arXiv:0909.1944v1 [cond-mat.str-el] 10 Sep 2009
Electronic self-organization in the single-layer manganite Pr1−xCa1+xMnO4
F. Ye,1, ∗Songxue Chi,2J. A. Fernandez-Baca,1,2A. Moreo,2,3E. Dagotto,2,3
J. W. Lynn,4R. Mathieu,5Y. Kaneko,5Y. Tokura,5,6,7and Pengcheng Dai2,1
1Neutron Scattering Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393, USA
2Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA
3Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393, USA
4NIST Center for Neutron Research, Gaithersburg, Maryland, 20899, USA
5ERATO Spin Superstructure Project and Multiferroics Project, JST, Tokyo 113-8656, Japan
6Cross-Correlated Materials Research Group (CMRG),
RIKEN Advanced Science Institute, Wako 351-0198, Japan
7Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
(Dated: September 10, 2009)
We use neutron scattering to investigate the doping evolution of the magnetic correlations in the
single-layer manganite Pr1−xCa1+xMnO4, away from the x = 0.5 composition where the CE-type
commensurate antiferromagnetic (AF) structure is stable. We find that short-range incommensurate
spin correlations develop as the system is electron doped (x < 0.5), which coexist with the CE-type
AF order. This suggests that electron doping in this system induces an inhomogeneous electronic
self-organization, where commensurate AF patches with x = 0.5 are separated by electron-rich
domain walls with short range magnetic correlations. This behavior is strikingly different than for
the perovksite Pr1−xCaxMnO3, where the long-range CE-type commensurate AF structure is stable
over a wide range of electron or hole doping around x = 0.5.
PACS numbers: 75.47.Lx, 75.30.Kz, 25.40.Dn
Understanding how electrons are distributed in nar-
row bandwidth manganese oxides remains one of most
intriguing unresolved problems in the physics of colos-
sal magnetoresistance (CMR) manganites .
perovksite R1−xCaxMnO3 (R = rare earth ions) and
single-layer R1−xCa1+xMnO4 manganites (the n = ∞
and n = 1 end members of the Ruddlesden-Popper se-
ries Rn(1−x)Canx+1MnnO3n+1 manganese oxides), the
orbitals and magnetic spins of the Mn ions order at low
temperature at the doping level x = 0.5, and form a
checkerboard-like pattern, resulting in a commensurate
(CM) antiferromagnetic (AF) CE-structure [2, 3, 4]. Our
research here clarifies what occurs in the manganites near
x = 0.5 when their structures evolve from the three-
dimensional (3D) perovskite to the single layer struc-
ture which is the most two-dimensional (2D) member of
the Ruddlesden-Popper series. Are novel charge-ordered
states formed, or do the excess of electrons/holes be-
come randomly distributed and localized, or does a self-
organization occur involving mixed-phase tendencies? In
the 3D perovskite manganites such as Pr1−xCaxMnO3
[5, 6], the CE-type orbital and magnetic order persist in
a wide doping range (0.3 < x < 0.7). Doping this system
away from x = 0.5 to form Pr0.7Ca0.3MnO3induces a fer-
romagnetic component below the AF CE-ordering tem-
perature . This has been interpreted as evidence for
phase coexistence involving ferromagnetic clusters and
the AF CE structure , although the data are also con-
sistent with a canted antiferromagnet [9, 10].
In the case of the single-layer La1−xSr1+xMnO4
(LSMO), extensive neutron and x-ray scattering experi-
ments [3, 4, 11, 12, 13] have shown that the system at
x = 0.5 has a checkerboard charge ordering-orbital order-
ing (CO-OO) and a CE-type spin configuration similar
to that of the perovskite manganites. However, as soon
as electrons are doped into the x = 0.5 compound, the
CE spin structure is destroyed and the system behaves
like a spin-glass while CO-OO is maintained . But is
this a generic feature or does it depend on the bandwidth
and electron-phonon coupling of the material?
In this Letter, we report a systematic neutron scat-
tering study of the magnetic correlations in the single-
layer manganite Pr1−xCa1+xMnO4(PCMO). Contrary
to LSMO, electron-doping into the x = 0.5 PCMO
[14, 15, 16] is found to suppress, but not fully elimi-
nate, the commensurate CE AF order. In addition, a
set of new incommensurate (ICM) magnetic peaks are
observed near the CM scattering from the CE structure.
These results are compatible with a self-organized mixed
phase scenario where the state at x < 0.5 is composed of
CE patches separated by electron-rich but magnetically
disordered domain walls (Fig. 1). This result establishes
potentially interesting analogies between the doping of
some Cu oxide cuprates that leads to stripes, and the
doping of the CE state in manganites that also seems to
induce electron-rich domain walls.
Single crystals of PCMO (mass ≈ 4 to 6 grams) were
grown using the floating zone method. The phase pu-
rity and cation concentrations were checked by neutron,
x-ray powder diffraction and inductively coupled plasma
atomic emission spectroscopy, no noticable composition
defects were found. At room temperature, PCMO has
an orthorhombic structure slightly distorted from the
tetragonal symmetry, with lattice parameters a ≈ 5.38
FIG. 1: (a) Phase diagram of Pr1−xCa1+xMnO4. Solid sym-
bols are from our measurements, open symbols from Ref. .
TCO denotes the transition temperature of CO-OO, Tab and
TN are the transition temperatures of 2D and 3D AF order.
(b) Schematics of the experimental observations in recipro-
cal space. The pattern in lighter color originates from the
90-degree twinned domain. Orbital and spin configurations
within the MnO2-plane that may explain the neutron results:
(c) are diagonal and (d) horizontal domain walls, where extra
electrons congregate. Mn4+ions are denoted by black circles.
The Jahn-Teller active Mn3+ions have additional orbitals.
The blue and red lines illustrate the ferromagnetic zig-zag spin
chains which are coupled antiferromagnetically. (e) Fourier
transform of the spin configurations in (c) and (d) combined.
Note the dominant spectral weight at (1/4−δ/√2,1/4−δ/√2)
or (3/4 + δ/√2,3/4 + δ/√2) for the Mn3+spins. (f) Experi-
mentally observed doping dependence of incommensurability
from both the Mn3+and Mn4+sublattices.
˚ A, b ≈ 5.40˚ A, and c ≈ 11.85˚ A. For simplicity, we use
the tetragonal unit cell (a = b ≈ 3.84˚ A). The experi-
ments were carried out using triple-axis spectrometers at
the NIST Center for Neutron Research with final neutron
energy fixed at Ef= 14.7 or 13.5 meV. The momentum
transfers q = (qx,qy,qz) in units of˚ A−1are at positions
(h,k,l) = (qxa/2π,qyb/2π,qzc/2π) in reciprocal lattice
Figures 1(a)-1(b) summarize the main results of our
neutron scattering measurements. In Pr0.5Ca1.5MnO4,
the Mn spins form two magnetic sublattices. Compati-
ble with a CE state, the characteristic wavevector associ-
ated with the Mn3+spins appears at q1= (1/4,/1,4,0)
and the corresponding wavevector for the Mn4+spins
is at q2 = (1/2,0,0).However, the electron doping
of Pr0.5Ca1.5MnO4 induces additional ICM spin corre-
lations at (1/4 − δ/√2,1/4 − δ/√2,0) and (1/2,±δ,0),
respectively. The incommensurability (defined as the dis-
tance δ between the CM and the ICM peaks) of both sub-
lattices shows a robust doping dependence [Figure 1(f)].
FIG. 2: Comparison of the low-T magnetic scattering orig-
inating from the Mn3+spins, for the x = 0.35, x = 0.40,
and x = 0.45 samples. The corresponding wavevector scans
through the peaks, as indicated by the arrows, are presented
in the lower panels. The data reveal that a separate ICM
component develops as electrons are added from the x = 0.5
point, which coexists with the x = 0.5 AF order. The ICM
scattering is short range, and separates further from the CM
position and becomes broader as x is reduced.
Figure 2 shows the evolution of the magnetic scattering
from the Mn3+sublattice for the doped samples. A wide
range of reciprocal space near the Bragg point (1/4,1/4,0)
and equivalent positions in higher Brillouin zones was
surveyed. At x = 0.35, the additional scattering con-
sists of two parts. First, magnetic scattering is located
at positions identical to those observed at x = 0.50 ,
but with weaker magnetic correlations between MnO2
planes along the c-axis. Second, there is ICM scattering
at wavevector (1/4−δ/√2,1/4−δ/√2,0). This scatter-
ing becomes strongest near (3/4,1/4,0) and decreases in
intensity near (3/4,3/4,0). The ICM scattering is highly
anisotropic with a rod-like profile elongated along the
[1,1,0] (longitudinal) direction indicating a shorter cor-
relation length in this direction. As the doping evolves
toward x=0.5, the diffusive ICM scattering sharpens and
gradually moves towards the CM position. At x = 0.45,
the scattering remains anisotropic, but the difference be-
tween the two orthogonal directions becomes smaller. As
displayed in the wavevector scans, the longitudinal scan
shows a broader width when compared to the transverse
scan along the [1,1,0] direction. The corresponding cor-
relation lengths ξLand ξT from the ICM scattering, af-
ter deconvoluting the instrumental resolution, are listed
in Table 1. Both numbers increase substantially as the
doping approaches x = 0.5.
The contour plots and the wavevector scans of the
TABLE I: Doping dependence of the magnetic scattering cor-
relation length ξ from the Mn3+and Mn4+sublattices. “L”
and “T” denote the longitudinal and transverse directions.
x = 0.35
12.2 ± 0.3
20.2 ± 0.4
116.8 ± 4.5 139.4 ± 6.4 127.1 ± 6.6
9.8 ± 1.1
131.4 ± 2.8 127.3 ± 5.3 121.0 ± 7.2
x = 0.40
21.1 ± 0.4
37.6 ± 0.9
x = 0.45
52.5 ± 1.5
66.5 ± 1.8
15.9 ± 1.3 44.6 ± 1.4
Mn4+spins probed near q2 = (1/2,0,0) are illustrated
in Figure 3. The intense peaks at CM positions are
surrounded by broad diffuse scattering. The CM com-
ponent is sharper than the ICM fluctuations, but the
Lorentzian profiles in the wavevector scans indicate the
lack of true long-rangeorder. Similar to the Mn3+sublat-
tice, the incommensurability of the diffuse scattering can
be tuned by sample composition. As the ICM peaks move
closer to the CM position with increasing x, the width of
the diffuse peak narrows and the intensities become en-
hanced. The short-range correlations are less anisotropic
than those in the Mn3+sublattice.
To further characterize the magnetic correlations, we
investigate the T-dependence of the wavevector scans at
x = 0.45 in Figs. 4(a) and 4(b). At T =10 K, distinct CM
and ICM peaks are observed. Upon warming, the ampli-
tude of the ICM peak is rapidly suppressed with little
variation in peak position and the scattering evolves into
a broad feature as the temperature is raised. The scat-
tering profile of the CM component, on the other hand,
remains well resolved to a much higher temperature. The
concave shape of the peak intensity vs. temperature from
the ICM scattering [Figs. 4(c)-4(d)] reveals the expected
FIG. 3: Comparison of the magnetic diffuse scattering origi-
nating from the Mn4+spins at T = 10 K for the (a) x = 0.35,
(b) x = 0.40, and (c) x = 0.45 samples. Wavevector scans
across the ICM and CM peaks are in the panels (d)-(f).
FIG. 4: Wavevector scans of magnetic diffuse scattering from
(a) Mn4+and (b) Mn3+sublattices of the x = 0.45 sample at
selected temperatures. Temperature dependence of the peak
intensities of the CM (red) and ICM (blue) peaks from the (c)
Mn4+and (d) Mn3+sublattices for x = 0.35,0.40, and 0.45.
diffusive nature for the short-range correlations, in con-
trast to the order-parameter-like CM scattering.
The suppression of the long range CE magnetic order
and the surprising emergence of the ICM spin fluctu-
ations in PCMO are different from the insulating per-
ovskite Pr1−xCaxMnO3, where the CE-type spin order
survives over a broad carrier doping range . Our re-
sults suggest a form of electronic self-organization in this
single-layer compound.One might speculate that the
ICM scattering results from the formation of an ICM
charge density wave, with an associated spin density wave
(SDW) . In this picture, the overall magnetic struc-
ture would resemble the usual CE-type checkerboard spin
configuration, but the amplitudes of the spins would have
a smooth spatial modulation to accommodate the extra
electrons. While such a configuration naturally brings
about the ICM magnetic peaks, they should be symmet-
ric with respect to the CM positions  and the CE
peaks should be absent, in contrast to the experimental
observations. An alternative model consists of a mixed
phase of the CE structure and the competing ferromag-
netic state. There is ample evidence of this mixed state
in the CMR regime near the Curie temperature [9, 10].
However, the present case is for low temperatures, and
more importantly, we do not observe any ferromagnetic
scattering. Therefore phase separation involving large
size CE and FM clusters does not provide an explana-
tion of our results either.
A model that is consistent with the overall experimen-
tal observations involves the formation of a stripe phase
similar to those in the high-Tcsuperconducting cuprates
. For doping below x = 0.5, the system would form
magnetic clusters or domains which preserve the CE-type
spin configuration with distinct neighboring Mn3+and
Mn4+sites. The excess electrons would congregate at
the domain boundaries with random spin and orbital
orientations. We explored a variety of real-space spin
arrangements and found two different ones that, when
combined, characterize the observations. The first one
[Fig. 1(c)] describes a diagonal Mn3+domain boundary
separating two CE clusters in which the Mn3+spins are
in anti-phase while the Mn4+spins are not. The indi-
vidual magnetic domain contributes to the CM scatter-
ing, while the ICM peak along the diagonal arises from
the correlation between domains . This configura-
tion reproduces the magnetic scattering originating from
the Mn3+sites, but leaves the scattering near (1/2,0,0)
undisturbed. The second one [Fig. 1(d)] describes spin
arrangements with a horizontal domain boundary. There
is an extra phase shift (1/4 or 3/4 of the 4ac, the pe-
riodicity of the CE-phase) between adjacent magnetic
domains.It introduces two symmetric ICM peaks at
q = (1/2,±δ,0) but not at q = (0,1/2±δ,0). As demon-
strated in Fig. 1(e), the Fourier transformation of the
above described combined configurationssuccessfully cre-
ates a pattern qualitatively similar to the experimental
results . Our identification of the inhomogeneous and
textured spin states, unveils another degree of similarity
with the cuprates in terms of electronic self-organization
and spin incommensurability , and provides a useful
comparison to investigate the competing order and com-
plexity in the strongly correlated electron system.
It was pointed out that the quenched disorder is impor-
tant in determining the stability of the CE-type magnetic
phase . Monte Carlo simulations suggest that a small
amount of disorder or randomness in 2D or 3D systems
may destroy that phase. However, the inherent quenched
disorder  in PCMO caused by A-site solid solution is
small, (1 ∼ 2×10−7for the doping range we studied) be-
cause of their comparable Pr3+/Ca2+ionic size. There-
fore, the preservation of CE-type fluctuations at lower
doping in PCMO confirms that the CE-phase could be
a robust feature, in contrast to its quick disappearance
in LSMO with more quenched disorder . On the other
hand, the striking difference between single-layer PCMO
and the 3D perovskite manganites highlights the crucial
role of the magnetic interactions between planes, which
is believed to stabilize the CE-type order [12, 25].
We are grateful to D. Khomskii, Y. Ren, and M.
Braden for their helpful discussions. The experimental
work was partially supported by the Division of Scien-
tific User Facilities of the Office of Basic Energy Sciences,
US Department of Energy and by the U.S. NSF DMR-
0756568 and DOE Nos. DE-FG02-05ER46202 grants.
The theory effort was supported by the NSF grant DMR-
0706020, and by the Div. of Materials Sciences and Eng.,
U.S. DOE under contract with UT-Battelle, LLC.
∗Electronic address: email@example.com
 E. Dagotto et al., Phys. Rep. 344, 1 (2001); M. Salamon
and M. Jaime, Rev. Mod. Phys. 73, 583 (2001).
 E. O. Wollan and W. C. Koehler, Phys. Rev. Phys. Rev.
100, 545 (1955). John B. Goodenough, Phys. Rev. 100,
 B. J. Sternlieb et al., Phys. Rev. Lett. 76, 2169 (1996).
 S. Larochelle et al., Phys. Rev. Lett. 87, 095502 (2001).
 Z. Jir´ ak et al., J. Magn. Magn. Mater. 53, 153 (1985).
 Y. Tomioka et al., Phys. Rev. B 53, R1689 (1996).
 H. Yoshizawa et al., J. Phys. Soc. Japan, 65, 1043 (1996).
R. Kajimoto et al., Phys. Rev. B 58, R11837 (1998).
 A. Moreo et al., Science 283, 2034, (1999). J. Burgy et
al., Phys. Rev. Lett. 92, 097202, (2004). H. Sha et al.,
Phys. Rev. B 78, 052410 (2008).
 H. Yoshizawa et al., Phys. Rev. B 52, R13145 (1995).
 J. A. Fernandez-Baca et al., Phys. Rev. B 66, 054434
 S. Larochelle et al., Phys. Rev. B 71, 024435 (2005).
 D. Senff et al., Phys. Rev. Lett. 96, 257201 (2006).
 D. Senff et al., Phys. Rev. B 77, 184413 (2008).
 Songxue Chi et al., Proc. Nat. Acad. Sci, U.S.A. 104
 R. Mathieu and Y. Tokura, J. Phys. Soc. Japan 76,
 X. Z. Yu et al., Phys. Rev. B 75, 174441, (2007).
 J. C. Loudon et al., Phys. Rev. Lett. 94, 097202 (2005).
 An homogeneous incommensurate spin configuration for
the Mn4+ions in the CE pattern that produces peaks in
the structure factor at (1/2,±δ,0) as in Fig. 3 arises from
correlation functions that in real space have the form
S(x,y,0) = A(−1)xcos(δy). However, a Fourier trans-
form of this expression produces a structure factor with
peaks at (1/2,±δ,0) and also at (0,1/2 ± δ,0) which is
not observed in the experiments.
 J. M. Tranquada et al., Nature 375, 561, (1995).
 A small amount of disorder to the spin orientations about
the CE state has been added to make the system more
realistic but similar results are obtained without disorder.
 Note that our model combines two configurations “in-
coherently”. A more complicate “coherent” model might
reveal other novel features (like extra satellite peaks) and
deserves future investigation.
 N. Mannella et al., Nature 438 474, (2005).
 G. Alvarez et al., Phys. Rev. B 73 224426, (2006).
 This is characterized by σ2=?
the fractional occupancies of A-site species, ri and ¯ r =
 C Ma et al., J. Phys.: Cond. Matt. 21 045601, (2009).
i− ¯ r2), where xi is
ixiri are individual radii and averaged ionic radius.