1. Coherently photo-induced ferromagnetism in diluted magnetic semiconductors J. Fernandez-Rossier ( University of Alicante, UT ), C. Piermarocchi (MS), P. Chen ( UCB ), L. J. Sham (UCSD), A.H. MacDonald (UT) Paramagnetic semiconductor (II,Mn)VI can become ferromagnetic when illuminated by coherent unpolarized light of frequency below the semiconductor band-gap.

2. EGEG EFEF Properties of the Diluted paramagnetic (II (1-x),Mn x )-VI (II (1-x),Mn x )-VI (Zn (1-x),Mn x )-Se (Zn (1-x),Mn x )-S (Cd (1-x),Mn x )-Te Mn-Mn interaction: only first neighbors. For x=0.012 0.002 coupled to nn (2%) 0.01 is free (80%) -  PARAMAGNET If doped with holes, FERROMAGNET at Tc<2 Kelvin

3. Laser features: Frequency below gap:  =E G -  L >0 No Photocarriers, no doping Intensity (  =d cv E 0 >0.1 meV) Polarization state: not relevant Coherently photo-induced ferromagnetism

4. This prediction is a logical consequence of: Experimentally established facts Theoretical concepts in agreement with experiments

5. =0 Exchange Interaction. Giant Spin Splitting Selection Rules LL j sd c Mn j pd c Mn B

6. Macroscopic Explanation of optical ferromagnetism Reactive optical energy, due to matter-laser interaction: U depends on : U(M) Ferromagnetism (  0) minimizes U (M) But entropy favours =0 Competition between reactive optical energy and entropy Electric Field of the Laser Real part of retarded Optical Response function

7. Entropic Penalty Paramagnetic Gain (Optical Energy) Functional of Carrier Density Matrix What is the density matrix of the laser driven (II,Mn)-VI semiconductor?

8. Density matrix: effect of the laser LL  Rotating Frame RWA E U (k) E L (k)  >  >(T 1 ) - 1 Coherent Occupation

9. No absorption= No real carriers  eff =  -|J|>0

10. Interaction“Bosonic Model” Laser MatterLinear response (*) h-Mn, e-MnMF VCA Electron-HoleAll orders e-e and h-hIrrelevant (linear response) Microscopic Theory: Relevant Interactions (*) Linear Response: Good if  >  OK, since  >|J|> and |J|>20 meV

11. Microscopic Theory: Bosonic Model

12. 012 M -1.45 -1.44 -1.43 -1.42 G (10 -2 meV nm -3 ) (b) -0.4 -0.2 0 S (10 -2 meV nm -3 ) T=115 mK T=105 mK (a) -2012 M -1.2 U (10 -2 meV nm -3 ) 00.51 T /T C 0 1 2 M  =26 meV, T C =780 mK  =41 meV, T C =114 mK  =71 meV, T C =22 mK Results for (Zn 0.988,Mn 0.012 ) S

13. 1.50 1.00 0.50 Transition Temperature for (Zn 0.988,Mn 0.012 ) S T c  2 T c  -3 Linear response fails there

14. Isothermal transitions for (Zn,Mn) S T=0.5 K Switching ferromagnetism on and off !!!

15. Materials and Lasers Important material properties: Robust Excitons Not much Mn (x=1%) (Zn,Mn)S, (Zn,Mn)Se (Zn,Mn)O ?? Laser properties: Tunable, around material band-gap Intense lasers T c <50 mK with cw laser Pulse duration longer than Switching time Switching time: interesting question !!!!

16. ORKKY vs coherently photo-induced FM j pd  j sd   The SAME than Bosonic Model (*) C. Piermarocchi, P. Chen, L.J. Sham and D. G. Steel PRL89, 167402 (2002)

17. Conclusions New way of making semiconductors ferromagnetic Ferromagnetism mediated by virtual carriers Originated by optical coherence Possible at T>1 Kelvin (with the right laser)

18. Phase Diagram Always absorbing T (  /J) Absorbing FM Coherent PM Always coherent PM FM T=1.5 K T=2.0 K

19. Interaction ‘BCS’ “Bosonic Model” Laser Matter All orders Linear response (*) h-Mn, e-Mn MF VCA Electron-Hole Pairing All orders Mn-Mn AF s-exc x replaced by x eff e-e and h-h Hartree-Fock Irrelevant (linear response) Microscopic Theory: Relevant Interactions * Linear Response: Good if  >  No absorption= No real carriers= Optical Coherence:  eff =  -|J|>0, where

20. Carrier mediated ferromagnetism Entropic Penalty Paramagnetic gain Functional of carrier density matrix What is the density matrix of the laser driven (II,Mn)-VI semiconductor?

21. BC AlSi NO PS GaGe InSn AsSe Sb II Zn Cd Hg IV V III VI Te EGEG EFEF II-VI Zn-Se Zn-S Cd-Te II BC AlSi NO PS GaGe InSn AsSe Sb IV V III VI Te Zn Cd Hg Mn EGEG EFEF Diluted paramagnetic semiconductor (II,Mn)-VI (Zn,Mn)-Se (Zn,Mn)-S (Cd,Mn)-Te Laser features: Frequency below gap:  =E G -  L >0 No Photocarriers Intense (  =d cv E 0 >0.1 meV) Non circularly polarized Coherently photo-induced ferromagnetism

22. II BC AlSi NO PS GaGe InSn AsSe Sb IV V III VI Te Zn Cd Hg Mn