Quantized spin-waves in 2D step levels, probe the metallic state of manganites M. Hennion, S. Petit, F. Moussa, D. Lamago LLB-Saclay A. Ivanov, ILL, Grenoble, France Y. Mukovskii, MISIS, Moscow, Russia -1)Phase diagram of La(Sr)MnO3 and La(Ca)MnO3: 5 steps towards metallic state -Summary of the spin wave spectra in the low doping regime -2)Comparison of the x(Sr)=1/8 and and x(Sr)=0.15, model of “orthogonal stripes” -3)New measurements of magnetic excitations in the metallic state with high energy resolution, Proposed model and simulation

Evolution to metallic state in 5 steps 1 2 3 5 Diagr. De phase Home/llb9/mhenn/lettr/Paraskevopoulos.xfig.gif 4 1 2 3 4 5 Evolution to metallic state in 5 steps 1 2 New measurements of magnetic excitations in x(Sr)=0.15,0.175,0.2,0.3,and x(Ca)=0.3, with a good energy resolution For all x :cubic indexation. Samples are twinned (coincidence of a, b, c )

Résistivity 1 2 La1-xSrxMnO3 Tc 4 To’o’’ 3 5

Metallic state: large anomalies of w(q) 5 Metallic state: large anomalies of w(q) Endoh et al. PRL 94 (2005), Ye et al. PRL 047204 96 (2006) , F. Moussa et al. PRB 76, 0644403 (2007) In theory (DE), spin wave dispersion: w(q)~fn cos) All compounds exhibit at large q “broadening”, “flattening”, “ softening” , Taken into account by 2 cts: J1,J4, Generic features of all manganites? What is the role of the orbital state of Mn? Which orbital state? La(Ca,Sr)MnO3 Arguments of continuity:same orbital state (fluctuating) as in low doping

1 2 SE=superexchange AF Ferro Ferro SE along a*, or b* SANS (M. H. et al PRB 73 104453 (2006) x=16Å in (a,b) planes AF SE along c* Charges Spins DE,Ferro, along a*,b*,c* Soft boundaries G. Biotteau et al 64 PRB ( 2001) AF Bragg peak Ferro Bragg peak

3 SE,2D SE,2D ~3D 2D x~1/8:ferro percolation,quasi metallic behavior M. Hennion et al. PRB 73 104453(2006) Sr x=0.15; Tc=230K x(Sr)=1/8; Tc=180K EB111= 2*EB100 SE,2D SE,2D (3) (22meV) (3) (2) (17 meV) (2) (1) (11 meV) (1) ~3D 2D x=4a,sharp or soft boundaries? q<0.25, propagative, no gap, appears at Tc, typical of DE q>0.25, local modes, exist above Tc, typical of SE along a*, or b* (~8,12,17,22 meV, (close to phonons TA,LA,LO) Sr15il/omega_001_225KmeV.xfig.gif Percolation of the 2D hole-rich clusters: segregated state of orbital-ordered (OO) clusters (SE coupling) in DE matrix

3 TO ’O ’ ’ <T<Tc’  X(Sr)=0.125,T=165K (Tc=180K) X(Sr)=0.15, T=225K (Tc=230K) 17 meV,22 meV) tex/art-Sr12/omega_001_166K_meVbis.xfig.gif et R027.xfig.gif node_1.eps, etc IN8, ILL

X(Sr)=1/8 x(Sr)=0.15 4 T<100K) (22 meV) (22 meV) (17 meV) (17 meV) a*,b* Tex/art_17%/omega_001_13K_meV.eps C* F. Moussa et al. PRB 67 (2003) 1)2D clusters are still there, but now organised 2)Coupling along c defined at small q only: No SE coupling (large q) along c

4 Sr15il/omega_001_14KmeV1.xfig.gif Sr15/spectres_100_14K.xfig.gif

4 Model of orbital-ordered domains (x=4a) organised to provide a 4a periodicity: holes on the oxygen sites between the domains (x=1/8 is perfectly adequate) All planes are identical . Arrangement along c ? “Orthogonal stripe picture” M. Hennion PRB 73 104453,(2006) O-- Mn3+ (SE coupling) O- Proposed model for high Tc (Boris Fine,cond. matt. 2004) 2D simulation, 2 parameters: J (SE), lJ (at boundary): Sharp or soft boundaries? No associated static surstructures! Differ from model based on static superstructures as (0,0,1/4) Geck et al. PRL 95 235401(2005) Same spin wave spectrum for Ca (x=0.17,0.2),M. H. et al. PRL 94 (2005), Ba (x=0.15), whatever (0,0,1/4) peaks exist or not

4 EB111= 2*EB100 Limitation: Small q: 3D Nearly quantitatif agreement with lJ=0.2 Limitation: Small q: 3D Large q: 1 additional level, weak Tex/art_Sr12/omega_001_150K_Koln2.xfig tex/art_Sr12/omega_001_150K_Koln1.xfig.fig bali:/Sr15il/omega_001_14KmeV1.xfig conf/Seillac/don1.xfig.gif

5 Ye et al. PRL 96 (2006)

5 x(Sr)=0.175, Tc=250K 3D 32meV 22meV x(Sr)=0.15 2D Sr20il_mac/R934.xfig.eps Sr2004_mac/R033.eps [100]: One broad mode at high energy and small modulations (remind OO platelets) [111]:6 levels caract. of the OO platelets + 4 levels EB 111=2EB100+EB001 EB100~32meV: the additional levels restore 3D character of the coupling at large q!

x(Sr)=0.175, dir. [111], 14K 5 IN8,ILL

x(Sr)=0.2, Tc=325K 5 At low T (T<200K), 2 distinct sets of modes, w(q) of the main mode is “normal” at T=14K Sr20il/omega_001_meVbis.xfig.eps

Coupling of wi(T) with the energy E(T) of the mean ferromagnetic state x(Sr)=0.2 42 meV 32 meV Coupling of wi(T) with the energy E(T) of the mean ferromagnetic state 22 meV 17meV 8meV Sr20il_mac/R934.xfig.eps Sr2004_mac/R033.eps Sr2004/omega_1.45_temp.eps Sr2004_mac/R015.eps

x(Sr)=0.3 With additional charges, regular levels,with 3 modulations above those carac. of the OO platelets: “softening”, “flattening” 22meV 17meV 22meV 17meV Sr3001/omega_100_31K.meV.xfig.eps

x(Ca)=0.3 Tc=270K 22 meV 17 meV 8 meV Ca3017_mac/R006.eps

5 3D Simulation The large-q anomalies can be understood as an hybridization of the typical levels the 2D platelets with a 3D ferromagnetic state Model: 5 planes of 20*20 spins each with periodic conditions at the limits, Heisenberg first neighbourg, 3 param.: J (2D or 4 neighbourgs) and lJ at boundary (nearly magn. isolated by electronic screening), J’ (3D or 6 neighbourgs) 2D Density of platelets:25%

Along [111]:4 additional levels restore a 3D char. [100] DIRECTION 100 [ 111] Direction Along [111]:4 additional levels restore a 3D char. 2 new levels above 17 meV et 22 meV and intensity in the gap Very close to obervations at x(Sr)=0.175

Summary and Conclusion Evidence for orbital correlations of 4a size through its confined spin waves in the ferro state (fluctuate at time larger than spin waves fluct. ) “quantitatif” agreement to interpret the magnetic excitations for all sym. directions in La(1-x)SrxMnO3 x~1/8 : model of charge segregation (orthogonal stripes) High-energy resolution measurements of spin excitations lead us to propose a similar model in the metallic state: coupling of a 3D magnetic matrix (DE) with spins of 2D orbital-ordered platelets (SE) Surprising stability of these 2D platelets: why 4a? (as in the canted state) Is it the max. of size that can be screened? What is the role of the elastic energy (lattice vibration spectrum) to explain the stability of the orbital correlations? Sr3002_mac/R043.eps

Field effect (H=3.5T~0.04meV) x(Sr)==0.125,T=140K Field effect (H=3.5T~0.04meV) For x(Sr)=0.125 q=0.25 q=0.175 Takouma/tex/art_sr12/ Takouma/tex/art_sr12/champ_165K.eps et champ_140K.eps M. Hennion et al. PRB 73 (2006)

4 Direction [111] Energie de bord de zone, EBZ[111]~2EBZ[100] à toute température Pour un hamiltonien Heisenberg 1er voisin: Jc~0 (2D)