Critical Behavior in Double-Exchange Ferromagnets ${\hbox{Nd}}_{0.5}{\hbox{Sr}}_{0.5}{\hbox{Mn}}_{1 \hbox{-} x}{\hbox{Co}}_{x}{{\hbox{O}}_3}$

The critical behavior around the paramagnetic-ferromagnetic phase transition in perovskite manganites Nd
_0.5
Sr
_0.5
Mn
_1-x
Co
_x
O
₃
( x = 0.03 and 0.05) has been studied in detail by using various techniques, such as the modified Arrott plot and critical isotherm analysis. Basing on the modified Arrott plot method, we obtained the critical parameters of T
_C
≈ 234.3 K, β = 0.414 ±0.047 and γ = 1.488 ±0.312 for x = 0.03, and T
_C
≈ 221.9 K, β = 0.450 ±0.10 and γ = 1.113 ±0.033 for x = 0.05. The determined values of the critical exponents are in between those expected for the 3-D Heisenberg and mean-field models. With these values, isothermal magnetization data of the samples around T
_C
fall into two branches of a universal function M(H, ε) = |ε|
^β
f
_±
(H/|ε|
^{β+ γ}
), where ε = (T-T
_C
)/T
_C
is the reduced temperature, f
₊
for T > T
_C
and f for . This proves that the critical parameters determined are reliable and in accordance with the scaling hypothesis. Our results also demonstrate an existence of short-range ferromagnetic order in Nd
_0.5
Sr
_0.5
Mn
_1-x
Co
_x
O
₃
. Particularly, the Co doping at high concentrations has a tendency leading to long-range ferromagnetic order.