PIEZOMAGNETIC PROPERTIES OF THE Ni-Mn-Co-Cu FERRITES IN THE RANGE OF ANISOTROPY COMPENSATION

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PIEZOMAGNETIC PROPERTIES OF THE

Ni-Mn-Co-Cu FERRITES IN THE RANGE OF

ANISOTROPY COMPENSATION

Z. Kaczkowski

To cite this version:

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JOURNAL DE PHYSIQUE Colloque CI, supplbment au no 4, Tome 38, Avril 1977, page C 1-203

PIEZOMAGNETIC PROPERTIES OF THE Ni-Mn-Co-Cu FERRITES

IN THE

RANGE OF ANISOTROPY COMPENSATION

Z. KACZKOWSKI

Polish Academy of Sciences, Institute of Physics, Warsaw, Poland

R h r n k . - On prksente des resultats sur I'influence de la temperature et du champ magnktique sur les proprietes piezomagnetiques de ferrites de Ni-Mn-Co-Cu dans la zone de compensation de I'anisotropie. Dans cette zone on a observe des extremums des coefficients magnetiques, mkaniques et magneto-mecaniques.

Abstract.

-

The temperature and the magnetic polarization dependence of the piezomagnetic properties of Ni-Mn-Co-Cu ferrites in the range of anisotropy compensation are presented. In

this range extrema of magnetic, mechanical and magnetomechanical coefficients were observed.

1. Samples.

-

The investigations concern ferrites force. For these reasons magnetic induction B and (Table I), elaborated by professor Dr. R. Wadas. mechanical strain S will be :

Toroidal samples of an average diameter of 17 mm,

B = pH

+

AB = p, H

+

d7',

thickness ranging from 5.3 to 6.0 mm and weight of (1) 5 g were investigated. 7' T

S = - + A S = - + d H ,

E E,, (2)

TABLE I

Chernicul composition and density of the samples

Ni~.p8-x-yMn0.02C0xCuyFe204

No. N10 COO CuO g/cm3

- - -

-

- 1 0.98 0 0 5.09 2 0.968 0.012 0 5.10 3 0.965 0.015 0 5.12 4 0.953 0.027 0 5.11 5 0.8 18 0.01 2 0.15 5.23

2. Investigations. - Piezomagnetic properties in the range of anisotropy compensation were investigated. This range is changing from - 30 (sample No. 2) to

+

300C (No. 4). Magnetic reversible permeability, Young's moduli, magnetomechanical coupling coefficient k, magnetostriction constant h and stress-

sensitivity coefficient d cersus magnetic polarization and temperature were determined. It can be verified that o n the one hand majority of magnetic materials show in the presence of magnetic field deviation from conventional Hooke's law ( A E effect) and, on the other hand, these materials exhibit in most cases variation of their magnetic parameters under the influence of applied mechanical stresses (Villari's effect). These interactions manifest themselves by variation of the elasticity modulus or variation of the magnetic permeability and in the case of hysteresis loop as variation of the remanence and the coercive

where

H

is magnetic field, p, = magnetic permeability at constant stress (free sample), d = stress-sensitivity coefficient, T = stress, E,, = Young's modulus at constant magnetic field. The increments AB and A S

representing the influence of mechanical and magnetic reactions can assume positive or negative values, according to the sign of magnetostriction. When these variations are very small, processes become reversible and increments can be replaced by differentials and in matrix form will be :

It is posible to obtain three another sets of piezomagnetic equations, in which next three piezomagnetic (magnetomechanical) coefficients will appear [l

,

21. In each of piezomagnetic sets two independent types of variables appear : magnetic (B or H) and mechanical (T or S ) one magnetic coefficient ( p , or ps or their reciprocals), one mechanical coefficient (E,,, EB or their reciprocals) and one magnetomechanical coefficient (d, h, e or g, appearing in each equation of given

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set [I, 21. These magnetomechanical coefficients are defined (in SI units) as follows [ I ]

This identity is derived from thermodynamic relation, e. g. [3]. A very important piezomagnetic coefficient is the magnetomechanical coupling coefficient k. The ratio of this part of energy (magnetic or mechanical), which is converted into another energy We to the total energy WT stored in sample is given by k2, i. e.

Coefficient k is connected with any of coefficients appearing in particular sets of piezomagnetic equations, for instance

3. Magnetic permeability. - In the range of small amplitudes, which have been applied in the course of investigations, incremental permeability is almost equal to reversible permeability [4]. The values of permeability of free pT and clamped sample ,us at fixed polarization differ from each other and the value of this difference varies as a function of magnetic polarization. In the state of demagnetization, magnetic saturation and in the proximity of coercive forcepoints, the value of these pcrmeabilities are equal one to another. This effect is connected with vanishing of magnetomechanical coupling just in these points. Figure 1 presents reversible permeabilities at constant

FIG. 1.

-

Relative reversible permeabilities at constant stresses pi. (free samples) of Ni-Mn No. 1 and Ni-Mn-Co ferrites No. 4 versus magnetic polarization at dry ice and room tempe-

ratures.

stress as a function of permanent magnetic field determined at room temperature (about 300 K) and at dry ice temperature (about 200 K ) for cobalt samples No. 1

and No. 4. Sample containing no cobalt shows very small temperature changes and for x = 0.027 compa- rison of these characteristics reveals pronounced changes. For other samples changes are smaller [5]. Figure 2 presents characteristics of permeability at

FIG. 2. - Relativc reversible permeabilities pk at different magnetic polarizations versus temperature of Ni-Mn-Co ferrites

( x = 0.027) determined from isotherms.

constant magnetic field for No. 4 determined from isotherms. The same results are obtained directly from measurements [ 5 ] . With increasing bias the maxima in both cases decreased and were displaced to lower temperatures.

This was observed in all ferrites containing cobalt [5]. The higher is the cobalt content, the higher is the temperature of the maximum.

4. Moduli of elasticity and magnetomechanical coeficients : k, d and h. - Young's moduli and magne-

tomechanical coupling coefficient k were determined by using resonant-antiresonant methods 161. For

EH

characteristics (Fig. 3) there are minima observed (negative AE-effect). Figure 4 presents temperature characteristics of

EH

at various constant magnetic field (No. 4). Similar characteristics were observed for

EB and for all the ferrites containing cobalt. The

minima of EH or EB were decreased and displaced to

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PIEZOMAGNETIC PROPERTIES O F THE;N~-Mn-Co-Cu FERRITES

FIG. 4. -Young's modulus at constant magnetic field EH at different magnetic polarization versus temperature for No. 4

ferrite.

FIG. 5.

-

Magnetomechanical coupling coefficient k at different temperatures versus magnetic polarization for No. 4 ferrite.

FIG. 3. - young's modulus at constant magnetic field EH _{Stress-sensitivity}_d_{and magnetostriction constant h}

and at constant magnetic induction EB versus magnetic polariza-

tion of Ni-Mn No. 1 and Ni-Mn-Co ferrites No. 2, 3,4 at room were determined from magnetic and mechanical temperature a and EH at different temperatures versus magnetic measurements. For these coefficients two minima on

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C1-206 Z. KACZKOWSKI

FIG. 6.

-

Temperature cal coupling coefficient

characteristics of the magnetomechani- at different magnetic polarization for No. 4 ferrite.

5. Discussion of results and conclusions. - The presence of Co-ions in Ni-Mn and Ni-Mn-Cu ferrites influences the values of magnetocristalline anisotropy constants and their temperature dependences. For

x = 0.027 (No. 4) compensation range of anisotropy constant Kl is near 30 OC and for x = 0.012 (No. 2) near

-

30 0C. Extrema of magnetic permeabilities (maxima) and moduli of elasticity (minima) depend not only on K , but on K, and on the magnetomechanical

(magnetostrictive) anisotropy. This energy changes

FIG. 7.

-

Temperature characteristics of the magnetostriction constant h at different magnetic polarizations for No. 4 ferrite.

with polarization. These are responsible for the displacement of extrema on temperature scale. It is in agreement with Globus theory and observations 171.

For sample No. 1 (no cobalt) in this range of temperature monotonous changes in coefficients are observed without any extrema. The extrema and shiftings for low cobalt content ferrites were smaller. Maxima of permeability were shifting to lower temperature (from 30 OC to 00 for No. 4) when increasing polarization and minima of moduli of elasticity were shifting to higher temperature (to about 50 OC for No. 4). Maxima of k coefficient were shifting also to higher temperature. These phenomena are the reason for two minima (negative maxima) of magnetomechanical coefficient d and h.

References

[I] VAN DER BURGT, C. M., Phil& Res. 8 (1953) 91. [2] KACZKOWSKI, Z., Proc. Vibr. Probl. 2 (1961) 237. [3] KACZKOWSKI, Z., Rozpr. Elektrotechn. 7 (1961) 245. [4] KACZKOWSKI, Z., Electron. Technology 7 (1974) 93.