Quantum effects in Magnetic Salts

04/19/23

London Centre for NanotechnologyLondon Centre for Nanotechnology

Quantum effects in Magnetic Salts

G. Aeppli (LCN)

J. Brooke (NEC/UChicago/Lincoln Labs)

T. F. Rosenbaum (UChicago)

D. Bitko (UChicago)

H. Ronnow (PSI/NEC)

D. McMorrow (LCN)

R. Parthasarathy (UChicago/Berkeley)

outline

Introduction – saltsquantum mechanicsclassical magnetism

RE fluoride magnet LiHoF4 – model quantum phase transition

1d model magnets

2d model magnets – Heisenberg & Hubbard models

Not magnetic, so need to look for a salt containing a simple magnetic ion…

consult periodic table on Google

4f76s2

EuO

Eu

O

From quantum mechanics

• Electrons carry spin• Spin uncompensated for many ions in solids• e.g. Eu2+(f7,S=7/2), but also Cu2+(d9,S=1/2), Ni2+ (d8,S=1), Fe2+

(d6,S=2)

put atoms together to make a ferromagnet-

Classical onset of magnetizationin a conventional transition metal

alloy(PdCo)

1.5x10-3

1.0

0.5

0.0

M (

emu)

400350300250200150T (K)

H=100G out of plane H=100G in plane

Hysteresis

3x10-3

2

1

0

-1

-2

-3

M (e

mu)

-4000 -2000 0 2000 4000H (G)

300 K 360 K

300K

Hysteresis comes from magnetic domain walls

Perpendicular recording medium 3 m

conventional paradigm for magnetism

Curie(FM) point Tc so that

for T<Tc, finite <Mo>=(1/N)<Sj>

<Mo>=(Tc-T)Tc-T|-Tc-T|-

for T<Tc, there are static magnetic domains,

from which most applications of magnetism are derived

+ classical dynamics

Dispersion relations:La2-2xSr1+2xMn2O7 (x=0.4)

[h 0 0]

0.0 0.1 0.2 0.3 0.4 0.5

En

erg

y (m

eV)

0

20

40

60

acousticopticPhonon

Perring et al, Phys. Rev. Lett. 81 217201(2001)

What is special about ordinary ferromagnets?

[H,M]=0 order parameter is a conserved quantity classical FM eigenstates (Curie state | ½ ½ ½ … ½ >,| -½ -½ -½ … -½ > & spin waves) are also quantum eigenstates

no need to worry about quantum mechanics once spins exist

Do we ever need to worry about quantum mechanics for real magnets?

0],[

zz SHt

S

i

need to examine cases wherecommutator does not vanish

Why should we ask?

Search for useable - scaleable, easily measurable - quantum degrees of freedom, e.g. for quantum computing

many hard problems (e.g. high-temperature superconductivity) in condensed matter physics involve strongly fluctuating quantum spins

04/19/23


Simplest quantum magnet

c~kTc~J

N

i

xi

zj

zi

N

jijiJ

,,H

0],[

zz SHt

S

i

Ising model in atransverse field:

Quantumfluctuationsmatter for 0:

FM

PMc

cTT1

1

0 0.5

0.5

Plan of talk

Experimental realization of Ising model in transverse fieldThe simplest quantum critical pointNuclear spin bathQuantum mechanics with tunable massPossible applications

04/19/23


Realizing the transverse field Ising model, where can vary –

LiHoF4

c

a

b

Ho

Li

F

•g=14 doublet•9K gap to next state•dipolar coupled

04/19/23


c

a

b

Ho 3+

Li+

F-

Realizing the transverse field Ising model, where can vary –

LiHoF4

•g=14 doublet (J=8)•9K gap to next state•dipolar coupled

04/19/23


04/19/23


Susceptibility

dh

dm

• Real component diverges at FM ordering

• Imaginary component shows dissipation

fiff

04/19/23


vs T for Ht=0

•D. Bitko, T. F. Rosenbaum, G. Aeppli, Phys. Rev. Lett.77(5), pp. 940-943, (1996)

04/19/23


Now impose transverse field …

04/19/23


04/19/23


165Ho3+ J=8 and I=7/2 A=3.36eV

04/19/23


W=A<J>I ~ 140eV

04/19/23


Diverging

04/19/23


Magnetic Mass

• The Ising term energy gap 2J

• The term does not commute with

Need traveling wave solution:

• Total energy of flip

N

i

xi

zj

zi

N

jijiJ

,,H

DW

DW =

mkk 222222 kaJE

2

2

2 am

a

04/19/23


1 1.5 2

Ene

rgy

Tra

nsfe

r (m

eV)

Spin Wave excitations inthe FM LiHoF4

0,0,ah

04/19/23


What happens near QPT?

04/19/23


•H. Ronnow et al. Science 308, 392-395 (2005)

04/19/23


W=A<J>I ~ 140eV

04/19/23


04/19/23


=f|<f|S(Q)+|0>|2-E0+Ef) where

S(Q)+ =mSm+expiq.rm

04/19/23


Where does spectral weight go & diverging correlation length

appear?

Ronnow et al, unpub (2006)

04/19/23


summary

• Electronic coherence limited by nuclear spins

• QCP dynamics radically altered by simple ‘spectator’ degree of freedom

• Nuclear spin bath ‘pulls back’ quantum system into classical regime

04/19/23


wider significance

• Connection to ‘decoherence’ problem in mesoscopic systems

‘best’ Electronic-TFI

Quantum effects in Magnetic Salts

Documents

Transcript of Quantum effects in Magnetic Salts