PHYSICAL REVIEW B 75, 014427 共2007兲

Anomalous pressure effect on the remanent lattice striction of a „La, Pr…1.2Sr1.8Mn2O7 bilayered
manganite single crystal
M. Matsukawa,1,* A. Tamura,1 S. Nimori,2 R. Suryanarayanan,3 T. Kumagai,1 Y. Nakanishi,1 M. Apostu,3 A. Revcolevschi,3K. Koyama,4 and N. Kobayashi41

Department of Materials Science and Technology, Iwate University, Morioka 020-8551, Japan
2National Institute for Materials Science, Tsukuba 305-0047, Japan
3Laboratoire de Physico-Chimie de L’Etat Solide, CNRS, UMR8182 Université Paris-Sud, 91405 Orsay, France
4Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
共Received 11 September 2006; published 22 January 2007兲
We have studied the pressure effect on magnetostriction, both in the ab plane and along the c axis of a
共La, Pr兲1.2Sr1.8Mn2O7 bilayered manganite single crystal over the temperature region where the field-induced
ferromagnetic metal 共FMM兲 transition takes place. For comparison, we have also examined the pressure
dependence of magnetization curves at the corresponding temperatures. The applied pressure reduces thecritical field of the FMM transition and it enhances the remanent magnetostriction. An anomalous pressure
effect on the remanent lattice relaxation is observed and is similar to the pressure effect on the remanent
magnetization along the c axis. These findings are understood from the viewpoint that the double-exchangeinteraction-driven FMM state is strengthened by the application of pressure.
DOI: 10.1103/PhysRevB.75.014427

PACS number共s兲: 75.47.Lx, 75.50.Lk, 75.30.Et, 62.50.⫹p

I. INTRODUCTION

The observation of a phenomenon of a colossal magnetoresistance 共CMR兲 effect has renewed the interest for doped
manganites with perovskite structure.1 Though the insulatorto-metal 共IM兲 transition and its associated CMR are well
explained on the basis of the double exchange 共DE兲 model, it
was pointed out that the dynamic Jahn-Teller 共JT兲 effect due
to the strong electron-phonon interaction, plays a significant
role in the appearance of CMR as well as of the DEinteraction.2,3 Furthermore, Dagotto et al. proposed a phaseseparation model where ferromagnetic 共FM兲 metallic and antiferromagnetic 共AFM兲 insulating clusters coexist, whichstrongly supports recent experimental studies of the physics
of manganites.4
Moritomo et al. have reported that the La1.2Sr1.8Mn2O7
bilayered manganite exhibits a paramagnetic insulator-共PMI兲
to-ferromagnetic metal 共FMM兲 transition around Tc⬃ 120 K and an associated CMR effect.5 The Pr共Nd兲 substitution on the La site leading to 兵La1−z , Pr共Nd兲z其1.2Sr1.8Mn2O7
causes an expansion along the c axis but a shrinkage along
the a共b兲 axis, resulting in a change of the eg electron occupation from the dx2−y2 to the d3z2−r2 orbital.6,7 These findings
accompany not only a suppression of the PMI to FMM transition temperature Tc, but also a variation of the easy axis ofmagnetization from the ab plane to the c axis. For the z= 0.6 crystal, the spontaneous ferromagnetic metal phase disappears at the ground state but the field-induced PMI to
FMM phase is obtained over a wide range of temperatures.
The magnetic phase diagram in the 共H , T兲 plane, establishedfrom magnetic measurements carried out on the z = 0.6 crystal, is presented in Fig. 1, with three regions labeled as PMI,
FMM, and mixed states 共white area兲. The white area is characterized by a hysteresis in the magnetization curves. The
application of physical pressure is a powerful tool to investigate the lattice effect on magnetic and electronic propertiesof doped manganites as well as the chemical-pressure effect1098-0121/2007/75共1兲/014427共6兲

due to the other rare-earth ion substitution on the La site.8
Many studies have been carried out so far on the effect ofpressures on structural, magnetic and transport properties inbilayered manganites.9–11 In half-doped bilayered manganite
La2−2xSr1+2xMn2O7共x = 0.5兲, near the x = 0.4 crystal studied
here, a long-range orbital- and charge-ordered state appears
over a limited temperature range between 100 and 210 K.12
This finding is taken to be related to the polaronic state of the
optimally doped crystal exhibiting the CMR effect throughFIG. 1. 共Color online兲 Magnetic phase diagram in the 共H , T兲
plane established from the magnetic measurements carried out on
the z = 0.6 crystal 共H 储 c兲. Three regions are distinguished and labeled as PMI, FMM, and mixed states 共white area兲. The white area
is characterized by a hysteresis in the magnetization curves. The
phase-transition lines between PMI 共or mixed phase兲 and FMM aredefined as a maximum of dM / dH. For comparison, we show the
PMI to the FMM phase-transition line under a pressure of 1 GPa
determined from the pressure data of MH curves, as shown in thetext.

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MATSUKAWA et al.

an orbital frustration in the PI phase.13 We report here theeffect of pressure on magnetostriction, both in the ab plane
and along the c axis, associated with the field-induced IM
transition of a 共La1−z , Prz兲1.2Sr1.8Mn2O7 bilayered manganite
single crystal. Just after removing the field, the system still
remains in a metastable FMM state and it then comes back to
the original PMI state through a mixed state made of FMM
and PMI regions. Here, the FMM state lies in a local energy
minimum and the PMI state is located in a global minimumof free energy, when the applied field is switched off. Next,
we examine the giant pressure effect observed on the relaxation time of remanent magnetostriction. Furthermore, we
compare the present results with the magnetic relaxation dataon the z = 0.6 crystal.
II. EXPERIMENT

Single crystals of 共La0.4 , Pr0.6兲1.2Sr1.8Mn2O7 were grownby the floating-zone method using a mirror furnace. The calculated lattice parameters of the tetragonal crystal structureof the crystals used here were shown in a previous report.14
The dimensions of the z = 0.6 sample are 3.4⫻ 3 mm2 in theab plane and 1 mm along the c axis. Measurements of magnetostriction, both in the ab plane and along the c axis, weredone by means of a conventional strain gauge method at the
Tsukuba Magnet Laboratory, the National Institute for Materials Science 共NIMS兲, and at the High Field Laboratory for
Superconducting Materials, Institute for Materials Research,
Tohoku University. First, the sample was cooled down to theselected temperatures in zero field and we then started measuring the isothermal magnetostriction upon increasing 共or
decreasing兲 the applied fields at a sweep rate of 0.2 T / min.
Finally, we recorded the isothermal remanent magnetostriction as a function of time just after switching off the field.
Hydrostatic pressures in both magnetostriction and magnetization experiments were applied by a clamp-type cell using
Fluorinert as a pressure-transmitting medium. The pressure
was calibrated by the critical temperature of lead. The magnetization measurements were made with a superconducting
quantum-interference device magnetometer both at Iwate
University and NIMS.
III. RESULTS AND DISCUSSION

Figure 2 shows the ab-plane and c-axis magnetostrictions,dLa共H兲 / La共0兲 and dLc共H兲 / Lc共0兲, both under ambient pressure and a hydrostatic pressure of 0.8 GPa at different temperatures, where the applied field is parallel to the c axis
共H 储 c兲. Here, the value of dLi共H兲 is defined as Li共H兲 − Li共0兲.
First, we observe that the c axis rapidly shrinks near 2 T
upon applying the field, but the a axis expands at the same
field value. The field-induced IM transition accompanies astable decrease of the c axis by ⬃0.2%, in contrast with asmall increase of the a axis by ⬃0.06%, resulting in a volume shrinkage of ⬃−0.08% 关dV共H兲 / V = 2dLa共H兲 / La共0兲+ dLc共H兲 / Lc共0兲兴 共Ref. 15兲. This value is in good agreementwith the volume striction dV / V ⬃ −0.09% associated withthe spontaneous IM transition of the parent compound
La1.2Sr1.8Mn2O7, indicating that a volume shrinkage in the

FIG. 2. The ab-plane and c-axis magnetostrictions
dLa共H兲 / La共0兲 and dLc共H兲 / Lc共0兲, both under ambient pressure and ahydrostatic pressure of 0.8 GPa, at different temperatures 共a兲 12 K,
共b兲 20 K, 共c兲 25 K, and 共d兲 30 K. The applied field is parallel to thec axis 共H 储 c兲.

metallic state is a consequence of the charge
delocalization.16,17 Here, the variations of the lattice parameters of the parent manganite, ⌬a / a ⬃ −0.08% and ⌬c / c⬃ 0.07%,areestimatedfromneutron-diffraction
measurements.18 At selected temperatures, a clear hysteresis
in the magnetostriction curves was observed, which has aclose relationship to a memory effect in magnetoresistance,magnetization, and magnetothermal conduction of the z= 0.6 crystal.14,19,20 Next, the application of pressure to themagnetostrictions reduces the critical fields and also enhances the remanent magnetostriction just after removing theapplied field. We show in Fig. 3 the pressure effect on theab-plane and c-axis magnetostrictions dLa共H兲 / La共0兲 and

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ANOMALOUS PRESSURE EFFECT ON THE REMANENT…

FIG. 3. The ab-plane and c-axis magnetostrictions
dLa共H兲 / La共0兲 and dLc共H兲 / Lc共0兲, both under ambient pressure and ahydrostatic pressure of 0.8 GPa, at different temperatures 共a兲 20 K,
共b兲 30 K, and 共c兲 40 K. The applied field is parallel to the ab plane
共H 储 ab兲.

dLc共H兲 / Lc共0兲 in the case of the field applied in the ab plane
共H 储 ab兲. The magnetostriction behavior in H 储 ab is qualitatively similar to that in H 储 c. We note that quantitative differences in dL / L between H 储 ab and H 储 c are higher criticalfields and larger hysteresis regions in the former case. Thisfinding is probably related to the easy axis of magnetization
through the orbital occupation of the eg electron between thedx2−y2 and d3z2−r2 states as mentioned below.
Now, we examine the c-axis magnetization under different pressures 共0, 0.5, and 1.0 GPa兲 as shown in Fig. 4. For
comparison, the ab-plane magnetization data are given in
Fig. 5. Here, the value of M c共5 T兲 reaches the ⬃3.5␮B / Mnsite, close to the full moment of the 3.6␮B / Mn site while thevalue of M ab is ⬃3.0␮B / Mn site, which is by about 20%
smaller than the ideal value.14 The difference in the saturated
magnetizations between M ab and M c at 5 T probably arises
from the easy axis of magnetization along the c axis associated with the rise of the d3z2−r2 orbital occupancy at z = 0.6.21
This finding is naturally understood by considering the importance of the spin-orbit interaction in the bilayered manga-

FIG. 4. c-axis magnetization under different pressures 共0, 0.5,
and 1.0 GPa兲 at selected temperatures 共a兲 15 K, 共b兲 20 K, 共c兲 25 K
and 共d兲 30 K. The data are normalized by the saturated magnetization at 5 T.

nite system.22 We note that the ab-plane magnetization exhibits no remanent value at all temperatures, in striking
contrast with the substantial values of remanent magnetostriction, remanent magnetoresistance, and remanent magnetothermal conduction.14,20 This discrepancy is not the central
issue discussed here, but it has a close relationship with theformation of magnetic domains, keeping their local
moments.23 First, the application of pressure on magnetization suppresses the critical field inducing the PMI to FMM
transition to the system, as well as the pressure effect onmagnetostriction. The phase transition lines in Fig. 1 are defined as a maximum of dM / dH because the MH curves show
metamagnetic behavior. At higher temperatures 共30 K兲, it istrue that the remanent magnetization is also enhanced uponincreasing the pressure. However, at lower temperatures 共15
and 20 K兲 the remanent M c shows a rapid decrease with the014427-3

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FIG. 5. ab-plane magnetization under different pressures 共0 and
1.0 GPa兲 at selected temperatures 共a兲 20 K, 共b兲 30 K, and 共c兲 40 K.
The data are normalized by the value of M ab at 5 T.

applied pressures. The negative-pressure effect on remanent
M c, at lower T, contrasts with the positive-pressure dependence of remanent magnetostriction at the corresponding T.
Recently, neutron-diffraction studies under pressure on bilayered manganite crystal with the same composition haveshown similar results for the pressure influence onmagnetization.24 We comment now on the pressure effect on
the MnO6 octahedron sites in the parent bilayered manganite
La1.2Sr1.8Mn2O7. Argyriou et al. have reported that upon increasing pressure up to 0.6 GPa, in the PMI state, both the
Mn-O共1兲 and Mn-O共3兲 bond lengths shrink but the Mn-O共2兲
bond length elongates.9 Here, the O共1兲 and O共2兲 oxygen atoms are located at the apical site along the c axis, where O共1兲lies between two MnO2 layers and O共2兲 within a rocksalttype La/ Sr-O layer. The O共3兲 oxygen atom is within the
MnO2 layer. Assuming such a variation of the MnO6 octahedron in the PMI state of Pr-substituted La1.2Sr1.8Mn2O7, the
Mn-O共1兲-Mn interactions along the c-axis and the MnO共3兲-Mn interactions in the ab plane are expected to bestrengthened upon application of pressure. In other words,
the double-exchange 共DE兲 interaction between Mn3+ and
Mn4+ within the MnO2 single layer and the DE interaction
along the c axis within the bilayer are enhanced and this is

closely related to the decrease of the critical fields of the
FMM state with pressure. On the other hand, the reciprocal
response of Mn-O共2兲 to the applied pressures causes an elongation of the distance between adjacent bilayers, and it thus
weakens the superexchange interactions between adjacent bilayers, keeping the DE interaction in the bilayer. This assumption describes well the negative-pressure effect on theremanent M c at lower temperatures and is consistent with thepositive effect on the remanent magnetostriction. Accordingly, the DE interaction-driven FMM state within a bilayer
is enhanced with pressure but the SE interaction-driven ferromagnetic state between adjacent bilayers is suppressed.24
Finally, we examine the pressure effect on the relaxation
time of remanent magnetostriction. Just after the removal of
the applied fields, both the ab-plane and the c-axis remanent
magnetostrictions are recorded as a function of time. The
normalized remanent magnetostriction d共c / a兲 / 共c / a兲 isshown as a function of time in Fig. 6 where the anisotropic
lattice striction d共c / a兲 / 共c / a兲 is estimated from the ab-planeand c-axis remanent data using dLc / Lc − dLa / La. The data
points are normalized in such a manner that we make theinitial value, just after the removal of field, to be zero, whilethe virgin value before the application of field becomes unity.
In our case, the lattice variation along the c axis is by a factorof ⬃3 as large as the value in the ab plane and the value of
d共c / a兲 / 共c / a兲 is almost taken as dLc / Lc. As reported in previous papers,19,25,26 the temporal profile of the remanent
magnetization and magnetostriction follows a stretched exponential function 1 − exp关−共t / ␶兲␤兴, where ␶ and ␤ represent
the characteristic relaxation time and exponent, respectively.
The stretched exponential behavior of the relaxation curvesindicates the existence of frustrations among competing interactions such as the FM and AFM interactions in spin-glass
systems. We believe that the remanent magnetostriction
shows a stretched exponential decay because of the competition between the double-exchange and JT-type latticeorbital interactions.25 The former interaction causes a suppression of the local lattice distortion along the c axis
through the itinerant state, but the latter favors lattice deformation through the local JT effect.17 Neutron-scattering measurementsontheparentbilayeredmanganiteLa2−2xSr1+2xMn2O7 共x = 0.38兲 have revealed the presence ofan orbital frustration in the paramagnetic insulating state,
which prevents the system from the formation of a longrange orbital- and charge-ordered state.13 We expect that thistype of frustration survives for the Pr-substituted crystal withnearly the same doping and is relevant to the phenomenon ofslow relaxation observed in remanent striction.
For a stretched exponential fit to the data points at 12 K,
we get ␶ = 4.0⫻ 105 s under ambient pressure. Under a pressure of 0.8 GPa, ␶ becomes 3.7⫻ 107 s, which is much
longer than the relaxation time without pressure. As a result,in Fig. 7, we summarize the relaxation time of both the remanent striction and remanent magnetization as a function of
1 / T. The application of pressures up to ⬃0.8 GPa to thesystem increases the relaxation time of the lattice by about
two orders of magnitude, giving a more stable metallic state
coupled with a suppression of MnO bond lengths in the
MnO6 local lattice. The relaxation data of remanent magne-

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ANOMALOUS PRESSURE EFFECT ON THE REMANENT…

FIG. 6. 共a兲 Normalized remanent magnetostriction d共c / a兲 / 共c / a兲
as a function of time at 12 K, just after the field along the c axis was
switched off 共H 储 c兲. The solid lines correspond to a fit to the data
points by a stretched exponential function 1 − exp关−共t / ␶兲␤兴, where ␶and ␤ represent the characteristic relaxation time and exponent,
respectively. In this case, we get ␶ = 4.0⫻ 105 s with ␤ = 0.22 and␶ = 3.7⫻ 107 s with ␤ = 0.17, at 0 and 0.8 GPa, respectively. 共b兲 The
normalized remanent magnetostriction at 30 K, just after the field in
the ab plane was switched off 共H 储 ab兲. ␶ = 4.0⫻ 104 s with ␤= 0.47 at 0 GPa and ␶ = 1.4⫻ 106 s with ␤ = 0.37 at 0.8 GPa. 共c兲 The
normalized remanent magnetization at 20 K, just after the fieldalong the c axis was switched off 共H 储 c兲 ␶ = 3.1⫻ 106 s with ␤= 0.16 at 0 GPa and ␶ = 3.4⫻ 109 s with ␤ = 0.1 at 1.0 GPa. The data
points are fitted using M共t兲 / M共0兲 = 1 − exp关−共␶ / t兲␤兴.

tization under a pressure of 1 GPa at 20 K are presented inFig. 6共c兲. In spite of the negative-pressure effect on the remanent M c at lower T, as mentioned before 关Figs. 4共a兲 and4共b兲兴, the relaxation time is strongly enhanced at 1 GPa by
more than two orders of magnitude and shows a positivepressure dependence. The difference in the relaxation time
between remanent magnetization and magnetostriction canprobably be explained by the fact that the magnetostriction
observed here is not associated with a long-range order parameter such as the long-range orbital order reported in the

FIG. 7. 共a兲 Pressure effect on the relaxation time of the remanentlattice striction as a function of 1 / T. 共b兲 Pressure effect on therelaxation time of the remanent c-axis magnetization. For comparison, the inset represents the remanent M c versus 1 / T taken from thedata in Fig. 4.

x = 0.5 crystal. On the other hand, the magnetization isclosely related to it.26

IV. SUMMARY

We have demonstrated the effect of pressure on magnetostriction, both in the ab plane and along the c axis, in abilayered manganite single crystal of 共La, Pr兲1.2Sr1.8Mn2O7
over the temperature region where the FMM transition takes
place. For comparison, we have examined the pressure dependence of the magnetization curves at the corresponding
temperatures. The applied pressure reduces the critical fieldof the FMM transition and it also enhances the remanent
magnetostriction. The quantitative differences observed in
dL / L between H 储 ab and H 储 c are higher critical fields andlarger hysteresis regions in the former case, which is probably related to the easy axis of magnetization along the c axis
through the orbital occupation of the eg electron between the014427-5

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dx2−y2 and d3z2−r2 states. An anomalous pressure effect on theremanent lattice relaxation is observed to be similar to thepressure effect on the remanent magnetization along the caxis. In spite of the negative-pressure effect on remanent M c
at lower T, the relaxation time is strongly enhanced at 1 GPa
by more than two orders of magnitude and shows a positive
pressure dependence. These findings are understood considering that the double-exchange interaction-driven FMM state
within a bilayer is strengthened upon application of pressure.
Application of pressure reinforces the DE interaction, both in
the ab plane and along the c axis, through a shrinkage of
Mn-O共1兲 and Mn-O共3兲 bond lengths, resulting in a giant effect on the relaxation time of remanent striction and rema-

nent magnetization. We believe that the slow relaxation observed here correlates to the orbital frustration existing in theparamagnetic insulating state of parent bilayered manganite.

ACKNOWLEDGMENTS

This work was partially supported by a Grant-in-Aid for
Scientific Research from Japan Society of the Promotion of
Science. We thank H. Noto for his technical support. One of
the authors 共M.M.兲 would like to thank T. Naka and A. Matsushita, NIMS for their help in pressure measurement onmagnetostriction.

14*Electronic address: matsukawa@iwate-u.ac.jp
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