Multiferroic BiFeO 3. Sang-Wook Cheong. Seongsu Lee. Partially supported by NSF-MRSEC

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1 Multiferroic BiFeO 3 Seongsu Lee Chenglin Zhang YoungJai Choi Seongsu Lee Soonyong Park Y. Horibe Valery Kiryukhin Y. J. Cho L. Balicas Florida SU. X. S. Xu J. Musfeldt U. of Tennessee J. G. Park SKKU Y. S. Oh K. H. Kim SNU Sang-Wook Cheong D. Talbayev Los Alamos NL M. O. Ramirez V. Gopalan Penn State U R. Ramesh UC. Berkely W. Ratcliff Jr. J. W. Lynn NIST Maxim Mostovoy U of Groningen Partially supported by NSF-MRSEC

2 Multiferroics Ferrum(Lat)=iron (Anti)Ferromagnets (M) (Anti)Ferroelastics (ε) (Anti)Ferroelectrics (P)

3 Multiferroics: multiple orientational order Ferrum(Lat)=iron (Anti)Ferromagnets (M) (Anti)Ferrotoroidics (T) (Anti)Ferroorbitics (O) (Anti)Ferroelastics (ε) (Anti)Ferroelectrics (P)

4 Multiferroics: multiple orientational order Ferrum(Lat)=iron (Anti)Ferromagnets (M) (Anti)Ferrotoroidics (T) (Anti)Ferroorbitics (O) (Anti)Ferroelastics (ε) (Anti)Ferroelectrics (P) Charge

5 BiFeO 3 : the only room-temperature and large P multiferroic.

6 BiFeO 3 single crystals: birth in 1957 (P. Royen and K. Swars, Angew. Chem. 24, 779 (1957). BiFeO 3 S. Lee and S-W. Cheong Small BiFeO 3 crystals; available for the last about 50 years!!

7 BiFeO3 Old sample BiFeO 3 : T c (FE) 1050 K T N 643 K M/H (10-3 emu/mole) ρ (012)hex (Ωcm) Temperature (K) H//(012) hex (a) (b) Temperature (K)

8 New magnetic phase transitions in BiFeO 3 Manoj K Singh 1, Ram S Katiyar 1,3 and J F Scott J.Phys.: Condens. Matter 20, (2008).

9 Metal?? Ferroelectric T c

10 P [111] =P [100] /cos(54.7 o )=~86 µc/cm 2 Theory: 95 μc/cm 2 : Neaton, Ederer, Waghmare, Spaldin, & Rabe, PRB 71, (2005)

11 C. L. Jia et al., Nature Materials 2007 Pb(Zr,Ti)O 3

12 C. L. Jia et al., Nature Materials 2007 Pb(Zr,Ti)O 3 p

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15 Ferroelastic/ferroelectric domain walls: 71, 109, and 180 domains [010] [010] [100] [100] [100] 71 Domain wall 109 Domain wall: 180 Domain wall [010] [100] [100] [100] 71 Domain wall: charged! 109 Domain wall: charged! 180 Domain wall: charged!

16 Complex ferroelectric domains in BiFeO 3 films R. Ramesh et al.

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19 [010] [100]

20 [010] [100]

21 BiFeO 3 : Single ferroelectric domains!!!

22 Spin/Lattice coupling F=α 1 E+α 2 H+α 3 EE+α 4 HH+α 5 EH+α 6 EEE + α 7 HHH+α 8 HEE+α 9 EHH+α 10 EEEE α 1 =polarization α 2 =magnetization α 3 =electric χ α 4 =magnetic χ α 5 =magnetoelectric χ α 6 =non-linear electric χ (χ (2) ): Pockels effect α 7 =non-linear magnetic χ: Mockels effect α 8 =1 st non-linear magnetoelectric χ α 9 =2 nd non-linear magnetoelectric χ α 10 =2 nd non-linear electric χ (χ (3) ): non-linear Kerr effect Polarization= F/ E ε= 2 F/ E 2 Magnetization= F/ H χ= 2 F/ H 2

23 Induced P= αe + α E2

24 ~100 Femto-Second duration θ 0.8 μm: 2.7 Femto-second ~600 μm: ~2000 Femto-second Optical rectification!!

25 Optical rectification!!

26 BiFeO 3 T N 640 K (G-type AFM) T C (FE) 1,050 K c-axis [001] hex [001]cubic [100]cubic [010]cubic b-axis [010] hex

27 BiFeO 3 T N 640 K (G-type AFM) T C (FE) 1,050 K c-axis [001] hex [001]cubic [100]cubic [010]cubic b-axis [010] hex

28 Dzyaloshinskii-Moriya interaction S 1 2 O ϕ 1 2 S 2 Weak ferromagnetism (La 2 CuO 4 ) E DM [ S ] = D 12 1 S2 D 12 λsinϕ O 2- Cu 2+ Inverse DM effect Weak ferroelectricity (RMnO 3 ) M weak O 2- e Q P e Q

29 (a) (c) (c) (d) S. Park et al. PRL (2007) J AF J F P e Q μ 0 H=0 T a b c 10 μm b a P c 30 (b) (e) nn J 25 F 11 ± 3 mev and nnn J AF +7 ± 3 mev; Τ (Κ) 20 Paraelectric/Paramagnetic 15 J AF /J F > ¼; a spiral order with 2πξ=cos -1 (1/ 4J AF /J F ) ε a (T) Step 10 ε a (T) Peak P a (T) P c J AF /J F 0.5 LiCu 2 O 2 (0.5, 0.826, μ 0 H 0): b =9 ξ=0.174 T (the 5pitching angle of 62.6 ε a (H) ) c P b a P a (H) [T. Masuda et al., PRL a (2004)] μ 0 H b (T) P a (pitching angle = 2πξ)

30 S. Seki et al., PRL 2008

31 Spin-FET Rashiba spin-orbital interaction Spins precess in E

32 Dzyaloshinskii-Moriya interaction AFD+AFM O 2- M weak AFD+FM O 2- M FD+AFM O 2- P e Q FD+FM O 2- e Q P e Q

33 n monolayer on W [110] Atomic-scale Spin-polarized STM M. Bode et al., Nature 2007 Mn [110] [001]

34 n monolayer on W [110] M. Bode et al., Nature 2007

35 n monolayer on W [110] M. Bode et al., Nature 2007 Cycloidal spiral

36 BiFeO 3 T N 640 K (G-type AFM) T C (FE) 1,050 K c-axis [001] hex [001]cubic [100]cubic [010]cubic b-axis [010] hex

37 P=[111] q=[1-10] e=[11-2]

38 τ 1 τ 2 τ 3

39 [111] 0 [111] 1/ 2

40 [111] 0 P [111] x [111] 1/ 2 [111] 0 x Spiral plane contains [111] x [111] 1/ 2

41 Polarized neutron scattering on BiFeO Å modulation [010] Single chiral domain!! [100]

42 τ 1 τ 2 τ 3

43 τ 1 τ 2 τ 3

44 τ 1 τ 2 τ 3

45 τ 1 τ 2 τ 3

46 Check what happens with the other paper: French? What happens with τ 1 prime, τ 3 Prime?

47 [111] 0 P [111] x [111] 1/ 2 [111] 0 x Spiral plane contains [111] x [111] 1/ 2

48 [111] 0 P [111] x [111] 1/ 2 [111] 0 x Spiral plane contains [111] D [111] x x [111] 1/ 2 [111] 0 x 0 0 Sinusoidal modulation on (111) x 0 [111] 1/ 2

49 x [111] 0 x 0 0 Sinusoidal modulation on (111) x 0 [111] 1/ 2 H 110]

50 x [111] 0 x 0 0 Sinusoidal modulation on (111) x 0 [111] 1/ 2 [111] 0 H [111] 1/ 2 110]

51 x [111] 0 x 0 0 Sinusoidal modulation on (111) x 0 [111] 1/ 2 [111] 0 H [111] 1/ 2 110] Spiral unwinding

52 BiFeO 3 : the only room-temperature and large P multiferroics [1] Xtals with single ferroelectric and single magnetic chiral domain [2] THz induced by femtosecond laser. [3] Large magnetoelectric coupling: significant dielectric and d-d transition anomalies at the spiral unwinding transition (metamagnetic transition)