With such the optimal ratio, colossal magnetore-sistance and magnetocaloric effects would be obtained around the FM-paramagnetic PM phase transition temperature TC [6–10].. data of magne
Trang 1Ferromagnetic short-range order and magnetocaloric effect
The-Long Phana, P.Q Thanhb, P.D.H Yenc, P Zhanga, T.D Thanha,d, S.C Yua,n
a
Department of Physics, Chungbuk National University, Cheongju 361-763, South Korea
b 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
a r t i c l e i n f o
Article history:
Received 16 May 2013
Accepted 14 June 2013
by M Grynberg
Available online 21 June 2013
Keywords:
A Perovskite manganites
D Critical behavior
D Magnetocaloric effect
a b s t r a c t
We have studied the critical behavior and magnetocaloric effect of a perovskite-type manganite LaMn0.9Fe0.1O3with 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, β¼0.35870.007, γ¼1.32870.003, and δ¼4.7170.06 Comparing to standard models, the critical exponent values determined in our work are close to those expected for the 3D Heisenberg model (withβ¼0.365, γ¼1.336, and δ¼4.80) 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 kg−1 K−1for the appliedfield of 50 kOe Particularly, its magnetic-field dependence obeys the power law|ΔSmax|∝Hn, where n¼0.63 is close to the value calculated from the relation n¼1+(β−1)/(β+γ)
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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
inter-actions of Mn3+(3d4, t3
2ge1
g) cations located in an octahedral crystal field formed by six oxygen anions (i.e., MnO6octahedron) A strong
coupling between the electron spins on egand t2gorbitals 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
man-ganites with general formula La1−xAxMnO3[5], where Mn4+
con-centration 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
com-pounds with x≈0.3 With such the optimal ratio, colossal
magnetore-sistance and magnetocaloric effects would be obtained around the
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 (M¼Ni, 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 con-tributes 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−yFeyO3compounds, 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 investi-gated its critical behavior and magnetocaloric effect based on the
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E-mail address: scyu@chungbuk.ac.kr (S.C Yu)
Trang 2data 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 kg−1 K−1 for an
applied field of 50 kOe Additionally, its magnetic-field
depen-dence can be described by the power lawΔSmax∝Hn, which was
proposed by Oesterreicher and Parker for a material with a second
order magnetic phase transition (SOMT)[18]
2 Experiment
A perovskite manganite LaMn0.9Fe0.1O3was prepared by
con-ventional 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 11001C 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 12001C
for 24 h The single-phase rhombohedral structure (space group
R-3c) of the obtained product was confirmed by an X-ray
diffracto-meter (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
super-conducting quantum interference device (SQUID) magnetometer
3 Results and discussion
Fig 1 shows temperature dependences of zero-field-cooled
(ZFC) andfield-cooled (FC) magnetizations (denoted as MZFCand
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, seeFig 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
anisotropyfield or by an external field Depending on the magnetic
homogeneity of a FM sample and on the applied-field magnitude,
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, perform-ing the temperature dependence ofχ−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 TCandθ 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 magneticfield (M–T–H), with T¼120–160 K One can see that M increases nonlinearly with increasing H At a given magneticfield, M gradually decreases with increasing T because of thermal energy Though the phase transition temperature TCis about 137 K, there is no linear feature observed for the M–H curves at T4TC This reflects an existence of FM short-range order in LaMn0.9Fe0.1O3 More evidence of FM short-range order can be seen clearly from performing the H/M versus M2curves (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 M2curves in the vicinity of TCare 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 inFig 2(b) Notably, the slopes of the H/M versus M2curves are positive This proves the system LaMn0.9Fe0.1O3
undergoing a second order magnetic phase transition (SOMT)[26]
0
3
6
9
12
-0.6 -0.4 -0.2 0.0
ZFC
FC
T (K)
137 K
H = 100 Oe
Fig 1 (Color online) Temperature dependences of ZFC and FC magnetizations for
LaMn 0.9 Fe 0.1 O 3 under an applied field of 100 Oe The inset shows χ −1 (T) data fitted
to the Curie–Weiss law.
0 15 30 45 60 75
0 3 6 9 12
160 K
120 K
H (kOe)
2, Oe.g/emu)
ΔT = 2 K
160 K
120 K
Fig 2 (Color online) (a) Magnetic-field dependences of magnetization (M–H), and (b) an inverse performance of Arrott plots (H/M versus M 2
) for LaMn 0.9 Fe 0.1 O 3 recorded around T , where a temperature increment is 2 K.
Trang 3According 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]
where a and b are constants, and ε¼(T−TC)/TC is the reduced
temperature The critical exponentsβ 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/γversus M1/β
curves with β¼0.5 and γ¼1.0[25]leads to their linear property
However, the absence of such the feature demonstrates thatβ and γ
values characteristic of our system LaMn0.9Fe0.1O3are 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]
Msð Þ ¼ MT 0ð−εÞβ; εo0 ; ð2Þ
χ0 –1ðTÞ ¼ ðh0=M0Þεγ; ε40; ð3Þ
where M0, h0, and D are critical amplitudes, andδ is associated with
the critical isotherm With the correct values ofβ 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/βand (1/χ0)1/γ¼(H/M)1/γ, respectively These
Ms(T) andχ0(T) data are thenfitted to Eqs.(2)and(3), respectively, to
achieve betterβ, γ, and TCvalues The new values of β, γ, and TC
obtained are continuously used for the next modified Arrott plots
until they converge to stable values InFig 3(a), it shows Ms(T) and
χ0(T) data fitted to Eqs (2)and (3), respectively, and the critical
parameters obtained from thefinal step of modified Arrott plots,
where the critical exponents areβ¼0.35870.007 and γ¼1.3287
0.003 The TCvalues 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, TCobtained 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
long-range order With the obtained values ofβ and γ, M1/βversus (H/M)1/γ
curves at highfields around TCare linear, as can be seen clearly in
Fig 3(b) Forδ, 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 valueδ¼4.7170.06 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 jεjβf7ðH=jεjβþγÞ; ð5Þ
where f+and f−are regular functions for T4TCand ToTC,
respec-tively The equation hints that plotting M/|ε|βversus H/|ε|β+γmakes all
data points falling into two universal branches characteristic of
temperatures ToTCand 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 valuesβ, γ, δ, and TCdetermined
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 β¼0.365, γ¼1.336, and
δ¼4.80) This reflects an existence of FM short-range order in
LaMn0.9Fe0.1O3, where FM interactions persist at temperatures above
T As proved by Tong and co-workers [13], there are magnetic
inhomogeneous regions (FM clusters) in LaMn1−xFexO3due to inter-action 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 super-exchange 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−xTixO3compounds, with 0.359≤β≤0.378, 1.24≤γ≤1.29 and 4.11≤δ≤4.21, depending on
Fig 3 (Color online) (a) M s (T) and χ 0 −1 (T) data fitted to Eqs (2) and (3) , respectively (b) Modified Arrott plots of M 1/β versus (H/M)1/γwith T C ¼135.7 K, β¼0.358 and γ¼1.328.
0.0 2.0x107 4.0x107 6.0x107
0 50 100 150 200 250 300
H/| | (Oe)
Fig 4 (Color online) Scaling performance of M/|ε| β versus H/|ε| β+γ shows two universal curves for temperatures T oT C and T4T C The inset shows the same scaling performance in the log–log scale.
Trang 4Ti-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
β¼0.415, γ¼1.470, 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
LaMn0.9Fe0.1O3can 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]
ΔSmðT; HÞ ¼Z H
0
∂M
∂T
H
Fig 5(a) shows temperature dependences of−ΔSmwith various
magneticfields 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 H¼50 kOe, the −ΔSm(T)
curve has|ΔSmax| and the full-width-at-half maximum (δTFWHM) of
about 40 K and 3.8 J kg−1 K−1, respectively If using this material
for magnetic refrigeration application, its relative cooling power
defined by RCP¼|ΔSmax| δTFWHMis about 152 J/kg, and
compar-able to some perovskite manganites[10] InFig 5(b), it shows the
field dependence of −ΔSmaxat T¼TC For a material with the SOMT,
this dependence obeys the power law
jΔSmaxj∝Hn
where n¼1+(β−1)/(β+γ) is assigned to a parameter characteristic
of magnetic ordering [18,30] With β¼0.358 and γ¼1.328, 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), seeFig 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 LaMn0.9
-Fe0.1O3exhibiting the SOMT in the vicinity of TC≈136 K Basing on the modified Arrott plots and universal scaling law, we determined the critical exponents β¼0.35870.007, γ¼1.32870.003, and δ¼4.7170.06, 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 magnet-ism Due to magnetic inhomogeneities (or FM short-range order), the magnetic-field dependences of |ΔSmax| obey the power law
|ΔSmax|∝Hn with n¼0.63, instead of the law with n¼2/3 for the mean-field case Under an applied field interval of 50 kOe, we obtained|ΔSmax|¼3.8 J kg−1 K−1andδTFWHM≈40 K, which corre-spond 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
References
1 2 3 4
1 2 3
4
50 kOe
40 kOe
30 kOe
20 kOe
Sm
-1.K -1)
Smax
-1.K -1)
T (K)
10 kOe
H (kOe)
Smax Hn (at T
C, with n = 0.63)
Fig 5 (Color online) (a) Temperature dependences of −ΔS m with magnetic-field intervals of 10–50 kOe (b) The magnetic-field dependence of −ΔS max at T¼T C fitted to the power law, Eq (7) , with n¼0.63.
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[10] A.M Tishin, Y.I Spichkin, The Magnetocaloric effect and its applications (IOP
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