Voltage-Controlled High-Bandwidth Terahertz Oscillators Based On Antiferromagnets Mike A. Lund1Davi R. Rodrigues2Karin Everschor-Sitte3and Kjetil M. D. Hals1 1Department of Engineering Sciences University of Agder 4879 Grimstad Norway

2025-05-06 0 0 800.6KB 6 页 10玖币

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Voltage-Controlled High-Bandwidth Terahertz Oscillators Based On Antiferromagnets

Mike A. Lund,1Davi R. Rodrigues,2Karin Everschor-Sitte,3and Kjetil M. D. Hals1

1Department of Engineering Sciences, University of Agder, 4879 Grimstad, Norway

2Department of Electrical and Information Engineering,

Polytechnic University of Bari, 70125 Bari, Italy

3Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE),

University of Duisburg-Essen, 47057 Duisburg, Germany

(Dated: October 20, 2023)

Producing compact voltage-controlled frequency generators and sensors operating in the tera-

hertz (THz) regime represents a major technological challenge. Here, we show that noncollinear

antiferromagnets (NCAFM) with kagome structure host gapless self-oscillations whose frequencies

are tunable from 0 Hz to the THz regime via electrically induced spin-orbit torques (SOTs). The

auto-oscillations’ initiation, bandwidth, and amplitude are investigated by deriving an eﬀective the-

ory, which captures the reactive and dissipative SOTs. We ﬁnd that the dynamics strongly depends

on the ground state’s chirality, with one chirality having gapped excitations, whereas the oppo-

site chirality provides gapless self-oscillations. Our results reveal that NCAFMs oﬀer unique THz

functional components, which could play a signiﬁcant role in ﬁlling the THz technology gap.

The terahertz (THz) technology gap refers to a fre-

quency range of electromagnetic radiation in the THz

regime where current technologies are ineﬃcient for gen-

erating and detecting radiation [1–3]. While traditional

electronics work well for producing and sensing mi-

crowaves and optics typically operate in the infrared re-

gion, few devices can utilize the THz range. THz devices

are expected to have widespread applications ranging

from improving the sensibility of biological and medical

imaging techniques [4] to enhancing the functionality of

information and communication technologies [5]. There-

fore, developing compact and reliable THz components

is one of the main challenges of today’s electronics.

In this context, antiferromagnetic spintronics has po-

sitioned itself as a promising future technology due to

the intrinsic THz spin dynamics of antiferromagnets

(AFMs) [6–11]. Notably, several works have demon-

strated that the antiferromagnetic order couples to elec-

tric ﬁelds [12–27] – either indirectly via electrically gen-

erated spin currents or directly via spin-orbit torques

(SOTs). This implies that it is possible to manipulate

AFMs by electric ﬁelds and that AFMs can be used to

modulate electric currents. Speciﬁcally, the latter ef-

fect has been proposed as a possible mechanism for de-

veloping nano-scale THz generators [28–36]. The nano-

oscillators use DC electric ﬁelds to create self-oscillations

in the AFM, which are sustainable cyclic modulations of

the spin order driven without the stimulus of an external

periodic force. The self-oscillations act back on the elec-

tronic system, producing a THz electric output signal.

Generally, there exists a frequency window in which both

the amplitude and frequency of the AC output signal are

tunable via the electric ﬁeld. This frequency window rep-

resents the bandwidth of the nano-oscillators. The ability

to maintain and control the self-oscillations over a broad

range of frequencies is critical for the applicability of the

nano-oscillators [37, 38].

FIG. 1. (color online). a. A kagome AFM with broken mirror

symmetry sandwiched between two metals. An electric ﬁeld

combined with spin-orbit coupling (SOC) generates an out-

of-equilibrium spin density scollinear with the electric ﬁeld,

which can drive self-sustained oscillations in the AFM. b. (c.)

A spin conﬁguration with (+)-chirality ((−)-chirality). The

phase hosts gapped (gapless) self-oscillations corresponding

to a rotation θ(t) of the sublattice spins about z.

Previous works on AFM nano-oscillators have been

theoretical and concentrated on so-called collinear

AFMs [28–34], i.e., spin systems characterized by an an-

tiparallel arrangement of the neighboring magnetic mo-

ments. However, in several AFMs, the spin sublat-

tices are noncollinearly ordered. These spin systems are

known as noncollinear AFMs (NCAFMs). In contrast to

the collinear AFMs, where a staggered ﬁeld parametrizes

the spin order [39], a rotation matrix describes the spin

order of NCAFMs [40]. Consequently, the NCAFMs ex-

hibit more complex and intriguing spin physics than most

ferromagnets and collinear AFMs. For example, recent

works have revealed novel topological phenomena [41]

and a signiﬁcant spin Hall eﬀect [42, 43]. However, de-

spite the great interest in NCAFMs, their current-driven

self-oscillations remain largely unexplored [35].

arXiv:2210.01529v2 [cond-mat.mes-hall] 19 Oct 2023

Here, we investigate the SOT-driven self-oscillations

in a trilayer system consisting of a thin-ﬁlm NCAFM

with a kagome structure sandwiched between two met-

als. The external electric ﬁeld is applied perpendicu-

lar to the thin-ﬁlm plane (see Fig. 1a). Surprisingly, we

ﬁnd that the dynamics of the self-oscillations strongly de-

pend on the chirality set by the relativistic Dzyaloshin-

skii–Moriya interaction (DMI) of the system. Despite the

large in-plane and out-of-plane magnetic anisotropies, we

show that one of the two chiral structures hosts gap-

less self-oscillations that are highly tunable via intrinsic

SOTs. In contrast, the structure of opposite chirality

has gapped oscillations. Notably, the gapless oscillations

enable voltage-controlled NCAFM nano-oscillators with

exceptional bandwidths, where the frequency is tunable

from 0 Hz to the THz regime via the applied DC electric

ﬁeld. Our results thus demonstrate that the NCAFMs

oﬀer distinct chiral magnetic properties that are particu-

larly attractive for bridging the gap between technologies

operating in the microwave and infrared regions.

The material systems we consider are thin-ﬁlm kagome

AFMs, where the mirror symmetry of the kagome lattice

plane is broken. These systems are described by the point

group D6[44]. Important candidate materials include

Mn3X (X= Ga, Ge, Sn), which in isolation are charac-

terized by the point group D6h[45], sandwiched between

two diﬀerent metals. The broken spatial inversion sym-

metry of the system has two signiﬁcant consequences: 1)

it leads to a magnetoelectric eﬀect, and 2) it induces a

DMI. The main eﬀect of the DMI is that it determines the

chirality of the ground state (see Fig 1b-c). The magneto-

electric eﬀect refers to the out-of-equilibrium spin density

produced by electric ﬁelds [46], which in magnetic sys-

tems yields an SOT [47–50]. Below, we start by deriving

the magnetoelectric eﬀect of NCAFMs with D6symme-

try from symmetry arguments [51]. Then, based on the

symmetry analysis, we phenomenologically add the cou-

pling terms between the spin system and electric ﬁeld in

a microscopic model, which is used as starting point for

deriving an eﬀective action and dissipation functional of a

uniform NCAFM. Further, the eﬀective theory is applied

to investigate the voltage-controlled self-oscillations.

In linear response, the out-of-equilibrium spin density

sproduced by the electric ﬁeld Eis given by [46]

si=ηij Ej.(1)

Here, ηij is a second-rank axial tensor, which satisﬁes the

following symmetry relationships [48, 49]

ηij =|G|Gii′Gjj′ηi′j′,(2)

dictated by the generators Gof the system’s point group.

|G|represents the determinant of the symmetry oper-

ation G. Throughout, we apply Einstein’s summation

convention for repeated indices. For kagome AFMs de-

scribed by the point group D6, the symmetry relations in

Eq. (2) imply that ηij is diagonal and parameterized by

two independent parameters [52]: ηxx =ηyy ≡η⊥and

ηzz ≡ηz. Here, the xand yaxes span the kagome plane,

whereas the z-axis is perpendicular to the lattice plane

(Fig. 1a). Consequently, the out-of-equilibrium spin den-

sity produced by the electric ﬁeld can be written as





sz

=



η⊥0 0

0η⊥0

0 0 ηz



Ex

Ez

.(3)

Interestingly, we see that the electric ﬁeld in kagome

AFMs can polarize the spin density along any axis (also

the out-of-plane axis z). This is diﬀerent from most thin-

ﬁlm systems, which usually are characterized by Dressel-

haus or Rashba SOC where the electric ﬁeld only gener-

ates spin densities polarized along an in-plane axis of the

thin-ﬁlm magnet [47–49]. In what follows, we investigate

how the spin density (3) couples to the NCAFM.

The kagome AFM is modeled by the spin Hamiltonian

H=He+Ha+HD+HE.(4)

Here, He=JP⟨ι˜ι⟩Sι·S˜ιdescribes the isotropic

exchange interaction (J > 0) between the neighbor-

ing lattice sites ⟨ι˜ι⟩, whereas Ha=Pι[Kz(Sι·ˆ

z)2−

K(Sι·ˆ

nι)2] represents the easy axes (K > 0) and easy

plane (Kz>0) anisotropy energies. The unit vector

nιdenotes the in-plane easy axis at lattice site ι. The

kagome AFM consists of three spin sublattices with in-

plane easy axes ˆ

n1= [0,1,0], ˆ

n2= [√3/2,−1/2,0], and

n3= [−√3/2,−1/2,0], respectively (Fig. 1b-c). HD=

P⟨ι˜ι⟩Dι˜ι·(Sι×S˜ι) is the DMI where Dι˜ι=Dzˆ

z[53].

HE=−PιgrSι·ηEexpresses the reactive coupling to

the electric ﬁeld, where gris the coupling strength.

The ground state of the spin Hamiltonian (4) depends

on the ratio Dz/K. If Dz/K < 1/4√3, the spins are

aligned parallel or anti-parallel to the in-plane easy axes,

i.e., Sι=±ˆ

nι(see Fig. 1b). We will refer to these

two ground states as (+)-chiral. On the other hand,

if Dz/K > 1/4√3, the spins attain a conﬁguration of

opposite chirality, which we will refer to as having (−)-

chirality (Fig. 1c). The (−)-chiral conﬁguration is related

to (+)-chiral structure by a reﬂection about the xz-plane.

The dynamics of the spin system is described by the ac-

tion S=PιℏRdtA(Sι)·˙

Sι−RdtHand the dissipation

functional G=PιℏRdt[(αG/2) ˙

ι+gd˙

Sι·(ηE×Sι)] [54–

58]. Here, ˙

Sι≡∂tSι,Ais deﬁned via ∇×A(Sι) =

Sι/S,αGis the Gilbert damping parameter, and the

term proportional to gdcharacterizes the dissipative cou-

pling to the current-induced spin density. To derive an

eﬀective description of the dynamics, it is convenient to

express the three sublattice spins as [54]

Sι(t) = SR(t) [ˆ

nι+aL(t)]

∥ˆ

nι+aL(t)∥, ι ∈ {1,2,3}.(5)

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Voltage-ControlledHigh-BandwidthTerahertzOscillatorsBasedOnAntiferromagnetsMikeA.Lund,1DaviR.Rodrigues,2KarinEverschor-Sitte,3andKjetilM.D.Hals11DepartmentofEngineeringSciences,UniversityofAgder,4879Grimstad,Norway2DepartmentofElectricalandInformationEngineering,PolytechnicUniversityofBari,70125Bari...

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Voltage-Controlled High-Bandwidth Terahertz Oscillators Based On Antiferromagnets Mike A. Lund1Davi R. Rodrigues2Karin Everschor-Sitte3and Kjetil M. D. Hals1 1Department of Engineering Sciences University of Agder 4879 Grimstad Norway

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