Probing magnons with X-rays

Kramers-Heisenberg relation:

Energy conservation

Dipole operator

Intermediate states

with

Detuning fromresonance

Core-hole exists ashort time: ≈ 2-3 eV

Core-hole creates local potential from which electrons of the solid are scattered. System can be left behind in excited state. One measures elementary excitations of the solid!

3d electrons

J modified bycore-hole potential

Core hole

Conclusions & Outlook

F. Forte, L.J.P. Ament, J. van den Brink

Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

Indirect RIXS

Theory

Synchrotron radiation

Momentum transfer q & Energy loss

Unoccupied valence level

4p

wres (5-10 KeV)

1s

Core level

Magnetic RIXS on La2CuO4

Theory applied to La2CuO4

La2CuO4: 3d electrons on Cu form Mott-Hubbard insulator effective Heisenberg Hamiltonian:

initial

intermediate

final

4p

4p

4p

3d

3d

3d

1s

1s

1s

Core-hole

qin , win

qout , wout qin, win

Elementary excitations are magnons.

Conservation of Sz only 2-magnon processes allowed!

Core-hole modifies superexchange interaction Jij

Results

Theoretical predictions

> En: we can resum Afi and retain the leading order term in J’/:

ExperimentTheoryTheory + exp. resolution

a 4-spin correlation function! We used linear spin-wave theory to obtain the spectra.

We established a general procedure to find indirect RIXS spectra. Application to La2CuO4 shows:

1. Only 2-magnon processes allowed2. Quantitative agreement with experiments3. RIXS complements neutron scattering (2-spin correlation functions)

The next step will be to apply this theory to other elementary excitations like orbital waves.

At q = (0,0) there is no energy loss: RIXS intensity = 0.

Experiments: J.P. Hill et al.1,magnetic parameters from neutron scattering2.

No free magnetic parameters!

1Unpublished

2Coldea et al. Phys. Rev. Lett. 86, 5377 (2001)