Frustration-driven magnetic order on the Shastry-Sutherland lattice - PowerPoint PPT Presentation

Frustration-driven magnetic order on the Shastry-Sutherland lattice Pinaki Sengupta Nanyang Technological University Singapore Workshop on Current Trends in Frustrated Magnetism Jawaharlal Nehru University, New Delhi 10 th Feb., 2015

Collaborators Theory: • Keola Wierschem, NTU • Zhifeng Zhang, NTU • Naoki Kawashima, ISSP, U. Tokyo • Takafumi Suzuki, U. Hyogo Expt.: • Christos Panagopoulos, NTU • Sunku Sai Swaroop, NTU • Tai Kong, Ames Lab, Iowa • Paul Canfield, Ames Lab, Iowa

Outline v Rare earth tetraborides – a “new” family of Shastry- Sutherland compounds v Generalized Shastry-Sutherland model v Magnetization plateaus in TmB 4 v Spin supersolid in the generalized SSM v Proliferation of plateaus in the generalized SSM v Conclusion

“Other” realizations of the SSL model 
 v Rare earth tetraborides: TmB 4 , ErB 4 , HoB 4 , DyB 4 , GdB 4 , TbB 4 v R 2 T 2 M: Yb 2 Pt 2 Pb, Ce 2 Pt 2 Pb q Weakly coupled layers q R 3+ ions arranged in SSL geometry eff ( µ Β ) T N2 ZF order Θ (K) T N1 ( K ) D(K) µ ef Σ J ij ( TmB 4 6.6 -63 11.7 9.8 -4.8 -6.4 Ising-AFM ( π , π ) ErB 4 8.4 -22.7 15.3 -1.4 -4.6 Ising-AFM ( π , 0 ) HoB 4 9.2 -12.7 7.4 6.3 -1.3 0.3 Ising-AFM ( π , π ) Mata’s. et.al., J. Phys: Conf. Ser., 200, 032041 (2010)

Magnetization plateaus in RB 4 q Ground state has long range magnetic TmB 4 ordering in most of the rare earth 1.0 tetraborides 0.14 M/M sat 0.8 0.1359 q Field-induced plateaus observed in all 0.12 0.1235 0.6 members 1.5 1.6 1.7 1.8 M/M sat B (T) 0.5092 0.51 0.4 M/M sat q Sequence of plateaus differ across the 0.50 0.2 family 0.4962 0.49 2.0 2.5 3.0 3.5 B (T) 0.0 0 1 2 3 4 5 q Multi-step melting of magnetic order B (T) (a) magnetization plateaus, (b) phase diagram observed in many RB 4 compounds Uniform susceptibility Magnetization and field dependent plateaus in HoB 4 magnetization in ErB 4

Rare earth tetraborides 
 Generic features Ø Low saturation field (~ 10T) – low-T neutron scattering possible Ø Span wide parameter regime including magnetic ground state at zero field Ø Higher spins, single ion anisotropies effective exchange anisotropy Ø Additional interactions E x tf nsive insight in tp ti e in tf rplay of compe tj ng s ts ong in tf rac tj on s and geome ts ic fs us ts a tj on in ti e Shas ts y-Su ti erland la tu ice Metallic ground state – interaction of itinerant electrons with localized magnetic moments in a frustrated configuration – interesting magneto-electric effects

Magnetization Plateaus in TmB 4 
 Stripe superstructures modulate underlying short-range structures K. Siemensmeyer et. al., PRL 101 , 177201 (2008)

Low energy effective model 
 S = 6 Ø Large magnetic moment for Tm 3+ : 2 , D J ≈ 5 S z = ± 4 ( ) z Ø Large single-ion anisotropy: − D S i S z = ± 5 ~100 K Effective low energy model involving the S z = ± 6 lowest 2 levels Ising limit Ferromagnetic exchange term – sign problem in QMC simulations alleviated Stochastic Series Expansion QMC algorithm used for simulation

Generalized Shastry-Sutherland model Ø S=1/2 XXZ model with large Ising anisotropy Ø J and J’ along the SSL lattice axes Longer range interactions mediated by itinerant electrons Ø NNN interaction (J 3 ) along the diagonals of the plaquettes with no J Ø Additional 3 rd neighbor interaction J 4 Ø Same anisotropy for all interactions. q Rich variety of magnetic phases q Potentially realized in the different members of the rare-earth tetraborides

Low energy effective model for TmB 4 
 Start with the generalized Shastry Sutherland model with J and J’ inconsistency with experimental observation Ising limit : Extended 1/3 plateau followed by a direct transition to full saturation TmB 4 : Extended ½ plateau, no 1/3 plateau N eed addi tj onal in tf rac tj ons Longer range RKKY interactions mediated by itinerant electrons Ø AFM J 3 necessary to account for the appearance of ½ plateau Ø FM J 4 necessary to explain the suppression of 1/3 plateau Together they explain the principal plateau structure observed in TmB 4 . Suzuki, et. al., PRB 80 , 180405 (2009); PRB 82 , 214404 (2010)

Modeling TmB 4 ü Correct critical values for m/m s =1/2 plateau reproduced ü Correct saturation field reproduced ü No evidence of lower magnetization plateaus for the current model ü No evidence for “hysteresis” effects. Suzuki, et. al., PRB 80 , 180405 (2009); PRB 82 , 214404 (2010)

Fractional plateau in TmB 4 1.0 Ø Fractional plateau observed in TmB 4 at 0.14 M/M sat 0.8 m/m s ~1/8 0.1359 0.12 0.1235 Ø Magnetic hysteresis observed at the 0.6 1.5 1.6 1.7 1.8 fractional plateau M/M sat B (T) 0.5092 0.51 0.4 Ø Neutron scattering modulated M/M sat 0.50 AFM ground state with 0.2 0.4962 incommensurate periodicity 0.49 2.0 2.5 3.0 3.5 B (T) Ø Provides simple explanation for 0.0 0 1 2 3 4 5 B (T) observed magnetic behaviour Fractional plateau and Ø Predict modulated structure for both hysteresis in TmB 4 fractional and ½ plateaus – need to be confirmed experimentally J1 Modulated AFM J2 3 4 J3 1/8 plateau Neutron scattering data 1 2 Michimura, et.al., 2009 3 4 ½ plateau Schematic spin configuration 1 2

Magnetization in generalized SSM q Varied sequence of magnetization plateaus as the parameters are varied q Fertile framework for investing frustration drivn field induced magnetic phases – plateaus, spins-supersolid (?) q Potentially realizable in the different members of the rare earth tetraboride family of compounds q Help identify dominant interactions driving observed magnetic phases

Magnetization plateaus in extended SSM Ø Effect of J 3 explored in detail J1 Ø ZF: ( π , π ) AFM order for FM and weak AFM J 3 J2 in the Ising limit J3 Ø ( π ,0 ) AFM order for moderate to strong AFM J 3 – observed in ErB4 Ø 1/3 plateau persists to finite J 3 Ø ½ plateau appears for any J 3 ≠ 0 Ø Finite exchange interactions induce superfluidity at boundary between plateaus Magnetic phases driven by J 3 Columnar AFM order K. Wierschem and P.S., PRL 110 , 207207 (2013)

Spin supersolid in extended SSM Ø Spin supersolid GS observed at densities 1 0.25 0.12 h z =1.75 L=12 0.8 0.1 close to, but less that half-filling 0.2 L=24 0.08 0.6 0.06 h z =2.75 2 0.15 m z m c 0.04 0 0.05 0.1 0.15 0.2 0.4 0.1 1/L Ø Longitudinal AFM order at ( π ,0 ) and ( π , π ) 0.2 0.05 0 0 0.05 0.08 0.01 0.04 h z =3.75 Ø Transverse AFM order at ( π , π ) 0.06 0.03 h z =1.75 2 0.02 ρ s m s 0 0.05 0.1 0.15 0.2 0.04 0.005 1/L 0.02 Ø Simple mechanism based on 0 0 1 2 3 4 1 2 3 4 delocalization of holes in the half-plateau h z h z Simulation results showing the by 1 st order process appearance of spin SSOL Ø Magnetization behaviour qualitatively similar to ErB4, but spin SSOL phase not yet reported Transverse and longitudinal structure factors (b) in the spin SSOL Delocalization of a single phase flipped spin at the ½ plateau K. Wierschem and P.S., PRL 110 , 207207 (2013)

Magnetic phases in generalized SSM (b) J Ø Inclusion of J 4 changes plateau 4 J1 sequence significantly J2 II I Ø AFM J 3 and J 4 destabilises the ½ J3 J 3 III IV plateau – emergence of the 5/9 plateau Ø Different structures for same plateau realised for different parameters Ø Spin-SSOL stablised over extended parameter ranges 1 0 - 1/3 - 1/2 - 5/9 - 1 0 - 1/3 - 5/9 - 1 0.5 SS2 0 - 1/2 - 1 0 - 1/3 - 1/2 - 5/9 - 1 J 4 0 0 - 1/3 - 1/2 - 1 ErB 4 TmB 4 -0.5 SS1 0 - 1 Evolution of plateau sequence 0 - 1/2 - 1 for finite J4 in the XXZ model -1 -2 -1 0 1 2 J 3 Plateau sequence in the Ising limit for finite J 4

Understanding plateaus in generalized SSM Ø Explain spin textures at plateaus in terms of a plaquette unit cell Ø Construct a “pinwheel” around a square with no diagonal bond Ø Many different configurations possible (for Ising spins) Columnar AFM Ø Local dimer states determine nature of spin modulation Ø Many possibilities for same plaquette magnetic moment ½ plateau Ø Leads to multiple distinct plateaus with same magnetization Ø Possible because of additional interactions 1/3 plateau Ø Stable for finite exchange - Confirmed by QMC simulations in XXZ model

Electronic transport in rare earth tetraborides Ø Itinerant electrons in rare earth tetraborides couple to local moments Ø Electronic transport affected significantly by underlying magnetic texture Ø Study within the framework of Shastry Sutherland Kondo lattice model (SSKLM) Ø Control electronic transport by applied magnetic field and magnetism by driving current Ø Small change in applied magnetic field changes magnetic structure – interesting magneto-electric phenomena

Conclusions v Interplay between geometric frustration, strong interaction and high magnetic field results in many novel quantum phases on the Shastry-Sutherland lattice v Rare earth tetraborides present experimental realizations of many of these phases v Metallicity makes these quantum magnets even more interesting v Magnetic phases explored in great detail – transport promises new phases and phenomena Ti e best is yet tp come !