Electronic and magnetic structure of Fe ions in NiCr2S4Jae Yun Park, Heung Moon Ko, Woon Hwa Lee, Sang Hee Ji, and Chul Sung Kim

Citation: Journal of Applied Physics 73, 5739 (1993); doi: 10.1063/1.353609 View online: http://dx.doi.org/10.1063/1.353609 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/73/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Structural and magnetic resonance investigations of CuCr2S4 nanoclusters and nanocrystals J. Appl. Phys. 116, 054302 (2014); 10.1063/1.4891993 Magnetic anomaly around orbital ordering in FeCr2S4 J. Appl. Phys. 109, 07E144 (2011); 10.1063/1.3562449 61Ni Mössbauereffect studies of the hyperfine interaction in the magnetic spinel NiCr2O4 J. Appl. Phys. 49, 269 (1978); 10.1063/1.324378 NMR in HgCr2S4: Dependence on Magnetic Structure J. Appl. Phys. 40, 1022 (1969); 10.1063/1.1657512 Magnetic Structures in FeCr2S4 and FeCr2O4 J. Appl. Phys. 35, 954 (1964); 10.1063/1.1713556

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Electronic and magnetic Ftructure of Fe ions in NiCr2S4 Jae Yun Park Department of Materials Science and Engineering, Incheon University, Incheon 402-749, Korea

Heung Moon Ko, Woon Hwa Lee, Sang Hee Ji, and Chul Sung Kim Department oj- Physics, Kaokmin Univemity, Seoul 136-702, Korea

The magnetic semiconductor Ni,Fet-,Cr& (x=0.985, 0.97, 0.96) has been investigated over the temperature range from 12 to 600 K using a Mijssbauer technique. The electronic structure of Fe ions in NiCr& was calculated with the Hamiltonian incorporating free-ion term, axial and rhombic crystal field, spin-orbital couplings, and exchange interactions. The ground orbital state is separated by 9.64 ]A] from the first excited state, thereby making the quadrupole splitting somewhat insensitive to temperature. Using x-ray crystallographic data, the contribution of direct lattice sum to the electric-field gradient has been considered. In calculating the temperature dependence of quadrupole splitting, the axial field parameter At = - 3.0 1 /i. I, the rhombic field parameter A, = - 2.8 1 ,I I , and the covalency factor a2=0.73 in NicsssFecoIsCr+S4 were determined. Magnetic hyperfhte and quadrupole interactions in the antiferromagnetic state of Ni0.96Fee03CrZS4 at 12 K have been studied, yielding the following results: H= 147.8 kOe, +&p(l+f$)t~~= - 1.96 mm/s, 0=&Y, Q; =90”, and q= 1.0. The line broadening which suggests the electron relaxation was observed with decreasing temperature.

I. INTRODUCTION

There have been a number of investigations of the elec- trical and magnetic properties of a number of ternary transition-metal chalcogenides with the formula A B2& (A, B-Fe, Co, Ni, Ti, V, Cr: X=S, Se, To) .tw5 Several compounds were prepared that were isostructural with Cr$+ NiCr& exhibits the monoclinic defect Ni-As struc- ture at room temperature. Andron and Bertaut’ carefully determined that the magnetic properties of NiCr,S, are antiferromagnetic at 4.2 K in a neutron-diffraction study. The susceptibility curve does not show a sharp peak at the N&l point and does not follow Curie-Weiss behavior above this point. Morris and co-workers’ reported that this may be interpreted as the competing interaction between five different superexchange interactions. A cubic spine1 N&Fe, ,-,Cr$~ (O.O<x<O.3) has shown that Curie temper- ature Tc increases with Ni substitution, which can be ex- plained with increasing A-B interaction strength.”

In this article the electronic energy levels of an Fe ion in Ni,Fet~~ -XCr2S4 (x=0.985, 0.97, 0.96) and the effect of Fe ions on NiCr.& are reported using Miissbauer and s-ray data.

II. EXPERIMENTAL PROCEDURE

The samples were prepared by reaction of stoichio- metric amounts of the high-purity elements, Ni (99.99%), Fe (99.995%), Cr (99.999%) and S (99.999%) in an evacuated quartz ampoule. For the heat treatments, the mixture was fired at 480 “C for 1 day and at 1000 “C for 4 days, and then slowly cooled down to room temperature at a rate of -10 “C/h. The second firing at 1000 “C! for 4 days, with intermediate grindings, was necessary to achieve homogeneity.

The sample was enriched in 57Fe for Miissbauer mea- surement. X-ray-diffraction patterns showed that the sam- ple had the defect Ni-As structure (monoclinic 12/m).

Mossbauer spectra were obtained using a conventional Mossbauer spectrometer of the electromechanical type with a 57Co source in a palladium matrix.

Ill. THEORY

The Fe’+ ions of Ni,Fet-,Cr& (x=0.985, 0.97, 0.96) are in octahedral sites, surrounded with six S2- ions. The ground term 5D of the free Fe” + ion was split into the 5T,g level and ‘Eig level by the octahedral crystal field,6

V,,,=-~D,(35L~-155L~-tl2--5Jz[L:(2L,+3)

+L:(~L,-3)13. (1)

We obtain five orbital eigenfunctions, +i (i= 1,2,3,4,5), by diagonalizing 5x5 perturbation matrix (2ML 1 V,,, 12&f>) (M&f; = 0, f 1, f 2). However, the ‘Eg level was separated by as much as 1ODq ( - 14 400 K) from “rZP So we do not need to consider the ‘Eg level. The 5T? level will be split more due to axial cryst.al field and rhombic crystal field,7

V,,M=-A,(&2), (2)

V rhombic=-$2(L?+ + LL), (3)

and we can remove the spin degeneracy of the ‘TQ level, considering the spin-orbit interaction

v,=F --/zLS, (4)

where the spin-orbit coupling constant A can be expressed by ,I =(r2& under consideration of the covalency effect (a2; covalency factor, /2,=103 cm-’ for the free Fe’+ ion).* Letting +!Q refer to one of the three orbital eigenfunc- tions in the ‘T2, level, and ,yi to one of the five spinors corresponding to S=2, there will now be 15 state functions of the form

Y,=I,!J~~ (i= 1,2,3; j= 1,2,3,4,5). (5)

5739 J. Appl. Phys. 73 (IO), 15 May 1993 0021~8979/93/ 105739-03$06.00 @ 1993 American Institute of Physics 5739

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Diagonalizing the 15 x 15 matrix,

Hi,= Wu, 1 H’ 1 *yl> (6)

Y (H’=Vaid+ Vrho&ic+vgos W=1,2,3,-*- ,15)

will give the energy eigenvalue I?,, and eigenfunction via computer,

15 @,= 2 .4,,Y, [m,n= 1,2,3 ,... ,115). (71

!?I=1 Assuming thermal transitions, the electric-field gradi-

ent (EFG) tensor of the vaIence electron taken over the above 15 states <p, at temperature Tbecomes the following statistical average:

( vij)vd=

%I<@,] FtjIQ,)exp(-E,JkT) ZtL *exp( -E,/kT) ’ (8)

whereas the direct lattice contribution to EFG from the surrounding ions can be calculated by the form

( FJAt= ( - 14/e) (AI/@) 1, (9)

(F-L- F$,h= (We)&/(?)>. (10)

The total EFG tensor can be written as

( F7f$ = ( 1 -RI (( F’ij>vaI) + (1 W-Y,,, I( v~j)~at(hj=-~~), (11)

0.04 100 K

0.05

0,06 t--

0.00 -

0.01

0.02 -

0.03 -

0.04 I 1.2 K

0.05 I _.._L__L J___... -12 -6 -4 0 4 6 12

FTFLLOGITY (mm/s)

FIG. 1. Mijssbauer spectra of N&~q,Fq,,&r2S4 at low temperature. The first and the eighth linewidths (IT) are shown.

0.00 0.02

0.04

0.06 0.06 0.10

3 O.OO

5 0.02

8 0.03

1 0.04

0.06

0.00

0.01

0.02

0.03

0.04

ko.36

295 K * l

+$z+sG$+$ $i?$** 1 ..- .

'r=o.ss

800 K

0.05 - -I- L-L _-...A -.... i... 1, _L_

1” ^ --l#z -n -4 ” 4 6 12

VELOCITY (mm/s)

FIG. 2. Mijssbauer spectra of Ni0,,&,&r2S, near the N&e1 tempera- ture. The first and the second linewidths (I-) are shown.

where (( Yjj) )v.a, is the statistical average of the EFG ten- sor of the valence electron, and the Stemheimer factors ( 1 -R ) and ( 1 - y, ) represent the effect of polarization of the ferrilike (6S,3ds) core by the EFG of t.he valence and lattice charge distributions. This 3 x 3 EFG matrix must be diagonalized to obtain the principal values ( VX~5t), ( P’,,,Y,), and ( V,,,). The quadrupole splitting can be written as

AEp= (eQ/2) ( Vzfzf) (1 +$r$)“2, (12)

where Q is the nuclear quadrupole moment of the 14.4 keV state in 57Fe, and q is the asymmetry parameter of the EFG. x’, y’, z’ axes are chosen in such a way that

I (VW) I ;2 I ~~y’,J I > I ( F’xkf> I *

IV. RESULTS AND DISCUSSION

The structures of Ni,Fel-,Cr2S4 (x=0.985, 0.97, 0.96) were found to be monoclinic. with similar cell param- eters using x-ray diffraction. The lattice constants of Ni,-,gs,Feo.O&rzS~ are a=5.890 A, b=3.409 & c= 11.09 %L, and /3=91.40”.

The most characteristic Miissbauer spectra of Nii.96Fe0.04Cr2S4 at various temperatures ranging from 12 to 600 K are shown in Figs. 1 and 2. Above the Ntel temperature T, of 190 K the Mijssbauer spectra consist of two lines split by quadrupole interaction of 57Fe nuclei with the axially symmetric EFG by surrounding electric

5740 J. Appl. Phys., Vol. 73, No. IO, 15 May 1993 Park et al. 5740

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I-- _ ----____? -4.0

3 -8.0

h 2 -2.0

5 -1.0

0.0 i N-&uasF~aoraCrr~+ .._r--ii_l.lL-l -1 l--i

0 2oLl 400 600

TM.

FIG. 3. Temperature dependence of the quadrupole splitting of Ni,,,ssFq.,,,CrzSI. The solid line represents the theoretical values.

charges. The doublet hliissbauer spectra splits into several lines due to antiferromagnetic ordering. These spectra were analyzed by diagonalizing a 4x4 magnetic hyperfine and quadrupole interaction matrix for the first excited state of ‘?Fe (Refs. 9 and 10) and fitting eight Lorentzians with the calculated relstive line position and relative line intensities via computer. The best result of the samples in Ni,Fer -,Cr$, with x=0.985,0.97, and 0.96 was obtained. The following parameters were found at 12 K in J%.96~kdW4:

Hhf= 147.8 kOe, AEQ= - 1.96 mm/s,

S=O.89 mm/s, 8=66”, 1$=90”, v=l.O.

The isomer shift of 0.89 mm/s relative to iron metal indi- cates that Fe ions are ferrous.” Comparing Figs. 1 and 2, it is obvious that the absorption lines broaden progressively with decreasing temperature. Much workg~‘z has reported that this kind of line broadening may be interpreted in terms of slow electron relaxation rate, which is due to the slow fluctuation rate of the magnetic hyperfine field com- pared to nuclear-spin precession frequency. We analyzed the temperature dependence of the quadrupole splitting AEQ by applying the c.rystal-field theory. In order to fmd the energy structure and the corresponding eigenfunctions of Fe”, the diagonalization of a 15 x 15 interaction ma- trix, which took into account the combined axial and rhombic crystalline field and spin-orbit coupling, was car-

TABLE I. .4xial field parameter A,, rhombic tield parameter A?, and covakncy factor o2 for the monoclinic phase of Ni, Fe, _ x Cr2 SJ.

Al x (p-1, $1 ff2 0.36 -3.8 -3.5 0.71 0.97 -3.5 -3.0 0.72 Cl.985 -3.0 -2.8 0.73

SE0

-6.96* -6.96 $36’ -7829

V act. Vaxkd f ‘v’t-homblc+ v&l.

FIG. 4. The energy-level scheme for Fe’ ’ in NiasrsFeaslsCr,S,.

ried out (see Fig. 3).7,9 By fitting the thermal average of quadrupole splittings of the levels to the experimental data, we found the best parameters as shown in Table I. The fifth excited level is 1255 K higher than the fourth excited level, SCJ the value of AEe in Ni,~98,F~~,&r,S4 below 200 K is almost independent of the temperature as Fig. 3 shows (see also Fig. 4).

Comparing the Mossbauer data of x=0.985, 0.97 and 0.96, it was found that the magnetic hyperfine field and the quadrupole splitting decrease with Fe ion substitution. The TN suppression by the Fe ions suggests that the Fe-S-Cr super-exchange interaction is stronger than the Ni-S-Cr su- perexchange interaction.

ACKNOWLEDOMENTS

This work was supported by the Non-Directed Re- search Fund, Korea Research Foundation, 1991, and the Korea Science and Engineering Foundation.

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5741 J. Appt. Phys., Vol. 73, No. IO, 15 May 1993 Park et a/. 5741

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