A magnetocaloric study on the series of 3d-metal chromites ACr2O4 where A = Mn, Fe, Co, Ni, Cu and Zn

Article abstract of DOI:10.1016/j.jmmm.2019.166253

The 3d-metal chromites ACr₂O₄ where A is a magnetic ion, show the paramagnetic to ferrimagnetic phase transition at T_C while for non-magnetic A-site ion, ACr₂O₄ show paramagnetic to antiferromagnetic phase transition at T_N. In this report, we present the detailed study of magnetic and the magnetocaloric effect (MCE) of the 3d-metal chromites ACr₂O₄ (where A = Mn, Fe, Co, Ni, Cu, and Zn) near T_C and T_N. We find the magnitude of MCE (-ΔS_M) decreases on decreasing the magnetic moment of A-site ion with an exception for CuCr₂O₄. Additionally, to know more about the order and nature of phase transition, we have made a scaling analysis of (-ΔS_M) for all the chromites across the phase transition temperatures T_C and T_N.

Full text of DOI:10.1016/j.jmmm.2019.166253

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A magnetocaloric study on the series of 3d-metal chromites ACr2O4 where A =
Mn, Fe, Co, Ni, Cu and Zn
Anzar Ali, Yogesh Singh
PII:
S0304-8853(19)33297-4
DOI:
https://doi.org/10.1016/j.jmmm.2019.166253
MAGMA 166253
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Journal of Magnetism and Magnetic Materials
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29 November 2019
Please cite this article as: A. Ali, Y. Singh, A magnetocaloric study on the series of 3d-metal chromites ACr2O4
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10.1016/j.jmmm.2019.166253
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A magnetocaloric study on the series of 3d-metal chromites ACr2O4 where A = Mn,
Fe, Co, Ni, Cu and Zn
Anzar Ali1, ∗ and Yogesh Singh1
1Department of Physical Sciences, Indian Institute of Science Education and Research Mohali,
Knowledge city, Sector 81, SAS Nagar, Manauli PO 140306, Mohali, Punjab, India
The 3d-metal chromites ACr2O4 where A is a magnetic ion, show the paramagnetic to ferri-
magnetic phase transition at TC while for non-magnetic A-site ion, ACr2O4 show paramagnetic to
antiferromagnetic phase transition at TN . In this report, we present the detailed study of magnetic
and the magnetocaloric effect (MCE) of the 3d-metal chromites ACr2O4 (where A = Mn, Fe, Co,
Ni, Cu, and Zn) near TC and TN . We find the magnitude of MCE (-∆SM ) decreases on decreasing
the magnetic moment of A-site ion with an exception for CuCr2O4. Additionally, to know more
about the order and nature of phase transition, we have made a scaling analysis of (-∆SM ) for all
the chromites across the phase transition temperatures TC and TN .
I. INTRODUCTION
Generally, the rare-earth-based compounds have a
large effective magnetic moment and show a giant mag-
netocaloric effect29–31. A lot of experimental, theoreti-
cal work has been carried out to understand the mag-
1
Spinel compounds with general formula AB2O4
,
where A-site is occupied by divalent cations and the B-
site is occupied with trivalent cations, have attracted
much attention in recent years due to their large
netocaloric behavior of rare-earth-based materials32,33
.
The rare-earth-based based materials are expensive and
get sometimes get oxidized in air. So it is customary to
search materials which cost less and have higher stability
in air. Recently, the transition metal oxide compounds
have attracted much attention due to their interesting
multifunctional behavior such as multiferroic and mag-
netocaloric effect. These interesting physical properties
are due to an interplay among different degrees of free-
dom, such as spin, lattice, and orbital. The study of
MCE on the series of spinel chromites may give some in-
dications to understand and control such multifunctional
behavior.
magnetocapacitance2,3
,
colossal magnetoresistance3–5
In spinel
and tunable magnetocaloric effect6–8
.
chromites ACr2O4 (A= 3d transitional metals, Mn,
Fe, Co, Ni, Cu and Zn), the spin, orbital,
and lattice degree of freedom play an essential
role in the enhancement of multifunctional behav-
ior such as magnetoelastic9,10
,
magnetodielectric11,
multiferroic12–16 and magnetocaloric effect6. A deeper
understanding of the interactions between spin, lattice,
and orbital may provide a great way to use these spinels
chromites with their fullest application potential.
The work we are presenting in this report includes the
comprehensive study of the magnetocaloric effect in the
vicinity of the ferrimagnetic phase transition for ACr2O4
(A = Mn, Fe, Co, Ni, and Cu) and across the antiferro-
magnetic transition for ZnCr2O4. We also include MCE
results on NiCr2O4 from the previous reported work8 to
be able to make a comparison. Additionally we have also
made a entropy scaling analysis across these transitions
to get insight into the governing mechanism and order of
the magnetic phase transition.
The spinel chromites ACr2O4 where A-site is non-
magnetic (Zn, Mg, Cd) show
a high degree of
frustration17. In such compounds, the antiferromag-
netic nearest neighbor interaction between Cr3+ ions
do not order to the lowest measured temperatures18.
The spinel chromites where A-site is a magnetic 3d-
transition metal ion show a ferrimagnetic ordering on
cooling below some specific temperatures.The coupling
between spin, lattice, and orbital degree of freedom leads
to several magnetostructural transitions. All the spinels
chromites ACr2O4 where A-site is Mn, Fe, Co, Ni, and
Cu go through the ferrimagnetic ordering at the tem-
perature TC = 4119, 10120, 9721, 6822, and 129K23 re-
spectively, while ZnCr2O4 order antiferromagnetically
at TN = 13K24. The coupled magnetostructural tran-
II. EXPERIMENTAL DETAILS
The polycrystalline samples of spinels ACr2O4 where
A = Mn, Fe, Co, Ni, Cu and Zn have been synthesized
using solid state reaction method. The starting materi-
als AO (99:995%, Alfa Aesar) and Cr2O3 (99:999%, Alfa
Aesar) were taken in the stoichiometry ratio. The reac-
tants were mixed thoroughly and then pelletized using
5-ton pressure. All the pelletized materials then placed
in alumina crucibles covered with a lid except MnCr2O4
and FeCr2O4. The pelletized mixture of MnCr2O4 and
FeCr2O4 were sealed in the evacuated quartz tube and
then loaded into box furnace. Several heat treatments
sitions have been observed and studied well for the
11
chromites such as MnCr2O411, FeCr2O425, CoCr2O4
and NiCr2O4
,
26
. In such spinels chromites with mag-
netic A-site, the structural changes occur at the ferri-
magnetic ordering where system goes from tetragonal
to orthorhombic symmetry27,28
. In general, the mag-
netostructural transitions are of first order in nature.
In first order transitions, the order parameter changes
abruptly and hence a massive change in the entropy of a
system at the transition point is expected.

2
Figure 2. Isothermal curves of magnetization verses magnetic
field for all the ACr2O4 where A = Mn, Fe, Co, Ni, Cu and
Zn compounds at various temperatures indicated in the plots.
Figure 1. Field cooled (FC) magnetization curves recorded
under magnetic field H = 0.1T for all the compounds indi-
cated in the plots.
further transition at low temperatures resulting from the
short range ordering of spiral component which leads to
a conical magnetic structure which are discussed in detail
by Tomiyasu et.al.35.
with intermediate grindings were given with tempera-
tures as mentioned in the Table I.
Room temperature powder X-ray diffraction of all
spinels compounds are refined by Rietveld refinement
method using GSAS software. The spinels MnCr2O4,
FeCr2O4, CoCr2O4, and ZnCr2O4 crystallize in cubic
Figure 2 shows magnetization versus field, M(H) mea-
sured at various temperatures indicated in the plots for
all the spinels MnCr2O4, FeCr2O4, CoCr2O4, NiCr2O4,
CuCr2O4, and ZnCr2O4 compounds. All the spinels
shows the characteristic of soft ferrimagnet with a ten-
dency for rapid saturation accompanied by a small co-
ercivity except ZnCr2O4, which shows a linear field de-
pendent magnetization, which is typical behavior for an
antiferromagnetic phase. In these spinels FeCr2O4 shows
highest coercivity and MnCr2O4 shows minimum coer-
civity. The values of coercivity for FeCr2O4, NiCr2O4,
and CuCr2O4 are 10.5kOe, 5.6kOe, and 3.8kOe respec-
tively. The M(H) however, never saturates even at our
highest applied magnetic fields suggesting that there is
a paramagnetic or antiferromagnetic component at all
measured temperatures. This suggests that some mag-
netic ions do not participate in ferrimagnetic ordering.
To understand field dependent magnetic behavior of
these samples over a broad temperature range and to
calculate its magnetocaloric potential, M(T, H) is ob-
tained from measurement of M vs H at various temper-
atures. Figure 3 shows the series of isotherms M(T,H)
measured for all the spinel compounds in the temper-
ature and field ranges indicated in the plots. M(T,H)
isotherms were measured at different temperature with 2
K interval. When an external magnetic field is applied to
a magnetic material, its atom’s magnetic moment try to
align along the applied magnetic field and hence its mag-
¯
group Fd3m while NiCr2O4 and CuCr2O4, which con-
tain Jahn-Teller active Ni2+ and Cu2+ ions crystallize
in tetragonal space group I41/amd. The refined lattice
parameters are match well with literature7,23,25,26,34 and
listed in Table (II). The magnetic measurements were
performed using Quantum Design (QD) physical prop-
erty measurement system (PPMS).
III. RESULT AND DISCUSSION
Figure 1 shows magnetization versus temperature,
M(T), measured under field cooled (FC) protocol in
an applied field of 0.1T. The sharp increase of mag-
netization at temperature TC = 41, 101, 97, 68, and
129K in MnCr2O4, FeCr2O4, CoCr2O4, NiCr2O4, and
CuCr2O4 respectively indicate the ferromagnetic or fer-
rimagnetic ordering. These transitions are well studied
in literature7,23,25,26,34 and identified as ferrimagnetic or-
dering between A2+ and Cr3+. ZnCr2O4 order antiferro-
magnetically at TN = 13K. However the observed tran-
sition temperature for all ferrimagnetic compounds are
slightly higher due to slightly high value of applied mag-
netic field (H = 0.1T), which is typical behavior of any
ferri or ferromagnet. MnCr2O4 and CoCr2O4 show a

3
8
6
4
2
0
18
16
14
12
10
8
20K
50K
68K
Mn
Fe
8
6
4
2
0
Co
146K
80K
6
150K
4
2
0
0
20
40
60
80
100
0
20
40
60
80
100
0
20
40
60
80
100
H(kOe)
H(kOe)
H(kOe)
18
16
14
12
10
8
40K
8
6
4
2
0
76K
Zn
2K-50K
3
2
1
0
Ni
Cu
DT=2K
100K
6
4
200K
2
0
0
20
40
H(kOe)
60
80
100
0
20
40
60
H(kOe)
80
100
0
20
40
H(kOe)
60
80
Figure 3. Series of isotherms of magnetization with a step size of ∆T = 2K for ACr2O4 where A = Mn, Fe, Co, Ni, Cu and
Zn compounds in the temperature ranges indicated in the plots.
2.5
2.0
1.5
1.0
0.5
0.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
7
6
5
4
3
2
1
0
1T
2T
3T
4T
5T
6T
7T
8T
9T
1T
2T
3T
4T
5T
6T
7T
8T
9T
1T
2T
3T
4T
5T
6T
7T
8T
9T
Co
Mn
Fe
20
30
Ni
40
50
60
70
80
60
80
100
T(K)
120
140
70 80 90 100 110 120 130 140
T(K)
T(K)
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
1T
1T
2T
3T
4T
5T
6T
7T
8T
9T
0.05
Cu
Zn
2T
3T
4T
5T
6T
7T
8T
0.00
-0.05
-0.10
-0.15
-0.20
1T
2T
3T
4T
5T
6T
7T
8T
9T
40
50
60
70
80
90 100
50
100
150
T(K)
200
0
10
20
30
T(K)
40
50
T(K)
Figure 4. The thermal profile of field induced change in magnetic entropy, −∆SM , calculated from Maxwell’s equation 1 using
isothermal magnetization curves in the vicinity of transition temperature for all the ACr2O4 where A = Mn, Fe, Co, Ni, Cu
and Zn compounds at various external magnetic field as indicated in the plots.

4
Table I. Synthesis temperature conditions for ACr2O4.
Heat Treatments
ACr2O4
Environment
First
Second
Third
110◦/24h
NiCr2O4
CoCr2O4
CuCr2O4
ZnCr2O4
MnCr2O4
FeCr2O4
800◦/24h
800◦/24h
1100◦/24h
800◦/24h
1100◦/24h
800◦/24h
1100◦/24h
1000◦/24h
1200◦/24h
1200◦/24h
1200◦/24h
1000◦/24h
in air
in air
1000◦/24h
1200◦/24h
1200◦/24h
1300◦/24h
13000◦/24h
in air
in air
in inert
in inert
Table II. Space group and refined lattice parameters of ACr2O4 for the powder X-ray diffraction data taken at room temperature.
˚
a (A)
˚
b(A)
˚
c (A)
ACr2O4
MnCr2O4
FeCr2O4
CoCr2O4
NiCr2O4
CuCr2O4
ZnCr2O4
Space group
α = β = γ
90◦
¯
Fd3m
8.4374(1)
8.3922(1)
8.3364(1)
5.8763(1)
6.0327(2)
8.3284(1)
8.4374(1)
8.3922(1)
8.3364(1)
5.8763(1)
6.0327(2)
8.3284(1)
8.4374(1)
8.3922(1)
8.3364(1)
8.3180(2)
7.7958(3)
8.3284(1)
90◦
¯
Fd3m
90◦
¯
Fd3m
I41/amd
I41/amd
90◦
90◦
90◦
¯
Fd3m
netic entropy decreases . Under adiabatic process , the
temperature of the material increases. Conversely when
applied magnetic filed is removed adiabatically, the tem-
perature of material decreases. This thermal response of
magnetic material in the varying magnetic field is called
magnetocaloric effect (MCE). The magnetocaloric effect
is related to the change in magnetic entropy −∆SM and
it can be calculated by applying Maxwell’s thermody-
namic relation as stated below6:
transition at TC and TN are shown in figure 4. All com-
pounds show highest change in magnetic entropy at tran-
sition temperature TC and the magnitude of the peak of
−∆SM increases with increasing magnetic field as ex-
pected. The temperature range for significant magne-
tocaloric effect can be estimated from the full width at
half maximum (FWHM) of −∆SM . The values of maxi-
mum entropy change −∆SM , ∆TF W HM , RCP and tran-
sition temperature (TC) have been calculated for all the
spinel samples. All the ACr2O4 where A is magnetic ion
show the positive value of maximum entropy change (-
∆SM ) while ZnCr2O4 has negative value of maximum
entropy change (-∆SM ) which is expected across AFM-
PM transition37. The magnetocaloric parameters for all
the ACr2O4 where A = Mn, Fe, Co, Ni, Cu and Zn com-
pounds in a external magnetic field of strength 9T, to-
gether with some other spinels materials are listed in the
Table III for comparison. The maximum entropy change
(-∆SM ) and RCP increase with the increase of A-site
spin magnetic moment and we get highest -∆SM and
RCP for MnCr2O4. This behavior suggest that the de-
gree of magnetization in these spinels near paramagnetic
to ferrimagnetic phase transition is highly coupled with
the A-site magnetic moment. However, this trend devi-
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
Z
HMAX
dM
dT
∆SM (T, H0→HMAX ) = µ0
dH
(1)
0
H
where HMAX is the maximum applied field and µ0 is the
permeability of of free space or vacuum. Another im-
portant parameter of a MCE material is the cooling effi-
ciency also called relative cooling power (RCP)36. RCP
is defined by the expression:
RCP = −∆SM (T, H) × ∆TF W HM
(2)
The temperature dependence of −∆SM vs T thus ob-
tained from a series of isothermal magnetization at var-
ious temperature for all the spinels across the magnetic

5
which the scaling analysis is being made, and θ is a re-
T −Tc
duced temperature given by θ = −T
for T ≤ Tc
r1−Tc
for T > Tc. The Tr1 and Tr2 are the
T −Tc
and θ =
Tr2−Tc
temperatures at the full width at half maximum of the
anomaly in ∆SM . We have performed the above scaling
analysis for all the spinels MnCr2O4, FeCr2O4, CoCr2O4,
NiCr2O4, CuCr2O4, and ZnCr2O4 compounds.
The plot of ∆SM /∆SMmax at various fields versus the
reduced parameter θ is shown in Fig. 6 for all the com-
pounds. We see that all the ∆SM curves for the different
magnetic fields approximately collapse onto a single uni-
versal master curve except for ZnCr2O4 . This is strong
evidence of the second order nature of the magnetic tran-
sition at TC in spinels MnCr2O4, FeCr2O4, CoCr2O4,
NiCr2O4, and CuCr2O4 compounds while the magnetic
transition in ZnCr2O4 is of first order.
Figure 5. ∆SMmax versus H2/3 data showing a linear depen-
dence expected for a mean-field transition.
IV. CONCLUSIONS
In this work we study the magnetocaloric (MCE) re-
sponse (−∆SM ) of all the spinels MnCr2O4, FeCr2O4,
CoCr2O4, NiCr2O4, CuCr2O4, and ZnCr2O4 compounds
across their magnetic transition TC and TN . The spinels
ACr2O4 where A2+ is a magnetic ion show paramag-
netic to ferrimagnetic phase transition at temperature
TC. The spinels ACr2O4 where A2+ is non-magnetic
ion show paramagnetic to antiferromagnetic phase tran-
sition at temperature TN . We observed that MnCr2O4
shows a maximum value of MCE in all the studied here
spinel chromites while ZnCr2O4 shows inverse MCE. It is
clear to say that the degree of MCE (-∆SMmax) depends
on the magnetic moment of A-site ion in ACr2O4. The
MCE (-∆SMmax) of the spinels decrease on decrease of A-
site spin magnetic moment for all the spinels except for
CuCr2O4. Further microscopic probe studies will be re-
quired to clarify the origin of this exception for CuCr2O4.
ate for the spinel CuCr2O4. To find the origin of this
deviation further microscopic investigation are needed.
In order to get insight about the nature of the mag-
netic transition in the vicinity of the transition temper-
ature we have done scaling analysis of the maximum en-
tropy change. According to mean field model the mag-
netic entropy change at the transition is expected to fol-
low a power law behavior given by |∆SM | ∝ Hn with
n = 2/3 42–44. Figure 5 shows the plot of ∆SM versus
H2/3 for the magnetic transition at T0 for all the spinels
MnCr2O4, FeCr2O4, CoCr2O4, NiCr2O4, CuCr2O4, and
ZnCr2O4 compounds. FeCr2O4, CoCr2O4, and NiCr2O4
show a nearly linear plot, which strongly suggests that
these transition are mean-field like. The plots ∆SM ver-
sus H2/3 for MnCr2O4, CuCr2O4, and ZnCr2O4 deviate
from linearity, indicating non mean filed like transitions
in these compounds.
Franco et al.45 gave a model for the materials which has
second order magnetic phase transition. They proposed
that the ∆SM (T) curves at different magnetic fields are
expected to collapse onto a common universal curve when
they are plotted as ∆SM /∆SMmax versus θ, where ∆SMmax
is the value of ∆SM at the transition temperature around
V. ACKNOWLEDGMENT
We acknowledge the support of the X-ray facility at
IISER Mohali for powder XRD measurements.
∗
1
anzarali@iisermohali.ac.in
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Table III. Table for each A site ion the value of S, effective magnetic moment38, magnetocaloric parameters and transition
temperature for all the ACr2O4 where A = Mn, Fe, Co, Ni, Cu and Zn compounds in a external magnetic field of strength 9T).
ACr2O4
MnCr2O4
FeCr2O4
CoCr2O4
NiCr2O4
CuCr2O4
ZnCr2O4
S
2.5
2.0
1.5
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M(µB)
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–
–
–
–
57
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–
–
–
–
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0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1T
3T
5T
7T
9T
1T
3T
5T
7T
9T
1T
3T
5T
7T
9T
Mn
Co
Fe
-4
-2
0
2
4
6
-2
0
2
4
6
8
-2
0
2
4
6
q
q
q
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1T
1T
3T
5T
7T
9T
1T
3T
5T
7T
9T
Zn
Cu
3T
5T
7T
8T
Ni
-4
-2
0
2
4
6
-2
0
2
4
-12-10 -8 -6 -4 -2 0
2
4
6
8 10
q
q
q
Figure 6. The collapse of all the ∆SM data at different magnetic fields onto a universal curve when plotted as ∆SM /∆SMmax
vs θ

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