Physics of multiferroic hexagonal manganites RMnO 3 Je-Geun Park Sungkyunkwan University KIAS 29 October 2005

Outline Introduction Part 1: Phonon scattering due to short-ranged spin fluctuations of YMnO 3 Part 2: Direct evidence of coupling among spin, lattice, and electric dipole moment for YMnO 3 and LuMnO 3 Part 3: Doping and Pressure effects on the magnetic structure Summary

What is multiferroic behavior? Ferromagnetism Fe 3 O 4 Ferroelectricity PbTiO 3 Examples : Ni 3 B 7 O 13 I, BiMnO 3, BiFeO 3, RMnO 3 (R=Ho-Lu, Sc, Y), RMn 2 O 5 (R=Tb,Dy)

Renaissance of Multiferroic Multiple State Memory Device Write E / Read M Write M / Read E Magnetic valve Data storage Tunable sensors Spin transistor Key Issue : Coupling among P, M, and  N. A. Spaldin and M. Fiebig Science (2005)

T. Lottermoser et al., Nature (2004) HoMnO 3 Control of Magnetic Phase by E

Controlling Polarization by Magnetic field N. Hur, S.-W. Cheong et al., Nature (2003) A similar demonstration was presented by Prof. Tokura’s group for TbMnO 3. see T. Kimura Nature (2003)

Multiferroic Hexagonal Manganites RMnO 3

antiferromagnet ic ordering temperature (K) ferroelectric ordering temperature (K) a (Å) c (Å) ScMnO 3 129~ YMnO HoMnO 3 76~ ErMnO TmMnO 3 86~ YbMnO LuMnO 3 96~ Summary of properties of Hexagonal Manganites

T.Katsufuji et al., PRB (2001) Wo-chul Yi et al.Appl. Phys. Lett., (1998) Ferroelectric Antiferromagnetic Multiferroic Behavior

Hexagonal structure Othorhombic structure AMnO 3 O1 O2 O3 O4

Crystal field level of Mn 3+ Orthorhombic manganites Jahn-Teller active egeg t 2g 3z 2 -r 2 x 2 -y 2 xz,yz xy Hexagonal manganites J. S. Kang, JGP et al., PRB 71, (2005) Jahn-Teller inactive egeg t 2g x 2 -y 2 yzxz xy 1.7 eV : IR 5~6 eV : PES 3z 2 -r 2

antiferromagnet ic ordering temperature (K) ferroelectric ordering temperature (K) a (Å) c (Å) ScMnO 3 129~ YMnO HoMnO 3 76~ ErMnO TmMnO 3 86~ YbMnO LuMnO 3 96~ Origin of FE transition?

The ferroelectric instability is due to Y-O displacement, which is accompanied by MnO 5 rotation. See B. van Aken et al., Nature Materials (2004)

2D Triangular lattice of Mn moments O1 O2 O3 O4 Mn

Irreducible representations   1 representation   2 representation   3 representation   4 representation A. Munoz et al., PRB (2000)

11 33 a (Å) = (1) b (Å) = (2) V (Å 3 ) = (1) a (Å) = (1) b (Å) = (2) V (Å 3 ) = (1) Magnetic Moment (  B ) 3.30(2) Magnetic Moment (  B ) 3.25(2) Reliability factors R p = 5.79 % R wp = 7.93 % R mag = 7.88 %  2 = 2.70 Reliability factors R p = 5.83 % R wp = 7.98 % R mag = 7.35 %  2 = 2.74 Magnetic structure YMnO 3 Junghwan Park, JGP et al., Applied Physics A (2002)

Inelastic Neutron Scattering of YMnO 3 Junghwan Park, JGP et al., Phys.Rev.B (2003) J=3 meV,  =0.95, D=0.03 meV

Spin dynamics of single crystal YMnO 3 T. Sato et al., Phys.Rev. B (2003) J 1 =-3.4(2) meV, J 2 =-2.02(7) meV J’ 1 -J’ 2 =0.014(2) meV D 1 =-0.028(1) meV D 2 =0.0007(6) meV

Questions What are the effects due to the short-ranged magnetic fluctuations on their physical properties? How are the magnetic and electric dipole moments coupled to one another? What are doping effects on the magnetic properties?

Part 1: Phonon scattering due to short- ranged spin fluctuations of YMnO 3 Phys. Rev. B 68, (2003) Phys. Rev. Lett. 93, (2004)

Geometrical frustration Triangular lattice with AF interaction Part 1 YMnO 3

Diffuse scattering seen in YMnO 3 well above T N : Evidence of short ranged magnetic correlation, i.e. spin liquid phase Data taken at HANARO, Korean research reactor Part 1 HANARO 30MW

: measured difference curve : the form factor of Mn 3+ : the distance between nearest neighboring spins E.F. Bertaut et al. Solid State Commun. 5, 279(1967) 80 K Data subtracted off by the 300 K data Part 1

Fitting of I(Q)/F 2 (Q) of YMnO 3 Å Å Part 1 Junghwan Park, JGP et al., Phys.Rev.B (2003)

Spin liquid phase in the paramagnetic phase Part 1

Additional scattering of acoustic phonons due to spin liquid phase Part 1

YMnO 3 P. Sharma, JGP et al., PRL (2004) (Å)(Å) Part 1

Part 2: Direct evidence of coupling among spin, lattice, and electric moments for YMnO 3 and LuMnO 3 Phys. Rev. B Rapid Comm. 71, (2005)

(Å)(Å) c ( Å ) Junghwan Park, JGP et al., Applied Physics A (2002) Temperature dependence of moment and lattice constants exex eyey plane z=0 plane z=1/2 Г1 magnetic structure Part 2

Temperature dependence of a, c, and volume up to 1200 K : High temperature neutron diffraction data HT: P 63/m mc LT: P 63 cm Part 2 J. Park, JGP (unpublished)

SIRIUS （ High resolution and high intensity powder diffractometer KENS Part 2

Refinement results : TOF diffractometer SIRIUS at KEK 10K300K Y(1)z0.2773(7)0.2727(8) Y(2)z0.2318(6)0.2320(7) Mnx0.3423(1)0.3330(1) O(1)x0.3007(4)0.3076(4) O(1)z0.1606(7)0.1625(7) O(2)x0.6399(4)0.6414(4) O(2)z0.3339(7)0.3360(7) O(3)z0.4804(8)0.4754(9) O(4)z0.0193(7)0.0163(8) R wp 6.29%4.19% RpRp 4.89%3.42% Part 2

Temperature dependence of atom positions Refinement results Å (Å)(Å) (Å)(Å) (Å)(Å) O1 O2 O3 O4 Mn Part 2

u KEK YMnO 3 results Part 2

Coupling among magnetic moments, lattice, electric dipole moments Y : 3+ Mn ; 3+ O : 2- Part 2 Seongsu Lee et al., PRB (2005)

Part 3: Doping and Pressure Effects on the magnetic properties Phys. Rev. B 72, (2005) JETP 82, 212 (2005)

2D Triangular lattice of Mn moments O1 O2 O3 O4 Mn Part 3

Doping effects of (Er 1-x Y x )MnO 3 Part 3

Irreducible representations  1 representation  2 representation  3 representation  4 representation Part 3 YMnO 3 ErMnO 3

Magnetic structure of (Er 1-x Y x )MnO 3 Part 3

2D Triangular lattice of Mn moments O1 O2 O3 O4 Mn Part 3

Mn-site doping effects in Y(Mn,X)O 3 with X=Zn, Al, and Ru Part 3 Mixing of  1 and  2 structures

1.Mixing of magnetic structure Γ 1  Γ 1 + Γ 2 : for 2.5 GPa, μ ord = 1.52 μ B with  =60 o at 10K: 2.Diffuse scattering enhanced with pressure Part 3 External Pressure Effects on YMnO 3

Summary Spin liquid phase evidenced by the diffuse peaks scatters acoustic phonons through unusually strong spin-phonon coupling, which then gives rise to a significant reduction in thermal conductivity in the paramagnetic phase. We have shown that below T N the magnetic moments of YMnO 3 and LuMnO 3 are strongly coupled to the lattice degrees of freedom with further coupling to the ferroelectric moments. However, an underlying microscopic mechanism for such a coupling is not clear yet. The magnetic ground states of RMnO 3 are so subtle that even a small doping can induce mixing between different magnetic states.

Acknowledgements Seongsu Lee, Misun Kang, Jung Hoon Han, H. Y. Choi, A. Pirogov: Sungkyunkwan University Changhee Lee: KAERI, Korea W. Jo: Ewha Womans University, Korea S-W. Cheong: Rutgers University, USA T. Kamiyama: KEK, Japan R. Bewley: ISIS, UK Jeongsu Kang: Catholic University, Korea D. Kozlenko: Frank Laboratory, Russia