Physics Procedia
Volume 75, 2015, Pages 468–474
20th International Conference on Magnetism

Slow thermodynamics in the phase separated state of thebilayered manganite (La0.4Pr0.6)1.2Sr1.8Mn2O7
Haruka Taniguchi1∗, Yuma Nakamura1 , Takahisa Konno1, Michiaki Matsukawa1, andRamanathaan Suryanarayanan212Department of Materials Science and Engineering, Iwate University, Morioka 020-8551, Japan
Laboratoire de Physico-Chimie de L’état Solide, CNRS, UMR8182, Université Paris-Sud, 91405 Orsay, France

Abstract
Bilayered perovskite (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 exhibits a ﬁeld-induced paramagnetic-insulator to ferromagneticmetal transition, and a phase-separated state is realized after the ﬁeld is switched oﬀ. In order to clarify
the thermodynamic properties of the phase-separated state which is a common feature in many manganites, we performed speciﬁc heat measurement with ﬁeld along the magnetization easy axis. We haverevealed that the remanent specifc heat might exhibit a stretched exponential decay and the relaxation
time is remarkably long. These results indicate the importance of magnetic frustration originating fromthe competition between double-exchange interaction and superexchange interaction.
Keywords: phase separation, manganite, thermodynamics, frustration

1

Introduction

Perovskite-type manganites fascinate many researchers with their various exotic phenomena. For example, bilayered La2−2x Sr1+2x Mn2 O7 exhibits a charge/orbital ordered (CO/OO) state or a colossal
magneto-resistance (CMR) eﬀect [1]. In La2−2x Sr1+2x Mn2 O7 , Mn3+ and Mn4+ coexist and the ratioof Mn3+ to Mn4+ is (2 − 2x)/2x. Since one of the four 3d electrons of a Mn3+ occupies an eg orbitalin the perovskite structure, Jahn-Teller (JT) lattice-orbital eﬀect acts on Mn3+ O6 octahedra. In contrast,
Mn4+ O6 octahedra with empty eg orbitals and half-occupied t2g orbitals are free from JT eﬀect. Therefore, at the half doping (x = 0.5), CE-type long-range CO/OO state in which the eg electrons occupy the
3z2 − r2 orbital is stabilized with the Neel temperature of 220 K [2, 3]. With decreasing x, the CO/OO
correlation transforms into short-range one because of the mismatch between the number of Mn3+ and
Mn4+ , and double-exchange (DE) interaction which induces itinerancy is enhanced [4, 5, 6, 7]. Thus, acharge frustration emerges and results in a metal-insulator transition and a CMR eﬀect [8, 9, 10]. Latticeorbital frustration also exists in this system: DE interaction makes the lattice structure homogeneous via
itinerant electrons, whereas the coexistence of JT active Mn3+ O6 and nonactive Mn4+ O6 octahedra induces lattice inhomogeneity. Therefore, when the metallic phase is induced, Mn3+ O6 octahedra shrink∗ tanig@iwate-u.ac.jp

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Selection and peer-review under responsibility of the Scientiﬁc Programme Committee of ICM 2015c The Authors. Published by Elsevier B.V.


doi:10.1016/j.phpro.2015.12.058

Slow thermodynamics . . .

Taniguchi, Nakamura, Konno, Matsukawa and Suryanarayanan

along the c axis and eg electrons transfer to the x2 − y2 orbital. Moreover, magnetic frustration plays
an important role to determine the electronic state in La2−2x Sr1+2x Mn2 O7 : DE ferromagnetic interaction and superexchange (SE) antiferromagnetic interaction competes and a ferromagnetic-paramagnetictransition accompanies the metal-insulator transition [11].
We have been focusing on La1.2 Sr1.8 Mn2 O7 , which is close to the largest-CMR compositionx = 0.38 [10] and the highest-Curie-temperature composition x = 0.36 [8], and on its Pr-substituted
compound (La1−z Prz )1.2 Sr1.8 Mn2 O7 . The substitution of Pr for La keeps the hole density constant andaﬀects the lattice structure: it elongates MnO6 octahedra along the c-axis [12]. As a result, the transition temperature of the paramagnetic-insulator (PMI) to ferromagnetic-metal (FMM) transition is suppressed and in (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 the PMI phase is sustained down to 0 K [12, 13]. A FMM
phase is induced in (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 by magnetic ﬁeld, accompanied by the lattice shrinkage
along the c-axis similarly to the PMI-FMM transition in La1.2 Sr1.8 Mn2 O7 [14]. Notably, the amplitudeof the CMR eﬀect in (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 is as much as 6 orders of magnitude, which is highly
enhanced compared with that in La1.2 Sr1.8 Mn2 O7 (2 orders of magnitude) [15]. This result reﬂects
the enhancement of the frustration which originates from the increase of short-range CO interaction
by Pr-substitution. Interestingly, the temperature dependence of the magnetization is diﬀerent between
zero-ﬁeld-cooling and ﬁeld-cooling, suggesting spin-glass-like properties [16]. This result suggests
the existence of a magnetic frustration in (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 . Another important feature is large
hysteresis reported in the ﬁeld dependence of thermal conductivity, magnetization, resistivity, and magnetostriction [16, 15, 13, 14, 17, 18]. These hystereses indicate the existence of the phase-separated
phase after switching oﬀ a ﬁeld.
In this study, to better understand the thermodynamic properties of phase-separated manganites, wemeasured the speciﬁc heat of (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 under magnetic ﬁeld and clariﬁed the hysteretic
behavior. Moreover, we investigated the time dependence of the remanent speciﬁc heat and estimatedthe relaxation time.

2

Methods

The single crystal of (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 was grown from a sintered rod of the same nominal
composition by the ﬂoating-zone method using an image furnace. The calculated lattice parametersof the tetragonal crystal structure of this crystal were shown in a previous report [16]. The mass ofthe sample cut out for the speciﬁc heat measurement is 73.0 mg. The dimensions of the sample are
3.4×3.0 mm2 in the ab plane and 1.0 mm along the c axis. The direction of the c axis was determinedby utilizing the fact that (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 cleaves along the ab plane.
Speciﬁc heat C was measured by a relaxation method using the Physical Properties Measurement
System (PPMS, Quantum Design). The sample was mounted on the stage for the direction of magnetic
ﬁeld to be parallel to the c axis, which is the magnetization easy axis of the FMM phase [19]. The
ﬁeld-induced PMI-FMM transition of (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 is of ﬁrst-order, and electrons slowly
transfer from the metastable FMM state to the stable PMI state when an applied ﬁeld is reduced below
the critical ﬁeld Hc [16]. Thus, in order to obtain the virgin state in which only the PMI phase exists,
before each measurement the sample was left above 200 K under zero ﬁeld for about 2 hours and thencooled in zero ﬁeld. Temperature-dependence measurements at ﬁxed ﬁelds (0 and 6 T) were performed
from 2.5 to 150 K. Field-dependence was measured in both increasing and decreasing ﬁeld at the rateof 0.60 T/min, between 0 and 8 T for 2.5, 4, 6 and 8 K, and between 0 and 6 T for 10, 20 and 25 K.
Moreover, since substantial remanent magnetic speciﬁc heat was observed, we investigated the relaxation of the remanent C at 20, 25 and 30 K, covering a large to small hysteresis region. The rate of
the ﬁeld sweep was 0.26 T/min, which was chosen as comparable as that for the relaxation measurement of remanent magnetization and magnetostriction in Ref. [14] and [17] in order to compare these469

Slow thermodynamics . . .

Taniguchi, Nakamura, Konno, Matsukawa and Suryanarayanan

relaxation phenomena. The ﬁeld sweep rate before the relaxation measurement of magnetization andmagnetostriction was 0.26 T/min and 0.2 T/min, respectively.

3

Results

We successfully detected a ﬁeld-induced transition in speciﬁc heat measurements. As shown in Fig. 1(a),the temperature dependence of C/T of (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 diﬀers between 0 and 6 T: C/T exhibitsa peak at 88 K under 6 T, whereas there is no anomaly under 0 T. This anomaly is caused by the ﬁeldinduced PMI-FMM transition.
Figure 1(c) and (d) represent the ﬁeld dependence of the speciﬁc heat at several ﬁxed temperatures.
Here, the value of C(H, T ) is normalized by the speciﬁc heat before applying ﬁeld, Cvirgin (T ). With
increasing ﬁeld, the speciﬁc heat is notably suppressed at a certain ﬁeld, indicating the transition from
PMI to FMM, which is accompanied by entropy reduction. The existence of large hysteresis betweenﬁeld-increasing and decreasing processes implies that the transition is of ﬁrst-order. Interestingly, thespeciﬁc heat does not recover completely even if the applied ﬁeld is switched oﬀ. This result demonstrates that the PMI and FMM phases coexist with spatially separated. Focusing on the diﬀerence ofC(H) among diﬀerent temperatures, C(H) below 10 K exhibits a sharp step-like transition, whereas thetransition above 20 K is broad and continuous. Similar step-like transition of speciﬁc heat is reported in
cubic perovskite La0.225 Pr0.40 Ca0.375 MnO3 [21]. However, to our knowledge, the relaxation of remanent
speciﬁc heat had not been investigated yet in manganites.
Therefore, we focused on the remanent speciﬁc heat and clariﬁed its relaxation at several temperatures as shown in Fig. 2(a). ΔcR is deﬁned to represent the relaxation rate:ΔcR (t) ≡ (CR (t) − CR (0))/(Cvirgin − CR (0)).

(1)

Here, Cvirgin and CR (t) are the speciﬁc heat before ﬁeld is applied and that when time passes by t afterswitching oﬀ the ﬁeld, respectively. We have revealed that the relaxation curves are roughly ﬁtted bystretched exponential functions:f (t) = 1 − exp(−(t/τ)β ) ,(2)in which τ and β represent the characteristic relaxation time and exponent, respectively. The correlationcoeﬃcient r is 0.97 for 20 and 25 K, and 0.88 for 30 K. r indicates the accuracy of a ﬁtting and ranges
between 0 and 1: the larger r means the better ﬁtness. Therefore, these ﬁttings with r ∼ 1 especiallythose for 20 and 25 K are considered to be successful. The relaxation described by a stretched exponential function, which is known to be applicable to spin glass, indicates that the relaxation process iscomplicated. Importantly, the relaxation time estimated from the ﬁtting is remarkably long: τ exceeds
one day with β = 0.39 at 25 K, for example.

4

Discussion

We consider that the origin of the step-like transitions in C(H) below 10 K is the phase-separated groundstate caused by frustration. When the FMM phase is realized partially, accompanying latent heat lowers
Hc of the neighbor region. Here, Hc is deﬁned as the ﬁeld at which dC/dH exhibits a minimum. This
reaction is repeated and results in an avalanche transition and a step-like drop of speciﬁc heat. We
expect that the phase-separated ground state is mainly caused by the magnetic frustration between DE
and SE interactions. Moreover, the lattice-orbital frustration between DE and JT interactions and thecharge frustration between DE and CO interactions would also play an important role. These frustrations
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1.4

(a)

6T

1.2

60

1
40

0.8

T (K)

C/T (J/K2 mol)

(b)

PMI

50

0T

0.6

FMM

30
20

0.4
10

H // c

0.2

0

0

0

20

40

60

0

1

2

80 100 120 140 160

T (K)

(c)

1

5

6

(d)

1
30 K

0.9

0.95 25 K
virgin0.8

C/C

virgin

4

1.05

1.1

C/C

3

μ0H (T)

0.7
10 K
0.6
8
2.5 , 6
0.5 4 K

0.9
20 K

0.85
0.8

0.4
0.3

H // cH // c
-1

0

1

2

3

μ0H (T)

4

5

6

0.75
-1

0

1

2

3

μ0H (T)

4

5

6

Figure 1: (a) Temperature dependence of C/T in (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 under the ﬁeld of 0 and
6 T along the c axis. C/T exhibits an anomaly only under 6 T, suggesting a ﬁeld-induced PMI-FMM
transition. (b) Field-temperature phase diagram of (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 . In the gray shaded area,
in which c-axis magnetization and speciﬁc heat exhibit hysteretic behavior, a phase-separated state isrealized. Red circles and black rectangles indicate transition points determined from the magnetic ﬁeld
dependence of speciﬁc heat (this study) and c-axis magnetization (Ref. [20] and [17]), respectively.
Critical ﬁelds Hc s estimated from speciﬁc heat are deﬁned as the ﬁeld at which dC/dH exhibits aminimum in a ﬁeld-scan measurement at a ﬁxed temperature. (c, d) Magnetic-ﬁeld dependence of thespeciﬁc heat of (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 at several temperatures. The ﬁeld direction is parallel to the caxis and the ﬁeld scan rate is 0.60 T/min. A substantial drop by applying ﬁeld reﬂects the PMI-FMM
transition.
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Slow thermodynamics . . .

1

Taniguchi, Nakamura, Konno, Matsukawa and Suryanarayanan

(a)

10

7

(b)
0.8
10

6

10

5

10

4

C

30 K

τ (s)

Δ cR

0.6

0.4

Mc

25 K
0.2

ρab

1000

20 K

dLc

0
0

1

2

3

4
4

5

t (10 sec)

6

7

8

100
0.01

0.02

0.03

0.04

0.05

0.06

1/T (K)

Figure 2: (a) The relaxation process of the remanent speciﬁc heat of (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 afterswitching oﬀ the c-axis magnetic ﬁeld of 6 T. ΔcR represents the relaxation rate, as the detail is mentioned in the main text. Each broken line demonstrates a stretched exponential function which is ﬁtted
into the experimental result at each temperature. (b) Comparison of the relaxation time of the remanent component in (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 among the speciﬁc heat (this study), c-axis magnetization(Ref. [17]), ab-plane resistivity (Ref. [17]) and c-axis magnetostriction (Ref. [14]). Broken lines are
ﬁtted thermally-activated functions. For reference, the PMI-FMM transition temperature at 6 T deﬁned
as the peak temperature in C(T ) of Fig. 1(a) is indicated by the arrow.
enhance the instability of the PMI state under magnetic ﬁeld and induces the transition to the FMM state
at a ﬁeld lower than the intrinsic value of critical ﬁeld Hc .
For this reason, we expect that C(H) in this study displays the intrinsic Hc above 20 K in which C(H)exhibited a broad transition, and estimated Hc above 20 K as shown in Fig. 1(b). We have revealed inFig. 1(b) that the thermodynamic phase diagram obtained from the speciﬁc heat coincides well with thatfrom the c-axis magnetization [20, 17]. The transition shifts to a lower ﬁeld with increasing temperature, similarly to the magnetization, magnetoresistance and magnetostriction in the same temperature
range [16]. These results suggest that the ﬁeld-induced transition has a thermally-activated character.
The tendency that the relaxation curve of remanent component might be ﬁtted by a stretched exponential function is known to be true also for other physical quantities like magnetization [15, 14, 17],
which is consistent with the existence of frustrations in (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 mentioned above. In
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Taniguchi, Nakamura, Konno, Matsukawa and Suryanarayanan

Fig. 2(b), the relaxation time τ estimated from the speciﬁc heat is compared with those from the c-axis
magnetization [17], ab-plane resistivity [17], and c-axis magnetostriction [14].
We have clariﬁed two common features among these τs: one is long τ, and the other is the temperature dependence described by a thermally-activated function, τ(T ) = τ0 exp(Δ/kB T ). Long τ suggests strong frustration between competing interactions in (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 . The thermallyactivated-type temperature dependence of the relaxation time is consistent with the lower critical ﬁeld at
higher temperature in the same temperature range. The thermal activation energy Δ estimated from theﬁtting is of the same order among the four cases: 18 meV for speciﬁc heat, 34 meV for magnetization,
39 meV for resistivity, and 30 meV for magnetostriction.
The quantitative diﬀerence of τ among diﬀerent physical quantities reﬂects the detailed diﬀerence
among the phenomena detected in each measurement. A slow relaxation of remanent magnetization
is caused by magnetic frustration between DE and SE interactions. The corresponding relaxation ofremanent speciﬁc heat represents a slow decrease in the volume fraction of the FMM phase associatedwith a spontaneous transition from the FMM to PMI states. We believe that speciﬁc heat measurements
reveal the entropy changes associated with phase transitions and provide direct information about therelaxation processes in phase-separated states of doped manganites. In contrast, additional factors areincluded in the relaxation of magnetization, resistivity, and magnetostriction. The factor for magnetization is the domain eﬀect: even if the FMM phase sustains large volume, the relaxation rate increases
when the alignment of the spin directions among domains is suppressed, resulting in the suppression of
τ. In resistivity measurement, we should note that the relaxation rate is enhanced when a metallic pathis destroyed. For magnetostriction, it should be noted that the lattice relaxation is not due to the structural transition associated with cooperative phenomena but arises from a local lattice distortion of MnO6octahedra without a long-range order. It is contrast to the relaxations in the thermodynamic, magnetic
and transport properties which are taken as signatures of the phase transition from metastable FMM tostable PMI states in the long time scale. Additionally, at the higher temperature, a technical diﬃcultycauses the larger discrepancy between τ estimated from speciﬁc heat and those from the others. Since
speciﬁc heat C is measured using the relaxation method in this study, obtaining one value of C requires
the longer time at the higher temperature: for example, about 13, 10 and 7.5 min was required at 30, 25
and 20 K, respectively. This time-passing eﬀect will overestimate τ.

5

Summary

On the bilayered manganite (La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 , which exhibits the ﬁeld-induced paramagneticinsulator to ferromagnetic-metal transition, we performed speciﬁc heat measurement of a single crystal
under magnetic ﬁeld along the c axis and examined the thermodynamic phase diagram and thermal relaxation process in the phase-separated state. In the ﬁeld dependence, we have clariﬁed a large hysteresis
and a remanent component after switching oﬀ the ﬁeld, which reﬂect the phase-separated character of(La0.4 Pr0.6 )1.2 Sr1.8 Mn2 O7 . Moreover, we have revealed that the critical ﬁeld below 30 K is enhancedwith cooling. This result suggests the thermally activated character of this transition. In this study,
what is new to the research ﬁeld of manganites is the observation of the relaxation of remanent speciﬁc heat, which is expected to directly detect how the volume fraction of the metastable FMM phaseis reduced. We have clariﬁed that the relaxation curve is roughly described by a stretched exponentialfunction and the relaxation time τ is remarkably long, which indicates the existence of a strong frustration. The main origin of this frustration is considered to be the competition between double-exchange
and superexchange interactions.
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Acknowledgments
We thank Y. Nakanishi and M. Nakamura for their support in the measurement. This work is supported
by ”Positive Action Grant for Women Researchers” in Iwate Univ.

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