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A.Gukasov (polarized neutron experiments)

Magnetic Ground state of R 2 Ti 2 O 7 pyrochlores (R= Tb , Er ) under applied field a neutron diffraction study. Isabelle Mirebeau Laboratoire Léon Brillouin CE-Saclay, 91191 Gif sur Yvette France. A.Gukasov (polarized neutron experiments)

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A.Gukasov (polarized neutron experiments)

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  1. MagneticGround state of R2Ti2O7pyrochlores (R= Tb, Er) underappliedfield a neutron diffraction study Isabelle Mirebeau Laboratoire Léon Brillouin CE-Saclay, 91191 Gif sur Yvette France A.Gukasov (polarized neutron experiments) P. Bonville: (Crystal field and molecular field calculations) H. Cao (post doc 2007-09); A. Sazonov : post-doc (2010) G. Dhalenne and C. Decorse (single crystal synthesis) PPHMF7, december 2010

  2. Summary Local susceptibility in pyrochlores : the precursor effects • Crystal field: Ising vs. XY behavior • exchange interactions : Mean Field approach Field induced ground states with H//110 • Tb2Ti2O7: (AF, axial): spin ice versus spin flip structures. • Er2Ti2O7 (AF, planar): through a quantum critical point.

  3. R2Ti2O7 pyrochlores: the ground states c c Tb2Ti2O7 Ho2Ti2O7 Spin liquid or quantum spin ice ? The key points: R-R interactions J (F or AF) R anisotropy D (axial or planar) Spin ice • The study: • field induced paramagnetic states • low temperature ground states H//110 : (Tb, Er) by single crystal neutron diffraction Er2Ti2O7 Yb2Ti2O7 F short range order ? Planar AF

  4. Tb2Ti2O7:ground state at H=0 • Non Kramers ion, J=6 • Ising-like : low energy crystal field levels (18K) • M. J. P. Gingras et al PRB 62, 6501 (2000); I.Mirebeau, P. Bonville, M. Hennion PRB 76, 184436 (2007) • Spin liquid Ground state J. Gardner PRL 82, 1012, (1999) • Quantum spin ice Molavian, GinGras , Canals PRL 98, 157204 (2001). • No Long Range Order and fluctuating spins • LRO induced by H and/or P • I.Mirebeau et al Nature 420, 54,(2002), PRL 93, 187204 (2004); KC Rule et al PRL 96, 177201 (2006)

  5. Magnetization in pyrochlores: what is behind? Yasui et al. JPSJ 71, 599 (2002) R anisotropy Zeeman H • R-R interactions • superexchange • dipole-dipole H

  6. Oz H 111 M Tb Local anisotropy in pyrochlores The local symmetry is axial (R-3m) 111 is a privileged axis (hard or easy) The experiment Molecular field approach CF anisotropy 0 Exchange  = Single crystal polarized neutron diffraction LRO structures induced by H in the paramagnetic state measure Inelastic neutron scattering Crystal field scheme measure 0 • for small  • general case : Self consistent calculation  :exchange tensor

  7. Local susceptibility in Tb2Ti2O7 Cao et al, PRL 103, 056402 (2009) Crystal field only CF +Hmol J=6 AF, Ising l //= -0.05 (1) T/µB l= -1.0(2) T/µB The exchange tensor is AF and anisotropic

  8. Origin of the anisotropic exchange ? Local susceptibility (trigonal symmetry) Anisotropic exchange tensor  (in molecular field approximation) • Where does it come from ? • 2 super-exchange paths • Dipolar interactions • Distortion? Consequences on the GS. Crystal field scheme+  tensor Field induced ground states …and compare to experiment

  9. field induced ground states Single crystal Neutron diffraction • Hot neutrons (0.8A) • many Bragg peaks (~300) for each data set • Small extinction and absorption corrections • Lifting arm • in and out of the scattering plane • Single counter • accurate integration of the intensities, • same efficiency for all Bragg reflections • cryostat +dilution inset Tmin~0.03K • Superconductive coil 0<H<7T or 12T • Goniometer head • adjusts small misalignment • (measure at 1.5K) spectrometers 6T2 @LLB and D23 @ILL H//110 Axis Refine magnetic structures (Fullprof, CHILSQ) using Symmetry analysis (BasIreps) few parameters ( 4-6 with S. A, 12 when unconstrained)

  10. Magnetic Field along 110 in R2Ti2O7 The pyrochlore lattice splits into 2 subsytems: H αchains βchains Oz: local anisotropy <111> axis αchains: //H α moments: βchainsH βmoments (Oz, H) =36 deg (Oz, H) = 90°

  11. Tb2Ti2O7 spin liquid under H//110 -chain -chain Tb: Oz is easyaxis 2 sets of moments 2 sets of Bragg peaks fcc lattice (200, 111,113,) K=0 (canted ferromagnetic) cubic lattice (211,..) N± K with K=(0,01) AF order stabilized only For H>2T, T<2K α –moments -moments ? I.Mirebeau, P. Bonville, M. Hennion PRB 76, 184436 (2007) Not so simple!

  12. Tb2Ti2O7 H «  close to » 110 Bragg peak intensities fcc lattice F-like Simple cubic AF-like T=1.6 K, H=7T  • K=(0,0,1) order is stabilized : • Below 2K for H>2T • only for H very close to 110 A. Sazonov et al PRB 82, 174406 (2010)

  13. Tb2Ti2O7 H «  close to » 110 Phase diagram depends on the misorientation! H(T) Measurements up to 12T and down to 30 mK A. Sazonov et al PRB 82, 174406 (2010)

  14. Tb2Ti2O7 Low field (K=0) magnetic structures well aligned misaligned MF calculation

  15. well aligned misaligned  H (small) -moments flip on H axis (Larger) -moments gradually reorient throughspin-icelike local structures A. Sazonov et al PRB 82, 174406 (2010) H Sazonov et al PRB 82, 174406 (2010) H. Cao PRL 101, 196402 (2008)

  16. Tb2Ti2O7 Low field magnetic structures α –moments -moments MF calculation H/H Tuning of the -moments by the misalignment Symmetry analysis in I41/amd SG. H Hc~1.5T Same irreducible representation whatever  no phase transition -moments flip by « melting » on the H axis ! Perfect agreement with MF calculation flipping field : measure of the anisotropic exchange Sazonov et al PRB 82, 174406 (2010)

  17. High field magnetic structure H=7 T Tb2Ti2O7 this work Yasui et al JPSJ (2002) Ho2Ti2O7 Spin ice • Sazonov et al • submitted to JPCM (nov 2010)

  18. Tb2Ti2O7 Summary H//110 Strong sensitivity of the microscopic order to  Tuning the AF order and -moments values • Original magnetic orders • Spin ice structures  ~2-4° • « Spin flip » or « spin melting» structures  <=1° • Hc=1 T : paramagnetic -moments : EH ~Eex • well understood: • anisotropic susceptibility (high T) • MF self consistent approach spin melting not seen in M(H) but consistent with it

  19. From weak AXIAL anisotropy Tb2Ti2O7 <111> easy axis to weak PLANAR anisotropy Er2Ti2O7 • « Weak » : • GS and ES crystal field doublets • with low energy splitting • D=17K (Tb), 75K (Er) • c // and c  both active D (111) easy plane AF (effective) R-R exchange in both cases

  20. Er2Ti2O7 ground state at H=0 Er J=15/2 AF, XY l //= -0.15 (1) T/µB l= -0.45(5) T/µB • Kramers ion • Weak planar anisotropy  >// • gap GS and ES doublets = 6.3 mev or 75 K • strong reduction of the moment by the crystal field (M=3.4µB <<free ion value 9µB • AF interactions : • anisotropic exchange (II > I//I) • planar , ordered AF Ground state at H=0 • K=0 (cubic unit cell) • First order transition TAF=1.2K • 5 2 state : moments along 211 axes • Selected by order by disorderprocess Champion et al. PRB(2003) Poole et al. JPCM(2007) Mc Clarty et al J.Phys. (2009) M=3.5µB: agreeswith CF

  21. Er2Ti2O7 with H//110 as before.. Oz: local anisotropy <111> axis αchains: //H α moments: βchainsH βmoments (Oz, H) =36 deg (Oz, H) = 90° Er: Oz is a hardaxis But now: 2 state at H=0 α and β moments along 211 axes Under applied field α1 -moment flips at Hc  moments rotate in their easy plane How does this flip occur? crossing a (quantum) critical point… Previous field study J.Ruff et al.PRL (2008)

  22. Er2Ti2O7 field induced ground state • single crystal neutron diffraction @ 6T2 (LLB) • T=0.3K • H 0- 6T • Hot neutrons (~300 Bragg) • Out of plane reflections Hc~2T: critical point H <0.5T : single domain refinements of the moments values and angles (Fullprof) b a1 a2 H = 0 1.5 T Hc~2 T 6 T H // [110] H.Cao et al PRB 82, 104431 (2010)

  23. Er2Ti2O7: crossing the critical point MF calculation minimum of all moment values flip of the α1moment at Hc~2T E (Zeeman) ~E (exchange) • all moments along H

  24. Er2Ti2O7 Asymptotic behavior β-moments along H α- moments at an intermediate direction symmetric vs. H

  25. Other consequences of the model • 2 order at H=0 (P. Bonville) • Temperature variation of the α1 moment :TN • critical field Hc where TN=0 : Hc=1.85 T • specific heat cP(T) • Field variation of the CF energy level • ( data of Ruff (2009) • Paramagnetic susceptibility H<Hc H>Hc

  26. Er2Ti2O7 with H//110 : Is it really a QCP? • Close to classical • H=0 2 state + CF reduction: M~3.5µB • 0<H<Hc single domain • H=Hc EZeeman ~Eexchange • H>Hc field induced F but original ! • at Hc • minimum of the moment values • all moments //H • strong fluctuations : spin waves softening? • (Ruff PRL 101, 147205, 2008) • No true level crossing at Hc • degeneracy of the GS doublet lifted at Hc (d=0.25 meV) • real mixing with ES (D=7meV) would require H~20-30T softening of the 7 meV mode connected with the minimum of the moment values?

  27. Summary • Original behavior of R2Ti2O7 pyrochlores in applied field (H//110) • in Tb2Ti2O7 spin liquid : Spin melting Hc~1.5T • in Er2Ti2O7 planar AF : Spin flip Hc~2T well described by single crystal neutron diffraction Short , lifting arm and symmetry analysisare important R =NBragg / Nparams~300/6 ~ 50 for each (T, H,  ) set • provides stringent tests of the microscopic interactions • Crystal field • anisotropic exchange

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