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.
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= coupled to nn (2%) 0.01 is free (80%) - PARAMAGNET If doped with holes, FERROMAGNET at Tc<2 Kelvin
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
This prediction is a logical consequence of: Experimentally established facts Theoretical concepts in agreement with experiments
=0 Exchange Interaction. Giant Spin Splitting Selection Rules LL j sd c Mn j pd c Mn B
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
Entropic Penalty Paramagnetic Gain (Optical Energy) Functional of Carrier Density Matrix What is the density matrix of the laser driven (II,Mn)-VI semiconductor?
Density matrix: effect of the laser LL Rotating Frame RWA E U (k) E L (k) > >(T 1 ) - 1 Coherent Occupation
No absorption= No real carriers eff = -|J|>0
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
Microscopic Theory: Bosonic Model
012 M G (10 -2 meV nm -3 ) (b) S (10 -2 meV nm -3 ) T=115 mK T=105 mK (a) M -1.2 U (10 -2 meV nm -3 ) T /T C 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 ) S
Transition Temperature for (Zn 0.988,Mn ) S T c 2 T c -3 Linear response fails there
Isothermal transitions for (Zn,Mn) S T=0.5 K Switching ferromagnetism on and off !!!
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 !!!!
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, (2002)
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)
Phase Diagram Always absorbing T ( /J) Absorbing FM Coherent PM Always coherent PM FM T=1.5 K T=2.0 K
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
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?
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
II BC AlSi NO PS GaGe InSn AsSe Sb IV V III VI Te Zn Cd Hg Mn