Transcript ppt - Instituut-Lorentz

Probing magnons with X-rays
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
Kramers-Heisenberg relation:
Synchrotron radiation
Energy conservation
Unoccupied
valence level
Momentum
transfer q &
Energy loss 
4p
Dipole operator
with
wres (5-10 KeV)
Detuning from
resonance
1s
Core level
Intermediate states
Core-hole exists a
short 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!
Magnetic RIXS on La2CuO4
initial
intermediate
final
4p
4p
4p
3d
3d
3d
1s
1s
1s
Theory applied to La2CuO4
La2CuO4: 3d electrons on Cu form Mott-Hubbard insulator 
effective Heisenberg Hamiltonian:
3d electrons
Core hole
qin , win
Core-hole
qout , wout  qin, win
Core-hole modifies superexchange interaction Jij
J modified by
core-hole potential
Elementary excitations are magnons.
Conservation of Sz  only 2-magnon processes allowed!
Results
Theoretical predictions
 > En: we can resum Afi and retain the leading order term in J’/:
Experiment
Theory
Theory + exp. resolution
a 4-spin correlation function! We used linear spin-wave theory
to obtain the spectra.
Conclusions & Outlook
We established a general procedure to find indirect RIXS
spectra. Application to La2CuO4 shows:
1.
Only
2-magnon
processes
allowed
2.
Quantitative
agreement
with
experiments
3. RIXS complements neutron scattering (2-spin correlation
functions)
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!
The next step will be to apply this theory to other elementary
excitations like orbital waves.
1Unpublished
2Coldea
et al. Phys. Rev. Lett. 86, 5377 (2001)