Collin Broholm- Composite Spin in Fluctuating Magnets

8/3/2019 Collin Broholm- 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

* 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










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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


70 K

10 K

0.0

0.1

0.0

0.1

0.2

JH


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Strongly fluctuating spin trimer AFM


300K 2.6K


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Outline

1. Introduction










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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


b. How to tell using neutrons








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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


b. How to tell using neutrons








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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

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Collin Broholm- Composite Spin in Fluctuating Magnets

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