magnétisme quantique dans un composé à chaînes de...

Magnétisme quantique dans un composé à chaînes de spins

Béatrice GrenierUGA & CEA-INAC-MEM, Grenoble

Journée Fédération Française de Diffusion Neutronique& Séminaire Techniques Neutroniques (spectroscopie/petits angles)

Grenoble, 17-18 décembre 2018

Outline

2

x Introduction- Strongly correlated systems- Classical phase transitions- Conventional 3D vs Quantum 1D antiferromagnets- Motivations of our work

x Neutron scattering study of the BaCo2V2O8 spin chain compound- BaCo2V2O8: Crystallographic structure and magnetic model- Magnetic structure- Magnetic excitations

x Conclusion and perspectives- Conclusion: A topological phase transition- On-going work

Journée 2FDN, Grenoble, Décembre 2018 - Magnétisme quantique - Béatrice Grenier

Quantum magnetism in a spin chain compound

at zero-field and in a transverse magnetic field

x Introduction- Strongly correlated systems- Classical phase transitions- Conventional 3D vs Quantum 1D antiferromagnets- Motivations for studying BaCo2V2O8

Introduction: Stronly correlated electron systems in 3D

3

Condensed matter physics → Study of many-body systems (Cu: 8.5 x 1022 electrons/cm-3)

Strong interactions→ Strongly correlated electron systems:collective phenomena = one of the most difficult problem to describe

The Rubik’s cube→ 3D correlated (classical) system

Courtesy of Andrés Felipe Santander-Syro


Magnetic material→ 3D Strongly correlated electron system

Paramagnet at high 𝑇 (disordered)

Introduction: Stronly correlated electron systems in 1D

4

And at one dimension (1D) ?


A simple model: the spin chain!

Strong quantum fluctuations(especially for low spins)

𝐽 𝐽

Courtesy of Quentin Faure

Introduction: Classical phase transition – Liquid/Solid

5

Classical phase transition:Phase transition between two different phases (phase change) upon cooling / warming

When 𝑇 increases: ice → liquidSpontaneous symmetry breaking

Liquid water


Example 1: water→ Long range ordering (translational & rotational) of the O et H atoms at 𝑇 < 0 °C (273 K)

𝑇120°

𝑇 (°C)

0Ice water

Order parameter = mass density 𝝆

𝑇 (°C)

-100 -50 0 50 100

1000

980

960

940

920

𝜌 (kg/m3)

𝑇 (K)𝑇𝐶

Paramagnet(disordered)

Introduction: Classical phase transition – Ferromagnet

6Journée 2FDN, Grenoble, Décembre 2018 - Magnétisme quantique - Béatrice Grenier

Order parameter = magnetization 𝑴

Example 2: conventional 3D ferromagnet

→ Long range ordering of the spins at 𝑇 < 𝑇𝐶

Ferromagnet(ordered)

𝑱𝒊𝒋 𝑱𝒊𝒋

H = <𝒊,𝒋>

𝑱𝒊𝒋 𝑺𝒊 . 𝑺𝒋 Hamiltonian

(simplest case)𝑱𝒊𝒋 < 0

𝑇 (K)𝑇𝐶

𝑀 (𝜇𝐵)

FM PM

𝑀𝑠𝑎𝑡

0

𝑇 (K)

Introduction: Classical phase transition – Antiferromagnet


H = <𝒊,𝒋>

𝑱𝒊𝒋 𝑺𝒊 . 𝑺𝒋 Hamiltonian

Antiferromagnet(ordered)

Example 3: conventional 3D antiferromagnet

→ Long range ordering of the spins at 𝑇 < 𝑇𝑁

𝑱𝒊𝒋 > 0

𝑇𝐶

(simplest case)

Paramagnet(disordered)

𝑱𝒊𝒋𝑇 (K)𝑇𝑁

𝑀𝑠𝑡𝑎𝑔 (𝜇𝐵)

AF PM

Order parameter = staggeredmagnetization 𝑴

𝑀𝐴𝐹

0𝑱𝒊𝒋 𝑆𝑗 = − 𝑆𝑖 𝑆𝑖

Introduction: Magnetic excitations in 3D vs 1D AFs


Example 3: conventional 3D antiferromagnet

→ Magnetic excitations

Excitation spectrum:

One well defined dispersion branch

𝑞

4𝐽𝑆

0 0 𝜋/𝑎 2𝜋/𝑎En

ergy

𝐸 𝑞 = 4𝐽𝑆 |sin(𝑞𝑎)|

𝐿

(𝑞 = 2𝜋/𝐿)

= spin waves = magnons at 𝑇 < 𝑇𝑁

𝐽 𝐽

𝑎

0 1 20

1

2

q /S

E /J

𝜋𝐽

Ener

gy0

q0 𝜋/𝑎 2𝜋/𝑎

→ ungapped 2-spinon continuum

Introduction: Magnetic excitations in 1D vs 3D AFs


Example 4: quantum 1D antiferromagnet (spin ½ case)

→ No long range ordering down to 𝑻 = 𝟎 (only a quasi AF LRO)→ Magnetic excitations

𝑞

4𝐽𝑆

0 0 𝜋/𝑎 2𝜋/𝑎

Ener

gy

spinons { domain walls created in pairscarry a spin 1/2

spinons propagate with no energy cost

= deconfined spinons at low 𝑻

KCuF3

Nagler et al., Phys. Rev. B (1991)KCuF3: Heisenberg (isotropic) spin ½ chain

Ener

gy

𝜋𝐽

0

𝝐 = 𝟏

𝝐 → +∞

𝝐 = 𝟎

H = 𝐽 𝑖

𝝐 𝑆𝑖𝑥𝑆𝑖+1𝑥 + 𝑆𝑖𝑦𝑆𝑖+1

𝑦 + 𝑆𝑖𝑧𝑆𝑖+1𝑧

Introduction: Motivation for studying BaCo2V2O8

10

x Magnetic anisotropy

Heisenberg Isotropic

XY Planar

Ising Uniaxial


x Spin chains = Playground for studying quantum phase transitions

x BaCo2V2O8: AF effective spin ½ chain with sizable interchain coupling (quasi-1D) and weak Ising anisotropy (𝜖 = 0.5)

quantum

Phase transition upon the variation of a physical parameter (𝑯, 𝒑,…) at 𝑻 = 𝟎

Consequences on the static and dynamical properties?What happens in a magnetic field? → topological quantum phase transition

Outline



x Neutron scattering study of the BaCo2V2O8 spin chain compound- BaCo2V2O8: Crystallographic structure and magnetic properties- Magnetic structure- Magnetic excitations



BaCo2V2O8: an effective spin ½ XXZ quasi-1D AF

12

x Screw chains of effective spin ½ ∥ c-axis 𝐼41/𝑎𝑐𝑑 (𝑎 = 12.44 Å, 𝑐 = 8.42 Å)

Intrachain interaction: 𝑱 AF

𝑱𝑱

x Ising-like anisotropy (XXZ): 𝜖 ∼ 0.5 (𝑍 { 𝑐) H = 𝐽 𝑖

𝝐 𝑆𝑖𝑎𝑆𝑖+1𝑎 + 𝑆𝑖𝑏𝑆𝑖+1𝑏 + 𝑆𝑖𝑐𝑆𝑖+1𝑐R. Wichmann et al., Z. Anorg. Allg. Chem. (1986)


𝑱′

x Non-negligible inter-chain interactions (quasi-1D)

𝑱′

Dominant interchain interaction: 𝑱’ AF

𝐽′ ≪ 𝐽

BaCo2V2O8 in a transverse magnetic field 𝑯 ∥ 𝒃


𝑏 𝑎

𝑐

x Crystallographic peculiarities

S. Kimura et al., J. Phys. Soc. Jpn. (2013)

∼ 5°Non diagonal 𝑔 tensor

𝑯 ∥ 𝒃

→𝑯 ∥ 𝒃 (uniform)

𝒉𝒂

−𝒉𝒂

−𝒉𝒂𝒉𝒂

induces 𝒉𝒂 ∥ 𝒂 (staggered)

𝒉𝒂

Nature of the phase transition and of the phase above?

BaCo2V2O8𝐻 ∥ 𝑏

?

S. K. Niesen et al., Phys. Rev. B (2013)

𝐻 (T)

x Macroscopic measurements

𝐻𝑐 ≪ 𝐻𝑠𝑎𝑡

Neutron diffraction set up

14

DIFFRACTION = elastic scattering (𝛥𝐸 = 0)

- Bragg peaks positions: periodicity of the magnetic structure

- Bragg peak intensities:Arrangement (directions + amplitude) of the magnetic moments in the unit cell


x Single-crystal diffractometer D23 @ ILL𝜆 = 1.28 ÅTechnical support: Pascal Fouilloux

𝐻 = 0: Orange cryostat𝐻 ∥ 𝑏: 12 T vertical field cryomagnet

𝐻

x Crystal synthesis:Floating zone method @ Institut Néel, GrenobleP. Lejay et al., Journ. Cryst. Growth (2001)

Magnetic ordering below and above 𝑯𝒄

15

𝑯 = 𝟎

antiparallel

𝐻 0=

𝑘 = (1,0,0)

𝐻 0=

×1

𝑏

𝑎

𝑎

𝑐

c

𝑏

E. Canévet et al., Phys Rev B (2013)


𝒎𝒄 = 𝟐. 𝟑 𝝁𝑩/Co2+

𝑯 = 𝟏𝟐 𝐓

parallel

𝐻||𝑏

𝑘′ = (0,0,0)

𝐻||𝑏

×2.4

Q. Faure et al.,Nature Phys. (2018)

𝒎𝒂 = 𝟎. 𝟒 𝝁𝑩/Co2+

Magnetic field dependence of 𝒎𝒄 and 𝒎𝒂

16

Staggered 𝒎𝒄: typical behavior of an order parameter


0.0 0.5 1.0 1.50.0

0.5

1.0

1.5

2.0

2.5

Mag

netic

mom

ent (P B

/Co2+

)

H / Hc

2 0 1 (𝑚𝑐)

𝐻𝐻𝑐


𝑀𝐴𝐹

0

⇒ Unconventional quantum phase transition

→ field-induced AF order along 𝒂 stabilized by the effective staggered field 𝒉𝒂 induced by 𝑯𝒃

0 5 10 15𝐻 (T)

3 0 3 (𝑚𝑎)

Staggered 𝒎𝒂: unusual behavior

𝐻𝐻𝑐


𝑀𝐴𝐹

0

0.0 0.5 1.0 1.50.0

0.5

1.0

1.5

2.0

2.5

Mag

netic

mom

ent (P B

/Co2+

)

H / Hc

Inelastic neutron scattering set-up

17

x Cold neutron Triple-Axis Spectrometers (TAS) ThALES and IN12 @ ILL𝑘𝑓 = 1.3 Å-1 ; scattering plane ( 𝑎∗, 𝑐∗) ; orange cryostat (0 T) & 12 T vertical field cryomagnetTechnical support: Eric Villard, Bruno VettardLocal contacts: Martin Boehm, Stéphane Raymond

ThALES, non polarized neutrons IN12, (un)polarized neutrons at (0 T) 12 TJournée 2FDN, Grenoble, Décembre 2018 - Magnétisme quantique - Béatrice Grenier

Neutrons "measure"spin fluctuations ⊥ 𝑸Measurement of 𝑺(𝑸,𝝎) with 𝑄 = 𝑘𝑖 − 𝑘𝑓

ℏ𝜔 = (𝐸𝑖 − 𝐸𝑓)

Magnetic excitations → determination of 𝑱, 𝑱′ , 𝝐, …

x Discretization

(2, 0, 𝑄𝐿)

IN12

B. Grenier et al.,Phys. Rev. Lett. (2015)

Zero-field magnetic excitations


Ener

gy

1D Heisenberg spin ½ AF

q0 𝜋/𝑎 2𝜋/𝑎

𝜋𝐽

0

BaCo2V2O8, quasi-1D Ising-like effective spin ½ AF

x Gap (∼ 1.8 meV) ← Ising-like anisotropy

H. Shiba, Prog. Theor. Phys. (1980)

u uu

← Confined spinons ← 𝐽′

𝐽′

Constant 𝑸 energy-scan

Zero-field magnetic excitations


BaCo2V2O8, quasi-1D Ising-like effective spin ½ AF

(2, 0, 𝑄𝐿)

Shintaro Takayoshi and Thierry GiamarchiDQMP, University of Geneva, Switzerland

Infinite Time Evolution Block Decimation (iTEBD)

𝐽 = 5.8 meV, 𝜖 = 0.53, 𝐽′ = 0.16 meV

IN12

Magnetic excitations in a transverse magnetic field


𝐻 (T)0 2 4 6 8 10 12

Ener

gy(m

eV)

4

3

2

1

0𝐐 = 3,0,1𝐻 ∥ 𝑏

ThALES

1 2 3 4

E (meV)

Q = (3, 0, 1)P

0H = 3 T3 T 12 T

1 2 3 1 2 3 1 2 3 4

x 0.1

E (meV)

Q = (3, 0, 1)P

0H = 12 T

300

200

100

0

E (meV) E (meV)

Neu

tron

cou

nts

Q. Faure et al.,Nature Phys. (2018)

𝐻𝑐



𝐻 (T)0 2 4 6 8 10 12

Ener

gy(m

eV)

4

3

2

1

0𝐐 = 3,0,1𝐻 ∥ 𝑏

ThALES

Polarized neutrons (IN12): separation between fluctuations ∥ 𝑏 (𝑆𝑏𝑏) and ⊥ 𝑏 (𝑆𝑎𝑎 and 𝑆𝑐𝑐)

𝑺𝒃𝒃

𝑺𝒂𝒂 + 𝑺𝒄𝒄

Anisotropy of the magnetic neutron scattering (𝑆𝛼𝛼 ⊥ 𝑄): separation between 𝑆𝑎𝑎 and 𝑆𝑐𝑐

𝑺𝒂𝒂 + 𝑺𝒃𝒃 𝑺𝒄𝒄

𝑺𝒂𝒂

𝑏 𝑎

𝑐

𝒎 ∥ 𝒄

𝑺𝒃𝒃

Magnetic excitations ⊥ ordered magnetic moment over the complete field range

𝑯𝒉𝒂

−𝒉𝒂

𝑏 𝑎

𝑐

𝒎 ∥ 𝒂

𝑺𝒄𝒄

𝐻𝑐



𝐻𝑐𝐻 (T)0 2 4 6 8 10 12

Ener

gy(m

eV)

4

3

2

1

0 𝐐 = 3,0,1𝐻 ∥ 𝑏

𝐻𝑐

Experiment (ThALES) Theory (iTEBD)Shintaro Takayoshi and Thierry Giamarchi

Q. Faure et al., Nature Phys. (2018)S. Takashoshi, Phys. Rev. B (2018)

Outline



x Neutron scattering study of the BaCo2V2O8 spin chain compound- BaCo2V2O8: Crystallographic structure and magnetic properties- Magnetic structure- Magnetic excitations



Conclusion: Topological quantum phase transition

24

x Field theory (S. Takayoshi & T. Giamarchi) Competition Ising anisotropy (low 𝐻) / staggered field (high 𝐻)→ competition between two dual topological excitations

BaCo2V2O8 = first realization of the double sine Gordon model


x Numerical calcultations: exact diagonalization (Q. Faure) & iTEBD (S. Takayoshi & T. Giamarchi) → phase transition induced by the staggered field

Low field: topological excitations = spinons

𝜋

2𝜙

𝑆𝑧 = +12

𝑆𝑧 = −12

𝑐

𝑎

𝑐𝑏

High field: dual topological excitations

2𝜋𝜃

𝜋

𝑆𝑥 = +1 𝑆𝑥 = −1

𝑧

𝑎

𝑐𝑏

On-going work / Perspectives


x Magnetic field ∥ chains:

Incommensurate dynamics(Tomonaga Luttinger liquid theory)

Ener

gy(m

eV)

(3, 0, 𝑄𝐿)-1.8 -1.6 -1.4 -1.2 -1.0

5

4

3

2

1

0

𝐸 min at 𝑄𝐿 = −1.108

TASP, PSI

Technical support: M. BartkowiakLocal contacts: J. S. White, M. Månsson

x Doping by non magnetic impurities (Mg):

Chain cuts → flat modes

(2, 0, 𝑄𝐿)

IN12, ILL

Technical support: B. VettardLocal contact: S. Raymond

Virginie SIMONET Institut Néel, Grenoble, FranceSylvain PETIT LLB, CEA – Saclay, France

Shintaro TAKAYOSHI, Thierry GIAMARCHI DQMP, Univ. Geneva, SwitzerlandShunsuke FURUYA, RIKEN, Japan

Stéphane RAYMOND, Louis-Pierre REGNAULT INAC/MEM, CEA – Grenoble, FranceMartin BOEHM ILL, Grenoble, FranceChristian RÜEGG PSI, Villigen, Switzerland

Benjamin CANALS, Pascal LEJAY Institut Néel, Grenoble, France

Acknowledgments

26

Emmanuel CANEVET (Ph-D 2007-2010)

UJF & ILL, Grenoble, Francenow at PSI, Villigen, Switzerland

Quentin FAURE (Ph-D 2015-2018)

UGA, CEA & CNRS, Grenoble, France


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