magnon pairing in quantum spin nematic -...

Magnon pairing in quantum spin nematic

Mike Zhitomirsky (Grenoble)

in collaboration with Hiro Tsunetsugu (Tokyo)

Outline

Introduction

Bound magnon states: from 1D chain to

frustrated square lattice

Condensate of bound magnon pairs: spin

nematic state

Mike Zhitomirsky Introduction

Spin Liquids

‘Traditional’ quantum magnetism: ordered magnetic states,

spin chains, ladders,…

Mordern theories: possibility of spin liquids in arbitrary dimension

short-range RVB, long-range RVB, Z2, U(1), topological,…

Recent experiments: triangular organics, (hyper)kagome,

3He monolayers,


anything else exotic?

3 + 1 states of Matter


Matter Magnetic Matter Defining property

gas paramagnet dilute

liquid spin-liquid isotropic

solid ordered magnets anisotropic

liquid crystal spin-nematic* partial symmetry

breaking

*(a.k.a. multipolar states) described by tensor order parameters, searched for the past 40 years, were rarely observed so far

magnets with S ≥ 1 and biquadratic exchange

on site tensor

’preformed’ CEF multipoles: such that

, while

spin-nematic order from strong correlations in a system of

magnetic dipoles


Blume & Hseich (1969)

Spin nematics in literature and in nature

K ji

2)( SS

SS ii

)(, l

nmJ

0)()( l

n

l

k J0)()( l

n

l

k JJ

NpO2 , CexLa1-xB6

zero magnetic field, irreps of SO(3), classification in L

finite magnetic fields, irreps of SO(2) , classif. in Lz,

spin nematic Lz= ± 2


Multipoles: symmetry classification

Bosons


Magnon BEC in applied field

U(1) gauge invariance

condensate wavefunction

chemical potential µ

Spins

SO(2) rotation symmetry

staggered magnetization

magnetic field H

)(r y

j

x

jj iSSM

change bosons: add flavor, valley index, triplet polarization,…

change kinetic energy: localized magnons in flat bands

Schulenburg et al (2002)

change potential energy: add attraction, competing

ferro- and antiferromagnetic bonds


Magnon BEC: quest for new physics

pair condensation versus density collapse

Valatin (1958), Noziéres (1982)

constrained Bose-Hubbard model, ni ≤ 2

Bonnes & Wessel (2011)


Pair superfluidity in attractive Bose gases

chain materials LiCuVO4,

Li2CuO2, Li2ZrCuO4…


Frustrated ferromagnets

layered square-lattice afms

90o Cu-O-Cu bonds yield FM n.n. exchange J1<0 with AF n.n.n. J2>0

by A. Tsirlin

Mike Zhitomirsky Bound pairs

Magnon pairing in strong fields

fully polarized state ]

single spin-flips (magnons) unstable at Hs1

pair of spin flips unstable at Hs2= Hs1 + ½EB

0 cf. Wortis (1963)

01

iiSf

)( 021 JJH kk

02

jiij SSf

p

kqkqkqpqpkqkqk pfJJJJqf )()()()( 2/2/21

2/2/2


Magnon pairs in 1D

frustrated spin chain

bound magnon pairs with k = π and

numerical studies

Chubukov (1991), Kuzian et al (2007), Ueda et al (2009)

)/( 12

2

1 JJJEB

Honecker et al (2006), Hikihara et al (2008), Sudan et al (2009) Nishimoto et al (2011)


Magnon pairs in LiCuVO4

weakly coupled chains

J1 = -1.6meV, J2 = 3.6meV, J5 ~ -0.4meV

pair condensation

Hs2 = 47.1T and Hs1 = 46.5T

Enderle et al (2004)

Tsunetsugu & MZ (2010)


Magnon pairs in 2D: J1-J2 SAFM

cf . Shanon et (2006)

bound pairs with k=(0,0)

)cos(cos)( yxk qqqf j

B jeE 2


Magnon pairs in 2D

antiferromanetic chains coupled by frustrating ferromagnetic bond

frustration is essential as it suppresses the kinetic energy of single spin flips

Mike Zhitomirsky Pair Condensate

Condensate of magnon pairs

Bogolyubov theory via the coherent boson states

single-magnon condensate = canted AF state

coherent pair condensate

00|| 0

0

a

ea

0)exp( QS iiQr

i eS ||

► dipolar symmetry

0|exp| jiij SSf ||zC► nematic symmetry

|| zC

)( 0 a

Tsunetsugu & MZ (2010)


Spin correlations

absence of the sub-lattice magnetization

exponential decay in transverse and longitudinal channels

quadrupolar (nematic) order parameter

0||

iS

lj

l

ilji ffSS *2||

22`

|| ij

z

j

z

i fSS

jijiij SSSSQ

2

1

ijji

xy

ij

xx

ij fSSiQQ22

1


Self-consistent BCS-type theory

bosonization via Holstein-Primakoff tranformation

mean-field averages

quasiparticle excitations: unpaired magnons

jiij aa

krqrnnrJBAr

rqqqk 21sinsin

21)(22

2/

riir aan

krqrnnrJHA rq 21coscos

21)( qrrJB rq cos)(


Self-consistentctheory: results

energy-field diagram

► for LiCuVO4: Hs2 = 47T and Hc = 44T

magnon excitations

Tsunetsugu & MZ, EPL 92, 37001 (2010)


New ultra-high-field phase in LiCuVO4

► the ultra high-field phase is a transverse spin-nematic state

pulsed field experiments

Banks et al (2006)

ultra-high field phase

Svistov et al (2011)


New high-field phases in LiCuVO4

► relation to the transverse spin-nematic at higher fields?

‘not so’ high-field phase: longitudinal SDW in isotropic AFM?

Banks et al (2006) Buetgen et al (2008,10)


Longitudinal SDW in LiCuVO4

neutron diffraction Masuda et al (2011)

)21(2

1 zmQ ► long-range SDW order?


2D spin-nematic?

spin-nematic phase in frustrated SAFM BaCdVO(PO4)2? Tsirlin et al (2008)

the high-field region is easily

achievable in a Lab: Hs=4.2 T;

various experimental techniques

may be applied

Summary

Mike Zhitomirsky The End

magnon pair condensate = spin nematic (quadrupole) state

smoking gun for spin-nematic:

hidden-order transitions, i.e. without evident order parameters

dynamical properties: collective quadrupole mode in longitudinal channel?

instabilities in the spin nematic phase: longitudinal IC state in LiCuVO4

nematic LRO in BaCdVO(PO4)2 and other frustrated 2D FMs

Magnon pairing ar a root to spin-nematic

Thank you!

magnon pairing in quantum spin nematic -...

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