Magnetic properties and specific heat of Tm1−xLuxCu2Si2

Journal of Magnetism and Magnetic Materials 68 (1987) 95-101 North-Holland. Amsterdam

MAGNETIC

PROPERTIES

95

AND SPECIFIC HEAT OF Tm, _ ,Lu,Cu,Si

A. KOZLOWSKI, A. MAKsYM~WICZ, and L. ANIOLA-JEDRZEJEK

z. TARNAWSKI,

Solid State Physics Department, Academy of Mining and Metal&v,

z

A. LEWICKI, J. iu~R0wSKl

al. Mickiewicza 30, 30-059 Cracow, Poland

Received 20 January 1987

The tetragonal TmCu,Si, compound is the only magnetically ordered material of the RECurSi, group for which crystal field parameters were determined. Quadrupole splitting measured by means of Mijssbauer spectroscopy showed that two lowest lying states are nonmagnetic singlets. Therefore, this material is likely to have an induced magnetic moment, mainly due to mixing of the two lowest states. We performed specific heat and magnetic susceptibility measurements of Tmr_,Lu,Cu,Si, (x = 0,0.025,0.050, 0.10,0.25, 0.50 and 1) alloys to determine the crystal field level scheme and compare it with the Mossbauer data. The saturation magnetization of the antiferromagnetic phase was calculated to be 3.2~~ and the moment is directed along the tetragonal c axis. No direct experimental evidence is known to support this prediction.

1. Introduction Main

reasons

for widespread

interest

in proper-

ties of the RECu,Si2 compounds are: the common crystallographic tetragonal ThCr, Si *-type structure, the presence of three materials with unstable 4f-shell and the fact that magnetic and crystal field interactions are of comparable magnitude [1,2]. Magnetically ordered materials seem to be antiferromagnetic but till now only four of them have their magnetic structure determined by means of neutron analysis. Three of them: DyCu,Siz and HoCu,Si, show the TbCu,Si,, AF3 magnetic structure with magnetic moment p perpendicular to the tetragonal c axis. Only PrCu,Si, was found to have the AFl structure with p along the c axis (see fig. 1). Some magnetostriction data suggest [1,3] that p should be perpendicular to the c axis when RE stands for Pr, Nd, Tb and Dy, while in TmCu 2Si z it is probably parallel to this axis. Magnetic ordering temperatures in the range from 1.6 to 20 K suggest that the magnetic interaction is of comparable magnitude with the typical strength of the crystal field in 4f materials. So there is a strong interplay of magnetic and crystal field interactions. TmCu,Si, is the only magnetically ordered

material where crystal field parameters were determined [4]. Quadrupole splitting obtained from Mossbauer effect showed that the lowest lying CF states were nonmagnetic singlets while the other levels were far higher in the energy scale. Magnetic ordering at about 3 K was confirmed by susceptibility measurements [5] and by the Zeeman splitting observed in Mossbauer effect [4].

P

7

P Fig.

0304-8853/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

1. The

magnetic structures observed in RECu,Si,. the magnetic ions are shown.

Only

96

A. Kozlowski et al. / PropertIes and specific heal of Tm, _ 1 Lu,Cu,Si,

However, the detailed character of this ordered phase is not quite that clear as can be seen from different (even as to the sign) values of the paramagnetic extrapolated temperature 8 [1,6,7]. Specific heat measurements were chosen as an alternative experimental technique to the Mossbauer experiment to get the crystal field parameters. As it was mentioned, the observed energy levels are strongly dependent on the magnetic characteristic of the system. It is only above the magnetic ordering temperature that we observe nonperturbated crystal field levels as predicted by the crystal field Hamiltonian HCF only. It is commonly assumed that crystal field levels are the same for all isostructural Tm, _ x Lu,Cu 2Si 2 alloys which are nonmagnetic for x > 0.1. For smaller x, the alloys are magnetic and the observed energy levels are different from the crystal field levels of HCF due to the magnetic contribution. So we are able to extract some information about the magnetic interaction from the specific heat data.

2. Experiment Samples of Tm,_,Lu,Cu,Si, (x = 0, 0.025, 0.050, 0.10, 0.25, 0.50 and 1) were prepared in by melting stoichiometric argon arc furnace amounts of Tm(99.99), Lu(99.99) Si(99.999) and Cu(99.999). The samples were then annealed at 800 o C for two weeks. The standard X-ray diffraction pattern revealed that the amount of parasitic phases was less than 5%. In specific heat measurements we used apparatus, described elsewhere [8], which allowed the heat capacity to be determined with an error less than 3% in the temperature range from 1.6 to 77 K. All the samples except LuCu,Si, were measured by adiabatic technique; the small calorimeter heat capacity contribution was subtracted from the measured total heat capacity. For nonmaga more accurate technique was netic LuCu,Si,, the relaxation method [9] in the temperature range up to 6 K. Here we accounted for both calorimeter heat capacity and heat capacity of about 1 mg Apiezon N grease used as a thermal contact. Values of the specific heat of Tm, _,Lu,Cu ,Si Z are presented in fig. 2; in the insert we show the

01 0

I

2

20

40

3 45 to 2030 50 TEMPERATURE [KI

60

80

T=[Ky

loo

Fig. 2. Specific heat of Tm, ,Lu,Cu,Si, alloys. The insert shows specific heat of nonmagnetic LuCu,Si, as a C/T vs. T2 function.

specific heat C,, of LuCu 2Si 2 in commonly used variables C/T vs. T2. The magnetic susceptibility was measured by an ac (76 Hz) induction method with a magnetic field of 30 G amplitude, in the temperature range from 1.6 to 77 K. The absolute value of the susceptibility was obtained by comparison with Er,O,. Sample holder and electron Pauli paramagnetism (as measured by LuCu,Si, susceptibility) contributions were less than 1% of the total susceptibility of other samples and so we just ignore this correction. The results of the measurements in the low temperature range up to 20 K are presented in fig. 3. Two samples were additionally measured in a wider temperature range from 77 to

A. Kozlowski et al. / Properties and specifc heat of Tm, _ x Lu,Cu,Si,

97

where

Hc,=w(x,0,0/3+x,0,0/60+x,0,4/12 +x,0,0/7560+x,0~/180)

is the crystal field contribution with &xi = 1, x1 2 0. The second and third terms in eq. (1) are the Zeeman energy and the magnetic interionic interactions, presumably of the RKKY origin. Sharp, lambda-like peaks in the specific heat (figs. 2 and 5) and characteristic maxima in the susceptibility (fig. 3) strongly suggest that TmCu 2Si2 is ordered antiferromagnetically. Additionaly, while searching for possible spin-glass behaviour we carefully measured susceptibility in the vicinity of the maximum during cooling down in an external magnetic field of 2.0 kG. Contrary to the usual spin glass behaviour, the shape of the susceptibility remains the same apart from a shift of its maximum towards lower temperatures (see fig. 4). To account for possible antiferromagnetic ordering, one has to consider two sublattices. For the antiferromagnetic structure as shown in fig. 1, we need at least three different exchange integrals. In the molecular field approximation and in the

. t

*. -

wsl-

-*++* .

40-

+.

A

.

*** +* **

.

.

+ .

.

1 *.

+ .

’ ,x=0.050

+*

.

+

. +

.

36-

. +

.

*. -.. .-

32-

x-0110

tf

l z,.x=a25

l .

28,b

l

. .

+ 1

.

+

.

*. . %

24

, .

+*

2 I !2 1

I

I

II

o

I

2

4

I”’

1’

11

3

5

6

7

‘s

9

IOqfl-

(2)

1

Fig. 3. Susceptibility x vs. T for Tm,_,Lu,Cu,Si, at low temperatures. The insert shows l/x vs. T for x = 0 and 0.05 at high temperatures.

300 K with a magnetic balance method; we show l/x vs. T in the insert of fig. 3. Finally, the net error for the specific heat and magnetic suscptibility is less than 10% if we also take into account possible errors due to the determination of crystallographic phases and/or alloys composition.

3. Analysis and discussion We assumed the Hamiltonian at experimentally Tm,_,Lu,Cu,Si, temperatures in the usual form:

describing accessible

1

0

I

I

I

I

2

3

J ‘,

TEMPERATURE [K]

(1)

Fig. 4. Susceptibility x of Tm,,,,Lu,,,Cu,Si, different external magnetic fields.

measured

for

98

A. Koziowski et al. / Properties and specrfic heat of Tm,

paramagnetic regime we have H = HCF. Then, by standard diagonalisation of HCF on the 1J, .I;) basis the energy levels are found and so the CF specific heat formula (Schottky specific heat) may be determined. We assume that the contribution to the total specific heat, arising from the lattice and the electronic parts, are the same throughout the Tm,_,Lu,Cu,Si, series and, therefore, equal to the measured specific heat of isostructural nonmagnetic LuCu 2Si 2. The difference between the specific heat of Tm,_,Lu,Cu,Si, and that of LuCu,Si, devided by 1 - x is then the magnetic contribution to the specific heat. This is shown in fig. 5 for low temperatures up to 12 K. For temperatures higher than TN the magnetic specific heat depends mainly on crystal field states (fig. 6). This specific heat is usually refered to as “Schottky specific heat”. In fig. 6 we also presented the best fit of the theoretical Schottky formula. The relevant CF parameters, energy levels and eigenstates are collected in table 1. Corresponding results determined by the Mossbauer effect [4] are also shown for comparison in fig. 6. Both methods yield that the two lowest levels are nonmagnetic singlets separated by several kelvin, 7.2 K in this paper or 8.6 K in ref. [4], with the next levels lying about 10 times higher in the energy scale. These

1Lu,Cu,Si,

crystal field parameters were then subsequently used in analysis of the ground state properties. By treating the two-sublattice model Hamiltonian in the molecular field approximation we obtain two one-ion Hamiltonians for each of the sublattices:

where M, and M2 are sublattice magnetisations and

(4) 72 = 2(;,;’

(k-f,

+ z22Jz + z32J3).

Here ./,‘s are exchange integrals between ith nearest neighbours and z,,‘s are numbers of magnetic ions of the jth sublattice among the ions of the ith coordination sphere of the ion which belongs to the first sublattice. Magnetisations of the sublattices should be now self-consistently calcu-

Tm,, LuxCu2S~, . x=0 0 x ~0.025 0 x =0.050 . XZQIO 0 X~O.25 . x-o.50

Fig. 5. Magnetic

specific heat C,

= (C - C L,,)/(l

- x) vs. temperature.

A. Koztowski et al. / Properties and specific heat of Tm, _ x Lu,Cu,Si,

99

F -

9

E

$9

Expermcnt Model,ref [Q] Modei thus work

--

65432-

i

I-

O 2

I

3

I

I

4

5

,,,,I 6 78910

I

I

20

30

I

I,,,,

40 50 60 T[t(l

Fig. 6. Schottky specific heat Cs = (C - C,,)/(l - x) (full line) of Tm, _,Lu,Cu,Si, vs. T. The bars indicate the uncertainty as approximated by the scattering of experimental points for different samples. The dashed line is a fit of the Schottky formula to the experimental results. Results from ref. [4] give the dashed-dotted line.

lated from the formula

we have

C(EilJIEi)eXP(-PEi)

Cexp(-/3E,)

’

(5)

where Ei and 1E,) are eigenvalues and eigenfunctions of Hi and Hz. In the paramagnetic region and in the absence of an external magnetic field

We assumed A4r = --A& = M as in fig. 1. Crystal-field-only susceptibilities x1 and xz are found to be defined by the equations

Table 1 Eigenstates and eigenvalues of the CF Hamiltonian of TmCu,Sia as obtained from the fit of the Schottky specific heat to the experimental values. The results from ref. [4] are shown for comparison. CF parameters, although confirmed by susceptibility are less sensitive to experiment than eigenvalues. CF parameters: w = 4.42 K, x1 = 0.24, x2 = -0.24, x3 = 0.04, xq = - 0.44, x5 = 0.04 Mixed states of J,

IG)l6)> l2h l-2)> IV 16h 12>, I -2h l6), l2), I -2), I5>, l3h II>* I-3), I-5)

Multiplicity

l-6) l-6) l-6) I--l>?

XexP(-P&o)

Energy (K) this work

ref.

1 1 1

0 7.2 91.5

0 8.4 86.4

2

97.5

-

[41

’

CexP(-P40)

I

( CeXP(-pE.o))-lT

(7)

i

where Ii), (k) and Eio, the Eke denote eigenstates and eigenvalues of the Hamiltonian HCF. Eqs. (6) have nonzero solutions for A4 only if x1 (ri - r2) - 2 = 0 or x2(r1 - TV)- 2 = 0, thus describing the antiferromagnetic TN temperature as the higher of the two temperatures which fulfill

A. Kozlowski et al. / Properties and specific heat of Tm,

100 Table 2 Magnetic

parameters

for Tm,

Tme.as Lua.as Cu z Si z TmO.wLuO.tOCuPi~

2

ym7;‘1

1 2 i;o;iy,j

2.80 + 0.05 2.7OkO.05 2.60 + 0.05 2.30 i 0.05

3.20*0.02 3.24+0.02 3.29 + 0.02 3.41 f 0.02

0.625 0.617 0.608 0.586

t + + +

I 2 ;m;i;;i-x)L

0.004 0.004 0.004 0.004

0.625 0.633 0.640 0.651

a TN was evaluated by means of specific heat data. ’ x2 (T = TN) is the theoretical value for the crystal field-only susceptibility 1. ’ Values (7, - 7*)/(1 - x) for different x were obtained from. the equation ’ Critical

composition

x,,,r of Lu was determined

from equation

the above conditions. Taking TN from experiment we then calculate r1 - r2 as a function of x (table 2). Additionally, when we take x, or xz at T = 0 K, we obtain the condition for the minimum value of the exchange parameters when magnetic ordering still exists at absolute zero. In our model x is the only parameter in 7, - r2 that varies when the alloy changes its composition. So taking the previously determined average ( r1 - r,)/(l - x) (see table 2) we obtain xcrit = 0.16, which is the critical composition of Lu above which the alloy is nonmagnetic. The exchange field is relatively small as compared to the third crystal field energy level. So it is reasonable to assume, that only the two lowest levels are mixed. Then the ground state, ]G’)=coscr]G)+sina]E), and excited state, ]E’)=

-sinaIG)+cosaIE),

2

‘:Lu,Cu z Si z alloys

Alloy

TmCu z Si z Tm os,,5Lua,025Cu2Siz

_ ~Lu Ju,SI

(8)

may be used as a complete base for the calculation of M, from eq. (5). This problem was treated in detail by Bleaney [lo] and Cooper [ll]. It is evident from the structure of ] G) and 1E), see table 1, that (G’IJIG’) and (E’IJIE’) are nonzero only in the z direction. So in the ordered state the moments of sublattices in TmCu,Si, are necessarily directed along the tetragonal c axis. The value (Y in eqs. (8) must be determined selfconsistently for every temperature (see for example ref. [lo]). For T = 0 the system is in its ground

k i k +

0.004 0.013 0.013 0.013

in the z direction xz

p$;‘-.v)

-vcRt

0.64 + 0.02

0.16+0.03

for CF parameters

as shown

m table

(TN) (7, - TV)= 2. ) (7, - 7, )/( 1 ~ x ) = 2.

~~(0) (1 ~ x,,,,

state

I G’) and the magnetic

~c1,= -RP~(G’

moment

is equal to

I4 I G’)

where 6 is separation between I G) and I E). Using 7, - r2 = 0.64 mol Tm/cm3 we have I”_ = 3.2~~ at T = 0 K. As a result of our specific heat analysis the overal crystal field splitting seem to be as large as 400 K. This indicates that the Curie-Weiss law may be not satisfied in the experimentally accessible temperature range. Thus it is difficult to get reliable information about the exchange parameters from the extrapolated 8 temperature. The effective moment is much less sensitive to details of the fitting procedure and we got the value (7.5 + 0.2)pB, very close to the theoretical value of 7.57~~ for the J= 6, L = 5, S = 1 Tm3’ ion ground state.

4. Conclusions By means of specific heat measurements we have found crystal field levels in Tm, ~ 1Lu $Zu ,Si 2. The system is magnetic for x < 0.1.

A. Koztowski et al. / Properties and specific heat of Tm, _ x Lu,Cu2Si,

The obtained level scheme is very similar to the one determined earlier by Miissbauer measurements. The two lowest levels are nonmagnetic singlets and the other levels he much higher on the energy scale. As a result, the magnetic order comes from the mixing of these two lowest levels. The magnetic moment in the ordered phase is directed along the tetragonal c axis and is equal to 3.2~~. No phase transition at about 7 K, reported in refs. [l] and [5] was detected. Such a transition was explained in refs. [l] and [5] as a result of quadrupole interaction. Also some other interactions should perhaps be included in the theoretical treatment as for example the magnetic dipole interaction. References [l] W. Schlabitz, J. Baumann, G. Neumann, D. Pliimacher and K. Reggentin, Crystalline Electric Field Effects in

101

f-electron Magnetism, eds. R.P. Guertin, W. Suski and Z. Zolnierek (Plenum Press, New York, 1982) p. 289. PI H. Pinto, M. Melamud, M. Kuznietz and H. Shaked, Phys. Rev. B31 (1985) 508. [31 N. Riissmann, H.U. H%fner and D. Wohlleben, Crystalline Electric Field Effects in f-electron Magnetism, eds. R.P. Guertin, W. Suski and Z. Zolnierek (Plenum Press, New York, 1982) p. 333. 141 G.A. Stewart and J. Zukrowski, Crystalline Electric Field Effects in f-electron Magnetism, eds. R.P. Guertin, W. Suski and Z. Zdnierek (Plenum Press, New York, 1982) p. 319. PI E. Cattaneo and D. Wohlleben, J. Magn. Magn. Mat. 24 (1981) 197. WI H. Osterreicher, Phys. Stat. Sol. (a) 34 (1976) 723. [71 Ch. Routsi and J.K. Yakinthos, Phys. Stat. Sol. (a) 68 (1981) K153. PI Z. Tamawski, Thesis, Cracow, Poland (1986). (91 R. Bachmann, F.J. Di Salvo, T.H. Geballe, L.R. Greene, R.E. Howard, C.N. King, H.C. Kirsch, K.N. Lee, R.E. Schwa& H.U. Thomas and R.B. Zubeck, Rev. Sci. Instr. 43 (1972) 205. WJI B. Bleaney, Proc. Roy Sot. 276A (1963) 19. WI B.R. Cooper, Phys. Rev. 163 (1969) 444.