FMR investigations of half-metallic ferromagnets

phys. stat. sol. (a) 203, No. 7, 1503–1512 (2006) / DOI 10.1002/pssa.200563103

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Original

Paper

FMR investigations of half-metallic ferromagnets

B. Rameev*, 1, 2, F. Yildiz1, S. Kazan1, B. Aktas1, A. Gupta3, L. R. Tagirov4, D. Rata5,

D. Buergler5, P. Gruenberg5, C. M. Schneider5, S. Kämmerer6, G. Reiss6, and A. Hütten6

1 Gebze Institute of Technology, 41400 Gebze-Kocaeli, Turkey 2 Kazan Physical-Technical Institute, 420029 Kazan, Russia 3 University of Alabama, Tuscaloosa, Al 35487, USA 4 Kazan State University, 420008 Kazan, Russia 5 Forschungszentrum Jülich-IFF, 52425 Jülich, Germany 6 University of Bielefeld, 33615 Bielefeld, Germany

Received 5 July 2005, revised 30 January 2006, accepted 6 March 2006

Published online 7 April 2006

PACS 75.30.Gw, 75.50.Cc, 75.70.Ak, 76.50.+g

Thin films of various half-metallic ferromagnets, such as chromium dioxide (CrO2) and Heusler alloys

(Co2Cr

0.6Fe

0.4Al, Co

2MnSi) have been investigated by ferromagnetic resonance (FMR) technique. It is

demonstrated that FMR is a very efficient method to study the nanoscale magnetic properties, in particular

to probe the magnetic anisotropy and magnetic inhomogeneities of ferromagnetic thin films. Epitaxial

CrO2 thin films of various thicknesses (25–535 nm) have been deposited on TiO

2(100) substrates by

chemical vapor deposition process. It is shown that the magnetic behavior of the CrO2 films results from a

competition between the magnetocrystalline and strain anisotropies. For the ultrathin CrO2 film (25 nm)

the magnetic easy axis switches from the c-direction to the b-direction of the rutile structure. Thin-film

Co2Cr

0.6Fe

0.4Al samples (25 nm or 100 nm) have been grown by DC magnetron sputtering either on un-

buffered SiO2(100) substrates or on the substrates capped by a 50 nm thick V buffer layer. The effects of

the vanadium buffer layer and of the film thickness are revealed by FMR studies of the Co2Cr

0.6Fe

0.4Al

samples. Well-resolved multiple spin-wave modes are observed in the unbuffered Co2Cr

0.6Fe

0.4Al sample

with a thickness of 100 nm and the exchange stiffness constant has been estimated. Thin films of

Co2MnSi (4–100 nm) have been grown by DC sputtering on silicon substrates on top of a 42 nm thick V

seed layer and capped either by Al2O

3 or by Co and V layers. A set of the 80 nm thick films has been an-

nealed at different temperatures in the range of 425–550 °C. FMR studies of the Co2MnSi samples shows

that at the fixed annealing temperature (450 °C) the highest magnetization is observed in the sample with

a thickness of 61 nm, while the thicker samples (100 nm) reveal not only a lower magnetization but

greater magnetic inhomogeneity as well. An annealing treatment at T ≥ 450 °C is essential to obtain

higher magnetization as well as uniform magnetic properties in the Co2MnSi films. Weak SWR modes

have also been observed in the thick Heusler films.

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

The spin polarization of the conduction electrons is the most important parameter determining the per-

formance of various magnetoelectronic (“spintronic”) devices [1]. For that reason, half-metallic ferro-

magnets, which have highly spin-polarized electrons at the Fermi level (100% in the ultimate limit),

appear to be very promising for spintronic applications, first of all for use in magnetic tunnel junctions

(MTJ). There are a number of half-metallic materials that have been extensively explored as potential

* Corresponding author: e-mail: [email protected], Phone: +90 262 605 1314, Fax: +90 262 653 8490

1504 B. Rameev et al.: FMR investigations of half-metallic ferromagnets

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-a.com

candidates to use as ferromagnetic electrodes in such devices. The examples are chromium dioxide,

Heusler alloys, manganites, double perovskites, etc. (see, for instance, [2]). However, attempts to con-

struct a real MTJ device using half-metallic electrodes result in a tunnel magnetoresistance effect much

smaller than theoretically predicted, especially at ambient temperatures. One of the reasons for this is the

spin depolarization at the material surface or interface. In this respect it is important to understand

whether the effect is intrinsic to the surface/interface (because of different effective magnetic interac-

tions) or is it a result of surface disorder? Besides, it has been shown for Heusler alloys that the structural

atomic disorder of the bulk material appreciably decreases the spin polarization [3, 5]. Thus, any effects

of surfaces/interfaces and bulk inhomogeneities should be studied thoroughly both to understand the

physics involved and to realize in practice a half-metallic MTJ device. On the other hand, the construc-

tion of multilayered MTJ structure implies that the magnetic anisotropies of a thin-film material are

known to tailor them in a desirable way. It is well known that the surface/interface anisotropies become

very important and even overcome the effect of bulk (magnetocrystalline) anisotropy in very thin films.

Therefore, magnetic anisotropies of half-metallic thin films are the subject of separate interest to study.

It is well known that ferromagnetic resonance (FMR) is a very efficient technique to study the nano-

scale magnetic properties of various ferromagnetic materials. In this work thin films of various half-

metallic ferromagnets, such as chromium dioxide (CrO2) and Heusler alloys (Co2Cr0.6Fe0.4Al, Co2MnSi)

have been investigated using FMR technique.

2 Experimental procedures

Epitaxial CrO2 thin films of various thicknesses (25–535 nm) were grown on TiO2(100) single-

crystalline substrates by a chemical vapor deposition process. Epitaxial (100) thin films of CrO2 have

been fabricated by the chemical vapour deposition (CVD) on TiO2(100) single-crystal substrates using

the CrO3 solid precursor, as described previously [6]. A set of films (27, 65 and 434 nm) was prepared by

deposition onto the HF pre-etched TiO2 substrates [6]. A film with the thickness of 535 nm was also

grown on the unetched TiO2 substrate.

Thin-film Co2Cr0.6Fe0.4Al samples (25 nm or 100 nm) were grown by DC magnetron sputtering either

on unbuffered SiO2(100) substrates or on the substrates capped by a 50 nm thick V buffer layer. Thin-

film samples of Co2MnSi (4–100 nm) were grown by DC sputtering on silicon substrates on a 42 nm

thick V seed layer and capped either by Al2O3 or by Cu and V layers. A set of the 80 nm thick films

(capped by Cu and V layers) were annealed in the range of 425–550 °C. Another set of Co2MnSi films

were capped by an Al2O3 layer and have various thicknesses: 4, 8, 15, 61 and 100 nm. For this set the

post-annealing temperature was fixed at 450 °C.

FMR spectra have been recorded by using a Bruker EMX X-band spectrometer (9.8 GHz) at room

temperature. The static magnetic field has been varied in the range of 0–16000 G. The field derivative of

microwave power absorption (dP/dH) has been registered as a function of the static magnetic field (H).

The angular dependences of EPR spectra have been recorded with the static magnetic field rotated either

in the film plane (“in-plane” geometry) or in the two perpendicular planes (“out-of-plane” geometry) that

cross the film plane nearly at the hard- or easy-axis directions.

3 Experimental results and discussion

3.1 Chromium dioxide thin films

FMR measurements of the 535 nm CrO2 film grown on untreated TiO2 substrate reveal a single reso-

nance mode. In contrast to this, both in-plane and out-of-plane spectra of the thick (65 and 434 nm) CrO2

films deposited on HF pre-etched substrates show splitting into a few components (see details in [7, 9]).

As is typical for thin films, a dominant contribution of the shape anisotropy is observed in the out-of-

plane FMR measurements of all CrO2 samples, and the easy axis of magnetization is oriented in the

plane of the CrO2 film. The effect of the magnetocrystalline anisotropy is clearly observed in the in-plane

phys. stat. sol. (a) 203, No. 7 (2006) 1505

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Original

Paper

measurements, where the easy axis of magnetization corresponds to the minimal in-plane FMR reso-

nance field, and the hard axis corresponds to the maximal in-plane resonance field. The largest magni-

tude of the in-plane anisotropy is observed in the 535 nm CrO2 film prepared on the unetched substrate.

In this respect a very unusual thickness dependence of the in-plane resonance fields (Hres) was observed

for the “pre-etched” CrO2 films (Fig. 1). As seen in the figure, the thinnest (27 nm) film of this series

shows the minimal resonance field for the direction of DC magnetic field along the b-axis of the CrO2

film, while the in-plane FMR spectra of the “unetched” CrO2 film with a thickness of 535 nm reveal the

easy axis along the c-direction. There is accordingly a switching of the easy axis from the c-direction to

the b-direction, in agreement with the static magnetic measurements for this set of CrO2 samples [10].

FMR measurements of the CrO2 film of intermediate thickness (65 nm) show a very unusual angular

dependence (Fig. 1) revealing two primary FMR modes with “antiphase” behavior, that is the minimal

resonance field of the first mode corresponds to the maximal field for the second one, and vice versa.

This implies the existence in this film of two magnetic phases in this film with mutually perpendicular

easy axes along the c- and b-directions. The situation is much more complicated for the thickest film of

the pre-etched series, where one could count 4 major components along the c- (easy) and a- (perpendicu-

lar) axes of the (100) CrO2 film and even more components for intermediate angles under rotation in the

out-of-plane geometry from the a-axis to the b- (hard) direction. It is worthy of note that one of these

components shows behavior very similar to the signal from the 27 nm film and one of the two FMR lines

in the 65 nm film, i.e. very smooth dependence of the in-plane resonance field versus the in-plane

angle ϕ.

Detailed analysis of the depth-dependent anisotropies of the “pre-etched” CrO2 films will be published

elsewhere. Here we present only a brief analysis of the experimental data.

1. Our XRD measurements showed that the “unetched” CrO2 film is essentially strain-free and only

tetragonal magnetocrystalline (bulk) anisotropy with an easy axis parallel to the c-crystalline axis of the

CrO2 rutile structure is to be taken into account: Eani = K1 sin2 θ + K2 sin4 θ, where θ is the angle between

the magnetization vector M and the c-axis of the CrO2 crystal, Ki are the anisotropy constants of crystal-

line anisotropy. Computer simulations with use of a specially developed program show that the last ani-

sotropy term may be neglected, and we obtain K1/MS = 510 Oe for the room-temperature saturation mag-

netization MS = 470 Oe, which are in rather good agreement with the results reported previously for bulk

CrO2 crystals [11] and CrO2 films [6].

0 45 90 135 1800.4

0.8

1.2

1.6

2.0

2.4

2.8 27 nm65 nm434 nm535 nmsimulation

b-axis

c-axis

Hre

s,k

Oe

ϕ , degree

In-plane

Fig. 1 Experimental and modelled in-plane angular dependences of the resonance field for CrO2 films.



2. The analysis of the in-plane and out-of-plane resonance field dependencies for the CrO2 films de-

posited onto the pre-etched surface shows that the effect of strain anisotropy should be taken into ac-

count. To fit the experimental dependences the following model has been used: Eani = K1eff sin2 θ + K2

sin4 θ, where a single parameter K1eff = K1eff – K1σ takes into account not only the second-order term of

magnetocrystalline anisotropy but the magnetoelastic anisotropy term (–K1σ) as well. It is known [6] that

both the CrO2 epitaxial film and the TiO2 single-crystalline (100) substrate have the rutile structure

(tetragonal symmetry), and the lattice mismatch of CrO2 with (100) TiO2 substrate, –3.79% along the

[010] b-direction and –1.48% along the [001] c-direction, results in an anisotropic tensile strain in the

plane of the CrO2 films [6]. There is a competition between magnetocrystalline and strain anisotropies

favoring the b- and c-directions of magnetization, respectively. For the heavily strained film with a thick-

ness of 27 nm our simulations provide the negative value of the effective anisotropy field K1eff/MS of

about –65 Oe. The forth-order anisotropy parameter (K2) has also to be taken into account to reproduce

theoretically the rather smooth in-plane dependence for the 27 nm film around the b-axis direction, and

we obtained K2/MS = 25 Oe.

3. Unusual angular dependence of the double-mode FMR and the multiple-mode FMR in the 65 nm

and 434 nm films could be simulated in a rough model separately for each magnetic phase. Essentially,

that one of the magnetic phases could be attributed to the heavily strained sublayer near the interface.

This layer has very small anisotropy, for instance, in the 65 nm film we have: K1eff /MS = –45 Oe, K2/MS

= 25 Oe. The other magnetic phases are ascribed to the top layers of the CrO2 film with a partially re-

laxed strain.

4. The out-of-plane resonance field dependences reveal an essential effect of perpendicular anisotropy

in the films on the pre-etched substrates. The latter is observed in FMR modelling as an increase of the

“effective” magnetization: Meff = MS – K⊥/2πMS, where K

⊥ is the perpendicular anisotropy constant. The

additional perpendicular anisotropy with the symmetry axis along the film normal results from a com-

pression in the direction perpendicular to the film along the a-axis, which in turn is induced by stretching

in the film plane. In this case, the negative sign of the perpendicular anisotropy constant K⊥ (i.e. an in-

crease of the effective magnetization) means that the hard axis is in the direction perpendicular to the

film plane.

In conclusion, the effectiveness of the FMR technique to probe the depth-dependent anisotropies in

the strained CrO2 films has been demonstrated. The analysis of the FMR data for these CrO2 films re-

veals the strong effect of the magnetoelastic anisotropy that appears due to the lattice mismatch of CrO2

with (100) TiO2 substrate. There is a competition between magnetocrystalline and strain anisotropies

favoring the b- and c-directions of magnetization, respectively. In the thinnest film, which is under the

largest strain, a switching of the easy axis from the c-direction to the b-direction is observed at room

temperature. Furthermore, FMR results show that the strain does not relax completely even in the thick

(434 nm) strained films. The multiple FMR modes in the 65 nm and 434 nm films indicate the step-wise

strain relaxation, and in a rough model the strained film may be considered as consisting of various lay-

ers with different effective magnetic anisotropies in each region.

3.2 Thin films of Co2Cr0.6Fe0.4Al Heusler alloy

No anisotropy has been observed in the in-plane FMR measurements. This indicates that there is not a

preferential in-plane direction for aligned growth of the crystalline grains in these films. Therefore, an

anisotropy observed in the out-of-plane FMR measurements (see, the FMR spectra at extremal orienta-

tions in Fig. 2) provides the effective magnetization value that is expected to be very close to the true

magnetization due to the averaging over magnetocrystalline anisotropies in the polycrystalline films.

However, as seen in Fig. 2, the multicomponent FMR spectra are observed for all samples if the DC

magnetic field applied along the film normal (the perpendicular orientation), and for the 100 nm

Co2Cr0.6Fe0.4Al Heusler film with the DC magnetic field in the film plane (the parallel orientation).

Therefore, before we proceed with the magnetization estimations it is necessary to examine these split-

tings in the FMR spectra.

phys. stat. sol. (a) 203, No. 7 (2006) 1507


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0 1 2 3 4 6 7 8 9 10

0 10 20 30 40 50

5

6

7

8

9

10

dP/d

H,a

.u.

Magnetic Field, kOe Magnetic Field, kOe

weak modes

25nm on V buffer

25nm (unbuffered)

100nm on V buffer

100nm (unbuffered)

Hre

s,k

Oe

n2

Fig. 2 FMR spectra of Co2Cr

0.6Fe

0.4Al Heusler thin films for the DC magnetic field applied parallel (left)

and perpendicular (right) to the film plane. Inset: Spin wave mode positions Hres

versus square of mode

quantum number n are presented for the unbuffered sample with a thickness of 100 nm. The straight line

is the fit using the quadratic dispersion law. The open squares, which correspond to the modes with a

nearly linear mode separation, are excluded from the fit.

Remarkable splitting into various components, which are due to the spin wave resonance (SWR)

modes, is revealed in the FMR spectra of the thick (100 nm) Co2Cr0.6Fe0.4Al Heusler films, grown both

with and without the vanadium buffer layer (Fig. 2 (right panel)). Well-resolved SWR modes observed in

the unbuffered 100 nm film allow us to estimate the exchange stiffness constant D in the Co2Cr0.6Fe0.4Al

Heusler film. We suppose that the so-called asymmetrical pinning conditions are realized in this film,

where the spins at one surface unpinned (free surface) while those at the other surface are strongly pinned

(film/substrate interface) [12, 13]. In this case the uniform FMR mode is absent, while both odd and integer

spin wave modes are excited. Fitting using this model provides a reasonable value of D ~ 1 × 10–9 Oe cm2

(see, inset in Fig. 2). In this fit only the higher-order spin wave modes, which obey a quadratic law

(Hres = H0 + Dk2, where k ~ nπ/L, n is mode quantum number, L is the film thickness, and H0 is the reso-

nance field for the uniform mode) were used. It is worthy of note that for the first spin wave resonances a

nearly linear mode separation as well as quite large mode intensities are observed. This may be explained

by a nonuniform magnetization profile through the film thickness, i.e. so-called “volume inhomogeneity”

(Portis) model [12, 14] is to be applied to analyse accurately the spin wave resonances of this film. How-

ever, one could obtain an estimation of the stiffness constant using the higher-order spin waves, where a

crossover to the quadratic behavior happens.

Spin wave resonance modes are also observed in the buffered 100 nm film. These modes are essen-

tially broadened that points to a higher magnetic inhomogeneity of this film. Even so, the rough estima-

tion using the four modes observed in the experiment provides nearly the same value of the stiffness

constant D. Furthermore, a very distant mode at lower field, observed in both buffered and unbuffered

25 nm films, may be also attributed to the spin wave excitation. In fact, a tenfold increase in separation

between the main and the additional modes agrees well with the 1/L2 scaling of the spin wave modes

with film thickness L.

Another interesting feature of the FMR spectra of the Co2Cr0.6Fe0.4Al Heusler films is the additional

peaks observed near the main mode at higher fields. These modes may be attributed to the excitation of



the surface spin waves [12, 13]. They are in particular evident for the 100 nm Heusler films. For the

100 nm film with V buffer layer they are observed in the perpendicular orientation as the distorted right

wing of the main mode (Fig. 2 (right panel)), while for the unbuffered 100 nm Heusler film a single

surface spin-wave mode is revealed in the parallel geometry as the second higher-field mode (Fig. 2 (left

panel)). As was mentioned above, a set of possible spin wave excitations observed in FMR is defined by

the pinning conditions at the film/substrate interface and the film surface. Therefore, one could expect

that the different substrate/film interfaces in the buffered and unbuffered films are responsible for obser-

vation of the surface excitations in either parallel or perpendicular orientations. Although to analyse

quantitatively the surface anisotropies of these samples we need more studies (e.g. low-temperature

measurements), it is possible, however, to explain qualitatively the main features of the observed SWR

spectra. For instance, a simple model, which takes into account only a surface anisotropy of uniaxial

symmetry as well as a constant surface-energy term, is usually sufficient to explain most of the features

of the spin wave resonance experiments in thin films. For the dominant uniaxial term in the surface ani-

sotropy, the spin pinning will change from the unpinned conditions to the pinned ones upon sample rota-

tion with respect to the external magnetic field. On the other hand, it is known that surface spin excita-

tions are observed in the case of the unpinned surface spins [12, 13]. Therefore, depending on the sign of

the surface anisotropy constant the surface spin wave mode will be excited either between the normal

direction and some critical angle or between the critical angle and the parallel orientation. Such behavior

is in fact observed in our case. That is, for the unbuffered Heusler film in the direct contact with the SiO2

substrate we have unpinned interface spins in the parallel orientation, while for the V-buffered Heusler

film we have unpinned surface (interface) spins in the perpendicular orientation. Of course, one should

also take into consideration the volume inhomogeneities through the film thickness (see discussion

above) as well as the possible effect of the strain-induced anisotropies at the film/substrate interface.

These effects should be taken into account to explain, in particular, a rather high intensity (comparable

with the main one) of the surface spin-wave mode observed in parallel geometry for the unbuffered

100 nm film (Fig. 2a). Anyway, a strong effect of the V buffer layer on the surface anisotropies of the

Heusler films is evident from our FMR studies. Other experimental information provided by our FMR studies is related to the effective magnetization of the Co2Cr0.6Fe0.4Al Heusler films. In the simplest model considering only the shape anisotropy and neglecting the magnetocrystalline and surface anisotropies we obtain the effective g-factor and magneti-zation values, as presented in Table 1. As seen from Table 1 the effective magnetization is noticeably smaller in thinner films, in agreement with SQUID data, see Ref. [15]. The smaller magnetization for thinner samples may be attributed to the formation of a nonmagnetic (weakly magnetic) interface layer similar to the “dead” layer observed in our FMR studies of another Heusler system (Co2MnSi, see the next paragraph). Besides, a contribution of the surface or strain anisotropy with the easy direction paral-lel to the film normal may also reduce the value of the effective magnetization. A noticeable decrease in the effective magnetization as well as a change in pinning conditions (as evident from more intense low-field spin wave mode) in the 25 nm unbuffered film compared with the V-buffered one indicates that the contribution of the surface/strain anisotropies may be essential. Additional measurements at low tem-peratures and higher frequencies are needed to separate between the various contributions that decrease the effective magnetization in thinner films. However, a general tendency of the V-buffer layer to pre-serve a higher effective magnetization for the Heusler samples of various thicknesses is evident from our room-temperature data.

Table 1 Effective magnetization and g-factor values estimated from FMR results.

sample g-factor magnetization [emu/cm3]

25 nm 2.061 440

V (50 nm) + 25 nm 2.029 465

100 nm 2.127 510

V (50 nm) + 100 nm 2.021 512

phys. stat. sol. (a) 203, No. 7 (2006) 1509


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Discussing the linewidth observed for various samples it is obvious that the FMR signal of the 100 nm

film prepared on V-buffer layer is much wider than for other samples. In particular, a larger linewidth is

observed in the parallel orientation (about 740 Oe in the parallel orientation against 110 Oe in the per-

pendicular one). The linewidth, which is a characteristic of magnetic inhomogeneities through a sample,

points to a different morphology of the film grown with and without a vanadium buffer layer. In our

opinion, the formation of larger grains and/or decrease of the intergrain exchange interaction are the

reasons responsible for the large linewidth in the buffered sample. In the case of the grain [5] larger than

the exchange length (typically ~100 nm) the magnetocrystalline anisotropy of the polycrystalline film is

averaged less effectively by the exchange interactions, especially in the film plane. In this respect, essen-

tially the larger linewidth in the parallel orientation comparing with the perpendicular may be treated as a

sign of the “out-of-plane” textured growth (i.e. the grains have a preferential direction for growth in the

direction perpendicular to the film but not in the film plane).

In conclusion, the bulk and surface spin wave resonance modes have been observed in the FMR stud-

ies of the Co2Cr0.6Fe0.4Al Heusler films. In particular well-resolved bulk SWR modes have been observed

in the unbuffered 100 nm film. The exchange stiffness constant of the Co2Cr0.6Fe0.4Al Heusler material

has been estimated to be D ~ 1 × 10–9 Oe cm2. A strong effect of the V-buffer layer on the surface aniso-

tropies of the Heusler films has been established. Besides, use of a V seed layer preserves higher effec-

tive magnetization of the Co2Cr0.6Fe0.4Al thin films. The FMR line for the 100 nm thick film prepared on

a V-buffer layer is much wider than for other samples, which reflects higher magnetic inhomogeneity of

this film. The effective magnetization is noticeably smaller for the thinner films (25 nm) that indicates that

the interface layer has essentially different magnetic properties from those of bulk Co2Cr0.6Fe0.4Al thin

films.

3.3 Thin films of Co2MnSi Heusler alloys

No FMR signal has been observed in the thinnest Co2MnSi film with a thickness of 4 nm, while an in-

tense FMR signal has been detected in all other samples. That is, a formation of a “dead” layer with

thickness of few nanometers [5] is confirmed by FMR measurements.

Besides, no appreciable anisotropy has been observed in the in-plane FMR measurements that points

to the nonepitaxial growth of the polycrystalline Heusler films as expected for the DC magnetron sputter-

ing preparation technique. A textured growth reported in Refs. [5, 16] means preferential alignment of

the material grains by [110] axes only in the out-of-plane (perpendicular to film) direction, while there is

no “in-plane” texture due to some preferential axes for the grains with respect to the substrate.

In any case, the magnitude of in-plane anisotropies, if any, does not exceed 10 Oe (that is about 10%

of the linewidth or 1% of the resonance field).

On the other hand, a very high anisotropy has been observed in the out-of-plane FMR measurements

(see, Figs. 3 and 4). As was mentioned above (see the previous paragraph on the Co2Cr0.6Fe0.4Al system),

the out-of-plane anisotropy provides the effective magnetization value, which is in our case very close to

the saturation magnetization. Possible contributions due to the bulk magnetocrystalline and surface ani-

sotropies may be neglected because in the case of the polycrystalline films consisting of a material with

the bulk cubic anisotropy even having an “out-of-plane” texture this contribution is expected to be very

small. Thus, it is possible to estimate the effective g-factor and magnetization considering only the shape

anisotropy contribution in the out-of-plane FMR dependence of the resonance field.

However, additional splittings are again observed in the FMR spectra of some samples for the perpen-

dicular orientation of the DC magnetic field with respect to the film plane (see the rights panels in Figs. 3

and 4). Analysis of the orientational and temperature dependences of the splitting observed for the sam-

ple with a thickness of 100 nm (Fig. 3) reveals that this splitting is most likely due to the layers with

various magnetizations. It should be noted that the FMR lineshape of this sample in the parallel orienta-

tion also looks as if it consists of two overlapped signals (narrower and wider ones). The same reason is

probably responsible for the partially resolved signal splitting in the perpendicular orientation observed



0 500 1000 1500 2000 10000 12000 14000 16000

8 nm

15 nm

61 nm

100nm

dP/d

H,a

.u.

Magnetic field , Oe

Thickness

Magnetic field , Oe

Fig. 3 FMR spectra of Co2MnSi Heusler thin films with various thicknesses for the DC magnetic field

applied parallel (left) and perpendicular (right) to the film plane.

for the sample with a thickness of 80 nm (Fig. 4). Therefore, to obtain some rough estimation of the

effective magnetization value in these cases we have used a weighted average of the spectra components

near the perpendicular orientation. The effective magnetizations of the Co2MnSi films with various

thickness and annealed at T = 450 °C are presented in Table 2, while the effective magnetizations of the

films with fixed thickness (80 nm) but annealed at various temperatures are presented in Table 3.

0 500 1000 1500 2000 15000 15500 16000

0 4 8 12 1611

12

13

14

15

16

dP/d

H,a

.u

Magnetic field , Oe

550oC

525oC

500oC

475oC

450oC

425oC

Annealing Temp.

Magnetic field , Oe

Hre

s,k

Oe

n2

Fig. 4 FMR spectra of Co2MnSi Heusler thin films with thickness 80 nm and various annealing tem-

peratures for the DC magnetic field applied parallel (left) and perpendicular (right) to the film plane. In-

set: Spin wave mode positions Hres

versus square of mode quantum number n are presented for the sample

annealed at T = 525 °C.

phys. stat. sol. (a) 203, No. 7 (2006) 1511


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Paper

Table 2 Effective magnetization and g-factor values for the Co2MnSi Heusler thin films with various

thicknesses extracted from FMR results.


8 nm 2.050 904

15 nm 2.038 980

61 nm 2.047 1012

100 nm 2.030 712

The cause of the decrease in magnetization (Table 2), as well as the splitting of FMR signal (Fig. 3) in

the sample with a thickness of 100 nm, is not clear yet. In particular, it is in contrast with the results for

the sample in the same series with thickness of 61 nm. Apparently, further studies on additional samples

of similar thickness and preparation at the same conditions are needed to check this point. However, it is

obvious that apart from this sample the effective magnetization increases very systematically both with

annealing temperature and with thickness of the films.

Furthermore, the linewidth increases for thinner films (Fig. 3, both orientations) and for higher anneal-

ing temperatures (Fig. 4, the parallel orientation). In our opinion an increase of the linewidth for higher

annealing temperatures is related to the [110] texture formation in the out-of-plane direction, as con-

firmed by XRD studies [16]. In this case the very small linewidth in the perpendicular orientation reflects

the preferential alignment of the material grains by [110] axes perpendicular to the film plane, while the

random orientation of the grains in the plane of film increases the linewidth in the parallel direction. As

was mentioned above (see the previous paragraph), this mechanism is effective if the size of grains [5] is

comparable with the exchange length (~100 nm) because in this case the magnetocrystalline anisotropy

is not effectively averaged by the exchange interactions along the film plane. On the other hand, large

linewidth in the very thin film (8 nm) is related to the influence of the “dead” layer near the interface

between the film and the substrate. The highly defective structure of this layer and/or an influence of the

strain anisotropies as well as inhomogeneous magnetization near the interface are probable factors that

cause the linewidth broadening of FMR signal in the 8 nm Heusler film.

Similar to the Co2Cr0.6Fe0.4Al Heusler films, spin wave resonance (SWR) modes have been observed

in the FMR spectra of some Co2MnSi Heusler films. The SWR modes have been revealed both in the

sample with a thickness of 61 nm for the series with fixed annealing temperature as well as in the sam-

ples annealed at temperatures in the range of 450–525 °C for the series with fixed thickness. However,

as is obvious from Figs. 3 and 4 the intensity of these modes is very small compared with the main

mode. The very low intensity of these modes indicates that both interface and surface spins of the films

are not far from the so-called “free surface” conditions [12]. However, we succeeded in tracing the first

four modes for the sample annealed at 525 °C, where the most resolved SWR has been observed, as

presented in the inset in Fig. 4.

It is possible to estimate the exchange stiffness constant D in the Co2MnSi Heusler alloy using two

models: (1) excitation of only odd spin wave modes, and (2) both odd and integer spin wave modes are

Table 3 Effective magnetization and g-factor values for the Co2MnSi Heusler thin films with various

annealing temperatures extracted from FMR results.


425 °C 2.00 955

450 °C 2.025 1009

475 °C 2.034 1005

500 °C 2.023 1021

525 °C 2.047 1024

550 °C 2.059 1025



excited. However, fitting using the second model (solid line in the inset in Fig. 2) provides a more realis-

tic (higher) value of the exchange stiffness constant of about 1.9 × 10–9 Oe cm2 (otherwise we have a

very small D = 0.6 × 10–9 Oe cm2) which is comparable with a value obtained from the temperature de-

pendence of the saturation magnetization in Ref. [17]. The second model implies that the asymmetrical

pinning conditions are realized in these films: the spins at one surface are (weakly) unpinned, while those

at the other one are (weakly) pinned. As seen in the inset in Fig. 4, the quadratic law for the mode separa-

tion fits very well the spin wave resonance positions. That is, in comparison with the unbuffered 100 nm

Co2Cr0.6Fe0.4Al Heusler film there is a rather uniform magnetization profile through the film thickness in

the Co2MnSi Heusler film.

In conclusion, the FMR studies of the Co2MnSi Heusler films have revealed that no FMR signal is

observed in the thinnest sample with a thickness of 4 nm. That is, formation of a “dead” layer with a

thickness of a few nanometers has been confirmed by the FMR measurements. The highest magnetiza-

tion is observed in the sample with a thickness of 61 nm, while the thicker sample of 100 nm reveals not

only a lower magnetization but higher magnetic inhomogeneity as well. An annealing treatment at T ≥

450 °C improves the sample quality (magnetic homogeneity) and provides higher magnetization. Weak

SWR modes have been observed in the thick Heusler films. The exchange stiffness constant of the

Co2MnSi Heusler material has been estimated to be D ~ 1.9 × 10–9 Oe cm2.

Acknowledgements This work was partially supported by DPT (State Planning Organization of Turkey) through

the grant No. 2003K 120530 and by TUBITAK through the grant No. 104T176.

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FMR investigations of half-metallic ferromagnets

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