Probing magnons with X-rays

1. Probing magnons with X-rays Luuk Ament In collaboration with Fiona Forte & Jeroen van den Brink Lorentz-Institute, Leiden University

2. Indirect RIXS Synchrotron radiation Interestingsample 4p wres (5-10 keV) 1s

3. Why RIXS? • Second order process • Momentum dependence • Supplementary to neutron scattering

4. La2CuO4 • Perovskite layers of CuO2:

5. La2CuO4 • Perovskite layers of CuO2: • Cu 3d eg holes behave as Heisenberg spins: • Ground state is antiferromagnetically ordered

6. La2CuO4 • Perovskite layers of CuO2: • Cu 3d eg holes behave as Heisenberg spins: • Ground state is antiferromagnetically ordered • Collective excitations: magnons

7. What happens in RIXS? • Actually, the Heisenberg model can be derived from a Hubbard model in the limit U >> t with J = 2t2/U • The 1s core-hole creates a potential which effectively changes U, and therefore J.

8. What happens in RIXS? • Actually, the Heisenberg model can be derived from a Hubbard model in the limit U >> t with J = 2t2/U • The 1s core-hole creates a potential which effectively changes U, and therefore J.

9. Calculation • Kramers-Heisenberg relation gives the cross section:

10. Calculation • Kramers-Heisenberg relation gives the cross section: • Approximate  >> En

11. Calculation • Kramers-Heisenberg relation gives the cross section: • Approximate  >> En • Hamiltonians conserve Sz: only 2-magnon processes!

12. Results • Good agreement with recent experiments by John Hill et al. at Argonne: • Vanishing intensity at q = (0,0) and q = (,) • Peak in intensity at q = (,0) and  = 500 meV Theory Theory + experimental resolution