Superconductivity with T c up to 4.5 K

3d 6 3d 5 Crystal field splitting Low-spin state:

Co 3+ Co 4+ x=0.82

Muon Spin Rotation establishes: - bulk magnetic order - commensurate order (guess A-type AF) -the moment is about 0.3  B. Meanwhile confirmed by neutrons: S. Bayrakci et al, PRL 94, (2005); L.M. Helme et al., PRL 94, (2005).

Ist not likely to be a spin density wave (SDW) state ! -Strictly commensurate magnetic order. - Nearly doping independent transition temperature -Almost isotropic exchange coupling despite of large FS anisotropy. μSR S. Bayrakci et al., Phys. Rev. B 69, (2004), P. Mendels et al., Phys. Rev. Lett. 94, (2005). Neutrons S. Bayrakci et al., Phys. Rev. Lett. 94, (2005) L.M. Helme et al., Phys. Rev. Lett. 94, (2005)

Idea of Giniyat Khaliullin: Hole doping induced Co spin-state transition.

Reduced Symmetry

May sound like a wear idea but its actually realized in the isoelectronic compound La 1-x Sr x CoO 3 New buzz-word “Spin-state degree of freedom”

>Antiferromagnetic clusters with small total spin of S=1/2. > Strong geometrical frustration! G. Khaliullin, Prog. Theor. Phys. 160, 155 (2005). M. Daghofer, P. Horsch, and HG. Khaliullin, cond-mat/ Important differences to La 1-x Sr x CoO 3

Bulk magnetic x=0.75

LS, S=1/2 IS, x=0.75

Ellipsometry on Na 0.82(2) CoO 2 C. Bernhard et al., PRL 93, (2004).

8066 cm -1 = 1 eV C. Bernhard et al., PRL 93, (2004).

Co 3+ Co 4+ x=0.97

Muon Spin Rotation (  SR) on Na 0.97 CoO 2

μSR data on Na 0.97 CoO 2 establish:  Magnetic volume fraction of  40% with sizeable magnetic moments.  Glassy freezing transition around T f  K  Evidence for nanoscopic clusters.

Na-content from EDX and ICPS analysis Consistent with c-axis parameters from x-ray Q. Huang et al., Phys. Rev. B 70, (2004). Chemical phase separation due to segregation of Na vacancies? C. de Vaulx et al., Phys. Rev. Lett. 95, (2005); G. Lang et al., Phys. Rev. B 72, (2005). We investigated two growth batches with x= one is pure  -phase - other has a minor phase with lower Na content  Both give virtually identical μSR results! Chemical segregation is NOT the primary mechanism!

Optics shows that the x=0.97 sample is on the verge of percolation ! Consistent with 40% volume fraction from μSR

Na 0.97 CoO 2

dc-suszeptibility  small moment of J  1/2 per cluster.

Evolution with hole doping, 1-x.

Evolution of magnetic signal with hole doping, 1-x

x=0.75

Na 0.78 CoO 2 ; T N =22 K

Evidence for geometrical frustration from μSR data at T>T N,T f Very fast spin fluctuations for bulk magnetic state at x=0.78 (  T N ) Very slow spin fluctuations for nanoscopic clusters at x=0.97 (  >10-9 s up to 250 K>>T f =20 K)

Inconsistent with chemical phase separation since fluctuations should be enhanced for finite size clusters! Evidence for frustrated magnetic interaction in ordered state!  SST model gives a Kagome lattice geometry. Degeneracy is lifted for isolated clusters. - Disorder due to interaction with Na vacancies. - Single, double and triple hole clusters. - Weak dipolar interaction between clusters.

Remember this is just a naive model that neglects all additional complexities of Na x CoO 2 ! The IS Co 3+ ions (S=1) form a Kagome lattice with geometrical frustration and thus strong fluctuations. The amplitude of the charge modulation may be smaller. Charge order may not be static.

This is the end of the talk but not the end of the story !