PRL 98, 267204 (2007)

PHYSICAL REVIEW LETTERS

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29 JUNE 2007

Steplike Lattice Deformation of Single Crystalline La0:4 Pr0:6 1:2 Sr1:8 Mn2 O7
Bilayered Manganite
M. Matsukawa,1,* Y. Yamato,1 T. Kumagai,1 A. Tamura,1 R. Suryanarayanan,2 S. Nimori,3 M. Apostu,2 A. Revcolevschi,2K. Koyama,4 and N. Kobayashi412Department of Materials Science and Technology, Iwate University, Morioka 020-8551, Japan
Laboratoire de Physico-Chimie de L’Etat Solide, CNRS, UMR8182 Universite Paris-Sud, 91405 Orsay, France
3
National Institute for Materials Science, Tsukuba 305-0047, Japan
4
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan(Received 21 December 2006; published 28 June 2007)
We report a steplike lattice transformation of single crystalline La0:4 Pr0:6 1:2 Sr1:8 Mn2 O7 bilayered
manganite accompanied by both magnetization and magnetoresistive jumps, and examine the ultrasharp
nature of the field-induced first-order transition from a paramagnetic insulator to a ferromagnetic metal
phase accompanied by a huge decrease in resistance. Our findings support that the abrupt magnetostriction
is closely related to an orbital frustration existing in the inhomogeneous paramagnetic insulating phaserather than a martensitic scenario between competing two phases.
DOI: 10.1103/PhysRevLett.98.267204

PACS numbers: 75.80.+q, 64.70.Kb, 71.30.+h, 75.47.Lx

The lattice transformation associated with a fieldinduced metamagnetic transition, observed in perovskite
manganites and a class of rare-earth intermetallic compounds, gives rise to significant information for our understanding of the dynamics of first-order phase transitions insolid-state physics [1]. For example, the structural transformation of intermetallic compounds from an austinite(parent) to a martensite phase upon increasing an external
field is accompanied by a metamagnetic transition from anantiferromagnetic (AFM) to a ferromagnetic (FM) state[2]. This type of transition contrasts with that activatedthermally where thermal fluctuations drive the system froma metastable towards a stable state at constant externalparameters (external magnetic field, temperature, and external stress) [3]. A martensite transformation is associatedwith a significant change of the unit cell from the parent to
the new phase and takes place as a sequence of avalanches
between metastable states due to local strain fields stored in
the lattice [4].
Recent experimental and theoretical studies on doped
manganites exhibiting a colossal magnetoresistance(CMR) effect have revealed the inhomogeneous coexistence of charge-ordered AFM insulating and FM metallic
phases in a phase-separated ground state [5]. The lowtemperature phase-separated state is composed of acharge-ordered (CO) matrix phase with a large lattice
distortion due to a cooperative Jahn-Teller effect and metallic FM clusters with a different unit cell from the former
phase, indicating the presence of substantial strains at CO/
FM interfaces. Several recent studies on metamagnetictransitions of manganites have also shown that ultrasharp
magnetization steps appear at low temperatures. To account for this, a model based on a martensitic scenario
between competing CO/FM phases has been proposedthough questions have been raised against this model[6 –10].
0031-9007=07=98(26)=267204(4)The purpose of this Letter is to present a detailed
investigation of anisotropic magnetostrictions of single
crystalline La0:4 Pr0:6 1:2 Sr1:8 Mn2 O7 , and to examine thedynamics of a steplike first-order transition from a paramagnetic insulating (PMI) to a ferromagnetic metal(FMM) phase in CMR manganites. Our data strongly favor
an orbital frustration to account for our findings.
For the Pr-substituted La0:4 Pr0:6 1:2 Sr1:8 Mn2 O7 crystal,a spontaneous ferromagnetic metal phase (originallypresent with no Pr substitution) disappears at groundstate, but a field-induced PMI to FMM transformation isobserved over a wide range of temperatures. A
magnetic (H; T) phase diagram, established from magnetic
measurements, is separated into three regions labeled as
PMI, FMM, and phase-separated (PS) states (seeRefs. [11,12]). The proximity of free energies between
the PMI and FMM states is of importance to stabilize the
PS state. Application of an external field destabilizes the
PMI ground state and drives the transition to the FMM
state through the intermediate PS state. As seen from themagnetic phase diagram, a stronger field is needed toinduce the PMI to FMM transition at low temperatures
since the thermal energy is reduced upon lowering temperature. This tendency points to a thermally activatedcharacter of the metamagnetic transition.
Single crystals of La0:4 Pr0:6 1:2 Sr1:8 Mn2 O7 were grownby the floating zone method using a mirror furnace. The
lattice parameters as well as the chemical homogeneity ofthe tetragonal crystal were reported earlier [13]. The dimensions of the z  0:6 sample are 3:4  3 mm2 in the abplane and 1 mm along the c axis. Measurements of magnetostriction, both in the ab plane and along the c axis,
were done by means of a conventional strain gauge method
at the Tsukuba Magnet Laboratory, the National Institutefor Materials Science (NIMS), and at the High Field
Laboratory for Superconducting Materials, Institute for267204-1© 2007 The American Physical Society

PHYSICAL REVIEW LETTERSPRL 98, 267204 (2007)

Materials Research, Tohoku University. The magnetization
measurements were made by using a VSM magnetometer
at NIMS. The sample was zero-field cooled from 300 K
down to low temperatures and we then started measuring
the isothermal magnetostriction upon increasing (or decreasing) the applied fields, parallel to the c axis. The
normal sweep rate was set to be 0:26 T= min .
Figure 1 shows the isothermal magnetostriction data of a
La0:4 Pr0:6 1:2 Sr1:8 Mn2 O7 single crystal at T  4:3 and
10 K. First of all, we emphasize qualitative differences in
the magnetostriction between ultrasharp transformations at
low T observed here and broad variations at higher T(a)H||c0.001

a-axisdL(H)/L(0)

0
H||ab

c 4.3Ka 4.3K
c 10K
a 10K
c 4.2K-0.001c-axis-0.002

M(H)/M(8T)

1
0.8
0.6
0.4
c 4K
c 15K
c 30K
ab 3.5K0.2(b)0

c 4.2K

1

c 15K
c 27K

R(H)/R(0)(c)

a 4.2K

0.1

0.01
0

1

2

3

4
5
µ H(T)

6

7

8

0FIG. 1 (color online). (a) The c-axis and ab-plane isothermal
magnetostriction of a La0:4 Pr0:6 1:2 Sr1:8 Mn2 O7 single crystal at
T  4:3 and 10 K (H k c). A dotted curve represents the c-axis
data at 4.2 K in the case of H k ab. The small magnetoresistanceeffect of the strain gauge itself gives a slight increase in both dLc
and dLab . (b) Field dependence of the isothermal magnetizationof the same crystal at selected temperatures (H k c). For comparison, the ab-plane magnetization data are given at 3.5 K (H kab). (c) c-axis magnetoresistances of the same crystal at selected
temperatures in the cases of H k c. For comparison, the ab data
at 4.2 K (H k ab) are cited.

week ending
29 JUNE 2007previously reported in [11] (width is approximately theorder of 1 T). Both dLc and dLab are independent of theapplied field up to 5 T. However, upon further increasing
the field, the c axis abruptly shrinks by 0:2% at low T,
whereas the ab axis expands simultaneously. The transition widths are estimated to be within 0.1% of the magnitude of the critical field Hc from the present data.
Following a steplike change of the magnetostriction at
Hc , the values of dLc and dLab then remain almost constant upon increasing H up to 8 T and decreasing it down tozero field. Finally, the dLc H and dLab H curves exhibit
a large hysteresis and the remanent striction remains very
stable for about one day after switching off the field. For
comparison, the isothermal magnetization and magnetoresistance of the same composition crystal are presented in
Figs. 1(b) and 1(c). Here, the value of Mc (8 T) reaches3:5B =Mn site, close to the full moment of 3:6B =Mn
site, while the value of Mab is 3:0B =Mn site, which isby about 20% smaller than the ideal value [13]. The
corresponding magnetization and magnetoresistance dataalso exhibit a steplike transition at the same critical field.
We note that a steplike behavior of the magnetostriction is
not observed for polycrystalline Sm; SrMnO3 manganitein spite of the appearance of both a steplike magnetizationand magnetoresistance [8]. The steps observed in dLH,
MH, and H are almost independent of the field
direction.
Next, we present in Fig. 2(a) the c-axis magnetostriction
data as a function of cooling field, because the cooling field
affects a fraction of the FMM region [6]. All dLc H data
show a smooth decrease and then follow a steplike drop.
The value of dLc H decreases from 0:18% at the FC-1T
run down to 0:1% at the FC-1.6T run [see the caption ofFig. 2(a)]. The substantial difference in dLc H between
the FC-1T and FC-1.6T runs indicates that the FMM phaseis partially formed within the PMI matrix through each FC
run, before magnetostriction measurements are done. The
remarkable jump observed in dLc H is monotonicallydecreased upon increasing the cooling field from 1 T up
to 1.6 T, accompanied by a nonlinear dependence of Hcfrom 5.6 T up to 7.6 T. For all measurements exhibiting the
steplike transition, a divergent behavior of bath temperature was observed at the corresponding Hc , as shown in
Fig. 2(b). The larger steps in dLc H accompany a moresudden temperature rise. In addition to it, the apparent
striction in both dLc H and dLa H at the steplike transition suggests a rapid rise of the sample’s temperature dueto the released heat [14] [see the caption of Fig. 2(a)]. It has
been reported from the magnetocaloric measurement on
polycrystalline La0:225 Pr0:4 Ca0:375 MnO3 that a released
heat at the ultrasharp field-induced transition gives rise to
the abrupt increase of the sample temperature T  30 K
[9]. When the cooling field exceeds 1.6 T, the steplike
behavior of dLc H disappears.
Then, after a first scan in zero-field cooling, we carriedout successive measurements of the isothermal magnetostriction. At the beginning of further scans, we reset the267204-2

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PHYSICAL REVIEW LETTERSPRL 98, 267204 (2007)
0.001

c-axis(a)4.3K H||c(a)4.3K H||c0.001

a-axis1dL(H)/L(0)-0.001dL(H)/L(0)

0
2
4
3

1T
1.4T
1.45T
1.5T
1.6T

-0.004dL(H)/L(0)-0.003

10

3
1.4T aµ H(T) 6

5.5

a-axis

6.5

0

4.45

7

6.5

4.4

0
-0.001c-axis-0.002

6

5.5

0

0.5
1
1.5
cooling field (T)2nd scan-0.0032(c)4.3K H||c

0.001

4.35

a-axisdL(H)/L(0)bath temperature (K)7.5
critical field (T)

1T
1.4T
1.45T
1.5T
1.6T

(b)4.3K H||c0.001

1.45T aa-axis8

4.5

1st scan

1T a-0.001(b)H||cc-axis-0.002-0.0032-0.0005

4.55-0.00140.001
0.0005dL(H)/L(0)-0.002

0

4.3
5

5.5

6

6.5
µ H(T)

7

7.5

8

0

FIG. 2 (color online). (a) c-axis magnetostriction as a functionof cooling field (1, 1.4, 1.45, 1.5, and 1.6 T). For comparison, thea-axis data are displayed in the inset of (a). First, warming thesample from 4.3 K up to 200 K in the absence of field and thencooling it from 200 K down to 4.3 K in the respective field during
30 min (FC), the applied field was removed. Finally, we startmeasuring the magnetostriction upon increasing the field up to
8 T. For each measurement, we repeated the same procedure.
The arrows labeled 1 and 4 mark dLc H, before and after thetransition, respectively. Arrow 2 represents the net lattice deformation, while arrow 3 points to the apparent change caused by
the rise of sample temperature. (b) The corresponding bathtemperature versus applied field. The slight decrease in thebath temperature as a function of H arises from the magnetoresistance effect of the cernox thermometer. The inset of (b)represents the critical field Hc versus the cooling field, at 4.3 K.

sample from the remanent FMM to the PMI virgin state bya local heating (see Ref. [15]). In the second scan[Fig. 3(b)], once dLH shows a continuous variation
with the insulator-metal transition, near 6.3 T, a sudden
jump along both the c axis and the a axis is also observed.
However, the third scan data show no discontinuous step,similar to the normal dLH curves at higher temperatures.
The critical field of the second scan is increased up to 6.3 Tfrom 5.3 T in the first scan. The qualitative differences inthe dLH curves among the three scans probably arise
from a training effect due to the local heating from thestrain gauges attached on the sample. Such a local heatingerases the memories experienced by the sample, removes
frustrations existing within the PMI matrix, and stabilizes
the PMI state, resulting in a widely broad transition, as seenin the third scan. For comparison, we examine how thecooling rate from high temperatures down to 4.3 K affects

0-0.001c-axis-0.002
3rd scan-0.0032

345µ H [T]

6

7

8

0

FIG. 3. Field dependence of the c-axis and a-axis isothermal
magnetostriction, dLc and dLab , at 4.3 K (H k c). (a) Firstscan, (b) second scan, and (c) third scan. Here, first scan of
the applied field denotes 0 ! 8 ! 0 T. Second (third) scan:
local heating ! 0 ! 8 12 ! 0 T. (For details, see the text).

the critical field. In both rapidly and slowly cooling procedures, the step phenomena appear (Fig. 4), and we get
the comparable valuers of Hc  5:36 T (rapid) and 5.2 T(slow) in the case of 300 K. In a similar way, Hc  5:63
and 5.58 T, rapid and slow cooling rates from 200 K,
respectively. We found out that Hc is almost independentof the cooling rate and is suppressed in the cooling processfrom a higher temperature of 300 K. In addition, checking
the sweep rate dependence of Hc , we get 5.6 T in both 0.52
and 0:26 T= min and 5.8 T at the slow rate of 0:052 T= min(not shown here).
Finally, we discuss now the origin of the magnetostrictive jump observed here. The parent bilayered manganite
La1:2 Sr1:8 Mn2 O7 exhibits a PMI to FMM transition aroundTc  120 K and an associated CMR effect [16]. In the halfdoped bilayered manganite of La22x Sr12x Mn2 O7 x 
0:5, near the x  0:4 crystal, a long-range orbital- andcharge-ordered (OO/CO) state is established, accompanied
by a CE-type (zigzag FM chains with AFM interchain
coupling) antiferromagnetic structure [17]. Neutron scattering measurements on a bilayered manganite near optimal doping show that CE-type OO/CO clusters (short-

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PHYSICAL REVIEW LETTERSPRL 98, 267204 (2007)
0.00054.3K

c-axisslow 300K
rapid 300K
slow 200K
rapid 200K

5.4

6

0

dL(H)/L(0)-0.0005

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free energy has some relation with the transition, but it
never reproduces quite different isothermal behaviors
under the same external field scans.
In summary, we observed a steplike magnetostriction ina single La0:4 Pr0:6 1:2 Sr1:8 Mn2 O7 sample, accompanied bysteps in both magnetization and magnetoresistance. Ourdata suggest that the abrupt lattice transformation reported
here cannot be described by a martensitic transformation
but is closely related to an orbital frustration existing in theinhomogeneous PMI phase.
This work was supported by a Grant-in-Aid for
Scientific Research from Japan Society of the Promotionof Science.

-0.001-0.0015-0.002-0.0025
5

5.2

5.6
5.8
µ H (T)

6.2

0

FIG. 4 (color online). Cooling rate dependence of dLH from
200 and 300 K down to 4.3 K. In the case of 200 K, rapid andslow cooling rates are set at 30 min and 12 h. At 300 K, rapid andslow cooling rates in 20 min and 15 h, respectively.

range polaron correlations) freeze upon cooling to T 
310 K (T  : glass transition temperature), as a magnetic
frustration between FM and AFM interactions leads to aspin-glass state [18]. This finding strongly suggests theexistence of an orbital frustration in the PMI phase, which
prevents the formation of the CO phase. Thus, we believethat an orbital frustration exists within the PMI state of thepresent Pr-substituted sample. Once this type of frustration
is initially formed at high temperatures within the sample,
one expects that it survives down to low temperatures. In
the successive isothermal scans (Fig. 3), the local heatingprocess relaxes the frustration existing within the matrix ofthe sample, giving a standard broad transition. In otherwords, in the first scan, the frustration existing probably
enhances the instability of the metastable state of the freeenergy under the magnetic field, resulting in a steplike
behavior. These findings are consistent with the fact thatthe critical field is sensitive to the thermal profile undergone by the sample from high temperatures. This scenario
also accounts for the cooling field dependence of Hc
observed here and reported in magnetization steps [6,10].
The field-cooled run suppresses the CO clusters but increases the FM clusters. Accordingly, the reduced frustration affects a steplike transition, increasing the value of Hc ,which is consistent with the positive dependence of Hc on
the cooling field. The nucleation and growth of FMM
domains due to an external field reduce the magnetic
energy by the Zeeman energy, while they increase theelastic energy arising from strains stored at the interfaceof two-phase domains. It is true that this competition in*matsukawa@iwate-u.ac.jp[1] Colossal Magnetoresistive Oxides, edited by Y. Tokura(Gordon and Breach, New York, 2000).
[2] V. K. Pecharsky et al., Phys. Rev. Lett. 91, 197204 (2003);
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[3] Francisco J. Perez-Reche et al., Phys. Rev. Lett. 87,
195701 (2001).
[4] Eduard Vives et al., Phys. Rev. Lett. 72, 1694 (1994);
Lluis Carrillo et al., Phys. Rev. B 56, 11 508 (1997).
[5] Nanoscale Phase Separation and Colossal Magnetoresistance, edited by E. Dagotto (Springer, New York,
2003).
[6] R. Mahendiran et al., Phys. Rev. Lett. 89, 286602 (2002).
[7] V. Hardy et al., Phys. Rev. B 68, 220402 (2003).
[8] L. M. Fisher et al., Phys. Rev. B 70, 212411 (2004).
[9] L. Ghivelder et al., Phys. Rev. B 69, 214414 (2004).
[10] Da-qian Liao et al., Phys. Rev. B 74, 174434 (2006).
[11] M. Matsukawa et al., Phys. Rev. B 70, 132402 (2004).
[12] M. Matsukawa et al., Phys. Rev. B 72, 064412 (2005).
[13] M. Apostu et al., Phys. Rev. B 64, 012407 (2001).
[14] Upon decreasing T from 30 K down to 4 K, the resistanceof the commercial strain gauges used (KYOWA) for bothab-plane and c-axis low-temperature measurements increases by about 103 . At low temperatures, the thermal
contraction of solids is negligible (at most dL=L is approximately the order of 105 ) in comparison to theapparent change of the strain gauge itself. Accordingly,
we conclude that the apparent striction associated with thestep transition is caused by a heat generation within the
crystal.
[15] For the local heating, a current of 15 mA was applied to aseries of two gauges during 10 sec so that the gauge
resistance returned rapidly to an initial value before theapplication of field, corresponding to the PMI virgin state.
After checking the stability of the bath temperature, wethen restarted measuring dLH. For each measurement,
the excited current of the gauge was set to be 1 mA.
[16] Y. Moritomo et al., Nature (London) 380, 141 (1996).
[17] D. N. Argyriou et al., Phys. Rev. B 61, 15 269 (2000).
[18] D. N. Argyriou et al., Phys. Rev. Lett. 89, 036401 (2002).

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