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Magnetic and resonance properties of Fe nanowire arrays on oxidised step-bunched silicon templates
Author’s Accepted Manuscript Magnetic and resonance properties of FE nanowire arrays on oxidized step-bunched silicon templates D.M. Polishchuk, A.I. Tovstolytkin, S.K. Arora, B.J. O'Dowd, I.V. Shvets www.elsevier.com/locate/physe
PII: DOI: Reference:
S1386-9477(14)00424-X http://dx.doi.org/10.1016/j.physe.2014.11.019 PHYSE11787
To appear in: Physica E: Low-dimensional Systems and Nanostructures Received date: 4 September 2014 Revised date: 9 November 2014 Accepted date: 25 November 2014 Cite this article as: D.M. Polishchuk, A.I. Tovstolytkin, S.K. Arora, B.J. O'Dowd and I.V. Shvets, Magnetic and resonance properties of FE nanowire arrays on oxidized step-bunched silicon templates, Physica E: Low-dimensional Systems and Nanostructures, http://dx.doi.org/10.1016/j.physe.2014.11.019 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Magnetic and resonance properties of Fe nanowire arrays on oxidized step-bunched silicon templates
D.M. Polishchuk1*, A.I. Tovstolytkin1, S.K. Arora2, B.J. O’Dowd2, I.V. Shvets2 1
Institute of Magnetism, 36b Vernadsky Ave., Kyiv 03142, Ukraine
2
Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN) and School of Physics,
Trinity College Dublin, Dublin 2, Ireland *Corresponding author: Institute of Magnetism, 36b Vernadsky Ave., Kyiv 03142, Ukraine. Tel.: +380 44 424 90 95; fax.: +380 44 424 10 20; e-mail: [email protected].
Abstract Room-temperature magnetic properties of planar nanowire arrays of Fe have been studied using comprehensive analysis of FMR and magnetometry data. It has been shown that the Fe NWs are ferromagnetic at room temperature and their magnetic properties are mainly governed by shape anisotropy. Combining parameters derived from the FMR study with experimental data of magnetometry, simulations of hysteresis loops had been performed based on Stoner-Wohlfarth approach. Calculations show that magnetisation reversal of Fe NWs has a coherent-rotation type of localized character. As NW thickness decreases, localization of the magnetisation reversal mode is found to enhance due to increased inhomogeneity of thinner NWs.
Keywords: nanowires, magnetic properties, magnetization reversal, ferromagnetic resonance, StonerWohlfarth model.
1. Introduction One-dimension nanostructures, e.g. planar and out-of-plane nanowires (NWs), nanotubes and nanoribbons of different types, attract considerable interest of researchers due to their application potential as constructive elements in nano- and spin-electronic devices [1,2]. Furthermore, they are of
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great interest in terms of fundamental physics issues: reduced dimension effects, mechanism of remagnetisation, etc. [3,4]. There is a wide variety of technological methods to produce such state-ofthe-art nanostructures, ranging from top-down to simpler, bottom-up techniques [5-8]. Planar NW arrays on self-assembled templates are highly topical for planar electronics [1,8]. They are usually realized using bottom-up methods, such as reactive epitaxy [9,10] and shallow angle deposition [11,12] providing faster throughput and improved physical characteristics of these objects (better structural homogeneity, enhanced magnetism, etc.) compared to some other fabrication methods [1214]. At the same time, the forward plan for use of magnetic nanowires in emerging technologies requires a comprehensive understanding of their physical properties. Despite the advantages of bottom-up methods mentioned above self-assembly has been demonstrated to produce planar NW arrays exhibiting undesirable effects for application purposes, e.g. superparamagnetic behavior at room temperature (RT) due to small thickness of NWs, and high structural inhomogeneity (large width (w) and thickness (t) fluctuations along the wire length). However, the use of an innovative shallow angle deposition method called ATLAS (Atomic Terrace Low Angle Shadowing) [12-14] allows controlled growth of magnetic nanostructures on highly periodic step-bunched templates that are thick and uniform enough to exhibit ferromagnetism at RT. In Refs. [13,14] the temperature and thickness dependent magnetisation studies of planar NW arrays of Co (w ~ 25 nm, t ~ 3 nm) and Fe (w ~ 30 nm, t ~ 3 nm) showed that they exhibit ferromagnetic behavior at RT with shape anisotropy being the dominant contribution to the effective magnetic anisotropy throughout the temperature range studied (down to 10 K). By carrying out a temperature dependent study of magnetisation, coupled with an analytical model that takes into account the effect of thermal activation and magnetostatic interactions, it was possible to determine the magnetisation reversal mechanism present in arrays of Co nanowires [13]. It was concluded that the magnetisation reversal is governed by the curling mode reversal for thick wires (t ≈ 5-9 nm) whereas thinner wires (t ~ 3 nm) exhibit a more complex behavior, leading to a localization of the reversal modes, that is related to thermal effects and size distribution of the crystal grains that constitute the NWs. Note that all the former conclusions were based on the analysis of vibrating magnetometry data only.
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Accompanying investigations by other experimental techniques such as ferromagnetic resonance with its inherent formalism would serve as additional confirmation and strengthen the model suggestions. Ferromagnetic resonance (FMR) is a useful and very sensitive tool to study magnetically inhomogeneous and multiphase, including nanoscale systems, which are not always possible to probe with other techniques [15,16]. Based on the parameters extracted from FMR spectra, one can make conclusions about magnetic anisotropy, magnetic phase composition, degree of inhomogeneity etc. [17,18]. In this report, we present a systematic analysis of the magnetic behaviour of the planar NW arrays of Fe and show that the magnetisation reversal is described by coherent-rotation model of localized character.
2. Samples and details of experiment Planar nanowire (NW) arrays of Fe used in the present study were fabricated on highly regular step-bunched templates of oxidized vicinal Si (111) by employing a shallow angle deposition technique named ATLAS. Two samples of Fe-NW arrays were used in the study presented. For both samples, the growth was carried out under identical conditions at room temperature by depositing Fe at an angle of 3 in an ascending step direction. The templates used in the present study were highly regular with 140 nm average periodicity step-bunched surfaces of vicinal Si (miscut of 3 along the [11–2] crystallographic direction). The details of the template preparation method and ATLAS deposition technique are given elsewhere [13,14]. The two samples used for the studies differ from one another only by the NW thickness, t = 7 nm (sample 1) and t = 4.5 nm (sample 2), but have the same average wire width of wn = 25 nm. All samples were capped by a 20 nm MgO layer, which was deposited on top of the NW array at normal incident angle. Step-and-terrace periodicity of the vicinal substrates was 140 nm leading to an average interwire separation of pn=115 nm. Average width, periodicity and thickness of the Fe-NWs were determined from the analysis of atomic force microscopy (AFM) scans taken over various locations on the NW array samples deposited without a capping layer.
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FMR studies were carried out at room temperature with the use of X-band ELEXSYS E500 spectrometer supplied with an automatic goniometer. The operating frequency was
= 9.44 GHz. The
samples for FMR investigations had dimensions of 3×3×0.5 mm3. The axes relating to the FMR measurements of the NW arrays are shown in Fig. 1. Zero value of theta (θh = 0 ) corresponds to the perpendicular orientation of Hext to the macroscopic sample surface. FMR measurements were carried out with θh varied from 0 to 360 . Magnetic properties of the NW arrays were examined using a vibrating sample magnetometer (PPMS, Quantum Design) with a sensitivity of 5 10–7 emu. Uncertainty in the NWs volume determination could be as large as 10% arising mostly from the statistical fluctuations in the terrace coverage that are related to the distribution of step-terrace periodicity of the template, whereas the thickness of the deposited material is accurate within ~2% [14]. It should be noted that MgO-capped NWs may exhibit oxidation with time [19,20], so all measurements were performed within 2 weeks after the samples were fabricated.
3. Results and discussions 3.A. Ferromagnetic resonance in arrays of Fe NWs Typical FMR spectra for an array of Fe NWs are presented in Fig. 2(a). The signal from NWs can be reliably distinguished at θh = 0о and its position can be traced as the angle deviates from 0 . Because of the spread in the geometric parameters of the nanowires, the FMR signal is substantially broadened and has a distinctive asymmetric shape that differs from the commonly observed resonance signals described by the derivative of a Lorentzian or Gaussian [16,21]. The low-field background signals at ≈3.5 kOe, which are almost independent of θh, are the signals from the impurities inside a substrate [17,22]. They will be excluded from our further consideration. Resonance fields Hres and linewidths ΔHpp were extracted for samples 1 and 2. The angular dependencies of the resonance field are shown in Fig. 2(b). The dependency of Hres on θh is as expected for an oblate cylindrical ferromagnet whose behaviour is governed by shape anisotropy (Hres achieves a maximum when the applied magnetic field Hext is directed along the short axis of the
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cylinder, and diminishes as Hext deviates from this direction) [16]. However, the maximal and minimal values of Hres are different for samples 1 and 2, since the samples differ in shape from each other. More detailed analysis of these dependencies will be presented below. The solid lines in Fig. 2(b) represent simulated angular dependencies of the resonance field which fit experimental data with a good accuracy. The calculation model is described in Section 3.C.
3.B. Magnetometry measurements H ) to NW In-plane hysteresis loops with external field parallel (M–H||) and perpendicular (M–H length, as shown in Fig. 3 (a), were obtained for all samples at room temperature by vibrating sample magnetometry (Fig. 3 (b), (c)). The s uare-like M–H|| loops and sheared M–H H loops, with apparent difference in the parallel (Hc||) and perpendicular (Hc ) coercive fields, indicate that the magnetic behavior is mainly governed by shape anisotropy [14,23]. It should be noted that parameters of shape anisotropy can also be calculated from FMR measurements, which makes it possible to compare and complement data of mentioned techniques. With such purpose, simulations of hysteresis loops had been performed with the use of parameters derived from FMR study (see section 3.C for simulations’ H loops well agree details). As seen from Figs. 3 (a) and 3 (b), the experimental and simulated M–H with each other for sample 1, while there is a notable discrepancy for sample 2.
3.С. Discussion The obtained FMR data were analyzed within the Smit-Beljers approach [16] according to which the resonance conditions can be determined from the angular dependency of the free energy (U) of the system. As follows from the above considerations, as well as from the related data of Refs. [14,19], the magnetic anisotropy of the NWs arrays is dominated by the shape anisotropy. Thus, for our particular case, it is pertinent to include in the expression of the free energy only the Zeeman energy (UZ) and the demagnetising energy (UF) terms. In an idealized case of a uniform ferromagnetic ellipsoid the expression for U reads
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U
UZ UF
MH sin i sin i
1 2 M N a sin 2 cos 2 2
h
cos((
h
Nb sin
2
) cos cos
sin
2
h
N c cos
2
(1)
,
where Na, Nb and Nc are the demagnetising factors along the principal axes a, b, c of the ellipsoid, M = (M, φ, θ) is the magnetisation, H = (H, φh, θh) is the applied field. The characteristic feature of NWs is the large aspect (length-to-width) ratio, which makes it possible to consider the shape of these objects as highly elongated ellipsoids with b >> a > c (here, b, a, and c are the NW length, width, and thickness, respectively). This, in turn, means that Nb = 0 and Na, Nc
0. Since Na + Nb + Nc = 4π, one can write Na = 4π – Nc. Taking this into account, one can obtain
the system of equations for the calculation of the out-of-plane resonance field for the case where inplane azimuthal angle φh = φ = 0 :
2
H cco cos( o os((
h
) (4 (
2 N c ) M cos 2 H sin i
H
4 (4
h
si sin
(4 (
Nc )M ,
(2)
s 2 2 N c ) M sin . 2 i ( h 2sin( )
The system of equations (2) was used to fit the experimental Hres( h) dependencies for the samples under study and calculate the M and Nc parameters for each of the samples. As seen from Figs. 2(b), the fitted curves (solid lines) agree well with the experimental data, which implies that the above approach quite well describes the behavior of the Fe NWs. According to the analysis, the effective magnetisation of sample 1 (t = 7 nm) is 1100 emu/cm3, compared to 990 emu/cm3 for sample 2 (t = 4.5 nm, see Table 1). This difference can be related to the difference in the level of morphological inhomogeneity of the NWs. It is noteworthy that the surface topograhic studies using AFM showed the island-type morphology at the initial stages of NW growth (
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t
5 nm ) that, with increasing thickness ( t 5nm
5 nm ), eventually lead to the formation of a NW of 5nm
coalesced islands [12,14,19]. Having attained a value for the demagnetising factor Nc, which is characteristic of NW geometry, one can calculate the shape anisotropy field HSA (the demagnetising field along Ox axis in Fig. 3(a)):
HSA
4 – Nc M eff .
(3)
Table 1 contains HSA values for the samples under study. The sample with thinner Fe NWs (sample 2) is characterized by larger HSA values compared to sample 1. Under the assumption that Fe NWs are single-domain and magnetostatic interactions between them are negligible (due to a large distance between the NWs), the shape anisotropy field HSA should H loop [24]. Markers in Fig. 3 (b), (c) show the positions correspond to the saturation field Hs in M–H of the shape anisotropy field HSA obtained from the FMR studies. It is seen that the HSA values are H loops presented. quite close to the saturation fields Hs for the M-H The values of various parameters determined from FMR measurements and M–H loops are summarized in table 1. For both M–H|| and M–H H measurement geometries, coercivity is greater in the sample with thicker NWs array (sample 1). A similar trend was observed in Co NW arrays of comparable sizes [13]. It should be noted that Hc||, is strongly enhanced as compared to the Hc of continuous Fe films (a few tens of Oe at RT, see for example Ref. [25] for the film on a glass substrate), which points to complexity of the remagnetisation processes in the samples under investigation, partly due to enhanced magnetic inhomogeneity. Certain information about the magnetic inhomogeneity of a sample can be extracted from the shape of a M(H) hysteresis loop. As magnetic field varies, the magnetisation switching for an inhomogeneous sample occurs in a rather wide range of magnetic fields close to Hc. Quantitatively this process can be characterized by the width (δHSW) of the curve of switching field distribution. To make
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quantitative estimations, the first derivative of the M–H loops was fitted with Gaussian and its width was calculated for each of the samples (see Table 1). It is seen that the distribution of switching fields is quite wide for both samples: δHSW||, ranges from 1.6 to 2.4 kOe. To get further insight into the nature of the remagnetisation processes, we have performed simulations of hysteresis loops with the use of parameters derived from the FMR study. In ferromagnetic materials with reduced dimensions, especially those with lateral dimensions on the order of nm, the magnetisation reversal occurs through coherent-rotation or/and curling processes [26]. In an ideal case the coherent-rotation and curling modes are delocalized in the sense that they extend throughout the wire. However, the experiments indicate that in transition-metal nanowires the magnetisation reversal is often initiated by localized modes (see [27] and references therein). The localization is a quite general phenomenon caused by morphological inhomogeneities and occurring in both polycrystalline and single-crystalline wires. In the polycrystalline limit, the competition between interatomic exchange and anisotropy gives rise to a variety of random-anisotropy effects, whereas nearly single-crystalline wires do not exhibit notable localization of the nucleation mode [26,27]. Below we argue that the magnetisation reversal in the arrays of Fe NWs under discussion obeys some intermediate mode between the coherent-rotation and curling owing to a localized character of nucleation modes. In an ideal infinite oblate cylinder, coherent or uniform rotation occurs when the wire thickness is smaller than tcoh, with the value of tcoh being determined by tcoh = 3.68(2A/(4π–Nc)Ms2)1/2, where A is the exchange stiffness and Ms is the spontaneous magnetisation [23]. Taking that A ≈ 1·10-6 erg/cm [23], Nc ≈ 10 and Ms ≈ 1000 emu/cm3, the estimations for the Fe-NWs at RT give tcoh ≈ 30 nm. As the thicknesses of the NWs in samples 1 and 2 are smaller than the estimated tcoh, one can expect that the coherent-rotation model should adequately describe the M–H loops within Stoner-Wohlfarth approach [23]. However, a more precise look at the magnetisation data shows that, although the experimental loops behave generally within the Stoner-Wohlfarth description, there are few noticeable deviations. First, the coercive fields of the M–H|| loops (Hc||) are much smaller than corresponding effective anisotropy fields HSA. According to the model, Hc|| should be equal to HSA [23]. This effect is well-
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known as Brown’s coercive paradox, and is explained by thermal activation over a single energy barrier as proposed by Neel and Brown [28]. Second, the coercive fields (Hc ) and remanent H loops are nonzero, whereas theory predicts Hc = 0. magnetisation for the M–H H loops were simulated under additional assumptions beyond the Stoner-Wohlfarth The M–H model: the orientations of the effective anisotropy axes slightly vary along the wire and magnetisation reversal is initiated by localized modes. The simulated M–H H loops for samples 1 and 2 are depicted in Fig. 3 (b), (c), respectively. Each blue curve is calculated by averaging the loops with parameters Nc, M and α, which have normal (Gaussian) spreads. The central values of Nc and M were taken from FMR data (see Table 1) and were fixed, but a distribution of these quantities was implemented in the simulation in order to achieve the best agreement between simulated and experimental data. The distributions of Nc, M and α for samples 1 and 2 are shown in insets to Fig. 3 (b), (c). The remanence H loops we interpret as deviation of local magnetic moments from the Oy axis owing to a of the M–H certain distribution of the axis misorientation, α, of effective magnetic anisotropy after application of the external field, Hext (see Fig. 3 (a)). Distribution half-widths 2σNc, 2σM and 2σα can be used as parameters of magnetic and structural inhomogeneity. Particularly, for sample 1(2), σNc = 1.8(2), σM = 430 G (400 G) and σα = 18o(16o). For the thicker NWs (sample 1), there is a good agreement between experimental and simulated data, with a standard deviation of Δst ≈ 3·10–3. For the thinner NWs (sample 2), the agreement is much worse (Δst ≈ 1·10–2). Such features may be assigned to more evident localization in the thinner NWs, with weaker interactions between localized areas along the wire [13,19]. To further explore the nature of the remagnetisation process, we have examined the expression for the coercive field that takes into account thermal activation (see Eq. 7 in Ref. [29]) adapted to our case. Under the assumptions that the magnetisation at T = 0 K equals the spontaneous magnetisation at RT (M0 ≈ Ms), and that both coercive field Hc0 and energy barrier E0 at T = 0 K can be set HSA and 0.5HSAMeffVeff, respectively, one can determine the effective volume, Veff, involved in the magnetisation reversal from the formula [29]:
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H c (T )
1 H SA S
50kBT 50k HSA M effVeeff
1m
.
(4)
Here, the parameter m varies between values of 3/2 (curling mode) and 2 (coherent rotation mode). If experimental values Hc|| are substituted for Hc(T) in Eq. (4), one can estimate the effective magnetic volume Veff ~ 109 nm3, which is much smaller than the NW volume. One can rewrite formula (4) to estimate how the effective volume Veff changes with a reduction of sample thickness:
Veff(1) Veff(2)
(2) ( ((2)) ((2) 1 H c||(2) H SA H SA M eff S e (1) (1) (1 ( ) ((1)) 1 H c||(1) H SSA H SA M eff ||
m
,
(5)
where m = 2 is chosen, in our case. The ratio (5) is about 1.4 for the samples under investigation, whereas the ratio of nominal thicknesses is t(1)/t(2) ≈ 1.6. Detailed analysis of (5) using parameters from Table 1 makes it possible to relate this discrepancy to enhanced inhomogeneity of thinner NWs (sample 2) in comparison to the thicker (sample 1).
4. Conclusions Our studies on planar Fe NW arrays show that the NWs magnetic behavior is governed by the shape anisotropy which dominates over other types of anisotropy. The shape anisotropy fields HSA calculated from the FMR studies are quite close to the saturation fields Hs from the magnetometric MH
loops. As NW thickness grows, such magnetic parameters as effective magnetization and
coercivity are increased, while HSA is decreased. It was concluded that magnetisation reversal is described by coherent-rotation model of localized character. The samples with thinner NWs were shown to exhibit more evident localization with weaker interactions between localized areas along the
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wire. The use of FMR and the associated magnetic modelling makes it possible to understand the micromagnetic behavior of planar arrays of Fe NWs.
Acknowledgements The work was partially supported by grant No. 1.1.8.5 of the Ukrainian State Program ‘Nanotechnology and nanomaterials’. REFERENCES [1] A. Fert, L. Piraux, J. Magn. Magn. Mater. 200 (1999) 338–358. [2] C. Teichert, Appl. Phys. A 76 (2003) 653–664. [3] P. Schio, F. Vidal, Y. Zheng, J. Milano, E. Fonda, D. Demaile, B. Vodungbo, J. Varalda, A.J.A. de Oliveria, V.H. Etgens, Phys. Rev. B 82 (2010) 094436 (9pp). [4] A. Enders, R. Skomski and J. Honolka, J. Phys.: Condens. Matter. 22 (2011) 433001. [5] J. F. Smyth, S. Schultz, D. Kern, and H. Schmid, J. Appl. Phys. 63 (1988) 4237. [6] J. I. Martin, J. Nogues, K. Liu, J. L. Vicent, I. K. Schuller, J. Magn. Magn. Mater. 256 (2003) 449–501. [7] P. Gambardella, A. Dallmeyer, K. Maiti, M.C. Malagoli, S. Rusponi, P. Ohresser, W. Eberhardt, C. Carbone, K. Kern, Phys. Rev. Lett. 93 (2004) 077203. [8] C. Carbone, S. Gardonio, P. Moras, S. Lounis, M. Heide, G. Bihlmayer, N. Atodiresei, P. H. Dederichs, S. Blügel, S. Vlaic, A. Lehnert, S. Ouazi, S. Rusponi, H. Brune, J. Honolka, A. Enders, K. Kern, S. Stepanow, C. Krull, T. Balashov, A. Mugarza, and P. Gambardella, Adv. Funct. Mater. 21
(2011) 1212–1228. [9] K. Radican, N. Berdunov, and I.V. Shvets, Phys. Rev. B 77 (2008) 085417. [10] S. Liang, R. Islam, D.J. Smith, P.A. Bennet, J.R. O’Brien, and B. Taylor, Appl. Phys. Lett.
88 (2006) 113111. [11] J. Oster, M. Kallamayer, L. Wiehl, H.J. Elmers and H. Adrian, J. Appl. Phys. 97 (2005) 014303.
12
[12] F. Cuccureddu, V. Usov, S. Murphy, C.O. Coileain, I.V. Shvets, Rev. Sci. Instr. 79 (2008) 053907 (4pp). [13] S. K. Arora, B. J. O’Dowd, B. Ballesteros, P. Gambardella, I. V. Shvets, Nanotechnology 23 (2012) 235702 (7pp). [14] S.K. Arora, B.J. O’Dowd, P.C. McElligot, I.V. Shvets, P. Thakur, N.B. Brookes, J. Appl. Phys. 109 (2011) 07B106 (3pp). [15] M. Farle, Rep. Prog. Phys. 61 (1998) 755–826. [16] A. G. Gurevich, G. A. Melkov, Magnetization Oscillations and Waves, CRC Press, Boca Raton, 1996. [17] X. Moya, L.E. Hueso, F. Maccherozzi, A.I. Tovstolytkin, D.I. Podyalovskii, C. Ducati, L. Phillips, M. Chidini, O. Hovorka, A. Berger, M.E. Vickers, E. Defaÿ, S.S. Dhesi, N.D. Mathur, Nat. Mater. 12 (2013) 52–58. [18] V.O. Golub, V.V. Dzyublyuk, A.I. Tovstolytkin, S.K. Arora, R. Ramos, R.G.S. Sofin, I.V. Shvets, J. Appl. Phys. 107 (2010) 09B108 (3pp). [19] S.K. Arora, B.J. O’Dowd, D.M. Polishchuk, A.I. Tovstolytkin, P. Thakur, N.B. Brookes, B. Ballesteros, P. Gambardella, and I.V. Shvets, J. Appl. Phys. 114 (2013) 133903 (7pp). [20] D.M. Polishchuk, A.I. Tovstolytkin, S.K. Arora, B.J. O’Dowd, and I.V. Shvets, Low Temp. Phys. 40 (2014) 165–170. [21] A. I. Tovstolytkin, V. V. Dzyublyuk, D. I. Podyalovskii, X. Moya, C. Israel, D. Sanchez, M. E. Vickers, and N. D. Mathur, Phys. Rev. B 83 (2011) 184404 (6pp). [22] M.D. Glinchuk, I.P. Bykov, S.M. Kornienko, V.V. Laguta, A.M. Slipenyuk, A.G. Bilous, O.I. V'yunov, O.Z. Yanchevskii, J. Mater. Chem. 10 (2000) 941–947. [23] A. Aharoni, Introduction to the Theory of Ferromagnetism, Oxford University Press, Oxford, 1996. [24] S. Chikazumi, Physics of Ferromagnetism, Oxford University Press, New York, 2005. [25] X.-J. Xu, Q.-L. Ye, G.-X. Ye, Phys. Lett. A 361 (2007) 429–433.
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[26] J. Sanchez-Barriga, M. Lucas, F. Radu, E. Martin and M. Multigner, Phys. Rev. B 80 (2009) 184424 (8pp). [27] R. Skomski, H. Zeng, M. Zheng, and D.J. Sellmyer, Phys. Rev. B. 62 (2000) 3900–3904. [28] L. Neel, Ann. Geofis. 5 (1949) 99 [W. F. Brown, Phys. Rev. 130 (1963) 1677]. [29] H. Zeng, R. Skomski, L. Menon, Y. Liu, S. Bandyopadhyay, and D.J. Sellmyer, Phys. Rev. B. 65 (2002) 134426 (8pp).
Figure captions Fig. 1. Schematic illustration of a cross section of an array of NWs on step-bunched oxidized vicinal Si (111) substrates and experimental geometry used for the FMR measurements.
Fig. 2. (a) Typical FMR spectra for sample 1. The values of θh are indicated on the lines. (b) Angular dependencies of the resonance field for samples 1 and 2. Circles show experimental data, solid lines – simulated dependencies (see section 3.C).
Fig. 3. (a) Illustration of the parallel (H|| along Oy axis) and perpendicular (H along Ox axis) Hdirection with respect to the NW length orientation (along Oy axis). The picture also illustrates a remnant alignment of localized magnetic moments after the application of H in the direction of Ox axis. Misorientation angle α shows possible local deviations of the direction of NW effective anisotropy axes from Oy axis. (b), (c) In-plane hysteresis loops measured when the external field is applied in parallel (H||) or perpendicular (H ) configurations at room temperature. Values of effective anisotropy field, HSA, are calculated using eq. (3) with Nc, Meff, derived from the FMR data. Blue H curves – simulated M–H
loops. Insets in (b), (c) show spreads of demagnetising factor Nc,
H loops. Markers 1 magnetisation M and axis misorientation α found from fitting of experimental M–H and 2 indicate corresponding spreads of α used for simulations of upper and lower branches of each M–H H loop.
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Table 1. Magnetic parameters of NW arrays, determined from FMR and magnetometry studies. S ample
t , nm
1 2
Mef 3 f, emu/cm
N c
7
1 0.3
4 .5
11 00
9 .5
99 0
δH ,
HS (a) A , kOe
δH (b) SW|| , kOe
2.5
1.6
2.4
3.0
1.6
1.7
SW
(c)
H (d) c|| , c
Oe
kOe
H , Oe
(e)
6 30
1 40
4 50
(a)
demagnetising field along NW width (see expression (3)) width of the switching field distribution curve for M–H|| and M–H H loops, respectively (d),(e) coercivity for M–H|| and M–H H loops, respectively (b),(c)
Highlights: We carry out FMR and VSM investigations of planar nanowire (NW) arrays of Fe. Experimental results are supported by model calculations and simulations. The Fe NWs are ferromagnetic at room temperature. Magnetisation reversal of NWs has a coherent-rotation type of localized character. Localization of the magnetisation reversal mode depends on inhomogeneity of NWs.
1 20
Figure1
Figure2
Figure3
Figure1(color_online)
Figure2(color_online)
Figure3(color_online)
PII: DOI: Reference:
S1386-9477(14)00424-X http://dx.doi.org/10.1016/j.physe.2014.11.019 PHYSE11787
To appear in: Physica E: Low-dimensional Systems and Nanostructures Received date: 4 September 2014 Revised date: 9 November 2014 Accepted date: 25 November 2014 Cite this article as: D.M. Polishchuk, A.I. Tovstolytkin, S.K. Arora, B.J. O'Dowd and I.V. Shvets, Magnetic and resonance properties of FE nanowire arrays on oxidized step-bunched silicon templates, Physica E: Low-dimensional Systems and Nanostructures, http://dx.doi.org/10.1016/j.physe.2014.11.019 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Magnetic and resonance properties of Fe nanowire arrays on oxidized step-bunched silicon templates
D.M. Polishchuk1*, A.I. Tovstolytkin1, S.K. Arora2, B.J. O’Dowd2, I.V. Shvets2 1
Institute of Magnetism, 36b Vernadsky Ave., Kyiv 03142, Ukraine
2
Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN) and School of Physics,
Trinity College Dublin, Dublin 2, Ireland *Corresponding author: Institute of Magnetism, 36b Vernadsky Ave., Kyiv 03142, Ukraine. Tel.: +380 44 424 90 95; fax.: +380 44 424 10 20; e-mail: [email protected].
Abstract Room-temperature magnetic properties of planar nanowire arrays of Fe have been studied using comprehensive analysis of FMR and magnetometry data. It has been shown that the Fe NWs are ferromagnetic at room temperature and their magnetic properties are mainly governed by shape anisotropy. Combining parameters derived from the FMR study with experimental data of magnetometry, simulations of hysteresis loops had been performed based on Stoner-Wohlfarth approach. Calculations show that magnetisation reversal of Fe NWs has a coherent-rotation type of localized character. As NW thickness decreases, localization of the magnetisation reversal mode is found to enhance due to increased inhomogeneity of thinner NWs.
Keywords: nanowires, magnetic properties, magnetization reversal, ferromagnetic resonance, StonerWohlfarth model.
1. Introduction One-dimension nanostructures, e.g. planar and out-of-plane nanowires (NWs), nanotubes and nanoribbons of different types, attract considerable interest of researchers due to their application potential as constructive elements in nano- and spin-electronic devices [1,2]. Furthermore, they are of
2
great interest in terms of fundamental physics issues: reduced dimension effects, mechanism of remagnetisation, etc. [3,4]. There is a wide variety of technological methods to produce such state-ofthe-art nanostructures, ranging from top-down to simpler, bottom-up techniques [5-8]. Planar NW arrays on self-assembled templates are highly topical for planar electronics [1,8]. They are usually realized using bottom-up methods, such as reactive epitaxy [9,10] and shallow angle deposition [11,12] providing faster throughput and improved physical characteristics of these objects (better structural homogeneity, enhanced magnetism, etc.) compared to some other fabrication methods [1214]. At the same time, the forward plan for use of magnetic nanowires in emerging technologies requires a comprehensive understanding of their physical properties. Despite the advantages of bottom-up methods mentioned above self-assembly has been demonstrated to produce planar NW arrays exhibiting undesirable effects for application purposes, e.g. superparamagnetic behavior at room temperature (RT) due to small thickness of NWs, and high structural inhomogeneity (large width (w) and thickness (t) fluctuations along the wire length). However, the use of an innovative shallow angle deposition method called ATLAS (Atomic Terrace Low Angle Shadowing) [12-14] allows controlled growth of magnetic nanostructures on highly periodic step-bunched templates that are thick and uniform enough to exhibit ferromagnetism at RT. In Refs. [13,14] the temperature and thickness dependent magnetisation studies of planar NW arrays of Co (w ~ 25 nm, t ~ 3 nm) and Fe (w ~ 30 nm, t ~ 3 nm) showed that they exhibit ferromagnetic behavior at RT with shape anisotropy being the dominant contribution to the effective magnetic anisotropy throughout the temperature range studied (down to 10 K). By carrying out a temperature dependent study of magnetisation, coupled with an analytical model that takes into account the effect of thermal activation and magnetostatic interactions, it was possible to determine the magnetisation reversal mechanism present in arrays of Co nanowires [13]. It was concluded that the magnetisation reversal is governed by the curling mode reversal for thick wires (t ≈ 5-9 nm) whereas thinner wires (t ~ 3 nm) exhibit a more complex behavior, leading to a localization of the reversal modes, that is related to thermal effects and size distribution of the crystal grains that constitute the NWs. Note that all the former conclusions were based on the analysis of vibrating magnetometry data only.
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Accompanying investigations by other experimental techniques such as ferromagnetic resonance with its inherent formalism would serve as additional confirmation and strengthen the model suggestions. Ferromagnetic resonance (FMR) is a useful and very sensitive tool to study magnetically inhomogeneous and multiphase, including nanoscale systems, which are not always possible to probe with other techniques [15,16]. Based on the parameters extracted from FMR spectra, one can make conclusions about magnetic anisotropy, magnetic phase composition, degree of inhomogeneity etc. [17,18]. In this report, we present a systematic analysis of the magnetic behaviour of the planar NW arrays of Fe and show that the magnetisation reversal is described by coherent-rotation model of localized character.
2. Samples and details of experiment Planar nanowire (NW) arrays of Fe used in the present study were fabricated on highly regular step-bunched templates of oxidized vicinal Si (111) by employing a shallow angle deposition technique named ATLAS. Two samples of Fe-NW arrays were used in the study presented. For both samples, the growth was carried out under identical conditions at room temperature by depositing Fe at an angle of 3 in an ascending step direction. The templates used in the present study were highly regular with 140 nm average periodicity step-bunched surfaces of vicinal Si (miscut of 3 along the [11–2] crystallographic direction). The details of the template preparation method and ATLAS deposition technique are given elsewhere [13,14]. The two samples used for the studies differ from one another only by the NW thickness, t = 7 nm (sample 1) and t = 4.5 nm (sample 2), but have the same average wire width of wn = 25 nm. All samples were capped by a 20 nm MgO layer, which was deposited on top of the NW array at normal incident angle. Step-and-terrace periodicity of the vicinal substrates was 140 nm leading to an average interwire separation of pn=115 nm. Average width, periodicity and thickness of the Fe-NWs were determined from the analysis of atomic force microscopy (AFM) scans taken over various locations on the NW array samples deposited without a capping layer.
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FMR studies were carried out at room temperature with the use of X-band ELEXSYS E500 spectrometer supplied with an automatic goniometer. The operating frequency was
= 9.44 GHz. The
samples for FMR investigations had dimensions of 3×3×0.5 mm3. The axes relating to the FMR measurements of the NW arrays are shown in Fig. 1. Zero value of theta (θh = 0 ) corresponds to the perpendicular orientation of Hext to the macroscopic sample surface. FMR measurements were carried out with θh varied from 0 to 360 . Magnetic properties of the NW arrays were examined using a vibrating sample magnetometer (PPMS, Quantum Design) with a sensitivity of 5 10–7 emu. Uncertainty in the NWs volume determination could be as large as 10% arising mostly from the statistical fluctuations in the terrace coverage that are related to the distribution of step-terrace periodicity of the template, whereas the thickness of the deposited material is accurate within ~2% [14]. It should be noted that MgO-capped NWs may exhibit oxidation with time [19,20], so all measurements were performed within 2 weeks after the samples were fabricated.
3. Results and discussions 3.A. Ferromagnetic resonance in arrays of Fe NWs Typical FMR spectra for an array of Fe NWs are presented in Fig. 2(a). The signal from NWs can be reliably distinguished at θh = 0о and its position can be traced as the angle deviates from 0 . Because of the spread in the geometric parameters of the nanowires, the FMR signal is substantially broadened and has a distinctive asymmetric shape that differs from the commonly observed resonance signals described by the derivative of a Lorentzian or Gaussian [16,21]. The low-field background signals at ≈3.5 kOe, which are almost independent of θh, are the signals from the impurities inside a substrate [17,22]. They will be excluded from our further consideration. Resonance fields Hres and linewidths ΔHpp were extracted for samples 1 and 2. The angular dependencies of the resonance field are shown in Fig. 2(b). The dependency of Hres on θh is as expected for an oblate cylindrical ferromagnet whose behaviour is governed by shape anisotropy (Hres achieves a maximum when the applied magnetic field Hext is directed along the short axis of the
5
cylinder, and diminishes as Hext deviates from this direction) [16]. However, the maximal and minimal values of Hres are different for samples 1 and 2, since the samples differ in shape from each other. More detailed analysis of these dependencies will be presented below. The solid lines in Fig. 2(b) represent simulated angular dependencies of the resonance field which fit experimental data with a good accuracy. The calculation model is described in Section 3.C.
3.B. Magnetometry measurements H ) to NW In-plane hysteresis loops with external field parallel (M–H||) and perpendicular (M–H length, as shown in Fig. 3 (a), were obtained for all samples at room temperature by vibrating sample magnetometry (Fig. 3 (b), (c)). The s uare-like M–H|| loops and sheared M–H H loops, with apparent difference in the parallel (Hc||) and perpendicular (Hc ) coercive fields, indicate that the magnetic behavior is mainly governed by shape anisotropy [14,23]. It should be noted that parameters of shape anisotropy can also be calculated from FMR measurements, which makes it possible to compare and complement data of mentioned techniques. With such purpose, simulations of hysteresis loops had been performed with the use of parameters derived from FMR study (see section 3.C for simulations’ H loops well agree details). As seen from Figs. 3 (a) and 3 (b), the experimental and simulated M–H with each other for sample 1, while there is a notable discrepancy for sample 2.
3.С. Discussion The obtained FMR data were analyzed within the Smit-Beljers approach [16] according to which the resonance conditions can be determined from the angular dependency of the free energy (U) of the system. As follows from the above considerations, as well as from the related data of Refs. [14,19], the magnetic anisotropy of the NWs arrays is dominated by the shape anisotropy. Thus, for our particular case, it is pertinent to include in the expression of the free energy only the Zeeman energy (UZ) and the demagnetising energy (UF) terms. In an idealized case of a uniform ferromagnetic ellipsoid the expression for U reads
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U
UZ UF
MH sin i sin i
1 2 M N a sin 2 cos 2 2
h
cos((
h
Nb sin
2
) cos cos
sin
2
h
N c cos
2
(1)
,
where Na, Nb and Nc are the demagnetising factors along the principal axes a, b, c of the ellipsoid, M = (M, φ, θ) is the magnetisation, H = (H, φh, θh) is the applied field. The characteristic feature of NWs is the large aspect (length-to-width) ratio, which makes it possible to consider the shape of these objects as highly elongated ellipsoids with b >> a > c (here, b, a, and c are the NW length, width, and thickness, respectively). This, in turn, means that Nb = 0 and Na, Nc
0. Since Na + Nb + Nc = 4π, one can write Na = 4π – Nc. Taking this into account, one can obtain
the system of equations for the calculation of the out-of-plane resonance field for the case where inplane azimuthal angle φh = φ = 0 :
2
H cco cos( o os((
h
) (4 (
2 N c ) M cos 2 H sin i
H
4 (4
h
si sin
(4 (
Nc )M ,
(2)
s 2 2 N c ) M sin . 2 i ( h 2sin( )
The system of equations (2) was used to fit the experimental Hres( h) dependencies for the samples under study and calculate the M and Nc parameters for each of the samples. As seen from Figs. 2(b), the fitted curves (solid lines) agree well with the experimental data, which implies that the above approach quite well describes the behavior of the Fe NWs. According to the analysis, the effective magnetisation of sample 1 (t = 7 nm) is 1100 emu/cm3, compared to 990 emu/cm3 for sample 2 (t = 4.5 nm, see Table 1). This difference can be related to the difference in the level of morphological inhomogeneity of the NWs. It is noteworthy that the surface topograhic studies using AFM showed the island-type morphology at the initial stages of NW growth (
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t
5 nm ) that, with increasing thickness ( t 5nm
5 nm ), eventually lead to the formation of a NW of 5nm
coalesced islands [12,14,19]. Having attained a value for the demagnetising factor Nc, which is characteristic of NW geometry, one can calculate the shape anisotropy field HSA (the demagnetising field along Ox axis in Fig. 3(a)):
HSA
4 – Nc M eff .
(3)
Table 1 contains HSA values for the samples under study. The sample with thinner Fe NWs (sample 2) is characterized by larger HSA values compared to sample 1. Under the assumption that Fe NWs are single-domain and magnetostatic interactions between them are negligible (due to a large distance between the NWs), the shape anisotropy field HSA should H loop [24]. Markers in Fig. 3 (b), (c) show the positions correspond to the saturation field Hs in M–H of the shape anisotropy field HSA obtained from the FMR studies. It is seen that the HSA values are H loops presented. quite close to the saturation fields Hs for the M-H The values of various parameters determined from FMR measurements and M–H loops are summarized in table 1. For both M–H|| and M–H H measurement geometries, coercivity is greater in the sample with thicker NWs array (sample 1). A similar trend was observed in Co NW arrays of comparable sizes [13]. It should be noted that Hc||, is strongly enhanced as compared to the Hc of continuous Fe films (a few tens of Oe at RT, see for example Ref. [25] for the film on a glass substrate), which points to complexity of the remagnetisation processes in the samples under investigation, partly due to enhanced magnetic inhomogeneity. Certain information about the magnetic inhomogeneity of a sample can be extracted from the shape of a M(H) hysteresis loop. As magnetic field varies, the magnetisation switching for an inhomogeneous sample occurs in a rather wide range of magnetic fields close to Hc. Quantitatively this process can be characterized by the width (δHSW) of the curve of switching field distribution. To make
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quantitative estimations, the first derivative of the M–H loops was fitted with Gaussian and its width was calculated for each of the samples (see Table 1). It is seen that the distribution of switching fields is quite wide for both samples: δHSW||, ranges from 1.6 to 2.4 kOe. To get further insight into the nature of the remagnetisation processes, we have performed simulations of hysteresis loops with the use of parameters derived from the FMR study. In ferromagnetic materials with reduced dimensions, especially those with lateral dimensions on the order of nm, the magnetisation reversal occurs through coherent-rotation or/and curling processes [26]. In an ideal case the coherent-rotation and curling modes are delocalized in the sense that they extend throughout the wire. However, the experiments indicate that in transition-metal nanowires the magnetisation reversal is often initiated by localized modes (see [27] and references therein). The localization is a quite general phenomenon caused by morphological inhomogeneities and occurring in both polycrystalline and single-crystalline wires. In the polycrystalline limit, the competition between interatomic exchange and anisotropy gives rise to a variety of random-anisotropy effects, whereas nearly single-crystalline wires do not exhibit notable localization of the nucleation mode [26,27]. Below we argue that the magnetisation reversal in the arrays of Fe NWs under discussion obeys some intermediate mode between the coherent-rotation and curling owing to a localized character of nucleation modes. In an ideal infinite oblate cylinder, coherent or uniform rotation occurs when the wire thickness is smaller than tcoh, with the value of tcoh being determined by tcoh = 3.68(2A/(4π–Nc)Ms2)1/2, where A is the exchange stiffness and Ms is the spontaneous magnetisation [23]. Taking that A ≈ 1·10-6 erg/cm [23], Nc ≈ 10 and Ms ≈ 1000 emu/cm3, the estimations for the Fe-NWs at RT give tcoh ≈ 30 nm. As the thicknesses of the NWs in samples 1 and 2 are smaller than the estimated tcoh, one can expect that the coherent-rotation model should adequately describe the M–H loops within Stoner-Wohlfarth approach [23]. However, a more precise look at the magnetisation data shows that, although the experimental loops behave generally within the Stoner-Wohlfarth description, there are few noticeable deviations. First, the coercive fields of the M–H|| loops (Hc||) are much smaller than corresponding effective anisotropy fields HSA. According to the model, Hc|| should be equal to HSA [23]. This effect is well-
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known as Brown’s coercive paradox, and is explained by thermal activation over a single energy barrier as proposed by Neel and Brown [28]. Second, the coercive fields (Hc ) and remanent H loops are nonzero, whereas theory predicts Hc = 0. magnetisation for the M–H H loops were simulated under additional assumptions beyond the Stoner-Wohlfarth The M–H model: the orientations of the effective anisotropy axes slightly vary along the wire and magnetisation reversal is initiated by localized modes. The simulated M–H H loops for samples 1 and 2 are depicted in Fig. 3 (b), (c), respectively. Each blue curve is calculated by averaging the loops with parameters Nc, M and α, which have normal (Gaussian) spreads. The central values of Nc and M were taken from FMR data (see Table 1) and were fixed, but a distribution of these quantities was implemented in the simulation in order to achieve the best agreement between simulated and experimental data. The distributions of Nc, M and α for samples 1 and 2 are shown in insets to Fig. 3 (b), (c). The remanence H loops we interpret as deviation of local magnetic moments from the Oy axis owing to a of the M–H certain distribution of the axis misorientation, α, of effective magnetic anisotropy after application of the external field, Hext (see Fig. 3 (a)). Distribution half-widths 2σNc, 2σM and 2σα can be used as parameters of magnetic and structural inhomogeneity. Particularly, for sample 1(2), σNc = 1.8(2), σM = 430 G (400 G) and σα = 18o(16o). For the thicker NWs (sample 1), there is a good agreement between experimental and simulated data, with a standard deviation of Δst ≈ 3·10–3. For the thinner NWs (sample 2), the agreement is much worse (Δst ≈ 1·10–2). Such features may be assigned to more evident localization in the thinner NWs, with weaker interactions between localized areas along the wire [13,19]. To further explore the nature of the remagnetisation process, we have examined the expression for the coercive field that takes into account thermal activation (see Eq. 7 in Ref. [29]) adapted to our case. Under the assumptions that the magnetisation at T = 0 K equals the spontaneous magnetisation at RT (M0 ≈ Ms), and that both coercive field Hc0 and energy barrier E0 at T = 0 K can be set HSA and 0.5HSAMeffVeff, respectively, one can determine the effective volume, Veff, involved in the magnetisation reversal from the formula [29]:
10
H c (T )
1 H SA S
50kBT 50k HSA M effVeeff
1m
.
(4)
Here, the parameter m varies between values of 3/2 (curling mode) and 2 (coherent rotation mode). If experimental values Hc|| are substituted for Hc(T) in Eq. (4), one can estimate the effective magnetic volume Veff ~ 109 nm3, which is much smaller than the NW volume. One can rewrite formula (4) to estimate how the effective volume Veff changes with a reduction of sample thickness:
Veff(1) Veff(2)
(2) ( ((2)) ((2) 1 H c||(2) H SA H SA M eff S e (1) (1) (1 ( ) ((1)) 1 H c||(1) H SSA H SA M eff ||
m
,
(5)
where m = 2 is chosen, in our case. The ratio (5) is about 1.4 for the samples under investigation, whereas the ratio of nominal thicknesses is t(1)/t(2) ≈ 1.6. Detailed analysis of (5) using parameters from Table 1 makes it possible to relate this discrepancy to enhanced inhomogeneity of thinner NWs (sample 2) in comparison to the thicker (sample 1).
4. Conclusions Our studies on planar Fe NW arrays show that the NWs magnetic behavior is governed by the shape anisotropy which dominates over other types of anisotropy. The shape anisotropy fields HSA calculated from the FMR studies are quite close to the saturation fields Hs from the magnetometric MH
loops. As NW thickness grows, such magnetic parameters as effective magnetization and
coercivity are increased, while HSA is decreased. It was concluded that magnetisation reversal is described by coherent-rotation model of localized character. The samples with thinner NWs were shown to exhibit more evident localization with weaker interactions between localized areas along the
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wire. The use of FMR and the associated magnetic modelling makes it possible to understand the micromagnetic behavior of planar arrays of Fe NWs.
Acknowledgements The work was partially supported by grant No. 1.1.8.5 of the Ukrainian State Program ‘Nanotechnology and nanomaterials’. REFERENCES [1] A. Fert, L. Piraux, J. Magn. Magn. Mater. 200 (1999) 338–358. [2] C. Teichert, Appl. Phys. A 76 (2003) 653–664. [3] P. Schio, F. Vidal, Y. Zheng, J. Milano, E. Fonda, D. Demaile, B. Vodungbo, J. Varalda, A.J.A. de Oliveria, V.H. Etgens, Phys. Rev. B 82 (2010) 094436 (9pp). [4] A. Enders, R. Skomski and J. Honolka, J. Phys.: Condens. Matter. 22 (2011) 433001. [5] J. F. Smyth, S. Schultz, D. Kern, and H. Schmid, J. Appl. Phys. 63 (1988) 4237. [6] J. I. Martin, J. Nogues, K. Liu, J. L. Vicent, I. K. Schuller, J. Magn. Magn. Mater. 256 (2003) 449–501. [7] P. Gambardella, A. Dallmeyer, K. Maiti, M.C. Malagoli, S. Rusponi, P. Ohresser, W. Eberhardt, C. Carbone, K. Kern, Phys. Rev. Lett. 93 (2004) 077203. [8] C. Carbone, S. Gardonio, P. Moras, S. Lounis, M. Heide, G. Bihlmayer, N. Atodiresei, P. H. Dederichs, S. Blügel, S. Vlaic, A. Lehnert, S. Ouazi, S. Rusponi, H. Brune, J. Honolka, A. Enders, K. Kern, S. Stepanow, C. Krull, T. Balashov, A. Mugarza, and P. Gambardella, Adv. Funct. Mater. 21
(2011) 1212–1228. [9] K. Radican, N. Berdunov, and I.V. Shvets, Phys. Rev. B 77 (2008) 085417. [10] S. Liang, R. Islam, D.J. Smith, P.A. Bennet, J.R. O’Brien, and B. Taylor, Appl. Phys. Lett.
88 (2006) 113111. [11] J. Oster, M. Kallamayer, L. Wiehl, H.J. Elmers and H. Adrian, J. Appl. Phys. 97 (2005) 014303.
12
[12] F. Cuccureddu, V. Usov, S. Murphy, C.O. Coileain, I.V. Shvets, Rev. Sci. Instr. 79 (2008) 053907 (4pp). [13] S. K. Arora, B. J. O’Dowd, B. Ballesteros, P. Gambardella, I. V. Shvets, Nanotechnology 23 (2012) 235702 (7pp). [14] S.K. Arora, B.J. O’Dowd, P.C. McElligot, I.V. Shvets, P. Thakur, N.B. Brookes, J. Appl. Phys. 109 (2011) 07B106 (3pp). [15] M. Farle, Rep. Prog. Phys. 61 (1998) 755–826. [16] A. G. Gurevich, G. A. Melkov, Magnetization Oscillations and Waves, CRC Press, Boca Raton, 1996. [17] X. Moya, L.E. Hueso, F. Maccherozzi, A.I. Tovstolytkin, D.I. Podyalovskii, C. Ducati, L. Phillips, M. Chidini, O. Hovorka, A. Berger, M.E. Vickers, E. Defaÿ, S.S. Dhesi, N.D. Mathur, Nat. Mater. 12 (2013) 52–58. [18] V.O. Golub, V.V. Dzyublyuk, A.I. Tovstolytkin, S.K. Arora, R. Ramos, R.G.S. Sofin, I.V. Shvets, J. Appl. Phys. 107 (2010) 09B108 (3pp). [19] S.K. Arora, B.J. O’Dowd, D.M. Polishchuk, A.I. Tovstolytkin, P. Thakur, N.B. Brookes, B. Ballesteros, P. Gambardella, and I.V. Shvets, J. Appl. Phys. 114 (2013) 133903 (7pp). [20] D.M. Polishchuk, A.I. Tovstolytkin, S.K. Arora, B.J. O’Dowd, and I.V. Shvets, Low Temp. Phys. 40 (2014) 165–170. [21] A. I. Tovstolytkin, V. V. Dzyublyuk, D. I. Podyalovskii, X. Moya, C. Israel, D. Sanchez, M. E. Vickers, and N. D. Mathur, Phys. Rev. B 83 (2011) 184404 (6pp). [22] M.D. Glinchuk, I.P. Bykov, S.M. Kornienko, V.V. Laguta, A.M. Slipenyuk, A.G. Bilous, O.I. V'yunov, O.Z. Yanchevskii, J. Mater. Chem. 10 (2000) 941–947. [23] A. Aharoni, Introduction to the Theory of Ferromagnetism, Oxford University Press, Oxford, 1996. [24] S. Chikazumi, Physics of Ferromagnetism, Oxford University Press, New York, 2005. [25] X.-J. Xu, Q.-L. Ye, G.-X. Ye, Phys. Lett. A 361 (2007) 429–433.
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[26] J. Sanchez-Barriga, M. Lucas, F. Radu, E. Martin and M. Multigner, Phys. Rev. B 80 (2009) 184424 (8pp). [27] R. Skomski, H. Zeng, M. Zheng, and D.J. Sellmyer, Phys. Rev. B. 62 (2000) 3900–3904. [28] L. Neel, Ann. Geofis. 5 (1949) 99 [W. F. Brown, Phys. Rev. 130 (1963) 1677]. [29] H. Zeng, R. Skomski, L. Menon, Y. Liu, S. Bandyopadhyay, and D.J. Sellmyer, Phys. Rev. B. 65 (2002) 134426 (8pp).
Figure captions Fig. 1. Schematic illustration of a cross section of an array of NWs on step-bunched oxidized vicinal Si (111) substrates and experimental geometry used for the FMR measurements.
Fig. 2. (a) Typical FMR spectra for sample 1. The values of θh are indicated on the lines. (b) Angular dependencies of the resonance field for samples 1 and 2. Circles show experimental data, solid lines – simulated dependencies (see section 3.C).
Fig. 3. (a) Illustration of the parallel (H|| along Oy axis) and perpendicular (H along Ox axis) Hdirection with respect to the NW length orientation (along Oy axis). The picture also illustrates a remnant alignment of localized magnetic moments after the application of H in the direction of Ox axis. Misorientation angle α shows possible local deviations of the direction of NW effective anisotropy axes from Oy axis. (b), (c) In-plane hysteresis loops measured when the external field is applied in parallel (H||) or perpendicular (H ) configurations at room temperature. Values of effective anisotropy field, HSA, are calculated using eq. (3) with Nc, Meff, derived from the FMR data. Blue H curves – simulated M–H
loops. Insets in (b), (c) show spreads of demagnetising factor Nc,
H loops. Markers 1 magnetisation M and axis misorientation α found from fitting of experimental M–H and 2 indicate corresponding spreads of α used for simulations of upper and lower branches of each M–H H loop.
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Table 1. Magnetic parameters of NW arrays, determined from FMR and magnetometry studies. S ample
t , nm
1 2
Mef 3 f, emu/cm
N c
7
1 0.3
4 .5
11 00
9 .5
99 0
δH ,
HS (a) A , kOe
δH (b) SW|| , kOe
2.5
1.6
2.4
3.0
1.6
1.7
SW
(c)
H (d) c|| , c
Oe
kOe
H , Oe
(e)
6 30
1 40
4 50
(a)
demagnetising field along NW width (see expression (3)) width of the switching field distribution curve for M–H|| and M–H H loops, respectively (d),(e) coercivity for M–H|| and M–H H loops, respectively (b),(c)
Highlights: We carry out FMR and VSM investigations of planar nanowire (NW) arrays of Fe. Experimental results are supported by model calculations and simulations. The Fe NWs are ferromagnetic at room temperature. Magnetisation reversal of NWs has a coherent-rotation type of localized character. Localization of the magnetisation reversal mode depends on inhomogeneity of NWs.
1 20
Figure1
Figure2
Figure3
Figure1(color_online)
Figure2(color_online)
Figure3(color_online)