1. Origin of Thickness Dependent Spin Reorientation Transition of B2 Type FeCo Alloy Films Dongyoo Kim Applied Materials Physics, Department of Materials Science and Engineering, Royal Institute of Technology, Stockholm, Sweden. Royal Institute of Technology, Stockholm, Sweden.

2. K U = 700 ~ 800 µeV/atom M S = 2.1 µ B /atom Chemical composition : 0.55 ≤ x ≤ 0.65 Tetragonal distortion : 1.2 ≤ c/a ≤ 1.25

3. about 15 MLs SRT at 15 ML

5. Giant MCA Energy Tetragonal distortion Chemical Composition To account SRT of FeCo films at 15 ML  We have considered film structures. MCA of bulk FeCo cannot explain SRT of FeCo at 15 ML. We calculated FeCo film with coverage of 6, 8, 10, 12, 14, and 16 ML thickness

6. FLAPW method (Full potential linearized augmented plane wave) Exchange correlation potential : GGA Spherical harmonics (l max ) : 8 Energy cut-offs : 225 Ry and 13.7 Ry Muffin-tin radius of Fe and Co atoms : 2.2 a.u. Lattice Constant: 2.866 Å (experimental value, [PRB, 64, 132102 (2001)] ) K-points: 420 points The optimized atomic structure in vertical direction  Force and total energy minimization procedure.

7. Calculated interlayer distance (in Å) Thin Thick c/a = 1.07

8. Calculated spin magnetic moment (in µ B ) in MT region.

9. Linearly increasing M s

10. E MCA = E // – E ㅗ EㅗEㅗEㅗEㅗ E // MAE = E MCA - E Sh

11. About 15 ML E MCA = E // – E ㅗ Positive value: Perpendicular MCA Negative value: in-plane MCA E sh = ½ µ 0 M s 2 E MCA = Torque method [1] [1] X. D. Wang, R. Q. Wu, D. S. Wang, A. J. Freeman, Phys, Rev, B 54, 61 (1996)

12. EㅗEㅗEㅗEㅗ E // K = K V + 2K S /d K V : Volume contributions K S : Surface contributions d : Film thickness [J. Hong, et. al, PRL, 92, 147202 (2004)]

13. K v = 67.04 µeV/atom K s = 594.7 µeV/atom K v = 142.42 µeV/atom K s = 132.61 µeV/atom ~ 90 ML = K = K V + 2K S /d 15 ML Average E sh

14. [FeCo(3ML) /Pt(7ML)] 23

15. K v = 142.42 µeV/atom K s = 132.61 µeV/atom Cal: E MCA = 227.82 µeV/atom at FeCo(3ML) Exp: E MCA = (208±14) µeV/atom at FeCo(3ML) K = K V + 2K S /d

16. We have investigated the thickness dependent magnetic anisotropy of B2 FeCo Films. FeCo films show perpendicular MCA, but MCA energy rapidly decrease as the film thickness increase. The crossover of shape and MCA energies occurs at approximately 15 ML thickness.  This agrees well with many experimental observations. The competition of shape and MCA energies can nicely account for universal behavior of thickness dependent SRT of FeCo alloy films