferrites,
(for R = Lu to Sm having eightfold coordination) as well as
the impact of structure on the magnetic properties in terms
of magnetostriction is not explicitly explored.
The present work is intended to understand the effect of
the ionic radii sizes on the structural and magnetic properties of nanoparticles, exploring the cases of SmFeO3 ,
HoFeO3 , DyFeO3 , and LuFeO3 . The reason to consider
these orthoferrites are as follows: (i) Their ionic radii
are significantly different (Sm ∼ 0.958 Å; Dy ∼ 0.912 Å,
Ho ∼ 0.901 Å, and Lu ∼ 0.861 Å). (ii) Sm3+ has less than
half-filled “4f5 ” shell, Ho3+ and Dy3+ have more than half
filled “4f10 ” “4f9 ,” and Lu3+ has completely filled “4f14 ”
shell. Their magnetic/ferroelectric properties are affected
by the dynamics of their structural parameters (bond
lengths, bond angles, etc.). Changes in the size of the RE
ion induce distortion in the structure, also termed “chemical pressure.” Probing the impact of the local dynamics
of R and Fe atoms due to changes in chemical pressure
and understanding the overall magnetic behavior driven
by these changes is intriguing.
CHATURVEDI et al.
RE orthoferrites (RFeO3 ) demonstrate rich magnetic
properties. They are significant candidates for developing multiferroics.11 RE orthoferrites (with space group
Pnma) are weak ferromagnetic materials owing to
Dzyaloshinsky–Moriya interaction. These ferrites exhibit
large antisymmetric exchange interactions, very small
anisotropy of Fe spins in the “a–c” lattice plane, and
very large anisotropy toward b axis. Various significant
magnetic transitions observed within the RE ferrite system
are as follows: (i) spin reorientation-TSR , (ii) antiferromagnetic ordering of iron-TN1 , (iii) compensation effect
(Tcomp ), (iv) ordering of RE ions-TN2 , (v) canted antiferromagnetism, (vi) existence of spin–phonon coupling, and
(vii) magnetostriction of orthoferrites.
The current study aims to understand the effect of
the size of ionic radii on structural parameters, magnetic
properties, and magnetostriction in RFeO3 (RFO) nanoparticles. We have investigated their magnetic behavior in
context of spin–orbit coupling and magnetostriction in the
system. Nanoparticles of SmFeO3 (SFO), HoFeO3 (HFO),
DyFeO3 (DFO), and LuFeO3 (LFO) orthoferrites were synthesized via sol–gel synthesis and structurally characterized using field emission scanning electron microscopy
(FESEM) and powder X-ray diffraction (XRD).
The structural characterization further correlated with
the magnetic and magnetostriction measurements. The
magnitude of these phenomena is affected by chemical
pressure in the lattice. It is observed that the value of
magnetostriction is highest for HFO and lowest for DFO.
2
MATERIALS AND METHODS
RFeO3 (RFO) nanoparticles were synthesized using
a similar sol–gel route combined with post-synthesis
annealing reported elsewhere.12 Stoichiometric ratios of
R(NO3 )3 ⋅5H2 O and Fe (NO3 )3 ⋅9H2 O in the presence of
tartaric acid at T = 573 K were reacted. The precipitate was
then heated in an oven at a temperature of 423 K. Samples
were annealed at 993 K for 2 h. The annealed powder was
washed in Milli-Q water several times before complete
drying.
The room-temperature XRD of the powder samples
of RFO was performed in air using a Bruker AXS D8
ADVANCE diffractometer. The lattice parameters were
obtained by Rietveld refinement using the software FULLPROF SUITE (version July 2016). Scanning electron
microscopy (SEM) methods of all the synthesized powder
samples (drop-casted on a copper grid, after dispersing in
ethanol) were carried out using a PHILIPS CM 200 microscope. SEM images were recorded using a Zeiss Ultra Plus
FESEM at a 3-kV operating voltage. EDAX were recorded
at operating voltages of 20 kV using an X-Max EDS detec-
CHATURVEDI et al.
tor fitted in the Zeiss Ultra Plus FESEM. The sample was
dispersed in DMF and drop-casted on a silicon substrate
for FESEM and EDAX characterization. Elemental compositions of R and Fe were estimated by ICP-AES on a
SPECTRO ARCOS spectrometer.
For FESEM imaging, the samples were dispersed in
ethanol, drop-cast on a silicon wafer, and dried under
vacuum. EDAX is also obtained during FESEM. The
elemental composition was confirmed for the samples.
The room-temperature Raman spectra were recorded
using Jobin Yvon HORIBA Lab RAM HR visible micro
Raman system, employing 488 nm laser. The laser was
focused to a spot of ∼2 μm, and a 50× objective lens was
used for the collection of the scattered light. Room temperature Raman mapping was performed over an area of
approximately 10μm × 10 μm, using 10 integrations with a
5-s acquisition time with ×10 objective and 600 lines per
mm grating (giving a spectral resolution of 0.5 cm−1 ) for
the Raman shift range of between 20 and 800 cm−1 . The
magnetic measurements were carried out using QD PPMS
model 6000. The hysteresis behavior of samples was studied at different temperatures of 5, 70 and 300K with the
magnetic field varied in the range of −9 T to +9 T.
The measurement of magnetostriction has been performed using standard strain-gauge method. The sample
used in the form of pellets of 10 mm diameter with ∼2 mm
thickness. The standard strain-gauge method (MicroMeasurement Group Strain Indicator—Model 3800 and
series WK strain gauges) and an electromagnet with a maximum field of 5 kOe were used for the measurement of λ.13
3
3.1
RESULTS AND DISCUSSION
Structural parameters
XRD and FESEM are performed to study the structural
parameters morphology and particle size of the samples. Figures S1 (XRD) and S2 (FESEM) are provided
in the Supplementary Information (SI) section. FESEM
images (Figure S1) confirmed the nanoscale morphology
of the synthesized orthoferrite NPs with an average particle size of ∼ 70 ± 10 nm for all synthesized samples. To
obtain structural parameters for the orthoferrite NP samples, Rietveld refinements were performed on the room
temperature XRD data (see Figure S2 for the modeled
datasets).
Figure 1B–D shows the critical structural parameters as
a function of the size of RE ionic radii. Figure 1A shows
the Goldschmidt tolerance factor (t), which describes the
structural stability of the perovskite ABO3 structure with a
value of 1 for the stable perovskite aristotype.14 The structural stability of the prepared compounds was estimated by
3
Goldschmidt tolerance factor given by
𝑡 = (𝑅𝑎 + 𝑅𝑂 )
√
2 (𝑅𝑏 + 𝑅𝑂 )
(1)
where Ra , Rb , and RO refer to the ionic radius of R,
Fe, and oxygen, respectively. From Figure 1A, it can be
observed that the calculated tolerance factor approaches
unity as the size of the ionic radius increases. From these
calculations, it is seen that from Lu to Sm the value of t
varies from 0.86 to 0.96. The material is said to be stable
if the t value lies between 0.80 and 1.00. Moreover, the
smaller the tolerance factor, the more severe the buckling
of the oxygen octahedra. This is due to the fact that the
smaller A-site ion cannot fill the empty space fully and
instead the octahedra tilt, shrinking the space.
Figure 1B shows the variation in lattice constants with
respect to the RE ionic radius. The lattice constants and the
unit cell volume exhibit an increase as the RE ionic radii
increase in size, with the lattice constant a deviating from
linearity for the HFO and DFO samples, whereas b and c
show lesser deviation from linearity. Deviations from cubic
symmetry increase with increasing atomic number as a
result of the observed decrease of a and c but not much of b,
in this direction.15 The angle also increases in this direction
(Figure 1B). A deviation from linearity is also observed in
the average Fe–O and average R–O distances for the HFO
and DFO NPs as shown in Figure 1C.
The variation in the average Fe–O–Fe angle and average tilt angle φ with increasing ionic radius can be seen
in Figure 1D. The average tilt angle of FeO6 octahedra is defined as φ = (180◦ − ⟨Fe–O–Fe⟩)/2. From Lu
to Sm (increasing RE ionic radius), the average ⟨Fe–O–
Fe⟩ angle is observed to increase nonlinearly, whereas φ
is observed to decrease nonlinearly.16 Therefore, the perovskite structure undergoes less distortion with increase in
RE ionic radii, which is confirmed by the calculated value
of tolerance factor.17
Figure 1C shows that Sm to Lu, bond lengths R–O
and Fe–O change, indicating that RE ion moves from its
plane to keep the Fe coordination intact. Thus, in RE
orthoferrites moving from larger radius to smaller radius
(Sm ∼ 0.958 Å to Lu ∼ 0.861 Å), the predominant change in
crystal system is the shift of RE ion from its plane to maintain the sixfold coordination of Fe. The observed decrease
in the average Fe–O bond lengths with decrease in the
radius of the RE ion supports this observation.
From Sm to Lu, the average Fe–O–Fe angle decreases
nonlinearly, as shown in Figure 1D, which indicates that
average tilt angle increases nonlinearly. This supports the
values of tolerance factor observed for the samples that
as the value of “t” decreases (due to decrease in radius
of RE), the system tries to maintain the coordination of
Fe ion.
4
CHATURVEDI et al.
F I G U R E 1 Structural parameters and tolerance factors for the nanoparticles of SFO, DFO, HFO, and LFO: (A) tolerance factor; (B)
lattice constants a, c (x-axis), and b, volume (y-axis); (C) average Fe–O (x-axis) and R–O (y-axis) distances; and (D) average Fe–O–Fe angle
(x-axis) and average tilt angle phi (y-axis).
T A B L E 1 The structural parameters for single crystal RFO (R = Lu. Ho, Dy, and Sm) compared with the structural parameters of
respective nanoparticles studied in current work.
a
Xal
NP
b
Xal
5.588
7.768
NP
c
Xal
NP
V (A3 )
Xal
NP
phi
Xal
SmFeO3
5.584
7.711
NP
5.400
5.398
234.23
232.61
15.6
17.2
DyFeO3
5.598
5.591
7.623
HoFeO3
5.598
5.587
7.602
7.627
5.302
5.304
226.26
226.18
17.3
17.9
7.615
5.278
5.284
224.61
224.88
17.7
18.9
LuFeO3
5.547
5.546
7.565
7.559
5.213
5.209
218.75
218.45
19.5
19.6
Upon comparing the structural parameters of nanoparticles with their single crystal counterparts (Table 1), it
is observed that in nanoparticles, the tilt angle increases
and lattice constant c decreases as compared to their bulk
counterparts. Nanoparticles have larger surface to volume
ratios, which distorts their unit cells to reduce their overall
free energy.18,19 This results in either a structural distortion to reduce the coordination of the RE ions occurs
while keeping the coordination of the Fe ions as 6, or RE
ion moves out of the RO plane, or by rotating the FeO6
octahedra.20
To explore further this case, the electron density (ED)
maps of the nanoparticles are obtained from the refined
XRD data. Inverse Fourier transformation of the structure
factors Fhkl obtained from the Rietveld refinement gives
the ED ρ(x, y, z) as12,21
𝜌 (𝑥, 𝑦, 𝑧) =
∑ 𝐹ℎ𝑘𝑙 ⋅ 𝑒{−2𝜋𝑖(ℎ𝑥+𝑘𝑦+𝑙𝑧}
ℎ𝑘𝑙
𝑉
(2)
Figure 2A shows the (1 0 0) lattice plane. As we proceed
from Sm to Lu, the ED of Fe ion and O1 ion does not
change significantly, whereas the ED of RE ion changes.
Alongside increasing number of electrons on the RE ion
across the series, this increase also indicates that RE ion
moves from its plane to maintain Fe ions coordination
intact. This observation suggests that, in RE orthoferrites,
with decreasing ionic size from Sm to Lu, the predominant
change in crystal system is a shift of the RE ion from its
plane in order to maintain the sixfold coordination of the
Fe ion. In this process, slight changes in FeO6 octahedra are
also observed, particularly in the ED of neighbor oxygen
ions and its surroundings.
Figure 2B shows the (0 10 ) plane to visualize the ED
in the equatorial plane of FeO6 octahedra. In this plane,
the Fe–O2 bonds are visible and appear to form a rhombus composed of the Fe ion at the center and O2 ions at
the vertices (the white-dotted rhombus is guiding the eye
in Figure 2B). The O2 ions appear to be moving closer to
the Fe ion at the center of the octahedra as the radius of
CHATURVEDI et al.
5
F I G U R E 2 The Electron density plots for SFO, DFO, HFO, and LFO nanoparticles at room temperature (A) for the plane 100 and (B) for
the plane 010, respectively. The plane shows rare-earth ions (purple), Fe ions (green), and oxygen ions (yellow). The slice of the structure for
the corresponding plane is shown at the right-hand side of the figure for the one-to-one correspondence for anion and cations of the RFO
system.
6
CHATURVEDI et al.
RE ions decreases. As the radius is decreased from Sm to
Lu, the equatorial plane of the FeO6 octahedra appears to
become smaller. This is because the average Fe–O bond
lengths decrease with decreasing RE ionic radii.
To further understand the changes in the structure and
its impact on magnetic properties of the samples, we
have performed Raman spectroscopy measurements on
the samples.
3.2
Raman spectroscopy
Raman spectroscopy is an ideal probe to study the local
structural changes due to magnetic ordering effects in
materials.22–24 It is a suitable technique to: (i) probe the
lattice distortions and changes in octahedral rotations
which can affect the physical properties of orthoferrites
and (ii) demonstrate existence of spin–phonon coupling.
The changes in lattice parameters due to chemical pressure and its effect on magnetic behavior can be understood
by analyzing the change in phonon parameters, that is,
spin–phonon coupling.22,25–27
The RFeO3 structure is an orthorhombically distorted
perovskite with alternately tilted FeO6 octahedra. The
magnitude of this distortion depends on the size of the RE
ion. Smaller the RE ion, greater the distortion, and hence,
larger the deviation in Fe–O–Fe bond angle (from 180◦ ). In
turn, the tilting of the FeO6 octahedra causes a distortion
of the RO8 polyhedra. In the Pnma structure, antiparallel
A-site (occupied by RE ion in RFeO3 ) displacements are
permitted by symmetry.10,28 The tilt, octahedral distortion,
and A-site displacement activate Raman modes by breaking the cubic symmetry. The orthorhombic Pnma structure
(with four formula units per unit cell) possesses 24 Ramanactive modes (ΓRaman = 7 Ag + 5 B1g + 7B2g + 5B3g ). The
deconvoluted Raman spectra of SFO, DFO, HFO, and LFO
NPs in the spectral range 100–700 cm−1 are presented in
Figure 3A. Mode assignments were done based on previous
reports.21,24,29
The phonon modes in RFO can be attributed to different symmetry operations: (1) those below 200 cm−1
are related to lattice modes involving R ion vibrations
and (2) the modes in the region above 200 cm−1 consist
of various modes involving vibrations of the R ion and
oxygen. The modes can be categorized in the following
manner (i) the Ag (1) mode is related to the antisymmetric
stretching vibrations of FeO6 octahedra; (ii) B1g (3), Ag (2)
are octahedral rotations around the crystallographic y-axis
and B1g (4), Ag (4) are rotations around the x-axis (Pnma
setting); (iii) the singlet Ag (7) in SFO is related to R–O
vibrations; and (iv) B3g (3) arises due to bending of FeO6
octahedra. When the packing of the molecules in the crystal changes, the intermolecular distance changes and thus
the intermolecular force contents will change, resulting
in frequency shift. Variations in the phonon frequency of
modes Ag (2), Ag (3), Ag (5), Ag (7), and B2g (5) as a function of ionic radius are shown in Figure 3B. It is observed
that the phonon frequencies of modes related to Fe–O
motion, namely, B2g (5) and Ag (7) (representing FeO6 bending) decrease gradually with an increase in ionic radius.
Modes related to R–O motion—Ag (3) and R–O vibration—
Ag (5) are also observed to decrease as the RE ionic radius
increased.
The softening of the modes due to increase in ionic
radius reflects the effect of chemical pressure within the
lattice as we move from small radius to large radius. This
leads to change in lattice parameters and displacement
of RE ion. Therefore, it can be attributed to anharmonic
effect/magnetostriction.23,25,30 With an increase in RE ion
radii, most of the Raman modes shift to lower frequency,
this is direct effect of increase in volume and bond lengths.
Since, the frequencies of the Raman modes are differently
sensitive to the change of RE, the decrease is nonlinear.
Figures 3B and C show the Raman shift and change in
linewidth of modes B2g (5), Ag (2), Ag (3), Ag (5), and Ag (7)
as a function of ionic radius, respectively. Small changes in
mode position accompanied by an unaffected (negligible)
linewidth indicate existence of magnetostriction within
the system.23
Mode Ag (3) and Ag (5) (R–O motion and R–O vibration)
experience larger changes as compared to other modes
reflecting the considerable change in size of ionic radii
change from Sm to Lu. The linewidths of mode Ag (3) and
Ag (5) show small change with change in ionic radius for
Sm and Lu.
The change in value of linewidth with the change in
size of ionic radii indicates change in volume of lattice
and other related structural changes, such as average tilt
angle of octahedra with temperature and changes in Fe–O
and R–O bond lengths. Ag (7) mode(Fe–O rotation) shows
very small change in phonon frequency and almost negligible change in phonon linewidths. These observations for
Ag (3), Ag (5), and Ag (7) modes indicate presence of presence of magnetostriction in the system.12 Upon comparing
the Raman modes of nanoparticles with their respective
bulk counterparts (Table 2), broadening of the Raman
peaks and an increase in the linewidths are observed.
According to the phonon confinement model for nanoparticles, broadening of the Raman peaks is expected as the
particle size is decreased.31
3.3
Magnetostriction
Magnetoelastic interactions of material are mainly the
result of either (i) a change in the size and shape of
CHATURVEDI et al.
7
F I G U R E 3 (A) Raman Spectra of the samples SFO, DFO, HFO, and LFO, (B) Raman shift of modes Ag(2), Ag(3), Ag (5), Ag (7), and
B2g(5) are plotted as a function of ionic radius, and (C) the full-width at half-maximum (FWHM) of modes Ag(2), Ag(3), Ag (5), Ag (7), and
B2g(5) plotted as a function of ionic radius.
TA B L E 2
this work.
Raman modes for bulk RFO (R = Lu, Ho, Dy, and Sm) compared with the respective Raman modes of nanoparticles studies in
LuFeO3 32
LFO
NP
HoFeO3 33
HFO
NP
DyFeO3 33
DFO
NP
SmFeO3 34
SFO
NP
Main atomic motion35
Ag(1)
109
108
109
109
110
110
108
107
R(x), in-phase (x–z), out-of-phase (y)
Ag(2)
134
135
138
137
140
138
140
139
R(z), out-of-phase
178
270
175
Modes
Ag(3)
173
Ag(4)
Ag(5)
431
407
340
377
Ag(6)
Ag(7)
516
372
370
[1 0 1]pc FeO6 rotation, in-phase
Fe–O(2) stretching, in-phase
495
495
489
491
465
463
O(1)–Fe–O(2) scissor-like bending
270
269
261.3
261
232
233
[0 1 0]pc FeO6 rotation, out-of-phase
368
425
B2g(2)
160
158
277
288
452
422
B2g(4)
157
340
B2g(6)
495
650
631
350
347
660
359
350
[0 1 0]pc FeO6 rotation, out-of-phase
424
425
Fe–O(2) stretching, out-of-phase
161
158
156
154
R(x), out-of-phase
311
291
258
287
[1 0 1]pc FeO6 rotation, in-phase
418
O(1)-Fe–O(2) scissor-like bending
339
421
412
O(1) x–z plane
419
494
632
612
336
311
B3g(1)
B3g(2)
375
513
B2g(3)
B2g(7)
336
223
B1g(4)
B2g(5)
332
[0 1 0]pc FeO6 rotation, in-phase
O(1)x–z plane
409
B1g(2)
B1g(3)
163
315
O(2)-Fe–O(2) scissor-like bending,
in-phase
635
625
631
Fe–O(2) stretching, in-phase
310
O(1)-Fe–O(2) in-phase
138
the sample upon a change in the magnetic state (magnetostriction), (ii) a change in the magnetic state upon
deformation of the sample, or (iii) both the above. The
behavior of magnetoelastic interactions is based on the
dependence of the parameters of magnetic properties on
crystallographic parameters, that is, interatomic distances
and bond angles.36
R(y) out-of-phase in x–z, y
334
The magnetostriction λ is an important parameter for
theoretical estimates of magnetoelectric-voltage coefficient of the material. In the ferromagnetic phase, the
magnetostriction due an ac field dH in the presence of
a bias field H leads to pseudo-piezomagnetic effects,
which in turn give rise to the necessary coupling to the
piezoelectric phase in the material.
8
CHATURVEDI et al.
F I G U R E 4 (A) Magnetostriction as a function of applied magnetic field for samples SFO, DFO, HFO, and LFO when the sample (pellet
of 10 mm diameter and ∼2 mm thickness) is placed in parallel (B) magnetostriction as a function of ionic radii for samples SFO, DFO, HFO,
and LFO when the sample is placed in parallel to magnetic field.
TA B L E 3
Comparison of magnetostriction values of rare-earth ferrites in the current study with some high magnetostrictive materials.
Materials
structure
Orientation
Magnetostriction
(ppm)
Ref.
TbF2
Single crystal
111
1640
Grössinger et al.3
SmFe2
Single crystal
111
−2000
Grössinger et al.3
Terfenol-D
Single crystal
100/111
90/1640
Grössinger et al.3
Ni
Single crystal
100/111
−46/−24
Grössinger et al.3
Fe
Single crystal
100/111
20/−21
Grössinger et al.3
HoFeO3
Polycrystalline NP(pellet)
Parallel to magnetic field
19
Present work
LuFeO3
Polycrystalline NP (pellet)
Parallel to magnetic field
17
Present work
SmFeO3
Polycrystalline NP (pellet)
Parallel to magnetic field
16
Present work
DyFeO3
Polycrystalline NP (pellet)
Parallel to magnetic field
14
Present work
We have measured the magnetostriction in the RE
orthoferrites under consideration at room temperature.
The measurement of magnetostriction has been performed using standard strain-gauge method. The standard
strain-gauge method (Micro-Measurement Group Strain
Indicator—Model 3800 and series WK strain gauges) and
an electromagnet with a maximum field of 5 kOe were
used for the measurement of λ11 .13 Figure 4A shows the
static magnetic field dependence of parallel (λ11 ) magnetostriction, and Figure 4B shows the chemical pressure
dependence of parallel (λ11 ) magnetostriction, respectively.
The perpendicular magnetostriction is observed to be
considerably smaller than the parallel values.
It is observed that all the samples are showing the
presence of magnetostriction. However, the value of magnetostriction is decreasing in the following order: HFO,
SFO, LFO, and then DFO as shown in Figure 4B. Table 3
shows the values of magnetostriction of RE orthoferrites
and of some reported materials for comparison.
The change in size and other factors such as number
of electrons in f orbitals, and the spin–orbital coupling
contributes toward the magnetostriction of these RE orthoferrites. Experimentally we found that the magnetostriction in HFO is dominant than that of other samples. The
strong magnetic nature of Ho ion and favorable spin orbit
interaction in HFO system contribute toward considerable magnetostriction. Trends observed in Raman modes
in terms of Raman shift and frequencies support different
degrees of distortion of FeO6 octahedra as the size of RE
ion changes.
As observed in ED plots, there is displacement of RE ion
with respect to Fe and O, as the radius of ion increases from
Lu to Sm. This displacement gives rise to exchange striction, which is function of atomic displacements/distance
between the magnetic ions (R and Fe).37 This exchange
striction affects the dynamics between 4f–3d moments and
hence on Fe ordering of the system and is one of the
decisive factor for the existence of magnetostriction.28
The magnetic transitions are affected by magnetostriction and structural arrangement in the system.38 The
ionic moments associated with RE ion size in orthoferrites impact the crystal field of Fe ions and the anisotropy
CHATURVEDI et al.
9
F I G U R E 5 (A–D) and (E–H) M–H hysteresis loops and their zoomed view, respectively, for SFO, DFO, HFO, and LFO nanoparticles for
temperature 2 and 300 K. (I–K) Derived remanent magnetization, coercivity, and shift on x-axis as a function of ionic radii.
energies of Fe sublattice, which in turn influences the overall magnetic behavior.39–41 It is established that the size of
RE ion is one of the significant factor, but certainly there
are more factors (beyond the scope of this manuscript)
driving the strength/extent of magnetostriction of the
system.42
3.4
Magnetism
Figure 5A–D shows the observed magnetization (M)
response for the LFO, HFO, DFO, and SFO NPs as a
function of the applied field (H) for 2 and 300 K. M–H
curves were obtained at 2, 70 (shown in SI), and 300 K.
Figure 5E–H shows the zoomed view of the corresponding
M–H curves. Figure 5I–K shows remanent magnetization,
coercivity, and exchange bias, respectively, as a function
of the RE ionic radius. These values are derived from
the M–H data. The data suggests that HFO shows the
most ferromagnetic behavior among all studied samples
(both at room temperature as well as low temperatures).
As shown in Figure 5A–D, for all the samples, the M–H
plots at low temperatures show characteristically different behavior from those at high temperatures. The M–H
loops at 300 K are symmetric and well-formed, as in
typical ferromagnets, but without any signs of saturation up to the highest applied field. At 2 K, R sublattice
magnetization starts growing upon cooling and it reflects
10
CHATURVEDI et al.
T A B L E 4 Observed remanent magnetization values at 300 and
2 K for SFO, DFO, HFO, and LFO.
Sample
Mr
Temperature (emu/
mol)
(K)
Molecular Mr (emu/g
mass
or
(g/mol)
A m2 /kg)
SFO
300
56.0
254.20
DFO
300
153.0
266.34
0.57
HFO
300
163.0
268.77
0.61
LFO
300
SFO
2
0.22
91.0
278.81
0.33
−55.0
254.20
−0.22
DFO
2
790.0
266.34
2.97
HFO
2
8235.0
268.77
30.64
LFO
2
42.0
278.81
0.15
antiferromagnetic coupling between the R/Fe sublattices,
and the strong single-ion anisotropy of the R moments,
in the M–H loops. The ED maps at 300 K suggest that
the 4f electron cloud surrounding the R3+ ion in RFO
is anisotropic in shape. This is established to impart
strong single-ion anisotropy to the RE moment. Therefore,
unless the applied field exceeds the anisotropy field or the
field equivalent to the f–d exchange, the magnetization is
expected to remain linear.
There is significant variation in the values of critical
parameters like Hc and Mr for the cases of Ho and Dy. This
change is not as systematic as the change in radii, but it is
consistent with changes in critical structural parameters
and changes in phonon modes. The changes in structural parameters, such as R–O bond lengths, Fe–O–Fe
angle, R–Fe distance, distortion in FeO6 octahedra, and
Fe ion ordering, induce changes in the dynamics of superexchange between R–R and Fe–Fe. This in turn contributes
to changes in the magnetic structures. This is observed
and supported by Raman measurements. The existence of
magnetostriction in all the samples with dominant magnetostriction in the case of HFO at room temperature is in
coherence with the observed magnetic behavior.
As shown in Figure 5I, at room temperature the values
of remanent magnetization for LFO, HFO, DFO, and SFO
are comparable. At room temperature, the value of remanent magnetization for HFO is 0.61 emu/g (163 emu/mol)
and at 2 K the value is 30.64 emu/g (8235 emu/mol), which
is highest among all the samples. HFO and DFO show
higher remanent magnetization owing to the ferromagnetic nature of the compound. However, this is noteworthy
that Hc and Mr are also dependent on extrinsic factors such
as defect pinning, polycrystallinity, as well as the particle
size. For reference, values of remanent magnetization are
given in Table 4 in emu/g.
The RE ions in orthoferrites are paramagnetic and can
be magnetized by the Fe moments. The contribution of
the Fe moment (remanence) is greatly reduced in the SFO
and LFO samples. Hence, the Fe–R exchange interaction,
which is responsible for the magnetization of R, is also
expected to be different, which will also contribute to the
observed values of the magnetization. As the temperature decreases, the spin correlations build up and hence
the spin–phonon coupling becomes important at lower
temperature.43,44 The coercive field Figure 5J, on the other
hand, shows the lowest value for DFO at room temperature. The temperature dependence of the coercive field
Hc shows strong single-ion anisotropy of the RE ions. In
the case of SFO and LFO, the coercive field Hc initially
increases with decreasing temperature below Neél temperature due to the ferromagnetic Fe sublattice ordering along
the applied magnetic field.17 At a certain temperature,
the weak ferromagnetism due to the Fe sublattice reaches
saturation and then the contribution from the R sublattice starts to contribute up to the RE sublattice ordering
temperature. Therefore, the combined ferromagnetic and
paramagnetic (or antiferromagnetic) contributions result
in a decreased coercive field as the temperature is further
lowered. This trend deviates in the case of HFO.
Figure 5K shows the shift of M–H loops of the RFO samples. LFO shows negative shift and SFO shows positive
shift on x-axis, whereas HFO and DFO show no shift and
their MH loops are symmetric to the x-axis. As the hysteresis loops of LFO and SFO are not saturated, these loops are
minor loops, and hence the observed shift cannot be unambiguously attributed to the exchange bias effect.12,45 LFO
and SFO show vertical shift with small horizontal shift.
The horizontal and vertical shifts are observed generally
due to exchange bias originated from competing FM–
AFM interactions in the system. To be able to observe the
exchange bias, the system should be cooled from T > TN
in the presence of a bias field and then measure the M–H
loop. The shift in the loop is in general proportional to the
amount of bias field.46 As the TN is much higher than RT
for all the samples in the current work, the measurements
in the present study are done without any bias field. This
resulted in considerable vertical shift for the samples. The
vertical shift observed is due to pinned moments that are
not rotated by the applied field and hence, define the bias
direction. Several studies have established the close connection between EB and vertical shift, owing to the role of
pinned/frozen uncompensated interfacial spins in the EB
effect.25,47,48
4
CONCLUSIONS
Magnetostriction and magnetic properties play an important role in multiferroic behavior of the material. In the
present study, RE orthoferrites demonstrated existence
of magnetostriction in their nanoscale form. The highest
CHATURVEDI et al.
value of magnetostriction (19 ppm) and remanent magnetization (0.61 emu/g at 300 K and 30.64 emu/g at 2 K) is
demonstrated by HoFeO3 nanoparticles. The effect of RE
ionic radii sizes on magnetostrictive behavior is established
based on detailed structural analysis, Raman spectroscopy,
and magnetization results. It is established that the size
of RE ion is one of the significant factors in the observed
macroscopic properties. The distortion of FeO6 octahedra,
R–O bond dynamics, magnetic moment of RE ion, and
spin orbit interaction also influence magnetostriction and
magnetic behavior.
AC K N OW L E D G M E N T S
This work was carried out under the grant number
TAR/2022/000621 from the Department of Science and
Technology, Ministry of Science and Technology, India,
and a Fulbright Fellowship grant number 2372/F-N APE
FLEX/2018 availed by S.C. The research at Oakland University was supported by grants from the National Science Foundation (ECCS-1923732, ECCS-EAGER-2236879,
and DMR-1808892) and the Air Force Office of Scientific Research (AFOSR) Award No. FA9550-20-1-0114. S.C.
acknowledges support from Dr. Surjeet Singh, IISER Pune.
S.C. acknowledges support by Dr. Y.D. Kolekar, Department of Physics, SPPU.
ORCID
Smita Chaturvedi https://orcid.org/0000-0001-77449605
Priyank Shyam https://orcid.org/0000-0002-0043-797X
REFERENCES
1. Belov KP, Kataev GI, Levitin RZ, Nikitin SA, Sokolov V I. Giant
magnetostriction. Sov Phys Uspekhi. 140:271.
2. Adhikari R, Sarkar A, Limaye MV, Kulkarni SK. Das AK.
Variation and sign change of magnetostrictive strain as a function of Ni concentration in Ni-substituted ZnFe2 O4 sintered
nanoparticles. J Appl Phys. 2012;111:1–8.
3. Grössinger R, Turtelli RS, Mehmood N. Materials with high
magnetostriction. IOP Conf Ser Mater Sci Eng. 2014;60:012002.
4. Ramirez S, Chan K, Hernandez R, Recinos E, Hernandez E,
Salgado R, et al. Thermal and magnetic properties of nanostructured densified ferrimagnetic composites with graphene–
graphite fillers. JMADE. 2017;118:75–80.
5. Issa B, Obaidat IM, Albiss BA, Haik Y. Magnetic nanoparticles: Surface effects and properties related to biomedicine
applications. Int J Mol Sci. 2013;14:21266–305.
6. Zhao HJ, Yang Y, Ren W, Mao AJ, Chen XM, Bellaiche L. Creating multiferroics with large tunable electrical polarization from
paraelectric rare-earth orthoferrites. J Phys Condens Matter.
2014;26:472201.
7. Zhao HJ, Ren W, Yang Y, Chen XM, Bellaiche L. Effect of
chemical and hydrostatic pressures on structural and magnetic
properties of rare-earth orthoferrites: a first-principles study. J
Phys Condens Matter. 2013;25:466002.
11
8. Hu S, Chen L, Wu Y, Yu L, Zhao X, Cao S, et al. Selected multiferroic perovskite oxides containing rare earth and transition
metal elements. Chin Sci Bull. 2014;59:5170–79.
9. Marezio M, Remeika JP, Dernier PD. The crystal chemistry
of the rare earth orthoferrites. Acta Crystallogr Sect B Struct
Crystallogr Cryst Chem. 1970;26:2008–22.
10. Marezio M, Remeika JP, Dernier PD. On the space group of the
rare earth orthoferrites and related compounds. Acta Crystallogr
Sect B Struct Crystallogr Cryst Chem. 1970;26:300–302.
11. Zhou Z, Guo L, Yang H, Liu Q, Ye F. Hydrothermal synthesis
and magnetic properties of multiferroic rare-earth orthoferrites.
J Alloys Compd. 2014;583:21–31.
12. Chaturvedi S, Shyam P, Bag R, Shirolkar MM, Kumar J, Kaur
H, et al. Nanosize effect: Enhanced compensation temperature
and existence of magnetodielectric coupling in SmFe O3 . Phys
Rev B. 2017;96:1–13.
13. Srinivasan G, Rasmussen ET, Gallegos J, Srinivasan, R. Magnetoelectric bilayer and multilayer structures of magnetostrictive
and piezoelectric oxides. Phys Rev B. 2001;64:1–6.
14. Chaturvedi S, Bag R, Sathe V, Kulkarni S, Singh S. Holmium
induced enhanced functionality at room temperature and structural phase transition at high temperature in bismuth ferrite
nanoparticles. J Mater Chem C. 2015;4, 780–92.
15. Eibschütz M. Lattice constants of orthoferrites. Acta Crystallogr.
1965;19:337–39.
16. Martinez-Lope MJ, Alonso JA, Retuerto M, Fernandez-Diaz MT.
Evolution of the crystal structure of RVO3 Perovskites from
neutron powder diffraction data. Inorg Chem. 2008;47:2634–40.
17. Xu X, Wang W. Multiferroic hexagonal ferrites (h-RFeO3 , R
= Y, Dy—Lu): a brief experimental review. Mod Phys Lett B.
2014;28:1430008.
18. Ayyub P, Palkar VR, Chattopadhyay S Multani M. Effect of
crystal size reduction on lattice symmetry and cooperative
properties. Phys Rev B. 1995;51:6135–38.
19. Ateia EE, Ismail H, Elshimy H Abdelmaksoud MK. Structural and magnetic tuning of LaFeO3 orthoferrite substituted
different rare earth elements to optimize their technological
applications. J Inorg Organomet Polym Mater. 2021;31:1713–25.
20. Sarkar T, Manna K, Elizabeth S, Anil PS. Investigation of
multiferroicity, spin–phonon coupling, and unusual magnetic
ordering close to room temperature in LuMn0.5 Fe0.5 O3 . J Appl
Phys. 2017;121:0–10.
21. Sands D. Introduction to crystallography. Mineola, NY: Dover
Publications; 1993.
22. Weber MC, Kreisel J, Thomas PA, Newton M, Sardar K, Walton
RI. Phonon Raman scattering of RCrO3 perovskites (R = Y, La,
Pr, Sm, Gd, Dy, Ho, Yb, Lu). Phys Rev B. 2012;054303:1–9.
23. Bhadram Srinu V, Rajeswaran B, Sundaresan A, Narayana C.
Spin–phonon coupling in multiferroic RCrO3 (R-Y, Lu, Gd, Eu,
Sm): a Raman study. EPL. 2013;101:17008.
24. Laverdière J, Jandl S, Mukhin AA, Ivanov VY, Ivanov VG, Iliev
MN. Spin–phonon coupling in orthorhombic RMnO3 (R = Pr,
Nd, Sm, Eu, Gd, Tb, Dy, Ho, Y): a Raman study. Phys Rev B.
2006;73:214301.
25. Chaturvedi S, Shyam P, Apte A, Kumar J, Bhattacharyya A,
Awasthi AM, et al. Dynamics of electron density, spin–phonon
coupling, and dielectric properties of SmFeO3 nanoparticles at
the spin-reorientation temperature: role of exchange striction.
Phys Rev B. 2016;93:174117.
12
26. Venugopalan S, Dutta M, Ramdas A Remeika J. Magnetic
and vibrational excitations in rare-earth orthoferrites: a Raman
scattering study. Phys Rev B. 1985;31:1490–97.
27. Chanda S, Saha S, Dutta A Sinha TP. Raman spectroscopy and
dielectric properties of nanoceramic NdFeO3 . Mater Res Bull.
2013;48:1688–93.
28. Venugopalan S, Becker MM. Raman scattering study of LuFeO3 .
J Chem Phys. 1990;93:3833–36.
29. Weber MC, Guennou M, Zhao HJ, Íñiguez J, Vilarinho R,
Almeida A, et al. Raman spectroscopy of rare-earth orthoferrites RFeO3 (R = La, Sm, Eu, Gd, Tb, Dy). Phys Rev B. 2016;94:
1–8.
30. Granado E, García A, Sanjurjo JA, Rettori C, Torriani I, Prado
F, et al. Magnetic ordering effects in the Raman spectra of
La1–xMn1–xO3. Phys Rev B—Condens Matter Mater Phys.
1999;60:11879–82.
31. Richter H, Wang ZP, Ley L The one phonon Raman spectrum
in microcrystalline silicon. Solid State Commun. 1981;39:625–
29.
32. Pakalniškis A., Alikin DO, Turygin AP, Zhaludkevich AL,
Silibin MV, Zhaludkevich DV, et al. Crystal structure and
concentration-driven phase transitions in Lu(1−x)Scx FeO3 (0
≤ x ≤ 1) prepared by the sol–gel method. Materials (Basel).
2022;15:1048.
33. Gupta HC, Singh MK Tiwari LM. Lattice dynamic investigation of Raman and infrared wavenumbers at the zone center of
orthorhombic RFeO3 (R = Tb, Dy, Ho, Er, Tm) perovskites. J.
Raman Spectrosc. 2002;33:67–70.
34. Tyagi S., Sathe VG, Sharma G, Gupta MK, Mittal R, Srihari
V, Poswal HK. Detail investigations of SmFeO3 under extreme
condition. Mater Chem Phys. 2018;215:393–403.
35. Weber MC, Guennou M Zhao HJ. Raman spectroscopy of rareearth orthoferrites RFeO3 (R = La, Sm, Eu, Gd, Tb, Dy). Phys
Rev B. 2016;214103:1–8.
36. Moskvin A. Structure—property relationships for weak ferromagnetic perovskites. Magnetoscemistry. 2021;7:111.
37. Náfrádi, B, Keller T, Hardy F, Meingast C, Erb A, Keimer B.
Magnetostriction and magnetostructural domains in antiferromagnetic YBa2 Cu3 O6 . Phys Rev Lett. 2016;116:1–5.
38. Yuan X, Tang Y, Sun Y, Xu M. Structure and magnetic properties of Y1−x Lux FeO3 (0 ≤ x ≤ 1) ceramics. J Appl Phys.
2012;111:053911.
39. Parida SC, Rakshit SK Singh Z. Heat capacities, order-disorder
transitions, and thermodynamic properties of rare-earth orthoferrites and rare-earth iron garnets. J. Solid State Chem.
2008;181:101–21.
CHATURVEDI et al.
40. Tsymbal LT, Bazaliy YB, Derkachenko VN, Kamenev VI,
Kakazei GN, Palomares FJ, Wigen PE. Magnetic and structural
properties of spin-reorientation transitions in orthoferrites. J
Appl Phys. 2007;101:123919.
41. White RL. Review of recent work on the magnetic and spectroscopic properties of the rare-earth orthoferrites. J Appl Phys.
1969;40:1061–69.
42. Filho RBME., Ayala AP De Araujo Paschoal CW. Spin–phonon
coupling in Y2 NiMnO6 double perovskite probed by Raman
spectroscopy. Appl Phys Lett. 2013;102:192902.
43. Kumar P, Saha S, Serrao CR, Sood AK, Rao CNR. Temperaturedependent infrared reflectivity studies of multiferroic TbMnO3 :
evidence for spin–phonon coupling. Pramana—J Phys.
2010;74:281–91.
44. Liu W, Shi L, Zhou S, Zhao JY, Li Y, Guo Y. Griffiths phase, spinphonon coupling, and exchange bias effect in double perovskite
Pr2 CoMnO6 . J Appl Phys. 2014;116:193901.
45. Geshev J. Comment on: ‘exchange bias and vertical shift in
CoFe2 O4 nanoparticles’ [J. Magn. Magn. Mater. 313 (2007) 266].
J Magn Magn Mater. 2008;320:600–602.
46. Leelashree S., Srinath S. Investigation of structural, ferroelectric,
and magnetic properties of La-doped LuFeO3 nanoparticles. J
Supercond Nov Magn. 2020;33:1587–91.
47. Ohldag H. Scholl A, Nolting F, Arenholz E, Maat S, Young AT,
et al. Correlation between exchange bias and pinned interfacial
spins. Phys Rev Lett. 2003;91:2–5.
48. Ohldag H, Shi H, Arenholz E, Stöhr J, Lederman D. Parallel versus antiparallel interfacial coupling in exchange biased Co/FeF2 .
Phys Rev Lett. 2006;96:1–4.
S U P P O RT I N G I N F O R M AT I O N
Additional supporting information can be found online
in the Supporting Information section at the end of this
article.
How to cite this article: Chaturvedi S, Shyam P,
Liu Y, Srinivasan G. Manifestation of chemical
pressure: Magnetism and magnetostriction in
nanoscale RFeO3 (R = Sm, Dy, Ho, and Lu). J Am
Ceram Soc. 2024;1–12.
https://doi.org/10.1111/jace.19663