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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. w res (5-10 keV). 1s. Why RIXS?. Second order process Momentum dependence

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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
Indirect RIXS

Synchrotron radiation

Interestingsample

4p

wres (5-10 keV)

1s


Why rixs
Why RIXS?

  • Second order process

  • Momentum dependence

  • Supplementary to neutron scattering


La 2 cuo 4
La2CuO4

  • Perovskite layers of CuO2:


La 2 cuo 41
La2CuO4

  • Perovskite layers of CuO2:

  • Cu 3d eg holes behave as Heisenberg spins:

  • Ground state is antiferromagnetically ordered


La 2 cuo 42
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
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 rixs1
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
Calculation

  • Kramers-Heisenberg relation gives the cross section:


Calculation1
Calculation

  • Kramers-Heisenberg relation gives the cross section:

  • Approximate  >> En


Calculation2
Calculation

  • Kramers-Heisenberg relation gives the cross section:

  • Approximate  >> En

  • Hamiltonians conserve Sz: only 2-magnon processes!


Results
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


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