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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 66, 2018 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Songying Zhao, Yougang Sun, Ye Zhou 
Copyright © 2018, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-63-1; ISSN 2283-9216 

Frustration-Induced Relaxation in Polycrystalline Nd1-

xSrxCoO3 (x=0.10, 0.15, 0.20) 

Yiyun Yang 

College of Electronic and Information Engineering, Ankang University, Ankang 725000, China 

yangyiyun@aku.edu.cn 

This paper attempts to examine the details on the magnetic relaxation and aging effect of cobaltite Nd1-

xSrxCoO3 (x=0.10, 0.15, 0.20). To this end, a series of polycrystalline Nd1-xSrxCoO3 samples were prepared in 

the traditional way, and their properties were investigated from the DC magnetization, relaxation and aging 

effect. The field-cooled and zero-field-cooled test curves were in obvious mirror symmetry, an evidence of the 

disorder and frustration in the system. This situation obeys the extended exponential relationship at low 

temperature for Nd1-xSrxCoO3. Based on the relaxation rate W (t), the author confirmed that the spin glass 

state is the coexistence of the spin glass and the ferromagnetic cluster. In other words, the system is 

spontaneously separated into the ferromagnetic cluster, the spin glass and the non-magnetic base. In 

addition, the relaxation and aging effect were inherent properties of the system, and the results of the 

interaction of ferromagnetic clusters and spin glass at the low temperature. Therefore, in Nd1-xSrxCoO3 

system, the spin glass behavior was determined by ferromagnetic interaction and spin glass phase; the 

magnetic relaxation and aging effect of Nd1-xSrxCoO3 system originate from the magnetic structure of the 

system.    

1. Introduction 

In recent years, perovskite cobaltites have set off a new wave of research, because of the rich magnetic 

phenomena in doped cobaltite system. The exchange bias and magnetic relaxation of cobaltite were explored 

in great details, leading to the discovery of spin glass in cobaltite system. Some scholars suggested that 

magnetic phase separation is an obvious trend in perovskite cobaltite system, and presented a rich phase 

diagram of cobaltite system (Wu and Leighton, 2003; Luo et al., 2006; Yang, 2014; Kundu, et al., 2006). In 

particular, the cobaltite La1-xSrxCoO3 (LSCO) has been a research hotspot, due to the competition between 

spin glass/cluster glass and the ferromagnetic cluster (Huang et al., 2016; Mukherjee et al., 1996). For 

example, Tang and Sun concluded that the LSCO does not have long-range ferromagnetic order because of 

its magnetic exchange bias (Tang et al., 2006). Thus, the LSCO system consists of ferromagnetic cluster and 

spin glass order, i.e. short-range ferromagnetic cluster embedded in non-magnetic region. Nam et al. obtained 

the spin glass dynamics according to the critical slowing down formula (Nam et al., 2000), and confirmed that 

spin glass exists in cobaltite La0.95Sr0.05CoO3 after probing into the magnetic relaxation and aging effects. In 

these studies, a lot of magnetic properties of samples have been obtained through characterization methods, 

but there are still differences in the details (Paraskevopoulos et al., 2001; Yoshii et al., 2001; Stauffer and 

Leighton, 2004; Nam et al., 1999). This calls for further research into the properties of perovskite cobaltite. 

In light of the above, this paper attempts to examine the details on the magnetic relaxation and aging effect of 

cobaltite Nd1-xSrxCoO3 (NSCO) samples. The research results show that the magnetic relaxation and aging of 

the system are not induced by external conditions, but the inherent properties of the system. 

                                

 
 

 

 
   

                                                  
DOI: 10.3303/CET1866003 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Yang Y., 2018, Frustration-induced relaxation in polycrystalline nd1-xsrxcoo3 (x=0.10, 0.15, 0.20), Chemical 
Engineering Transactions, 66, 13-18  DOI:10.3303/CET1866003   

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2. Experiments 

2.1 Materials  

High-purity raw materials Nd2O3, Co2O3 and SrCO3 were prepared for the experiments. Prior to sample 

preparation, the differential thermal analysis was conducted at the air temperature of 20 C ~1,000 C to 

remove the moisture from the rare earth oxide Nd2O3.  

2.2 Synthesis of samples 

The perovskite cobaltite NSCO (x=0.10, 0.15, 0.20) samples were obtained by the traditional solid-state 

reaction method. First, the high-purity Nd2O3 powder was burned for 4 h at 800 C; second, the SrCO3, Co2O3 

and Nd2O3 powders were mixed with alcohol at the ideal ratios; third, the mixtures were ground into powders 

and then pressed into pellets at the air temperature of 1,000 C for 48 h; fourth, the pellets were reground and 

sintered again at 1,100 C; finally, the sintered objects were slowly cooled to room temperature to complete 

the sample preparation. 

20 30 40 50 60 70

  

 

2 ( )

x=0.2

 

 

 

In
e
n
s
it
y
(A

rb
.U

n
it
s
)

x=0.15

 

 

 

 

x=0.1

(2
0
0
)

(2
1
0
)

(0
0
2
)

(3
0
0
)

(1
1
2
)

(2
2
0
) (0

2
2
)

(1
2
2
)

(0
3
1
)

(1
1
3
)

(2
3
1
)

(3
3
1
)

(0
4
0
)

 

Figure 1: The room temperature X-ray diffraction pattern of Nd1-xSrxCoO3 (x=0.10, 0.15, 0.20) 

2.3 Characterization techniques 

The test of powder X-ray diffraction (XRD) is based on a D1 X ray diffractometer produced by Bede. The 

instrument uses the Cu Kα radiation. The measurements of aging effect, dc magnetization and relaxation 

effects are based on the physical properties measurement system designed by Quantum Company. 

3. Results and discussion 

3.1 Dc magnetization 

According to the XRD pattern of room temperature (Figure 1), the samples are of single phase and 

orthorhombic perovskite structure. 

Figure 2 shows the M (T) curve of the NSCO (x=0.10, 0.15 and 0.20) polycrystalline samples with field cooled 

(FC) and zero field cooled (ZFC) thermal magnetic curve. It can be seen from the figure that the FC and ZFC 

curves separated from each other at low temperature, forming an obvious bifurcation (i.e. irreversible 

behavior). With the reduction of temperature, the FC curve gradually increased, while the ZFC curve first 

increased to the peak value and then decreased. The width of the peak slowly widened with the increase in 

doping ratio. In short, the FC and ZFC curves are bifurcated, and the peak of the ZFC curve is commonplace 

in the spin glass system (Fondado et al., 2000; Zobel et al., 2002; Wu et al., 2015; Yang, 2017). 

14



x=0.1 samples showed different behaviour compared with other samples, and the magnetization decreased 

sharply in value compared with other doping ratio. In particular, its magnetization declined at a much faster 

rate than the samples of the other doping ratios. The magnetization intensified with the temperature, but at a 

rather slow rate, and peaked at low temperature. This trend echoes with the low doping La1-xMxCoO3 (M=Sr, 

Ca and Ba) in Reference (Kriener et al., 2004). This indicates when the number of Co4+ is less, that the double 

exchange function is weak. With a weak ferromagnetism, the samples exhibited little ferromagnetic behaviour 

in magnetization curve. The ZFC peak of x=0.10, 0.15 sample is produced by spin freezing effect. This effect 

means the magnetic spin in the spin-glass system cannot rotate freely at low temperature. According to the 

microstructure of the test systems, there were significant differences in the environment of magnetic moments. 

Hence, the magnetic spins in the systems froze in different directions.  

The ZFC peak of x=0.20 sample is attributable to the competition between the unidirectional and anisotropic 

local field and the external magnetic field (Gruyters, 2005). Because of the gradual increase of the 

ferromagnetic cluster in the nonmagnetic base, the cluster randomly arranged to form a local anisotropic field 

similar to the La0.5Sr0.5CoO3 system (Nam et al., 1999). While ZFC curve peak of x=0.15 sample appeared 

near Tf=35 K, the ZFC peak of x=0.20 sample emerged near Tf=47 K. This behaviour agrees well with that of 

the LSCO system, that is, the behaviour of spin glass/cluster glass (Tang et al., 2006). The ZFC peak of spin 

glass is often observed at freezing temperature.  

0.00

0.04

0.08

0.12

0.16

0.00

0.01

0.02

0.03

0.04

0 50 100 150 200

0.0

0.1

0.2

0.3
 

 

 

M
 (

u
B
/f

.u
.)

x=0.15

 

 

 

 

 ZFC

 FC

x=0.10

  

 

T (K)

H =1000 Oe

x=0.20

 

Figure 2: Field cooled and zero field cooled magnetization of Nd1-xSrxCoO3 (x=0.10, 0.15, and 0.20) 

3.2 Magnetic relaxation and aging effects 

The spins of perovskite cobaltites are disorder, producing setbacks to the system. In other words, the spin 

glass system is frustrated. The frustrated system does not have a lowest energy state. Instead, there is 

countless metastable state at low temperature. Any change of test state will lead to the variation in the free 

energy of the system, which in turn alters the spin state. Of course, the spin state does not change 

immediately, due to the barrier in the phase space. Under a constant temperature, the barrier is positively 

correlated with the distribution of relaxation time. Thus, the magnetic relaxation is another prominent feature of 

spin glass system (Caiuffo et al., 1999; Yamaura et al., 1999; Saron et al., 2016; Li et al., 2016). To detect the 

spin glass properties of the object, the author conducted a relaxation phenomenon test, seeking to gain more 

insights into the system. Figure 3 presents the FC and ZFC residual magnetization of the NSCO at different 

measuring times under 10 K for x=0.15. 

It can be seen from Figure 3 that the magnetization varied with the measuring time. With the increase of 

measuring time, the residual magnetization gradually reduced under the FC condition, and increased under 

the ZFC condition. There is an obvious mirror symmetry between FC and ZFC curves, that is, the two curves 

were exactly opposite in this system under the same test field, temperature and wait time (DeFotis et al., 

1998).  

The test results show that relaxation and aging, as the intrinsic properties of the system, solely rely on the 

magnetic structure of the system. A lot of spin glass system also have characteristics of relaxation 

phenomenon which are the characteristic of spin glass system. (Tang et al., 2006). Hence, the relaxation and 

15



aging of the NSCO are not caused by external factors, but the magnetic structure of spin glass. The change of 

the test conditions are only different research means. Double exchange coupling in ferromagnetic clusters are 

very obvious, relaxation and aging is due to exist frustration and result in slow growth of the ferromagnetic 

clusters in the system. In essence, the aging effect demonstrates the disorder and frustration of the system.  

The relaxation effects are due to the disorder and frustration in the NSCO system. The NSCO is frustrated 

system, resulting in slow growth ferromagnetic clusters. 

In the spin glass system, the relaxation phenomenon usually obeys the stretched exponential relationship 

equation (DeFotis et al., 1998): 

1 n

2

p

t
M(t) M exp[ ( ) ]

t


   

(1) 

 

where M2 is the contribution of spin glass; tp is the constant time. M2, tp and n are undetermined parameters. 

The former two parameters are associated with temperature and waiting time, and the last parameter only 

depends on the temperature. 

0 1000 2000 3000 4000 5000 6000
2.67

2.68

2.69

2.70

2.71

2.72

2.73

0 1000 2000 3000 4000 5000 6000
2.67

2.68

2.69

2.70

2.71

2.72

2.73

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.50

 FC
 

 

M
 (

e
m

u
/g

)

t (s)

x=0.15

M
 (e

m
u
/g

)

 

 

 ZFC

t (s)

M
 (

e
m

u
/g

)

 

x=0.15

 

Figure 3: The remanent magnetization of Nd1-xSrxCoO3(x=0.15). The solid line is the best fits Eq. 1 

Using the equation (1) fit the experimental data in the FC conditions. According to the fitted results, the 

relaxation data is in line with the stretched exponential relationship. Experimental fitting parameters of x = 0.10 

and x = 0.15 samples are displayed in table 1. The results was similar to the behavior observed in the spin 

glass system by DeFotis (DeFotis et al., 1998). 

Table 1: The experimental fitted parameters of Eq. 1 for x = 0.10 and x = 0.15 

stretched exponential form M2(emu/g) tp(s) n 

x=0.10 0.13(1) 5.2(1)×105 0.62(5) 

x=0.15 7.27(8) 4.7(2)×103 0.97(2) 

To sum up, the relaxation and aging effects confirm the spin glass properties of the NSCO (x=0.10, 0.15, 0.20) 

system. In fact, the two effects are determined by the magnetic features of spin glass, rather than the external 

influence. The Magnetic relaxation phenomenon of cobaltite system is inherent in the system. 

To further explore the magnetic relaxation phenomenon, the relaxation rate W (t) was introduced to analyse 

the magnetic phenomenon under the FC. Ulrich et al. using Monte Carlo relationship of ferromagnetic particles 

system (Ulrich et al., 2003), found that for all the different grain density, system of relaxation rate W (t) 

according to the exponential decay.  




n
W(t) At  (2) 

where n is the particle density; A is the leading factor related to temperature. 

The relaxation rate W (t) can be expressed as: 

 W(t) (d / dt)lnM(t)  (3) 

16



Here, the relaxation rate W (t) is discussed based on the residual magnetic moment. Figure 4 presents the 

attenuation of the relaxation rate at 10 K (solid line: the data fitted by equation (2)).   

From Figure 4, it is clear that the test data are in accordance with the relationship in equation (2). The n value 

was close to 1, an indicator of the strong interaction between clusters. Thus, it is confirmed that the system 

was spontaneously separated into the ferromagnetic cluster, the non-magnetic base and the spin glass. This 

is similar to the case of La0.82Sr0.18CoO3 system (Huang et al., 2008). When the ferromagnetic clusters are 

embedded in the non-magnetic substrate or the magnetic cluster size is small enough, a spin disordered 

interface layer or surface layer forms, resulting in the formation of the spin glass phase. The magnetic 

behaviour of spin glass in cobaltite is not like manganese compound, only consider the interaction between 

clusters. In the cobaltite system, the interaction of ferromagnetic cluster and spin glass phase resulted in the 

behaviour of spin glass. The above tests and analyses on magnetization and relaxation provide valuable 

insights on the magnetic interaction of the NSCO series.  

100 1000 10000

1E-7

1E-6

1E-5

1E-4

 

 

 

W
 (

t)

W (t) = At
 -n

 

t (s)

  n = 0.87  

   T=10 K

 

Figure 4: W vs log10t for x=0.15. The solid line is the best fits Eq. 2 

4. Conclusions 

This paper digs deep into the DC magnetization and magnetic relaxation of polycrystalline NSCO (x=0.10, 

0.15, 0.20) samples. Several tests were performed to determine the DC magnetization and magnetic 

relaxation of the object. The DC magnetization data indicate that x=0.10 and x=0.15 samples are in the spin 

glass phase, while the x=0.20 sample is in the cluster glass phase. The test results on relaxation shows the 

system exhibited glassy magnetic behaviour in low doping. From the relaxation rate W (t), the author 

confirmed that the spin glass state is coexistence of the spin glass and the ferromagnetic cluster, and the 

system is spontaneously separated into the ferromagnetic cluster, the spin glass and the non-magnetic base. 

The FC and ZFC curves show a good mirror relationship, indicating the disorder and frustration in NSCO 

(x=0.10, 0.15, 0.20) system. The magnetic relaxation and aging effect of NSCO system are determined by the 

magnetic structure of the system, and the relaxation and aging phenomenon are the characteristics of the spin 

glass system. 

Acknowledgments 

The work is supported by the Special Scientific Research Program Funded of Ankang University (Program 

No.2015AYPYZR05), Project from Scientific Research Fund of Shaanxi Provincial Education Department 

(Grant No. 16JK1015). 

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