Stephen Nagler

Oak Ridge National Laboratory

Possible Kitaev spin liquid physics and

topological transitions in a-RuCl3

2 SEN CNLS 2019

Outline

I. Kitaev’s model• Quick reminder of possible relevance to materials

• Basics of a-RuCl3

II. Some inelastic neutron scattering• Magnons and fractional excitations in INS

• Inelastic neutron scattering in a-RuCl3

III. Recent results• Higher fields and 3rd dimension

• Magnetocaloric effect and T- B phase diagram

3 SEN CNLS 2019

Neutron Scattering Collaborators:A. Banerjee, A. Aczel, C. Balz, C. Batista, S. Bhattacharjee, C.

Bridges, H. Cao, B. Chakoumakos, G. Ehlers, O. Garlea, G.

Granroth, Y. Kamiya, J. Knolle, D. Kovrizhin, P. Lampen-Kelley, L.

Li, Y. Liu, Z. Lu, M. Lumsden, D. Mandrus, R. Moessner, M.

Stone, D, Pajerowski, A. Samarakoon, D. A. Tennant, B. Winn, J.-

Q. Yan, Y. Yiu, S. Zhang.

Christian Balz

arXiv:1903.00056

Additional collaborators:

X. Hu, S. M. Yadav, Y. Takano

4 SEN CNLS 2019

Outline

I. Kitaev’s model• Quick reminder of possible relevance to materials

• Basics of a-RuCl3

5 SEN CNLS 2019

Kitaev’s model on honeycomb lattice – a special QSL

6 SEN CNLS 2019

Kitaev’s model on honeycomb lattice – a special QSL

• Kitaev interaction: Bond-directional

dependent Ising coupling

• Exactly solvable Hamiltonian

→ quantum spin liquid ground state

7 SEN CNLS 2019

Dynamics of Kitaev QSL

Majorana: a = a† ~ (f + f†)

8 SEN CNLS 2019

Kitaev interactions in materials

d5 in low spin

octahedral

configuration

edge-sharing

octahedra

strong spin-

orbit coupling

See also:

H. Takagi et al.,

Nature Reviews Physics 1, (2019)

9 SEN CNLS 2019

Heisenberg – Kitaev Phase Diagram

K

J

10 SEN CNLS 2019

=

Effect of additional interactions

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a-RuCl3 : quasi - 2D honeycomb material

• Honeycomb lattice

• Ru3+ in octahedral low spin

• J1/2 → J3/2 transition 200 meV

Transition to zig-zag order at TN = 7 K

12 SEN CNLS 2019

Field dependence of TN BC 7.3 T

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Additional ordered phase 6 – 7.3 T

14 SEN CNLS 2019

Evidence of fractionalization from thermal Hall ?

15 SEN CNLS 2019

Outline

II. Some inelastic neutron scattering• Magnons and fractional excitations in INS

• Inelastic neutron scattering in a-RuCl3

16 SEN CNLS 2019

KCuF3 – a one dimensional S=1/2 HAFC•Tetragonal structure

•Chains of Cu2+ ions along c axis

•“Orbitally ordered” • Heisenberg AF chains of

S=1/2 Cu2+ ions

• Inter-chain coupling

leads to 3D AF order at

TN = 39 K

• Above TN the response

follows that expected for

the isolated S=1/2 chain

– which is much different

from that predicted for

classical spins

17 SEN CNLS 2019

Energy dependence of the response below TN

3 fold degenerate

2 fold degenerate

18 SEN CNLS 2019

Expectations for spin waves in a zigzag state

• Dispersion minima at ordering wavevectors (M points)

• Low energy constant E slices show cone shaped dispersion surfaces

around the M points

• Less general, but true for Heisenberg-Kitaev model:

G points show flat modes sharp in energy

-1

-0.5

0

0.5

1

[K,-

K,0

]

0

5

10

-0.5 0 0.5-1

-0.5

0

0.5

1

[H,H,0]

[K,-

K,0

]

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a-RuCl3 single crystal - INS

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Experiment: G point signal inconsistent with SW

T = 5 K

T= 10 K

• At TN 7 K the spin waves disappear throughout the Brillouin zone

• Above TN the continuum near the G point persists

21 SEN CNLS 2019

Q,T dependence of the continuum scattering

• circular column centered on H=K=0, extending to higher energies

• at low T, moderate energy SW peaks and column merge and scattering

resembles a six pointed star

• scattering persists to high T

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How does field affect the magnetic excitations?

4.8 K 10.2 K

4.8 K 10.2 K

Npj Quantum Materials 3, 8 (2018).

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Outline

III. Recent results• Higher fields and 3rd dimension

• Magnetocaloric effect and T- B phase diagram

C. Balz et al., arXiv:1903.00056

24 SEN CNLS 2019

FLEXX triple-axis-spectrometer

K. Habicht et al., EPJ Web of Conferences 83, 03007

(2015)

monochromator analyzer

13.5 T superconducting cryomagnet

detectorneutron beam

sample

25 SEN CNLS 2019

Constant Q scans, zero field

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Constant Q scans, B > 7.3 T

27 SEN CNLS 2019

Constant Q scans, B > 9 T

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Dispersion along L

Takeaway:

L dependence

consistent with

antiferromagnetic

interlayer

interaction (unit cell

has 3 layers)

29 SEN CNLS 2019

Recall B dependence of line shape

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B dependence of G point gap from INS

C. Balz et al.,

31

Magnetocaloric Effect Y. Takano group

∆𝑇 ∝ −𝑇 𝜕𝑀

𝜕𝑇 𝐻∆𝐻

32 SEN CNLS 2019

More complete phase diagram

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Comparison with Kasahara et al. phase diagram

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Some conclusions

• Inelastic neutron scattering in a-RuCl3 is

consistent with fractional excitations

• An external magnetic field applied in-plane leads

to a magnetically disordered state, with a higher

field transition to a state that seems to be

partially polarized and supports magnons

• The intermediate field state is consistent with a

QSL

35 SEN CNLS 2019

References on a-RuCl3

Neutron scattering experiments:

• A. Banerjee et al. Nature Materials 15, 733(2016).

• H. Cao, A. Banerjee et al. PRB 93, 134423 (2016).

• A. Banerjee et al. SCIENCE 356, 1055 (2017).

• P. Lampen–Kelley et al. PRL 119, 237203, (2017).

• A. Banerjee et. al., Npj Quantum Materials 3, 8 (2018).

• C. Balz et al., arXiv:1903.00056

Others:

• M. Ziatdinov et al. Nat. Comm. 7, 13774 (2016).

• A. Samarakoon et al. PRB 96, 134408 (2017).

• A. Little et al. PRL 119, 227201 (2017).

• A. N. Ponomaryov et al., PRB 96, 241107(R), (2017).

• R. Hentrich et al., PRL 120, 117204 (2018).