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High field magnetostriction in a meta-magnetic FeRh alloy
J.A. Ricodeau, D. Melville
To cite this version:
J.A. Ricodeau, D. Melville. High field magnetostriction in a meta-magnetic FeRh alloy. Journal de Physique, 1974, 35 (2), pp.149-152. �10.1051/jphys:01974003502014900�. �jpa-00208138�
HIGH FIELD MAGNETOSTRICTION IN A META-MAGNETIC FeRh ALLOY
J. A. RICODEAU and D. MELVILLE
Department of Physics, The University of Southampton, U. K.
(Reçu le 24 août 1973, révisé le 24 septembre 1973)
Résumé. 2014 Des mesures de la magnétostriction, parallèlement et perpendiculairement au champ magnétique, ont été faites sur un alliage équi-atomique FeRh polycristallin.
La phase antiferromagnétique et la transition antiferro-ferromagnétique induite par le champ magnétique ont été étudiées jusqu’a 15 T. La magnétostriction antiferromagnétique perpendiculaire
est de l’ordre de 3 x 10-4 à 10 T et dépend de la température. La magnétostriction parallèle à 10 T
est de l’ordre de 5 x 10-5 et ne dépend pas de la température. La variation du paramètre du réseau
à la transition est en accord avec les mesures d’expansion thermique.
Abstract. 2014 Measurements have been carried out of the parallel and perpendicular magnetostric-
tion of a polycrystalline equi-atomic FeRh alloy. Measurements were made in pulsed magnetic
fields up to 15 T in the antiferromagnetic phase and at the antiferro-ferromagnetic transition induced
by the field. The perpendicular antiferromagnetic magnetostriction is of the order of 3 x 10-4
at 10 T and temperature dependent. The parallel magnetostriction at 10 T is of the order of 5 x 10-5 and independent of temperature. The lattice parameter change at the transition agrees with the value found in thermal expansion measurements.
Classification
Physics Abstracts
8.570
1. Introduction. - The properties of the ordered
equi-atomic FeRh alloy have been extensively inves- tigated during the last decade. Most of the references
can be found in the article by McKinnon, Melville and Lee [1]. The alloy orders with the CsCI structure and exhibits a first order phase transition at a tempe-
rature (To) around 320 K. This transition is accom-
panied by a volume change of approximately 1 % and
is associated with a change from antiferromagnetic (af ) .
to ferromagnetic (f) ordering as temperature is increased. At temperatures below To the af-f transi- tion can be excited by applying a magnetic field (H,).
Several workers have found a linear relation between
H,, and T, but McKinnon et al. and Flippen [2] report
a parabolic dependence
This dependence has been recently confirmed by
Ponomarev [3]. The latter relation is more satisfac- tory thermodynamically and has been shown (Lom-
mel [4], McKinnon et al. [1], Ricodeau and Mel- ville [5]) to conform to existing theories.
The earliest theory to be applied to FeRh was the exchange inversion model of Kittel [6]. In this approach the transition is considered to take place
because a volume dependent exchange interaction is
driven from a negative (antiferromagnetic) value to
a positive (ferromagnetic) value by the thermal
expansion of the lattice.
A characteristic feature of the exchange inversion
model is the existence of a critical value a, of the lattice parameter. The af-f transition takes place
when the lattice parameter is brought to this critical value. Although indirect comparisons with exchange
inversion theory made by Zacharov et al. [7] and
McKinnon et al. [1] have shown large discrepancies,
no direct check for the existence of a critical lattice parameter has been made. Such considerations sug-
gested the measurement of magnetostriction, since
at temperatures below To where a a~ the critical value of lattice parameter can only be reached through
the existence of a large magnetostriction in the antiferromagnetic region.
I he thermal expansion of FeRh has been measured in zero magnetic field over a wide range of tempera-
ture (Zakharov et al. [7], Zsoldos [8], McKinnon
et al. [1]). Levitin and Ponomarev [9] measured in pulsed magnetic fields the longitudinal magneto- striction at the transition only. We present here mea-
surements of longitudinal and transverse
magnetostriction in the antiferromagnetic phase and
of the strain discontinuity 11 and at the af-f
transition.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01974003502014900
150
2. Experimental details. - Magnetic fields of up to 15 T were produced by capacitor discharge into
copper wire-wound coils. Measurements were taken
on the exponentially decaying part of the field pulse
which has a time constant of about 70 ms. The strain gauge technique used to measure magnetostriction
has already been fully described (Ricodeau et al. [10]).
The magnetic field can be determined to + 3 % while
the error involved in magnetostriction measurement is typically ± 7 % at 10 T. The maximum sensitivity
is 5 x 10 - 6 strain equivalents.
The specimen was an alloy containing 51 1 at % Rh
whose preparation has already been described by
McKinnon et al. [1]. The sample was spark machined
to the form of an approximately rectangular paralle- lopiped of dimensions 6 mm x 4 mm x 1 mm and strain gauges were attached to the largest face.
3. Results.- 3.1 MAGNETOSTRICTION AT THE af-f
TRANSITION. - Figure 1 shows the magnetostriction
at 239 K for fields sufficiently large to induce the af-f transition. The size of the strain discontinuity (As)
differs slightly for the two situations where the gauge is parallel and perpendicular to the field. This is not
surprising since the magnetostriction in the af phase
differs for the two orientations. The large hysteresis
is in agreement with that found in magnetization
measurements.
FIG. 1. - Magnetostriction at the antiferro-ferromagnetic tran-
sition.
Llé:11 11 is found to be independent of temperature within experimental error while LlE 1- varies slightly
with temperature. This may be due to the fact that )’1-
varies with temperature in the af phase.
The values obtained are
Thermal expansion measurements on the same
sample gave at the zero field transition temperature of 328 K = (2.5 + 0.1 ) x 10 - 3. The agreement with the relation = 3 jj + ~ is quite good,
taking into account the temperature dependence
of Excellent agreement is not expected since AE I, and AE1 contain magnetostrictive effects not present in
Because of the large entropy change associated
with the transition (AS = 15 J /kg-l /K -1) and the pulsed nature of the field, magneto-caloric effects
must be taken into account. The temperature change
is given by
AT = - Teat the transition C
or by
within a given magnetic phase, where M is the sub- lattice magnetisation and C the specific heat. In the
af phase this correction was found to be negligible (0.2 K) but at the transition it can be as large as 10 K.
The data to compute the magneto-caloric effect is
taken from Ricodeau and Melville [5].
Figure 2 shows a plot of critical field versus T2 with magneto-caloric corrections. These results confirm relation (1) with the values
FIG. 2. - Temperature dependence of the critical field from
magnetostriction measurements.
Using these values in the Clapeyron equation and assuming a magnetization change,
we get an entropy change at the zero field transition,
3.2 MAGNETOSTRICTION IN THE ANTIFERROMAGNE- TIC PHASE. - In figure 3 we show the longitudinal (Jw « )
and transverse magnetostriction in the af phase.
FIG. 3. - Magnetostriction in the antiferromagnetic phase.
FIG. 4. - Volume magnetostriction in the antiferromagnetic phase AV/V = 3 E0 .
The curves are those obtained in that part of the pulse
where the field is slowly decreasing. The shape of
the curve was found to depend on the highest field applied in the pulse if this was sufficiently intense to partly induce the transition. It can be seen that unlike is temperature dependent. Figure 4 shows the
volume strain
4. Discussion. - Magnetostriction in antiferro- magnetic materials has received little experimental
and theoretical attention. We can only attempt to point out the interesting features of figures 3 and 4
and relate them to other properties of FeRh.
In figure 3 it can be seen that the curves for tem-
peratures of 142 and 134 K cut through the other
curves. This corresponds to the fact that at these temperatures the maximum field in the pulse is large enough to partly induce the ferromagnetic phase.
Since the magnetostriction is measured at decreasing
field it is to be expected that the hysteresis of the
transition will account for this behaviour. The modi- fication at fields less than 2 T is however likely to be
associated with the antiferromagnetic domain struc-
ture. It would be expected that when the material is
returning from a high field ferromagnetic state the
final domain structure will be different from that found in the normal antiferromagnet. This appears to show itself in a change in sign of the initial magne- tostriction.
The large antiferromagnetic magnetostriction is to
be compared with the large antiferromagnetic suscep-
tibility [3], [11] of this phase 1.4J/kg~/T’~).
Let be the angle of the antiferromagnetic
sub-lattice moments relative to their direction in
zero field. The af phase corresponds to oc = 0 and
the f phase to a = ~c/2. We will make the simple assumption that the quantity So defined in eq. (2)
varies sinusoidally with the angle a i. e.
where a(x) is the lattice parameter for a particular
value of a and 8o(7r/2) = Aet, = 2.5 x 10-3.
This assumption is made to obtain agreement with the somewhat linear field dependence of 80 shown in figure 4 but it cannot at present be justified theoretically. (The sharp change of slope of the magnetostrictive curves at fields of about 2 T may
correspond to a value of field large enough to induce
the rotation of the aligned direction of the antiferro-
magnetic domains.)
The angle x may be estimated from the antiferro-
magnetic susceptibility. We have laf = 1.4 /T -2
which is equivalent to the appearance of 4 x 10-2 per FeRh. The total moment per FeRh is 4 it,. If
we assume that Xaf is due mainly to zi the appearance
152
of 4 x 10-2 PB T-1 is due to a canting of the moments by an angle a = 10 - 2 rad T -1. Using this value in
eq. (3) we get 80 = 3 x 10-sIT. For a field of 10 T
we find Eo = 3 x 10 -4 compared to the experimental
value of 2 x 10-’. This order of magnitude agree- ment serves to indicate the relation between the
antiferromagnetic susceptibility and magnetostric-
tion. We cannot however account for the anisotropy
of the magnetostriction. This may be related to the electronic band structure as well as the interatomic .
exchange and their field dependences.
It is likely (Pal [12]) that !J1 antiferromagnetic FeRh
the sub-lattice structure is such that the intra-sub- lattice interaction is ferromagnetic and strong, thus accounting for the high Neel and Curie temperatures.
However the inter-sub-lattice interaction is antiferro-
magnetic and weak leading to the large susceptibility
and magnetostriction of the af phase.
It is possible to estimate the magnitude of the two exchange interactions a, and 3af as follows.
If a, is related to the ordering temperature ( ~ 700 K)
we can estimate
3f ~ 10 - 21 J/at .
We can write for the change in exchange energy when
a magnetic field H is applied to the af phase
where N ( ~ 4 x 1 O24 kg-’) is the number of magne- tic atoms, Z is a numerical factor (~6) taking into
account the number of nearest neighbour interac-
tions and 0 = x - 2 a is the angle between sub- lattice moments. Taking S = 1 we obtain for the
antiferromagnetic exchange integral
This value accounts for the higher energy of the f phase = 2.2 x 103 J/kg-1 of Ricodeau and Melville [5]) if it is assumed that in this phase the antiferromagnetic exchange interaction is being opposed.
Although it is large the antiferromagnetic magne- tostriction is not sufficiently large to support the exchange inversion theory proposed by Kittel [6].
As outlined above, this theory assumes that the tran-
sition takes place at a constant critical lattice para- meter value which corresponds to a change of sign
of the exchange interaction. For this theory to hold
the difference between the lattice parameter at a
particular temperature, and that at To must be made
up by the antiferromagnetic magnetostriction, before
the transition can take place at the same given cri-
tical lattice parameter. From thermal expansion data given by McKinnon et al. [1] the value of the lattice parameter deficit at 123 K is Aala = 1.6 x 10 - 3.
This is to be compared with the value of ~,1 of 4 x 10 - 4
shown in figure 3 for the antiferromagnetic magne- tostriction required to induce the transition. Thus Ai
is a factor of four too small, while )"11 is small by a
factor of about 20.
5. Conclusions. - Metamagnetic Fe Rh alloys dis- play a significant dependence of lattice dimensions
on their magnetic state. This dependence cannot be
accounted for by simple exchange inversion theory.
It was proposed by the authors [5] that the electronic band structure dependence of interatomic exchange
interactions should be taken into account but a
quantitative theory is not yet available. The large antiferromagnetic magnetostriction can however be
simply related to the magnetic susceptibility of that phase.
References
[1] MCKINNON, J. B., MELVILLE, D., LEE, E. W., J. Phys. C (Metal Physics) 3 (1970) Suppl. 1 546.
[2] FLIPPEN, R. B., J. Appl. Phys. 34 (1963) 2026.
[3] PONOMAREV, B. K., Sov. Phys. JETP 36 (1973) 105.
[4] LOMMEL, J., J. Appl. Phys. 40 (1969) 3880.
[5] RICODEAU, J. A., MELVILLE, D., J. Phys. F 2 (1972) 337.
[6] KITTEL, C., Phys. Rev. 120 (1960) 335.
[7] ZAKHAROV, A. I., KADOMTSEVA, A. M., LEVITIN, R. Z., PONYA- TOVSKII, E. G., Sov. Phys. JETP 19 (1964) 1348.
[8] ZSOLDOS, L., Phys. Stat. Sol. 20 (1957) K 25.
[9] LEVITIN, R. Z., PONOMAREV, B. K., Sov. Phys. JETP 23 (1966) 984.
[10] RICODEAU, J. A., MELVILLE, D., LEE, E. W., J. Phys. E 5 (1972) 472.
[11] ZAVADSKII, E. A., FAKIDOV, I. G., Sov. Phys. Solid State 9 (1967) 103.
[12] PAL, L., Acta. Phys. Hung. 27 (1969) 47.
