3. Backgrounds Fert et al, Nature Nanotech. (2013) Tokunaga et al, Arxiv (2015)

4. Backgrounds

5. Holstein & Primakoff Phys. Rev. (1940) Holstein-Primakoff boson approach NLσM Zeeman DM Nagaosa & Tokura Nature Nanotech. (2013)

6. Rotating frame scheme Holstein-Primakoff boson approach Vector potential emerges! NLσM Zeeman DM

7. Hamiltonian for the Holstein-Primakoff boson Holstein-Primakoff boson approach

8. Heisenberg equation for HP bosons Holstein-Primakoff boson approach Non-Abelian vector potential (a 1, a 2, a 3 ) emerges Effective magnetic field

9. One sets the background spin configuration to be a Skyrmion to explore magnon-Skyrmion scattering Magnon-Skyrmion scattering Han et al, PRB (2010) R:Skyrmion radius Different from the previous research ! Iwasaki et al, PRB (2014)

10. One sets the background spin configuration to be a Skyrmion to explore magnon-Skyrmion scattering Magnon-Skyrmion scattering κR<1κR=1κR>1 Scattering angle is changed as “κR” crosses the threshold value 1

11. LLG simulations to confirm the HP theory Magnon-Skyrmion scattering We observed that the scattering angle has tendency to change the direction as “κR” increases Skyrmion radius dependence of magnon Hall effect is possible κR=0.9 κR=1.5κR=2 LLG equation

12. We establish the HP boson theory for “NLσM”+“DM”+“Zeeman” term We investigated the nature of magnon-Skyrmion scattering; scattering angle varies by “κR” crossing the threshold value “1” Numerical simulations support our results