Multiferroic behavior in spin-chirality- and exchange-striction-driven compounds

1. Multiferroic behavior in spin-chirality- andexchange-striction-driven compounds Jung Hoon Han (SungKyunKwan U, Korea)

2. Collaboration Jung Hoon Kim, Jin Hong Park (SKKU) Kee Hoon Kim (SNU) Shigeki Onoda (RIKEN) Naoto Nagaosa (U. Tokyo) Chenglong Jia (Germany) Raoul Dillenschneider (Augsburg)

3. Motivation A class of materials with strong coupling of spin & lattice or electronic degrees of freedom were (re)discovered. One stark manifestation of the coupling is the control of ferroelectric polarization using only the magnetic field. TbMnO3 Nature 426, 55 (2003)

4. Motivation Nature 429, 392 (2004) TbMn2O5 Magnetic field along a switches polarization from +b to -b axis in TbMn2O5

5. Two types of multiferroics • Exchange-striction-driven, • symmetric spin exchange • (e.g. TbMn2O5) • Spin-chirality-driven, • anti-symmetric spin exchange • (e.g. TbMnO3)

6. Part I • Spin-chirality-driven, • anti-symmetric spin exchange • (e.g. TbMnO3)

7. From spin chirality to ferroelectricity Connection of spin chirality (for noncollinear magnetism) to local dipole moment, or ferroelectricity, was noticed after some key neutron experiment T

8. Vector spin chirality (vSC) It was soon realized that the relevant physics was in the coupling of the local dipole moment to the local vector spin chirality (vSC) Noncollinear magnetic states possess a nonzero vSC vSC breaks inversion symmetry, preserves time-reversal, that’s the same symmetry as the local dipole moment Mostovoy PRL96, 067601 (2006)

9. Microscopic Theories (mean-field) For general d-electron configurations M O

10. Microscopic Theories (mean-field) Spiral, helical, conical spins give uniform polarization • H. Katsura, N. Nagaosa, and A. V. Balatsky, PRL 95, 057205 (2005) • JONH, PRB 74, 224444 (2006) • JONH, PRB 76, 023708 (2007)

11. vSC-driven multiferroics RED = magnetic ions

12. Microscopic Theories (LDA) • Mean-field calculation reflects distortion of electronic wave functions • due to spiral magnetic order • The mechanism is the spin-orbit coupling • The wave function distortion would generically lead to internal electric field, • which would tend to displace ions, and generate dipole moments • LDA calculation reflects the atomic movement better than MF calculation • Xiang & Whangbo, PRL (2007) • Recent LDA works on TbMnO3

13. Existing Experiments Often, there is first a magnetic transition to COLLINEAR spin states, for which no polarization is induced A second transition at a lower temperature to spiral spin states cause nonzero polarization T, frustration Spiral Magnetic Collinear Magnetic Paramagnetic Ferro- electric

14. What’s possible Can we envision a phase without magnetic order, but still has the remnant of vSC (vector spin chirality) ? Theoretically certainly possible. vSCL (vector spin chiral liquid) Chiral spin states ! T, frustration Magnetic Chiral Paramgnetic Ferroelectric

15. Villain’s idea of vSC Villain, JPhysC (1977)

16. Villain’s idea of vSC

17. vSC liquid (vSCL) ? Can we have an example of non-magnetic, chirality-ordered phase? There had been discussions of vSCL in classical models of AFM with frustration No analogous efforts for quantum spin cases until recently It is entirely possible that coupling to ferroelectric moment occurs in non-magnetic, yet vSC-ordered phase (a exotic new matter?) Perhaps low-D, small-S (highly quantum), highly frustrated spin systems are a good place to look for vSCL

18. vSCL found ? Cinti et al. PRL 100, 057203 (2008)

19. Quantum spin S=1/2 Multiferroic Seki et al. arXiv:0801.2533 Park et al. PRL (2007)

20. Quantum spin S=1/2 Multiferroic Enderle et al. EPL (2005) Naito et al JPSJ (2007)

21. Search for models of vSCL Both materials are exciting due to quantum nature of S=1/2 spins and the 1D character of spin network However, the ferroelectricity is concomitant with spiral magnetic ordering Not a true vSCL yet

22. 1D model of vSCL (quantum) XXZ spin chain (S=1) with nearest and next-nearest neighbor exchange Hikihara et al. JPSJ 69, 259 (2000) vSC correlation is long-ranged vSCL found for XY-like, J2-dominant regime of the model =J2/J1

23. Furukawa et al. arXiv:0802.3256v1 A recent calculation of Furukawa et al. confirmed existence of vSCL phase in the same model with S=1/2

24. 2D model of vSCL (classical) - - - + + + - - - + + + We recently re-examined AFM XY model on triangular lattice with huge bi-quadratic exchange Magnetic ordering naturally leads to vSC, but can the converse be also true?

25. J1-J2 model on triangular lattice PONH, arXiv:0804.4034 PM = paramagnetic aM = (algebraic ordered) magnetic aN = (algebraic ordered) nematic C = chirality-ordered

26. Chirality for J1-J2 model Introduce a vector potential From the corresponding free energy define the spin current Staggered sum of the spin current is the vSC

27. Monte Carlo results for chirality Finite- Size Scaling Binder cumulant

28. Summary (Part I) • We have come a long way since the initial discovery of multiferroicity in • understanding the coupling of vSC and local electric dipoles • An interesting possibility of purely vSC-ordered liquid phase is opening up • (GL theory, 1D quantum spin models and compounds) • A 2D classical model which supports vSCL phase seems feasible • (2D AFM XY on triangular lattice) • 2D quantum model with vSCL ground state will be exciting

29. Nature 429, 392 (2004) Exchange-striction-driven Multiferroics TbMn2O5 Magnetic field along a switches polarization from +b to -b axis in TbMn2O3

30. Exchange-striction-driven Multiferroics Radaelli et al. PRB (2005); PRL (2004,2006) Two types of Mn ions: Mn3+ (oxygen tetrahedron) Mn4+ (oxygen octahedron)

31. Looking at the Mn Lattice: Mn3+ (RED) Mn4+ (BLUE) Interactions along c-axis either FM or AFM (no frustration) Project down to 2D (ab plane) without loss of generality

32. Frustrated Mn spin interactions Intra-chain interaction is AFM (no frustration) Inter-chain is also AFM, every other bond is frustrated Shifting the spin orientation by one lattice does not lower energy -> 2-fold degeneracy between every chains -> macroscopic degeneracy

33. Exchange-striction Primer J J According to pure Heisenberg exchange, the middle spin is frustrated J+J J-J It can choose one spin orientation and move toward atoms of opposite spins, lowering the overall exchange energy

34. Lifting of Degeneracy by Exchange-striction L (c) R R L L (a) D D D U U U R R L R L L R U U U D D D L R R L R L D D U U U D D D R R U U L R U L L D B L R R L L R (d) (b) D D U U D U R L R R L L U U U D D D L L R L R R D U D U D U R L R L R L U U U D D D B Exchange striction causes displacement of Mn3+ resulting in net polarization along b axis (consistent with exp.) Lifts macroscopic degeneracy All this well known (S.-W. Cheong, Radaelli, etc.) before I got interested… OR

35. Effects of B field along a-axis on BiMn2O5 Kee Hoon Kim et al. Submitted Dielectric constant along b-axis shows pronounced increases where P=0. Electric polarization, initially along +b, reverses direction due to magnetic field (magneto-electric coupling)

36. Scaling

37. Phase diagram of BiMn2O5 First-order PT P>0 and P<0 regions are separated by a line as if by a phase transition Genuine 2nd order PT is impossible

38. What we need to know Why P changes sign under H field? Why apparent critical behavior near Hc ?

39. Understanding Polarization Reversal L (c) R R L L (a) D D D U U U R R L R L L R U U U D D D L R R L R L D D U U U D D D R R U U L R U L L D B L R R L L R (d) (b) D D U U D U R L R R L L U U U D D D L L R L R R D U D U D U R L R L R L U U U D D D B In an ordinary AFM, H field will cause spin flop. All spins will rotate either CW or CCW as to be orthogonal to B field The relative spin orientations will be the same after spin flop, hence no change in exchange striction force (~Si * Sj) -> Can’t explain experiment Suggestion: Perhaps each spin chain undergoes spin flop with different sense of rotations… (possible since inter-chain coupling is weak)

40. Preliminary MC data The spins do rotate CW for even chains, CCW for odd chains; good pairs become bad pairs and vice versa -> explains polarization reversal Surprisingly, susceptibility (dielectric constant) shows a peak!

41. Summary (Part II) • A class of compounds RMn2O5 are examples of exchange-striction-driven multiferroicity • An interesting polarization reversal and sharp increase in dielectric susceptibility was observed in high-field experiment on BiMn2O5 • A model with both frustrated spin-spin interaction and exchange-striction coupling with reasonable agreement with experimental findings • The precise critical nature of P remains to be understood

42. 2D model of vSCL (quantum) ?? In 2D we do not seem to have any idea how to write down a quantum spin model with long-range vSC correlation 2D vSC solid state can be generated easily with Dzyaloshinskii-Moriya interaction 1D example:

43. Analogy with persistent current For S=1/2, Jordan-Wigner mapping gives Spin chirality maps onto bond current A current-flowing ground state in the fermion picture corresponds to vSC-ordered state in the spin picture (Dillenschneider et al. arXiv:0705.3993)