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1. Determination of the size of Fe nano-grains in Ag J. Balogh, D. Kaptás, L. F. Kiss, and I. VinczeResearch Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, HungaryA. KovácsThe Institute of Scientific and Industrial Research,8-1 Mihogaoka, Ibaraki 567-0047, Osaka, JapanM. Csontos and G. MihályDepartment of Physics, Budapest University of Technology and Economics, 1521 Budapest, P.O. Box 91, HungaryE-mail: baloghj@szfki.huhttp://www.szfki.hu

2. When discussing the physical properties of different nano-materials the determination of the size is a basic task. There are several image forming and diffraction methods that can be used in the case of nano-size objects (e.g. transmission electron microscopy, atomic force microscopy, x-ray diffraction line-broadening and small angle scattering), but in the case of magnetic elements, size determination from the magnetic properties is also of great interest. It is an especially important issue when the standard methods are hindered for some reason, as it is the case for very small Fe grains (up to a few hundred atoms) in Ag. (See: Y. Xu et al. J. Appl. Phys. 76 (5), 2969 (1994), M. Csontos et al., Phys. Rev. B 73, 184412 (2006)) If the size of a magnetic particle is smaller than the domain wall width then it will form a single domain, and its volume can be estimated from the appearing superparamagnetic properties. (For a review see: J. L. Dormann, D. Fiorani, and E. Tronc, Adv. Chem. Phys. 98, 283 1997.) According to the model of Néel for interaction free particles with uniaxial anisotropy and a supposed uniform rotation of the magnetisation: the blocking temperature (TB,) and the external field and temperature dependence of the magnetisation (M) above TB are determined by the magnetic anisotropy energy (K) and the volume (V), or in proportion to it the magnetic moment (), of the particle. The experimentally measured TB should also depend on the ratio of the characteristic time scale of the measuring technique (tm) and the inverse jump frequency (t0). (1) where(2) Our aim is to compare the grain size determined by Mössbauer spectroscopy to those measured by two other powerful methods, bulk magnetization and magnetoresistance measurements. The Fe-Ag system studied is a good choice, since the average grain size can be easily varied in the most interesting 1 to 10 nm range. The understandig of the giant magnetoresistance (GMR) behavior gives a further motivation to these studies.

3. Forming Fe nano-grains in the immiscible Fe-Ag system Discontinuous multilayers (by vacuum evaporation) Granular alloys (co-evaporation, co-sputtering) Fe28Ag72 10x[2.6nm Ag / 0.7nm Fe] High resolution transmission electron microscopy images of two typical samples TB (i.e. the average grain size) can be tuned by: the Fe and the Ag layer thickness the Fe concentration (On the role of the Ag layer thickness see: J. Balogh et al., Appl. Phys. Lett. 87, 102501 (2005))

4. Size determination from the bulk magnetisation The bulk magnetization of the thin films could be measured by a superconductingquantum interference device (SQUID)type magnetometer. EXAMPLE: Two multilayer samples: A:Si/ 75x[5.4 nm Ag/0.2 nm 57Fe] B: Si/ 75x[2.6 nm Ag/0.2 nm 57Fe] The temperature dependence of the magnetizationmeasured by the SQUID in an applied field of 1 mT afterzero-field cooling (ZFC) and field cooling (FC) in 1 mT is shown in the left panels in red and black, respectively. Samples A and B show magnetic irreversibility, typical of superparamagnetic systems, with aTBof 12 K and 40 K. A characteristic property of non-interacting SPM particles is the scaling of the magnetization curves measuredat different temperatures when they are plotted as a functionof H/T, i.e., the applied field divided by temperature. The right panels show that this scalingcan be observed above TBforboth samples. Fitting by eq. (2) yields 200 and 600 B for the average cluster moment (about 90 and 270 Fe atoms which means about 1.2 and 1.8 nm grain diameters supposing sperical particles), in good agreement with the observed variation of TB. Applied Physics Letters 87, 102501 (2005)

5. Size determination from external field induced hyperfine field (see also: P. H. Christensen, S. Mørup, and J. W. Niemantsverdriet, J. Phys.Chem. 89, 4898 1985.) Si/ [5.4 nm Ag/0.2 nm 57Fe]75(sample A in the SQUID measurements) In large external fields: Phys. Rev. B 76,052408 (2007) These fits yield,=420(12)B, B0=37.0(1)T and =307(12)B, B0=32.7(1)Tfor the high and lowfield components. The grain diameters calculated from the two components are 1.6 and 1.4 nm (supposing sphericalparticles and 2.2Batomic moments), slightly larger than the 1.2 nm value which was estimated from the SQUID measurement. The difference hardly exceeds theaccuracy of determining an average size by x-ray diffraction or electron microscopy methods when they can be applied succesfully. The magnetically split components of the Mössbauer spectra were fitted by two broad sextets and the remaining parts of the spectra were described by two singlets, not shown here.

6. Size determination from the static hyperfine fields A:Si/ [5.4 nm Ag/0.2 nm 57Fe]75 B: Si/ [2.6 nm Ag/0.2 nm 57Fe]75(These samples were studied by SQUID) Spectra measured at 4.2K in perpendicular external field For both samples, thespectra exhibit broad but definitely structured lines, whichallow a separation into two components described by two HF distributions. Since the hyperfine field is aligned oppositeto the magnetization, the saturation of B+=Bobs+Bext,i.e., the sum of the measured HFand the external field, indicates the ferromagnetic alignment of the magnetic momentsalong the applied field in accordance with the disappearance of the 2nd and 5th spectral lines. This study proves that the observed spectrum features belong to static properties. Phys. Rev. B 76, 052408 (2007) The relative fraction ofthe two components varies in accordance with the grain sizedetermined from the SQUID measurements(D=1.2 and 1.8 nm) if, in a simplemodel, they are associated with Fe atoms at the surface andin the volume of the grains. The assignment of the low field (blue) component to surface atoms is in accordance with theoretical calculations. ((R. N. Nogueira and H. M. Petrilli, Phys. Rev. B 60, 4120 (1999), C. O. Rodriguez et al., Phys. Rev. B 63, 184413 (2001)) low field component: 53% and 70%

7. Fe grain size from magnetoresistance measurements The giant magnetoresistance (GMR) in multilayer structuresof alternating ferromagnetic and nonmagneticlayers and granular composites have been explained by elasticscattering of the conduction electrons on magnetic momentsofdifferently aligned magnetic entities. In superparamagnetic granular alloys this consideration (Gittleman et al.Phys. Rev. B 5, 3609 (1972)) leads to a magnetoresistance proportional to thesquare of themagnetization. Deviations from this proportionality can be a result of a grain size distribution, i.e. a distribution of the magnetization of the particles. (For review see: X. Batlle and A. Labarta, J. Phys. D: Appl. Phys. 35 (2002) R15–R42.) Since the resistivity can be influenced by as little as a few ppmof magnetic impurities, it is an effective method to search for the extremely small grains. sample:Si/ [2.6 nm Ag/0.2 nm Fe]75 (nominally equal to sample B, but with natural Fe) Deviation from the simple ΔR(B) M2quadraticbehavior signifies the presence of small clusters, which barely contributeto the magnetization but dominate the scattering in highfields. Phys. Rev. B 73, 184412 (2006)

8. Grain size from the temperature dependence in large field Separation of the phonon and the magnetic scattering In zero magnetic field, well above theblocking temperature (40K) the magnetic moments of all the grainsare fully disordered and we can assume that the temperature dependence arises solelyfrom the phonon contribution. The phonon term is linear above the Debye temperature (210 K) and the strength of phonon scattering (a1) canbe determined from the high temperature slope. The curve calculated according to the formula above for phonon scattering isshown by the dashed line. The remaining part (dotted line) is attributed to the magnetic scattering. Since the phonon term is magnetic field independent, the calculated ρph(T) curvecan be used to separate the magnetic scatteringcontribution in the B=12T measurement. Grain size from ρmagn(T, B =12 T). We assume that in high fieldthe magnetic scattering of the spin-polarized electrons is proportionalto the spin disorder of the small clusters and thisgives rise to the strong temperature dependence ofρmagn(T,B=12T). The spin disorderfor a characteristic moment S can be expressed by theBrillouin-function: The left figure shows the resistivity change attributed to magnetic scattering in B=12T. The fitted curve shown bythe solid line belongs to S=16.6 B. Phys. Rev. B 73, 184412 (2006)

9. Magnetoresistance curves - large grains and small clusters The SQUIDmagnetization measurements of this sample indicated the presence of largegrains with 500 B average moment, while the temperature dependenceof the resistivity in high magnetic field has shown the presence of small clusters with S17 B. The magnetoresistance curves can be described with these two characteristic magnetic moments. The magnetoresistance curves are well described by electron scattering from grain to grain, between a grain and a cluster and from cluster to cluster with amplitudes b1, b2, and b3, respectively. (L and BS are the Langevin and the Brillouin functions.) Since the volume fraction of the clusters is small (see below), b3 is negligible. At low temperature scattering between grains and clusters is responsible for the non-saturating magnetoresistance. Phys. Rev. B 73, 184412 (2006) The Mössbauer spectra clearly show that the vast majority of the magnetic moments can be ferromagnetically aligned along the external field direction at 4.2 K. (See also results for samples A and B shown previously). With considerations to the statistical errors, the ratio of Fe atoms with paramagnetic or superparamagnetic moments can be estimated as less than 2%.

10. Comparison of the three methods The cluster moments, determined from the external field induced hyperfine fields above TB, are significantly larger than those determined from the SQUID measurements. The evaluationbased on the description of the magnetically split sharp features of the spectraobviously overestimates the grain size, because it does nottake into account those small grains that do not exhibit wellresolvedpeaks in the field range. In the studied few nm grain size range, however, the corresponding difference of the calculated grain diameters hardly exceeds theaccuracy of determining an average size by x-ray diffractionor electron microscopy methods. The static hyperfine field distributions evaluated from measurements at 4.2 Kin variousapplied fields are also found to reflect the grain-size difference. The relative fraction ofthe observed two components varies in accordance with the grain sizedetermined from the SQUID measurements if, in a simplemodel, they are associated with Fe atoms at the surface andin the volume of the grains.Since the ground state static HF is not influenced bymagnetic or exchange interactions between the grains, it isan important check of the grain size determined from thedynamic properties. The magnetoresistance measurements can reveal the presence of tiny clusters that give negligible contribution to the magnetization. The magnetic field and the temperature dependence of the resistivity could be described in consistancy with the SQUID and the Mössbauer results. • Mössbauer spectroscopy can supply unique information: • in multicomponent systems (e.g. Fe-Co-Ag, Fe-Ni-Ag) • in heterogeneous systems (e.g. bimodal size distribution, heterostructures) • when magnetic interactions influence the dynamic behaviour (e.g. high concentration of the magnetic elements).