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Electron-lattice correlations and phase transitions in CMR manganites.

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Ann. Phys. (Berlin) 523, No. 8 – 9, 652 – 663 (2011) / DOI 10.1002/andp.201100040
Electron-lattice correlations and phase transitions
in CMR manganites
V. Moshnyaga∗ and K. Samwer∗∗
I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1,
37077 Göttingen, Germany
Received 16 February 2011, revised and accepted 5 April 2011
Published online 13 September 2011
Key words Perovskite manganites, colossal magnetoresistance, electron-phonon interaction, metal-insulator transition, structural phase transition, oxide films and superlattices.
This article is dedicated to Dieter Vollhardt on the occasion of his 60th birthday.
Interrelations between global and local structure and magnetism and transport in three-dimensional perovskite manganites is reviewed and compared with recent studies on thin films and superlattices. The concept of correlated Jahn-Teller (JT) polarons is discussed within the phase separation scenario; their role in
the local and global structural modifications of manganites is demonstrated. Polaron correlations, affected
by external control parameters (temperature, electric and magnetic fields, doping, light, strain) may be very
efficient to modify the ground state of manganites. Examples of electronic control of the structure by means
of interface modifications, electric field and mechanical strain are highlighted.
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction
Perovskite manganites with a general formula RE1−x Ax MnO3 (RE denote the rare earth elements, like
La, Nd, Pr; and A = Ba, Sr, Ca are alkali earth elements) stay for more than 50 years [1, 2] in the focus of fundamental research due to an unique combination of electronic and structural properties. The
rediscovering of the colossal magnetoresistance (CMR) effect in thin manganite films [3, 4] and the observed half-metallic behavior [5] have induced a great interest for potential applications in spintronics.
During the last few years the fundamental and applied interest in manganites did not subside, but rather
was enhanced due to the exciting theoretical ideas [6] and recent experimental advances in the multiferroic
behavior [7]. This phenomenon concerns the coexistence and coupling of more than one ferroic (ferromagnetic, ferroelectric, ferroelastic and ferrotoroidic [8]) orderings in a chemically homogeneous manganite
or in a specially designed composite material. Furthermore, new avenues in the manganite research may be
opened up due to the recently discovered [9] unconventional ground states at the LaAlO3 /SrTiO3 interfaces.
Metallic, ferromagnetic and even superconducting phases originate from the uncompensated charge at the
3+ 2−
O ) interfaces. The release of the charge by the corresponding electronic and/or orbital
(Ti4+ O2−
2 /La
reconstruction may lead to the doping by charge carriers [10] and to the appearance of new ground states.
All these phenomena underscore the fundamental importance of the manganite physics, which as well,
being a part of correlation physics, challenges our knowledge of the modern condensed matter physics,
especially in the description and/or prediction of collective responses and complex phenomena, like metalinsulator (MI) transition, CMR and high TC superconductivity [11].
Perovskite manganites belong to the family of strongly correlated transition-metal oxides, in which a
large Coulomb repulsion in half-filled 3d-like electronic band leads to a Mott-Hubbard insulating ground
∗
∗∗
Corresponding author E-mail: vmosnea@gwdg.de
E-mail: ksamwer@gwdg.de
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Ann. Phys. (Berlin) 523, No. 8 – 9 (2011)
653
state, like in a parent compound LaMnO3 [12]. Substitution of La3+ by a divalent metal ion (e.g. Ca2+ )
creates holes, presumably on Mn-ions, thus triggering a number of phase transitions [11]: metal/insulator,
ferromagnet/paramagnet, charge ordering and structural phase transition. The phase transitions in manganites as well as in many other transition-metal oxides can be influenced both by filling (FC) and by
bandwidth (BC) control [13]. The FC addresses the electronic part of the system, changing the charge carrier concentration by means of chemical doping, light excitation or electric field effect. The BC operates by
applying hydrostatic and/or chemical pressure as well as by other factors, directly affecting the interatomic
distances and, hence, the one-electron bandwidth. The properties of different manganites have been summarized in a very complex phase diagrams, containing a number of electronic and structural phases, which
reflect the nature of chemical constituents as well as the chosen control parameter [12–14]. A principal
difference between the manganites and “classical” strongly correlated metallic electronic systems, like, for
instance, heavy fermions [15], is the significantly larger electron-phonon coupling in manganites, which
leads to a strong “intermixing” of electronic and lattice subsystems. The reason for that is the Jahn-Teller
(JT) effect [16] (Mn3+ with one electron on an eg level is a JT ion), resulting in a removal of the (eg -t2g )
orbital degeneracy and to structural reconstructions to accommodate the corresponding JT distortions. Remarkably, the decisive role of electronic correlations in the determining of lattice structure by stabilizing
the JT distortions in systems with large electron-phonon coupling was theoretically demonstrated by D.
Vollhardt and coworkers [17]. As was shown in the earlier theoretical studies [18, 19] the electron-phonon
coupling in manganites seems to be strong enough to provide hole localization via the JT distortions – such
charge carriers are called JT polarons. Within this new concept of JT polarons one can explain the observed
insulating behavior in paramagnetic state for T > TC .
The aim of this short review is to discuss the key issues of the manganite physics, namely the metalinsulator transition and CMR, as manifestations of electronic-structural correlations [17], i.e. of correlated
polarons (CP), which develop within their specific energy scale and possess characteristic space and time
correlation lengths. Being predominantly nucleated at the phase boundaries, CP’s dramatically affect the
electron transport close to the phase transition, actuating the phase separation and percolative phase transition [14]. Moreover, recent theoretical and experimental studies reveal that polaronic correlations in a
manganite material, being tuned by the electron-phonon coupling strength and boundary conditions, may
be very sensitive to the external fields. They display very large responses to applied magnetic and electric
fields as well as to strain and electromagnetic radiation. The paper is organized as the following: in Sect. 2
we will discuss the phase diagrams and their relations to the crystal structure of perovskite manganites.
Competing interactions, ferromagnetic double exchange and antiferromagnetic superexchange, and resulting changes in the local structure will be reviewed in Sect. 3; also the role of chemical composition in
controlling the crystal structure and electronic properties will be reviewed. In Sect. 4 manifestations of
correlated polarons in magnetotransport as well as our recent experiments on the nonlinear electron transport, interface modifications in superlattices and resistance switching will be presented. In conclusion part
the role of correlated polarons in the field-induced phase transitions is highlighted.
2 Phase diagrams and structure
Doped manganites have been traditionally classified onto three groups [13], according to the value of
the one-electron bandwidth, W , which as well is controlled by the average radius of the A-site√cation, e.g.
rA = RLa (1−x)+RCa (x), or by the tolerance factor of the perovskite structure, t = (A-O)/ 2(Mn-O);
here (A-O) and (Mn-O) are the distances between the A-site and Mn and oxygen, respectively. Depending
on the ionic radii of the divalent (Ba, Sr, Ca) or trivalent (La, Pr, Nd) cations as well as on the doping level,
x, the tolerance factor changes in the range 0.98 < t < 1 for the large cations (La, Ba) and (La, Sr), then
further decreases to 0.96 < t < 0.98 for middle-size cations (La, Ca) and (Nd, Sr), and, finally, goes down
to t < 0.96 for the smallest cations (Pr, Ca). Accordingly, such materials are dubbed “large”, “middle”
and “small”-bandwidth manganites.
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V. Moshnyaga and K. Samwer: Electron-lattice correlations and phase transitions in CMR manganites
LSMO
LSCMO
300
250
200
150
100
50
Paramagnet
LCMO
TEMPE
ERATURE
Tempe
erature (K
K)
350
LPCMO
LPCMO
Ferromagnetic
metal
Charge-ordered
insulator
PCMO
0
O0
ELECTRON-PHONON COUPLING, O
1-t
Fig. 1 (online colour at: www.ann-phys.org) Generic phase
diagram from 20, superimposed on the experimental phase
diagram for optimally doped manganites with different tolerance factors, t, redrawn from [24].
In Fig. 1 we show a generic phase diagram of the manganite system, created by Mathur and Littlewood [20], which in our opinion presents a clear starting point to discuss electronic properties of different
manganite materials. There are two main magnetic phases, ferromagnetic (FM) and antiferromagnetic
(AFM), which reflect two main competing tendencies in this area of correlation physics. Namely, the delocalization or metallic character of charge carriers is favored by the FM ground state, and localization or
isolating behavior is favored by the AFM state. An important ingredient to the manganite physics, seen in
the generic phase diagram, is the electron-phonon coupling, which is presented as a control parameter for
the phases and phase transitions. Moreover, the type of the phase transition is also believed to be controlled
by the electron-phonon interaction, quantified by the constant λ, changing from a continuous or 2nd order
phase transition for small values, λ < λ0 , to discontinuous (1st order) for large numbers λ > λ0 . The
hatched area in Fig. 1, surrounding the phase boundary of the 1st order transition, illustrates the presence
of an electronically inhomogeneous or phase separated state [14] with coexisting metallic and insulating
domains. It is that peculiar state that is believed to be responsible for extremely large values of CMR [21].
Note, that the constant, λ = ΔE/hωL [22] (ΔE is the JT deformation energy and hωL is the energy of
longitudinal optical phonon), is poorly known for specific manganites, making the analysis of concrete
materials quite difficult. However, a qualitative comparison can be given. In Fig.1 we superimposed the
data on the optimally doped manganites (x ∼ 0.3) with different substitutions, i.e. (La, Ca)MnO3 [23],
(La, Sr)MnO3 , (La, Sr, Ca)MnO3 , (La1−y Pry )CaMnO and (Pr, Ca)MnO3 [24], onto the generic phase diagram [20]. Remarkably, the generic phase diagram fits quite nicely the experimentally obtained diagram if
we assume that electronc-phonon coupling constant is proportional to the tolerance factor, i.e. λ ∼ (1 − t).
Taking into account that for the ideal perovskite t = 1, one gets a simple result that the strength of the
electron-phonon interaction is proportional to the deviation of the real perovskite structure from a cubic
one. As the tolerance factor decreases, an orthorhombic distortion increases [24], resulting in the decrease
of the bandwidth, W , and enhance of charge/orbital ordering (CO) and AFM superexchange interaction,
which then compete or even prevail the FM double exchange for small t-values. In this way one can rationalize how the atomic structure may control the electron-phonon interaction. Another important factor,
known to influence the phase transition temperature, is chemical disorder due to the statistical distribution
of divalent cations (Ca, Ba)
the A-sites [25]. The resulting lattice distortions,
between
described by the
yi ri2 − rA 2 , (yi is the fractional occupancy of A-sites,
yi = 1) become
statistical variance σ 2 =
enhanced for very large cations (La, Ba) yielding to the decrease of TC ∼ 320 K [24] even for t ∼ 1 as is
the case for La0.7 Ba0.3 MnO3 .
3 Competing interactions and local structure
The important magnetic interactions, discussed in the literature, are the FM double exchange [26–28]
(DE) and an AFM superexchange interaction, formulated usually as Goodenough-Kanamori-Anderson
rules [28]. The applicability of DE to describe the insulating behavior in manganites and the CMR effect
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Ann. Phys. (Berlin) 523, No. 8 – 9 (2011)
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as well was questioned earlier [18, 19] and we will not discuss this problem here. More important for us is
that magnetic ground state, e.g. FM or AFM, is intimately coupled to the orbital and, finally, to the crystal
structure of a manganite. Indeed, as was shown already in the earliest studies [2, 30], the orbital structure of a manganite, e.g. LaMnO3 (LMO) with periodic and alternating spatial alignment of eg -orbitals
(d3x2−r2 and d3y2−r2 ), controls the magnetic ground state, which is an A-type AFM. Furthermore, crystalline structure undergoes a structural phase transition at TS = 770 K [31] from a pseudo-cubic, R-3c,
to a less symmetric orthorhombic [32] (Pnma ) or even to monoclinic (P2l /C) structure [33] under cooling.
The reason is the cooperative JT effect, which by means of the long range orbital ordering of d-orbitals,
stable for T < TS , releases the local atomic strain. Thus, the electron-lattice interaction, originated from
specific occupancy of eg orbitals and their ordering, strongly influences magnetism, structure as well as
electron transport. For example, the resistance of LMO jumps by 2 orders of magnitude at TS [30], showing
a behavior similar to the charge ordered insulators [13] at the Verwey transition.
For the doped manganites, LCMO, LSMO, LBMO, showing a MI transition and CMR, the cooperative
JT effect vanishes and the room temperature structure changes to a more symmetric R-3c structure by x ∼
0.175 [34]. Interestingly, this specific value of doping marks the phase boundary between FM insulating
and FM metallic phases [23, 34]. However, according to the pulsed neutron scattering and pair-density
function (PDF) analysis [35,36] the locally distorted JT regions with short (0.195 nm) and large (0.225 nm)
Mn-O distances can still survive up to x ∼ 0.4, hosting within the structurally “foreign” matrix with
averaged R-3c symmetry. The size of these local JT distorted regions, called as correlated polarons (CP)
[37], is 1.5–2.0 nm as estimated from PDF [35]. Considered as a short-range-ordered regions with both
charge and spin correlations, CPs show a wave vector q = (1/4, 1/4, 0) [37–39], which is characteristic
for CE-type charge/orbital ordering, observed in a half-doped LCMO [40]. Thus, CPs can be viewed as
CE-type regions, probably in the form of stripes [41] with characteristic charge and spin correlations,
embedded in an orbital/charge disordered matrix with an averaged Mn valence, 3 + x. According to the
neutron [37–39] and X-ray scattering experiments [42] the CP-induced scattering intensity demonstrates
a temperature evolution similar to that of electrical resistance, being maximal at TC , vanishing in the FM
state and decreasing in paramagnetic state. The correlation length, ξ ∼ 2 nm, however, does not depend on
the temperature and its value agrees well with PDF data [35, 36]. Moreover, in an applied magnetic field
the CPs are suppressed [43], showing a behavior similar to CMR. All this indicates an important role of
the correlated polarons or in other words of the short-range-ordered charge, spin, and lattice correlations
in manganite physics.
There are, however, some questions and, probably, not sufficient understanding of the concept of correlated polarons. Firstly, the concentration of CPs, i.e. the volume ratio of MnO6 octahedra with correlated
distortions, nCP , estimated from the above mentioned scattering experiments, is very small. For instance,
nCP ∼ 0.1% for optimally doped LCSMO [41] and nCP ∼ 2–4% for charge ordered manganites with
x ∼ 0.5 [44, 45] were revealed. Very recently Tao et al. [46] obtained a much larger value 22% for LCMO
(x = 0.45) in experiments with scanning electron nanodiffraction. Possibly these discrepancies are due to
an unsufficient accuracy in the estimation procedures. However, one cannot exclude also the case that the
amount of polarons is intrinsically very small; then our understanding of their role in the MI transition and
CMR seems to be even more poor than in the former case. Secondly, there is also a discrepancy between
the relations between CPs and global crystal structure: CPs have been observed in the earlier experiments
for the R-3c rhombohedral phase of LSMO [35] while more recent data [42] on LCSMO (R-3c) did not
confirm this.
4 Manifestations of correlated polarons in transport
According to the phase separation scenario [14] metallic and insulating phases coexist close to the 1st
order phase transition and the phase competition leads to a percolative MI transition and CMR. Recently
the phase coexistence model was further developed for a disorder free manganite [47] and the competing
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c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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V. Moshnyaga and K. Samwer: Electron-lattice correlations and phase transitions in CMR manganites
phases were specified to be FM and charge/orbitally ordered (COO) AFM. Moreover, the charge localization
√ length in the AFM insulating phase was found to be limited within a very few perovskite unit cells,
5aper , in a remarkable similarity with the size of correlated polarons evaluated from scattering experiments, ξ ∼1–2 nm [35, 42]. Given to the fact that FM domains in manganites are actually much larger,
aFM = 50–1000 nm, [48] one gets the only possibility to “place” correlated polarons at the domain boundaries. This result elucidates, in addition, the importance of interfaces, domain boundaries or, in general,
of the two-dimensional defects with a broken symmetry, where the correlated polarons can be preferably
stabilized. In this sense the interfaces in thin manganite films, whatever their origin is, seems to play a
triggering role in the development of the phase separation. Indeed, an interface induced phase separation
in very thin LCMO films was reported earlier [49]. Vice versa, to prevent phase separation one needs to
preserve the symmetry of MnO6 network as was realized in LCMO/LSMO multilayers [50]. The suppression of the MI transition in ultrathin manganite films [51], which was shown to be independent on the
film-substrate mismatch strain, was interpreted within the orbital reconstruction (ordering) of eg orbitals.
This interpretation confirms the possibility to “excite” correlated polarons at a symmetry breaking interface. Theoretical basis for these observation was given by L. Brey [52], who considered the interface as an
electronic potential barrier caused by the abrupt change of the charge carrier concentration at the interface
from the nominal optimal doping (x ∼ 0.3) with 0.7 electrons per Mn ion to the doping, x = 1, or MnO2
configuration without electrons. The electron depletion (or hole overdoping) at the surface in the presence
of Coulomb interaction (correlation or Hubbard term) leads to the formation of a CE-type phase, which becomes stable within a very thin surface (interfacial) layer of thickness, d ∼ 3–5 u.c. This low-dimensional
interfacial CE-phase, which is presumably a 2D-phase or even may be of stripe-like geometry [41], fits all
requirements for correlated polarons (see Sect. 3). Note that even in covalent materials like Si the polarons
were found to be preferably nucleated at the surface [53]. All this indicates an important role of polarons
for the interface phenomena in manganites as well as suggest new possibilities to detect and to monitor the
behavior of correlated polarons in thin films and superlattices by interface sensitive techniques.
Recently [54] we have shown that measurements of a third harmonic (3ω) electrical nonlinearity can be
useful to study manifestations of correlated polarons in CMR manganite films. In Fig. 2 one can see that 3rd
er
b)
LPCMO
Re
-30
B=0
-50
5T
-60
-70
LCMO
0
100
200
T (K)
-40
5T
-60
mSL
LSMO
300
-50
w
B=0
-80
-30
vie
K3ω(dB)
-40
cSL
400
100
-20
200
K3ω (dB)
a)
-20
-70
-80
300
400
T (K)
Fig. 2 (online colour at: www.ann-phys.org) Third harmonic coefficient, K3ω = U3ω /Uω , for individual
manganite films (a) and superlattices (b).
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Ann. Phys. (Berlin) 523, No. 8 – 9 (2011)
657
harmonic coefficient, K3ω = U3ω /Uω , which is the ratio between the nonlinear, U3ω , and the linear signal,
Uω , increases dramatically by approaching TC for LCMO films, whereas an LSMO film shows a very small
nonlinear coefficient, K3ω ∼ 80–85 dB, which, in addition, is temperature independent. Remarkably, an
applied magnetic field, B = 5 T, suppresses the 3ω-signal in LCMO down to the same level as seen for
LSMO. Furthermore, an optimally doped LPCMO film with Pr-doping, y = 0.4, and TC = 194 K reveals
even a stronger nonlinearity (see Fig. 2a), which also can be suppressed by applying magnetic field.
10
8000
н
Ͳ Ͳ
н
6000
8
6
4000
4
2000
2
0
0
0
50
100
150
200
250
300
R3ω (Ω)
CMR (7T), %
10000
350
T (K)
Fig. 3 (online colour at: www.ann-phys.org) A correlation between CMR = (R(0T ) − R(7T )/R(7T ))
and 3rd harmonic nonlinear resistance R3ω = dU3ω /dJ in LPCMO film; the inset shows schematically a
quadrupolar charge distribution (blue circle) in local region with CE-type charge and orbital ordering.
A close correlation between the CMR and 3ω-nonlinear resistance, R3ω = dU3ω /dJ, (J is the current)
is further evidenced by Fig. 3, where both quantities demonstrate almost the same temperature behavior
with an extremely sharp peak close to TC , i.e. they scale with each other.
We believe that electrical 3ω nonlinear technique provides an useful tool to study an electronically
inhomogeneous (phase separated) state close to the 1st order phase transition. Indeed, the development of
3ω-signal in different manganite films proceeds in remarkable agreement with the phase diagram in Fig. 1.
A “classic” double-exchange material, a metallic LSMO with 2nd order transition, shows an essentially
linear electric behavior. By increasing the electron-phonon coupling constant, λ ∼ 1 − t, one obtains
a “moderately nonlinear” LCMO. Finally, a strongly nonlinear LPCMO appears by further increase of
the lattice contribution. Moreover, we argued [54] that the 3rd harmonic coefficient probes the volume
fraction of correlated polarons, nCP . Considered as a short-range-ordered COO regions of CE-type (see
Sect. 3) CPs represent “droplets” with quadrupolar charge distribution, Δq(r), within a manganite material
with an average Mn-valency, 3 + x. As shown in the inset in Fig. 3, the local charges are formed by the
neighboring Mn3+ (negative charge) and Mn4+ (positive charge) ions. Then a nonlinear interaction of the
applied electric field interaction with quadrupoles, Δq = χE 2 [55], results in a 3rd harmonic resistance,
R3ω ∼ E 2 , which is then becomes proportional to the volume fraction of correlated polarons, nCP ∗ Δq.
Note, that even in the case of an incomplete Mn3+δ /Mn4−δ (0 < δ < x) charge imbalance and/or if
the charges would be localized along the (Mn-O) bonds [19, 56], the specific CE-type phase geometry
with diagonal to the lattice ordering of charges preserves the above quadrupolar distribution. The volume
fraction of correlated polarons, estimated from the nonlinear 3ω measurements in optimally doped LPCMO
films was ncp ∼ 0.5%, which agrees qualitatively with the neutron and X-ray scattering data [42].
The interface induced phase separation strongly suppresses spin polarization in the interfacial manganite layer. Thus, it reduces the performance of the manganite-based magnetic tunnel junctions – the low-field
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V. Moshnyaga and K. Samwer: Electron-lattice correlations and phase transitions in CMR manganites
magnetoresistance, being extremely large at low temperatures [57], TMR ∼ 2000%, vanishes already for
T ∼ 200 K TC . To compensate the charge depletion and to enhance magnetism, an interface engineering approach, exploiting electron doping by introducing of 2 unit cells (u.c.) of LMO at the LSMO/SrTiO3
interface, was realized by Yamada et al [58]. Another field where the interface engineering seems to be
also very important is artificial multiferroic materials [6, 59], epitaxially grown as superlattices of ferromagnetic manganite (LCMO) and ferroelectric titanite (BaTiO3 ) layers. Very recently [60], we have shown
that interfaces in the LCMO/BTO heterostructures not only play a decisive role in magnetotransport, but
also control the crystalline structure of the manganite phase. The LCMO/BTO superlattices (SL) were
grown on MgO(100) substrates by a metalorganic aerosol deposition technique [61]. Structure and magnetotransport of the two types of SL’s were compared: 1) conventional SL (cSL), described by the formula
[(LCMO40 )/(BTO20 )]10 , contain LCMO and BTO layers of the thickness 40 and 20 u.c., respectively,
grown on each other, starting from LCMO on the substrate; and 2) modified SL (mSL), in which 2 u.c.
of LMO were introduced at each interface, i.e. [(LMO2 )/(LCMO40 )/(LMO2 )/(BTO20uc )]10 . The transport properties were found to be drastically different. Namely, the cSL shows a behavior typical for an
electronically inhomogeneous medium with: a) large difference between the zero-field-cooled (ZFC) and
field-cooled (FC) resistance for T < TC ; b) decoupled magnetic and MI transitions with low values of
TC = 220 K and TMI = 150 K as well as low saturation magnetization. In contrast, the mSL demonstrates
a magnetotransport characteristic for electronically homogeneous material with no ZFC-FC irreversibility
in the resistance and magnetization; in addition mSL shows a coupled magnetic and MI transitions with
TC ∼ TMI = 250 K. The data on the 3rd harmonic coefficient, K3ω , elucidate the origin of such different behavior in the cSL and the mSL samples. As one can see in Fig. 2b) the nonlinearity in the cSL is
about 7 orders of magnitude larger than that in the mSL and, considering that the nonlinearity originates
from correlated polarons, we conclude that the amount of polarons in the interface engineered LCMO/BTO
superlattice is very small, comparable with the individual LSMO film (see Fig. 2a). In other words a conventional SL shows interface-induced phase separation, which is extraordinarily pronounced, whereas an
LMO-modified SL does not. According to Brey [52] the electron doping at the interface “suppresses” the
CE-phase and LCMO film behaves similar to the bulk material. But this is not a complete story! In Fig. 4 we
show the electron diffraction patterns of cSL and mSL samples taken along with the transmission electron
microscopy (TEM) measurements [61].
Fig. 4 (online colour at: www.ann-phys.org) Electron diffraction images of conventional (cSL) and modified (mSL)
LCMO/BTO superlattices (from [60]).
The structure for the cSL with characteristic doubling of the lattice parameter along the b-axis (vertical
direction in Fig. 4, left panel) was found to be an orthorhombic, Pnma , structure. In contrast, the electron
diffraction pattern of the mSL in Fig. 4 (right panel) with no superstructure reflexes with the wave vector
q(0, 1/2, 0) fits a pseudocubic, presumably rhombohedral R-3c structure. Thus, by means of electron doping at the LCMO/BTO interface one can suppress correlated polarons, i.e. static JT distortions, inducing a
structural transformation in 40 u.c. of LCMO. Perfectly linked with this observation is the striking similarity between the 3rd harmonic behavior in LSMO and mSL, shown in Fig. 2 – they both belong to the R-3c
structure and they both show a negligibly small nonlinearity because of the absence of correlated polarons.
Another illustration for an electronic control mechanism at the manganite interfaces is electric field induced resistance switching (EPIR), observed in many perovskite compounds like SrTiO3 [62], PCMO [63].
This is a bipolar switching from high (HRS) to low (LRS) resistance state; these states are both remanent. Provided the switching occurs at room temperature and the switching amplitude can be very large,
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Ann. Phys. (Berlin) 523, No. 8 – 9 (2011)
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RHRS /RLRS > 100, the EPIR effect is very promising for potential applications in resistive RAM. Although the underlying mechanisms, i.e. ionic [64, 65] and electronic [56], are still under debates one can
definitely say that surface (interface) plays a very important role. Recently [66] we have studied the switching at the surface of manganite films by means of the conductive atomic force microscopy (c-AFM), which
allowed us to monitor the development of HRS- and LRS-domains as a function of applied voltage and
pulse time. In Fig. 5 we show the contact geometry of c-AFM measurements and the resistance switching
at room temperature on the surface of a LCMO film (x = 0.2).
The initial highly insulating HRS state can be reversibly switched into a remanent LRS (blue dashed
curve) and then back to HRS (red curve) by alternating pulses of the amplitude +4 V and −4 V, respectively. The LRS state was then current mapped (see Fig. 5b) by varying the pulse amplitude and duration;
note that the spot (domain) size under these conditions was 10–50 nm, corresponding to the storage density
of about 1 Tb/inch2. A summarized analysis of the relative spot size, r/U , as a function of relative pulse
duration, t/U , for all points in the current map reveals then a logarithmic dependence (see Fig. 5c). Such
dependence infers a domain-wall creep mechanism of the resistance switching, similarly to that observed
for the switching of ferroelectric domains, obtained by PFM [67]. Considering the similarity in the time dependence of ferroelectric domains in BTO [67] and of our metallic spots (Fig. 5b) [66] we suggest that the
mechanism of the resistance switching could be a phase transition rather than oxygen diffusion. Additional
indications in the favor of phase transition are: 1) the existence of a threshold voltage, UC = 3 V (Fig. 5b);
Fig. 5 (online colour at: www.ann-phys.org) Conductive AFM switching experiments: a) current voltage
characteristics of an La0.8 Ca0.2 MnO3 /MgO film (the geometry is shown in the inset) in low and high resistance states, obtained after switching of the initial HRS state (black dashed curve) by pulses of +4 V
and −4 V, respectively; b) Current map (taken by U = 100 mV) written by pulses with varied amplitude
(4–8 V) and duration (10-1000 ms) and c) Normalized spot-size dependence on the relative pulse width,
indicating a logarithmic dependence as expected for domain-wall creep (taken from [66]).
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c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
660
V. Moshnyaga and K. Samwer: Electron-lattice correlations and phase transitions in CMR manganites
2) occurrence of switching even at low temperatures, 5–100 K, at which the rate of oxygen diffusion in
manganites [68] is low and probably not sufficient to actuate the switching. Thus, we believe that a realistic
mechanism for the resistance switching at the manganite interfaces can be an electric-field-induced phase
transition from an initial polaronic insulating CE-type phase, which is an orthorhombic (Pnma ) phase, to
a polaron-free metallic phase with a pseudo-cubic (R-3c) symmetry. A necessary coupling to the electric
field could be again provided by correlated polarons as electric quadrupoles [54], the density of which
is especially high at the interface (surface). Quite recently Alexandrov and Bratkovsky [69] have shown
theoretically that a quantum dot device, composed of a bipolaron linked to metallic leads, shows a very
similar hysteretic resistance switching or memristor (memory resistance) behavior. Necessary conditions
for switching are different energy states (in our case we have two states with and without JT distortions) and
strong coupling to the leads (seems to be provided by a quadrupolar susceptibility). An additional evidence
for the relevance of a polaronic mechanism of the resistance switching is given by an electric-field-induced
magnetic anisotropy change at Fe/MgO interfaces [70]. It was observed that a sufficiently large electric
field, Ec > 2 · 106 V/cm, induces an orbital reconstruction of eg orbitals (d3z2−r2 and dx2−y2 are getting unsymmetrically populated), leading to the change of magnetic anisotropy of ultrathin (2–5 u.c.) Fe
films on MgO substrates. Remarkably, to actuate resistance switching with conducting AFM as well as at
the vertical LSMO/LSMO interfaces in nanocolumnar films [71] we also need the threshold electric fields
EC ∼ (1–4) · 106 V/cm.
5 Conclusions
In Fig. 6 we present a picture, which in our opinion summarizes the role of correlated polarons in the
initiating and mediating of the coupled phase transitions; they may be induced by a generalized external
field, e.g. temperature, magnetic and electric field, strain [72]. A principal possibility to draw such sketch
is given by the fact that correlated polarons, with charges trapped by correlated JT distortions and shortrange-ordered AFM coupled spins, comprises naturally all three important degrees of freedom i.e. charge,
spin and lattice, which are believed to be in the essence of the manganite physics. The initial state is an
electronically inhomogeneous or phase-separated insulating state close to the 1st order phase transition,
in which the polarons nucleate at the interfaces (boundaries) between FM (PM) domains. Due to the CEtype geometry and, likely, because of long-range elastic interactions the correlated polarons as electric
and elastic quadrupoles, being nucleated at the phase boundaries, stabilize a low symmetry, orthorhombic
Pnma . An applied generalized field, by addressing the corresponding degree of freedom, destroys the shortrange-ordered charge, spin or structural correlations, yielding the melting of polarons; the system switches
then to a metallic FM state with higher symmetry. All this proceeds via the corresponding 1st order phase
transitions, indicated by a hysteretic behavior as a function of temperature, magnetic and electric field (see
Fig. 6). We would like to note an interesting analogy between the correlated polarons in manganites and
shear transformation zones (STZ) [73, 74] in metallic glasses. Namely, CPs and STZs have a very similar
size and volume, V ∼ (2.5 nm)3 ∼ 16 nm3 , and these special atomic groups seems to be responsible for
the relaxation of the shear (STZs) and JT (CPs) stresses by means of their spontaneous and cooperative
reorganization.
To obtain an extreme sensitivity to an external generalized field the system has to be tuned, by means
of chemical doping and/or substitution, to get an optimized electron-phonon coupling strength or equivalently the structural tolerance factor (see Fig. 1), which drives the material close to the FM/AFM boundary,
thus enhancing the field sensitivity. One of the opened questions is: “If this important boundary could be
shifted into the high temperature region, T 300 K”. Or in other words is it possible to have both high
TC and TCO (charge ordering temperature). Very recently Sadoc et al [75] demonstrated TC ∼ 1000 K in
LCMO/BTO superlattices with very thin individual layers of 3–4 unit cells. A superlattice approach [76] to
construct a correlated oxide material with desired chemical composition and without cation disorder [77]
seems to be very promising. Another open question is about the time scale of the phase transitions discussed
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Ann. Phys. (Berlin) 523, No. 8 – 9 (2011)
661
Generalizedfield:T,E,H,strain
Electric field
Temperature
HRS
Resistan
nce
Insulator
PM(AFM)
Metal
Corr.polarons
&
Interfaces
4
10
260
240
220
200
180
160
R (a.u.)
5
10
Isolator
LRS
Pnma
T(K)
E (a.u.)
Phasetransition
Mechanicstrain
Magnetic field
300
3
T~TMI
Insulator
R3Z(:)
10
10
Nopolarons
&
Nointerfaces
2
1
Metal
0
10
-1
PH (T)
10
0
10
1
200
100
FM
10
10
8
10
6
10
4
FM
P nma
RͲ3c
Metal
10
TMI, TC (K)
10
10
PI
R3c
0
10
-4
X
10
-2
XC=0.3
10
R @ 300
0 K (:)
Lattice
Phasetransition
Spin
Charge
Takenfrom>71@
0
Takenfrom>72@
Fig. 6 (online colour at: www.ann-phys.org) Summarizing sketch of “generalized field”-induced phase transitions
mediated and/or actuated by modifications of the local structure, i.e. by correlated polarons. The low right corner
shows the phase diagram in epitaxial (LCMO)1−x :(MgO)x nanaocomposite films; the second phase (MgO) actuates
negative (tensile) stress in a primary phase (LCMO).
above or how fast can be the phase transformation with participation of correlated polarons. Considering
the time scale is provided by the corresponding energy scale [78] via uncertainty relation, dE · dt ∼ h,
the “electronic” correlations should develop at the femtosecond time scale, whereas the ultimate speed
of the lattice correlations lies in the THz region. G. Müller et al [79] obtained recently that LSMO
as a half-metallic manganite with spin polarization close to 100% demonstrates demagnetization time,
τm ∼100–300 ps, in a qualitative agreement with above rough estimations. By exploring the time scale of
the electron-structure correlations one could also try to prove a fundamental theoretical idea, put forward
by D. Vollhardt [17], that electronic correlations do control the structure. Very recent and interesting result
was obtained by A. Cavalieri’s group [80]: by measuring of X-ray diffraction at the picosecond time scale
they demonstrated the appearance of “hidden” short-living phases in a Nd0.5 Sr0.5 MnO3 film, excited by
means of femtosecond laser pulses. The new transient phase differs from the equilibrium phase by the lattice parameters, is structurally homogenous and metastable. The role of electronic correlations in creating
transient photoexcited phases was emphasized.
Acknowledgements The authors thank W. Felsch for useful comments. Financial support by the DFG via SFB 602
(TP A2) and Leibniz-Program is acknowledged.
www.ann-phys.org
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
662
V. Moshnyaga and K. Samwer: Electron-lattice correlations and phase transitions in CMR manganites
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