APS123-QED Thermally-generated spin current in the topological insulator Bi2Se3

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APS/123-QED

Thermally-generated spin current in the topological insulator

Bi2Se3

Rakshit Jain,1, 2 Max Stanley,3Arnab Bose,1, 2 Anthony R. Richardella,3Xiyue S.

Zhang,2Timothy Pillsbury,3David A. Muller,2, 4 Nitin Samarth,3and Daniel C. Ralph1, 4

1Department of Physics, Cornell University. Ithaca, NY 14853, USA

2School of Applied and Engineering Physics,

Cornell University. Ithaca, NY 14853, USA

3Department of Physics and Materials Research Institute,

The Pennsylvania State University,

University Park, 16802, Pennsylvania, USA

4Kavli Institute at Cornell for NanoScale Science, Ithaca, NY 14853, USA

(Dated: October 12, 2022)

arXiv:2210.05636v1 [cond-mat.mes-hall] 11 Oct 2022

Abstract

We complete measurements of interconversions among the full triad of thermal gradients, charge

currents, and spin currents in the topological insulator Bi2Se3by quantifying the eﬃciency with

which thermal gradients can generate transverse spin currents. We accomplish this by comparing

the spin Nernst magneto-thermopower to the spin Hall magnesistance for bilayers of Bi2Se3/CoFeB.

We ﬁnd that Bi2Se3does generate substantial thermally-driven spin currents. A lower bound for

the ratio of spin current to thermal gradient is Js/∇xT= (4.9 ±0.9) ×106(~/2e)Am−2/

Kµm−1, and a lower bound for the magnitude of the spin Nernst ratio is −0.61 ±0.11. The

spin Nernst ratio for Bi2Se3is the largest among all materials measured to date, 2-3 times larger

compared to previous measurements for the heavy metals Pt and W.

I. INTRODUCTION

Topological insulators (TIs) provide the most-eﬃcient known transduction between

charge current density and spin current density (i.e., the spin Hall eﬀect) [1–5], thereby

producing spin-orbit torques capable of driving magnetization switching in magnetic mem-

ory structures [6–8]. In addition, TIs can also very eﬃciently transduce thermal gradients

to electric ﬁeld via the Seebeck eﬀect [9–11], with potential for thermoelectric applications.

Here, for the ﬁrst time we measure the eﬃciency of transduction for all three legs of the

triad between thermal gradients, charge currents, and spin currents for a topological insu-

lator/magnet bilayer (see Fig. 1(b)). In particular, we provide the ﬁrst measurement of the

eﬃciency by which a thin ﬁlm of the topological insulator Bi2Se3can transduce a thermal

gradient to spin current. Understanding thermally-generated spin currents in topological

insulators is important for characterizing the eﬀect of Joule heating on measurements of

current-induced spin-orbit torques [12]. If the thermal spin currents are suﬃciently strong,

they could in principle be put to use in generating useful torques [13, 14]. We ﬁnd that

the magnitude of the spin Nernst ratio of Bi2Se3is larger by a factor of 2-3 compared to

previous reports for the heavy metals Pt [15–18] and W [16, 18, 19].

II. BACKGROUND

We measure thermally-generated spin currents using the same physics by which electrically-

generated spin currents give rise to the spin Hall magnetoresistance (SMR) eﬀect. In the

electrically-generated case, an electric ﬁeld Eapplied in the plane of a spin-source/ferromagnet

bilayer gives rise to a vertically-ﬂowing spin current density Jsvia the spin Hall eﬀect, with

an eﬃciency characterized by the spin Hall ratio, θSH [20]: Js=~

θSH

ρSS E, where ~is the

reduced Planck constant, eis the magnitude of the electron charge, and ρSS is the elec-

trical resistivity of the spin-source material. The degree of reﬂection of this spin current

at the magnetic interface depends on the orientation of the magnetization ˆmin the mag-

netic layer. The reﬂected spin current produces a voltage signal by the inverse spin Hall

eﬀect, causing the resistance of the bilayer to depend on the magnetization angle [21–23]:

∆R( ˆm) = (1 −m2

y)∆RSMR.Here myis the component of the magnetization unit vector

that is in-plane and perpendicular to the electric ﬁeld. This resistance change corresponds

to a voltage signal amplitude:

∆V= ∆RSMRI=∆RSM R

REl =2e

∆RSMR

ρSS

θSH

lJs,(1)

with Ithe total current through the bilayer, Rthe total resistance of the bilayer, and lthe

sample length. Our analysis will assume that a thermally-generated spin current produces

the same voltage signal as an electrically-generated spin current (i.e., that Eq. 1 holds for

both cases with the same experimentally-measured value of ∆RSMR/R).

An in-plane thermal gradient ∇xTcan similarly give rise to a vertically-ﬂowing spin

current in a spin-source layer via the spin Nernst eﬀect [15, 18]. Upon reﬂection of this spin

current from a magnetic interface and then the action of the inverse spin Hall eﬀect, this

results in a voltage signal parallel to the thermal gradient that depends on the magnetization

angle, in direct analogy to the spin Hall magnetoresistance. For experiments measured with

an open-circuit electrical geometry (i.e., no net longitudinal charge ﬂow in the bilayer) we

will deﬁne the eﬃciency of spin current generation by the spin Nernst eﬀect in terms of a

spin Nernst parameter θSN

Js=−~

θSN

ρSS

SSS ∇xT. (2)

Here SSS is the Seebeck coeﬃcient of the spin-source layer and ∇xTis the in-plane thermal

gradient. The thermally-generated voltage takes the form [15, 16, 19]

th =−l∇xT(S+S1+ (1 −m2

y)SSNT ) (3)

where SSNT is the coeﬃcient of the spin Nernst magneto-thermopower, S1is a magnetization-

independent oﬀset arising from the spin Nernst eﬀect and inverse spin Hall eﬀect, and and S

denotes the total eﬀective Seebeck coeﬃcient of the bilayer given by S=ρSS SF M tF M +ρF M SSS tSS

ρSS tF M +ρF M tSS ≈

χSSS .This approximation holds when the spin-source layer is a topological insulator such

as Bi2Se3for which the Seebeck coeeﬁcient is much larger than for the ferromagnetic layer

(SSS SF M ), and we deﬁne a current shunting ratio χ=ρF M tSS /(ρF M tSS +ρSS tF M )

where ρF M is the resistivity of the ferromagnet and tF M and tSS are the thicknesses of

the two layers. As long as thermally-generated and electrically-generated spin currents are

transduced to voltage the same way, we can combine Eqs. 1-3 to obtain

∇xT=−SSNT

∆RSMR

θSH

ρSS

(4)

θSN =θSH

SSNT

SSS

∆RSMR

.(5)

These are the two equations we will use to evaluate the thermally-generated spin current

and the spin-Nernst ratio θSN .

For an open-circuit measurement, θSN will have contributions from both spin-current

generated directly by a thermal gradient and spin current generated by an electric ﬁeld that

is also present due to the Seebeck eﬀect. It is therefore also of interest to separate these

eﬀects and deﬁne a spin current that would be generated by a thermal gradient alone, in

the absence of any electric ﬁeld, i.e., to deﬁne a “bare” spin Nernst ratio θ0

SN such that

Js≡ − ~

2eθSN

SSS

ρSS

∇xT=~

θSH

ρSS

E−~

θ0

ρSS

SSS ∇xT(6)

2e(χθSH −θ0

SN )SSS

ρSS

∇xT(7)

Therefore, we can calculate

θ0

SN =θSN +χθSH .(8)

In our experimental geometry, a small vertical thermal gradient ∇zTcan also be present

when we apply an in-plane thermal gradient. This will produce additional background

signals due to the ordinary Nernst eﬀect (ONE), the spin Seebeck eﬀect (SSE) + inverse

spin Hall eﬀect, and the anomalous Nernst eﬀect (ANE):

th =VON E ∇zT By+VSSE∇zT my+VAN E ∇zT mz.(9)

These signals will be distinguished from the voltages arising from an in-plane thermal gra-

dient based on the diﬀerent dependences on the magnetization orientation ˆm.

III. RESULTS

We analyze bilayers of Bi2Se3(8 nm)/ Co20Fe60B20 (≡CoFeB) (5 nm). The 8 nm thick-

ness of the Bi2Se3was chosen to ensure negligible hybridization between states on the two

surfaces [24, 25]. The Bi2Se3thin ﬁlms were grown by molecular beam epitaxy and initially

capped with 20 nm of Se to protect them from air exposure while transporting them to a

separate system for the deposition of the CoFeB. Details about the MBE growth can be

found in the supplementary information. High-quality growth of Bi2Se3is conﬁrmed by

atomic force microscopy as well as x-ray diﬀraction measurements (see Fig. S1). The exis-

tence of a surface state on the Bi2Se3thin ﬁlms (with no Se cap or CoFeB overlayer) was

also conﬁrmed using angle resolved photoemission spectroscopy (ARPES), which measured a

Dirac-like dispersion as shown in Fig. 1(c). As is evident from the position of the Fermi-level

in Fig. 1(c), the Bi2Se3layer is electron-doped prior to the Se capping. This is consistent

with previous studies which have identiﬁed the cause of the doping to be Se vacancies [10].

After transfer to the separate vacuum system we heated the Bi2Se3/Se samples to a heater

thermocouple temperature of 285 ◦C for 3.5 hours to remove the Se cap. We then deposited

the CoFeB by DC magnetron sputtering followed by a 1.2 nm protective layer of Ta which

forms TaOxupon air exposure. Cross-sectional scanning transmission electron microscopy

(Fig. 1(a)) shows that the bilayers possess a sharp interface with no visible oxidation at the

interface.

We measure the spin current that is generated both electrically and thermally. As a ﬁrst

step, we measure the spin Hall magnetoresistance of the bilayer. We use optical lithography

to pattern a Hall-bar sample geometry with 9 pairs of Hall contacts (only 5 are depicted

in Fig. 1(d)) and make a 4-point measurement of the longitudinal resistance while rotat-

ing a magnetic ﬁeld with ﬁxed magnitude in the YZ plane as deﬁned by the diagram in

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摘要：

APS/123-QEDThermally-generatedspincurrentinthetopologicalinsulatorBi2Se3RakshitJain,1,2MaxStanley,3ArnabBose,1,2AnthonyR.Richardella,3XiyueS.Zhang,2TimothyPillsbury,3DavidA.Muller,2,4NitinSamarth,3andDanielC.Ralph1,41DepartmentofPhysics,CornellUniversity.Ithaca,NY14853,USA2SchoolofAppliedandEngineer...

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APS123-QED Thermally-generated spin current in the topological insulator Bi2Se3

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