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Tunable Strain in Magnetoelectric ZnO Micro Rod Composite Interfaces Stjepan Bozidar Hrkac, Christian Thorsten Koops, Madjid Abes, Christina Krywka, Martin Mueller, Manfred Burghammer, Michael Sztucki, Thomas G. Dane, Sören Kaps, Yogendra Kumar Mishra, Rainer Adelung, Julius Schmalz, Martina Gerken, Enno Lage, Christine Kirchhof, Eckhard Quandt, Olaf M. Magnussen, and Bridget M. Murphy ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b15598 • Publication Date (Web): 04 Jul 2017 Downloaded from http://pubs.acs.org on July 5, 2017

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ACS Applied Materials & Interfaces

Tunable Strain in Magnetoelectric ZnO Micro Rod Composite Interfaces Stjepan Bozidar Hrkac,

Krywka,

‡, ¶

Dane,

Schmalz,

⊥

†

Martin Müller,

§

Sören Kaps,

k

†

Christian Thorsten Koops,

‡, ¶

Manfred Burghammer,

Yogendra Kumar Mishra,

Martina Gerken,

⊥

Enno Lage,

Olaf Magnus Magnussen,

†, ¶

k

k

§

Madjid Abes,

†

Christina

Michael Sztucki,

Rainer Adelung,

Christine Kirchhof,

k

k

§

Thomas

Julius

Eckhard Quandt,

and Bridget Mary Murphy

k

∗,†,¶

†Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu

Kiel, Olshausenstr. 40, 24098 Kiel, Germany ‡Institute of Materials Research, Helmholtz Zentrum Geesthacht, 21502 Geesthacht,

Germany ¶Ruprecht Haensel Laboratory, Christian-Albrechts-Universität zu Kiel, Olshausenstr. 40,

24098 Kiel, Germany §ESRF - The European Synchrotron, CS 40220, 38043 Grenoble Cedex 9, France kInstitut für Materialwissenschaft, Christian-Albrechts-Universität zu Kiel, Kaiserstr. 2,

24143 Kiel, Germany ⊥Institut für Elektrotechnik und Informationstechnik, Christian-Albrechts-Universität zu

Kiel, Kaiserstr. 2, 24143 Kiel, Germany E-mail: [email protected]

Abstract The intrinsic strain at coupled components in magnetoelectric composites plays an 1

ACS Paragon Plus Environment


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important role for the properties and function of these materials. In this in

situ

X-ray

nanodiraction experiment the coating induced as well as the magnetic eld induced strain at the coupled interface of complex magnetoelectric micro composites were investigated. These consist of piezoelectric ZnO micro rods coated with an amorphous layer of magnetostrictive (Fe90 Co10 )78 Si12 B10 . While the intrinsic strain is in the range of 10−4 , the magnetic eld induced strain is with 10−5 one order of magnitude smaller. Additionally, the strain relaxation distance of around 5 µm for both kinds of strain superposes indicating a correlation. The value of both intrinsic and magnetic eld induced strain can be manipulated by the diameter of the rod like composite. The intrinsic interface strain within the ZnO increases exponentially by decreasing the rod diameter while the magnetic eld induced strain increases linear within the given range. This study shows that miniaturizing has a huge impact on magnetoelectric composite properties, resulting in a strongly enhanced strain eld and magnetic response.

Keywords X-ray nanodiraction, strain, magnetoelectric, ZnO, micro rod, magnetic eld

1 Introduction The possibility to tune the intrinsic interface strain to manipulate the response of functional composites is highly desirable.

Understanding the interaction of functional composites at

their shared interface is important to enhance the properties of said composite. Not only is the coupling at the interface important to transfer induced deformation

1

as witnessed in

magnetoelectric composites consisting of piezoelectric and magnetostrictive components, but it can be assumed that an intrinsic stress at the interface itself has a direct eect. For example, rst-principle calculations by Kou

2

predict a direct dependence of the charge carrier

separation within piezoelectric ZnO nanowires

3

as a function of the axial intrinsic surface

2


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strain. Thus, a direct inuence on the piezoelectric response is expected. Piezoelectric (PE) ZnO combined with magnetostrictive (MS) materials has the potential to create highly sensitive magnetoelectric (ME) composites for biomedical sensor applications

4,5

such as sensors for magnetoencephalography and magnetocardiography.

topic the research and development of sensor arrays is of high interest.

79

6

For this

Planar composite

designs with a layered structure are currently popular due to fabrication and conceptual simplicity. However, micro and nano structured ME composites with alternative geometries such as micro rods are gaining increased attention because they oer a substantial increase in sensor sensitivity.

1012

Quasi one-dimensional ZnO micro rods are an excellent choice as piezoelectric tronic

1517

13,14

or piezo-

materials for functional composites due to their very high piezoelectric and

piezotronic strain tensors. The ZnO PE strain tensor is among the highest of single crystal semiconductors

18

with its strongest tensor direction (z-direction) coinciding with the (001)

direction of ZnO, capable of creating a basis for powerful and sensitive PE micro components. A previous study by the authors

19

on ZnO micro rods with an amorphous layer of the soft

MS alloy (Fe 90 Co10 )78 Si12 B10 (FeCoSiB) vary with the composite geometry.

20

has shown that the properties of the coated layer

By moving from a planar thin lm

1

or even a macro

rod composite (Supporting Information, Figure S1) to a micro rod composite a signicant increase in saturation eld from

Bs ≈ 2 mT to Bs ≈ 10 mT 1

is achieved. This demonstrates

the huge inuence of size and composite design on the material properties, which are worth to be explored in detail. We recently demonstrated that the inuence of the MS coating and applied magnetic elds on the lattice strain in PE micro rods can be determined by X-ray nanodiraction (nXRD).

19

Employing the methodology of these proof of principle experiments, we here present systematic studies of FeCoSiB coated ZnO micro rods as a function of the rod diameter, rod length and layer thickness. The spatially resolved mapping of the strain allows direct insight into the coating induced lattice deformation and shows how the interface strain can be tuned by

3



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changing the aspect ratio of the micro rod to increase its absolute value by nearly an order of magnitude. Additionally, when designing ME composites with the ZnO rod as the basis, we show that this increased interface strain leads to an increase of the coupled magnetic eld induced strain. The diameter of the rod is of particular interest here, as it appears to be the driving parameter that inuences the strain. The rods have lengths ranging from 100 to 4000

µm

and diameters ranging from 3 to 60

µm.

Cross-sections of singular rods reveal

a hexagonal shape, with each prism surface corresponding to the (100), (010) and (1-10) orientation of wurtzite ZnO.

3

ME micro composites were prepared by coating the PE micro

rods with an amorphous layer of FeCoSiB of 0.1 to 0.5 traditional planar ZnO oers a magnetostriction of bending technique,

1

µm

thickness. FeCoSiB coated on

λs ≈ 4 · 10−5

estimated by the cantilever

a high permeability and a high piezomagnetic coecient

∆λ/∆H .

An

in-plane magnetic eld of 10 mT was applied perpendicular to the c-axis during the lm deposition process in order to induce a magnetic anisotropy in that direction. To map and characterize the local strain distribution of ZnO micro rods we perform scanning nXRD

19,21

in transmission geometry as depicted in 1b,c. The lattice structure of PE

ZnO micro rods and its local deformation at the interfaces were investigated by employing synchrotron X-ray radiation at the nanofocus endstations of beamlines P03, PETRA III, and ID13, ESRF. By measuring the Bragg reections and their shift due to the lattice deformation the local strain can be calculated. We follow the shifts of the scattering vector

qh00

perpendicular to the rod c-axis and parallel to the surface normal of the [100] facet (see

1b,c). Cross-section scans in y-direction perpendicular to the c-axis were performed to follow the lattice structure across the entire composite with high local resolution up to 200 nm. The coating induced lattice deformation of a series of samples with varying geometry factors such as micro rod diameter, micro rod length and coating thickness are characterized.

4


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a)

b)

c)

c B

ko

Vi

ko

qh00 ki

qh00 Vtot

θ y

B θ

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ki

Figure 1: (a) Scanning electron microscopy images of two hexagonally shaped ZnO micro rods of dierent sizes. (b-c) Schematic view of experimental setup in transmission nXRD geometry with

Vi

in situ

magnetic eld. (c) The focused beam is diracted at volume element

of the hexagonal ZnO. The dotted lines represent the incremental steps of a line scan and

its individually illuminated volume elements.

Vtot

is the sum over all

Vi .

2 Experimental Sample preparation: Mishra et al.

23

ZnO microstructures are grown by ame transport synthesis.

22,23

describes this procedure in detail. Inside a crucible 15 g of Zinc, PVB Poly-

◦ mer and Ethanol (1:1:2) have been burned for 2 hours at 900 C to create ZnO micro rods (diameter: 1-100

µm;

length: 200-5000

µm).

The fastest growth direction and c-axis of the

rods correspond to the ZnO(001) direction and therefore grow in the direction of the highest PE strain tensor of ZnO. Individual ZnO rods are mounted at the tip of glass pipettes using Ethyl-2-Cyanacrylat with a low dynamic viscosity ( η

= 10 mPa·s) to ensure multiple degrees

of freedom when handling the samples. Both glass and glue are transparent for X-rays. Inside a vacuum chamber (Fe 90 Co10 )78 Si12 B10 from 8 targets has been sputtered onto the micro rods using rf magnetron sputtering with 200 W, in an Argon atmosphere with

6 · 10−3

mbar pressure, to create layers of up to 500 nm. A 100 Oe magnetic eld was applied perpendicular to the micro rod axis to induce a magnetic anisotropy. The micro rods have been manually turned once by 180

◦

after the rst deposition to coat the rods on all surfaces. If

the rod is only coated on one side, the layer would otherwise induce a strong cantilever-like bending of the entire rod. The rods have not been annealed afterwards. Scanning electron

5



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microscopy has been used to verify that the entire sample is coated. An additional reference sample was coated during the sputtering process to estimate the layer thickness.

X-Ray Nanodiraction:

The authors describe the experimental method of transmission

Bragg nanodiraction on crystalline micro rods in detail in a previous publication.

19

The lat-

tice structure of the micro rods were investigated using the highly resolved nano focused synchrotron radiation provided by the nanofocus endstation of the MiNaXS-Beamline P03

26

at PETRA III and the nanofocus beamline of ID13 provided an X-ray beam ranging from

100 × 120

24,25

at ESRF. In both cases focusing mirrors

nm

2

to

400 × 800

nm

2

size (horz

× vert).

Multiple energies over multiple beamtimes were used ranging between 9 and 19 keV. The samples were mounted on a rotation motor which in turn was mounted on a hexapod allowing for set-up and preliminary adjustments of the sample. The rotation motor enables sample rotation around the c-axis providing access to ZnO (h00) Bragg reection. Between sample and rotation is another piezomotor attached allowing the sample to be moved in steps of 1

µm

and below in x-, y- and z-direction for ne adjustments. With the sample in

transmission geometry (1b,c) and employing a 2D Dectris 300k Pilatus Pixel detector (pixel size of

172 × 172 µm2

at P03 and a Maxipix (pixel size of

the diraction angle of the ZnO(200) Bragg reection. of the nano beam position perpendicular (y in 1 100

µm

50 × 50 µm2

at ID13 we measured

By monitoring

q200

as a function

steps and below) and parallel (z in

µm steps) to the micro rod axis the local ZnO lattice spacing d200

can be mapped across

and along the rod. As indicated by 1c we measure across the entire volume plane hexagonal rod. We illuminate volume elements

Vi

V

of the

from one prism facet across the center to

the opposite facet. The volume elements that include direct illumination of the prism facet are dened as the interface/surface area. Using these steps and the beam size there is no overlaying eect between spots. The permanent magnets (Nd 2 Fe14 B) were mounted on linear positioners in y-direction (perpendicular to rod and incoming beam direction) to create permanent magnetic elds. The magnetic elds have been calibrated using a teslameter. The scanning XRD method can accurately detect lattice parameter changes as small as

6


10−6

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as seen in the shape of the Bragg reections in 2a. shows some variation from sample to sample.

However the exact crystal structure

The peak position is determined by tting

the Bragg curves with a Pseudo-Voigt prole. The data points in 3a have been tted with a least squares t weight by the respective error bars. The diraction patterns were analyzed and the strain maps created with Matlab.

Finite-element-method simulation:

Finite-element-method (FEM) simulations are car-

ried out with the software package COMSOL Multiphysics

® to model the ZnO rod strain

behavior. The three-dimensional simulation geometry consists of a truncated ZnO pyramid with a hexagonal cross section. The top diameter of this rod is 10 is 50

µm,

and it has a length of 200

µm.

It is coated with a 1

µm

µm, the bottom diameter thin layer of FeCoSiB. In

the experiment, this FeCoSiB layer applies a stress to the ZnO rod. In the simulation, this stress is generated by applying a reduced temperature

TFeCoSiB = TZnO − ∆T

to the FeCoSiB

layer, as the driving force behind the strain is not relevant to the model itself. The stress

S

is then calculated using the following equation:

T = cS − α dT,

where

α

denotes the temperature coecient. The applied temperature

∆T

is adjusted such

that the calculated interface stress at the maximum diameter matches the measurements. Thus, the model has only one t parameter.

The strain is evaluated along the red line

shown in 4b(inset) in dierent heights of the rod. For the Wurtzite ZnO the following elastic constants

c44 = 44

13

are used:

c11 = 209

GPa,

c33 = 216

GPa,

c12 = 120

GPa,

c13 = 104

GPa,

GPa.

3 Results and discussion Coating Induced Intrinsic Strain: single micro rod with 9

2a shows the local ZnO(200) Bragg reection of a

µm diameter and a coated FeCoSiB layer of 500 nm. 7


The position of


a)

center: 0 mT edge: 0 mT

center: 30 mT edge: 30 mT

b)

c)

-2

ϵ100

Δϵ100(B)

-4 ϵ [10 ] -4 -3 -2 -1 0

15µm

0

ϵ [10-4 ]

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Page 8 of 21

uncoated coated

-4 -6 -8

-10

5µm -20

-10

0

10

20

y [µm] Figure 2: (a) ZnO(200) Bragg reection of a 9

o

µm

diameter ZnO rod coated with 500 nm

FeCoSiB at the center ( ) and the edge ( ×) without (red) and within (blue) an external magnetic eld. Dotted lines represent the center of Gaussian ts of the respective peak. The shift between center and edge peak denes the intrinsic strain due to FeCoSiB deposition, an additional shift is observed due to a magnetic eld. (b) Stack plot of cross-section scans along y-direction of rods with varying diameter. Line proles show compressive intrinsic strain

at the interface area. Dotted lines represent the respective 0 strain value. (c) Intrinsic strain prole

of a singular partly coated cone-shaped ZnO micro rod. The uncoated area shows −4 · 10−4 .

no strain, the coated area shows increased interface strain up to

8


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the reection diers between the dierent illuminated areas of the rod. A shift of the Bragg reection in the range of

∆q = 10−3

Å

−1

between the center of the rod and the interface

area can be observed. The shift in 2a corresponds to an intrinsic strain of

100 = −2.3 · 10−4 .

As all kinds of strain discussed in this work are in the [100] orientation, the index will be omitted. in 2b,c.

The local intrinsic strain for multiple samples with varying diameter are shown 2c shows a mesh scan across a cone shaped 230

ters ranging from 15

µm

and 3

µm.

µm

long ZnO rod with diame-

The tip of this specic rod is coated, the other half

is uncoated. The uncoated area shows no variation in the Bragg position within an error of

7.5 · 10−6

Å

−1

= 2 · 10−6

. This translates into a local intrinsic strain of

which is our

experimental limit of resolution, thus, showing no indication of strain in pure ZnO. Strain at the interface of composite materials is clearly induced as a result of the FeCoSiB coating process. The local compressive strain at the interface for all measured rod diameters is in the order of

≈ 10−4 .

The penetration depth of the strain is around 5

µm

(Supporting

Information, Figure S2). For comparison, the average strain on the entire cross-section area is calculated:

bulk = Σi (i · Vi /Vtot ) =

illuminated by the beam (see 1c),

Vtot

P

i (i

· Ii /Itot ),

with

Vi

being the volume element

being the sum of all volume elements, and

I

being the

corresponding integrated intensity. Both, the local maximal compressive strain at the interface

if

bulk

as shown in 3a. In both cases we

of a series of rods are plotted over the rod diameter

d

and the whole averaged strain

can see an exponential increase of the intrinsic strain as a function of the rod diameter in the form of and

= −A · exp(b · d).

For the local interface strain we get

b(if ) = (−0.036 ± 0.05)/µm

b(bulk ) = (−0.0926 ± 0.02)/µm.

and for the average strain Due to the

A(if ) = (4.3 ± 0.4) · 10−4

A(bulk ) = (3.9 ± 1.7) · 10−4

b(bulk )/b(if ) ≈ 2.5

and

times sharper decrease in

intrinsic strain, the average strain is already close to the limit of resolution at a rod diameter of 40 50

µm, while the local strain still has a measurable value of 5 · 10−5

reaching diameters of

µm.

As seen in 4 using FEM simulations a modeling of the coating induced intrinsic strain dis-

9



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Page 10 of 21

tribution across the rod diameter was performed. 4a shows the simulated strain distribution of the hexagonal ZnO rod and reveals a compressive strain in the range of

10−4

in the en-

tire rod cross-section with the exception of a very local strain excess at each corner of the hexagon. The corners experience a very local intrinsic strain due to coating of spatial range of less than 1

µm 2 .

10−3

within a

4b shows the strain distribution across the hexagonal ZnO

rod for dierent diameter along the marked one-dimensional line from 4b (inset). It shows a decrease in maximal interface strain

if

for increasing diameter, similar to the results of

gure 2b. Simulation and data are compared in 4c. Data and simulation show a very similar distribution, for both the maximum interface strain as well as the strain penetration depth. The simulation shows that the intrinsic excess strain at the corners increases in importance for the detected intrinsic coating induced strain

for decreasing diameter. Additionally, the

slight dierences in strain penetration between simulation and data are explained by the data points being a result of averaged volume elements

Vi

rather than from singular points

taken from a one dimensional line.

The FeCoSiB layer is predominantly amorphous as we deposited the material below to avoid a restructuring of FeCoSiB into crystalline laments.

7

250◦ C

Because of the lack of long-

range order, the observed intrinsic strain in the ZnO lattice does not result from the epitaxial relationship, but predominantly from thermal eects, i.e., the contraction during cooling to room temperature. Additional contributions may come from the presence of an additional interface layer that develops during the deposition process. According to nano small angle X-ray scattering (Supporting Information, Figure S3) experiments, this layer has thicknesses between 6-16 nm and is formed at the boundary between ZnO and FeCoSiB. Powder diraction studies (Supporting Information, Figure S4) indicate that the deposited lm exhibits a high concentration of elemental Fe (BCC), the main component (89.7%) of FeCoSiB, or Fe based precipitates with similar lattice parameters

7

(Fe3 Si, FeCo and Co 2 FeSi). It is likely

that in the region of the amorphous lm close to the ZnO surface the Fe particles chemically

10


-4

-10-5

-2 0 0

10 20 B [mT]

c)

-10-4

30 -1

if bulk

10

20 30 40 diameter [µm]

50

[10 -5]

b)

if (B)

a)

bulk (Bs

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


) [10-5]

Page 11 of 21

2

4 6 8 10 12 diameter [µm]

-10

Figure 3: (a) The intrinsic compressive strain in a series of ZnO micro rods as a function of the rod diameter

d.

The least square t() weight by the errorbars shows an exponential increase

of strain as a function of decreasing diameter. The average intrinsic strain

bulk

(green) on

the entire illuminated plane has a steeper decrease than the maximum local interface strain

if

(red).

if

increases by 0.8 orders of magnitude, the average strain

of magnitude from 50 resolution.

µm

to 3

µm.

bulk

up to 2 orders

The dashed line (- -) shows the experimental limit of

(b) Local magnetic eld induced strain

∆if (B)

at the interface of an 8

µm

diameter rod as a function of the external magnetic eld. The blue lines indicate the steps of the magnetic loop. The induced strain increases until reaching magnetic saturation

Bs ≈ 10

mT. After saturation is achieved, no variation of the lattice parameters is observed. (c) The average magnetic eld induced strain shaped rod (diameter 12

µm

∆bulk (Bs ) at magnetic saturation on one singular cone

and below) increases linearly as a function of decreasing rod −5 diameter. The induced strain is in the 10 range.

11



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react with oxygen ions of the ZnO surface,

27

Page 12 of 21

resulting in an Fe oxide layer.

It should be noted that other geometrical factors such as length of the micro rod or the thickness of the layer have been studied (Supporting Information, Figure S5) but in the range of our studies do not aect the intrinsic strain of the PE component. Unexpectedly, only variations of the rod diameter show an observable eect.

Magnetic Field Induced Strain:

This increase of coating induced interface strain by an

amorphous layer shows that changing the shape geometry of these ZnO rods can have a huge inuence on the performance of functional micro composites. In the case of ME composites the increased interface strain can lead to an increased ME response as is shown in

in situ

magnetic eld nXRD measurements on the ME micro rods. Within an external magnetic eld the MS component is deformed. Via the coupling of the PE/MS interface the strain is transferred to the PE component resulting in an electrical polarization.

11,12

The ME eect

of composite structures is the product of the MS properties, the PE properties, the elastic properties and the mechanical coupling at the interface.

28

As a result, this eect directly

depends on the interface strain. As shown in 2a within an external magnetic eld B, the coated ZnO rods experience, additional to the intrinsic strain, a magnetic eld induced strain

∆(B).

In this case the

magnetic eld is oriented perpendicular to the rod axis and nearly parallel to the (100) facet.

The magnetic eld induced lattice deformation is investigated in the same manner

as the intrinsic strain for magnetic elds ranging from 0 mT to 30 mT (3b) and in the range of strain

.

∆(B) ≈ 10−5 .

It is generally one order of magnitude smaller than the intrinsic

3c shows the average magnetic eld induced strain of the cone shaped rod from

2c. The magnetic eld induced strain is compressive and its average value over all diameters

∆(B) ≈ (−3 ± 2) · 10−5

corresponds well to the magnetostriction of a thin layer of FeCoSiB

on planar ZnO. Additionally, the strain shows a direct dependence on the rod diameter. An increase of local interface strain up to 3 times is observed by decreasing the diameter by a factor of 4 and reaches its highest value at

∆(B) = (−5 ± 1) · 10−5 .

12


Even if one assumes

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perfect coupling

k = 1 this results in the magnetostriction k · λs = ∆(Bs ) of the same value.

This is a 25% increase over the magnetic eld induced strain measured in planar composite ZnO/FeCoSiB systems.

1

From our planar system study we expect a coupling of

k = 0.8,

which would result in an even further increase of the magnetostriction to 56%. This indicates the high inuence of composite design and geometry on magnetic properties. It may be even possible to further increase the induced strain by reducing the diameter. In

19

the authors

showed that the magnetic eld induced strain for ZnO rods with diameters above 20

µm

is

relaxing. Even though the exact nature of the strain direction is not fully understood, the strain penetration depth can still be compared.

The area experiencing the magnetic eld

induced strain in the PE component is approximately the same range as the intrinsic strain. This results in the ZnO rods with 10

µm diameter and below to experience a magnetic eld

induced strain in their entire diameter. In a theoretical study, Glinchuk et al. predicted in their model a gigantic increase of ferroic parameters such as polarization and magnetization in cylindrical ferroic nano rods

29

when

decreasing their rod diameters. These parameters are directly correlated to mechanical properties such as stress. A surface stress is introduced by an adherent material. Nano particles with sizes less than 100 nm are considered due to the applicability with the shell and core model of nano particles

30

(only the surface of the particle within a few tens of nanometers

experiences certain eects, the core is unaected and acts like bulk material) and the shell acts as a ultrathin layer.

If the radius of the nano rods is small the thin quasi-layer acts

highly bend, then with decreasing radius the surface stress increases. As a result the surface stress depends on both the adherent material as well as the rod diameter. Glinchuk et al. states that for rods with larger sizes the model would be more complex but in general the eects would act more gradually from surface to center, so that the shell character is lost. Although in our experiments we study hexagonal rods with diameters in the

µm

range, the

tendencies resulting from the model are still in agreement with our experimental ndings that a decrease in rod diameter results in an increase of the intrinsic surface strain as seen

13



in 2b,c and 3a,c. As both polarization and magnetization are shown to correlate with the diameter of the rod, this model also states an increase of the magnetoelectric coupling coecient in the same diameter range. Additionally, Klockholm de Lacheisserie

33

et al.

31,32

et al. and du Trémolet

showed in their studies of magnetostriction and internal stresses

that the magnetostriction of thin layers, that are bend via the cantilever method, increases according to their deformation. This is a result of the increased mechanical energy inside the lm due to its bending induced internal stress. The deformation itself depends on the radius of the bend substrate, which in our case equates the radius of the rod. The increase of the magnetic eld induced strain by decreasing the rod diameter (see 3c) is explained by the increase of the magnetostriction. Tuning the ME response by tuning the intrinsic surface strain within the PE component itself is a crucial and viable information for ME composites and functional materials in general.

a

b

c

0

-1

[10-4]

-1.5

[10-4]

-1

-1.0

-1.5

-2

-2

-2.0

-3

-2.5

model data

-3 -20

20 µm

Figure 4:

0

-0.5

-0.5

[10-3]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 21

0

20

y [µm]

-4

-10

0

10

y [µm]

a) Finite-element-method Simulation of hexagonal ZnO pyramid with a 1

FeCoSiB layer.

µm

The corners of the hexagonal shape experience higher compressive strain

compared to the average volume. b) Simulated strain distribution for multiple rod diameters along the marked line (inset). c) Comparison between model and data for a ZnO rod with (red) 8

µm

and (blue) 27

µm.

Strain distribution and value are very similar, although the

strain penetration depths varies slightly. This likely is an eect due to the data points being a result of averaged volume elements

Vi

rather than a one dimensional cross-section.

14


Page 15 of 21

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4 Conclusion In summary, a study on magnetoelectric ZnO/(Fe 90 Co10 )78 Si12 B10 micro rods and their dependence on shape geometry has been performed using X-ray nanodiraction. It shows that miniaturizing has a huge impact on composite properties.

Especially, the local intrinsic

strain induced by the coating process at the composite interface is greatly inuenced by the diameter of the piezoelectric component, and that the interface strain can be exponentially increased by tuning the shape of the micro rod.

The average intrinsic compressive strain

increases by 2 orders of magnitude by reducing the diameter size by only one order of magnitude, while the local interface strain increases by 0.8 orders of magnitude in the same range. Additionally, a decrease in rod diameter increases the magnetic eld induced strain. In the course of this study, it was even shown that the induced strain inside the ZnO is even capable of exceeding the magnetostriction of (Fe 90 Co10 )78 Si12 B10 on traditional planar sample geometries. This study gives direct insight into the local strain distribution within complex quasi onedimensional micro composites. This strain behavior can be exploited and applied to a wide array of functional composites such as magnetoelectric composites.

A correlation of both

types of strain can be assumed via their shared dependence on the rod diameter.

An in-

crease of the magnetic eld induced strain will increase the magnetoelectric response. This should help to understand and further improve the sensitivity of magnetoelectric composites with an alternative approach in composite design and hints at possible inuences on other rod-based functional composites.

Acknowledgement We, the authors, thank the collaborative research center SFB855, MU-2888/4-1 and SFB1261 (Deutsche Forschungsgemeinschaft) for nancial support. Additionally, we thank Deutsches Elektronen-Synchrotron (DESY) and European Synchrotron Radiation Facility (ESRF) for

15



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Page 16 of 21

access and the sta of P03 and ID13 for the support during the experiments, Matthias Greve at University Kiel for technical assistance as well as Necdet Onur Urs at University Kiel for MOKE measurements.

The experimental setup at the Nanofocus Endstation of beamline

P03 as well as the operation of the instrument was supported by the German Federal Ministry of Education and Research (BMBF) through the grants 05K10FK3 and 05KS7FK3.

Supporting Information Available The following les are available free of charge. Magneto optical Kerr eect measurements on macroscopic glass capillary (diameter 1 mm) coated with FeCoSiB (Figure S1); strain penetration depth as a function of ZnO/FeCoSiB micro rod diameter (Figure S2); nano small angle x-ray scattering at ZnO/FeCoSiB micro interface (Figure S3); powder diraction of amorphous FeCoSiB micro layer (Figure S4); the average compressive strain as a function of the deposited FeCoSiB micro layer thickness for ZnO/FeCoSiB micro micro rods, and local compressive strain as a function of the rod length (Figure S5).

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