Pis’ma v ZhETF, vol. 111, iss. 12, pp. 813 - 814

June 25

Second-harmonic voltage responce for the magnetic Weyl semimetal

Co₃Sn₂S₂

V. D. Esin, A. V. Timonina, N. N. Kolesnikov, E. V. Deviatov¹⁾

Institute of Solid State Physics of the Russian Academy of Sciences, 142432 Chernogolovka, Russia

Submitted 29 April 2020

Resubmitted 29 April 2020

Accepted 29

April 2020

DOI: 10.31857/S1234567820120046

Recent interest to the time-reversal-invariant non-

Laue patterns confirm the hexagonal structure with

linear Hall (NLH) effect [1] is a part of a broad research

(0001) as cleavage plane. Magnetoresistance measure-

area of topological systems. In zero magnetic field, a

ments confirms high quality of our crystals: Co₃Sn₂S₂

non-linear Hall-like current arises from the Berry cur-

samples demonstrate [7, 8] giant anomalous Hall effect

vature, which can be be regarded as a magnetic field

and positive, non-saturating longitudinal magnetoresis-

in momentum space. It leads to a quadratic response

tance, which even quantitatively coincide with the pre-

to ac excitation current, so NLH effect should appear

viously reported ones.

as a non-zero transverse second-harmonic voltage with-

To obtain a definite sample geometry, the leads pat-

out magnetic field. Since Berry curvature concentrates

tern is formed on the insulating SiO₂ substrate by lift-

in regions where two or more bands cross [2], topological

off technique after thermal evaporation of 100 nm Au,

systems are the obvious candidates to observe the NLH

see Fig.1. Small (about 100 µm size and 1 µm thick)

effect [1]. It has been experimentally demonstrated for

Co₃Sn₂S₂ flakes are transferred to the Au leads pattern,

monolayer transitional metal dichalcogenides [3, 4] and

see [7-9] for details. We measure the second-harmonic

for three-dimensional Weyl and Dirac semimetals [5].

longitudinal V^2ωxx(I) and transverse V^2ωxy(I) voltage com-

First experimentally investigated Weyl semimetals

ponents in standard four-point lock-in technique, see the

(WSMs) were non-centrosymmetric crystals with bro-

principal circuit diagrams in Fig. 1a and b, respectively.

ken inversion symmetry. Even in this case, the magnetic

The potential contacts are always situated along the

field measurements allow to distinguish the NLH effect

sample edge, while the ac current I flows along the edge

from the thermoelectric response [5].

for V^2ωxx(I) investigations in Fig. 1a, and normally to it

Recently, giant anomalous Hall effect was reported

in Fig. 1b for V^2ωxy(I) ones.

for the kagome-lattice ferromagnet Co₃Sn₂S₂, as an in-

We observe significant second-harmonic longitudi-

dication for the existence of a magnetic Weyl phase. So-

nal voltage V^2ωxx(I) for two different samples. V^2ωxx(I) is

phisticated regimes of second-harmonic response should

strongly non-linear, it is proportional to the square of

also be expected in Weyl semimetals with broken time

the applied current. This behavior strongly contradicts

reversal symmetry. In addition to the expected Berry

to zero V^2ωxx(I) for non-magnetic monolayer transitional

curvature contribution to the Hall-like currents, the chi-

metal dichalcogenides [3, 4] and for three-dimensional

ral anomaly contribution to second-harmonic generation

Weyl and Dirac semimetals [5]. On the other hand, the

in the lowest order is linearly proportional to the ap-

inherent magnetization of a thick Co₃Sn₂S₂ flake is per-

plied magnetic field [6]. Moreover, in magnetic materi-

pendicular to the flake’s plane, so Nernst voltage ap-

als, Nernst voltage can be generated normally to the

pears as longitudinal V^2ωxx(I) ∼ I² in our experimental

temperature gradient even without an external mag-

setup, which is known as anomalous Nernst effect.

netic field, which is known as anomalous Nernst effect

It has been demonstrated [5] for non-magnetic three-

(ANE). ANE was reported for different Co₃Sn₂S₂ ther-

dimensional Weyl and Dirac semimetals, that magnetic

moelectric devices.

field measurements are important to establish an ori-

Co₃Sn₂S₂ single crystals were grown by the gradi-

gin of the second-harmonic voltage. The V^2ωxx(B) depen-

ent freezing method, see [7, 8] for details. The kagome-

dence is a nearly odd function, there is also a significant

lattice ferromagnet Co₃Sn₂S₂ can be easily cleaved, the

jump in zero magnetic field, like it is expected for ANE.

For the transverse V_xy(I) voltage component in zero

¹⁾e-mail: dev@issp.ac.ru

magnetic field, the linear Hall voltage V^1ωxy(I) ∼ I is

Письма в ЖЭТФ том 111 вып. 11 - 12

2020

813

814

V. D. Esin, A. V. Timonina, N. N. Kolesnikov, E. V. Deviatov

other hand, the low-field linear behavior with the zero-

field jump demands another explanation. On the one

hand, Berry curvature dipole NLH effect [1] should also

be seen in magnetically ordered WSMs. Berry curvature

acts analogously to a magnetic field in the momentum

space, so NLH voltage is linear in external magnetic

field [5] and also picks up the Co₃Sn₂S₂ magnetization.

The latter should lead to the zero-field jump, since the

V^2ωxy(B) branches correspond to different magnetization

directions. On the other hand, one can expect some con-

tribution from Fermi arcs to magnetothermal transport

in Weyl semimetals. For topological insulators the latter

effect is known to produce large and anomalous Seebeck

effects with an opposite sign to the Hall effect [10].

We wish to thank V. T. Dolgopolov for fruitful dis-

cussions, O. O. Shvetsov for samples preparation.

We gratefully acknowledge financial support par-

tially by the Russian Foundation for Basic Research

(project # 19-02-00203), Russian Academy of Sciences,

and RF State task.

Fig. 1. (Color online) Sketch of the sample with electri-

Full text of the paper is published in JETP Letters

cal connections. Au leads are formed on a SiO2 substrate,

journal. DOI: 10.1134/S0021364020120024

with 5 µm intervals between them. A thick Co3Sn2S2 flake

(≈ 100 µm size) is transferred [7, 8] on the top of the leads,

forming small Ohmic contacts (≈ 10 µm overlap between

1. I. Sodemann and L. Fu, Phys. Rev. Lett. 115, 216806

the Co3Sn2S2 flake and the leads). Current flows along

(2015).

the sample edge in (a) for V^2ωxx(I) investigations, and nor-

2. N. P. Armitage, E. J. Mele, and A. Vishwanath, Rev.

mally to it in (b) for V^2ωxy (I) ones. The second-harmonic

Mod. Phys. 90, 15001 (2018).

(2ω) component of the longitudinal voltage V^2ωxx (I) is mea-

3. Q. Ma, S.-Y. Xu, H. Shen et al. (Collaboration), Nature

sured in a standard four-point lock-in technique

565, 337 (2019).

4. K. Kang, T. Li, E. Sohn, J. Shan, and K. F. Mak, Nature

due to the finite Co₃Sn₂S₂ magnetization in zero ex-

Mater. 18, 324 (2019).

ternal field. We also obtain non-linear second-harmonic

5. O. O. Shvetsov, V. D. Esin, A. V. Timonina,

V^2ωxy(I) ∼ I², which is one magnitude smaller than for

N. N. Kolesnikov, and E. V. Deviatov, JETP Lett.

the xx configuration. In principle, finite V^2ωxy(I) ∼ I²

109, 715 (2019); DOI: 10.1134/S0021364019110018.

can be produced [5] both by NLH and by the thermo-

6. A. A. Zyuzin and A. Yu. Zyuzin, Phys. Rev. B 95,

electric effects. In the latter case, the second-harmonic

085127 (2017); DOI: 10.1103/PhysRevB.95.085127.

voltage reflects the Seebeck effect [5], because potential

7. O. O. Shvetsov, V. D. Esin, A. V. Timonina,

contacts are parallel to the temperature gradient.

N. N. Kolesnikov, and E. V. Deviatov, EPL

127,

We observe sophisticated magnetic field behavior

57002 (2019); doi: 10.1209/0295-5075/127/57002.

for the second-harmonic xy component: V^2ωxy(B) is al-

8. O. O. Shvetsov, V. D. Esin, Yu. S. Barash,

ways positive for both fields’ directions, it demonstrates

A. V. Timonina, N. N. Kolesnikov, and E. V. De-

strong nonlinear increase in high magnetic fields. How-

viatov, Phys. Rev. B

101,

035304

(2020);

ever, V^2ωxy(B) is obviously not symmetric, there is also

DOI:https://doi.org/10.1103/PhysRevB.101.035304.

a linear region between -1.1 T and +1.7 T with a small

9. O. O.

Shvetsov,

A. Kononov, A. V. Tim-

zero-field jump. This behavior strongly contradicts to

onina,

N.N. Kolesnikov,

and E. V. De-

the known one both for NLH and for the Seebeck ef-

viatov,

JETP Lett.

107,

774

(2018);

fects in non-magnetic materials [5].

https://doi.org/10.1134/S0021364018120020.

In our experimental setup, the longitudinal thermal

10. Y.

Xu, Zh. Gan, and Sh.-Ch. Zhang,

conductivity corresponds to the inverse V^2ωxy(B) value,

Phys.

Rev.

Lett.

112,

226801

(2014);

as described above, so the high-field behavior of V^2ωxy(B)

DOI:https://doi.org/10.1103/PhysRevLett.112.226801.

is in agreement with the theoretical predictions. On the

Письма в ЖЭТФ том 111 вып. 11 - 12

2020