Magnetic susceptibility and valence fluctuations in Sm3S4

Volume 58A, number 7

PHYSICS LETTERS

18 October 1976

MAGNETIC SUSCEPTIBILITY AND VALENCE FLUCTUATIONS IN Sm3 S4 P. WACHTER Laboratorium für FestkOrperphysik, ETH, HO’nggerberg, 8093 Zurich, Switzerland Received 6 August 1976 Revised manuscript received 8 September 1976 The magnetic susceptibility of Sm354 single 2~+crystals 2XSm3~. hasNbeen ear and measured above 100 between K the1.8 susceptibility K and 300 K. of the At low Sm3~ions temperatures is quenched the susceptibility due to the increasing is composed valence of XSm fluctuation rate.

Sm 3 S4 is a mixed valence compound as is evident by writing the net formula as Sm2+Sm~S~. It crystallizes in the Th3 P4 structure with a lattice constant of 8.5198 ±0.0003 A [11 In this crystal structure the divalent and trivalent cations occupy equivalent lattice sites and a temperature activated electron hopping between cations of different valency becomes possible. This is shown by electrical conductivity [1, 21 Hall effect [21and thermo power [21measurements. Just as in the similar, but more completely investigated, Eu3 S4 the isomer shift of the Mössbauer effect exhibits at room temperature only one line at .

25

-

~2O

15

,

an intermediate valence of 2.66, indicating a valence fluctuation faster than the time scale of the Mössbauer effect (~M 1 0~sec) [4]. Since the valence fluctuation rate is exponentially temperature dependent [1, 2] one has the ideal possibility of changing the fluctuation rate between about 1011 sec~at 300 K [31 and zero by simply cooling the material. SmRegarding the molar magnetic susceptibility2~of + 2XSm~~’ least ata very temperatures with prac3S4 oneatexpects valuelow composed of XSm ticaily static valence distribution. However, this was [5] who find no evidence of XSm3~(6H 512) on polynot the case in a recent measurement by Escorne et al. crystalline samples. Therefore, we reinvestigated the magnetic susceptibility of Sm3 S4 single crystals by means of a Faraday balance. The crystals have been

10

-

--

____________________________________________ 0

100

200 Ter’~perot~re(~)

Fig. 1. Molar magnetic susceptibility of Sm3S4 single crystals. The experimental error has about the size of the dots in the figure.

,

Quite in contrast to the prior results [5] we clearly observe a sharp increase of the susceptibility below about 3~ 50(6H K, giving evidence of the magnetic moment of Sm 512). To obtain a quantitative comparison 2~and Sm3~ are vanone Vleck and the with theory has ions to realize thatmolar both,susceptibility Sm for T ~ 300 K is given by:

~

,

characterized bythe chemical analysis (stoichiometry was achieved within limits of chemical precision, 0.5%), lattice constant, crystal structure, electrical conductivity and optical properties by Batlogg et al. [1]. The result is shown in fig. 1. 484

Lp~~_8 [4.5 XSm3S4 =

+

~

1

~E2—E1 E)] ex~~E1/kfl / 15 8 1 ÷3 exp(—E1/kT) (1)

)_~a~6~—~ + ~3 ~~,7/2)

~

exp(—~/kT)

exp(-~1/kfl) 1~ ________

j

Volume 58A, number 7

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PHYSICS LETTERS

__________________

04

//

2

/ I

/

03—

02

~

V 0

—~

//

>~m /1/ E

~-

=

20 T (K)

4Q ___•~

~,._/

~

~ ~_-~

50

100

indicating a J 0 magnetic ground state, in contrast to Escorne et al. [5]. The intercept with the ordinate permits the evaluation of the Curie constant of the lowest crystal field level. Assuming the IM~= ±-~)level as the lowest, we compute a much too large Curie con5 _3 stant,butwiththeaIMJ=±~)+bIMJ=+~-)being lowest and using a 0.4 we obtain an intercept of 0.042 emu~K/molein good agreement with the experi.

/

(21

/~

-

/

,~‘

I

/ 01

// //

‘~i

/ I

/

~

/

case and is shown fig. not 2. The of the line towards T-÷0indoes passextrapolation through the origin,

_____________

~

/ / (1)

18 October 1976

Temperature 150

C

K (

200

Fig. 2. Curve (1): (XSm3S4)~T. 2)(xsm The slope of the 2~)~T. line is 9.14 X i0~ (emu/mole). Curve ( 3S4 — X5m Dashed line: fit of the low temperature approximation of the 2~) second part of {eq. (1)}.T with 0 = —1 K. Slope of the dashed line is 1.5 X 10 line (emu/mole). Insert: 1/(XSm3S4 — X5m versus T. Dashed is theoretical initial slope.

mental From the fact that we observe a straight line for value. Xsm3s4~Tversus T up to about 40K we condude that the next crystal field level is at least ~2 —~i 40 K higher in energy. 2+ ions Wetonow the total want XSm to evaluate the contribution of Sm 3S4• Because the ener~separa6—5d in Sm tion of 4f 3S4 is comparable to the one in SmS [1] we expect a large, but2+. unknown, SditadmixTherefore, is not ture to the ground feasible to take E state of Sm 1 from spectroscopic literature [8] try or magnetic in Sm data [7]. Besides, the lower local symme3S4 compared to the one of SmS splits E1 into a doublet. Therefore we determined E1 and also the less important E2—E1 from Raman scattering of Sm 3 S4 at 4.2 K [9] For E1 we find an average value ofE1 ~272cm~ 392KandE2—E1 ~‘a500cm~ = 720 K. Thus the whole first part of eq. (1), i.e., the contribution of Sm2~to the total susceptibility can now be computed. .

2~and the The firstterm termtooftwo theSm3+ equation due LtoisSm second ions.isHere Avogadro’s number, and E the energies ofThe the ground excited 7F 7F 1 and F2 are2~, respectively. 1 and 2 states Sm to crystal field splitting state of Sm3~ will beofsubject and, being a Kramers ion, three doublets are expected for the S 3~ions [6]. point aIM symmetry of the Sm They are4oflocal the form ~>±6~ bIM, = ~ their with 2 + b2 = 1, and IM~= 1 =w± ith denoting ena ergy. F~1are the off-diagonal matrix elements of the susceptibility and ~i, 7/2 is the magnetic admixture of theJ=~1evelto the crystal field levels of the ground state. B is a possible, though small paramagnetic Curie temperature. Below about 80 K the first term of eq. (1) is constant [7]. There will also be a low temperature region where only the lowest crystal field level is occupied. In this temperature region the summation extends only over i = 1 and the exponentials can be dropped and thus, plotting the product XSm3S4 Twill yield a straight line for a not too large 0. This is indeed the

±4>,

.~)

This knowledge permits us to derive also Sm3~ (X~m3~4 X5m2+) which is the contribution of two ions to the total susceptibility. (Since above about 80 K the major part of the total susceptibility is given by the one of Sm2~,it has been made certain that none of the following difference (XSm conclusions is obtained only by the 3S4 — XSm2+), which is mainly used to help the reader, but that all the information can be obtained from the experimental XSm3 s4 alone.) Thus in fig. 2 we also plot (XSm3S4 XSm2+).Tversus T. Again we find a straight line up to about 40 K with the same ordinate for T = 0 as before. Below about 5 K we observe a significant deviation of the experimental points from the straight line. Most probably this is due to a negative paramagnetic Curie temperature 0. The fit of the low temperature approximation of the second part of ~eq.(l)}Twith the experimental points yields U = —l K, indicating antiferromagnetic order. This is not too surprising 485

VoluineS8A, number 7

PHYSICS LETFERS

since also SmP [10] analyzing the experimental points ,

in terms of x~Tasabove, yields 0

= —4 K and SmSb has been shown to be an antiferromagnet [11] Also Eu3S4 has with T~= 3.8 K [12] a Curie temperature of about ~ T~of EuS. To illustrate further a negative 0 for Sm3S4 we plot I/(XSm3S4 X5m2+) versus T and the theoretical initial slope in the insert of fig. 2. we have discussed only the low temperature partSooffar (XSm 3 54 XSm2+)~T.But between 50K and .

100 K we see from fig. 2 that a new effect is causing a departure from the expected theoretical behavior: the 3~be-

low frequency part of the susceptibility of 2Sm comes quenched. At temperatures above 100 K we ohserve again a straight line, now passing through the ongin, indicating aJ = 0 system. This unexpected behav-

ior must be related with the valence fluctuations in Sm3 S4. The valence fluctuation rate corresponding to, say 100 K, can be estimated fairly exactly. In the similar Eu3 S4 the life time of an electron at a cation before

hopping has been found to be [3] =

T0

exp(~E/kT),

and SmB6, both of which cxhibit a temperature independent configuration fiuctuation (ICF) [14] with fluctuation frequencies between l0~and 1016 Hz. If also in these compounds the critical frequency for quenching of the magnetic moment is near 106 Hz it is clear that one is always in the quenched magnetic moment condition. In fact, 3~has never been foundthein an magnetic moment of Sm ICF material. + electron

,

author is grateful theThe single crystals of Sm to Dr. E. Kaldis for supplying 3 S4. He is also very much obliged to K. Mattenberger for performing the susceptibiity measurements and to Dr. 0. Vogt permitting the use of his apparatus. It is a pleasure to acknowledge the support of Dr. L.M. Holmes with crystal field calculations and to thank Dr. F. Hulliger and B. Batlogg for useful discussions.

References (2)

with ~E the activation energy to be overcome in the hopping process and T0 a frequency factor, estimated to be r0 2.5 X 1014 sec [3]. On the other hand, by means of inelastic light scattering it has been shown that hr0 corresponds to an intrinsic phonon oscillation where only the sulphur ions move [13] : hr0 = 1.33 X 1013 sec~.In Sm3 S4, having practically the same lattice constant and crystal structure as Eu3S4, we expect also the same Since ~ has been found to be 0.14 eV [1] we compute ir(l00 K) = lO_6 sec. This means that for fluctuation frequencies 3~in Sm above

106 Hz the magnetic moment of Sm 3 S4 is quenched. The above experiments thus demonstrate for the first time the transition from a magnetic to a non-magnetic ground state. Sm3S4 may thus turn out to be a model material also for the susceptibility of

486

metallic SmS

18 October 1976

[1] B. Batlogg et al., Solid State Commun. 19(1976)673. [2] l.A. Smiinov et al., Soy. Phys. Solid State 14(1972)2412. 13] 0. Berkooz, M. Malamud and S. Shtrikman, Solid State Commun. 6(1968)185. 141 M. FibschUtz, R.L. Cohen, E. Bdhler and J.H. Wernick, Phys. Rev. B6 (1972) 18. 151 M. Escorne et al., Phys. Lett. 56A (1976) 475.

161 PT. Kripyakevich, Soy. Phys. Cryst. 7(1963)556. 171 F. Bucher, V. Narayanamurti and A. Jayaraman, J. AppI. Phys. 42(1971)1741. [81 G.H. Dieke, in: Spectra and energy levels of RE ions in crystals, eds. H.M. Crosswhite and H. Crosswhite (New York, 1968). [9] J. Vitins and P. Wachter, Proc. Int. Conf. Magneto-Optics, 1976, ZOrich, to appear in Physica B. [10] P. Junod, A. Menth and 0. Vogt, Phys. Kodens. Materie 8 (1969) 232. [11] F. Hulliger, private communication. 1121 E. Görlichet at., Phys. Stat. Solidi (b) 64(1974) K 147. [13] J. Vitins and P. Wachter, to be published. [141 F.M. Varma, Rev. Mod. Phys. 48(1976) 219.