STRESS MODULATION EFFECT ON TRANSMISSION AND RESISTIVITY NEAR THE CURIE TEMPERATURE

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STRESS MODULATION EFFECT ON

TRANSMISSION AND RESISTIVITY NEAR THE CURIE TEMPERATURE

J. Nadai, J. Lascaray, J. Desfours, M. Averous

To cite this version:

J. Nadai, J. Lascaray, J. Desfours, M. Averous. STRESS MODULATION EFFECT ON TRANSMIS-

SION AND RESISTIVITY NEAR THE CURIE TEMPERATURE. Journal de Physique Colloques,

1980, 41 (C5), pp.C5-87-C5-91. �10.1051/jphyscol:1980516�. �jpa-00219951�

JOURNAL

Colloque C5, supplkment au no 6 , Tome 41, juin 1980, page C5-87

STRESS MODULATION E F F E C T ON T R A N S M I S S I O N AND R E S I S T I V I T Y NEAR THE C U R I E TEMPERATURE

J.P. Nadai,

J.P.

J.P.

Universite' des Sciences e t Techniques du Languedoc, Centre drEtudes drEZectronique des ~ o ~ i d e s ' , PZ.

BatailZon

MontpeZZier Cedex - France.

Rgsum6.- La piezor6sistance et la piezotransmission de EuO montrent un comportement critique prBs de T C . Quand T dScroTt, dans le domaine paramagn6tique les signaux de piezorgsistance et de piezotransmission augmentent, passent par un maximum, puis diminuent trSs rapidement. 11s inversent leur signe et prgsentent un minimum dans le domaine ferromagn6tique. De plus, la piezor6sistance prgsente une structure

une tempgrature voisine de la transition isolant-m@tal. La variation dans la rggion paramagngtique est maintenant bien comprise, et est due

la variation de lt6nergie d'gchange avec la contrainte. Les effets de piezoresistance et de piezotransmission sont dtorigine diffgrente dans la region ferromagn6tique. Le premier effet est

au dgplacement de Tc avec la contrainte. La structure au voisinage de la tempgrature de la TIM gtant liBe

l'effet de contrainte sur le piegeage des Blectrons des polarons magnetiques. Le changement de signe de la piezotransnission provient de la prgsence de domaines magngtiques. L'application d'un faible champ magngtique inverse le signe et le spectre de piezotransmission correspond alors

la d6riv6e des

fonctions de correlation de spin.

Abstract.- piezoresistance and piezotransmission of EuO show a critical behaviour near the Curie temperature. When T decreases in the paramagnetic range towards TC, the piezoresistance as well as the piezotransmission increase, pass through a maximum, then decrease very fast, invert their sign at T C and in the ferromagnetic range exhibit a minimum and increase.

The piezoresistance in addition shows another peak near the temperature of the

isolant metal transition. In the two cases, the paramagnetic part is wellunderstood, and due to the change of the second order exchange energy

with the s t r a i n . ~ h e

ferromagnetic part of the piezoresistance and piezotransmission temperature depen- dence are due to different phenomena-The change of sign of the piezoresistance is explained only by the shift of T c under strain, and the second peak below T C by the pressure effect on the self trapping of electrons on magnetic polarons.The change of sign of piezotransmission effect is due to the presence of magnetic

domains very sensible to the strain-The application of a small magnetic field gives a piezotransrnission spectra which corresponds to the derivative of the spin corre- lation functions.

Introduction.- The stress modulation tech- nique on usual physical properties, like resistivity or transmission for instance, is an interesting one, because the deriva- tive nature of the effect consideratly enhances the structure in comparison with ordinary resistivity or transmission. Thus, much higher resolution and sensitivity can be obtained. This technique ena-ble us to point out in magneiic semiconductor like EuO, the phenomena due to lattice effect and magne- tism effect versus temperature. In this paper we report results obtained as well as in transport measurements than in optical ones and we try to explain them with an unique point of view.

le

associd au C.N.R.S. L.A. 21.

1.

Piezoresistivity .- The change of resis- tivity under uniaxial compression modulate2 stress of EuO has been studied in the tem- perature range 6-300K. The stress is paral- lel to the crystal axis which is oriented in (100) direction. Figure 1 shows the resistance versus temperature for a studied sample. A peak can be shown near the Curie temperature and a shoulder exists between 60-70K. The piezoresistance curve (1 _{R d X} ^dR)

versus temperature is given in figure 2.

The piezoresistance coefficient (nll, in this case, in the Smith notation /I/), is zero at room temperature and low tenpera- tures, it exhibits two extrema on each side of 76K and changes its sign at this ternpe- rature .

The stress variation of the resistance

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980516

JOURNAL DE PHYSIQUE

involves essentially two contributions.

dLnp dLnp

- - ^dLn

dx dx

lattice

magn .

The first term is a lattice contribution, the second one arises from the strainmodu- lation of the exchange constants between Eu spins and consequently the modulation of the Curie temperature.

We study now separately each contribution.

dLnp corresponds exactly to the'

T ' lattice pienoresistivity phenomena in classical semiconductor, when the exchange energy is zero.

It depends of the band struc- ture / 2/.

Fig.1

Resistivity temperature dependence of EuO studied sample.

Sig.2

Modulated piezoresistance tempera- ture dependence.

If the minimum conduction band is situated at the center of the Brillouin zone, with a spherical symmetry, the application of an

uniaxial compressionnal stress in (100) direction gives only a deformation of the shape whithout displacement of the band, and a "so-called" minor effect in piezore- sistivity measurement is observed. If the minimum conduction band is situated in X point, the band is a multivalley one, and under the same stress as defined above; the degeneracy between the valleys is removed and the electrons of the higher valleys are transferredtothe lower ones.Thus it appears an anisotropy in the conductivity tensor, but the total number of carriers is unchanged.

So the study of the anisotropic of the conductivity under stress gives information on the symmetry of the conduction band mini- mum. In EuO it has been shown /3/ that the minimum corresponds to a 5d band.

When the material is degenerate, the piezoresistance effect is screened through the Fermi Dirac function which is constant,

dLnp

and we obtained - ⁼

as in our case.

ax

*)mag which is the magnetic part could be

ax written as follow.

dLnp) -dLnp

- _ax

mag arc dx

and because p is a function of T-Tc dLnp dTc dLnp T c

-

dTc dx dT dx

In a previous work /3/ we have determined d Tc

under hydrostatic pressure - and find the dP

same value (0.48K/Kbar) as obtained by susceptibility measurement by Argyle et al.

/4/ and Stevenson et a1./5/. Under uniaxial strain the curve has the same shape that the curve obtained under hydrostatic pres- sure near Tc. We can thus conclude that near Tc, the resistivity peak is due to the effect of the strain on Tc. We obtained

dTc = 0 .O5K/Bar. This value is smaller by a factor 10 than the one obtained under hydro- dx static pressure, but it is not surprising, because the effect of uniaxial strain on magnetic interaction is smaller than the

effect of a hydrostaticpressure as demonstrated by ~artholin and Block /6/.

dLnp dTc versus T Figure 3 shows - - -

dLnp d~

where is deduced from figure 1, and

dTc 0.05K/bar. It can be shown that

figure dx 2 and figure 3 are exactly the same, this a good test of the validity of our assumption; in the vicinity of Tc, the piezoresistivity effect is due mainly to the effect of the uniaxial stress on magne- tic interaction.

* ^A

Fig.4a

Classical shape of transmission spectra versus energy.

dLnp dTc 4b

lodulated piezotransmission ATr Fig.3

Shows the variation of-- - versus energy. The max. corresponds to the versus temperature where dLnp isadeducd% inflexion point of 4a.

from figure 1 . ^{a 4c}

Piezotransmission ^{A Tr} versus energy. The max. corresponds to the infle- By piezoresistance measurement a critical xion point of the absorption coefficient a.

behaviour could be observed near the Curie

We stqdied here dL:pTr. Compared to the temperature. It is explained by the pressure piezoresistivity a supplementary parameter

effect on magnetic properties. At high dE

is introduced which is dp.

temperatures and low temperatures, the

d : : T

r spectra versus the In figure 5, the -

piezoresistance effect is due to the

enerav could be seen at various T. In the -

pressure effect on the electrons phonons paramagnetic range. (T>69R) they have the interaction. shape of figure 4 c . The amplitudeof the peak 2. Piezotransmission.- The piezotransmission increases when towards Tc.

method is now a well known technic /7/,/8/ crosses Tc the. curves reverse their sign, Figure 4a shows a classical transmission and the anplitude of thep'eakdecreaseswith T.

spectrum versus energy. Figure 4b shows the modulated transmission called A

which is

dTr dE

proportional to AP, and figure 4c shows the piezotransmission ATr proportio-

:: :: ^{AP. T ~ U S} the maximum of figure nal to - -

4b corresponds to the inflexion point of the figure 4a curve whereas, the maximum of figure 4c corresponds to the inflexion point of the absorption coefficient a.

As demonstrated by

.P. Lascaray

when a coplanar strain is applied on a EuO samples, we observe mainly the effect of

the isotropic part of the strain and it is Fig. 5

Piezotransmission spectra versus possible to assume that

dLn Tr dLn Tr energy at various T .

d x # T

JOURNAL DE PHYSIQUE

Figure 6 shows the evolution of the E is a function of T-Tc (red shift) peak amplitude withT. The point is the - ^dE dP could be written ^{dE dTc} - -

- - ^{dE dTc} -

critical behavior at Tc. dTc dP dT dP

- '5 is rather constant with temperature and taken equal to 0.48K/Kbar

.

Consequently - ^dLnTr) is proportioned to

dE dP mag

-- dP

The red shift is due to the variation of the exchange energy with T I so r dE T ^varies

like the derivative of the spin correlation

150 200 250 K

function~with respect to T/13/. Again, in the paramagnetic range near Tc the results are explained by the above discussion

L U ^{(Fig. 3) .} In the ferromagnetic range the

sign is in contradiction with this argumen-.

A Tr tation.

Fig .6

Variation of the

with the

temperqture . ^{Tr max} In the paper of Lascaray et a1./14/,

:

at zero magnetic field in session

it has been demonstrated that

+

at 950 oersteds

this surprising result in the ferromagnetic We can write again

range is due to magnetic domains light dLn Tr

dLn Tr)

- - ^{dLn Tr}

dP dP lattice dP magn 1

The~first term must be predominant at higher temperatures and lower temperatures when the spin system is completely disoriented or completely oriented

dLn Tr

- ^{da dE)}

dP 'lattice dE dP lattice

The transition energy corresponds to the well known 4f-5d transition /lo/ and thus the term a dE is the pressure coefficient of this transition due to the pressure effect on the electrons phonons interaction.

At various

the absorption coeffi- cient u versus temperature is shifted paral- lel to itself, thus da is rather constant.

dLn Tr

Consequently is proportional to

U Z

dE At higher temperatures the results dP

obtained is coherent with the Wachter's one /1'1/ (dE dP = -4.4 meV/Kbar) or the dE Desfour' s one /3/

= -5. heV/Kbar) but at low temperature, the opposite sign is very surprisinaand we shall explain it

diffusion. Under small magnetic field (950 oersteds) the piezotransmission spectra are reverse and the figure 6 (dotted line) is in complete agreement with the explanation proposed above.

Conclusion.- Stress modulation technique has been used as well as in transport measurements (resistivity) than in optical ones (transmission) . In the two cases, a critical behavior is observed near . ^In

piezotransmission the problem is complicated by the presence of magnetic domains under Tc. If a weak magnetic field is applied in

piezotransmission, the transport and optical measurements could be explained in the same way. At high and low temperatu~s there is a pressure effect on the lattice;

in the intermediate temperature range, the more important effect is a pressure effect on the spin correlation functions.

later.

The second term becomes dominant, when the magnetization varies very quickly with T , ^{i .e} . ^{near Tc} .

dLn Tc) - - - ^{da dE,}

dP magn dE dP magn .

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