1. M.Czapkiewicz Department of Electronics, AGH University of Science and Technology, POLAND Calculations of interplay between anizotropy and coupling energy in magnetic multilayers systems

2. Schedule one-domain S-W model MAGEN2 - program for simulation of magnetization process of multilayers systems examples of calculations and experiments –PSV –SV –Biased FP –TMR SV –SV AAF To-do tasks

3. Definitions Magnetization: monolayer bilayer AMR (ML) GMR (BL) Task to compute: how  depend on H ?

4. Stoner-Wohlfarth model Surface energy density (example for 2 layers with planar UA anisotropy): where Numerical gradient seeking of local minimum for each H field

5. Program interface Input: –Saturation magnetization –Effective anisotropy energy –Anisotropy axis definition –Interlayer coupling energy –Field range Output: –  angles for each layer –Total magnetization M(H) –Total energy –To do: GMR, TMR…

6. 1.example – PSV-type bilayer Measured example: Py 2.8nm /Co 2.1nm /Cu 2nm /Co 3nm Fit for: K u1 /K u2 = 31 GMR only in non-parallel state

7. Influence of ferromagnetic coupling on PSV switching AF-state only if J FF weak

8. 2. example – SV with AF layer Measured sample: Co 4.4nm /Cu 2.3nm /Co 4.4nm /FeMn 10nm exchange coupling energy J FP-FF = 7.9  10 -6 J/m 2 interface coupling energy J EB = 94  10 -6 J/m 2 anisotropy energy K FF = 580 J/m 3, effective AF anizotropy K AF = 80·10 3 J/m 3

9. Influence of FP-FF ferromagnetic coupling on GMR of SV structure Analytical simulation for

10. 3. Influence of effective anisotropy of AF layer on SV biased field Energy density model of AF-FP system: M.Tsunoda model: ordering of AF layer grains (during deposition for top-type SV or during field cooling for bottom-type SV) lead to increase total eff. anisotropy

11. Example of AF-FP system (after f.c.) Courtesy of Prof. C.G. Kim Chungnam University RECAMM, Taejon, Korea MnIr – 100Å CoFe – 25 Å Si/Ta 5nm /Cu 10nm /Ta 5nm /NiFe 2nm /Cu 5nm /MnIr 10nm /CoFe 2,5nm annealed: 200 o C/1h, field cooling 1kOe fit for: J EB = 200  10 -6 J/m 2, K AF = 40000 J/m 3.

12. 4. Influence of K AF to J EB ratio of FF/S/FF/AF structure on M(H) switching

13. Dependence of H EB on K AF

14. 4. MTJ example Fit for: anizotropy energy of FF layer K 1 = 210 J/m 3,  0 M s1 = 0.85 T, exchange coupling energy FF-FP J 12 = 1.04  10 -6 J/m 2 (FF). effective anizotropy energy of FP layer K 2 = 95000 J/m 3,  0 M s2 = 1.5 T, interface coupling energy FP-AF J EB = 470  10 -6 J/m 2. effective anizotropy energy of AF layer K AF = 50000 J/m 3 Buffer:Si/Ta 5nm /Cu 10nm /Ta 5nm /Ni 80 Fe 20 2nm /Cu 5nm AF layer: Ir 25 Mn 75 ( 10nm), FP layer Co 70 Fe 30 ( 2.5nm), isolator spacer and FF layer AlO x (1.5nm) /Co 70 Fe 30 (2.5nm) /Ni 80 Fe 20 (10nm)

15. 5. SV with Artificial AF – before annealing AFF-SV: AF/FP1/S1/FP2/S2/FF Example: Si(111)/Ta 10.5nm /PtMn 19.8nm / CoFe 2nm /Ru 0.77nm /CoFe 2nm / Cu 2.2nm /CoFe 0.8nm /NiFe 3.8nm / Ta 5nm /Cu 0.5nm

16. “To do” list for MAGEN2 program bugs fixing experimental data in background more layers 3D axis of anisotropy and field definition animation of magnetisation vector of each ferromagnetic layer during simulation process GMR/TMR characteristics

17. END

18. S-W model for monolayer Total energy E = E H + E U + E D Zeeman energy Anisotropy energy Demagnetizing energy Field in plane (N x =N y  0, N z  1):

19. 4. Example of Magnetic Tunneling Junction Substrate Si (100) Ta – 50 Å Cu – 100 Å Ta – 50 Å NiFe – 20 Å Cu – 50 Å MnIr – 100Å CoFe – 25 Å Al 2 O 3 – 15 Å CoFe – 25 Å NiFe – 100 Å Ta – 50Å Energy density model: