Electronic Supporting Information:
Octahedral distortion induced magnetic anomalies in LaMn0.5Co0.5O3 single
crystals
Kaustuv Manna1, Venkata Srinu Bhadram2, Suja Elizabeth1, Chandrabhas Narayana2 and
P. S. Anil Kumar1
1
Department of Physics, Indian Institute of Science, Bangalore-560012, India.
2
Chemistry and Physics of Materials Unit, Jawaharlal Nehru Centre for Advanced Scientific
Research, Bangalore- 560064, India.
Email: kaustuvmanna@gmail.com
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Laue pattern:
(a)
(b)
Figure 1 SI: (a) Result of Laue experiment on the LaMn0.5Co0.5O3 single crystal grown using
optical floating zone method and (b) superposed simulated pattern.
Compositional analysis:
Compositional analysis was performed at nearly 10 points on both single crystals as
well as polycrystalline LaMn0.5Co0.5O3 samples using Electron Probe Micro-Analysis (EPMA).
The compositional variation observed was ~ 2 – 4 %, which is within the experimental error.
[The average composition estimated are: La(0.99±0.02)Mn(0.48±0.03)Co(0.52±0.04)O(3.014±0.05) (single
crystal) and La(1.02±0.02)Mn(0.49±0.03)Co(0.51±0.03)O(2.979±0.04) (polycrystalline)].
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Critical behavior study:
To understand the effect of strain induced lattice distortion on the magnetic interaction, we
have performed the critical behavior study around the corresponding TC of the LaMn0.5Co0.5O3
single crystals. According to the scaling hypothesis, the second order phase transition from
ferromagnetic to paramagnetic, is characterized by a set of interrelated critical exponents , , ,
 etc.1 Here  can be calculated from the specific heat measurement. The exponents ,  are
obtained from the temperature dependent spontaneous magnetization MS(T) below TC and the
inverse initial susceptibility, 0-1(T) above TC respectively. The exponent  is calculated from the
critical isotherm, M(H) at the corresponding TC. All these computations are done based on the
following equations:1
M S (T ) = A(-e )b , for  < 0.
(1)
c 0-1 (T ) = B(e )g , for  > 0.
(2)
M (H,TC ) = C(H )1/d , for  = 0.
(3)
Where,  = (T - TC)/TC is the reduced temperature, and A, B and C are critical amplitudes.
Figures 2(a) and (b) present the M-H isotherms around the corresponding TC for the as grown
(AG) and strain-free annealed (AN) crystals respectively. In this measurement protocol, the
sample was first zero-field-cooled from 300 K to 138 K for AG (132 K for AN) and then kept
aside for 30 min to attain thermal equilibrium. Then the M(H) isotherm was recorded with an
increased field from 0 - 14 T and then decreased back to 0. For the next consecutive isotherms,
the temperature was raised to the corresponding value, and a 15 min delay was given before
recoding the data. Here, because of the high coercive field, the analysis was restricted only to the
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high field region (8 - 14 T). To find out the exponents  and , the Arrott method was employed
initially. It was observed that the M2 vs H/M plot did not reveal progressively parallel straight
lines around TC. This signifies that the class of interaction is not of the mean field type in this
system. So, a modified Arrott plot is used for this calculation, which follows the Arrott-Noaks
equation of state as2
(H / M )1/g = De + E(M )1/b ,
(4)
where, D and E are constants.
Figure 2 SI: M-H isotherms around the corresponding TC for (a) the as grown oriented single
crystal (AG) and (b) strain-free annealed crystal (AN). Modified Arrott plot isotherms [ M
1/b
vs
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(H / M )1/g ] for (c) AG and (d) AN. The solid lines present the linear fit to the corresponding
data.
Figures 2(c) and (d) present the modified Arrott plot for the samples AG and AN respectively
using equation (4). In order to obtain an optimum value of  and , a self-consistent method was
applied. The initial value of MS and 0-1 was calculated from the high field data in the Arrott
plot. Then  and  were estimated utilizing equations (1) and (2) for MS(T) and 0-1(T)
respectively. Using them, a modified Arrott plot was constructed and the whole process was
circled until a set of optimum value was obtained. Figures 3(a) and (b) present the final MS(T)
and 0-1(T) for the two LMCO crystals, AG and AN, respectively. The values of ,  and TC
obtained for AG are (0.394  0.004), (1.303  0.013) and 148.7 K respectively which agree very
well with those obtained from the modified Arrott plot in Figure 2(c) [ = 0.395,  = 1.28].
However, the values obtained for AN, are (0.350  0.003), (1.317  0.016) and 142.3 K
respectively which also match very well with those obtained from the modified Arrott plot in
Figure 2(d) [ = 0.354,  = 1.32].
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Figure 3 SI: Temperature dependence of the spontaneous magnetization MS(T) and inverse
initial susceptibility 0-1(T) for (a) AG and (b) AN LaMn0.5Co0.5O3 crystals. The solid lines are
the fit obtained using the equations (1) and (2) respectively.
In order to determine the critical exponents more precisely, the Kouvel-Fisher (KF) method3
was utilized, according to which the temperature dependence of MS(dMS/dT)-1 and 0-1(d0-1/dT)1
followed straight-line behavior with slopes (1/) and (1/) respectively. Figures 4(a) and (b)
show the experimental agreement for AG and AN, respectively, and the straight lines present the
best fit according to the KF model. The critical exponents and the TC calculated from the fittings
are, for AG:  = (0.399  0.006),  = (1.304  0.010), 148.7 K and for AN:  = (0.351  0.007), 
= (1.312  0.013), 142.4 K. It is evident that the values match very well with those obtained from
the previous analyses for both samples.
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Figure 4 SI: Kouvel-Fisher plot from the temperature dependent spontaneous magnetization and
inverse initial susceptibility for (a) AG and (b) AN crystals. The straight lines are the linear fit to
the data.
To calculate the critical exponent , we have chosen the M(H) isotherms at 249 and 242
K for AG and AN respectively which is the closest to the corresponding TC. Figures 5(a) and (b)
display the isotherms for AG and AN respectively. The linear fit to the log-log plot (shown in the
related insets) based on equation (3) yields a  of (4.33  0.04) and (4.73  0.05) for the two
samples. Now, using the scaling law1:  = 1+ (/), the value of  calculated from Figure 4 is:
4.27 and 4.74 for AG and AN respectively, which matches very well with that obtained from the
critical isotherm. This clearly demonstrates that the critical exponents calculated using the
modified Arrott plot method is self-consistent for both the crystals of LaMn0.5Co0.5O3.
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Figure 5 SI: Critical M(H) isotherm close to the TC for (a) AG and (b) AN crystals. The insets
display the same in log-log scale with the straight line as linear fit.
To corroborate further, we have checked whether the calculated set of critical exponents can
generate a magnetic equation of state for this system. According to the scaling hypothesis, the
field and temperature-dependent magnetization follows the scaling law1
M (H, e ) = e b f± [
H
e
( b +g )
],
(5)
where, f+ and f- are two regular functions applicable to T>TC and T<TC, respectively. This
denotes that for the proper selection of critical exponents ,  and , the (M e - b ) as a function of
(H / e ( b +g ) ) forms two sets of universal curves, where all the isotherms below and above TC
merge with each other. Figures 6(a) and (b) present the agreement of the above hypothesis for
AG and AN respectively. The critical exponents and TC obtained from the Kouvel-Fisher plot are
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used here. The insets present the corresponding plot in a log-log scale. It is evident that all the
curves below and above TC fall on top of each other for both AG as well as AN. This confirms
that the critical exponents calculated for AG and AN are reasonably accurate.
Figure 6 SI: Scaling plot below and above TC for (a) AG and (b) AN, with critical exponents
obtained from Kouvel-Fisher method. The insets present the corresponding plot in log-log scale.
Reference:
1
H. Eugene Stanley, Introduction to Phase Transitions and Critical Phenomena, (Oxford
University Press, New York, 1971).
2
A. Arrott, and J. E. Noakes, Phys. Rev. Lett. 19, 786 (1967).
3
J. S. Kouvel, and M. E. Fisher, Phys. Rev. 136, A1626 (1964).
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