Hour-glass magnetic spectrum in a stripe-less insulating transition metal oxide
HHour-glass magnetic spectrum in a stripe-lessinsulating transition metal oxide
Y. Drees , D. Lamago , A. Piovano & A. C. Komarek September 16, 2018
1. Max-Planck-Institute for Chemical Physics of Solids, N¨othnitzer Str. 49,D-01187 Dresden, Germany2. Laboratoire L´eon Brillouin, CEA/CNRS,F-91191 Gif-sur Yvette Cedex,France3. Institut Laue-Langevin (ILL), 6 Rue Jules Horowitz, F-38043 Grenoble,France
An hour-glass shaped magnetic excitation spectrum appears to bean universal characteristic of the high-temperature superconductingcuprates. Fluctuating charge stripes or alternative band structureapproaches are able to explain the origin of these spectra. Recently,an hour-glass spectrum has been observed in an insulating cobaltate,thus, favouring the charge stripe scenario. Here we show that nei-ther charge stripes nor band structure effects are responsible for thehour-glass dispersion in a cobaltate within the checkerboard chargeordered regime of La − x Sr x CoO . The search for charge stripe order-ing reflections yields no evidence for charge stripes in La . Sr . CoO which is supported by our phonon studies. With the observation ofan hour-glass-shaped excitation spectrum in this stripe-less insulat-ing cobaltate, we provide experimental evidence that the hour-glassspectrum is neither necessarily connected to charge stripes nor toband structure effects, but instead, probably intimately coupled tofrustration and arising chiral or non-collinear magnetic correlations. Charge stripes that have been initially predicted as a combined charge- andspin-density wave phenomenon [1, 2, 3] have been first observed experimen-tally in Nd-codoped La − x Sr x CuO Ref. [4] and in the isostructural nickelatesLa − x Sr x NiO δ (LSNO) Ref. [5] with a quasi-two-dimensional layered struc-ture. These charge stripes are characterized by hole-rich regions running invertical [4] or diagonal [5] direction within the M O planes ( M = Cu/Ni), thus,separating the remaining charge depleted regions where the antiferromagnetic(AFM) structure of the undoped parent compound recovers. Since charge stripes1 a r X i v : . [ c ond - m a t . s t r- e l ] M a y ct as antiphase domain walls, the magnetic structure appears modulated. Therole of this charge stripe instability for the high-temperature superconducting(HTSC) cuprates remains a matter of debate and it is puzzling that both phe-nomena can coexist though charge stripes tend to suppress superconductivity[6]. Another isostructural system where stripe ordering has been reported isLa − x Sr x CoO Ref. [7, 8]. Surprisingly, also an hour-glass magnetic spectrumhas been observed in La / Sr / CoO Ref. [8]. This hour-glass spectrum resem-bles the famous excitations in the cuprates [9, 10, 11, 12, 13, 14, 15, 16, 17, 18]which were found to be a universal feature of these HTSC materials and whichhas stimulated enormous efforts for explaining these spectra [19, 20, 21, 22].Very recently, theoretical simulations of the magnetic excitation spectra basedon a disordered charge-stripe model have been also reported for La / Sr / CoO Ref. [23]. These layered cobalt oxides are isostructural to the prototypicalcuprate materials La − x Sr x CuO . The quasi-two dimensional crystal structurearises from a stacking of CoO layers that are separated by (La,Sr)O rocksaltlayers acting as a charge reservoir. The substitution of trivalent La by divalentSr introduces holes into the CoO layers. In analogy with the isostructural nicke-lates (LSNO) these holes were proposed to segregate into diagonal charge stripes[7, 8]. However, whereas the incommensurate magnetic peaks can be clearly ob-served in La − x Sr x CoO Ref. [7] the corresponding unambiguous observation ofsharp and well separated charge-stripe ordering (CSO) superstructure reflectionsis missing. Hence, also a glassy charge ordered state with different commensu-rate superlattice fragments could be responsible for the observed broad signalsin Pr − x Ca x CoO Ref. [24] or even simply disordered magnetic contributionsspread around half-integer positions in reciprocal space for the reported featuresin La − x Sr x CoO Ref. [7].Here, we have studied the magnetism, magnetic excitations, charge orderingand electron phonon coupling in a cobaltate compound close to half-doping, i.e.in La . Sr . CoO and were able to observe the appearance of an hour-glassdispersion in this stripe-less cobaltate within the checkerboard-charge orderedregime of La − x Sr x CoO . In contrast to other studied cobaltates within the incommensurate magneticregime our sample exhibits comparably sharp incommensurate magnetic peaksand, thus, much less disorder than in previously studied compounds (see Fig. 1).Note, that it is shown in Ref. [23] that the sharpness of the CSO signal shouldbe roughly equal to the sharpness of the incommensurate magnetic peaks ina CSO scenario for La − x Sr x CoO Ref. [23]. Hence, our La . Sr . CoO ma-terial seems to be an ideal system to study any possible relationship betweenincommensurate magnetic peaks and charge stripes in these layered cobaltates.The results of our elastic neutron scattering experiments on La . Sr . CoO . Sr . CoO , see Fig. 1 (c). Instead, only one broad peak athalf-integer positions appears that is indicative for a (disordered) checkerboardcharge ordered (CBCO) state persisting up to high temperatures very similarto the optimum half-doped compound La . Sr . CoO (dashed line). Thus, wemanaged to find a La − x Sr x CoO sample within the CBCO ordered regimewhich exhibits clearly incommensurate magnetism. Next, we studied the magnetic excitations of this compound. In Fig. 2 (a-f) themagnetic excitation spectra of La . Sr . CoO are shown and compared withthose in La . Sr . CoO . In contrast to the half-doped reference material (thedashed lines in Fig. 2 (d,f) were derived from spin wave calculations using theMcPhase program code [25] closely following the analysis in Ref. [26]), all basicfeatures of an hour-glass magnetic spectrum can be observed in La . Sr . CoO -an inwards-dispersion of low-energy branches towards the planar AFM wavevec-tor, a suppression of the outwards-dispersing branches, a resonance-like mergingaround ∼
20 meV with increased intensity and an outwards dispersion of thehigh energy branches measured at positions rotated by 45 ◦ compared to theelastic magnetic satellites. Additional constant-Energy maps for La . Sr . CoO are shown in Fig. 2 (g-o). Remarkably, the high energy magnetic excitationsin La . Sr . CoO resemble on the isotropic high energy excitations recentlyreported for La . Sr . CuO Ref. [27]. The constant- Q scan at (3 / / ∼ . Sr . CoO , i.e. a single ion or small exchange anisotropy withinthe ab plane [26]. Also the existence of a gap in these hour-glass shaped ex-citations in La . Sr . CoO resembles on the observations in the isostructuralHTSC cuprates (e.g. in La . Sr . CuO Ref. [28]) even if their origin mightbe different.
We have also searched for signatures of charge ordering in the Co-O bondstretching phonon dispersion of La − x Sr x CoO . In Fig. 3 (a) two polariza-tion patterns of high-frequency Σ phonon modes are shown. In the left figure3t is shown schematically that the presence of diagonal charge stripes (indi-cated by the dashed lines) would induce a coupling of the Co-O bond stretchingphonon mode to stripes with the same propagation vector. That charge stripesin single layer perovskite oxide materials are able to induce such an electronphonon coupling and even giant electron phonon anomalies was already demon-strated for high-energy Cu-O bond stretching phonon modes in the isostructuralcuprates [29]. On the other hand, for CBCO one would expect bond stretchingphonon anomalies at the zone boundary as is shown schematically in the rightpart of Fig. 3 (a). Here, we have measured the topmost Co-O bond stretch-ing phonon dispersion of La . Sr . CoO and several La − x Sr x CoO referencesamples ( x = 0, 1 /
3, 0 . compound La CoO the La − x Sr x CoO -materials within the incommensuratemagnetic regime all exhibit a strong pronounced softening of the phonon disper-sion towards the zone boundary i.e. at (1 / / ζ ζ
0) with ζ = 2 · ε ∼ x (indicated by the black arrows in Fig. 3 (c,d)). In contrast to our observationsin La . Sr . CoO the corresponding Ni-O bond stretching phonon mode of a40% Sr-doped LSNO reference material with robust diagonal CSO exhibits acompletely different and almost complementary dispersion, see Fig. 3 (d). Thehigh-frequency Ni-O bond stretching mode starts at very similar energies for ζ = 0 but quickly softens around propagation vectors corresponding to CSOpropagation vectors and even exhibits a final upturn towards the zone bound-ary. Note, that we also observed phonon softening in other LSNO samples (with x =0 .
2) where the phonon softening appears at phonon propagation vectors thatexactly correspond to the propagation vectors of charge stripe ordering of thatparticular LSNO sample [30]. Hence, an opposing behaviour of bond stretchingphonon modes in cobaltates and in charge stripe ordered nickelates can be ob-served. In the cobaltates, the anomalous phonon softening at the zone boundaryis consistent with a robust CBCO persisting also below half-doping rather thanwith static (or dynamic) charge stripe phases and supports our elastic studies.
The absence of stripes in La . Sr . CoO and our observation of an hour-glass-shaped excitation spectrum in this compound (even with indications for a gap)sheds another light on the recent argumentation that the absence of any gapin the hour-glass-shaped excitations of the cobaltates (La / Sr / CoO ) withstatic stripe order and the appearance of a gap in the excitations of the HTSCcuprates points to a “collective quantum melting of stripe-like electronic order”in the cuprates [31]. Also the study of larger parts of the phase diagram ofLa − x Sr x CoO motivates a different mechanism for the emergence of incom-mensurate magnetism in La − x Sr x CoO ( x (cid:46) / . Sr . CoO exhibits the sharpestmagnetic peaks which broaden with increasing distance of hole-doping awayfrom half-doping. Similar observations have been reported in Ref. [7]. With4ecreasing Sr-doping the incommensurate magnetic regime finally breaks downslightly below 1 / -ions) into the ideal CBCO ordered AFM matrix induces frustra-tion. Thus, the substitution of Co -ions for non-magnetic Co -ions alters theAFM Co ↑ -Co -Co ↓ -Co -Co ↑ exchange paths resulting in frustratedspin arrangements Co ↑ -Co ↓ -Co -Co -Co ↑ , see Fig. 4 (d). In order torelieve the high amount of frustration that is generated by the introduction ofadditional large nearest neighbour exchange couplings J >> J (cid:48) the system canbe expected to turn into a chiral or non-collinear magnetic state. This scenariois not only in agreement with our observation of incommensurate magnetismtogether with the absence of charge stripes but it is also able to explain nat-urally the successively increasing peak broadening away from half-doping, seeFig. 4 (b). Also the kind of incommensurate magnetism naturally follows fromour frustration scenario. As shown in Fig. 4 (d) each doped electron into theundistorted AFM matrix of the ideal checkerboard charge ordered half-dopedsystem induces additional strong AFM nn-exchange interactions. Therefore,the nnn-interactions become ferromagnetic (FM) in total. Without electrondoping, these exchange interactions all had been AFM before. In order to re-lease frustration, the magnetic moments start twisting/spiralling (a spin-densitywave appears unlikely in this strongly localized system). The more electrons aredoped within a certain given distance in a -direction (in b -direction), the morecenters of frustration and the more spiralling occurs within this certain distancein order to release frustration. This machanism would be consistent with the in-creasing incommensurability away from half-doping. Furthermore, it is also ableto explain the direction of the incommensurate magnetic satellites: Since thesespiraling-effects appear concomitantly in x - and in y - direction (in-plane), the di-agonal direction of the incommensurate satellites arises from the presence of twoindependent AFM sublattices in the ideal optimum half-doped compound (see[26]) which are affected both together at the same time by the additional dopingof one electron, see Fig. 4 (d). Since there will be the same total twist of spins in a -direction and in b -direction after a certain distance the total modulation i.e.the propagation appears to be in [ ± ± x = 1 / x = 1 / x = 1 / − x Sr x CuO [32, 33, 34] exhibitingalso diagonal magnetic satellites and magnetic excitations with the characteris-tics of an hour-glass spectrum [10]. In this chiral model of the magnetic groundstate of La − x Sr x CuO frustration arises from doping of charges into the AFMmatrix of an AFM parent compound (La CuO ) Ref. [34, 32, 33]. Note, thatalso in bulk La − x Sr x CuO no CSO peaks have been found [35], and, that inboth isostructural systems ( M = Cu or Co respectively) frustration might arisefrom the doping of additional charges (holes or electrons respectively) to in-terstitial sites, thus, effectively introducing additional ferromagnetic exchangeinteractions into the unaltered AFM host structure (see Ref.[34] or Fig. 4 (d)respectively). Hence, frustration might not only play an important role for thetriangular lattice [36] but also for the hole-doped square lattice systems as wellas for the emergence of the hour-glass dispersion in these systems.Concluding, we studied the magnetic excitations and electron phonon cou-pling of a single layer perovskite cobaltate within the checkerboard charge or-dered regime. In this material with comparably sharp incommensurate mag-netic peaks we observe the appearance of a magnetic excitation spectrum withall basic features of an hour-glass spectrum in close vicinity to half-doping. Theabsence of any charge stripe superstructure reflections in this material indi-cates that the hour-glass dispersion might emerge concomitantly with the onsetof frustration and chiral or non-collinear magnetic ordering in La − x Sr x CoO ( x (cid:46) /
2) rather than with the onset of charge stripe ordering. We also studiedthe impact of electron-phonon coupling in these materials and were able to ob-serve large Co-O bond stretching phonon anomalies at the zone-boundary whichare consistent with our picture that robust checkerboard charge ordering is stillprevalent below half-doping in La − x Sr x CoO . Neither the existence of staticnor of dynamic charge stripe phases can be supported by these high-frequencyphonon studies. Our observation of an hour-glass-shaped excitation spectrumin a stripe-less insulating transition metal oxide goes one step further than therecent observation of an hour-glass spectrum in an insulating cobalt oxide [8]since it clearly shows that besides Fermi-surface effects also no charge stripes areneeded for the appearance of the hour-glass spectrum. Therefore, frustrationmight be the unifying property of all these systems that exhibit an hour-glass-shaped magnetic excitation spectrum and either band structure effects or (shortranged) charge stripe correlations are just additional side effects which are notdirectly connected to the appearance of this peculiar excitation spectrum. Single crystals of La − x Sr x CoO and LSNO materials have been grown by thefloating zone technique following a route as described elsewhere [37, 38]. Butin order to determin the oxygen content more carefully we have grown all the6rystals in Ar atmosphere. Only one of our single crystals, i.e. the nominally1/3 Sr-doped compound, has been grown in an oxygen enriched Ar-atmospherein order to obtain one single crystal that was grown under more oxidizing con-ditions like described for La / Sr / CoO in [8]. The high single crystal qualityhas been ascertained as described in the Supplementary Note 1. For most inelastic neutron measurements two or three large single crystals havebeen co-aligned with the crystallographic a tet - and b tet -axes in the scatteringplane. For measuring the magnetic excitation spectra, inelastic neutron scat-tering experiments have been performed at the 2T.1 triple-axis spectrometers(TAS) at the LLB in Saclay, France. A vertically focussing configuration ofthe PG-002 analyzer and a flat configuration of the PG-002 monochromatorhas been chosen and higher order contributions have been suppressed by twoPG-filters. All inelastic scans have been performed in the constant- k f -operationmode with k f = 2.662 ˚A − in most cases and k f = 4.1 ˚A − for the highest mea-sured energies solely. For measuring the high-frequency Σ phonon dispersionand the constant energy maps, inelastic neutron scattering experiments havebeen performed at the IN8 thermal TAS at the ILL in Grenoble, France. ACu200 double-focusing monochromator and a PG-002 double-focusing analyzerhave been chosen for measuring these high-energy phonon modes in constant- k f -operation mode with k f = 2.662 ˚A − . Higher order contamination was sup-pressed by two PG filters. For measuring the constant energy maps in Fig. 2a Si-111 monochromator has been used in order to suppress λ /2 contamina-tions. Powder lines originating from the cryostat and the sample holder areapparent in these measurements. In order to apply a background-correction wehave also performed measurements with empty sample holder (measurementswithout sample) for the most important constant-E maps: first, at the neckof the hour-glass, i.e. at 20 meV, and, second, at a distinctly higher energyof 27 meV. Thus, we were able to subtract the background from our samplesignal in order to confirm the shape of our observed magnetic signal. These twomaps are shown in Fig. 2 (n,o). Note that the spurious peaks could still notbe corrected this way since they might originate from monochromator phononsthat were scattered elastically by the sample etc. The magnon merging point aswell as the outwards dispersion can be clearly seen in these kind of (HK0)-mapsat 20 meV and 27 meV respectively. Additional inelastic neutron scatteringexperiments of the low energy magnetic excitations have been performed at thecold neutron TAS 4F.2 at the LLB in Saclay, France ( k f ∼ − ; Be-filterat 77 K). Elastic neutron scattering measurements have been performed at the3T.1 diffractometer and 1T.1 TAS at the LLB in Saclay, France and at the IN8TAS spectrometer at the ILL in Grenoble, France ( k i ∼ − ; two PGfilters have been used for suppression of higher order contamination).7 eferences [1] Zaanen, J. & Gunnarsson, O. Charged magnetic domain lines and themagnetism of high-T c oxides. Phys. Rev. B , 7391 (1989).[2] Schulz, H. J. Domain walls in a doped antiferromagnet. J. Phys. (Paris) , 2833 (1989).[3] Machida, K. Magnetism in La CuO based compounds. Physica C ,192 (1989).[4] Tranquada, J. M., Sternlieb, B. J., Axe, J. D., Nakamura, Y. & Uchida, S.Evidence for stripe correlations of spins and holes in copper oxide super-conductors.
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We thank Y. Sidis, D. I. Khomskii, E. Andrade, M.Rotter, P. Thalmeier, O. Stockert and L. H. Tjeng for helpful discussions.We thank H. Borrmann, Y. Prots and S. H¨uckmann for X-ray diffrac-tion measurements. We thank S. Subakti for titration measurements andwe thank A. Keil for help in cutting crystals. We thank the team ofU. Burkhardt for EDX measurements and the team of G. Auffermann forICP measurements. • Contributions
A. C. K. planned all experiments. A. C. K. synthesizedall studied materials. Y. D. and D. L. performed the elastic and inelasticneutron scattering experiments at the 3T.1 diffractometer and at the 2Tand 1T spectrometers. Y. D., A. P. and A. C. K. performed the elastic andinelastic neutron scattering experiments at the IN8 spectrometer. A. C. K.wrote the manuscript. • Competing Interests
The authors declare that they have no competingfinancial interests. • Correspondence
Correspondence should be addressed to A. C. K. (email:[email protected]). 10igure 1:
Elastic neutron diffraction study of charge and mag-netic correlations (a) Neutron scattering intensities in the HK . Sr . CoO at 12 K; (200 K background subtracted). (b) Magnetic peaksmeasured in scans across (1/2 1/2 0). (c) Diagonal ( H − H . Sr . CoO measured at 4 K and at 500 K. Also the difference of 4 K and500 K intensities is shown together with the expected CSO intensity (red line)derived from a CSO-ordered LSNO reference sample (inset) with the same Sr-doping ( I x =0 . calc CSO = α · I x =0 . magn. · I LSNOCSO /I LSNOmagn. ; α = ( m Ni /m Co ) · ( u Co /u Ni ) ∼ . Sr . CoO sample is still within the CBCOregime. Dashed cyan line: the charge ordering signal of the optimum dopedCBCO ordered sample La . Sr . CoO . Intensity error bars are statistical errorbars calculated by the square root of intensity.11igure 2: Neutron spectroscopy study of magnetic excitations (a-f)Inelastic neutron scattering intensities for La . Sr . CoO and La . Sr . CoO measured at the 2T spectrometer. (a-b) Neutron scattering intensities (shiftedby a value indicated by the horizontal bars); circles: diagonal scans across(1/2 1/2 0) in (a) and (3/2 1/2 0) in (b) as a function of H ; diamonds: ( H H -1 and H in (a) and (b) respectively; solid lineswere derived from symmetric gaussian fits. (c-f) Intensity maps as a functionof Q and energy transfer through (3 / / H ( K ) is ranging from 1 to2 (from 0 to 1) from left to right (from bottom to top) in each map. Insteadof interpolation, the whole area around one measured data point is filled withthe same colour. Fits of the dispersion (diamonds) which have been derivedfrom these maps are also included in (c,e). In (n,o) the background was sub-tracted (see supplementary material). (p) Constant-Q scan at (3 / / / ε / ε
0) measured at ∼
10 K at a cold neutrontriple-axis spectrometer (blue circles); additionally, the background is shown(green circles). Intensity error bars are statistical error bars calculated by thesquare root of intensity. Other error bars are standard deviations obtained fromGaussian peak fits. 12igure 3:
Inealstic neutron scattering study of lattice dynamics (a) Po-larization patterns for high-frequency Σ Co-O bond stretching phonon modes.The dashed lines indicate a coupling to charge stripes (left) or to CBCO(right). (b,c) Some representative phonon scans of La . Sr . CoO measuredat (3 − q − q
0) and for La . Sr . NiO measured at (3+ q q
0) correspondingto the focusing sides in both compounds. Clearly, the opposite | q | -dependence ofphonon peak positions can be observed in nickelates and cobaltates. (d) Inelas-tic neutron scattering intensity as a function of energy and momentum transferfor La . Sr . CoO . The white shaded area is biased by a spurious peak andalso measured at the defocusing side. An anomalous phonon softening is clearlyobserveable at ζ = 0 . . Sr . CoO , a phonon softening is observeablearound propagation vectors connected to CSO and not for ζ → . phonon dis-persions of La − x Sr x CoO for different x . The black dash-dotted line indicatesthe dispersion of La CoO shifted to higher energies. Intensity error bars arestatistical error bars calculated by the square root of intensity. Other error barsare standard deviations obtained from Gaussian peak fits.13igure 4: The frustration scenario in La − x Sr x CoO (a) Neutron scatter-ing intensities for ( H ± H − x Sr x CoO for different x showing acontinuous peak broadening below half-doping. (b) The peak width for different x as a function of incommensurability ∆ ε = ε − /
4. (c) The AFM structure inan ideal CBCO state. (d) Schematic drawing of our frustration scenario. Theintroduction of an additional electron (Co -ion) into the AFM matrix of theideal CBCO half-doped compound induces strong frustration due to a strongnn-exchange coupling J compared to the existing exchange couplings J (cid:48)(cid:48)