Thermally generated Magnons in Quasi Two Dimensional Antiferromagnets

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The spin-ﬂop transition in the quasi two dimensional antiferromagnet MnPS3

detected via thermally generated magnon transport

F. Feringa,1, ∗J. M. Vink,1and B. J. van Wees1, †

1Physics of Nanodevices, Zernike Institute for Advanced Materials,

University of Groningen, 9747 AG Groningen, The Netherlands

(Dated: October 5, 2022)

We present the detection of the spin-ﬂop transition in the antiferromagnetic van der Waals material

MnPS3via thermally generated nonlocal magnon transport using permalloy detector strips. The

inverse anomalous spin Hall eﬀect has the unique power to detect an out-of-plane spin accumulation

[1] which enables us to detect magnons with an out-of-plane spin polarization; in contrast to strips

of high spin orbit material such as Pt which only possess the spin Hall eﬀect and are only sensitive to

an in-plane spin polarization of the spin accumulation. We show that nonlocal magnon transport is

able to measure the spin-ﬂop transition in the absence of other spurious eﬀects. Our measurements

show the detection of magnons generated by the spin Seebeck eﬀect before and after the spin-ﬂop

transition where the signal reversal of the magnon spin accumulation agrees with the OOP spin

polarization carried by magnon modes before and after the SF transition.

The recent discovery of long range magnetic ordering

in two dimensional magnets [2,3] opens possibilities to

study and explore the magnetic structure and dynamics

in two dimensional magnets. Especially antiferromag-

netic materials have gained a great interest for informa-

tion storage and as a medium for spin currents in spin-

tronic devices because they do not possess stray ﬁelds, are

robust against magnetic perturbations and have ultra-

fast magnetic dynamics [4,5]. Antiferromagnets possess

a variety of spintextures, for example uniaxial, easy-plane

or noncolinear spintextures, determined by the material

speciﬁc values of the exchange ﬁeld and anisotropy ﬁeld

parameters. Additionally, magnetic van der Waals mate-

rials have often much stronger intralayer exchange inter-

actions than interlayer exchange interactions giving mag-

netic van der Waals materials a rich variety in spintex-

tures.

Characterizing and probing magnetic transitions in

(quasi) 2 dimensional magnetic van der Waals materials

is crucial to understand magnetism at a low dimensional

limit; for example by characterizing the spin-ﬂop (SF)

transition in uniaxial antiferromagnets (AFM). When the

applied magnetic ﬁeld H0exceeds the spin-ﬂop ﬁeld HSF

at the SF transition, the spin conﬁguration changes from

(anti) parallel to (almost) perpendicular to the magnetic

ﬁeld. The SF transition has been studied by magnetic

measurements [6]. This is diﬃcult for thin (small vol-

ume) magnetic layers however as an alternative magnons

can be used to study the SF transition electrically. At the

spin-ﬂop ﬁeld, the energy for certain magnon modes goes

to zero which should result in a strong modiﬁcation and

even sign reversal of the spin polarization of the magnon

generated by the spin Seebeck eﬀect.

Magnon spintronics uses magnons to transport angu-

lar momentum which is an unique tool to investigate

magnetic dynamics in magnetic materials because it can

characterize magnetic van der Waals materials down to

a monolayer using a heterostructure of a heavy (ferro-

FIG. 1. (a) Spin structure of MnPS3. The red and blue

arrows denote the spin direction in the absence of a magnetic

ﬁeld. (b) Magnetization measured for an applied out-of-plane

magnetic ﬁeld. The spin-ﬂop transition is observed around

3.7 T, indicated by the sharp increase of the magnetization.

magnetic) metal and the magnetic layer. Magnon trans-

port has been extensively studied in 3 dimensional mag-

nets via spin pumping [7–9], spin Seebeck eﬀect [10–12]

and electrical injection and detection [13,14]. Nonlo-

cal magnon transport has been observed in ferrimagnets

[13,15] and antiferromagnets [16–20]. It has been shown

that the SF transition in Cr2O3(3D), for which the spins

lie in-plane before and after the SF transition, can be

probed locally via the spin Seebeck eﬀect using a Pt

[21,22] and Py [23] contacts. The spin Hall magne-

toresistance detected the SF transition in Pt or Pd in

contact with the van der Waals AFM CrPS4. This was

detected locally and therefore SMR only probes the mag-

netic properties in the ﬁrst layer(s) of the AFM in contact

to the heavy metal [24]. Detecting the SF transition via

thermally generated magnons in a nonlocal geometry in

van der Waals magnets has not been investigated. This

has the beneﬁt of studying the SF transition in a mag-

netic material outside the proximity of a heavy metal.

Moreover, as we will show, no spurious (thermal) eﬀects

are present in the detector strips except for an anoma-

lous Nernst eﬀect which can be subtracted in a straight-

arXiv:2210.01418v1 [cond-mat.mes-hall] 4 Oct 2022

zH0

ωαωβ

H0 H0

ωαωβ

H0 H0

a) b) c)

I’ II’ III’

m1 m1 m1 m1

m1 m1

FIG. 2. (a), (b) and (c) The magnon modes I’, II’ and III’ for the corresponding spin conﬁgurations I, II and III. (a) I’ possesses

two circular polarized magnon modes ωαand ωβ. (b) After the spin-ﬂop transition, II’ possesses a magnon mode ωαlinearly

polarized in ~n and ~m, and a magnon mode ωβwhich is linearly polarized in ~n and circular polarized in ~m. (c) III’ possesses

similar magnon modes as for II’ but the order parameters ~n and ~m point in a diﬀerent direction. (d) k = 0 frequencies for the

magnon modes I’, II’ and III’ are plotted.

forward way.

In this work, we detect the SF transition in antiferro-

magnetic transition metal trichalcogenide MnPS3using

thermally generated magnons which we detect nonlocally

using Pt and Py contacts. A heater generates a tempera-

ture gradient in MnPS3which generates magnons via the

spin Seebeck eﬀect which are detected at a Pt or Py de-

tector (Fig. 3). This is very clean way of measuring due

to the lack of other spurious eﬀects in the detector strips

and in the absence of a temperature gradient across the

interface of the detector strips [25]. The magnetic easy

axis in MnPS3is out-of-plane (OOP), i.e. perpendicular

to the a−bplane, and therefore the generated magnons

carry spins with an OOP polarization. These spins can-

not be detected via the regular inverse spin Hall eﬀect

(ISHE) which only generates a charge current for a spin

current with an in-plane spin polarization. However the

inverse anomalous Hall eﬀect (IASHE) is able to detect a

spin current with an OOP spin polarization, for example

using Py contacts [1,26]. We show that the Py contacts

can detect the spin-ﬂop transition in MnPS3via magnons

which carry spins with an OOP spin polarization via the

IASHE in Py. We detect that the polarization of the

spins carried by the magnon changes sign when crossing

the SF transition and that the detected signal is maxi-

mum when the energy of the relevant magnon modes go

to zero.

Antiferromagnets are characterized by two order pa-

rameters, the N´eel vector ~n =~m1−~m2and the net mag-

netization ~m =~m1+~m2. An easy-axis antiferromagnet

undergoes a SF transition when the applied magnetic

ﬁeld strength along the easy axis exceeds the spin-ﬂop

ﬁeld HSF =p2HAHE−H2

A, where HAis the anisotropy

ﬁeld and HEis the exchange ﬁeld strength of the antifer-

romagnetic material. After the spin-ﬂop transition, the

spins cant towards the applied magnetic ﬁeld direction.

Dynamically, antiferromagnets possess a variety of

magnon modes depending on the state of the antiferro-

magnet, presented in Fig. 2(a), (b) and (c). Below the

SF transition, the degeneracy of the two magnon modes

is lifted by the Zeeman splitting when a magnetic ﬁeld

is applied and therefore one magnon mode, ωβdecreases

and magnon mode ωαincreases in energy, as shown in

Fig. 2(d) for the k= 0 magnon modes. When exciting

the magnon modes at a ﬁnite temperature, the lower en-

ergy mode, ωβis populated more which spin is oriented

along the magnetic ﬁeld direction. Above the SF, the

magnons, ωβ, carry spins with a polarizion in the z di-

rection opposite to the magnetization order parameter ~m

and therefore the spin polarization in the z direction of

the magnons are opposite to the applied magnetic ﬁeld

direction. Consequently, the spin polarization direction

of the magnons changes from parallel to anti parallel to

the applied magnetic ﬁeld direction crossing the SF tran-

sition.

In a magnetic insulator a magnon spin current can be

generated due to a temperature gradient in a magnetic

material via the spin Seebeck eﬀect (SSE) which can be

expressed as [27]:

S=Sz

S∇T(1)

At zero magnetic ﬁeld the magnon modes I’ are degen-

erate and therefore under the inﬂuence of a temperature

gradient both modes are populated equally. Both modes

carrier opposite angular momentum and therefore no net

spin current is present. An imbalance in population be-

tween the modes is present at a ﬁnite magnetic ﬁeld re-

sulting in a ﬁnite net spin current. The spin Seebeck

coeﬃcient Sz

Sdepends on the diﬀerence in occupation of

the diﬀerent magnon modes [28]. At the SF transition,

mode ωβreaches zero and therefore the largest Sz

Sis ex-

pected.

The total detected voltage is given by [29]:

VNL =GSz

S(2)

where G∝RNwλN2e

~θASH tanh( tN

2λN)Cg↑↓ ~

∇Twith RN

is the resistance, tNthe thickness, wthe width, θASH

the anomalous spin Hall angle and λNis the spin relax-

ation length of the detector strip. g↑↓ is the eﬀective

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摘要：

Thespin-optransitioninthequasitwodimensionalantiferromagnetMnPS3detectedviathermallygeneratedmagnontransportF.Feringa,1,J.M.Vink,1andB.J.vanWees1,y1PhysicsofNanodevices,ZernikeInstituteforAdvancedMaterials,UniversityofGroningen,9747AGGroningen,TheNetherlands(Dated:October5,2022)Wepresentthedetectio...

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Thermally generated Magnons in Quasi Two Dimensional Antiferromagnets

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