Magnetic Frustration At Triple-Axis - NIST
Magnetic Frustration at Triple-AxisS.-H. Lee, S. Park, P.M. GehringNCNR Magnetism, Neutron Scattering, Geometrical Frustration ZnCr2O4: The Most Frustrated MagnetHow are the fluctuating spins in the Spin Liquid phase correlated with each other?How does nature respond to the ground state degeneracy? Summary
ZnCr2O4Space group Fd3mLattice of B sites: Corner-sharing tetrahedraOACr3 (3d3)BEdge-sharingoctahedraegH -J Σ Si . Sjnn3dt2gFree Iondxy, dyz, dzxCubic Field
Magnetic Neutron ScatteringNeutron:¾ Wavelength comparable with interatomic spacings¾ Penetrating Æ bulk properties are measured¾ has spin s ½ so interacts with atomic momentsScattering by atomicmagnetic moments: I (0.54)2 S (S 1)Magnetic scattering intensities can be comparable to nuclear scattering !!
Neutron ScatteringSampleki , Ei , sIncident neutrons?Scattered neutronskf , Ef , smeasures scattering cross section as a function of Q and ωd2σ (Q,ω)dΩdω
Magnetic NeutronScattering Cross SectionSpin-SpinCorrelation FunctionFourier Transformd2σdΩdω SR(t) SR (0) The probability of finding a spin in a spin state SRatpositionmomentR at time t when another spin at R’ at time t 0OrderedFluctuatingmomentis in a spin stateSR/Γ h/τ0ω0TimeLong range orderShort range orderQΓ : relaxation timeκ : intrinsic linewidthκ 1/ξR-Rτ : lifetimeξ : correlation length
Phase Diagram for an Ordinary MagnetF Hmag – TS - Σ J Si Sj - TST (K)ParamagnetTS Hmag AFM or FM Hmag TSΘCW JzS(S 1)/3kBGround State : Long range (anti)ferromagnetically ordered state.Low Energy Excitations : linear spin waves around the ordered state.
ParamagneticNeutronScatteringNeelphase: ross Section(1) Any Elastic2signal?Fourier Transformdσ(2) Any Inelasticsignal?dΩdω SinR(t)(0) Q-space? If any, what kind of shapethe Sω-R andOrdered momentFluctuating momentΓ h/τ0ω0TimeLong range orderShort range orderQΓ : relaxation timeκ : intrinsic linewidthκ 1/ξR-Rτ : lifetimeξ : correlation length
Geometrical FrustrationMAFAFMA simplest example: a Triangle of three antiferromagnetic Ising spinsAFMH -J Σ Si . SjAll exchange interactions can not be satisfied.? E - J A tetrahedron with four isotropic spinsΣ Si 0Zero energy modesin the ground state manifoldGeometrical frustration leads to a large degeneracy in the ground state
Why ZnCr2O4 ?Space group Fd3mLattice of B sites: Corner-sharing tetrahedraOACr3 (3d3)BEdge-sharingoctahedraegInteraction between nearest neighbor Cr3 ionsthrough direct overlap of t2g orbitals is dominant.3dt2gFree IonGeometricallyfrustrateddxy, dyz, dzxCubic FieldBest candidate for a system withH -J Σ Si . Sjnn
Phase Diagram for Geometrical FrustrationF Hmag – TS - Σ J Si Sj - TST (K)ParamagnetΘCW JzS(S 1)/3kB?GeometricallyfrustratedWhat is the nature of the low temperature phase ?
Theory of spins with AFM interactions on corner-sharing tetrahedraH -J Σ Si . SjSPIN TYPE SPIN LOW TMETHODValue PHASEIsotropicS 1/2 Spin Liquid Exact Diag.IsotropicS Spin Liquid MC sim.REFERENCECanals and LacroixPRL ’98Reimers PRB ’92Moessner, ChalkerPRL ’98
Issues Nature of the Spin Liquid StateHow are the fluctuating spins in the SL phase correlatedwith each other? Novel Phase Transition?How does nature respond to the ground state degeneracy?You will be able to answer the questionsafter the demonstration session at SPINS!
A Phase Transition in ZnCr2O4A.P. Ramirez, unpublishedΘCW -390 KTN 12.5 KPhase transitionWhat is the nature of the phase transition?
Neutron Scattering from ZnCr2O4SHL et al., PRL 84, 3718 ions ininfrustratedfrustrated AFMAFMLocalLocal spinspin resonanceresonanceinin magneto-elasticmagneto-elasticLROLRO phasephase
Keep in mind udymagnetism!!magnetism!!Fourier Transformd2σdΩdω SR(t) SR (0) Ordered momentFluctuating momentΓ h/τ0ω0TimeLong range orderShort range orderQΓ : relaxation timeκ : intrinsic linewidthκ 1/ξR-Rτ : lifetimeξ : correlation length
SPINS : Cold Neutron Triple-Axis Spectrometer
Theory of spins with AFM interactions on corner-sharing tetrahedra H -J Σ Si . S j SPIN TYPE SPIN LOW T METHOD REFERENCE Value PHASE Isotropic S 1/2 Spin Liquid Exact Diag. Canals and Lacroix PRL ’98 Isotropic S Spin
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