Pergamon

Solid State Communications,

Pergamon

Vol.

102, No. 8. pp. 583-588,

1997

8 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1098/97 $17.Mk.O0

PII: s0038-1098(!qooo37-9

HIGH TEMPERATURE

MAGNETIC

SUSCEPTIBILITY

OF Hg I_xFe,Se

B. BabiC Stojic,” Z. So&id,” M. Stojic,” A. Szytulab and Z. Tomkowiczb ‘Institute

of Nuclear Sciences “VinEa’ ’ , P.O. Box 522, 11001 Belgrade, Yugoslavia ?nstitute of Physics, Jagellonian University, 30059 Krakow, Poland

(Received 18 November 1996; accepted 21 January 1997 by G. Bastard) Magnetic susceptibility of diluted magnetic semiconductor Hg I_,Fe,Se (x = 0.04, 0.08, 0.11) has been measured in the temperature range 50300 K. Observed temperature dependence above 90 K is analyzed in terms of the high temperature expansion of the magnetic susceptibility developed for Fe-type diluted magnetic semiconductors. The nearest neighbour exchange constant is estimated as JNN/ks = (- 11 ? 3) K. At higher temperatures, considerable deviation of the magnetic susceptibility from the Curie-Weiss law is detected. 0 1997 Elsevier Science Ltd Keywords: A. semiconductors, orbit effects.

D. exchange and superexchange,

1. INTRODUCTION Diluted magnetic semiconductors (DMSs) are a class of semiconductor materials in which a fraction of nonmagnetic cations is replaced randomly by magnetic ions. DMSs based on II-VI compounds containing Mn2+ ions have been most extensively studied [l]. Substitutional Mnzf has a d5 electronic configuration and 6A I spin-only ground state. DMSs containing iron have been studied during recent years [2-61. Substitutional Fe2+ ions with d6 configuration has different energy spectrum. The ground state of a Fe’+ free ion is split by a tetrahedral crystal field into a 5E orbital doublet and a ‘T orbital triplet separated from 5E by A = 10 Dq, where Dq is the crystal-field parameter. The ‘E term, which determines the magnetic properties of Fe-type DMSs, is furthermore split by spin-orbit interaction into five closely spaced levels separated by energy gaps of about 6X2/10 Dq, where X is the spin-orbit parameter [7, 81. The ground state of Fe2+ ion is a magnetically inactive singlet A I resulting in Van Vleck-type paramagnetism. Reported data on the low temperature susceptibility of Hg l_,Fe,Se are somewhat different. The samples with low iron concentration (0.3% 5 x 5 2%) reveals a Curietype component in the total susceptibility which was attributed to the presence of Fe3+ ions [9]. It was suggested [9], that this behaviour results from the 583

D. spin-

specific position of the d6 level in the band structure of Hg l_,Ge,Se which is located about 0.2 eV above the bottom of the conduction band [lo]. In the wide gap DMSs such as Cdl_,Fe,Se, the d6 level is situated in the energy gap between the valence and conduction band [lo]. For higher iron concentrations, the magnetic susceptibility of Hg l _,Fe,Se is dominated by a contribution of Fe” ions. Reported high-temperature data for two samples with x = 0.05 and 0.10 show a Curie-Weiss behaviour with typical antiferromagnetic interactions between Fe ions [ 111. Antiferromagnetic coupling between Fe ions and Curie-Weiss dependence of the high-temperature magnetic susceptibility were also found in the wide gap Cdl_Pe,Se [ll], Znl_,Fe,Se [12], Cdl _xFe,Te [13] and Cd I_Pe,rS [5]. It was suggested [4] that the magnetic properties of all Fe-type DMSs are mainly determined by superexchange interaction resulting from the p-d hybridization. However, available data on the strength of d-d exchange interaction in Hgl_,Fe,Se are rather poor. So, we found it worthwhile to study the d-d exchange in this material more carefully. 2. EXPERIMENT Hg,_,Fe,Se crystals were grown by the Bridgman method. The zinc blende crystalline structure was checked by X-ray diffraction. The iron concentration

MAGNETIC

584

SUSCEPTIBILITY

Vol. 102, No. 8

OF Hg ,_Ee,Se

.

. -0

x=0.04”

0

Temperature [ K ] Fig. 1. Inverse magnetic

susceptibility

of Hg ,_,Fe,Se with x = 0.04, 0.08 and 0.11 as a function

was determined by atomic absorption analysis. The possible presence of manganese was investigated by atomic absorption and by EPR measurements. No such paramagnetic impurity was detected in the studied samples. The a.c. magnetic susceptibility was measured in the range 50-300 K using a standard mutual-inductance technique. The frequency of the applied a.c. field was 21.5 Hz. The data were corrected for diamagnetic susceptibility of HgSe which was found experimentally, Xd = -0.30 x 10v6 emu-’ g [ll].

3. RESULTS

AND DISCUSSION

Temperature dependences of inverse magnetic susceptibility of Hg ,_,Fe,Se with x = 0.04, 0.08 and 0.11 are presented in Fig. 1. Unusual behaviour of the susceptibility has been detected for all three samples at higher temperatures. For the sample with x = 0.11 a pronounced deviation from the Curie-Weiss dependence occurs above 200 K. For the samples with x = 0.04 and 0.08 large deviation from the Curie-Weiss law is seen at temperatures above 140 K. In Fig. 2 temperature dependences of the magnetic susceptibility for two samples with x = 0.04 and x = 0.11 are compared with the data for x = 0.05 and x = 0.10 taken from [ll]. We find that the susceptibility data for x = 0.10 and 0.11 are nearly the same at temperatures below 120 K, there is a certain disagreement

of temperature.

in the range 120-200 K and the difference between the two sets of data progressively increases at higher temperatures. The difference between our susceptibility data for x = 0.04 and those for x = 0.05 is somewhat larger than one could expect on the basis of the difference in the iron concentration in the entire temperature range studied. Hg l_,Fe,XSe is a zero-gap semiconductor with the conduction electron concentration about 5 X lOI cmm3 for x > 0.0003 [lo]. In order to estimate the contribution of the Pauli susceptibility to the total susceptibility, we have taken the Pauli term in the form [14]

(1) where m*/mo is the relative effective mass, n is the concentration and g is the effective g-factor of the conduction electrons. The electron effective mass was taken to be equal to that in HgSe, m*lmo = 0.06, for the same electron concentration n = 5 X 1018 cme3. The effective g-factor for the light I’s band was calculated from the expression [ 151 k&Pm - -23c~B

M, H’

(2)

where the energy gap Eo, the energy of the s-p interaction E, and higher band parameters 7 and K were taken to be the same as in HgSe [ 161. The coefficient k is the

Vol. 102, No. 8

MAGNETIC

SUSCEPTIBILITY

OF Hg i _Pe,Se

585

10

: .

a .

8

P .

2

0

I

0

100

I

I

Temperature Fig. 2. Temperature dependences of the magnetic susceptibility data for x = 0.05 and x = 0.10 are from [li]. proportionality factor between the mean spin of an Fe’+ ion and its magnetic moment, (S) = - k(M) and was calculated for Fe*+ ion in Cd i_,Fe,Se as k = 0.444 [ 171. Parameter No/3 is the p-d exchange parameter and for Hg,_,Fe,Se we have taken No/3 = - 1.7 eV [ 181. In the expression (2) m is the mass of a Hg,_,Fe,Se molecule, M, is the macroscopic magnetization per unit mass, H is the magnetic field and pB is the Bohr magneton. Taking for M,,,IH = x,,, the susceptibility data from this experiment, we have calculated the Pauli susceptibility according to equations (1) and (2) and found that, in the temperature range studied, the Pauli susceptibility makes about l-3% of the total susceptibility. So, the Pauli susceptibility cannot explain the large deviation of the measured susceptibility from the Curie-Weiss dependence at higher temperatures. We suppose that the large deviation of the observed susceptibility from the Curie-Weiss dependence cannot arise from the substitutional iron in regular lattice sites. A possible origin of the unusual temperature behaviour could be the presence of Fe*+ ions at interstitial octahedrally coordinated sites. The existence of Fe*+ interstitials was assumed in Zni_Pe,S as a possible source of permanent magnetic moments which should

I

250

200

150

1

[K]

for Hg i_,Fe,Se: x = 0.04 and x = 0.11 - this work;

produce an excess susceptibility at low temperatures [ 191. However, the concentration of such magnetic impurities in our crystals should be much larger than the concentration of Fe3+ ions found m Hg ,_,Fe,Se or estimated concentration of permanent magnetic moments in Zni_,Fe,S [19]. In the further studies of the magnetic susceptibility we focus our attention on the temperature range where the susceptibility shows predicted high temperature behaviour. High temperature expansion for the magnetic susceptibility of random diluted magnetic systems has been derived for magnetic ions having orbital and spin momenta [12]. This expansion is based on the crystalfield model, where the crystal field, spin-orbit interaction, magnetic field and Heisenberg type exchange interaction are taken into account. Applying this model to Hg l_,rFe,Se, we take the expression for the high temperature susceptibility in the form [12] Xltl

=

+

-fw

T 1’

(3)

where C,(x) is the Curie constant, c

m

(4)

MAGNETIC

586

I

I

100

150

SUSCEPTIBILITY

OF Hg 1_Pe,Se

Vol. 102, No. 8

0 *,.,.,.,.,.,., 0.00 0.02 0.04 0.06

0.08

0.10

0.12

0.14

Temperature [K]

Fig. 3. Magnetic susceptibility of Hg i_,Fe,Se presented as a product xm T* vs temperature. Straight lines represent the least squares fit of equation (6) to the experimental data. I

and 19(x)is the Curie-Weiss

=A+&+

I

(5)

In equations (4) and (5) N is the number of cations in the unit volume of the crystal,x is the atomic fraction of magnetic ions, p is the density of the material, kB is the Boltzmann constant, M, = Lz + 2S, is the z component of a single ion magnetic moment operator, L: and SZ are the orbital and spin momenta operators along the magnetic field direction, E is the energy operator of an isolated ion submitted to the crystal field and spin-orbit interaction, (a..) means the statistical average in the limit T - to, H - 0, z, is the number of cations in the pth coordination sphere and J, is the d-d exchange constant between pth neighbours. The high temperature susceptibility in the form (3), is taken, instead of the commonly used expression for the Curie-Weiss susceptibility C/(T - @, to avoid large errors in determination of the parameters e(x) and C,(x) which are present if the condition T + 0 is not satisfied. Equation (3) can be also written as x,,,T* = C,,,(x)T + C,(xV(x).

Y

temperature,

(6)

Experimental data for the magnetic susceptibility of Hgi_,Fe,Se are presented in Fig. 3, where the product x,T* is plotted vs temperature. Measured values were corrected for the diamagnetic susceptibility of HgSe and for the Pauli susceptibility. Expression (6) was fitted to the experimental data in the range 90- 130 K for the

o/l,.

0.00

0.02

, . , .,

0.04

0.06

0.08

. , ., 0.10

0.12

,I

0.14

Fe concentration x Fig. 4. Concentration dependence of the Curie constant C,(x) and the Curie-Weiss temperature e(x) for Hg,_,Fe,Se: full circles - this work; open circles values obtained from the susceptibility data in [ll]. Solid lines represent the least squares fit of equations (4) and (5) to our experimental data. sample with x = 0.04, in the range 90-146 K for x = 0.08 and in the range 105-190K for x = 0.11. Appreciable deviation of the observed susceptibility from the expected high temperature dependence can be also seen in this figure at higher temperatures. The values of the fitting parameters C,(x) and 0(x) are presented in Fig. 4 as a function of iron concentration. We have also performed the same analysis of the high temperature susceptibility of the samples with x = 0.05 and 0.10 [ 1 l] as it was done for our samples. Fit of the expression (6) to these data gives the values of the Curie constant and for the Curie-Weiss temperature which are also plotted in Fig. 4 for comparison. It is seen that there is a good agreement between the parameters C,(x) and e(x)

Vol. 102, No. 8

MAGNETIC SUSCEPTIBILITY OF Hg r_,Fe,Se

obtained in this work and those deduced from the previous experiment. Higher values of 8 parameter reported for Hgr_pe,Se in [ 1l] were obtained using Curie-Weiss law in the temperature range where this approximation could not be considered as the high temperature limit. Fit of the expressions (4) and (6) to our experimental data for C,(x) and I?(X)gives the following values of the parameters

A = (+4.0 2 10.0) K,

f?c= (-582 ? 130) K.

(7)

For iron concentrations studied in this work, the number of Fe3+ ions in Hg,_,Fe,Se is much smaller than the number of Fe2’ ions. Therefore, the total number of Fe ions N, is taken to be equal to the number of Fe2’ ions. The quantity (Mz), for Fe2+ ions can be obtained from equation (4) using the experimental value of the Curie conctant Ci which gives (M,2), = 11.2. We have also calculated the statistical averages entering equations (4) and (5). Starting from the Fe*+ single ion wave functions it was shown [12] that these averages are described by the crystal-field parameter Dq and the spin-orbit coupling constant X. For Hg I _,Fe,Se, we take [4] Dq = 293 cm-’ and X = - 85 cm-‘. With these parameters one obtains: (&

= 10.89,

(& = - 11.71 h2/10Dq = -28.88

cm-‘,

(i&S,), = 4.22,

(8)

(MZE), = - 130.76 X2/10Dq = - 322.44 cm- ‘.

Calculated averages in equation (8) give the value of the parameter A from equation (5), A = + 1.1 K. We find that the calculated (Mt>mvalue is quite close to that obtained from the experimental Curie constant. Difference between the experimental and calculated parameter A is larger, but this parameter should be considered as a very small quantity. Calculated averages in equation (8) and the experimental Curie-Weiss temperature 13~enable us to determine the nearest neighbour d-d exchange constant

587

in HgFeSe and in HgCdFeSe 161,n = 5, we find that JNN

1 r‘kB&,,,x

1.33

B

which gives 2=(-11

+3)K.

According to this result, the nearest neighbor exchange constant for Hg,_,Fe,Se is about two times larger than that for Hg,_,Mn,Se (J,&kB = - 6 K) [20]. Strongest nearest neighbour exchange interaction was also found in other Fe-type DMSs [5] compared with that in corresponding Mn-type DMSs. It seems that the observed increase of the p-d exchange parameter N& as one passes from Mn to Fe in the same II-VI host lattice [21] could account for this property. authors would like to thank the colleagues at the Institute of Physics of the Polish Academy of Sciences for crystal preparation. This research was supported by the Ministry of Science and Technology of the Republic of Serbia, contr. No. OlE15. Acknowledgements-The

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SUSCEPTIBILITY

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Vol. 102, No. 8

Twardowski, A., Swagten, H.J.M. and de Jonge, W.J.M., Phys. Rev., B44,1991, 2220. Galazka, R.R., Dobrowolski, W., Lascaray, J.P., Nawrocki, M., Bruno, A., Broto, J.M. and Ousset, J.C., J. Mugn. Mugn. Mater., 72, 1988, 174. Lascaray, J.P., Hamdani, F., Coquillat, D. and Bhattacharjee, A.K., J. Mugn. Mugn. Muter., 104-107, 1992,995.