DSpace at VNU: Ferromagnetic short-range order and magnetocaloric effect in Fe-doped LaMnO3

Solid State Communications 167 (2013) 49–53

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Solid State Communications
journal homepage: www.elsevier.com/locate/ssc

Ferromagnetic short-range order and magnetocaloric effect
in Fe-doped LaMnO3
The-Long Phan a, P.Q. Thanh b, P.D.H. Yen c, P. Zhang a, T.D. Thanh a,d, S.C. Yu a,n
a

Department of Physics, Chungbuk National University, Cheongju 361-763, South Korea
Faculty of Physics, Hanoi University of Science, Vietnam National University, Thanh Xuan, Hanoi, Vietnam
c
Faculty of Engineering Physics and Nanotechnology, VNU - University of Engineering and Technogoly, Xuan Thuy, Cau Giay, Hanoi, Vietnam
d
Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam
b

art ic l e i nf o

a b s t r a c t

Article history:
Received 16 May 2013
Accepted 14 June 2013
by M. Grynberg
Available online 21 June 2013

We have studied the critical behavior and magnetocaloric effect of a perovskite-type manganite

LaMn0.9Fe0.1O3 with a second-order phase transition. Detailed critical analyses based on the modified
Arrott plot method and the universal scaling law gave the critical parameters TC≈135.7 K,
β¼ 0.35870.007, γ¼ 1.328 7 0.003, and δ ¼4.71 7 0.06. Comparing to standard models, the critical
exponent values determined in our work are close to those expected for the 3D Heisenberg model
(with β ¼0.365, γ¼ 1.336, and δ ¼4.80). This reflects an existence of ferromagnetic short-range order in
LaMn0.9Fe0.1O3. Around TC, the magnetic entropy change reaches the maximum value (ΔSmax), which is
about 3.8 J Á kg−1 Á K−1 for the applied field of 50 kOe. Particularly, its magnetic-field dependence obeys the
power law |ΔSmax|∝Hn, where n ¼0.63 is close to the value calculated from the relation n ¼1+(β−1)/(β+γ).
& 2013 Elsevier Ltd. All rights reserved.

Keywords:
A. Perovskite manganites
D. Critical behavior
D. Magnetocaloric effect

1. Introduction
It is known well that LaMnO3 (lanthanum manganite) is an
insulating antiferromagnetic (AFM) material with orthorhombic
perovskite structure, and has the Neél temperature TN≈140 K [1].
Its magnetic properties are generated from super-exchange interactions of Mn3+ (3d4, t 32g e1g ) cations located in an octahedral crystal
field formed by six oxygen anions (i.e., MnO6 octahedron). A strong
coupling between the electron spins on eg and t2g orbitals causes
the Jahn–Teller (JT) distortion of MnO6 octahedra around Mn3+
ions, as confirmed by Elemans et al. [2]. A small change related to
oxygen excess (LaMnO3+s) creates more Mn4+ ions [3]. This leads
to ferromagnetic (FM) double-exchange interactions of Mn3+–Mn4+
pairs, and AFM Mn4+–Mn4+ ones [4,5].
The creation of Mn4+ ions can also be carried out by replacing
partly La ions by an alkaline-earth ion A ( ¼ Ca, Ba, and Sr). These
A-doped compounds are known as hole-doped perovskite manganites with general formula La1−xAxMnO3 [5], where Mn4+ concentration is modified by varying A-doping content. It has been

discovered that the FM interaction becomes strongest when the
Mn3+/Mn4+ ratio is about 7/3, corresponding to La1−xAxMnO3 compounds with x≈0.3. With such the optimal ratio, colossal magnetoresistance and magnetocaloric effects would be obtained around the

n

Corresponding author. Tel.: +82-43-261-2269; fax: +82-43-275-6416.
E-mail address: (S.C. Yu).

0038-1098/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.
/>
FM-paramagnetic (PM) phase transition temperature (TC) [6–10].
Physically, these effects are explained by the double-exchange
mechanism in addition to dynamic JT distortions generated from
strong electron–phonon coupling [4,7,8]. The exchange interaction
strength of Mn ions thus depends on both the bond length 〈Mn–O〉,
and angle 〈Mn–O–Mn〉 of perosvkite manganites [11].
Together with the doping into the La site, the modification of
the FM phase can also be carried out by substituting a transition
metal into the Mn site, known as LaMn1−yMyO3 compounds
(M ¼Ni, Fe, Ti, Co, Cr, and so forth) [12–17]. This route usually
decreases the strength of FM Mn3+–Mn4+ interactions (i.e., TC
value decrease) with increasing M-doping concentration [12–14]
because its presence changes the bond length and angle of the
perosvkite structure, and results in additional contributions of
AFM and/or FM interactions related to M ions. Depending on the
doping level and nature of M, there is the possibility of double
exchange between Mn and M ions to enhance the magnetization
[13,17]. Typically, it was found double-exchange interaction of
Mn3+–Fe3+ besides Mn3+–Mn4+ in LaMn1−yFeyO3 [13], which contributes to an enhancement of magnetization for x¼0.1 (i.e.,
LaMn0.9Fe0.1O3) [12]. One can realize that though many previous

works focused on LaMn1−yFeyO3 compounds, the FM order related
to the magnetic mixed-valence state of Mn and Fe ions, and their
magnetocaloric effect have not been studied yet. To get more
insight into this problem, we prepared LaMn0.9Fe0.1O3 (an optimal
ferromagnet studied preliminarily in Ref. [12]), and then investigated its critical behavior and magnetocaloric effect based on the


T.-L. Phan et al. / Solid State Communications 167 (2013) 49–53

2. Experiment
A perovskite manganite LaMn0.9Fe0.1O3 was prepared by conventional solid-state reaction, used high-purity powders La2O3,
MnCO3, and Fe2O3 (99.9%) as precursors. These powders combined
with stoichiometric quantities were carefully ground and mixed,
and then calcinated in air at 1100 1C for 24 h. The obtained mixture
was reground and pressed into a pellet under a pressure of about
5000 psi by a hydraulic press. Finally, it was annealed at 1200 1C
for 24 h. The single-phase rhombohedral structure (space group
R-3c) of the obtained product was confirmed by an X-ray diffractometer (Bruker AXS, D8 Discover). Magnetic measurements versus
temperature (in the range of 4.2–350 K) and external magnetic
fields ranging from 0 to 50 kOe were carried out on a superconducting quantum interference device (SQUID) magnetometer.

3. Results and discussion
Fig. 1 shows temperature dependences of zero-field-cooled
(ZFC) and field-cooled (FC) magnetizations (denoted as MZFC and
MFC, respectively) for LaMn0.9Fe0.1O3 under an applied field (H)
100 Oe. With increasing temperature above 120 K, one can see
clearly a rapid decrease of magnetization associated with the
FM–PM phase, where magnetic moments become disordered
under the impact of thermal energy. If performing the dMFC/ZFC/
dT versus T curve, see Fig. 1, its minimum is the Curie temperature

(TC) of the sample, which is about 137 K. Particularly, below TC
there is the bifurcation of the MZFC(T) and MFC(T) curves, with
opposite variation tendencies as lowering temperature. Their
deviation is about 6.5 emu/g at 5 K (for H¼100 Oe), and gradually
decreases with increasing temperature. Such the feature is popular
in perovskite manganites [12,13,19], and assigned to the existence
of an anisotropic field generated from FM clusters (due to
magnetic inhomogeneity). Magnetic moments of Mn ions may
be frozen in the directions favored energetically by their local
anisotropy field or by an external field. Depending on the magnetic
homogeneity of a FM sample and on the applied-field magnitude,

-0.2

6
-0.4

ZFC

3

0

-0.6
40

80

120

160

160 K

45
30
15
0

0

10

20

30

40

50

60

H (kOe)

160 K

dMFC/dT (emu/g.K)

M (emu/g)

9

0

120 K

60

0.0

137 K

FC

75

12

H = 100 Oe

12

the deviation between MFC(T) and MZFC(T) would be different.
In general, a large deviation is usually observed in FM materials
exhibiting a coexistence of FM and anti-FM phases and exhibiting
magnetic frustration [19–21]. At temperatures above TC, performing the temperature dependence of χ−1( ¼H/M) reveals its variation
according to the Curie–Weiss (CW) law of χ(T)∝1/(T−θ), with the
CW temperature θ≈140 K, see the inset of Fig. 1. For doped
manganites, the high-temperature PM region is usually dominated

by FM fluctuation generating from dynamic double-exchange
interactions [22,23]. In other words, no real PM state exists above
TC. This is ascribed to the reason causing a small difference
between TC and θ values.
To further understand the magnetic nature of LaMn0.9Fe0.1O3,
we have studied its critical behavior around TC. Fig. 2(a) shows the
data of isothermal magnetization versus the magnetic field (M–T–H),
with T¼120–160 K. One can see that M increases nonlinearly with
increasing H. At a given magnetic field, M gradually decreases with
increasing T because of thermal energy. Though the phase transition
temperature TC is about 137 K, there is no linear feature observed for
the M–H curves at T4TC. This reflects an existence of FM shortrange order in LaMn0.9Fe0.1O3. More evidence of FM short-range
order can be seen clearly from performing the H/M versus M2 curves
(inverse Arrott plots [24]). Basically, if a magnetic system possesses
FM long-range order (as described by the mean-field theory [25]),
the H/M versus M2 curves in the vicinity of TC are parallel straight
lines. The straight line at the critical point TC goes through the
original coordinate. However, these criteria are not met in our
system, as can be seen in Fig. 2(b). Notably, the slopes of the H/M
versus M2 curves are positive. This proves the system LaMn0.9Fe0.1O3
undergoing a second order magnetic phase transition (SOMT) [26].

M (emu/g)

data of magnetic-field dependences of magnetization (M–H).
Experimental results indicate an existence of FM short-range order
in LaMn0.9Fe0.1O3. Around TC, the magnetic-entropy change
reaches the maximum value (ΔSmax) of ∼3.8 J Á kg−1 Á K−1 for an
applied field of 50 kOe. Additionally, its magnetic-field dependence can be described by the power law ΔSmax∝Hn, which was
proposed by Oesterreicher and Parker for a material with a second

order magnetic phase transition (SOMT) [18].

200

T (K)
Fig. 1. (Color online) Temperature dependences of ZFC and FC magnetizations for
LaMn0.9Fe0.1O3 under an applied field of 100 Oe. The inset shows χ−1(T) data fitted
to the Curie–Weiss law.

H/M (x102, Oe.g/emu)

50

ΔT
=

2K

9
120 K

6

3

0

0

1000

2000

M2

3000

4000

5000

(emu/g)

Fig. 2. (Color online) (a) Magnetic-field dependences of magnetization (M–H), and
(b) an inverse performance of Arrott plots (H/M versus M2) for LaMn0.9Fe0.1O3
recorded around TC, where a temperature increment is 2 K.


T.-L. Phan et al. / Solid State Communications 167 (2013) 49–53

51

According to the mean-field theory approximation for a ferromagnet
with the SOMT, the M–T–H relation obeys the scaling equation of
state [25,27]
ðH=MÞ1=γ ¼ aε þ bM 1=β ;

ð1Þ

where a and b are constants, and ε¼(T−TC)/TC is the reduced

temperature. The critical exponents β and γ are associated with the
spontaneous magnetization (Ms) and inverse initial susceptibility
(χ0–1), respectively. As described above, for a magnetic system with
true FM long-range order, the performance of (H/M)1/γ versus M1/β
curves with β¼ 0.5 and γ¼1.0 [25] leads to their linear property.
However, the absence of such the feature demonstrates that β and γ
values characteristic of our system LaMn0.9Fe0.1O3 are different from
those expected for the mean-field theory (MFT). To determined their
values and TC, one usually bases on modified Arrott plots [27], and
the asymptotic relations [25]
εo0 ;

χ 0 –1 ðTÞ ¼ ðh0 =M 0 Þεγ ;
M ¼ DH 1=δ ;

ε 4 0;

ε ¼ 0;

ð2Þ
ð3Þ
ð4Þ

where M0, h0, and D are critical amplitudes, and δ is associated with
the critical isotherm. With the correct values of β and γ, the M–H
data around TC fall into a set of parallel straight lines in the
performance of M1/β versus (H/M)1/γ. The method content can be
briefed as follows: starting from trial critical values (for example:
β¼0.34 and γ¼1.29), Ms(T) and χ0(T) data are obtained from the
linear extrapolation for the isotherms at high fields to the

co-ordinate axes of M1/β and (1/χ0)1/γ ¼(H/M)1/γ, respectively. These
Ms(T) and χ0(T) data are then fitted to Eqs. (2) and (3), respectively, to
achieve better β, γ, and TC values. The new values of β, γ, and TC
obtained are continuously used for the next modified Arrott plots
until they converge to stable values. In Fig. 3(a), it shows Ms(T) and
χ0(T) data fitted to Eqs. (2) and (3), respectively, and the critical
parameters obtained from the final step of modified Arrott plots,
where the critical exponents are β¼ 0.35870.007 and γ¼ 1.3287
0.003. The TC values obtained from extrapolating the FM and PM
regions are 135.870.1 and 135.570.2 K, respectively. Their average
value is thus about 135.7 K. In general, TC obtained from the M–H
data is smaller than that determined from the M–T data. This
deviation will be small if the magnetic system is true FM longrange order. With the obtained values of β and γ, M1/β versus (H/M)1/γ
curves at high fields around TC are linear, as can be seen clearly in
Fig. 3(b). For δ, it can be obtained from fitting the critical isotherm to
Eq. (4). At the temperature T¼136 K (≈TC), δ is about 4.25, which is
the value δ¼4.7170.06 calculated from the Widom scaling relation
δ¼1+γ/β [25]. Assessing the reliability of these critical values can be
based on the static-scaling hypothesis, which predicts that the M–T–H
behavior obey the universal scaling law [25]
MðH; εÞ ¼ jεjβ f 7 ðH=jεjβþγ Þ;

ð5Þ

where f+ and f− are regular functions for T4TC and ToTC, respectively. The equation hints that plotting M/|ε|β versus H/|ε|β+γ makes all
data points falling into two universal branches characteristic of
temperatures ToTC and T4TC. Clearly, such the conditions are fully
met for the M–T–H data of our magnetic system LaMn0.9Fe0.1O3, see
Fig. 4. This proves the reliability of the values β, γ, δ, and TC determined
from modified Arrott plots. If comparing these critical exponents to

theoretical models [25], one can see that their values are close to
those expected for the Heisenberg universality class relevant for
conventional isotropic magnets (with β¼ 0.365, γ¼1.336, and
δ¼ 4.80). This reflects an existence of FM short-range order in
LaMn0.9Fe0.1O3, where FM interactions persist at temperatures above
TC. As proved by Tong and co-workers [13], there are magnetic

Fig. 3. (Color online) (a) Ms(T) and χ0−1(T) data fitted to Eqs. (2) and (3),
respectively. (b) Modified Arrott plots of M1/β versus (H/M)1/γ with TC ¼135.7 K,
β¼ 0.358 and γ ¼ 1.328.

300
250

M/| | (emu/g)

M s ðT Þ ¼ M 0 ð−εÞβ ;

200
150
100
50
0
0.0

2.0x107

4.0x107

H/| |

6.0x107

(Oe)

Fig. 4. (Color online) Scaling performance of M/|ε|β versus H/|ε|β+γ shows two
universal curves for temperatures T oTC and T 4 TC. The inset shows the same
scaling performance in the log–log scale.

inhomogeneous regions (FM clusters) in LaMn1−xFexO3 due to interaction series …Mn3+–O–Fe3+–O–Mn4+…, …Mn3+–O–Fe3+–O–Mn3+…,
…Mn4+–O–Fe3+–O–Mn4+…, etc. It means that the mixed valence of
Mn and Fe ions promotes both FM double-exchange and AFM superexchange interactions. The FM interaction is favored to exist for Fe3+–
O–Mn3+ and Mn3+–O–Mn4+ [13], while the other interaction pairs are
assigned to be AFM. The coexistence of such the FM and AFM regions
leads to FM short-range order in LaMn0.9Fe0.1O3. Recently, Yang et al.
[14] also observed FM short-range order in LaMn1−xTixO3 compounds,
with 0.359≤β≤0.378, 1.24≤γ≤1.29 and 4.11≤δ≤4.21, depending on


52

T.-L. Phan et al. / Solid State Communications 167 (2013) 49–53

4

4

Smax H

n

(at T , with n = 0.63)
C

50 kOe

3
40 kOe

30 kOe

2

Smax (J.kg-1.K-1)

Sm (J.kg-1.K-1)

3

2
20 kOe
1
10 kOe

120

135

150

1
10

165

20

30

40

50

H (kOe)

T (K)

Fig. 5. (Color online) (a) Temperature dependences of −ΔSm with magnetic-field intervals of 10–50 kOe. (b) The magnetic-field dependence of −ΔSmax at T ¼ TC fitted to the
power law, Eq. (7), with n¼ 0.63.

Ti-doping content. For LaMnO3.14 [3], however, the FM phase is mainly
due to Mn3+–O–Mn4+. It has been found the critical exponent values
β¼ 0.415, γ¼ 1.470, and δ¼4.542 close to those expected for the MFT.
The above results prove that the critical property is sensitive to
impurities and defects. These important factors can be employed in
rounding the magnetic phase transition of manganites [28,29].
In the critical region, the magnetocaloric (MC) effect of
LaMn0.9Fe0.1O3 can be assessed upon the magnetic entropy change
(ΔSm). For a FM material undergoing the SOMT, the ΔSm in
a magnetic-field interval of 0−H is determined from Maxwell's

relation [10]
Z H 
∂M
ΔSm ðT; H Þ ¼
dH:
ð6Þ
∂T H
0
Fig. 5(a) shows temperature dependences of −ΔSm with various
magnetic fields from 10 to 50 kOe. At a given temperature, −ΔSm
increases with increasing the applied field. Particularly, the
−ΔSm(T) curves exhibit the maxima (denoted as −ΔSmax) in the
vicinity of TC. Under the applied field H ¼50 kOe, the −ΔSm(T)
curve has |ΔSmax| and the full-width-at-half maximum (δTFWHM) of
about 40 K and 3.8 J Á kg−1 Á K−1, respectively. If using this material
for magnetic refrigeration application, its relative cooling power
defined by RCP ¼|ΔSmax| Â δTFWHM is about 152 J/kg, and comparable to some perovskite manganites [10]. In Fig. 5(b), it shows the
field dependence of −ΔSmax at T¼ TC. For a material with the SOMT,
this dependence obeys the power law.
jΔSmax j∝H n ;

ð7Þ

where n¼ 1+(β−1)/(β+γ) is assigned to a parameter characteristic
of magnetic ordering [18,30]. With β¼0.358 and γ ¼1.328, the
calculated value of n is about 0.62, which is close to the value
n¼0.63 obtained from fitting the |ΔSmax| data to Eq. (7), see Fig. 5(b),
but different from that expected for the MFT (with n¼2/3 [18]). The
deviation in the n value from the mean-field behavior is due to
magnetic inhomogeneities. This is in good agreement with the

results deduced from analyzing the MZFC/FC(T) and M−T−H data, as
mentioned above.

4. Conclusion
The investigation into the critical behavior revealed LaMn0.9Fe0.1O3 exhibiting the SOMT in the vicinity of TC≈136 K. Basing on
the modified Arrott plots and universal scaling law, we determined
the critical exponents β¼ 0.358 70.007, γ¼1.328 70.003, and
δ¼4.71 70.06, which are close to those expected for the 3D
Heisenberg model. This reflects the existence of FM short-range
order in LaMn0.9Fe0.1O3. The mixed valence of Mn and Fe ions
promotes both the FM double-exchange and AFM super-exchange
interactions, and thus leads to inhomogeneous regions in magnetism. Due to magnetic inhomogeneities (or FM short-range order),
the magnetic-field dependences of |ΔSmax| obey the power law
|ΔSmax|∝Hn with n ¼0.63, instead of the law with n ¼2/3 for the
mean-field case. Under an applied field interval of 50 kOe, we
obtained |ΔSmax| ¼3.8 J Á kg−1 Á K−1 and δTFWHM≈40 K, which correspond to the RCP of about 152 J/kg.

Acknowledgment
This research was supported by the Converging Research
Center Program funded by the Ministry of Education, Science
and Technology (2012K001431) in Korea, and by the VNU Science
and Technology Project QG-11-02 in Vietnam.
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