Hybrid magnetization dynamics in Cu 2OSeO 3NiFe heterostructures

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Hybrid magnetization dynamics in Cu2OSeO3/NiFe heterostructures

Carolina Lüthi∗,1, 2 Luis Flacke∗,1, 2 Aisha Aqeel,2, 3 Akashdeep Kamra,4Rudolf Gross,1, 2, 3 Christian Back,2, 3 and

Mathias Weiler1, 2, 5, a)

1)Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching, Germany

2)Physics Department, Technical University of Munich, Garching, Germany

3)Munich Center for Quantum Science and Technology (MCQST), Munich, Germany

4)Condensed Matter Physics Center (IFIMAC) and Departamento de Física Teórica de la Materia Condensada,

Universidad Autónoma de Madrid, Madrid, Spain

5)Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technical University of Kaiserslautern, Kaiserslautern,

Germany

(Dated: 4 October 2022)

We investigate the coupled magnetization dynamics in heterostructures of a single crystal of the chiral magnet

Cu2OSeO3(CSO) and a polycrystalline ferromagnet NiFe (Py) thin ﬁlm using broadband ferromagnetic resonance

(FMR) at cryogenic temperatures. We observe the excitation of a hybrid mode (HM) below the helimagnetic transi-

tion temperature of CSO. This HM is attributed to the spin dynamics at the CSO/Py interface. We study the HM by

measuring its resonance frequencies for in plane rotations of the external magnetic ﬁeld. We ﬁnd that the HM exhibits

dominantly four-fold anisotropy, in contrast to the FMR of CSO and Py.

Chiral magnets exhibit non-collinear spin structures such

as spin helices and magnetic skyrmions below their critical

temperature Tcand critical ﬁeld Hc21. Skyrmions are topolog-

ically protected non-coplanar magnetization conﬁgurations

that can behave as particle-like objects. Furthermore, they are

small yet stable making them suitable to become the carriers

of information in future devices2–12. The non-collinear spin

structure of chiral magnets gives rise to intriguing magnetiza-

tion dynamics, in particular in their skyrmion lattice phase13.

The recently discovered low-temperature skyrmion phase14

leads to additional striking spin dynamical signatures15 in the

low-damping16 chiral magnet CSO. The periodicity of the

magnetic lattice leads to naturally formed magnonic crystals17

and the skyrmion eigenmodes can be coupled to photonic res-

onators with high cooperativity18. The chiral properties of

skyrmions give rise to non-reciprocal spin-wave dynamics19.

Thus, the emerging ﬁeld of spin dynamics of chiral magnets

has already revealed important fundamental insights with per-

spectives for practical applications.

In topologically trivial magnets, the now well studied

coupling between multiple magnetic layers20–26 resulted in

the discovery of some of the most technologically rele-

vant effects such as tunneling magnetoresistance27 or gi-

ant magnetoresistance28,29. Heterostructures of topologically

trivial magnets can exhibit coupled spin dynamics that can

lead to, e.g., excitation of nanoscale spin waves30. Much less

is known about spin dynamics in heterostructures of collinear

and chiral magnets. The coupling between distinct order pa-

rameters across interfaces has explained important phenom-

ena such as proximity effects, exchange bias or exchange

spring-induced hard magnets31. However, the studies of ex-

citations in chiral magnets are so far limited to a single mag-

netically ordered constituent32. Even though the formation of

*These authors contributed equally to this work

a)Electronic mail: weiler@physik.uni-kl.de

novel topological order at the chiral magnet/ferromagnet in-

terface was predicted by theory it has not yet been observed

in experiment33.

In this work, we investigate the hybrid magnetization dy-

namics of heterosturctures of thin ﬁlm metallic ferromagnets

and bulk chiral magnets, in this case the ferrimagnetic insula-

tor Cu2OSeO3(CSO). To study the magnetization dynamics

of the chiral magnet/ferromagnet heterostructures in the GHz

frequency regime we use broadband ferromagnetic resonance

spectroscopy. We experimentally determine and phenomeno-

logically model the resonance frequencies in such heterostruc-

tures. Thereby, we ﬁnd that a hybrid mode of the chiral mag-

net/ferromagnet heterostructure is excited, which we attribute

to the spin dynamics at the interface of the two magnetic lay-

ers. We investigate a CSO/Ni80Fe20 (CSO/Py) sample, where

FIG. 1. (a) Experimental setup: The (111)-oriented

Cu2OSeO3/NiFe heterostructure is placed on the CPW, which gen-

erates a magnetic ﬁeld (h) within the sample due to the application

of an ac current ﬂowing from port 1 (P1) to port 2 (P2) of the center

conductor. (b) Schematic phase diagram of the Cu2OSeO3crystal

deﬁning the helimagnetic transition temperature Tc=58.2 K34 as

well as the critical ﬁelds µ0Hc1and µ0Hc2(H: helical state, C: con-

ical state, S: skyrmionic state, F: ferrimagnetic state). The vertical

dashed line indicates the phases of the CSO at 5 K in dependence of

the external ﬁeld.

the Py thin ﬁlm has a thickness of 40 nm. The CSO crystal

arXiv:2210.00897v1 [cond-mat.mes-hall] 30 Sep 2022

is (111)-oriented and cut to a cuboid shape with dimensions

Lx=2.5 mm, Ly=1.5 mm, and Lz=0.8 mm. It was grown by

a chemical vapor transport method15(for details on the crystal

orientation of the CSO and the sample preparation see Sup-

plemental Material I and II35). We place the CSO/Py hybrid

on top of a coplanar waveguide (CPW) with a center conduc-

tor width of w=127µm as shown in Fig. 1 (a). The CPW is

connected to two ports P1 and P2 of a vector network analyzer

(VNA), which measures the change of transmission from P1

to P2 deﬁned as the complex transmission parameter S21 as a

function of frequency fand external magnetic ﬁeld µ0Hat a

ﬁxed microwave power of 1 mW (0 dBm). We then place the

CPW/CSO/Py assembly into the variable temperature insert

of a superconducting 3D-vector magnet. By applying a static

external magnetic ﬁeld µ0Hin the plane of the Py thin ﬁlm

and setting the temperature to 5 K we can access the helical

(H), conical (C), and ferrimagnetic (F)phases of the CSO as

schematically depicted in Fig. 1 (b).

FIG. 2. Measured broadband ferromagnetic resonance spectrum of

the CSO/Py sample at 5 K as a function of the frequency f. The

ﬁxed external magnetic ﬁeld µ0H=120 mT is applied along the

x-axis (φH=0◦) as indicated in the sample sketches. (a) The CSO

crystal faces the CPW. Thus, only ferrimagnetic CSO modes apppear

(grey marked frequency range). (b) The Py thin ﬁlm faces the CPW.

In addition to the CSO modes the Py FMR mode appears at high

frequencies as well as a hybrid mode (HM) at medium frequencies

(inset). This HM is attributed to the spin dynamics at the interface

of the CSO/Py sample, indicated as an interfacial layer in the sample

sketch.

As a reference measurement, we ﬁrst place the CSO/Py hy-

brid sample on the CPW with the Py facing away from the

CPW. Due to the large thickness of the CSO layer, the oscil-

lating magnetic ﬁeld generated by the CPW does not reach

the Py layer. In this way, we only excite the magnetization

in CSO itself with no inﬂuence of the Py layer. We apply a

ﬁxed external magnetic ﬁeld µ0H=120 mT along the x-

axis (φH=0◦) at 5 K, as illustrated schematically in the top

panel of Fig. 2 (a). For this temperature and external mag-

netic ﬁeld strength the CSO magnetization is in the ﬁeld po-

larized phase. To correct for the microwave background of

the complex transmission parameter S21 we use the derivative

divide method36, to obtain the ﬁeld derivative of the complex

transmission parameter ∂S21

∂Hdevided by S21. On the bottom

panel of Fig. 2 (a) Re(∂DS21/∂H)for the CPW/CSO/Py as-

sembly at 5 K is shown as a function of the frequency f. In

the grey marked frequency range several resonances appear.

These are attributed to the excitation of magnetostatic modes

of the cuboid-shaped CSO crystal. In the frequency range

7 GHz < f< 12 GHz no additional modes are observed (inset).

After determining the response of the isolated CSO magneti-

zation dynamics, we place the CSO/Py hybrid on the CPW

with the Py facing the CPW and again apply a ﬁxed magnetic

ﬁeld µ0H=120 mT along the x-axis as schematically shown

in the top panel of Fig. 2 (b). Now, the ﬁeld generated by the

CPW interacts with the Py layer as well as the CSO as the

Py layer is a thin ﬁlm. In the bottom panel of Fig. 2 (b),

Re(∂DS21/∂H)at 5 K is shown for the CPW/Py/CSO as-

sembly as a function of the frequency f. In addition to the

resonance lines of CSO (grey marked frequency range) also

the Py FMR line appears close to 10 GHz as expected. The

change in the CSO mode spectrum is attributed to the pres-

ence of the metallic ﬁlm and concomitant shielding of the mi-

crowave ﬁeld in the bulk of CSO. Furthermore, we observe

an additional medium frequency mode, which is shifted by

about 1 GHz to lower frequencies than the Py FMR mode.

This hybrid mode (HM) is also observed in the CSO/Py hy-

brid in the conical phase of CSO (see Fig. 6 in Supplemental

Material35). For the dependence of the HM on the magni-

tude of the external magnetic ﬁeld see Supplemental Material

III35. We attribute the appearance of this additional mode to

the spin dynamics at the CSO/Py interface. Thus, in a simpli-

ﬁed macrospin picture, we may treat our bilayer as a trilayer

with a new interfacial layer inheriting properties from both

sides. The HM is then modelled as a result of macrospin dy-

namics of the interlayer as discussed in the following.

To investigate the dependence of the HM on the direction

of the external magnetic ﬁeld we apply a ﬁeld with a ﬁxed

magnitude of µ0H=120 mT and rotate the ﬁeld direction

by 360◦in the Py ﬁlm plane. For a quantitative analysis of the

HM we simultaneously ﬁt the Py FMR peak and the HM peak

in the frequency domain of the transmission parameter S21 for

each ﬁxed external ﬁeld direction (for detailed informations

on the ﬁt model see Supplemental Material IV35). In Fig. 3

three exemplary ﬁts of the frequency spectrum are shown for

a ﬁxed magnitude of the ﬁeld µ0H=120 mT and for different

directions under which it was applied. In Fig. 3 (a) the exter-

nal ﬁeld is applied in the Py thin ﬁlm plane along the x-axis

as schematically depicted at the top of Fig. 3 (a). We ﬁnd the

peak of the hybrid mode at 9.2 GHz, which has a small am-

plitude compared to the Py FMR peak-dip at 10.4 GHz. In

Fig. 3 (b) we show the ﬁt result for the ﬁeld applied under

an angle φH=30◦with respect to the x-axis as depicted at

the top of Fig. 3 (b). Now, the two resonance frequencies of

the Py mode and the HM are less separated than in Fig. 3 (a),

as the hybrid mode moved to higher frequencies and the Py

mode to lower frequencies. In Fig. 3 (c) the ﬁeld is applied

under an angle φH=60◦. The two resonance frequencies

of the Py mode and the HM are not separable anymore as the

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HybridmagnetizationdynamicsinCu2OSeO3/NiFeheterostructuresCarolinaLüthi,1,2LuisFlacke,1,2AishaAqeel,2,3AkashdeepKamra,4RudolfGross,1,2,3ChristianBack,2,3andMathiasWeiler1,2,5,a)1)Walther-Meißner-Institut,BayerischeAkademiederWissenschaften,Garching,Germany2)PhysicsDepartment,TechnicalUniversityofM...

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Hybrid magnetization dynamics in Cu 2OSeO 3NiFe heterostructures

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