Neutron Scattering of Frustrated Antiferromagnets Satisfaction without LRO Paramagnetic phase Low Temperature phases Spin glass phase Long range order Spin Peierls like phase Conclusions Collin Broholm Johns Hopkins University and NIST Center for Neutron Research Supported by the NSF through DMR and DMR SrCr 9p Ga 12-9p O 19 KCr 3 (OD) 6 (SO 4 ) 2 ZnCr 2 O 4

HFM2000 6/11/00 Collaborators S.-H. LeeB. Hessen M. AdamsT. J. L. Jones G. AeppliT. H. Kim M. AzumaC. Kloc E. Bucher N. Lacevic C. J. CarlileT. G. Perring S.-W. CheongA. P. Ramirez M. F. CollinsW. Ratcliff III R. W. ErwinA. Taylor L. HellerWinkelmann

HFM2000 6/11/00 A simple frustrated magnet: La 4 Cu 3 MoO 12 Masaki Azuma et al. (2000) Cu trimer

HFM2000 6/11/00 Magnetization and LRO among spin trimers

HFM2000 6/11/00 Spins with AFM interactions on corner-sharing tetrahedra What is special about this lattice and this spin system? Low coordination number Triangular motif Infinite set of mean field ground states with zero net spin on all tetrahedra No barriers between mean field ground states Q-space degeneracy for spin waves

HFM2000 6/11/00 SrCr 9p Ga 12-9p O 19 : Kagome’ sandwich Isolated spin dimer Kagome’-Triangular-Kagome’ sandwich (111) slab of pyrochlore/spinel AFM A. P. Ramirez et al. PRL (1990)

HFM2000 6/11/00 Fe & Cr Jarosite: coupled Kagome’ layers A. S. Wills et al. (2000) AM 3 (OH) 6 (SO 4 ) 2 Townsend et al (1986) Lee et al. (1997) KCr 3 (OH) 6 (CrO 4 ) 2

HFM2000 6/11/00 ZnCr 2 O 4 : Corner sharing tetrahedra

HFM2000 6/11/00 Magnetic Neutron Scattering The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function Fluctuation dissipation theorem:

HFM2000 6/11/00 NIST Center for Neutron Research

HFM2000 6/11/00

Detection system on SPINS neutron spectrometer

HFM2000 6/11/00 Spatial correlation length saturates for T 0 SrCr 9p Ga 12-9p O 19 for T<  CW a  S(Q) 0 for Q 0 => Perfect AFM clusters S(Q) 0 for Q 0 => Perfect AFM clusters

HFM2000 6/11/00 Relaxation Rate decreases for T 0 Paramagnetic state: Fluctuating AFM spin clusters that largely satisfy exchange interactions dimer Kagome’ sandwich SrCr 9p Ga 12-9p O 19

HFM2000 6/11/00 Spin glass in concentrated frustrated AFM  Does quenched disorder play a role?  What is structure of SG phases?  What are excitations in SG phases?

HFM2000 6/11/00 Spin glass transition in SCGO(p=0.92)

HFM2000 6/11/00 The role of disorder at SG transition Higher Cr concentration Higher T f Sharper features in S(Q) Two scenarios remain viable : A) Strong sensitivity to low levels of disorder B) Intrinsic clean limit frozen phase Martinez et al. (1992)

HFM2000 6/11/00 Structure of frozen phase Short range in plane order Kagome’ tri-layer correlations

HFM2000 6/11/00 Excitations in a frustrated spin glass Gapless 2D Halperin-Saslow “Spin Waves” Gapless 2D Halperin-Saslow “Spin Waves” SCGO(p=0.92)

HFM2000 6/11/00 Long range order in frustrated AFM  Clarify role of symmetry breaking interactions, quenched disorder and “order by disorder” effects in stabilizing LRO.  Are there anomalous critical properties at phase transitions to LRO?  What are the excitations in the ordered phase of a highly frustrated magnet?

HFM2000 6/11/00 Phase transition to LRO in Cr-Jarosite >90% Cr 75-90% Cr

HFM2000 6/11/00 Weak order / strong fluctuations

HFM2000 6/11/00 Impurity enhanced LRO in (DO 3 )Fe 3-x Al y (SO 4 ) 2 (OD) 6 Wills et al (1998) Wills et al. (2000)  Intensity (arb) 100% Fe 89% Fe Only reported Jarosite w/o LRO Diamagnetic impurities yield LRO

HFM2000 6/11/00 Magneto-elastic effects in frustrated AFM  Can magneto-elastic coupling relieve frustration?  What is magnetic and lattice strain configuration in ordered phase?  What are excitations from the ordered phase?

HFM2000 6/11/00 First order phase transition in ZnCr 2 O 4 Dynamics: Low energy PM. Fluctuations form resonance Dynamics: Low energy PM. Fluctuations form resonance Statics: Staggered magnetization tetragonal distortion Statics: Staggered magnetization tetragonal distortion

HFM2000 6/11/00 Local spin resonance in ordered phase Paramagnetic fluctuations in frustrated AFM Paramagnetic fluctuations in frustrated AFM Local spin resonance in magneto-elastic LRO phase Local spin resonance in magneto-elastic LRO phase

HFM2000 6/11/00 Low T excitations in ZnCr 2 O 4 : Magnetic DOS Q-dep. of E-integ. intensity B B B B C C C C A A A A A: Bragg peaks B: Spin waves C: Resonance D: Upper band A: Bragg peaks B: Spin waves C: Resonance D: Upper band D D

HFM2000 6/11/00 Spectra at specific Q Spin waves Resonance

HFM2000 6/11/00 Dispersion relation for resonance ZnCr 2 O 4 single crystals T=1.5 K

HFM2000 6/11/00 Structure factor for resonance Extended sharp structures in reciprocal space Extended sharp structures in reciprocal space Fluctuations satisfy local constraints Fluctuations satisfy local constraints ZnCr 2 O 4 T=1.4 K

HFM2000 6/11/00 Comparing resonance and PM fluctuations Paramagnetic fluctuations and resonance satisfy same local constraints. Transition pushes low energy fluctuations into a resonance 15 K1.4 K

HFM2000 6/11/00 The Role of Tetragonal Strain at T N Edge sharing n-n exchange in ZnCr 2 O 4 depends strongly on Cr-Cr distance, r : Cr 3+ O 2- From series of Cr-compounds: r The effect for a single tetrahedron is to make 4 bonds more AFM and two bonds less AFM. This relieves frustration! Tetragonal dist. (J AFM <0)

HFM2000 6/11/00 Magnetic order in ZnCr 2 O 4 tetrahedra have zero net moment this is a mean field ground state for cubic ZnCr 2 O 4 Tetragonal distortion lowers energy of this state compared to other mean field ground states: In a strongly correlated magnet this shift may yield - View along tetragonal c-axis

HFM2000 6/11/00 Analysis of spin and lattice energies at T C T F tet, F cub TCTC Tetrag. AFM Cubic paramagnet From first moment sum-rule Based on scattering data above and below T C and assuming that nearest neighbor exchange dominates

HFM2000 6/11/00 Change in lattice energy change at T C From this we derive increase in lattice energy at transition Free energy of the two phases coincide at T C Compare to tetragonal strain energy Discrepancy calls for additional lattice changes at T C

HFM2000 6/11/00 Analogies with Spin Peirls transition? There are similarities as well as important distinctions!

HFM2000 6/11/00 Conclusions Challenges Fluctuating AFM clusters         Tk O B Cooperative Paramagnetic phase Study T-dependent excitations in quantum critical and gapped systems Neel order Reduced staggered moment and strong quantum fluctuations Indications that dilution yields order What pathologies are found in spin excitations when amplitude is large Understand critical properties of transition to LRO in frustrated magnets spin glass Q and  de-coupled in a purely dynamic phase transition spin wave like DOS Can there be spin glass without quenched disorder Why do spin waves survive Magneto-elastic transition Lattice distortion - a new way out First clear evidence for Q-space deg. Understand resonant mode Is there generality to this effect