Composite Spin in Fluctuating Magnets

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Composite Spin in Fluctuating Magnets
Collin Broholm Johns Hopkins University and NIST
Center for Neutron Research
M. Azuma R. Bewley W. J. L. Buyers Y. Chen S.-W.
Cheong G. Gasparovic D. V. Ferraris
W. Ratcliff II D. H. Reich J. Rittner M. B.
Stone M. Takano H. Yardimci
Q. Huang S. Ishiwata T. H. Kim T.
Lectka S.-H. Lee K. Oka Y. Qiu
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Outline

• Introduction
• Magnets, ordered and fluctuating
• How to distinguish using neutrons
• Whirlwind tour of fluctuating magnets
• Spin trimer magnetism in La4Cu3MoO12
• Frustrated spin liquid in organic magnet
• Fluctuating spin directors in spinel oxide
• Summary and Current Frontiers

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Filled shells non-magnetic materials
Un-filled shells magnetic materials
Ti V Cr Mn Fe Co Ni Cu
Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm
U Np Pu Am Cm
Partially filled shell in solid
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Magnetization of Solid with unfilled Shells
FeBr(C44H28N4) Dilute Fe in organic matrix
Susceptibility data for paramagnetic salt
Spin susceptibility diverges as T 0
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Coulomb Pauli Heisenberg
Coulomb interactions plus Pauli principle split
4-fold spin degeneracy
J
The level scheme is reproduced by Heisenberg
Exchange Hamiltonian
Triplet gnd. State J lt 0
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Interactions orient moments
Ferromagnetic EuO
?
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A brief story of Antiferromangetism
1970 Nobel Prize in Physics to Hannes Alfvén and
Louis Néel
L. Néel 1904-2000
L. Néel From Nobel lecture (1970).
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Staggered magnetization or QM singlet
1962 Nobel Prize in Physics
L. D. Landau 1908-1968
L. D. Landau from Phys. Zs. UdSSR (1933).
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Experimental Evidence for Néel order
C. G. Shull 1915-2001
1994 Nobel Prize in Physics to B. N. Brockhouse
and C. G. Shull
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Is Landaus vision of an AFM possible?
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Outline

• Introduction
• Magnets, ordered and fluctuating
• How to distinguish using neutrons
• Whirlwind tour of fluctuating magnets
• Spin trimer magnetism in La4Cu3MoO12
• Frustrated spin liquid in organic magnet
• Fluctuating spin directors in spinel oxide
• Summary and Current Frontiers

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La4Cu3MoO12 A lattice of spin-1/2 trimers
Magnetic susceptibility
(Azuma et. al., PRB 62 R3588)
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Frustrated quantum spin triangles
Yiming Qiu et al. cond-mat/0205018
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Spectroscopy of spin trimers
Phonons
Yiming Qiu et al. cond-mat/0205018
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Strongly fluctuating spin trimer AFM
Yiming Qiu et al. cond-mat/0205018
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Outline

• Introduction
• Magnets, ordered and fluctuating
• How to distinguish using neutrons
• Whirlwind tour of fluctuating magnets
• Spin trimer magnetism in La4Cu3MoO12
• Frustrated spin liquid in organic magnet
• Fluctuating spin directors in spinel oxide
• Summary and Current Frontiers

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Unconventional magnetism in CuHpCl

• Negative QCW indicates AFM interactions
• No phase transition and
• Spin ladder model consistent with c(T)

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Structure of CuHpCl
CuHpCl is hydrogen bonded crystal of
Cu2(C5H12N2)2Cl4
Molecules possess approximate centro
symmetry Exchange interaction within molecule
Jlt1 meV
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Two lattices from H-bond exchange
b
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Acid test for one-dimensionality
Q // to chain
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The cruel reality
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Detailed bond energy distribution
c
(101)
(001)
a
(100)
Point size First moment
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Frustrated three dimensional spin liquid
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Outline

• Introduction
• Magnets, ordered and fluctuating
• How to tell using neutrons
• Whirlwind tour of fluctuating magnets
• Spin trimer magnetism in La4Cu3MoO12
• Frustrated spin liquid in organic magnet
• Fluctuating spin directors in spinel oxide
• Summary and Current Frontiers

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ZnCr2O4 Corner sharing tetrahedra
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Signs of frustration short range order for
TltQCW

• Points of interest
• 2p/Qr01.4
• gt nn. AFM correlations
• No scattering at low Q
• gt satisfied tetrahedra

S.-H. Lee et al. PRL (2000)
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Fluctuating spin directors
Tchernyshyov et al. PRL (2001)
S.-H. Lee et al. Nature (2002)
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Summary

• Two visions for the behavior of substances with
  AFM interactions between spins
• Néel Two interpenetrating anti-parallel
  ferromagnets
• Landau singlet formation, cooperative
  paramagnetism
• Neutron diffraction shows that Néels state is
  possible
• Inelastic neutron scattering shows that quantum
  magnetism is also possible when there is
  frustration and/or weak connectivity
• The concept of weakly interacting composite spin
  is central for understanding strongly fluctuating
  magnets

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Outlook

• Complete mapping of S(Qw)
• Structural refinement of fluctuating objects
• Applicable to small samples early in materials
  development cycle
• Results under extreme thermodynamic conditions
• Theory and modeling needed to understand
  onslaught of data with wide Q-w space coverage

Design by T. D. Pike http//www.pha.jhu.edu/broho
lm/MACS