Russian Physics Journal, VoL 36, No. 10, 1993

THERMOMAGNETIC PHENOMENA IN HEXAGONAL

FERRIMAGNETIC MATERIALS

S. M. Zhilyakov, E. P. Naiden, and G. I. Ryabtsev UDC 537.638

The results of an investigation of the magnetocaloric effect in the CoTi -M and CoZn-W hexaferrite systems

in the 150-500 K temperature range are presented. It is shown that the maxima of the magnetocaloric effect

correspond to spontaneous spin-orientational transitions leading to transformation of the magnetic structure from easy-plane to uniaxial and to resultant changes in the values and signs of the magnetic anisotropy constant as

a function of the cotreposition and temperature. Estimates of the AT(T) relation taking into account the magnetic

anisotropy constants K 1, K 2, and K s, which are known for the compounds considered, agree well with

experiment. Hence, the main contribution to the magnetocaloric effect at temperatures far from the Curie point in the materials in question is governed by the rotation of the magnetization vector.

There are two main reasons for the interest in investigating the magnetocaloric effect or, in general, thermomagnetic phenomena in magnetically ordered materials. On the practical side it is of interest to find materials with a high value of the magnetocaloric effect, which could be used as working materials in magnetic refrigerators. The second aspect is the possibility of using this phenomenon to investigate various interactions in magnetically ordered materials, to study the effect of a magnetic field and other external factors on the processes and mechanisms of magnetic ordering, the relationship between the atomic and

magnetic structures, etc.

The overwhelming majority of publications on the magnetocaloric effect at the present time are concerned with investigations of the paraprocess in the temperature range close to the temperature at which a transition occurs into a disordered state (Tc). Considerably less attention has been given to the temperature range T ,~ T c, where the value of the effect is determined primarily by the rotation of the magnetization vector. The most interesting publications in this area are devoted to

investigations of the magnetocaloric effect of the rare earths and their intermetallides in the neighborhoods of spontaneous and induced spin-orientational magnetic transitions [1].

There is practically no information in the literature describing investigations of the magnetocaloric effect of such compounds as ferrimagnetic materials with a hexagonal structure, which are of considerable interest from the point of view of the physics of magnetism. In these materials, when there is a change in their chemical composition or in the temperature, a

sequence of spontaneous spin-orientational transitions is observed, and, under certain conditions, a reorientation of the spins in an external magnetic field can occur (magnetization processes of the first kind). The energy of magnetic crystallographic anisotropy is extremely high and may compete with the energy of superexchange interaction.

These facts also stimulated us to investigate the magnetocaloric effect in polycrystalline specimens of hexagonal ferrimagnetic materials of the following two systems:

BaFe12-~xCo~TixO1g, 0~x<.~3,0 (CoTi--M), BaCo2-xZnxFe160~z, 0 ~ x ~ 2 , 0 (CoZn~-W).

We have previously carried out a complex investigation of the magnetic state diagrams of these systems and of the macroscopic magnetic characteristics, determined the regions in which spontaneous spin-orientational transitions exist when the chemical composition and temperature are varied, and have investigated the nature of the observed magnetic transitions [2, 3]. In this

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Translated from hvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 63-68, October, 1993.

1064-8887/93/3610-0944512.50 © I994 Plenum Publishing Corporation

communication we present the results of investigations of the magnetocaloric effect of these compounds at temperatures considerably below the Curie temperature.

We will dwell briefly on the main ideas of the theory of the magnetocaloric effect. The free energy of a crystal of

magnetic material in an external magnetic field can, in general, be represented in the form

G=FI+F~_ +Fa+F4 (1)

and consists of parts due to exchange interaction F1, magnetic crystallographic anisotropy F 2, magnetoelastic properties F 3, and

the energy in a magnetic field. In adiabatic magnetization, the value of the magnetocaloric effect is given by the expression

A T ---- T ( ~)G ') aXH. (2) cn\OTOH/n,r

where c H is the heat capacity of the magnetic material. The value of the effect due to a change in the exchange energy for true

magnetization (the paraprocess) is equal to

ar_ a= __r (eM'l A. L -b-if/. (3)

and is a maximum in the region of the Curie temperature T o where the change in the magnetization M s is greatest. For crystals

of the hexagonal system, the expression for the energy of magnetic crystallographic anisotropy has the form

F2 = Kt sin -~ 0 + t(2 sin* 0 + Ka sin 6 0 + K' 3 sin ~ 0 cos 6% (4)

where 0 is the angle between the direction of the magnetic moment and the c axis of the crystal, and ~ is the angle between the

magnetic moment and the a axis in the basis plane. In this case the component of the magnetocaloric effect due to rotation of

the magnetization vector is equal to

hTan _ T ~ OK t a

j*:l=l

(5)

where otja are the direction cosines of the magnetization, and is determined by the gradients of the magnetic anisotropy constants,

and its field dependence has the form of a curve with saturation. Hence, an investigation of the AT(T) relationship gives, in

principle, information on the contribution of the different mechanisms in any temperature region.

The extremely small amount of information available on the behavior of the magnetostriction of hexagonal ferrimagnetic

materials prevents us from making quantitative estimates of the fraction of the magnetoelastic component in the magnetocaloric

effect. It should, however, be noted that when spin-orientational transitions occur in the form of phase transitions of the first

kind, i.e., accompanied by sudden changes in the structural parameters and, consequently, considerable temperature gradients

of magnetostriction deformations, the part played by this mechanism of the magnetocaloric effect may be considerable and

comparable with that discussed above. It follows from the above that the magnetocaloric effect of hexagonal oxide ferrimagnetic materials in the temperature

range T ,~ T c may have an extremely complex structure, and to interpret the behavior of the AT(T) relationship it is necessary

to include data on the temperature dependences of the magnetic and structural parameters.

An experimental investigation of the magnetocaloric effect in the 150-500 K temperature range was carried out using

equipment which consisted prhnarily of a measuring head of special construction for differential thermal analysis, mounted in

a cryostat and placed between the poles of an electromagnet. The sensitivity of the equipment in determining a differential

temperature is not worse than 2.10 -3 K, and the error in determining the latent heat of transitions is not greater than 2.10 -3

J/g. The system was calibrated using the heats of structural transitions of a standard specimen of NHaNO 3.

In Fig. 1 we show magnetic-state diagrams for specimens of the CoTi -M (x = 1, 2) and C o Z n - W (x = 1, 0) systems,

represented by curves of 8(T), namely, the angle of deviation of the magnetization vector from the C axis, obtained from

neutron-diffraction data [2, 3], and also curves of the effective anisotropy field Haft) . The indices M and W relate to materials

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0," deg . ..HA, ROe

0 L~ ~oo 200 300 400 T.,K

Fig. 1

~'l'r mK

400 J

'° L 4ooT, K

Fig. 2

400

350

"E,K j , '" i

";.'=o "- ~ T 2

2 4 6

C

-5C

-'i0C

-'IS( -20(~

I

M * ° ' * " ' 7 / 2 #

#

Ioo eoo z o.

~.%,.

T

4OO T K

Fig. 3 Fig. 4

with the corresponding structure. For general qualitative similarity - - the presence of a complete sequence of cone-plane-cone-

axis of easy magnetization ( C E M - P E M - C E M - A E M ) spin-orientational transitions - - there are certain differences. Thus,

phase transitions of the fL,'st kind C E M - P E M and P E M - C E M in an M-type structure occur over a narrower temperature range

compared with a W-structure. Moreover, on the 0(T) curve one can clearly see a difference in the rates of change of the aperture

angle of the cone in the temperature range of P E M - C E M - A E M transitions for a W-type hexaferrite.

A differential thermal analysis shows that there are additional magnetic transitions in the region of the high-temperature

conical phase. In Fig. 2 we show, as an example, part of the differential thermal analysis thermogram for the specimen of

C o Z n - W in question, plotted when there was no external magnetic field. The peak of the heat emission at T 1 = 310 K

corresponds to the P E M - C E M spin-orientational transition, while the kink in the base line at T 4 = 420 K corresponds to the

C E M - A E M transition. The weak absorption peaks at T 2 = 350 and T 3 = 390 K are related, we assume, to the temperatures

at which the higher-order magnetic anisotropy constants vanish (K 2 and K 3, respectively). The application of an external

magnetic field leads to a considerable fall in the transition temperature from the plane to the conical phase, whereas the

temperatures of the residual anomalies change only slightly. In Fig. 3 we show T i as a function of the field. The thermograms

plotted for heating and cooling exhibit temperature hysteresi s AT~ = 10 K for the P E M - C E M transition, but for the remaining

anomalies the hysteresis does not exceed the error of measurements. The P E M - C E M phase transition exhibits the features of

a phase transition of the first kind and is characterized by an enthalpy AH --- 0.2 kJ/mole at H o = 0; the external field depends

very much on this characteristic.

For the C o T i - M (x = 1, 2) specimen the differential thermal analysis thermograms showed that the temperatures of

the P E M - C E M and C E M - A E M spin-orientational transition increase considerably when an external magnetic field is applied.

The reasons for this difference in the behavior of Ti(H) compared with a W-type specimen are still unclear.

The results of measurements of the magnetocaloric effect in a field H 0 = 7 kOe in C o T i - M (x = 1, 2) and C o Z n - W

(x = 1, 0) specimens are shown in Fig. 4. The curves of AT(T) for the corresponding specimens are denoted by the letters M

and W.

For an M-type specimen the temperature dependence of the magnetocaloric effect has three pronounced maxima at T] =

340 K, T 2 = 380 K, and T 3 = 410 K. The magnetocaloric effect changes sign at T < 280 K and T > 420 K. comparison of

these results with the magnetic phase diagram shows that the maxima of the magnetocaloric effect at T1 and T 2 correspond to

C E M - P E M and P E M - C E M magnetic transitions, which occur via phase transitions of the first kind, while the maximum at

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~T, mK

I ' ' 3

40i

0. "

!)

i - 00 i

, + " " , , , i i

1 I

6 Ho, kOe

<r'10 6, org" c=

0 2 o 4oo 2o0 3co 1T, K

Fig. 5 Fig. 6

T 3 corresponds to a C E M - A E M transition of the second kind. In the T > T 3 temperature range the higher-order magnetic

anisotropy constants are negligibly small compared with K 1 and the behavior of the AT(T) curve in this region is determined

by the KI(T) relationship. For temperatures T < T 2 one must take into account all the magnetic anisotropy constants, since,

according to the phenomenological theory of spin-orientational transitions in magnetic materials of the hexagonal system, such

a phase transition occurs when K l, K 2, and K 3 ~ 0 [4, 5]. The behavior of AT(T) is obviously determined by competition

between the temperature gradients of K i.

For the C o Z n - W (x = 1, 0) specimen there are also several maxima on the AT(T) curve. As in the previous case, the

peaks at T l = 300 K and T 3 = 400 K correspond to the PEM-CEM and C E M - A E M orientational transitions. The maximum

of AT at T 2 = 350 K is due, as pointed out above, to the fact that the third magnetic anisotropy constant vanishes at this

temperature. The increase in the absolute value of the magnetocaloric effect at low temperatures correlates with the behavior

of the temperature dependence of the effective anisotropy field HA(T), but the available data are insufficient to be able to make

a quantitative estimate of the magnetocaloric effect resulting from rotation of the magnetization vector using expression (5).

In Fig. 5 we show graphs of AT(H) for C o Z n - W (x = 1, 0) at temperattu'es of T l, T 2, and T 3 (curves 1, 2, and 3,

respectively). In the region of the cone-axis of easy magnetization phase transition the higher-order magnetic anisotropy constants

are negligibly small compared with K 1 and the graph of AT(T) is satisfactorily described by (5). An estimate of the value of

the anisotropy field for which a change in the slope of the zaT(H, T3) curve occurs, taking into account the correction for the

demagnetizing field H A = H 0 - NM, gives a value of H A = 0.7 kOe, which agrees well with the results of magnetic

measurements. At temperatures T < T 2 one must take into account the higher-order uniaxial anisotropy constants and also the

anisotropy in the basis plane (K 3'). The form of the AT(H) curves in this temperature range indicates that the contribution from

the rotation of the magnetization vector in the basis plane to the value of the overall magnetocaloric effect plays a considerable

role.

The above discussion concerning the comparison of the z&T(T) curves with the betlavior of Ki(T) in the cases considered

are to some extent qualitative, since there is no information on the actual values of K i over this temperature range.

For the C o Z n - W (x = 1.38) specimen there are experimental data available regarding Ki(T ) [6]. In Fig. 6a we show

the results of measurements of the temperature dependence of the magnetocaloric effect in a field H o = 7 kOe for this

compound, while in Fig. 6b we reproduce curves of KI(T), K2(T), and K3(T) (curves I, 2, and 3, respectively). An estimate

of the relationship ,aT(T) using expression (5) showed qualitative and quantitative agreement as regards the sign and value of

the magnetocaloric effect with experimental data. The maxima in AT in the temperature ranges corresponding to zero K 2 and

the change in the sign of K1 clearly appear in the calculations. The values of the heat capacity for the compounds considered

in the literature are not known, and hence, in the estimation we used the data in [7] on the value of cp for BaFel2Olg. The

contribution of the paraprocess to the magnetocaloric effect is small over the temperature range considered, and by (3) is of the

order of 10 -3 K.

On the whole, our investigation has shown that in C o T i - M and C o Z n - W ferrimagnetic oxides with a hexagonal

structure in the region of spontaneous spin-orientational transitions, rotation of the magnetization vector is the main component

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of the magnetocaloric effect, while the paraprocess makes a much lesser contribution (of the order of 10 -3 K). The considerable difference in the values of the magnetocaloric effect at temperatures below 300 K for hexaferrites of the M and W structural types, containing approximately equal amounts of the Co 2÷ ions in the formula unit, indicates the exceptionally important role of positions with strong distortions of the anion polyhedra (W-type) in giving rise to the magnetic anisotropy of these

compounds.

REFERENCES

°

2. 3. 4.

5. 6. 7.

A. S. Andreenko et al., Usp. Fiz. Nauk, 158, No. 4, 553 (1989). E. P. Naiden et al., Izv. Vyssh. Uchebn. Zaved., Fizika, No. 1, 14 (1991). E. P. Naiden, V. I. Maltsev, and G. I. Ryabtsev, Phys. Star. Sol.(a), 120, No. 1,209 (1990). A. I. Mitsek et al., Fiz. Met. Metaloved., 41, No. 2, 464 (1976). G. I. Ryabtsev and E. P. Naiden, Fiz. Tverd. Tela, 32, 3, 944 (1990). E. P. Naiden and G. I. Ryabtsev, Izv. Vyssh. Uchebn. Zavexi., Fizika, No. 4, 44 (1990). B. P. N. Reddy and P. J. Reddy, Phys. Slat. Sol., A22, No. 4, 219 (1974).

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