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) 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.) 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 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 2+x 2-x 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 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) 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 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) 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? 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 • 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 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) • • • • 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 coexistence of LRO and mesoscopic orders • Mesoscopic: M= 1.3µ B /Tb • LRO: M=0.3 µ B /Tb Under pressure : a phase with larger unit cell is also stabilized I.M et al Nature (2002)Polarization + energy analysis
Low energy excitations
Nature of the static SRO? the ½ ½ ½ order
powder samples Tb
Ti
O
Symmetry analysis
The best structures (x=0)
The best structures (x=0)
The best structures (x=0)
Calculated diffuse scattering
The ½ ½ ½ order: summary
Probing the magneto-elastic coupling
Summary: what is new in TTO?
x=0.01
Pressure induced structures