Transcript Probing magnons with X-rays

Probing magnons with X-rays
Luuk Ament
In collaboration with Fiona Forte & Jeroen van den Brink
Lorentz-Institute, Leiden University
Indirect RIXS
Synchrotron radiation
Interesting
sample
4p
wres (5-10 keV)
1s
Why RIXS?
• Second order process
• Momentum dependence
• Supplementary to neutron scattering
La2CuO4
• Perovskite layers of CuO2:
La2CuO4
• Perovskite layers of CuO2:
• Cu 3d eg holes behave as Heisenberg spins:
• Ground state is antiferromagnetically ordered
La2CuO4
• Perovskite layers of CuO2:
• Cu 3d eg holes behave as Heisenberg spins:
• Ground state is antiferromagnetically ordered
• Collective excitations: magnons
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.
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.
Calculation
• Kramers-Heisenberg relation gives the cross section:
Calculation
• Kramers-Heisenberg relation gives the cross section:
• Approximate  >> En
Calculation
• Kramers-Heisenberg relation gives the cross section:
• Approximate  >> En
• Hamiltonians conserve Sz: only 2-magnon processes!
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