Enhanced skyrmion metastability under applied strain in FeGe M. T. Littlehales1L. A. Turnbull1M. N. Wilson1 2M. T. Birch3H. Popescu4N. Jaouen4J. A. T. Verezhak5G. Balakrishnan5and P. D. Hatton1

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Enhanced skyrmion metastability under applied strain in FeGe

M. T. Littlehales,1L. A. Turnbull,1M. N. Wilson,1, 2 M. T. Birch,3H.

Popescu,4N. Jaouen,4J. A. T. Verezhak,5G. Balakrishnan,5and P. D. Hatton1

1Department of Physics, Durham University, DH1 3LE, United Kingdom

2Department of Physics and Physical Oceanography, Memorial University, A1B 3X7, Canada

3Max-Planck-Institut f¨ur Intelligente Systeme, Heisenbergestraße, 70569, Stuttgart, Germany

4Synchrotron SOLEIL, Saint Aubin, BP 48, 91192, Gif-sur-Yvette, France

5Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom

(Dated: October 5, 2022)

Mechanical straining of skyrmion hosting materials has previously demonstrated increased phase

stability through the expansion of the skyrmion equilibrium pocket. Additionally, metastable

skyrmions can be generated via rapid ﬁeld-cooling to form signiﬁcant skyrmion populations at

low temperatures. Using small-angle x-ray scattering and x-ray holographic imaging on a thermally

strained 200 nm thick FeGe lamella, we observe temperature-induced strain eﬀects on the structure

and metastability of the skyrmion lattice. We ﬁnd that in this sample orientation (H k[1 1 0])

with no strain, metastable skyrmions produced by ﬁeld cooling through the equilibrium skyrmion

pocket vanish from the sample upon dropping below the well known helical reorientation tempera-

ture. However, when strain is applied along [1 1 0] axis, and this procedure is repeated, a substantial

volume fraction of metastable skyrmions persist upon cooling below this temperature down to 100

K. Additionally, we observe a large number of skyrmions retained after a complete magnetic ﬁeld

polarity reversal, implying that the metastable energy barrier protecting skyrmions from decay is

enhanced.

I. INTRODUCTION

Magnetic skyrmions, nanometric vortex-like whirls of

magnetization, typically exist in chiral magnets [1, 2] un-

der speciﬁc temperature and magnetic ﬁeld conditions

[3–5]. Skyrmions are normally stabilized by the compe-

tition of direct exchange, the Zeeman interaction, ther-

mal ﬂuctuations, and the Dzyaloshinskii-Moriya interac-

tion (DMI), which requires a non-centrosymmetric crys-

tal structure as present in conventional helimagnetic sys-

tems such as MnSi [3], FeGe [6], and the insulating ferri-

magnet Cu2OSeO3[7]. Characterised by an integer wind-

ing number, skyrmions arrange in a periodic hexagonal

crystal in two-dimensions, with a tube-like nature in the

third dimension [8, 9]. Their structure, size and dynami-

cal properties indicate promise for skyrmions as elements

in complex computing devices such as skyrmion racetrack

memory [10, 11], logic-gates [12], boolean processors [13],

skyrmion transistors [14] as well as neuromorphic [15],

stochastic [16] and reservoir computing [17].

A number of methods have been demonstrated to

increase the size of the skyrmion equilibrium pocket to

lower temperatures and higher magnetic ﬁelds [18, 19].

For example, reducing the thickness of the system along

the applied ﬁeld direction can expand the skyrmion

equilibrium region by surpressing the conical phase

[20, 21]. Additionally, metastable skyrmion states with

near-inﬁnite lifetimes can be formed by rapid ﬁeld

cooling through the equilibrium skyrmion pocket to

low temperatures [4, 22, 23]. Although not the energy

minimum of the system, metastable states with large

energy barriers present a greater operating region in

which skyrmions may be manipulated for potential

future device applications.

As a near-room-temperature skyrmion host, FeGe,

is a promising candidate for the above mentioned de-

vices. However, a major consideration in engineering

novel spintronic applications lies in exploiting extrin-

sic eﬀects such as mechanical strain [24]. As the mag-

netic spin conﬁguration in any material is fundamen-

tally dependent on the underlying crystal structure, un-

derstanding the connection between magnetism and me-

chanical strain, known as magnetoelastic coupling, is

paramount. Recent studies investigating strain eﬀects

on skyrmion spin textures have demonstrated anisotropic

modulations of the skyrmion lattice, eﬀectively modu-

lating the DMI and exchange strength [25, 26]. Simi-

lar anisotropic DMI has been observed in anti-skyrmion

systems caused by the D2d crystal symmetry [27, 28].

As a consequence of these energetic changes, mechanical

strain can increase the skyrmion stability region [29, 30],

(as is also seen for applied uniaxial pressure [19]) with

Monte-Carlo simulations of anisotropic DMI support-

ing these results [31, 32]. Additionally, there are re-

ports of room-temperature skyrmions existing in strain-

engineered FeGe thin ﬁlms [33]. These results also point

to a method of direct skyrmion creation, via voltage con-

trolled application of strain with piezoelectric substrates

[34, 35].

In this study, we employ resonant x-ray holography

[36, 37] to image the real space magnetization [38] of

metastable skyrmion states under the eﬀects of ther-

mally induced tensile strain on lamella of single crystal

FeGe [39, 40]. Through diﬀerential thermal contraction

between the sample and substrate, we conﬁrm ellipti-

cal skyrmion lattice deformation using small-angle x-ray

scattering (SAXS) and demonstrate enhanced metasta-

arXiv:2210.01702v1 [cond-mat.str-el] 4 Oct 2022

FIG. 1. a-b Scanning-electron-microscopy (SEM) images of control and strained lamellae respectively. Darker patches in the

substrate represent a 3 µm diameter circular aperture and 6 µm long and 15 nm wide reference slit milled through the substrate

using focused ion beam milling. Purple indicates the FeGe lamella, blue the platinum strips, and white the tungsten remaining

from the omniprobe micromanipulator detachment. c-e Schematic illustrations of spin textures present within lamella, c

Helical (H), dConical (C) and eSkyrmion Lattice (SkL). f-h x-ray holographic reconstructions of spin textures in FeGe

lamellae corresponding to the illustrations in c-e.i-j Phase diagram schematics of cooling protocols used within this study. i

zero-ﬁeld-cooled (ZFC) protocol including cooling in zero-ﬁeld to 240 K then increasing magnetic ﬁeld to 100 mT (orange) and

ﬁeld-cooled protocol at 100 mT to 240 K with a reduction in magnetic ﬁeld to 0 mT (green). jField-reversal protocol including

a ﬁeld-cool at 100 mT to 100 K followed by a reversal of the magnetic ﬁeld to -150 mT and back to 100 mT.

bility of the skyrmion against helical reorientations [41–

43] and magnetic ﬁeld reversals.

II. EXPERIMENTAL DETAILS

Single crystals of FeGe were grown via the chemical

vapour transport method using 2 g of prepared FeGe

powder and 2 mg/cm3of iodine transport agent with the

source maintained at 450 ◦C and a 50 ◦C temperature

gradient across the length of the furnace. After a period

of 1-2 weeks, several single crystals with dimensions 1.5 x

1.5 x 1.5 mm3were obtained at the furnace cold end. Two

200 nm thick lamellae were milled from one of the sin-

gle crystals with [0 0 1] and [1 1 0] directions in the plane

of the sample and [1 1 0] out of the plane of the lamella,

using focused gallium ion-beam (FIB) milling. The sub-

strate consisted of a 5×5 mm, 300 µm silicon chip with

200 nm thick Si3N4x-ray transparent windows masked

with 600 nm sputter-coated Au to avoid detector satu-

ration and minimise x-ray background, which was then

mounted on a copper holder. The lamellae were ﬁxed

to the Si3N4windows using platinum deposition at room

temperature. A 3 µm diameter aperture and a centrally

oﬀset 6 µm long and 15 nm reference slit [37] was milled

through the Au mask using FIB milling as shown in Fig.

1a & b.

A control sample was made by ﬁxing a single edge of

a lamella to allow free expansion and contraction with

temperature (Fig. 1a). The sample under strain was

produced by attaching opposite ends as shown in Fig.

1b. The silicon chip contracts more than FeGe when

cooling, therefore tensile strain up to a maximum of 0.25

% is produced at 100 K along the [1 1 0] direction (See

Appendix 1 for details of strain calculations).

X-ray holography was undertaken using the COMET

end-station on the SEXTANTS beam line at the SOLEIL

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EnhancedskyrmionmetastabilityunderappliedstraininFeGeM.T.Littlehales,1L.A.Turnbull,1M.N.Wilson,1,2M.T.Birch,3H.Popescu,4N.Jaouen,4J.A.T.Verezhak,5G.Balakrishnan,5andP.D.Hatton11DepartmentofPhysics,DurhamUniversity,DH13LE,UnitedKingdom2DepartmentofPhysicsandPhysicalOceanography,MemorialUniversity,A1B...

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Enhanced skyrmion metastability under applied strain in FeGe M. T. Littlehales1L. A. Turnbull1M. N. Wilson1 2M. T. Birch3H. Popescu4N. Jaouen4J. A. T. Verezhak5G. Balakrishnan5and P. D. Hatton1.pdf

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Enhanced skyrmion metastability under applied strain in FeGe M. T. Littlehales1L. A. Turnbull1M. N. Wilson1 2M. T. Birch3H. Popescu4N. Jaouen4J. A. T. Verezhak5G. Balakrishnan5and P. D. Hatton1

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