Post on 06-Apr-2018
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Composite Spin in Fluctuating Magnets
Collin Broholm*
Johns Hopkins University and NIST Center for Neutron Research
* Supported by the National Science Foundation
M. Azuma
R. Bewley
W. J. L. BuyersYing Chen
S.-W. Cheong
G. Gasparovic
Guangyong Xu
G. Aeppli
J. F. DiTusa
D. V. Ferraris
W. Ratcliff II
D. H. Reich
J. RittnerM. B. Stone
H. Takagi
M. Takano
M. E. Bisher
M. M. J. Treacy
R. Paul
H. Yardimci
C. D. Frost
Q. Huang
S. IshiwataT. Ito
T. H. Kim
T. Lectka
S.-H. Lee
K. Oka
T. G. Perring
Y. Qiu
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Outline
1. Introduction
a. Magnets, ordered and fluctuating
b. How to distinguish using neutrons
2. Whirlwind tour of fluctuating magnets
a. Spin trimer magnetism in La4Cu3MoO12
b. Cooperative singlet in spin-1 chain
c. Frustrated spin liquid in organic magnet
d. Fluctuating spin directors in spinel oxide
3. Summary and Current Frontiers
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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:
Un-filled shel
ls magnetic materials
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Magnetization of Solid with unfilled Shells
Susceptibility data forparamagnetic salt
! j jBg SHQH
HSM GQ |! j jB
Vg
Tk
SSg
B
B
3
)1(2
!
x
x!
Q
H
M
Spin susceptibility diverges as T 0
FeBr(C44H28N4)Dilute Fe in organic matrix
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S=1/2
S=1/2 S=1/2
Coulomb + Pauli = Heisenberg
Coulomb interactions plus Pauli principle split 4-fold spin degeneracy
jiJSS
!H
The level scheme is reproduced by Heisenberg Exchange Hamiltonian
|J|
1!totS
0!totS
S=1/2
|J|
0!totS
1!totS
Singlet gnd. State:J> 0
Triplet gnd. State:J< 0
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Interactions orient moments
G
1G
Ferromagnetic EuO
G
1G
Antiferromagnetic KNiF3
CWNT 5}
?
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A brief story of Antiferromangetism
1970Nobel Prize in Physics toHannes Alfvn and Louis Nel
L. Nel From Nobel lecture (1970).
L. Nel 1904-2000
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Staggered magnetization or QM singlet
1962Nobel Prize in Physics
12
oq qo
L. D.Landau from Phys. Zs. UdSSR (1933).
L. D.Landau 1908-1968
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Is Nels state possible?
C. G. Shull 1915-2001
1994Nobel Prize in Physics to
B. N. Brockhouse and C. G. Shull
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Magnetic Neutron Diffraction
fk
i f! Q k k
Reciprocal Space
ik
Real space
NuclearDiffraction: * * *h k l! Q a b cMagnetic Diffraction: * * *m m m
h k l! Q a b c
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Is Landaus vision of a AFM possible?
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Outline
1. Introduction
a. Magnets, ordered and fluctuating
b. How to distinguish using neutrons
2. Whirlwind tour of fluctuating magnets
a. Spin trimer magnetism in La4Cu3MoO12
b. Cooperative singlet in spin-1 chain
c. Frustrated spin liquid in organic magnet
d. Fluctuating spin directors in spinel oxide
3. Summary and Current Frontiers
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(Az
uma et. al., PRB 62 R3588)
z=3/4CuMoOplane
La4Cu3MoO12: A lattice of spin-1/2 trimers
Magnetic susceptibility
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Frustrated quantum spin triangles
133221 SSSSSS !JHJ
J J
J2
3
J2
3
133322211 SSSSSS ! JJJH
J1
J3
J2
22
3 JJ
H
2
132
322
2121 JJJJJJJ !H
JH
YimingQiu et al. cond-mat/0205018
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Inelastic Magnetic Neutron Scattering
fk
i f! Q k k
ik
2 21 1
2 2i fmv mv[ ! !
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Spectroscopy of spin trimers
Transition to quartet
YimingQiu et al. cond-mat/0205018
70 K
10 K
0.0
0.1
0.0
0.1
0.2
JH
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Strongly fluctuating spin trimer AFM
YimingQiu et al. cond-mat/0205018
300K 2.6K
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Outline
1. Introduction
a. Magnets, ordered and fluctuating
b. How to distinguish using neutrons
2. Whirlwind tour of fluctuating magnets
a. Spin trimer magnetism in La4Cu3MoO12
b. Cooperative singlet in spin-1 chain
c. Frustrated spin liquid in organic magnet
d. Fluctuating spin directors in spinel oxide
3. Summary and Current Frontiers
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Unconventional magnetism in NENP
K91}5CW
Negative Curie Weiss temperature indicates AFM interactions
No phase transition and 0forsmall pp TG
G
1G
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Haldane gap in Y2BaNiO5
40
20
60
00 0.5 1 1.5 2
q (T)
h[
(meV
)
Ba
Y
O2-
Ni
T. Ito, K. Oka and H. Takagi
MAPS (ISIS)
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singlet ground state of S=1 chain
Magnets with 2S=nz have a nearest neighborsinglet covering
with full lattice symmetry.
Excited states arepropagating bond triplets separated from the
ground state by an energy gap .J}(
Haldane PRL
(1983)Affleck, Kennedy,Lieb, andTasaki PRL (1987)
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Cutting chains in Y2BaNi1-xMgxO5
Mg2+on Ni2+ sites finite length chains
Kojima et al. (1995)
Pure
Ni2+
Mg2+
3
Mg2+ Y3+O2-
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Hole doping Y2-xCaxBaNiO5
Ca2+ on Y3+ sites mobile bond defects
Kojima et al. (1995)
Pure
Ca2+
Y3+
FMCa2+
Ni
O2-
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Gap modes in 4% Ca-doped Y2BaNiO5
qH
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Bond Impurities in a spin-1 chain: Y2-xCaxBaNiO5
Y3+
Ni
O
FM
Ca2+
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Gap modes in 4% Ca-doped Y2BaNiO5
EH
qH
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Minimal model of spin polaron
'J'J
2 2 212
2 2 21
2
12
12
'
'
' 1
' 1
LR LOR
L R O L R
LR L R
LOR O LR
S S LR LR
LOR LOR
J J
J
JE J J S S
J S S cst
!
!
!
S S S S S
S S S
S S S
H
32
'J
'J J
32
1LOR LRS S! !
12
1LOR LRS S! !
1
20
LOR LRS S! !
1 12 20,1LR LR LOR LRS S S S ! e e
J
LS RS
OS
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Outline
1. Introduction
a. Magnets, ordered and fluctuating
b. How to tell using neutrons
2. Whirlwind tour of fluctuating magnets
a. Spin trimer magnetism in La4Cu3MoO12
b. Cooperative singlet in spin-1 chain
c. Frustrated spin liquid in organic magnet
d. Fluctuating spin directors in spinel oxide
3. Summary and Current Frontiers
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Unconventional magnetism in CuHpCl
Negative 5CW indicates AFM interactions
No phase transition and
Spin ladder model consistent with G(T)
0for0 pp TG
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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 |J|
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Two lattices from H-bond exchange
b
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Building an enigma
Dispersion throughout a-c plane
Spin liquid on 3-dimensional lattice
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powder
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Detailed bond energy distribution
a*
c* (101)
(100)
(001)
Point size First momentw
Bond ID d0d SS J
(meV)
1 0.42(3)
2 0.06(4)
3 -0.29(3)
4 -0.18(1)
5 0.06(2)6 -0.05(4)
7 -0.09(7)
8 -0.15(3)
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Frustrated three dimensional spin liquid
Bond ID d0d SS J
(meV)
1 0.42(3)
2 0.06(4)
3 -0.29(3)
4 -0.18(1)
5 0.06(2)6 -0.05(4)
7 -0.09(7)
8 -0.15(3)
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Outline
1. Introduction
a. Magnets, ordered and fluctuating
b. How to tell using neutrons
2. Whirlwind tour of fluctuating magnets
a. Spin trimer magnetism in La4Cu3MoO12
b. Cooperative singlet in spin-1 chain
c. Frustrated spin liquid in organic magnet
d. Fluctuating spin directors in spinel oxide
3. Summary and Current Frontiers
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ZnCr2O4 : Corner sharing tetrahedra
CW5
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Signs of frustration: short range order for T nn. AFM correlations
No scattering at low Q
=> satisfied tetrahedra
S.-H.Lee et al. PRL (2000)
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Fluctuating spin directors
S.-H.Lee et al. Nature (2002)
2 2
i j
ij
tot i
i
J
JS J S
!
!
S SH
Tchernyshyov et al. PRL (2001)
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Summary: Two visions for the behavior of substances with
AFM interactions between spins Nel: Two interpenetrating anti-parallel ferromagnets
Landau: singlet formation, cooperative paramagnetism
Neutron diffraction shows that Nels state is
possible
Inelastic neutron scattering shows that quantummagnetism is also possible when there is frustrationand/or weak connectivity
The concept of weakly interacting composite spin iscentral for understanding strongly fluctuatingmagnets
Viewgraphs and publications at http://www.pha.jhu.edu/~broholm/homepage
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Outlook
1. Structural refinement of fluctuating objects
2. Applicability to a wide range of materials
3. Dynamic correlations under extremeconditions
4. Spin polarons in high TC superconductors?
5. Magnetism of interacting spin polaronsDesign by T. D. Pike
http://www.pha.jhu.edu/~broholm/MACS