1. Martin Lees Magnetic ordering in Ca 3 Co 2 O 6 Introduction: Why is Ca 3 Co 2 O 6 interesting? Zero field magnetic order and ordering in high field: Magnetization and heat capacity Resonant x-ray scattering Neutron diffraction Summary

2. A 3 MBO 6 A = Ca, Sr, Ba & M, B =..Mg 2+.. Co 2+, Co 3+,Co 4+.. Pt 4+ [Stitzer et al., Current Opinion in Solid State and Materials Science 5, 535 (2001). ] Ca 3 Co 2 O 6 Why is Ca 3 Co 2 O 6 interesting? Magnetism Geometrical Frustration Low Dimensionality Pyrochlore lattice Kagomé lattice + ☺ AFM ? ☺ AFM × Triangular lattice

3. Why is Ca 3 Co 2 O 6 interesting? CoO 6 trigonal prisms Co 3+ 3d 6 CEF=> high spin : S=2 MO 6 BO 6 CoO 6 octahedra Co 3+ 3d 6 CEF=> low spin S=0 s  2.6 Å A=Ca d  5.2 Å Chains that run along the c axis of the hexagonal cell

4. Ca 3 Co 2 O 6 J > 0 Ferromagnetic intrachain coupling AntiFerro Interchain Coupling 1 D + Frustration J’ < 0 _ + c ? c Very strong Ising-like anisotropy J FM(~ +15 K) J’ AFM(~ -0.2 K)  J    J’  Magnetic order below 25 K

5. Why is Ca 3 Co 2 O 6 interesting? S=0 S=2 S=0 S=2 S=0 Ca 3 Co 2 O 6 can be described as a model system of a triangular antiferromagnetic net of Ising ferromagnetic chains

6. Why is Ca 3 Co 2 O 6 interesting? Ca 3 Co 2 O 6 has been described as a model system of a triangular antiferromagnetic net of Ising ferromagnetic chains For T <8 K several irreversible steps in the high field magnetization data

8. Questions What is the nature of the magnetic ground state in zero field? What is the mechanism that produces the unusual step-like behaviour in the magnetization at low temperature? We have addressed these two questions and how the magnetization behaviour is related to the dynamics of the magnetic structure in this situation of geometrical frustration and low-dimensionality. We have used Laboratory Techniques, Neutron Diffraction, and Resonant X-ray Scattering.

9. Materials and methods High quality single crystals of Ca 3 Co 2 O 6 have been grown using the flux method. These are the biggest crystals of Ca 3 Co 2 O 6 ever grown. The ordering process has been characterized by measurements of magnetic susceptibility and magnetization (SQUID and vibrating sample magnetometers) and specific heat under applied magnetic field. Neutron diffraction measurements were carried out using a number of instruments including the PRISMA and SXD time-of-flight diffractometers and the GEM powder diffractometer at the ISIS pulsed neutron source. The X-ray Resonant Scattering measurements were made on the ID20 beamline of the European Synchrotron Radiation Facility (ESRF), Grenoble. 5 mm

10. Questions What is the nature of the magnetic ground state in zero field? What is the mechanism that produces the unusual step-like behaviour in the magnetization at low temperature? –2D Ising model –QTM We have addressed these two questions and how the magnetization behaviour is related to the dynamics of the magnetic structure in this situation of geometrical frustration and low-dimensionality. For this purpose we have used Laboratory Techniques, Neutron Diffraction, and Resonant X-ray Scattering.

11. Ferri Ferro HcHc V. Hardy et al. PRB 70, 064424 (2004). 4.8 /f.u. 2.3 B g   =

12. Hypothesis: The co-existence of several degenerate spin chain configurations 2D Ising model X. Yao et al. PRB 74, 134421 (2006). Y.B. Kudasov, Phys. Rev Lett. 96, 27212 (2006). Requirements: Rigid spin units along the chains and short magnetic correlation length in the ab plane.

13. Quantum Tunnelling of Magnetization (QTM) Hypothesis: Formation of intrachain finite spin units with S~2, 4 and 6 with degenerate g.s. separated by a potential barrier. The external field shifts the spin levels. At certain fields, levels on both sides of the barrier are degenerate. In this situation, magnetic moment can tunnel from one side to the other. Requirement: Short magnetic correlation length along the c-axis. A. Maignan et al., J. Mater. Chem. 14, 1231 (2004). V. Hardy et al. PRB 70, 214439 (2004).

14. Questions What is the nature of the magnetic ground state in zero field? What is the mechanism that produces the unusual step-like behaviour in the magnetization at low temperature? –2D Ising model –QTM ? We have addressed these two questions and how the magnetization behaviour is related to the dynamics of the magnetic structure in this situation of geometrical frustration and low-dimensionality. For this purpose we have used Laboratory Techniques, Neutron Diffraction, and Resonant X-ray Scattering.

15. LRO at T=25 K Ca 3 Co 2 O 6 V Hardy et al. PRB 68, 014424 (2003) Mass correction Ca 3 CaPtO 6 Pt 4+ (3d 6 ) octahedral site low-spin state S=0 C 0.05% Pt 4+ HS or 0.15% Pt 4+ IS Non-magnetic isostructural compound Lattice contribution to C Debye, Stout and Catalano  =  0 +C/T

16. De Jongh and Miedema Advances in Physics 50, 947 (2001). Broad peak: 1D Ising Ferro S=2

17. LRO at T=25 K Ca 3 Co 2 O 6 V Hardy et al. PRB 68, 014424 (2003) Mass correction Ca 3 CaPtO 6 Pt 4+ (3d 6 ) octahedral site low-spin state S=0 C 0.05% Pt 4+ HS or 0.15% Pt 4+ IS Non-magnetic isostructural compound Lattice contribution to C Debye, Stout and Catalano  =  0 +C/T

18. Upturn in M at 25 K. Magnitude of the signal is TIME dependent between 8 and 15 K. Below 8 K the systems enters a spin frozen state.

19. Neutron diffraction O.A. Petrenko et al. Eur Phys J. B 47, 79 (2005). PRISMA and SXD - ISIS 2 -15 mg single crystal GEM - ISIS powder

20. Neutron diffraction The transition to a magnetically ordered phase is accompanied by the appearance below 25 K of antiferromagnetic (AFM) Bragg peaks such as (100), (200), and (120). No peaks were found with non-integer indices – all peaks can be indexed using the trigonal unit cell. This means that the magnetic structure can be adequately described by considering only the three spins at the corners of a triangle. ?

21. Neutron diffraction Ferrimagnetic ordering (M, M, -M); Ferromagnetic component. Two different magnetic structures have been considered: No variations in the integrated intensities of the nuclear reflections, which excludes the onset of a ferrimagnetic ordering. Intensity versus temperature => not a “simple” PDA structure. Partially disordered antiferromagnetic state (M, 0, -M); NO FM component.

22. Single crystal neutron diffraction Refined value for the magnetic moment of the CoII at zero field: 5.0 and 4.4 ± 0.1 μ B for T = 20 and 4 K respectively. Magnetic dichroism (5.2 ± 0.1 μ B ) and magnetization at high field (4.7 ± 0.1 μ B ) Neutron data suggest: at T = 20 K the occurrence of the PDA ordering with CoII in a HS state. at T = 2 K the presence of the PDA ordering with a reduced moment

23. The width of the lattice reflections for all the investigated peaks was below 0.03 degrees underlining the excellent quality of the sample. In the magnetically ordered phase (T < T N = 25 K) new reflections appear in the  channel, while no intensity was observed in the  channel, which strengthens the conclusion drawn from the neutron data that the moments point along the c-axis. Resonant X-ray Scattering ID 20, ESRF Co K-edge

24. Temperature evolution of the (3 2 0) magnetic reflection (closed symbols) and (3 3 0) charge reflection (open symbols) As the T is reduced the magnetic peaks exhibit: a shift in L position of the magnetic peak. a reduction of the integrated intensity at low T a decrease in the correlation length along both the L and H- direction. Resonant X-ray Scattering S. Agrestini et al. PRB Rapid Comm. in press (2008).

25. Apart from a scaling factor the two spectra are indistinguishable => NO spin state transition Resonant X-ray Scattering S. Agrestini et al. PRB Rapid Comm. in press (2008). Photon energy dependence around the Co K absorption edge.

26. Single crystal neutron diffraction Temperature evolution of the (1 0 0) reflection. A broad contribution appears at low T superimposed on the narrower feature.

27. Summary Our results suggest that: –short range in-chain correlations above T N (HC & M)) –long range order at 25 K (HC & M)) –at T = 20 K the zero field magnetic structure is PDA (ND) We have investigated the magnetic structure of the geometrical frustrated Ising spin system Ca 3 Co 2 O 6 by : –Heat Capacity and Magnetization –Neutron Diffraction –Resonant X-ray Scattering

28. Summary The results suggest that: –The PDA structure at T=20 K is a highly correlated system of spins both along the FM chains (5000 Å) and in the hexagonal planes (2500 Å) (RXS) –The PDA structure is modulated along the c-axis (RXS & ND)

29. Possible interpretation Magnetic super-super-exchange interactions in Ca 3 Co 2 O 6 : J1 (black lines) FM J2 (red lines) AF J3 (blue lines) AF. A sinusoidal modulation of the PDA structure

30. Summary The results suggest that: –The PDA structure at T=20 K is a highly correlated system of spins both along the FM chains (5000 Å) and in the hexagonal planes (2500 Å) (RXS) –The PDA structure is modulated along the c-axis (RXS & ND) –On cooling the PDA structure becomes increasingly unstable and a phase separation develops, where long range PDA structure coexists with a shorter range order (ND) A further investigation of the evolution of the short range phase as a function of magnetic field is necessary in order to understand how the phase separation is related with the step-like behaviour in the magnetization

31. Warwick University Stefano Agrestini Oleg Petrenko Geetha Balakrishnan Contributors to this work ISIS, RAL Pascal Manuel Laurent Chapon Diamond Allesandro Bombardi ESRF Claudio Mazzoli CRISMAT, Caen Vincent Hardy Antoine Maignan