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THE MAGNETOSTRICTION CONTRIBUTION
FROM Ni2 + IONS ON TETRAHEDRAL SITES : A
THEORETICAL AND EXPERIMENTAL STUDY
K. Liolioussis, A. Pointon
To cite this version:
JOURNAL DE PHYSIQUE Colloque CI, supplbment au no 4, Tome 38, Acril 1977, page C1-191
THE MAGNETOSTRICTION CONTRIBUTION FROM Ni2
+IONS
ON TETRAHEDRAL SITES
:
A THEORETICAL
AND
EXPERIMENTAL STUDY
K. T. LIOLIOUSSIS and A. J. POINTON
Physics Department, Polytechnic, Portsmouth, Hants, U. K
Rhsumk. - On montre que les variations thermiques de la contribution a la magnetostriction des ions Ni2+ places dans les sites tetraedriques d'un ferrite peuvent &tre expliquks ti partir du
couplage spin orbite dans le triplet d'ktat de base T I . Toutefois, alors que la valeur du coefficient
1 1 o o A T = 0 K peut &tre calculCe avec une bonne approximation sans introduire de parametres ajustables, la thCorie simple donne le mauvais signe pour 1 1 I 1 ; il est necessaire dans ce cas
d'envisager I'introduction d'Ctats d'knergie plus Cleves dans I'etat de base du triplet, par I'inter- mCdiaire des ClCments de matrice du champ cristallin.
Abstract.
-
It is shown that the temperature variation observed in measurements of the contri- bution to the magnetostriction arising from Niz+ ions on tetrahedral sites in a ferrite can be explai- ned on the basis of spin-orbit coupling within the ground state T I triplet. However, while the magnitude of the coefficient l l o o at T = 0 K can be calculated to good approximation without the introduction of adjustable parameters, the simple theory gives the wrong sign for 1 1 1 1 and it isnecessary for this case to invoke the admixing of higher energy states into the triplet ground state through matrix elements of the crystal field.
1. Introduction and theory. - It has been shown [l] ions may be calculated on the same basis if it is assumed that, to good approximation, the observed contribu- that spin-orbit energy and first order strain energy tion of NiZf ions in tetrahedral sites to the magneto- terms may be combined in a perturbing Hamiltonian crystalline anisotropy of ferrites can be explained by which acts on the T I ground state, viz :
assuming that the energy level structure of this ion is
as shown in figure 1 and that, for the anisotropy, the H = A L . S
+
i >x
j K j A i jwhere A i j is the strain tensor and the Vii are the appropriate coefficients. Under the site symmetry, the only non-vanishing matrix elements are
V I = < < i I V i j I ~ j > t + j ;
T/,= <qi
I
l / , i ( p i > and V3 = < prl V j jI
<i > i + jwhere p i , i = x, y, z are the p-type states of 3F(T,). Following the treatment of Slonczewski [2, 31 we get for the two magnetostrictive coefficients
3-100 =
3
(V2-
V,) Nf (T)I(Cl,-
C , 2) (1)and
where N is the number of Ni2+ ions per unit volume on
FREE ~d E X C H A N G E 5.0.
I0 N tetrahedral sites, C,,, C,, and C4, are the compo-
nents of the elastic tensor and
FIG. 1.
-
Energy level structure of a tetrahedral site Ni*+ ion,including exchange and spin or bit energy.
f
( T ) =(
cosh(3 A/2 k T)-
1)I
(
2 cosh(3 j.12 k T)+
1)
dominant effect is second-order spin-orbit coupling 2. Estimation of V, and (V,
-
V,).-
On the between the 3F(T,) and 3F(T2) triplets, the coupling assumption that the ions behave as point charges, the coefficient being about A =-
110 cm-'. The magne- contributions to the coefficients V i j have been calcu- tostrictive coefficients of the tetrahedral site Ni2+ lated for the first eight layers of ions neighbouring anCl-192 K. T. LIOLIOUSSIS AND A. J. POINTON
Parameter Fit to results Eqs. (3) & (4) Anisotropy [6]
-
-
-
VI
-
2.5 x 10-l2 ergs+
1.63 x 10-l2 ergs 3(v2-
v 3 )-
8.0 x 10-l2 ergs-
8.69 x 10-l2 ergsIZ
-
190cm-'-
138cm-'NiZ+ ion on a tetrahedral site in nickel ferrite stress along a chosen axis. The shift in the resonance (NiFe,O,). The results obtained are field was found to be linear with stress up to an applied force of 900 g at which value shifts of up to 160 Oe V 1 = 2 I e l <cp,IxyIcp,> x were observed. (A full discussion of the method has
been given by Liolioussis [6].)
]
(3) Typical experimental results for the changes in the measured values of the magnetostrictive coefficients and which occured on quenching the specimens are shown in figures 2 and 3. Results for quenching temperatures2 s ( V 2 - V 3 ) = 2 1 e I < p , 1 3 z 2 - r 2 1 q , > x T ( & :
Q"
C 1 0 0 2CI: 3 0 0 4 Q - 2 + Q-2 +...I
(4)+--
[T
~3~
6(JJ a)'(dii
a)' o C u E N c f i E D FlicIA 1052°C+ C ; x i q C " E D FRDI* l i ; " ? ~
where e is the electron charge, Q-2 is the charge of an 0'- ion, Q" is the charge on an Fe3' ion and a
is the lattice parameter. If the normalised p-type wave - 5 0 -
functions are taken as cD 0 9
x(5 x2
-
3 r2)cp, =
f
(r) J7/16 71 -- -- , etc. ,r3
where f ( r ) is the 3d electron radial wave function, then
FIG. 2.
-
The variation with measuring temperature of theand change in the magnetostriction constant L l o o produced by 8, quenching nickel ferrite speciment.
2 < q Z 1 3 z 2 - r I c p , > = - r 15 where T ( K : 0 2 5 0
-
353 - w r2 =I
1
f
(r)l2
r 2 . r 2 d r = 1.146 A' 0for the Ni2+ ion. (This value [4] is more accurate than
F Z C M 1 ~ 5 0 ' C
+
Q j E k C - E D F7?C'd "CC'Cthat taken in reference [3]). The values of V, and
5
(Vz - V3) obtained from equations (3) and (4), with - 5. no adjustable parameters, are given in table I above. a0 X
-
-
...
3. Experimental results.
-
Measurements have been rCQ
made of the coefficients A l o O and A,,
,
as a function of-10-
temperature for specimens of nickel ferrite in which Nizf ions had been trapped, against their normal site
preference, on tetrahedral sites when the ferrite was o
quenched from an elevated temperature. (The number
of NiZ+ ions so trapped has been estimated from the -1 5-
activation energy derived from the observed change in the magnetic moment [5].) The method of measure- ment involved the determination of the shift in the
value of magnetic field for microwave resonance when FIG. 3. - The v a r i a t ~ o ~ of the change produced in A 1 l l o n
T H E MAGNETOSTRICTION CONTRIBUTION FROM Ni2+ IONS ON TETRAHEDRAL SITES C1-193
Change in I.,,, and A , , , produced on quenching NiFe20, from 1 050 OC
Krishnan [8] Present work
Temperature AA,,, x lo6 AA,,, x lo6 AibloO x lo6 x lo6
A
-
-
-
4 K
-
107-
45-
62.6 - 12.6 77 K - 111 - 38-
60.5-
10.6 293 K-
32-
46-
32-
5.7of 1 050 OC and 1 100 OC are shown for both AA,,,
and AA,,
,
.
The parameters used in fitting the curves by equations (1) and (2) are shown in table I, the density of Ni2+ ions on A-sites being taken as, for example, 2.6 x 1019 ions/cm3 for specimens quenched from 1 050 OC. (It will be noted that the extrapolated value of A,,, for a ferrite having all Ni2+ ions on tetrahedral sites, namely-
-
3 x at 4 K, is considerably larger in magnitude than the corresponding value of-
-
6 x lo-' for ordered nickel ferrite.)The agreement between experiment and theory for the case of A,,, is extraordinarily good considering the simple nature of the theory even though the magnitude for the spin orbit coupling coefficient is rather smaller than the value of
-
343 cm-' which has been obtained by calculation [7]. In addition, it is seen that, as predicted, the temperature variation is the same for both A,,, and A,,,.
However, for A , ,,,
there is the same difference in sign between theory and experiment as was found by Slonczewski [2] for the Co2+ ion. Comparison with other experiments (Krishnan 181,Smith and Jones [9]) shows that, while there is agree- ment in sign and order of magnitude for both A,,, and A,,,, for both slow cooled and quenched specimens of nickel ferrite, only in the present work is there found a self consistent variation with temperature. This is illustrated in table 11.
The discrepancy between the present results and those of Krishnan et al. is not easily explained, parti- cularly since, in calculating the stress, the value of 0.9 nR2 was used for the effective cross-section as had been the case for the latter work.
4. Contribution from higher order states.
-
It is expected (see, for example, Abragam and Pryce [lo]) that there will be mixing of the 3P state of figure 1 with the lowest of the 3 F triplets, with which it shares the sames T, symmetry, through terms in the cubic crystals field. (The coupling of the 3F(T,) and 3F(T2) terms through the spin-orbit coupling is not important in the present context.) However, while in general this mixing may be taken into account by modifying the value of the orbital angular momentum, in the present case the wave functionI
cpi>
must be replaced byI
qcpi+
5p1 > where p i is the relevant term in the 3 ~ ( T , ) states and q2+
t2
= 1. Then, in equation (3), < cp,I
xyI
cp,>
must be replaced byand the term
-
1/307
bywhich, to give agreement with the experimental result for A,,
,
requires5
= - 0.27. T o first order in the crystal field potential Vc,5
=<
pi1
Vc [ cpi>/EPF
where EpF, the energy separation of 3P(T,) and 3F(T,) is not known exactly. If it is assumed that E,, is of the same order as the crystal field splitting of the 3F(A2) and 3F(T,) levels then we have
5
-
-
0.35. The sign and magnitude of the A,,, term may, there- fore, be determined by the cross terms from ) cp, > and1
pi>
in the mixed ground state while the corres- ponding effect on A,,, would be simply to increase the calculated value by some 30%.
References
[I] POINTON, A. J. and WETTON, C . A., 18th Annual Confe- [6] L ~ o ~ ~ o u s s r s , K. T., 1975, PhD thesis, Portsmouth Poly- rence on Magnetism and Magnetic Materials (Denver) technic.
1573, 1972. [7] BLUME, M. and WATSON, R. E., Proc. R. Soc. A 271 (1963)
[2] SLONCZEWSKI. J. C., J. Phy.7. Chem. Solids 15 (1 960) 335. 565. [3] POINTON, A. J. and L~oLIoussls, K. T., 19th Annual Confe-
rence on Magnetism and Magnetic Materials (Boston) [81 KR'SHNAN, R. and R I ~ ~ ~ R E , M.9 PhF. Stat. Sol. (A) 7
1237 (1973). (1971) 39.
[4] MICHEL-CALENDINI, F. M. 0. and KIBLER, M. R., Theor. [9] SM1.W A. B. and JONES, R. V., J . A P P ~ . P ~ J ' s . 37 (1966)
Chinr. Acta 10 (1968) 367-71. 1001.
[5] RORBRTSON, J. M. and POINTON, A. J., Solid State Comnzun. [lo] ABRAGAM, A. and PRYCE, M. H. L., Proc. R. Soc. A 206
