I.Mirebeau

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Transcript I.Mirebeau

Magnetic structures and anisotropic excitations in Tb

2

Ti

2

O

7

spin liquid

I.Mirebeau, S.Petit , A. Gukasov, J.Robert, thesis S.Guitteny, Laboratoire Léon Brillouin, CEA-Saclay P.Bonville

DSM/IRAMIS/SPEC, CEA-Saclay C.Decorse

ICMMO, Université Paris XI H.Mutka, J.Ollivier, M.Boehm, P.Steffens

Institut Laue Langevin, Grenoble A.Sazonov

LLB, Aachen University

Tb

2

Ti

2

O

7

: a hot topic

7 Posters at HFM’14

Kermarrec Malkin Fennel Hallas Kao Sazonov Yin

Why is Tb 2 Ti 2 O 7 (or TTO) so interesting ?

Spin liquid

Tb

2

Ti

2

O

7

: a hot topic

quantum spin ice magneto elastic liquid

TTO

Antiferro magnetic spin ice Spin Glass

because nobody fully understands it!

Tb

2

Ti

2

O

7

: a hot topic

In the last 3 years More and more sophisticated experiments

• • Searching for a magnetization plateau : H //111 Probing dispersive excitations

Influence of tiny defects

• • ½ ½ ½ structure Competing SRO structures : Spin glass like vs. mesoscopic order

Coupling with the lattice

• • magneto-elastic mode Dynamic Jahn-Teller transition and/or interactions between quadrupolar moments

Towards a more realistic description ?

Dipolar Spin ices: The Ising case

R 2 Ti 2 O 7

Mc. Clarthy- Gingras Rev Modern Phys. (

pyrochlores R=Dy, Ho Effective interaction

J eff = J+D dip > 0 Tb Dy Ho

Tb nearby the threshold Quantum fluctuations at play: « quantum spin ice » Molavian, Gingras, Canals, PRL (2008) Molavian , Clarthy, Gingras arxiv0912.2957

Mc. Clarthy- Gingras Rev Progress Physics 77 056501(2014)

What about the Crystal field ?

AF FeF 3 4in-4out Dipolar spin ice Spin ice Den Hertog et al Phys. Rev. Lett. (1999) Bramwell et al Phys. Rev. Lett (2000)

The crystal field

Tb 3+ is a non-Kramers ion Δ = 200 – 300K Ho, Dy spin ices Δ = 10-20K (Tb) Δ ~ 1.5 meV

Gingras, PRB (2000) Bonville, IM, PRB( 2007) Bertin,Chapuis, JPCM(2012) Zhang, Fritsch, PRB (2014) Klekovina- Malkin J Opt. Phys. (2014) Cao et al PRL(2009)

Strong but finite <111> anisotropy

𝜓 1 𝑗 𝜓 2 = 𝜓 2 𝑗 𝜓 1 = 0 𝜓 1 𝐽 𝑧 𝜓 1 = −4𝑎 2 + 5𝑏 2 𝜓 2 𝐽 𝑧 𝜓 2 = 𝜓 1 𝐽 𝑧 𝜓 1 • • No exchange fluctuations allowed within the GS doublet No intensity scattered by neutrons

Splitting of the Ground state doublet

In molecular field approach

1st order perturbation

Quantum mixing in the GS

.

0th order perturbation h I α I α | 𝜓 ′ 1 ( ℎ ∆ ) 2

Δ ~ 1.5 meV

𝐽 𝜓 ′ 2 | 𝜓′ 1 = | 𝜓 1 | 𝜓′ 2 = | 𝜓 2 + ℎ Δ | 𝜓 1 𝑒 + ℎ Δ | 𝜓 2 𝑒 h: molecular field | 2 . 𝛿 𝜔 − 𝐸 1 − 𝐸 2 (g j µ B h/  ) 2  (0.75/15) 2  2.10

-3

g J µ B /k B = 1 for Tb !

d

Δ ~ 1.5 meV

| 𝜓′ 1 | 𝜓′ 2 | 𝜓 1 − | 𝜓 2 = = | 𝜓 1 + 2 | 𝜓 2 2 D: quantum mixing 1 2 ( 𝜓 1 𝐽 𝑧 𝜓 1 𝜓′ 1 𝜓 2 𝐽 𝑧 𝐽 𝑧 𝜓′ 2 𝜓 2 ) = = 𝜓 1 𝐽 𝑧 𝜓 1 ≠ 0 But 𝜓′ 1 𝐽 𝑧 𝜓′ 1 =0

Splitting of the Ground state doublet

In molecular field approach

1st order perturbation

Quantum mixing in the GS

.

0th order perturbation

Δ ~ 1.5 meV

h | 𝜓′ 1 = | 𝜓 1 | 𝜓′ 2 = | 𝜓 2 + ℎ Δ | 𝜓 1 𝑒 + ℎ Δ | 𝜓 2 𝑒 h: molecular field Virtual crystal field model • • Very small intensity associated with GS fluctuations (with resp. to CF ) Spin ice anisotropy: magnetization plateau Molavian, Gingras, Canals PRL(2007) Molavian, McClarthy, Gingras arxiv(2009) d

Δ ~ 1.5 meV

| 𝜓′ 1 | 𝜓′ 2 | 𝜓 1 − | 𝜓 2 = = | 𝜓 1 + 2 | 𝜓 2 2 Two singlet ground state • • • each singlet is non magnetic : no static signal the transition has a large spectral weight Jahn-Teller distortion?

Bonville et al PRB(2011), PRB (2014)

Searching for a magnetization plateau

Using Magnetization, susceptibility, MuSR : a controversial situation

low field anomalies of the susceptibility:

MuSR Baker PRB (2012)

No plateau in the isothermal magnetization

Yin et al PRL(2013)

cross over regime in the dynamics Spin glass-like freezing ? Fritsch , PRB(2014) T F ~200-400 mK

Lhotel et al PRB-RC (2012) Legl et al PRL (2012)

Searching for a magnetization plateau

Using neutrons : magnetic structure for H//111

• Exclude all-in all out structure • Gradual reorientation of the Tb moments in the Kagome plane (keeping 1in- 3 out) without Kagome ice structure

See poster A. Sazonov

Searching for a magnetization plateau

D=0 no mixing

A. Sazonov et al PRB(2013)

Field Irreversibilities • No evidence for the 1/3 plateau at ~2µB expected at very small fields (down to 80mK) • quantitative agreement with MF model assuming a

dynamical JT distortion:

• • 4 moment values and angles M(H) for H//100, 111, 110 Spin glass like freezing? •

see poster A. Sazonov

Spin fluctuations at very low temperature

Using unpolarized neutrons

• •

2 components in the neutron cross section elastic (dominant) inelastic (low energy) See also: Takatsu et al. JPCM (2011) Fritsch et al PRB(2013) inelastic elastic

• •

Pinch points diffuse maxima at ½ ½ ½ positions

D=0.25K

• •

becomes structured at low T well accounted for by 2 singlet model + anisotropic exchange

Static character not reproduced by the 2 singlet model

diffuse scattering

The main features of the diffuse scattering are reproduced

3d-map Experiment  b = -0.13T/µ B ; D Q =0.25K

6T2 ( LLB)

Energy integrated intensity

Simulation Phase diagram

P. Bonville et al Phys. Rev. B (2011)

• • • • • Simulation with anisotropic exchange dipolar interactions CF

JT distortion along equivalent 100, 010, 001 cubic axes

.( preserves the overall cubic symmetry)

Dynamical JT

(average Structure factors and not intensities)

Q dependence of the elastic scattering

• Pinch points in both compounds: Coulomb phase 𝑇𝑏 2 𝑇𝑖 2 𝑂 7

- 50 mK

no spectral weight at Q=0 ½ ½ ½ maxima : AF correlations 𝐻𝑜 2 𝑇𝑖 2 𝑂 7

- 50 mK

strong spectral weight at Q=0 S.Petit & al, PRB 86 (2012) T.Fennell & al, Science 326 (2009)

Analysis of the pinch points

Strongly anisotropic correlations of algebric nature conservation law in TTO spin liquid analogous to the ice rules

T. Fennell et al PRL(2012)

S.Guitteny & al, PRL 111 (2013)

What are the spin component involved?

Polarization analysis

Longitudinal polarimetry separates spin components

Fennell Science (2009) : Ho 2 Ti 2 O 7 PRL (2013) Tb 2 Ti 2 O 7

neutron polarization P// Z Neutron cross section • • Non spin flip: N+

z > Spin Flip

y > Ho 2 Ti 2 O 7 Z //110 1 1’ • • Correlations along Q (or x) between spin components M ┴ Q x// Q

M z

z

M y

x

Q

3 4 2 2’ NSF: correlations « up-down » 1-1’ or 2-2’: Weak (2 Spins, between T) SF: correlations « 2in-2 out » 1-2-3-4:

Strong

(4 spins, in a T)

Polarization + energy analysis

Longitudinal polarimetry separates spin components

Fennell Science (2009) : Ho 2 Ti 2 O 7 PRL (2013) Tb 2 Ti 2 O 7

neutron polarization P// Z Neutron cross section • • Non spin flip: N+

z > Spin Flip

y >

Tb

2 Ti 2 O 7 Z //110 1 T=50 mK 1’

Look at the dispersion

x// Q x y

Q

3 4 • • Correlations along Q (or x) between spin components M ┴ Q

M z

z

M y

2 2’ Mz: « up-down » correlations: relaxing (Quasi-E) My: « 2 in-2out » correlations : dispersing (Inel.)

Low energy excitations

First observation of a dispersive excitation in fluctuating disordered medium

• Mz In all directions • Quasi-élastic • Strong fluctuations My • • Along (h,h,h) • quasi-élastic along (h,h,2-h) et (h,h,0) • • • • propagating excitation no gap (Δres = 0,07meV) Disperses up to 0,3 meV intensity varies like 1/ω S. Guitteny et al PRL(2013) 18

Nature of the static SRO? the ½ ½ ½ order

Short range vs. mesoscopic order In single crystals

• • •

½ ½ ½ diffuse maxima

Short range ~8-10 A below ~0.4K

Fennel PRL (2012) Fristch PRB(2012) Petit PRB (2012)

Vanish in a small field ( ~200G)

In powders

• • •

½ ½ ½ Mesoscopic structure

Over 30-50A Associated with Cp anomaly tuned by minute defects in Tb content

Taniguchi PRB RC(2011)

See also poster E. Kermarrec

powder samples Tb

2+x

Ti

2-x

O

7+y

Mesoscopic structure for x=0 and x=0.01

T=50mK Difference pattern: I(50 mk)- I(1K) ½ ½ ½ ½ ½

3/2

N ½ ½

5/2 3/2 3/2 1/2 X=0 X=0

2 q (deg) exp: P. Dalmas de Réotier

space group Fd-3M, K= ½ ½ ½

Symmetry analysis

2 orbits with no common IR

N 1 2 3 4 site 0 0 0 ¾ ¼ ½ ¼ ½ ¾ ½ ¾ ¼

Champion, PRB (2001) Stewart, Wills JPCM(2004) Gd 2 Ti 2 O 7

site 1 Sites 2-4 No way to build a strong ½ ½ ½ peak for Ising spins!

K // local <111> axis no intensity at ½ ½ ½

• •

No vectors of the IR along the local <111> axes Contributions to ½ ½ ½ cancel by symmetry Needs to break either Ising anisotropy or cubic symmetry

• • •

Systematic search of magnetic structures

1T cfc translations (cubic cell : a) K= ½ ½ ½ (magnetic unit cell: 2a)

The best structures (x=0)

moments remain close to local <111>axes (3-10 deg)

« Monopole layered structure » « AF -Ordered spin ice »

X=0 X=0 M=1.9(4) µB/Tb; Lc =60 A (Y=1.4) Correlation length ~30 -50 A

The best structures (x=0)

moments remain close to local <111>axes (<10 degs)

« Monopole layered structure » « AF -Ordered spin ice »

Ferrimagnetic piling of

SI Tetrahedra AF packed OSI cubic cells ,

Fritsch PRB (2012) Z//001 M Z S. Guitteny (thesis) derived from Tb 2 Sn 2 O 7 I. M et al PRL (2005)

The best structures (x=0)

moments remain close to local <111>axes (<10 degs)

« Monopole layered structure » « AF -Ordered spin ice »

Ferrimagnetic piling of

SI Tetrahedra

separated by

monopole

layers Fritsch PRB (2012)

AF packed with M

OSI cubic cells

, separated by

SI tetrahedra

Z//001 M Z Full of monopoles, but compatible with a distortion No monopoles, but symmetry breaking at each cubic cell no possible LRO?

Calculated diffuse scattering

In a single crystal, correlation length reduced to 2 cubic cells « Monopole layered structure » « AF -Ordered spin ice »

4 4 3 3 2 2 1 1 1 2 h, h, 0

Experiments

Petit PRB (2013) Fennel PRL (2013) Fritsch PRB(2013) 3 4 1 2 h, h, 0 3 4

The ½ ½ ½ order: summary

• ½ ½ ½ order cannot propagate without breaking the cubic symmetry • different structures and/or K orientations may compete (in space, time) yielding: • • • SRO (single crystal) mesoscopic orders (powders, tuned by x) Spin glass like irreversibilities : Yin (2013), Fritsch PRB (2014) , Lhotel (2013) • 2 physical mechanisms at play for the magnetic excitations • Relaxation (quasielastic) • Dispersive excitations • Analog to the double dynamics in SP particles or quantum molecular magnets

Quasielastic or slow relaxations (thermally activated ,QT)

Magneto-elastic modes as a switching mechanism?

Inelastic modes

Probing the magneto-elastic coupling

Interaction between 1st excited CF doublet and acoustic phonon branch

Guitteny PRL(2013) see also: Fennel PRL(2013) this conf.

M. Ruminy : next talk Other probes

pressure induced magnetic order

IM et al Nature 2002, PRL(2004) •

Elastic constants

Klekovina-Malkin J. Phys. 2011, J. Opt. Phys. 2014 •

Thermal conductivity

Li et al PRB(2013)

Summary: what is new in TTO?

• • • •

Quantum mixing in the GS doublet due to quadrupolar order: a necessary ingredient

MF JT distortion « exchange » int. between quadrupolar moments Magnetoelastic coupling Non-Kramers character is crucial Gehring-Gehring (1985) Savary-Balents PRL(2012) Lee-Onoda-Balents PRB(2012) poster Malkin •

First observation of dispersive anisotropic excitations

in a fluctuating disordered medium Two types of dynamics : relaxation, excitations •

Competing SI correlations with K=½ ½ ½

• Not compatible with cubic symmetry • • Tuned by off-stoechiometries With different time and length scales • Associated with glassy behaviour

x=0.01

coexistence of LRO and mesoscopic orders • Mesoscopic: M= 1.3µ B /Tb • LRO: M=0.3 µ B /Tb

Pressure induced structures

Under pressure : a phase with larger unit cell is also stabilized

I.M et al Nature (2002)