1. Antiferromagnetic Resonances and Lattice & Electronic Anisotropy Effects in Detwinned La 2-x Sr x CuO 4 Crystals Crystals: Yoichi Ando & Seiki Komyia Adrian Gozar # G. Blumberg & B. Dennis CRIEPI, Japan # A. Gozar et al. Phys. Rev. Lett. ‘04

2. What is (detwinned) La 2-x Sr x CuO 4 ? 100 200 300 400 500 x(Sr) 0.20.1 T(K) AF SC LTO (orthorhombic) HTT (tetragonal) 0.02 adapted from B. Keimer et al. PRB 46, 14034 ‘92 HTT a b b a Y.Horibe PRB ‘00 LTO b = 5.4 A b - a ~ 0.05 A R.J. Birgeneau PRL ‘87

3. Swapping the Crystal Axes with Magnetic Field A.N. Lavrov Nature ‘02 room temperature 1 mm c a(b) bb La 1.99 Sr 0.01 CuO 4 T N ~ 210K  strong magneto-elastic coupling  net ferromagnetic moment ? H ~ 14 T H In a magnetic field H // CuO 2 planes the b orthorhombic axis follows the direction of the external field

4. Outline  Long Range Antiferromagnetic Order in La 2-x Sr x CuO 4  Magnetic Field Dependent Raman Data in La 2-x Sr x CuO 4 x(Sr)  0.01  low energy magnetic excitations ► anisotropic dispersions of spin wave gaps ► in H  11 T  observation of magnetic field induced spin ordering (H // b-axis)  Strong Lattice and Electronic Anisotropies ► detwinned La 2-x Sr x CuO 4 x(Sr)  0.03 ► CuO 6 tilt disorder at x(Sr) = 1/8 doping in (La,Nd) 2-1/8 Sr 1/8 CuO 4

5. Antiferromagnetic Order in La 2-x Sr x CuO 4 (x  0.02) CuO 2 plane c b JJ  d (3/4,1/4) R. Coldea PRL ’01 (1/2,0)(0,0) Excitations 0k  (k)  XY ~ m(2  J) 1/2  DM ~ md a b c Cu 2+ Spin Hamiltonian B. Keimer Z. Phys ’93 2D Heisenberg J ~ 140 meV ‘XY’ exchange anisotropy  / J ~ 10 -4 ‘DM’ Dzyaloshinskii-Moriya d / J ~ 7  10 -3 only in the LTO phase

6. Spin-Wave Gaps in La 2 CuO 4 0k  (k)  XY ~ m(2  J) 1/2  DM ~ md Neutron Scattering T = 80 K C.J. Peters PRB ’88 ~ 2 meV Raman Scattering 1 meV ~ 8 cm -1 La 2 CuO 4

7. 0k  (k)  XY ~ m(2  J) 1/2  DM ~ md Neutron Scattering T = 80 K Raman Scattering C.J. Peters PRB ’88 1 meV ~ 8 cm -1 Spin-Wave Gaps in La 2 CuO 4 La 2 CuO 4 CuO 2 plane c b H T. Thio PRB ’90

8. Spin-Wave Gaps in La 2 CuO 4 Raman Scattering 1 meV ~ 8 cm -1 Experiment b 2D Spin-Wave Model  DM = 17.0 cm -1 XY DM CuO 2 plane c

9. Spin-Wave Gaps in La 2 CuO 4 Raman Scattering 1 meV ~ 8 cm -1 Experiment b

10. Magnetic Field Induced Raman Modes in La 2 CuO 4 T (K) 0 H // b 300 200 100

11. (A) T = 10 K ► Spin-Wave calculation is consistent (up to 5%) with the dispersion of the XY gap B. Keimer Z. Phys. ’93 ►  XY ~ 5.5 meV (44 cm -1 ) ► For H // b  d  DM / d H b < 0  one expects a magnetic field induced transition c (B) T = 300 K ► T N (La 2 CuO 4 ) = 310 K & dT N / dH b ~ -1K/T CuO 2 plane c b H = 0 strong H // b Field Induced Spin Reorientation

12. (A) T = 10 K ► Spin-Wave calculation is consistent (up to 5%) with the dispersion of the XY gap (B) T = 300 K B. Keimer Z. Phys. ’93 ►  XY ~ 5.5 meV (44 cm -1 ) ► For H // b  d  DM / d H b < 0  one expects a magnetic field induced transition ► T N (La 2 CuO 4 ) = 310 K & dT N / dH b ~ -1K/T c strong H // b 300 K d ≠ 0  = 0  DM is this a ‘regular’ spin-flop like transition ? (continuous) spin reorientation in the (bc) plane

13. Field Induced Spin Reorientation T (K) 0 H // b 300 200 100 9 T

14. Field Induced Spin Reorientation La 2 CuO 4 La 1.99 Sr 0.01 CuO 4 T N (La 1.99 Sr 0.01 CuO 4 ) = 210 K dT N / dH b ~ -4 K / T TNTN

15. La 1.99 Sr 0.01 CuO 4 T N (La 1.99 Sr 0.01 CuO 4 ) = 210 K dT N / dH b ~ -4 K / T ► I(T) peaked at TN ►  (T) > 0 at all temperatures  XY  DM Field Induced Spin Reorientation TNTN

16. La 1.99 Sr 0.01 CuO 4 T N (La 1.99 Sr 0.01 CuO 4 ) = 210 K dT N / dH b ~ -4 K / T TNTN H = 0 net ferromagnetic moment c b

17. Lattice & Electronic Anisotropy - La 2-x Sr x CuO 4 x = 0 Raman response (rel. units) T = 10 K (aa) (bb) x = 0.01 (aa) (bb) x = 0.03 Raman shift (cm -1 ) (aa) (bb) 12 La/Sr 21 c a b

18. Local Structure at x ~ 1/8 Sr Doping La/Sr 21 La 2-x-y Nd y Sr x CuO 4 T = 10 K 1 2 A. Gozar PRB ’03 (cc) polarization ► no signatures of charge super modulation in (cc) polarized Raman spectra - group theory for the LTO phase predicts 5 fully symmetric Raman active modes ► at 1/8 Sr doping there exists substantial disorder in the CuO 6 octahedra tilt pattern

19. Conclusions  Magnetic Excitations ► DM and XY anisotropy induced spin-wave gaps ► For fields H // b  observation of magnetic field induced spin reorientation  Low Energy Lattice & Electronic Dynamics ► detwinned La 2-x Sr x CuO4 x(Sr)  0.03 - about 30% anisotropy in the electronic background - strong phononic anisotropy ► x(Sr) = 1/8 (La,Nd) 2-x Sr x CuO 4 - disorder in the local structure  lattice has to be taken into account when discussing possible spin or charge modulation in LaSrCuO