Fluxmetric-magnetooptical approach to broadband ...

JOURNAL OF APPLIED PHYSICS 109, 07A322 (2011)

Fluxmetric-magnetooptical approach to broadband energy losses in amorphous ribbons Alessandro Magni,a) Fausto Fiorillo, Ambra Caprile, Enzo Ferrara, and Luca Martino Istituto Nazionale di Ricerca Metrologica (INRIM), Strada delle Cacce 91, 10135 Torino, Italy

(Presented 17 November 2010; received 15 October 2010; accepted 29 November 2010; published online 30 March 2011) The magnetization process in field annealed amorphous ribbons has been investigated from dc to 10 MHz. Loss and permeability measurements, carried out both on single strips and ring samples by means of a broadband fluxmetric setup, have been associated with observations of the domain wall dynamics by high-speed stroboscopic Kerr apparatus. Transverse anisotropy Co-based ribbons exhibit a combination of rotational and domain wall processes, the latter being observed to progressively damp with frequency and coming to a halt on approaching the megahertz range. Given the vanishing direct contribution of the domain walls to the high-frequency magnetization process, the so-called classical loss formulation, associated with the rotational magnetization processes, is expected to correspondingly hold for the energy loss W(f). Under these conditions, W(f) tends to increase linearly with f, which, in view of the expected surge of the skin effect, does not agree with the f1/2 behavior accordingly predicted by standard formulas. This points to the specific properties of the rotational process and the role played by the exchange torque in C 2011 American Institute of Physics. [doi:10.1063/ connection with incomplete flux penetration. V 1.3556937]

I. INTRODUCTION

Amorphous and nanocrystalline ribbons display versatile soft magnetic behavior and their dc/ac response can be largely influenced and optimized by inducing low-to-moderate macroscopic anisotropy through mild magnetothermal treatments.1 With an easy axis transverse to the ribbon length, one can achieve excellent combination of very low losses and high permeabilities, favorably comparing with the properties of Mn–Zn and Ni–Zn ferrites up to the megahertz range.2,3 It is recognized that these good soft magnetic properties derive, at all frequencies, from limited domain wall (DW) activity and easy rotational processes in the low anisotropy environment. Direct observations of the domain structure and its evolution with frequency in these materials, while corroborating this viewpoint, have been pursued so far only up to some 10 KHz.4 On the other hand, on moving toward the megahertz range, one falls outside the region where the loss analysis has been up to now pursued and solidly assessed.5 In this paper, we provide significant results on the magnetic loss behavior in transverse anisotropy Co-based amorphous ribbons, characterized between dc and 10 MHz. The magnetic measurements are associated with observations of the domain structure versus frequency carried out, up to about 1 MHz, by a stroboscopic wide-field Kerr setup. In spite of the near-orthogonality of applied field and magnetization, substantial DW activity at low frequencies is observed, in accordance with previous literature results.1–4,6 The DW motion is observed to progressively relax with frequency, eventually ending into stillness on approaching the a)

Author to whom the correspondence should be addressed. Electronic mail: [email protected].

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megahertz range. The corresponding contributions to the energy loss W(f) [i.e., the hysteresis Wh and excess Wexc(f) loss components] concurrently disappear, and one is left with predicting the further evolution of W(f) with frequency, solely deriving from the dissipation by the rotational processes, through a classical formulation. With the quasilinear (J, H) dc magnetization curves exhibited by these materials, taking into account that low peak polarization values are involved, one can calculate the classical loss Wcl(f) in strip samples of given thickness, permeability, and conductivity by a closed expression.5 This appears, however, unable to provide a full prediction at the highest frequencies, under emerging skin effect. For the specific case of magnetization rotation, where the skin effect would result at any instant of time into a rotation angle changing in magnitude and sign on going from the strip surface to the core, the exchange torque is expected to play a role, leading to a magnetization profile through the sample cross-section different from the one predicted by the conventional classical approach. It is observed that one might phenomenologically account for such an effect by introducing the experimental frequency dependent permeability l(f) into the standard closed formula for Wcl(f), which turns then out to provide a correct prediction for the experimental high-frequency W(f) behavior. II. EXPERIMENTAL METHOD

Amorphous ribbons of composition Co71Fe4B15Si10 and Co67Fe4B14.5Si14.5, thickness varying between 6.1 and 19 lm, and width 5 – 10 mm, were heat treated, after stress relaxation annealing, under transverse saturating magnetic field for different times and temperatures. Quasilinear magnetization curves resulted upon these treatments, with macroscopic

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transverse anisotropies, as obtained by analysis of the magnetization curve, ranging upon different samples between 6 and 130 J/m3. The specimens for magnetic measurements were prepared both as single strips and few-turn wound ring samples (diameter 18 mm). Hysteresis loops and magnetic losses were obtained for a number of peak polarization values Jp from dc to 10 MHz under sinusoidal induction using a broadband hysteresisgraph-wattmeter,7 where the exciting current is supplied by combination of an Agilent 33220A arbitrary waveform generator and an NF HSA4101 power amplifier, and signal acquisition is made by a Tektronix 714L digital oscilloscope. The measurements on the single strip samples (width 5 mm) were carried out by placing them flat in the 14 mm wide gap of a Mn–Zn soft ferrite (N87 type) double-C yoke, having pole faces of area 9.72 5.25 mm2. The magnetic field was generated by a strip-enwrapping thin solenoid, exactly filling the gap. Inside it, a short centrally located pickup coil was used for detecting the induction derivative. To cover the desired many-decade frequency range, different configurations for primary and secondary windings were adopted. The magnetic path length for the single strip arrangement was determined by comparison with a calibrated strip. After removal of the upper portion of the double-C yoke, the strip sample was placed in the focal plane of a wide-field Kerr microscope, based on a Zeiss Axioscop 2 Plus device. The magnetooptical setup, derived from the one originally developed by Chumakov et al.,8 is schematically shown in Fig. 1. The C-yoke provides now both the exciting field and a low reluctance flux path. High time resolution is obtained by means of a gated intensified charge-coupled device (CCD) camera (Picostar LaVision), where the photointensifier works as an electronic shutter. The effective opening time of the intensifier can be varied from 50 ps to continuous exposure, allowing for investigation on a wide range of magnetizing frequencies. The domain observations were carried out while subjecting the sample to the same measuring conditions adopted for the fluxmetric experiments; the magnetization in the strip being detected, in particular, via a 3-turn pickup coil wound close to the illuminated area. This is a circular spot of diameter 1.3 mm, with pixel size 2.9 lm. An additional generator, slaved to the field signal generator, synchronously triggers the image acquisition sequence. At each frequency, equally time-spaced

FIG. 1. (Color online) Magnetooptical setup for broadband time-resolved observation of the domain structure in strip samples. The switch permits one to pass from stroboscopic measurement (lower position) to fluxmetric measurement (upper position). The specimen, endowed with primary and secondary windings, is placed flat between the pole faces of a soft ferrite C-core.

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images were acquired along the hysteresis half-loop and averaged over a large number N of acquisitions, ranging from N 104 at low frequencies (f < 1 kHz) to N 107 for f > 1 MHz. The final images were obtained by subtracting the background, taken on the magnetically saturated sample. Sample heating due to losses imposes the progressive reduction of the maximum measuring frequency with increasing the Jp value. With the present ribbon specimens, the problem becomes acute beyond about 1 MHz, and at 20 MHz, the upper Jp limit falls down to around 10 mT. III. EXPERIMENTAL RESULTS AND DISCUSSION

A basic outcome of the dynamic magnetooptical experiments in the transverse anisotropy ribbons is the observation of progressive relaxation of the DW motion with frequency. To provide a measure of this effect, we have analyzed the sequence of domain images taken between 6Jp at different frequencies and calculated the peak-to-peak DW span versus f. Figure 2, concerning a 19 lm thick Co71Fe4B15Si10 ribbon (saturation polarization Js ¼ 0.89 T) with transverse anisotropy Ku ¼ 50 J/m3, shows the observed frequency dependence of the percentage area of the measuring spot covered by the DW displacements upon a semiperiod for Jp ¼ 0.60, 0.40, 0.15 T. The images taken at reversal points of the 60.40 T hysteresis loop at four different frequencies illustrate the progressive stabilization of the walls. Observations at Jp lower than about 0.1 Js are made difficult by resolution limits and noise, and one has to rely, in case, on data extrapolation. The image noise observed at low frequencies is due to the low trigger rate and the ensuing low exposition time teff. Conversely, the problem at high frequencies comes from sample heating. Physically, it appears that the applied field, necessarily increasing with f in order to keep a given Jp value, inefficiently compensates for the local eddy current counterfields associated with the transverse DW displacements. In any case, with the DWs achieving stillness at high frequencies, we expect the system falling into a classical

FIG. 2. (Color online) Decrease of the DW span covered along a half-period for Jp ¼ 60.60 T (squares), 60.40 T (triangles), 60.15 T (circles) as a function of the magnetizing frequency f in a transverse anisotropy Co71Fe4B15Si10 amorphous ribbon (Ku ¼ 50 J/m3). The DW span area is determined by analysis of the Kerr domain images, examples of which, taken at different frequencies (labeled points 1–4) for Jp ¼ þ0.40 T (left) and Jp ¼ 0.40 T (right), are shown. The increase of the DW spacing at the highest frequency (image 4, f ¼ 500 kHz) is a specific feature of the chosen spot.


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context, that is, one of spatially homogeneous magnetization process and long range eddy currents. To deal with this matter, we can resort to the statistical theory of losses and the related concept of loss separation, having nevertheless in mind that such an approach has been developed and is chiefly applied to loss phenomena occurring in laminations at and around power frequencies. Figure 3 provides an overview, up to f ¼ 10 MHz, of the energy loss at Jp ¼ 50 mT in different types of transverse Ku amorphous and nanocrystalline ribbons. A variety of behaviors, depending on composition and Ku values (6 J/m3 Ku 130 J/m3) is observed at low frequencies, while on the high-frequency corner, the main loss-conditioning parameter appears to be the ribbon thickness and a close to W(f) ! f dependence is found. While the spread of quasistatic and low-frequency loss behaviors is interpreted as the natural result of anisotropydominated response of the DW system in the various materials, the chief role played by the sample thickness at high frequencies (the involved resistivities being in the restricted range 120108–140108 X m) consistently fits into a classical (uniform) loss generating magnetization process, with negligible DW role. This is what the previous magnetooptical DW observations suggest. The classical formulation for a material of dc permeability l, thickness d, and conductivity r is Wcl ðf ; Jp Þ ¼ ðp=2ÞðcJp2 =lÞðsh c sin c=ch c cos cÞ, where pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c ¼ prl d 2 f . This expression predicts for c >2, a condi1/2 5 tion associated with substantial skin effect, W(f) ! f , somewhat contrasting with the actually observed W(f) behavior, much closer to W(f) ! f. It is noted that, however, a skineffect related gradient of magnetization rotation versus depth makes an exchange field to appear. This might promote, depending on f and Jp, the creation of symmetric 90 -like domain walls, moving inward from the ribbon surface to the center, a process making inadequate the previous standard equation for Wcl(f). One might phenomenologically address this problem by introducing in the previous standard

J. Appl. Phys. 109, 07A322 (2011)

FIG. 4. (Color online) Energy loss measured vs frequency at Jp ¼ 50 mT in a 19 lm thick transverse anisotropy Co71Fe4B15Si10 ribbon with Ku ¼ 130 J/ m3 (full symbols). An example of loss separation with the classical loss component Wcl(f) calculated under the assumption of frequency dependent material permeability is provided.

equation q forffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Wcl(f), the frequency dependent permeability,

jlðf Þj ¼ l0 ðf Þ2 þ l00 ðf Þ, with l0 and l00 the measured real and imaginary permeability components. An example of the so-calculated Wcl(f) and ensuing loss decomposition is given in Fig. 4. It consistently shows a downturn of the excess loss beyond about 1 MHz.

IV. CONCLUSIONS

A fluxmetric-magnetooptical broadband investigation of magnetization process and losses has been carried out in transverse anisotropy near-zero magnetostriction amorphous ribbons. It is observed that the domain wall processes increasingly relax and eventually freeze on approaching the megahertz region. With the rotations surviving, the high-frequency magnetic losses appear to scarcely comply with the standard eddy current classical loss prediction. It is remarked that the skin effect associated with rotations is influenced by the exchange field. This is phenomenologically accounted for by introducing the experimental frequency-dependent permeability in the standard formula for the classical loss. 1

FIG. 3. (Color online) Energy loss vs frequency measured at Jp ¼ 50 mT up to 10 MHz in a number of transverse anisotropy amorphous and nanocrystalline (Finemet) ribbons. The transverse anisotropy constant and the ribbon thicknesses range between 6 and 130 J/m3 and 6.1 and 19 lm, respectively.

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