AC Magnetic Field Effect on the Complex PermeabilitySpectra of Soft Magnetic Fe73Cu1Nb3Si16B7Powder Cores

J. FÜZERa, S. DOBÁKa AND J. FÜZEROVÁba Institute of Physics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 041 54 Košice, Slovakia

b Faculty of Mechanical Engineering, Technical University, Letná 9, 042 00 Košice, Slovakia

15th Czech and Slovak Conference on Magnetism CSMAG’13

IntroductionIn this work, two soft magnetic Fe73Cu1Nb3Si16B7 powder core samples were inves-tigated. Influence of applied exciting AC magnetic field with various amplitudes wasstudied on the complex permeability spectra.

ExperimentalAmorphous ribbon with nominal composition Fe73Cu1Nb3Si16B7 was produced viamelt spinning technique (Vitroperm® 800, provided by Vacuumschmelze GmbH & Co.KG Hanau, Germany). Afterwards the ribbon were milled or cryomilled using a RETSCHPM4000 planetary ball mill (Fig. 1). The milling was performed under Ar atmospherewith speed of 180 rpm at a ball-to-powder mass ratio of 6:1 in hardened steel vials. Han-dling of the powder was done in a glove box with controlled atmosphere (O2 < 1 ppm,H2O < 1 ppm).

We prepared two samples:

• sample R – amorphous ribbon milled for 6 hours, consolidated at 500 °C for 5 min,annealed at 540 °C for 60 min,

• sample L – amorphous ribbon cryomilled for 6 hours, consolidated at 500 °C for5 min, annealed at 540 °C for 60 min.

Particle size of more than 95 % of particles after milling at room temperature is from50 µm to 300 µm, but cryomilled powders have smaller particle sizes, from 20 µm to150 µm (Fig. 2). The samples were consolidated at 700 MPa for 5 min at 500 °C intocylinders with diameter of 10 mm and thickness of 3 mm. An axial hole with diameterof 5 mm was drilled into the disc, which produced ring-shaped samples (Fig. 3).

FIG. 1 RETSCH PM4000planetary ball mill.

FIG. 2 The morphology of source powders for thesamples R and L observed by SEM.

FIG. 3 Compactedring-shaped core sample.

We have prepared coil for AC complex permeability measurement. A coil was woundaround the toroidal sample and complex permeability spectra were measured with animpedance analyzer (HP 4194A) from 100 Hz to 40 MHz with the contact electrodes intwo-terminal connection configuration (Fig. 4).The real and imaginary parts of the complex permeability were determined using theseries equivalent circuit (Fig. 5) by the relations

µ′ =LsL0, µ′′ =

Rs −R0ωL0

, (1)

where Ls andRs are the equivalent inductance and resistance of the core with winding,R0 is DC resistance of winding, ω is the angular frequency and L0 is the inductance ofempty toroid

L0 =µ02π

N2h ln

(D

d

), (2)

where µ0 is the permeability of free space, N is the number of turns of the coil, h is thethickness, D is the outer diameter and d is the inner diameter of the ring sample.

FIG. 4 HP 4194A impedance analyzer.

Rs Ls

FIG. 5 Series equivalent circuit of the ferromagneticring core with winding.

Results

ferromagnetic particle

air bubblepinning center

magnetic domain

domain wall

FIG. 6 Schematic draw of the ring sample, detail of the cross section of compacted powder particles andschematic domain structure of two particles. The both samples consist of a large number of ferromagnetic

powder particles with a broad limited size distribution and accordingly their macroscopic magneticproperties are mean values of contributions of total statistical ensemble of particles.

25,92 A/m10,32 4,75 2,19 1,07 0,27

102 103 104500

1000

1500

2000

2500

3000

3500

4000

f [Hz]

'

0

1000

2000

3000

4000

5000

Sample R

''

102 103 104300

400

500

600

700

800

900

Sample L

25,79 A/m15,73 7,05 2,38 0,54 0,27

f [Hz]

'

100

150

200

250

300

350

''

FIG. 7 Frequency spectra of real µ′ parts (solid symbols) and imaginary µ′′ parts (open symbols) of relativecomplex permeability of the sample R (left) and sample L (right) for selected amplitudes of AC magnetic

field.

0 5 10 15 20 25 30140

160

180

200

220

240

260

Sample R

fr = 0,32 Hm + 155,17

fr = 21,93 Hm + 254,64

f r [H

z]

Hm [A/m]

reversible + irreversible

irreversible + rotation

0 5 10 15 20 25 302650

2700

2750

2800

2850

2900

2950

3000

3050

fr = 7,90 Hm + 2886,63

f r [H

z]

Hm [A/m]

Sample L

fr = 29,95 Hm + 3001,08

reversible + irreversible

irreversible + rotation

FIG. 8 Relaxation frequency fr as a function of amplitude of AC magnetic field of the sample R (left) andsample L (right).

ConclusionThe influence of the AC magnetic field on the complex permeability spectra of softmagnetic bulk powder Fe73Cu1Nb3Si16B7 cores prepared by milling of alloy and com-paction were studied. With increasing of AC magnetic field values of real and imagi-nary parts increase (Fig. 7), mainly at low frequencies and the relaxation frequency ofthe both samples shifts toward lower values (Fig. 8). Relaxation frequency is associatedwith deactivation of domain walls movement magnetization process contributions tothe total magnetization of ferromagnetic sample. It was observed, that the relaxationfrequency vs. AC magnetic field amplitude show linear dependence in two regions.These regions are connected to the dominant magnetization processes (reversible andirreversible domain walls movement and magnetization vector rotation).

AcknowledgementThis work was realized within the frame of the projects, ITMS 2622012001, ITMS 26220220105, which aresupported by the Operational Program "Research and Development" financed through European RegionalDevelopment Fund. This work was also supported by the Slovak Research and Development Agency underthe contract No. APVV-0222-10 MAGCOMP and by the Scientific Grant Agency of the Ministry of Educationof Slovak Republic and the Slovak Academy of Sciences, project No. 1/0862/12. Special thanks to Mr. MilanVitovský of Vacuumschmelze GmbH & Co. KG Hanau, Germany for providing of Vitroperm® 800 samples.