Vivien ZapfNational High Magnetic Field Laboratory

Los Alamos National Lab

Bose-Einstein Condensation and Magnetostriction in NiCl2-4SC(NH2)2

National High Magnetic Field Laboratory

Pulsed magnets to 75 TM(H), (H), magnetostriction, ESR, optics, etc

300 T single-turn (s pulse)

Coming soon: 60 T and 100 T long pulse magnets (2 s)

300 T single-turn nondestructive magnetChuck Mielke, Ross McDonald, et al

Capacitor bank pulses a short (s) mega-amp current pulse to achieve ultra high magnetic fields.

10 mm long.10mm ID.

2 s rise time, dB/dt ≈ 108 Ts-1

3 orders of magnitude faster than standard short pulse magnets at the NHMFL.

Low inductance capacitor bank.L = 18 nH, C = 144 F, V = 60 kV, E = 259kJ.

Single turn magnet coil, L = 7 nH.

Peak current 4 MA.

1st megagauss shot (February 8th 2005)

Ni

Cl

Jplane/kB = 0.17 K

c

a

a

Ni S = 1

Cl

NiCl2-4SC(NH2)2 (DTN)No Haldane gap

Other BEC compoundsAll Cu spin-1/2 dimers

•TlCuCl3 (wrong symmetry)

•BaCuSi2O6

(3D -> 2D crossover)

• CsCuCl4

Jchain/kB = 1.72 K

0.2

0.4

0.6

0.8

1

-1 -0.5 0 0.5 1

kz

- -/2 -/20

Hc2 = 12.6 THc1 = 2.1 T

kz=0 (FM)

kz= (AFM)

Antiferromagnetic exchange

jiijv

v SSJ

NiCl2-4SC(NH2)2 (DTN)

2j

z

jSDH

Spin-orbitcoupling Zeeman term

j

zzB jSHg

Sz = +1

H

D~8K

E

Sz = 0

Sz = -1

Ni2+ S = 1: Triplet split by spin-orbit coupling Tetragonal lattice

Sz = +1

Sz = 0

Sz = -1

D~8K

Hc

Sz

a

S=1 M. Kenzelmann et al

Ni spins

Mz

(x10

3 em

u/m

ol)

0

2

4

6

8

10

12

14

0 5 10 15H (T)

H || c

A. Paduan-Filho et al, Phys. Rev. B 69, 020405(R) (2004)

Hc

a

BEC/AFM

Hc1 Hc2

10 ibea

10 zz SbeSa i spin language

boson language

H ~ Mz ~ N (# of bosons)

Sz = 1D

H || c

E

or T(K)

XY AFM orderAFMFM

b or N0 1

Boson filling fraction/Number of bosons

Occupied bosonEmpty site

Note: Approximate theory neglects Sz = -1 state. Complete theory:

H.-T. Wang and Y. Wang, Phys. Rev. B 71, 104429 (2005) K.-K. Ng and T.-K. Lee, cond-mat/0507663

Example: treat upper state as an energetically unfavorable double occupancy state

Sz = -1

jji

ii

ziB

i

zi SSJSHgSD

,

Η2

i

iieffji

ijjijjii bbDhbbbbbbbbJ

,

H

AFM exchangeSpin-orbit coupling

Zeeman term

Repulsion (2nd order in N)

hopping number operator

Spin language Hamiltonian

Boson language Hamiltonian (neglecting Sz = -1 term)

S+ -> b+ (boson creation operator)

(Hardcore Constraint: One boson per site)

Spins Bosons

|Sz = 1> state occupied boson |1>

|Sz= 0> state unoccupied boson |0>

Order parameter: Order parameter:Staggered magnetization Mx Boson creation operator b† = S+

Magnetic field Chemical potential (H ~ N ~ )

Boson mapping

This also works for S=1/2: |↑> = occupied, |↓> = unoccupied

Spins are prevented from obeying fermion statistics since no real-space overlap between states allowed

Why do the bosons obey number conservation?

Tetragonal symmetry of crystal:

U(1) symmetry of spins. Symmetric under rotation by in a-b plane

• Hamiltonian must be independent of

• Rotation by : b† → b† eiand b → be-i

• H can only contains b†b or bb† terms ( = number operator)

• (b† eibe-ib† b = N

• Hamiltonian commutes with boson number operator

• Boson number is conserved.

a

b

|Sz = 1> = occupied boson |Sz = 0> = unoccupied bosonb† = boson creation operator H

X

Energy landscape of spins

S

Symmetry in plane

X

Ni

HXY

model

Ising model

E()

Ni

H

• Boson number only conserved in statistical average• Spin fluctuations, lattice fluctuations limit super current

lifetimes• Small corrections to XY model: DM interactions, dipole-

dipole, and spin-orbit coupling

Limitations

Experimental Tests for BEC

Sz = 1D

H || c

E or T(K)

XY AFM order

0N

230

0 1

11

1

/

/

/

TMN

eNN

en

z

kTk

Tkk

Bk

Bk

23

32

32

/

/

/

~

~

~~

~

TH

HT

HMN

NT

C

C

C

0

2

4

6

8

10

12

14

0 5 10 15H (T)

H || c

Mz

2kk ~where

H

T

Hc1Hc2

Quantum Phase Transition (BEC)amplitude driven (d=3, z=2)

XY AFM

Thermal phase transition (XY AFM) phase driven (d=3, z=1)

Quantum Phase Transition:universality class of a BEC

• BaCuSi2O6

(3D -> 2D crossover)

• CsCuCl4

• NiCl2-4SC(NH2)2

THH

TM

cc

z

1

3D BEC: = 3/2

3D Ising: = 2

2D “BEC”: = 1

Sapphire platform

C=Q/T C=/Quasi-Adiabatic Thermal Relaxation Time

Measuring Specific Heat

C/T

(m

J/m

ol K

2 )Specific Heat

0

2

4

6

8

10

0 0.4 0.8 1.2 1.6T (K)

H = 10 T

T (

K)

Magnetocaloric Effect

0.39

0.4

0.41

0.42

0.43

0.44

10 11 12 13 14B(T)

inflec. point

increasing Hdecreasing H

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

Magnetocaloric effect

Specific heat

H (T)

V. S. Zapf, D. Zocco, B. R. Hansen, M. Jaime, N. Harrison, C. D. Batista, M. Kenzelmann, C. Niedermayer, A. Lacerda, and A. Paduan-Filho, Phys. Rev. Lett., 96, 077204 (2006)

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

Magnetocaloric effectSpecific heat

H (T)

H – Hc TN

H – Hc TN 2 (3D Ising

magnet)

3/2 (3D BEC)

1 (2D “BEC”)

H-Hc1 = aT

= 1.47 ± 0.10

= 1.5 BEC)

Ising magnet

2D BEC

3D BEC

Windowing Technique: see

THH cc 1TMz

V. S. Zapf, et al, Phys. Rev. Lett., 96, 077204 (2006)

S. Sebastian et al, Phys. Rev. B 72, 100404(R) (2005)

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Tmax/1.2 K A. Paduan Filho, unpublished

Tc

(K)

TH

TH

c

c

8510

22

2

1

.

.

Predictions (3-level system):

KJ

KD

av 690

128

.

.

Inelastic Neutron Diffractionand magnetization :

C. D. Batista, M. Tsukamoto, N. Kawashima, in progress

V. S. Zapf et al, Phys. Rev. Lett. 96, 77204 (2006).

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

Magnetocaloric effectSpecific heat

H (T)

predicted Hc1

predicted Hc2

Spin wave theory

Magnetostriction

Capacitance

Titanium Dilatometer(design by G. Schmiedeshoff)

CuBe spring

V. Correa, V.S. Zapf, T. Murphy, E. Palm, S. Tozer, A. Lacerda, A. Paduan-Filho

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0 2 4 6 8 10 12 14B (T)

L/L

(%

)Hc1

Hc2

T = 25 mK

H || c

Lc

La

Hc

a

JJJJJJJJJ = 1.7 K

J = 0.17 K

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0 2 4 6 8 10 12 14B (T)

L/L

(%

)

Magnetostriction

Hc1

Hc2

Lc

La

Ni++

c

a

H

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0 2 4 6 8 10 12 14B (T)

L/L

(%

)

Magnetostriction

Hc1

Hc2

Lc

La

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

Magnetocaloric effectSpecific heat

H (T)

predicted Hc1

predicted Hc2

Tc

(K)

Summary

BEC confirmed experimentally via H-Hc1 ~ T and M ~ T

Magnetostriction effect distorts phase diagram with increasing magnetic field

?

Future work:

Frustration-induced symmetry change?

Acknowledgements

LANLCristian Batista (T-11 theory group)

NHMFL-LANLDiego Zocco Marcelo Jaime Neil HarrisonAlex Lacerda

NHMFL-TallahasseeVictor Correa (Magnetostriction)Tim Murphy Eric PalmStan Tozer

Universidade de Sao Paulo, Brazil

Armando Paduan-Filho (Crystal growth and Magnetization)

Paul Scherrer Institute and ETH, Zürich, Switzerland

B. R. Hansen

M. Kenzelmann (Neutron scattering)

University of Tokyo

Mitsuaki Tsukamoto

Naoki Kawashima (Monte Carlo Simulations)

Occidental College

George Schmiedeshoff (dilatometer design)

NSF NHMFL DOE