Reentrant Orbital Order and the True Ground State of LaSr2Mn2O7
Reentrant Orbital Order and the True Ground State of LaSr2Mn2O7
Qing’An Li,1, 2 K.E. Gray,2, ∗ H. Zheng,2 H. Claus,2 S. Rosenkranz,2 S.
Nyborg Ancona,2 R. Osborn,2 J.F. Mitchell,2 Y. Chen,3, 4 and J.W. Lynn3
1Chinese Academy of Sciences, Beijing, CHINA
2Materials Sciences Division, Argonne National Laboratory, Argonne, IL 60439, USA
3NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
4 Department of Materials Science and Engineering,
University of Maryland, College Park, MD 20742, USA
(Dated: October 23, 2021)
Contrary to conventional wisdom, our purified La2−2xSr1+2xMn2O7 crystals exhibit CE-type or-
bital and charge order as the low-temperature ground state for a hole doping level h = 0.5. For
small deviations from h = 0.5, the high temperature CE phase is replaced at low temperatures by
an A-type antiferromagnet without coexistence. Larger deviations result in a lack of CE order at
any temperature. Thus, small inhomogeneities in cation or oxygen composition could explain why
others commonly see this reentrance with coexistence.
The quest to better understand strongly corre-
lated electrons is at the heart of condensed mat-
ter inquiry. Colossal magnetoresistive manganites ex-
hibit a particularly vigorous competition among or-
bital, charge and spin order [1, 2]. The phase di-
agrams, e.g., La1−xSrxMnO3 or the bilayer version
La2−2xSr1+2xMn2O7, display interesting features near
half doping (x ∼ 0.5) where, e.g., long-range orbital
and “checkerboard” charge ordering ( CE type) is pre-
dicted [3]. In bilayer manganites, it has been com-
monly accepted that CE order at x = 0.5 is reentrant
[4, 5, 6, 7, 8, 9, 10]: it forms below ∼210 K, but then
is replaced by an A-type antiferromagnet (AAFM) be-
low ∼100 K. The lack of a low-temperature CE ordered
ground state is surprising as it is found at x = 0.5 in
many perovskite manganites [11]. In bilayer manganites,
coexistence of CE order and AAFM between ∼100 K and
∼200 K is also universally reported [4, 5, 6, 7, 9].
All reports of reentrance in LaSr2Mn2O7 are based
on superlattice peaks in neutron [4, 5, 6, 7], x-ray
[6, 7, 8, 9, 10] and electron [12, 13, 14] diffraction and/or
a peak in the resistivity [4, 6, 8, 12]. However, consistent
with our own experience, these reported properties for
x = 0.5 doping are variable. This implies an exquisite
sensitivity to the exact value of hole doping, h = x − δ
in La2−2xSr1+2xMn2O7−δ. This dictates a vital burden
to obtain sample uniformity. Thus, in the present study
we have purified large single crystals, which often exhibit
compositional gradients, by cleaving them into very small
crystals (∼1 mg) and discarding those that do not pass
our test for uniformity (see below). Combining conduc-
tivity, magnetization, and neutron and high-energy x-ray
diffraction data on such highly homogeneous crystals, we
here show that the CE order predicted by Goodenough
[3] is the low-temperature ground state, presumably at
h = 0.5, and that coexistence of CE and AAFM order is
absent. We argue that re-entrance only occurs for small
deviations from 0.5 and propose a revised phase diagram
for bilayer manganites near h = 0.5.
Crystals were melt-grown in an optical image furnace
[15]. The c axis is perpendicular to the platelike crystals
(∼2 × 0.5 × 0.1 mm3) and four gold pads are deposited
along the top and bottom surfaces for transport measure-
ments. In order to obtain a direct measure of the different
order parameters, we performed high-energy synchrotron
X-ray scattering experiments at the 1-ID-C station of
the Advanced Photon Source at Argonne National Lab-
oratory and neutron scattering experiments at the BT-7
triple-axis instrument at the NIST Center for Neutron
Research. We utilize the (9/4,1/4,0) reflection obtained
using 80 keV X-rays and the neutron intensities of the
(1/4,1/4,3) and (1,1,3) reflections as measures of the CE
orbital order, the CE antiferromagnetic order (CEAFM),
and the A-type antiferromagnetic order, respectively [4].
Since four-terminal methods are unreliable for bulk
crystals, we use six terminals to determine each prin-
cipal component of conductivity, i.e., along the c-axis,
σc, and in the ab-plane, σab [16]. In transport method
A, current is injected through the outermost contacts on
one surface [Fig. 1(a)]. Laplace’s equation is solved and
inverted to get σab and σc from voltages measured across
the innermost contacts of each surface. In method B,
Laplace’s equation is solved for current injection through
the top and bottom contacts at one end of the crystal,
while voltages are measured between pairs of contacts on
the top and bottom of the crystal [Fig. 1(b)].
FIG. 1: Schematic of six-terminal configurations for method
A (a) and method B (b).
To test for homogeneity, we evaluate σab and σc in four
configurations. Two use method A with current applied
to the outer contacts of either the top or bottom surfaces
and two use method B with current applied to the end
contacts on either the right- or left-hand sides. We re-
quire both σab(T ) and σc(T ) to be qualitatively the same
for all four configurations and within a factor of 2-3 in
magnitude. Crystals used for Fig. 2 and 3 all pass our
criteria, as described in Ref. [17]. Homogeneous crystals
with a nominal x = 0.5 fall into three batches: batch-A
are reentrant, batch-B exhibits CE order as the predom-
inant low-temperature ground state, and batch-C never
exhibit CE order. Examples of these are indicated in the
highly schematic phase diagram of Fig. 4. The fact that
we see three, and only three, unique states using four
FIG. 2: Temperature dependence, shown for reentrant crys-
tals (a)−(e) and nonreentrant crystals (f)−(j), of magnetiza-
tion (a),(f), conductivity in ab-plane (b),(g) and along c-axis
(c),(h) and neutron diffraction for CEAFM (d),(i) and A-type
AFM (e),(j). Open symbols refer to cooling and filled symbols
to warming.
different bulk probes is unmistakable evidence of suffi-
cient compositional uniformity. Any broad distribution
of h = x − δ would result in the coexistence of these
states in some of the 12 crystals studied. The relevance
of δ is seen in one reentrant crystal that transformed into
a non-reentrant crystal after annealing in pure oxygen for
60 hrs at 600 ◦C. Our scattering probes show that our
samples consist of up to two or three slightly misaligned
crystallites but are free from any impurity phases within
our detection limits.
Most of our crystals of nominal x = 0.5 composition
display a transition from a paramagnetic insulator (PMI)
above ∼200 K into a CE-type orbital and charge ordered
state. This is often (batch-A) followed by a hysteretic
transition into a state with higher magnetization [Fig.
2(a)] and conductivity [Figs. 2(b) and 2(c)] below ∼100
K that does not exhibit the CE-type superlattice reflec-
tions [Figs. 2(d) and 3]. Our neutron diffraction data
[Fig. 2(e)] confirm that the low-temperature state is the
previously identified AAFM [4, 5, 6, 7]. However, in sev-
eral crystals (batch-B) no more than a few percent [Figs.
2(f)-2(j)] transformed into the AAFM. A natural expla-
nation is that CE order is the stable ground state only
over a very narrow range of h and there are crystal-to-
FIG. 3: Temperature dependencies of (a) σc and (b) x-ray
diffraction intensity of the superlattice reflection for CE order
(9/4,1/4,0), measured on the same crystal. Reentrance and
hysteresis show a perfect correlation upon cooling (open sym-
bols) and warming (filled symbols). Also shown in (a) are the
conductivity data (black diamonds) for a batch-C crystal.
FIG. 4: Schematic, qualitative phase diagram near h = 0.5.
Symbols are measured transition temperatures (open: cool-
ing; filled: warming). Except for h = 0.46 and 0.54, the h val-
ues are arranged to connect smoothly with other data since
we cannot determine them with sufficient precision. Reen-
trant crystal data are plotted symmetrically both above and
below 0.5. The metastable CEAFM is found on cooling but
not on warming. The width of the boxes labeled coexistent, A,
B, and C represent suggested range of h-values (i.e., 〈h〉±∆h)
for coexistent crystals and batches A, B and C.
crystal variations of the average hole doping 〈h〉 and a fi-
nite width of the distribution ∆h. Thus, when 〈h〉 is most
favorable for CE order, presumably at 0.5 as predicted
by Goodenough [3], a larger fraction of the crystal would
exhibit the CE ground state at low temperatures. Then
for sufficiently small ∆h, the CE ground state can be
the majority phase. For crystals exhibiting re-entrance
we believe 〈h〉 differs somewhat from 0.5. We also find
crystals (batch-C) without a transition to the CE-state,
implying that 〈h〉 is yet further from 0.5. The conductiv-
ity data for batch-C crystals are very similar to that of
Ref. [18] and are shown in Fig. 3(a) for a nominal dop-
ing x = 0.48. Note that the sharp decrease in σc at ∼
200 K, found in the reentrant and nonreentrant crystals,
is entirely absent, and the conductivity changes directly
from the PMI to the AAFM behavior.
Data on batch-A crystals display a striking tempera-
ture dependence and hysteresis in σab and σc and mag-
netization, as shown in Figs. 2(a)-2(c) and 3(a). Similar
hysteresis is also found in the diffraction data of Figs.
2(d), 2(f) and 3(b) and in the data of others [4, 7]. Such
hysteresis was also reported in resonant x-ray studies [9],
but we are unaware of reports of such dramatic hystere-
sis in the conductivity or magnetization of LaSr2Mn2O7.
The drops in our conductivity and magnetization data
exhibit a similar temperature range and hysteresis as all
the published diffraction data [4, 7, 9]. A striking con-
clusion of our neutron diffraction data for this batch-A
crystal is the lack of coexistence of CE and AAFM order,
which is universally found by others [4, 6, 7]. Neutrons
probe AAFM and CEAFM magnetic order [Figs. 2(d)
and 2(e)], the latter of which only occurs below ∼130 K
(above 130 K the CE state is paramagnetic). In warm-
ing and cooling cycles, one, and only one, state is ever
found. This conclusion is possible because of the small
∆h in our crystals. Near the lower-temperature transi-
tion of batch-A crystals, we found evidence for sluggish
kinetics that was assisted by magnetic fields of 7 T. This
may imply a small energy difference between these states
since the change in magnetization at the transition is
only ∼2 emu/g. Further, the broad thermal hysteresis
associated with reentrance implies there is only a slight
difference in the temperature dependencies of their free
energies.
Crystals from batch-B exhibit a similar high-
temperature transition, but only a trace of the lower tem-
perature transition to AAFM states. This is clearly seen
in magnetization [Fig. 2(f)] and conductivity [Figs. 2(g)
and 2(h)]. Apparently the free energy for CE order, that
is the majority phase of batch-B crystals, is sufficiently
low so that CE order remains stable down to low temper-
atures. Since CE order has a sharp minimum in its free
energy for h exactly 0.5, batch-B crystals should have 〈h〉
very close to that value. We confirm the low-temperature
CE state through the CEAFM reflection [Fig. 2(i)] by
neutron diffraction in a slightly larger nonreentrant crys-
tal. A minor part of batch-B crystals may transform into
the AAFM below ∼100 K [Fig. 2(j)]. Others [7, 10] have
identified a weak CE superlattice peak at low tempera-
tures which decays upon warming to above ∼50 K, but
then reappears as a strong peak at ∼120 K. This has the
appearance of a nonequilibrium “quenched-in” CE state,
that is then annealed out upon warming to ∼50 K. To
dispel this possibility and address thermodynamic stabil-
ity, we monitor these reflections during slow cooling (<∼ 1
K/min) that should minimize quenched-in CE-order due
to sluggish kinetics. We find that the CEAFM reflection
is reversible upon slow heating [Fig. 2(i)], and conclude
that the CE phase is the low temperature ground state
in a majority of each batch-B crystal.
For batch-B crystals, the succession of states with de-
creasing temperature (shown schematically in Fig. 4) can
be cast in terms of entropy. Transforming from the PMI
to a charge-ordered paramagnet (CEPM) gains orbital
and charge order while the onset of AF in the CE state
(CEAFM) at ∼130 K additionally gains magnetic or-
der. Transitions between the AAFM and CEAFM states
are more complex: the internal energy for a CEAFM
increases as h deviates from 0.5 while the broad hys-
teresis implies similar temperature dependenies of their
free energies. Therefore the phase boundary is almost
vertical versus h. Batch-A crystals also transform from
PMI to CEPM at ∼200 K but CE order appears to be
metastable at lower temperatures (dashed lines in Fig.
4) until it transforms at ∼100 K to the AAFM ground
state. Within this metastable region, the CE state de-
velops CEAFM magnetic order below ∼130 K due to a
gain in magnetic entropy. Upon warming, CEAFM order
is absent and AAFM order persists until CEPM order is
thermodynamically stable (T > 130 K). Thus it appears
that the magnetic entropy gain in the CEPM is necessary
to overcome the barrier between AAFM and CE states
upon warming.
Batch-C crystals show no evidence in conductivity or
high-energy x-ray diffraction for CE order although they
were made with a nominal composition of x = 0.5. The
CE superlattice reflections seen in batch-A and batch-B
crystals were missing at all temperatures down to 100 K.
Curiously, all previously published conductivity data [4,
6, 8, 11] and in particular [18] known to us for nominal x
= 0.5 look more like our batch-C crystals, although some
show a small hysteresis [4, 6, 8]. A resistivity comparison
[19] among these indicates a remarkable consistency in
temperature dependence and thus establishes our batch-
C crystals as a commonly seen variant of the nominal x =
0.5 layered manganite. The data of Refs. [6, 8] do show a
somewhat larger resistivity peak at ∼180 K that could be
the signature of some CE-order in their crystals and each
of these report the CE reflection. However, the resistivity
peak associated with CE order in our batch-A crystals is
at least 10 times larger than the maximum value reported
by others [6, 8]. This may imply CE order occurs in a
larger fraction of our purified batch-A crystals.
The electronic nature of AAFM states near h = 0.5
is not so easily determined. Conductivity for x = 0.58
crystals indicate ab-plane metals [20] , whereas insulating
behavior is seen for x = 0.46 [21]. Conductivity data
for the AAFM states of batch-A and batch-C crystals
fall between these two extremes. A possible scenario is
a continuous ab-plane-metal to insulator transition as h
decreases from ∼0.58 to ∼0.46. In this picture the CE
order replaces the AAFM over a limited h-range centered
at 0.5, but the h-dependence of the AAFM states are
otherwise unaffected.
In summary, contrary to published data and ac-
cepted wisdom for LaSr2Mn2O7, we show that the zero-
temperature ground state is the CE type predicted by
Goodenough [3]. We also find no evidence of CE and
AAFM coexistence. That we do not know the exact h-
values is not critical to these two new observations, but
compositional purity was crucial to these discoveries. It
was accomplished by stringent testing of small (∼1 mg)
crystals and verified by our observations with bulk probes
of only three, unique states in the 12 crystals tested. The
lack of sufficient purity could explain why others consis-
tently see coexistence of CE and AAFM order.
The authors thank Peter Lee for assistance with
synchrotron x-ray diffraction at the Advanced Photon
Source. This research was supported by the U.S. De-
partment of Energy, Basic Energy Sciences-Materials Sci-
ences, under contract No. DE-AC02-06CH11357.
∗ Electronic address: KenGray@anl.gov
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mailto:KenGray@anl.gov
	Acknowledgments
	References
