Response of acoustic phonons to charge and orbital order in the 50\% doped bilayer manganite LaSr 2 Mn 2 O 7
F. Weber, S. Rosenkranz, J.-P. Castellan, R. Osborn, H. Zheng, J. F. Mitchell, Y. Chen, Songxue Chi, J. W. Lynn, D. Reznik
aa r X i v : . [ c ond - m a t . s t r- e l ] N ov Response of acoustic phonons to charge and orbital order in the 50% doped bilayermanganite LaSr Mn O F. Weber,
1, 2, ∗ S. Rosenkranz, J.-P. Castellan, R. Osborn, H. Zheng, J.F. Mitchell, Y. Chen,
4, 5
Songxue Chi,
4, 5
J. W. Lynn, and D. Reznik
2, 6 Materials Science Division, Argonne National Laboratory, Argonne, Illinois, 60439, USA Karlsruher Institut f¨ur Technologie, Institut f¨ur Festk¨orperphysik, P.O.Box 3640, D-76021 Karlsruhe, Germany Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA Department of Materials Science and Engineering,University of Maryland, College Park, Maryland 20742, USA Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80309, USA (Dated: November 3, 2018)We report an inelastic neutron scattering study of acoustic phonons in the charge and orbitallyordered bilayer manganite LaSr Mn O . For excitation energies less than 15 meV, we observe anabrupt increase (decrease) of the phonon energies (linewidths) of a transverse acoustic phononbranch at q = ( h, h, h ≤ .
3, upon entering the low temperature charge and orbital orderedstate ( T COO = 225 K). This indicates a reduced electron-phonon coupling due to a decrease ofelectronic states at the Fermi level leading to a partial removal of the Fermi surface below T COO and provides direct experimental evidence for a link between electron-phonon coupling and chargeorder in manganites.
PACS numbers: 75.47.Gk, 63.20.dd, 63.20.kd,78.70.Nx
The complex phase diagrams of many transition metaloxides highlight the strong interplay and competition be-tween lattice, spin and charge degrees of freedom [1–4].Among the various different ground states, the so-calledCE-type [5] charge and orbital order (COO) has partic-ularly attracted scientific interest. Long range COO isthe ground state of half-doped manganites [4–6], andshort-range CE-type COO is believed to play a cru-cial role for colossal magnetoresistance at lower doping[7, 8]. The origin of the charge modulation is typicallyattributed to the ordering of Mn and Mn ions[6]producing Jahn-Teller-type distortions of the oxygen oc-tahedra around the Mn sites. Although these latticedistortions have been verified experimentally, the chargedisproportionation has been argued to be much smallerthan 1 [9–12]. More recently, it has been shown that thedoping dependence of the ordering wavevector for pseu-docubic manganites near half doping can be described ina charge-density-wave (CDW) picture [13] and, indeed,experimental evidence for such a scenario was found inLa . Ca . MnO [14] and Pr . Ca . MnO [15].Although the importance of electron-lattice interac-tion for manganites and, in particular, the CE-type or-dered state is based on theoretical considerations [7, 8]as well as experimental observations [16], detailed exper-imental information on phonon dispersions and electron-phonon coupling in manganites is scarce [17, 20–22].Here, we present results of an investigation of acous-tic phonons in the CE-type COO bilayer manganiteLa − x Sr x Mn O ( x = 0 . T COO =225 K, but in a way not expected from the standard CDW picture [18, 19].We chose the double layer manganite despite the largecrystallographic unit cell because it lacks structural com-plications of its pseudocubic counterparts such as twin-ning and tilted MnO octahedra [21]. As phonon soft-ening is often observed as a precursor to a structuralphase transition at the ordering wavevector, our focuswas on acoustic phonon dispersions along directions thatinclude wavevectors where superstructure peaks were re-ported [10, 23, 24]. To this end, we measured the ab -plane polarized transverse acoustic (TA) phonon branchin the crystallographic (110) direction, which includes theCOO wavevector q COO = (0 . , . , q = (0 . , ,
1) [25, 26] by comparing datafrom Q = (2 . , ,
0) and (2 . , , E f = 14 . . Sr . Mn O [28].Our single crystal sample of LaSr Mn O was meltgrown in an optical image furnace [29] having the shapeof a cylinder of 0 .
210 2250510 Q (2.3, 0, 1)(b) Q (1.25,0.75,0) i n t. i n t en s i t y ( a r b . un i t s ) temperature (K)(a) cooling heating T » T = 100 K225 K250 K c oun t s / s e c (1+h, 1-h, 0) (r.l.u.) temperature (K) heating T = 200 K (H,0,1) (r.l.u.)(c) T = 100 K
FIG. 1. (Color online) Elastic Q scans (heating cycles) at (a) Q = (1 . , . ,
0) and (c) (2 . , , (b)(d) Integrated intensities of the Q scans around Q = (1 . , . ,
0) and (2 . , , (b) shows thetemperature hysteresis near the phase transition temperature T COO ≈
225 K. crystal was mounted in a standard closed-cycle refriger-ator allowing measurements down to T = 5 K and upto room temperature. Measurements were carried out inthe h − k h − l scattering planes. The com-ponents ( Q h , Q k , Q l ) are expressed in reciprocal latticeunits (rlu) of (2 π/a, π/b, π/c ) with a = b = 3 .
88 ˚A and c = 19 . Q mode, Q = τ + q , and τ is a reciprocal latticepoint.The ground state of LaSr Mn O has been investi-gated extensively by both neutron and x-ray scattering.Whereas early neutron scattering experiments [10, 23, 24]reported COO only between 100 and 200 K, a laterstudy[4] showed that CE-type COO is indeed the groundstate of LaSr Mn O . However, already very small devi-ations from x = 0 . ∼ T = 5 K.We show temperature dependent measurements of theCOO superlattice peak at Q = (1 . , . ,
0) in Fig. 1.The onset of COO in our sample is at T COO = 225 Kin agreement with previous work [4]. On cooling below T ≈
100 K, the peak intensity decreases by about 40%.Furthermore, we observe a large temperature hysteresisbetween T = 50 K and 150 K. Both facts indicate a par-tially reentrant behavior. Previous data [4] on reentrantsamples show a strong competition with an A-type anti-ferromagnetic state at low temperatures with a similarlylarge hysteresis in the same temperature range. Morerecently, it was shown that the CE-type orbital orderingas we observe it for T ≤
225 K is susceptible to bothCE-type and A-type antiferromagnetism [30]. The re-duced integrated intensity of the COO superlattice peakat low temperatures can then be attributed to ferromag-netic fluctuations in the ab plane of an A-type antifer-romagnet, which favor double exchange and, therefore,slowly melt the Mn -Mn charge-order, which persistsin the CE-type antiferromagnetic regions.We also checked for the presence of short-range polaroncorrelations with a wavevector q ≈ (0 . , , Q = (2 + h, , h =0 . − .
4, and T = 100 and 200 K. We clearly observe thepresence of this type of superstructure in the partiallyreentrant state at low temperatures, but with a finitecorrelation length ξ ≈
40 ˚A and an amplitude that is anorder of magnitude smaller than the one observed for theCOO peak. The temperature dependence of the polaronpeak at q ≈ (0 . , ,
1) as observed in a heating cycle isroughly opposite to that of the COO peak at q COO , i.e.the polaron peak is barely present when the COO peakreaches its maximum intensity.From the measurements presented in Fig. 1 it is evi-dent that CE-type COO is reduced at low temperatures.However, the measured phonons (see below) react onlyto the onset of COO at T COO = 225 K and show no re-sponse to the reduction of COO at lower temperatures.Thus, we believe that CE-type COO is representative ofthe ground state of our specimen as far as phonons areconcerned. This view is corroborated by the fact thatthe competing A-type antiferromagnetic phase in princi-ple supports and only slowly melts the orbital order viaan increased double-exchange rate [30].We investigated the acoustic and low lying opticphonons along the transverse (110) direction, i.e. q =(+ h, − h, h = 0 .
25 corresponds to the symme-try and wavevector positions of the COO superlatticepeak. Raw data of constant Q scans at T = 5 K forthe TA phonon mode at Q = (2 + h, − h,
0) are shownin Fig. 2. For h ≤ .
3, a single well-defined excitationis observed. For larger wave vectors additional phononpeaks start to develop and finally three peaks can bedistinguished at the zone boundary, i.e. h = 0 .
5. Thefitted energies agree well with previous measurements onLa . Sr . Mn O [28]. Near the zone boundary, our mea-surements show additional peaks due to optic phononbranches, which come close in energy to the acoustic dis-persion. This is corroborated by measurements in a dif-ferent Brillouin zone adjacent to the zone center wavevec- h = 0.5h = 0.4h = 0.3h = 0.2 Q = (2+h, 2-h, 0) neu t r on c oun t s energy (meV) h = 0.1 ene r g y ( m e V )
300 K 5 K F W H M ( m e V ) (h, h, 0) (r.l.u.) exp.res. FIG. 2. (Color online) Constant Q scans of the TA phonon at Q = (2 + h, − h, h = 0 . − .
5, at T = 5 K. Solid lines areLorentzian fits convoluted with the instrumental resolution onan experimental background. Dashed horizontal lines indicatethe respective scan base line. The insets show energies mea-sured at Q = (2 + h, − h,
0) (squares) and (3 − h, h, (upper panel) and phonon linewidths (FWHM) at T = 300 K (squares) and T = 5 K (triangles) of the TAphonon (lower panel) . The black line is the calculated res-olution. tor τ = (3 , , T < T
COO . However, modes at T = 5 Kwith q ≥ (0 . , . ,
0) still have a significant intrinsiclinewidth.We made measurements at various temperatures 5 K ≤ T ≤
300 K and Q = (2 + h, − h, h = 0 .
25, at ∆ T = 25 K below and abovethe transition temperature T COO = 225 K. The phonon ene r g y ( m e V ) (b) Q = ( COO w i d t h ( m e V ) temperature (K)(d) Q = (
0) T = 200 K 250 K neu t r on c oun t s energy (meV)(a) Q = ( E K - K ( m e V ) energy (meV) (c) q = (0.3, 0.3, 0) FIG. 3. (Color online) Temperature dependent (a) back-ground subtracted data, (b) energy and (d)
Lorentzianlinewidth (full-width at half maximum) of the transverseacoustic phonon at Q = (2 + h, − h, h = 0 .
25. Ener-gies and linewidths were extracted from Lorentzian fits (solidlines) to the data convoluted with a Gaussian energy reso-lution ( ≈ (b) and (d) mark the onset of orbital order at T COO = 225 K. (c)
Energyshift of TA phonons at Q = (2 + h, − h, . ≤ h ≤ . T = 5 and 300 K plotted versus phonon energy at T = 5 K. energy increases and the linewidth decreases on enteringthe COO state. As a function of temperature, both theenergy and linewidth at h = 0 .
25 show sudden jumpsat T = T COO (Figs. 3b,d). Figure 3c shows that theeffect increases on an absolute scale for phonons with de-creasing energies, i.e. decreasing h . On the other side,the energy shift between low and high temperatures van-ishes (within experimental error) for a phonon energy ofroughly 15 meV or h > .
3. We note that no tempera-ture dependence was detected for the investigated opticbranch between T = 5 and 300 K, which further indi-cates that the observed effect is restricted to low energyacoustic phonons.Measurements of the longitudinal acoustic phononat wavevectors corresponding to the wavevector of theshort-range superstructure at q = (0 . , ,
1) agreedwell with shell model calculations developed for thecompound with x = 0 . q position.We note, however, that the statistical uncertainty here islarger than for the TA phonon data and changes of lessthan 0 . T COO .The effect is not localized at the ordering wavevector,i.e. q COO = (0 . , . , q ≤ (0 . , . , Mn O cannot be ex-plained by a sudden increase of anharmonic contribu-tions.EPC for a particular phonon mode requires the ex-istence of electronic states close to the Fermi energy E F , which can be excited by the phonon to unoccu-pied states above E F . If these decay channels are frozenout, the phonon lifetime increases and the linewidth isreduced. This is a well known effect in, e.g., conven-tional superconductors for phonon energies below thesuperconducting gap value 2∆ SC [31–33]. Further, theparticipating electronic states have to be connected bythe phonon wavevector q . Unfortunately, informationabout the Fermi surface in the half-doped bilayer man-ganite is scarce. Angle-resolved photoemission spec-troscopy reported only experiments in the COO state[34]. Here, the Fermi surface is such that phonon vectorswith q < (0 . , . ,
0) cannot connect different statesat E F . On the other hand, calculations of the electronicband structure via density-functional theory [35] in not-charge-ordered LaSr Mn O show the presence of a smallelectron pocket around the center of the Brillouin zone(Γ point) in addition to the Fermi surface observed inthe low temperature phase by angle-resolved photoemis-sion spectroscopy [34] allowing Fermi surface spanningwave vectors with q < (0 . , . , q < (0 . , . ,
0) and explain the observed ef-fect. The fact that the observed effects become muchweaker at q = (0 . , . ,
0) and are not detectable any-more at q ≥ (0 . , . ,
0) can be understood in terms ofthe published angle-resolved photoemission spectroscopydata [34]: Wave vectors q ≥ (0 . , . ,
0) can still con-nect parts of the Fermi surface in the COO state. Thus,phonons with these wavevectors lose only part of theirelectronic decay channels. This is corroborated by our re-sults for the linewidths of the TA phonon modes (Fig. 2):Despite the sudden decrease of the linewidth of the TAphonon at q = (0 . , . ,
0) (Fig. 3), it keeps a signifi-cant intrinsic linewidth even at the lowest temperatures.Thus, our results demonstrate the presence of significantEPC and a direct response of EPC to the COO phasetransition in manganites.We note that in the recent literature the CE-type or- dered low temperature state of half-doped La-Ca man-ganites is discussed in terms of a charge-density wave[11, 12, 14, 36, 37]. In this scenario, a gap ∆ in theelectronic excitation spectrum opens at the phase tran-sition [36]. Such a gap opening could cause a reducedphonon linewidth and changes in the energy, if the latterare smaller than 2∆ [32]. Our results would be consis-tent with 2∆ ≈
15 meV at T = 5 K. So far, however,there is no microscopic evidence from electronic probesfor the existence of such an energy gap in LaSr Mn O [40]. Furthermore, CDW compounds typically exhibitphonon softening at the ordering wavevector as predictedby standard weak-coupling theory. Some known CDWcompounds do not follow this phenomenology exactly.For example, in NbSe , phonons soften over a relativelylarge range of wave vectors around the ordering wavevec-tor [38]: NbSe , which is believed to be in the strong-coupling regime, shows not softening but line broadeningat the CDW wave vector on approach to the transition[39]. But all CDW compounds exhibit some anomalousphonon behavior tied to the ordering wavevector. In con-trast, acoustic phonons in LaSr Mn O do not show aKohn anomaly nor an enhanced linewidth at the order-ing wavevector, which rules out the conventional CDWpicture.In conclusion, we investigated acoustic phonons in thepresence of long- and short-range charge correlations inCE-type COO ordered LaSr Mn O via inelastic neu-tron scattering. We found a clear response to the on-set of COO at T COO = 225 K in the TA branch in the(110) direction. For this branch, the phonon linewidthsare significantly reduced for phonon modes with exci-tation energies smaller than 15 meV [ q ≤ (0 . , . , ∗ [email protected][1] E. Dagotto, Science , 257 (2005)[2] D. A. Bonn,
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