Nanostructures, disordered ferromagnetism and spin glasses
I. Vincze, T. Kem´eny, D. Kapt´as, L.F. Kiss and J. Balogh
Research Institute for Solid State Physics, P.O. Box 49, H-1525 Budapest, Hungary
Magnetic systems with a considerable amount of irregular interfaces were investigated by 57Fe M¨ossbauer spectroscopy. Chemically homogeneous ferromagnets around the per- colation threshold composition of disappearing magnetism and chemically heterogeneous alloys prepared by nanocrystallization of amorphous alloys belong to this class of materials.
Low temperature and high field measurements were performed on nanocrystalline FeZrBCu alloys, on ball-milled Fe with nano-size grains and on melt-quenched amorphous Fe–Zr and Fe–Y alloys in order to clarify the origin of large high-field susceptibility and to investigate the common features of the approach to magnetic saturation. Curie point determination of the residual amorphous phase in the nanocrystalline FeZrBCu alloys, results on the structure of the nanocrystalline b.c.c. phase and of the interfacial region will be reported.
1. Introduction
Unusual magnetic behaviour is often attributed to special exchange interactions:
the very good soft magnetic properties of some nanocrystalline (n.c.) materials are ex- plained by the ferromagnetic coupling of the nano-size b.c.c. crystalline precipitates via the intermediate amorphous matrix or the absence of magnetic saturation characteristic for spin glass materials is attributed to a noncollinear magnetic structure caused by the competition of ferromagnetic and antiferromagnetic exchange interactions. In the fol- lowing the role of these interactions will be studied in typical soft magnetic and spin glass systems by combination of bulk magnetic measurements and 57Fe M¨ossbauer spectroscopy.
The very good soft magnetic properties (high initial magnetic permeability and low coercivity) of nanocrystalline Fe–Cu–Nb–Si–B (i.e., FINEMET) alloys start to deteriorate above the Curie temperature of the residual amorphous matrix [1]. The hypothesis that exchange coupling via the intergranular amorphous matrix between adjacent crystallites plays an important role in the magnetic behaviour of the hetero- geneous systems is based on this observation. Recently good soft magnetic properties were found in the nanocrystalline Fe–Zr–B–Cu alloys [2–5]. However, the coercivity shows a slow gradual increase with temperature [3,4] and in the temperature dependent magnetization of the fully n.c. samples no features or only very weak effects hint at the Curie point of the residual amorphous phase [3–5]. The magnetic behaviour of n.c.- FeZrBCu alloys are attributed to the exchange interactions between the ferromagnetic
J.C. Baltzer AG, Science Publishers
grains dispersed in a paramagnetic amorphous matrix resulting in the enhancement and considerable smearing out of the Curie temperature of the amorphous interphase [6].
These chemically and magnetically heterogeneous systems were extensively stud- ied by M¨ossbauer spectroscopy (e.g., [7–10]). Majority of the measurements were performed at room (or lower) temperature and the results are controversial concern- ing the structure of the nanocrystalline b.c.c. phase and the interfacial zones. This is not surprising since already in binary alloys the interpretation of the spectra of ultra fine grained materials prepared by ball-milling is far from being simple [11]. The comparison of the spectra of bulk and nanophase f.c.c. alloys gives an upper limit of approximately 0.5 nm for the average grain-boundary widths [12].
Such soft magnetic nanocrystalline alloys do not show simple saturation behav- iour at low temperatures and high magnetic fields, i.e., they have a significant high- field susceptibility [13,14]. It is often attributed to antiparallel coupled spins due to frustrated exchange couplings [14]. This behaviour is analogous to that observed in nanocrystalline iron [15] or in Fe-based concentrated spin glasses [16].
In this work we compare the magnetic behaviour of nanocrystals with that of ultra fine grained Fe powder and typical spin glass materials. In the magnetically split
57Fe spectra the relative intensity of the second and fifth lines, I2,5 (corresponding to the ∆m = 0 nuclear transition) is given by I2,5 = 4 sin2θ/(1+cos2θ), where θ is the angle between the magnetic moment (hyperfine field) of Fe and the magnetic field Bext, applied parallel to the γ-beam direction which is perpendicular to the sample surface.
2. Experimental
The amorphous Fe100−xZrx (x=7–12), Fe100−xYx (x=15–60), Fe70Ni20Zr10, Fe86Zr7B6Cu1 and Fe90Zr7B2Cu1 samples were prepared by melt spinning in protec- tive atmosphere. The ribbon pieces are 12–20 µm thick, and 0.5–5 mm wide. The amorphous state of the alloys was checked by X-ray diffraction and M ¨ossbauer mea- surements.
The nanocrystalline samples (n.c.-Fe86Zr7B6Cu1 and n.c.-Fe90Zr7B2Cu1) were produced by 1 hour heat treatment of the amorphous ribbons at 625◦C and 650◦C, re- spectively, which results in the maximum initial permeability. The initial permeability at room temperature was monitored during the heat treatment resulting in nanocrystal- lization and was [17] in good agreement with literature data [18].
The nanocrystalline Fe sample was produced by ball milling a commercial (Aldrich) Fe-powder of spherical shape with 2µm average particle diameter. 80 hours ball milling in vacuum results in the nanocrystalline Fe (n.c.-Fe) sample of roughly oblate ellipsoid shape (40µm diameter and 7 µm thickness, as determined by TEM) and about 10 nm grain size (Szab´o, private communication).
The M¨ossbauer measurements were performed between 4.2 K and 1000 K us- ing a conventional constant acceleration spectrometer with 50 mCi57CoRh source at room temperature. The external magnetic field was applied parallel to the γ-beam
(i.e., perpendicularly to the sample plane) using a 7-T Janis superconducting mag- net. The magnetization was measured both parallel and perpendicular to the plane of the sample by a vibration sample (Foner-type) magnetometer with a resolution of 10−4 emu.
3. Results and discussion
3.1. Fe–Zr–B–Cu nanocrystalline alloys
A typical M¨ossbauer spectrum of n.c.-Fe86Zr7B6Cu1 well above the Curie tem- perature of the residual amorphous matrix Tca is shown in figure 1. Three features can be well distinguished in the spectrum as indicated in the figure. The strongest narrow sextet will be referred as the main line, its hyperfine field will be denoted by Bm. The M¨ossbauer parameters (line width, isomer shift, Bm) of this sextet at room temperature are the same as those of pure b.c.c.-Fe, though the systematical
Figure 1. M¨ossbauer spectrum of n.c.-Fe86Zr7B6Cu1 atT =651 K: the sextets of the nanocrystalline b.c.c.-phase are shown by the broken (main component) and the dotted (shoulder component) lines, respectively (a). The sum of these two components are subtracted from the measured spectrum resulting in the spectrum of the residual amorphous phase (b). The inset shows the hyperfine field distribution of
the residual amorphous phase.
error of the evaluation is greatly influenced by the line-overlap. However, Bm de- creases somewhat faster than the hyperfine field of pure b.c.c.-Fe as the function of temperature. The second well-distinguished feature of the spectrum is the shoulder on the low-field side of the main sextet. It is quite broad and its hyperfine field, Bs follows closely the temperature dependence ofBm as shown in figure 2(a). The devi- ation which can be observed at high temperatures is correlated with the narrowing of this component and it is the result of irreversible changes due to the long (1–2 days at each temperature) M¨ossbauer measuring times. Since the same shoulder structure and temperature behaviour is observed in the melt-quenched microcrystalline Fe–Zr solid solution [17], we suppose that both Bm and Bs belong to the nanocrystalline b.c.c. Fe phase (i.e., 2–3 at.% Zr but also some amount of B are dissolved in the b.c.c. structure). Magnetization measurements also indicate that the Curie temperature of the nanocrystalline phase is lower than that of pure b.c.c.-Fe [19]. In this Fe-rich nanocrystalline phase Bm is the hyperfine field of Fe atoms without Zr or B nearest and next nearest neighbours, whileBs is the average hyperfine field of Fe atoms with at least one impurity neighbour in the first two coordination shells. At high temper- atures rearrangement of the impurities in these shells causes the approach of Bs(T) to Bm(T). Our results do not support the identification of this shoulder structure as
(a) (b)
Figure 2. (a) Temperature dependence of the hyperfine fields of n.c.-Fe86Zr7B6Cu1: the mainBm and shoulderBscomponents of the nanocrystalline b.c.c.-phase are marked by full circles and down triangles, respectively. The average hyperfine fieldBa of the residual amorphous phase (empty circles) and the high field componentBpof the amorphous hyperfine field distribution (see figure 1(b) inset) above 420 K (crosses) are also shown. (b) Determination of the Curie temperature of the residual amorphous phase in
n.c.-Fe86Zr7B6Cu1: Ba3vs. temperature.
the interfacial zone of the nanocrystalline b.c.c. phase [10] since in that case signif- icant difference was expected between the temperature dependencies of Bs(T) and Bm(T) [20].
The third characteristic feature of the spectrum is the contribution of the remaining amorphous phase which is obtained after the subtraction of the nanocrystalline con- tributions from the original spectra. Below the Curie temperature of the amorphous phase a broad hyperfine field distribution can be observed. The average hyperfine field Baof the residual amorphous matrix is obtained from these distributions and shown in figure 2(a) as the function of temperature. The Curie temperature of this residual amor- phous matrix Tca =430 K is determined from a Ba3 vs. T plot shown in figure 2(b).
The transition is quite sharp and around this temperature no unusual behaviour can be found in the soft magnetic properties (initial permeability, coercivity). However, when the residual amorphous phase becomes paramagnetic the M¨ossbauer spectrum shown in figure 1(b) has the peculiar structure consisting of a broadened central line and side-wings.
The appearance of the side-wings in the spectra of the residual amorphous phase above Tca is unexpected. Both the width of the broadened central line and the peak
(a) (b)
Figure 3. M¨ossbauer spectra of n.c.-Fe86Zr7B6Cu1 (a) and n.c.-Fe90Zr7B2Cu1 (b) at 4.2 K in external magnetic fieldsBext=0, 2 and 5 T, respectively.
position of the side-wings are temperature dependent. The average value of the high- field part of the p(B) distribution (shown in the inset of figure 1(b)) corresponding to this wing-structure is denoted by Bp and it is plotted as a function of temperature in figure 2(a). Bp(T) follows closely the temperature dependence of the Bm nanocrys- talline component. Approximately 25% of the Fe atoms in the residual amorphous phase contribute to this feature. The characteristic size of the residual amorphous grains is about 3–5 nm, thus it is very tempting to attribute the Bp component to the Fe atoms on the boundary of the amorphous grains still directly exchange coupled to the ferromagnetic nanocrystallites. It would mean that the direct exchange interaction on the boundary is restricted to only two atomic layers. The value ofBp extrapolated to 0 K (using the temperature dependence of Bm(T)) corresponds to about 13 T, i.e., to about 1µB which suggests an increased number of Zr and B nearest neighbours.
The paramagnetic central component shows temperature dependent broadening which may be attributed to about 1 T dipole field originating from the neighbouring ferro- magnetic nanocrystallites. Similar magnitude was found in n.c.-FeSiBNbCu alloy by small angle neutron scattering (SANS) technique [21].
Although the presented and the related nanocrystalline alloys are very good soft magnets, surprisingly they do not follow a simple approach to magnetic saturation in high fields [13,14]. The absence of magnetic saturation inBext =2 T is also obvious from the M¨ossbauer spectra shown in figure 3 where the 2–5 lines of the nanocrystalline b.c.c. phase can clearly be seen. The applied field was perpendicular to the sample surface. In this geometry saturation should be observed when the applied field exceeds the value of the demagnetization fieldBdemag=µ0Ms. Bdemag=1.52 T and 1.64 T for the n.c.-Fe86Zr7B6Cu1 (Ms=160.8 emu/g=1.87µB) and for the n.c.-Fe90Zr7B2Cu1
(Ms = 173.5 emu/g = 1.99µB) samples, respectively. The 2–5 lines are absent in Bext = 5 T (within the experimental error). The comparison of these spectra explains the difficulty in the proper evaluation of p(B) of the residual amorphous phase: the 2–5 lines of the nanocrystalline b.c.c. phase directly overlap with the 1–6 lines of the amorphous phase. This overlap prevents the accurate determination of the n.c. I2,5 intensities, too, but the Bdemag value of the n.c. components is well determined.
The quantity defined as Bplus(Bext) =hBhf(Bext)i+Bext equalizes the decrease of Bhf caused by Bext and saturates above the demagnetization field with zero slope at the value (hBhf(Bext =0)i+Bdemag) as a function ofBext in an ideal ferromagnet.
Thus the value of the hyperfine field in zero Bext differs from the saturated value of Bplus by Bdemag if the external field does not induce any magnetic moment increase.
Figure 4 shows the Bplus values of the investigated n.c. samples. The main line and the shoulder give the same Bdemag = 1.5 T, which is significantly different from the value expected for isolated spheres of pure Fe (∼ 0.7 T). Bm and Bs show a similar external field dependence and in this way a significant magnetic anisotropy contributions (expected for Bs if this field would represent an interfacial phase) can be ruled out.
Figure 4. Magnetic field dependence ofBplusat 4.2 K for n.c.-Fe86Zr7B6Cu1and n.c.-Fe90Zr7B2Cu1(Bm: full and empty rhombs, Bs: full and empty squares), for Fe-powder (full circles), for n.c.-Fe (empty
circles), for amorphous Fe70Ni20Zr10(×), Fe93Zr7(∗) and Fe62Y38(+), respectively.
3.2. Ball-milled Fe powder
Figure 4 shows that commercial micron-size Fe powder satisfies the Bdemag = 0.7 T expectation. In this measurement the Fe powder was diluted in 1:10 ratio with nonmagnetic BN (and Al2O3) powder to ensure texture-free structure. At this ratio the measured magnetization vs. external field curves were independent of the direction of the applied field. Even at the same dilution some texture formation could not be avoided in the ball-milled n.c.-Fe sample due to the already mentioned deformation of the starting spherical shape. Bdemag=1.1 T was found for this sample.
Non-vanishingI2,5 line intensities were observed in external magnetic fields well above the values of Bdemag for both samples (figure 5(a)). In this field range the relationI2,5 =4(Ban/Bext)2 holds, whereBan is a proportionality constant determined from the experiment. This is shown in figure 5(b) (the coefficient 4 reflects that I2,5
(a) (b)
Figure 5. Relative intensities of the 2–5 lines I2,5 as the function of the external field for Fe-powder, n.c.-Fe and amorphous Fe93Zr7(full and empty circles, up triangles, respectively) (a) and for large fields as the function ofB−2ext (b). The inset shows the M¨ossbauer spectrum of n.c.-Fe at 4.2 K in perpendicular
Bext=3 T.
amplifies theB−2ext term found in magnetization measurements). This single-parameter fit givesBan=0.26 and 0.59 T for the bulk and for the n.c.-Fe sample, respectively.
A possible reason for this term is the hindered rotation of magnetic moments towards the applied magnetic field by dipole–dipole interaction.
3.3. Fe-based Fe–Zr and Fe–Y spin glasses
The bulk magnetization of Fe-based spin glasses (generally amorphous alloys with early transition metal components) shows the absence of saturation even in very large applied magnetic fields [16]. Figure 5 shows that the I2,5 vs. Bext curve of a typical spin glass, here amorphous Fe93Zr7, is similar to that of bulk Fe powder and n.c.-Fe. The value of Ban =0.88 T. However, in contrast to the saturation of Bplus
shown in figure 4 for the samples which do not show spin freezing at low temperatures (including also amorphous Fe70Ni20Zr10) a significant amount of magnetic field induced Fe magnetic moment is observed in this case. The slope of Bplus vs.Bext determines the local Fe high-field susceptibility.
It is advisable to introduce a direct (evaluation and model independent) value for the Fe local high-field susceptibility as
χFe = ∆Bplus
Bplus∆Bext
,
Figure 6. Composition dependence of the normalized high field susceptibility between 5 and 7 T for amorphous Fe100−xZrx(circles and squares) and Fe100−xYx(triangles). The full symbols corresponding to the local Fe susceptibility are the M¨ossbauer results, the empty symbols stand for bulk magnetization data which are taken from literature for Fe–Zr (circles [22], squares [23]) and preliminary Fe–Y results [29] obtained on the same samples used in the present M¨ossbauer measurements (down- and up-triangles
are in parallel and perpendicular geometry, respectively).
where
∆Bplus=Bplus(Bext =7 T)−Bplus(Bext =5 T), Bplus=12
Bplus(Bext =7 T)+Bplus(Bext =5 T) ,
∆Bext=2 T.
This combination eliminates the need to use a proportionality constant between the Fe hyperfine field and magnetic moment and reduces the effect of any possible system- atical errors in the evaluation ofhBhfi. Figure 6 shows thatχFe is in good agreement with the similarly normalized bulk high-field susceptibility corresponding to a collinear magnetic structure [24]. At high Fe content the spin freezing is caused by a magnetic decoupling of Fe atoms with only Fe nearest neighbours, but these Fe atoms pre- serve their magnetic moment of about 1µB. On the other hand, at high early transition metal content the local Fe magnetic moment disappears when the number of Fe nearest neighbours decreases under a critical number, as seen, e.g., in Fe–Y alloys.
Sputtered [25,26] and melt-quenched [27,28] Fe–Y amorphous alloys exhibit spin freezing (re-entrant spin glass or spin glass behaviour) accompanied by the absence of
(a) (b) (c)
Figure 7. M¨ossbauer spectra of amorphous Fe50Y50, Fe45Y55and Fe40Y60measured at room temperature (a), at 4.2 K (b) and in 7 T perpendicular applied field (c). The calculated spectra attributed to nonmagnetic
Fe atoms are also shown: in the calculation atBext=7 T collinearity (i.e.,I2,5=0) was assumed.
magnetic saturation at low temperatures in a broad composition range. The bulk and the local Fe high-field susceptibilities agree well in the re-entrant spin glass regime (above
∼ 55 at.% Fe content), corresponding to a collinear magnetic state in large external field (figure 6). Single spin glass transition was observed at and below 50 at.% Fe.
The freezing temperature decreases from Tf =49 K (Fe50Y50) to 14 K (Fe40Y60). At the same time an increasing amount of nonmagnetic contribution is observed in the 4.2 K M¨ossbauer spectra (figure 7). They correspond to the nonmagnetic Fe atoms having less than about six Fe neighbours due to the statistical distribution [28] and remain nonmagnetic even in Bext = 7 T (figure 7(c)). This explains the appearance of unusual sharp lines in the applied field spectra and it has often been misinterpreted to the 2–5 lines due to noncollinear spin arrangement. For the proper determination ofχFe it is essential not to take into account these nonmagnetic Fe as it was done for Fe40Y60 in figure 6.
4. Conclusion
Large high-field susceptibility materials (spin glasses and re-entrant spin glasses) were found to be collinear in magnetic fields not larger than 5 T. An analogous result
was reported for a metastable iron–mercury alloy [30]. The approach to magnetic saturation was found to be qualitatively similar in the soft magnetic and in the spin glass like alloys when perpendicular geometry is applied. No evidence was found for exchange frustration causing spin-canted structure and for an exchange coupling of ferromagnetic grains via the polarized residual amorphous matrix in nanocrystalline alloys. Dipole–dipole interaction between the nanosize grains or on the atomic scale in case of percolation clusters might play an important role in the explanation of the similar magnetic behaviour.
Acknowledgements
The authors gratefully acknowledge D.L. Beke, J. Lindenmaier, S. Szab´o (Lajos Kossuth University, Debrecen), S. M´esz´aros, K. Vad (Institute of Nuclear Research of the Hungarian Academy of Sciences Debrecen), J.W. Ross (The University of Manchester) and C. Socz´o (Technical University Budapest) for informing them of their experimental data prior to publication.
This work was supported by the Hungarian Research Fund (OTKA 017456), by the Hungarian Academy of Sciences (AKP 96-137/6) and by Copernicus (ERCIPACT 940155).
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