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Magnetic, electrical, and specific-heat properties of UPdSn and UAuSn
PHYSICA
Physica B 176 (1992) 275-287 North-Holland
Magnetic, electrical, and specific-heat properties of UPdSn and UAuSn F(R. de B o e r a, E. Br/Jck a'l, H. N a k o t t e a, A.V. A n d r e e v a'2, V. Sechovsky b, L. H a v e l a b, P. N o z a r b, C.J.M. Denissen c, K . H . J . Buschow c, B. Vaziri d, M. Meissner d, H. Maletta e and P. Rogl f aVan der Waals -Zeeman Laboratorium, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands bDepartment of Metal Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czechoslovakia ~Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands dTechnische Universitiit, Berlin, Germany ~IFF KFA, D-5170 Jiilich, Germany fInstitut fiir Physikalische Chemie der Universitiit Wien, Wiihringerstrasse 42, A-I090 Wien, Austria Received 26 June 1991 Revised manuscript received 13 October 1991
UPdSn orders antiferromagnetically below 40 K and undergoes another magnetic phase transition at about 27 K, which is connected with a re-arrangement of the antiferromagnetic structure. The magnetic properties of UPdSn are strongly anisotropic with the c-axis as the hard-magnetization direction. For UAuSn, the maximum at 36 K in the x(T) curve may also indicate the onset of antiferromagnetism. However, the very broad anomaly in the specific heat, the poorly resolved "gSn M6ssbauer spectra and the magnetic history phenomena at lower temperatures do not point to long-range magnetic order. The possibility of a frozen non-periodic arrangement of U magnetic moments is discussed in connection with atomic disorder within the A u - S n sublattice. The distinction between the electron properties of UAuSn and UPdSn is reflected in the different values of the 3' coefficient of the low-temperature specific heat, which is remarkably small for UPdSn (5 mJ/mol K 2) in contrast to UAuSn (80 mJ/mol K2). A possible localization of the 5f states in UPdSn is envisaged.
I. Introduction
UPdSn and UAuSn belong to the large family of ternary UTX compounds of uranium with a transition (T) and a non-transition (X) element [1-4]. The compounds with X = Sn and T = Co, Ru, Rh, Ir crystallize in the ordered hexagonal structure of the ZrNiAl-type. Investigating UTSn compounds with even later d-metals, we observe a tendency to form either the cubic MgAgAs-type structure (UNiSn and one of the two reported modifications of UPtSn) or the hexagonal Caln2-type structure (UPdSn and ~On leave from Ural State University, Sverdlovsk, USSR. 2 Present address Center for materials Research, Stanford University, Stanford, California.
UAuSn). In this article we concentrate on the magnetic and related properties of the latter two compounds. The development of the electronic properties of the UTX compounds is strongly influenced by the varying degree of hybridization of the U 5f-electron states with valence-band states of ligands. As the d states of the transition metal ions are gradually filled, the hybridization, which affects the localization of the 5f states, becomes weaker due to the reduced 5f-d degeneracy. For the compounds with the ZrNiAI structure, which have been studied relatively extensively, we can thus follow the development from itinerant systems with a broad, strongly hybridized 5f-d band, to the situation where the 5f-band is narrowing, which leads to formation of local 5f
0921-4526/92/$05.00 (~) 1992- Elsevier Science Publishers B.V. All rights reserved
F.R. de Boer et al. / Properties of UPdSn and UAuSn
276
magnetic moments [3-5]. An analogous development has been observed within the group of UTX compounds with the CeCu 2 (TiNiSi)-type structure [5]. The enhanced y-values (characterizing the electronic contribution to the specific heat) observed for all compounds of these two groups illustrate that the more or less narrow 5f band remains pinned at E v and that real localization of the 5f states connected with a shift of 5f states from E F is not achieved in these systems. Our motivation for investigating compounds with the Caln2-type structure was to follow features of 5f-electron localization to a higher degree than can be achieved within the ZrNiA1structure group. We can suppose that, at least in first approximation, the crystal structure is favourable for such a study. Each U atom has only two nearest uranium neighbours with an interatomic separation of 360-365 pm (dr_ U = c / 2 ) along the c-axis. The distance between U atoms within the basal plane is equal to the lattice parameter a ranging from 460 to 472 pm. UPdSn and UAuSn have already been studied by Palstra et al. [1, 2]. Both compounds were reported as antiferromagnets, with T N = 29 K for UPdSn and 35 K for UAuSn. In this paper we report results of measurements of the magnetic susceptibility, the electrical resistivity, the specific heat in magnetic fields up to 5 T, the high-field magnetization at 4.2 K in fields up to
35T and the l~9Sn M6ssbauer effect at various temperatures.
2. Sample preparation and structure analysis Polycrystalline samples of UPdSn and UAuSn were prepared by arc melting appropriate amounts of at least 99.9% purity metals under argon gas. In the case of UPdSn, we have succeeded in growing a single crystal of approx. I cm 3 by means of the tri-arc Czochralski technique. X-ray diffraction patterns were consistent with the Caln2-type structure with the lattice parameters given in table 1. A small amount of impurity (probably around 5% USn3) was found in UAuSn. We have prepared also samples of UCuSn, another compound with the Caln2-type of structure. Because of the metallurgical difficulties (fast decomposition), only preliminary experimental data could be taken and this compound is not the subject of this paper. For comparison, however, the rough data have been included into table 1. A neutron diffraction study has indicated that an ordered ternary modification of Cain 2 (GaGeLi-structure type, space group P63mc) is the most plausible structure of UPdSn [7] with Pd and Sn occupying somewhat different positions. As the existence of atomic ordering within
Table 1 Lattice parameters a and c, magnetic-transition temperatures, Curie-Weiss parameters fgp, /~o,, and Xo obtained from fits (* - r e p r e s e n t the fit to the corrected gO(T) data) and the linear coefficient of the specific heat y for U A u S n and UPdSn. For comparison, also data for the antiferromagnet U C u S n and the ferromagnet U P d S b are given. U C u S n I denotes preliminary m e a s u r e m e n t s on our sample, U C u S n II values taken from ref. [6]. Data on UPdSb have been taken from ref. [1] except for the high-field magnetization done by ourselves. M~a, represents the saturated m o m e n t obtained by m e a n s of the m e t h o d m e n t i o n e d in the text. In cases where this extrapolation was not feasible only the magnetization in 35 T is given as the lower limit. comp. UPdSn polycr. a,b axis c axis * UAuSn UCuSn I U C u S n II UPdSb
a
c
~p [K]
10 9 X XII
3'
Msat
[pm]
TN, Tc [K]
~'/'eff
[pm]
[/xB/f.u.]
[m3/mol]
[mJ/molK2l
[jz./f.u. l
460.8
731.0
27 (38)
471.7 452.7 454.5 458.7
720.8 721.9 724.1 721.5
36 22 60 65
-8 -2.5 -60 -113 12
3.1 3.31 2.9 3.31 2.7 3.1 3.2 2.9
2.1 0 4.5 0 4.5
25 70
5
80 70 53 62
1.8
1.55 >1.65 >1.75 >1.63
F.R. de Boer et al. / Properties of UPdSn and UAuSn
277
Table 2 A t o m i c and thermal parameters for UPdSn. Space group: P63mc-C~v, No. 186; origin at 3 ml on 63mc. Unit-cell dimensions at 295 K: a = 0.46165 n m , c = 0.73205 nm, V = 0.1351 n m ~, c/a = 1.586. Density: p~ = 11.513 M g m -3. Linear absorption: p.(Mo K , , A 0 . 7 1 0 7 3 ) = 7 2 . 3 7 m m -~. T h e anisotropic thermal factors are expressed as: T=expl(-2~r2(Ulth2a*2+ Uz2kZb*2+ U3flZc*2+ U~2hka*b* + U~3hla*c* + U23klb*c*) × 10--')l, by symmetry U H = U22, U~3 = U23 = 0 ; the anisotropic secondary extinction (Zachariasen) was g = 3.86(33) x 10 -s. Residual values: R v. = 0.0478, R w = 0.0384, R G = 0.0464, G O F = 4.11. Atom
U Pd Sn
Site
2a 2b 2b
A t o m parameters x
y
z
0.0 i/3 2/3
0.0 2/3 1/3
I/4 0.4301(12) 0.5247(9)
the In sublattice of the Cain 2 structure can be very important for the electronic properties, we have performed a more profound X-ray diffraction study of a small single-crystal of UPdSn obtained from polycrystalline material by mechanical fragmentation. X-ray intensity data were collected on an automatic STOE four-circle diffractometer in one hemisphere of the reciprocal space up to the limit of sin 0/A = 8.1 nm -1 using monochromatic Mo K~I radiation. A set of 137 symmetry independent reflections was obtained by averaging symmetry equivalent reflections out of a total number of 1232 recorded intensities. All observed intensities (131 for ]F0] >3o'(F0) ) were used in the structure refinement. An empirical absorption correction was applied using q,-scans of three independent reflections. The results, summarized in table 2, are in very good agreement with ref. [7], and prove unambiguously that UPdSn is an ordered ternary compound. Similar analysis performed on UAuSn shows that the diversification of the In sites of the Cain 2 structure does not occur here and that Au and Sn randomly occupy the equivalent In sites.
3. Magnetic properties The temperature dependence of the magnetization in the temperature range 1.6-300 K was measured by means of a pendulum magnetometer in fields up to 1.3T and with a Faraday balance in fields up to 6 T. The measurements were performed on samples consisting of finepowder particles fixed in random orientation by
occ.
UH(=U22 )
U33
U~2
1 1 1
1.21(6) 1.69(15) 1.10(9)
1.29(9) 2.32(29) 1.65(29)
0.60(3) 0.85(8) 0.55(4)
glue. The magnetization of the UPdSn single crystal was measured also in the pendulum magnetometer, with the magnetic field applied along the various crystallographic axes. The magnetization at 4.2K was studied in magnetic fields up to 35 T in the High Field Installation at the University of Amsterdam. In order to derive the influence of the magnetocrystalline anisotropy from measurements on polycrystals, the following two types of finepowder samples were used: (a) loose powder, free to be orientated by the applied magnetic field, and (b) randomly-oriented powder, fixed by frozen alcohol. The magnetization data obtained in the first case (Mor) are believed to represent the magnetic response in the easy magnetization direction, while in the latter c a s e (Mrnd) we observe the behaviour of an "ideal" polycrystal. When interpreting such data, we are aware of the limitations due to possibly not perfectly singlecrystalline grains and incomplete orientation by the magnetic field. Direct comparison of powder data with measurements on a single crystal for UPdSn show that the free-powder magnetization is indeed very similar (about 10% lower) to that of the single crystal in the easy-magnetization direction. As can be seen in fig. 1, the magnetic susceptibility of UPdSn is strongly anisotropic. Measuring with the magnetic field B oriented along the basal plane, we observe two distinct maxima at 28 and 38 K. Nearly equivalent behaviour is found for fields along the a and b axis (in the orthorhombic notation). For B parallel to the
F.R. de Boer et al. / Properties o f UPdSn and UAuSn
278
500
a
500
' a
'
400i
400
200
~ crystal ]~
0
\'~0 " ~ " ""~.~ 0
10
20
30
40
;
t
i
i
i
50
100
150
200
250
5£
300
T (K) Fig. 1. Temperature dependence of the magnetization susceptibility (M/B vs. T plot) of the UPdSn single crystal in the a-, b- and c-directions and powder sample measured in a magnetic field of 1 T. The data denoted by s represent a simulation of the polycrystal data by an average of single-crystal results (see the text). Inset: details of the anomalies. hexagonal c-axis, the susceptibility is much w e a k e r and the lower m a x i m u m appears only in the form of a shoulder. In the t e m p e r a t u r e range between 20 and 40 K, and especially around the lower m a x i m u m , M/B in the a and b directions is rather field-dependent, as apparent from fig. 2, where a gradual upturn develops already around B = 1 T. This effect means that the lower maxim u m is more pronounced in higher fields, and the m e a s u r e m e n t s in fields of several teslas display the u p p e r anomaly only as a weak shoulder. This has led to the original claim that magnetic ordering takes place only at T - - 2 8 K [1]. The magnetization for B Nc grows linearly in fields up to 1.3T. In fig. 1, we also compare M/B obtained on the powder sample with that obtained on the basis of the single-crystal data as an average of the contributions from the three crystallographic axes. Very good agreement is found except for the range form 20 to 50 K. The field d e v e l o p m e n t of M/B for higher fields is d o c u m e n t e d in fig. 3, where the measurements p e r f o r m e d on powder in B = 1, 2, and 4 T are compared• A strong non-linearity in M versus B at low temperatures appears in fields B below 4T.
In the t e m p e r a t u r e range from 50 to 300 K, where the magnetization is proportional to the magnetic field, the susceptibilities (X = M/B) for B[]a, b are the same within the experimental error, as expected for the hexagonal compound. T h e y are well described by the Curie-Weiss law: I). I 0
0.()~
h "J"
30 K
0.()I
T
1(I I,, A" ~'
().(~'2 A
:'~0 I(
•
0.(10 ().7
! .()
L.?~
1~ i T ) F i g . 2. M a g n e t i z a t i o n c u r v e s m e a s u r e d o n U P d S n at 30 a n d 4 0 K in d i f f e r e n t c r y s t a l l o g r a p h i c d i r e c t i o n s . T h e solid lines a r e g u i d e s to t h e e y e .
F.R. de Boer et al. / Properties o f UPdSn and UAuSn 400
~
~
r
279
2.0 ,
UPdSn
a-axis
4.2 K ©
~.~. 1 5 [
300
200
v~vvv
.']
! X7
~
~
b-axis
it ~o
LO
0.51
2T~-
100
©
o~
'~ c-axis
~-~ 1T 0.0 0
0
10
20
30
40
50
= c/(r-
Op),
20
30
40
Fig. 4. Magnetization curves m e a s u r e d at 4.2 K in magnetic fields up to 35 T on a U P d S n single crystal with the magnetic field oriented along the principal crystallographic directions (using the orthorhombic notation).
60
Fig. 3. The low temperature ( T < 6 0 K ) part of M / B vs. T curves m e a s u r e d in magnetic fields of 1, 2 and 4 T. The solid lines are guides to the eye,
x
10
(1)
with Op = - 2 . 5 K and C = 1.75 × 10 -s m3/molK, from which the effective moment IXeff = 3.31/.q3/ U can be obtained. The gO(T) data can be fitted by the Curie-Weiss law ( O p = - 6 0 K and txeff = 2.9/.%/U) if an additive temperature-independent term X0 = 3.4 × 10 -9 m3/mol is assumed. Alternatively, this type of behaviour may be understood as a parasitic contribution due to the projection of the easy-axis magnetization connected with either a slight mosaicity of the crystal or a small error in the crystal orientation. The corrected gC(T) data (allowing a deviation of less than 2 ° in the crystal orientation) then can be tentatively fitted to (1) yielding 8p around - 1 1 0 K where the same value of /&eft is used as obtained for the a and b directions. The results of high-field magnetization measurements performed at 4 . 2 K on the UPdSn single-crystal (fig. 4) prove the enormous magnetic anisotropy. The magnetization curves for Blla and Bllb are very similar. The magnetization is low and proportional to the magnetic field below 3 T. The field of 3 T, where dM/dB increases abruptly, can be taken as the field where a moment-reorientation commences. We cannot,
however, distinguish where the transition terminates, because a smooth field dependence of the magnetization gradually tending towards saturation is observed up to the highest field applied. Intuitively, we can attribute this type of behaviour to a non-collinear antiferromagnetic ground state as suggested by the neutron-diffraction measurement [7]. The magnetization processes may consist of a spin flop retaining the non-collinearity of moments in the initial stage of the transition (in fields close to 3 T ) and subsequent rotation of the moments towards parallel alignment in high fields. The magnetization in 35 T, yielding 1.7 and 1 . 6 ~ J f . u . for a and b, respectively, is already close to the saturation value. More precisely, the saturation magnetization M0 can be estimated from the extrapolation of M versus 1/B which is found to be linear above 10T. This procedure leads to M 0 = 1.9 and 1.8~B/f.u. for a and b, respectively, which is close to the value of ( 2 . 0 5 ± 0 . 1 3 ) ~ B / U , obtained from the neutron-diffraction experiment [7]. The difference between the results obtained for B]la and BHb may be an indication of anisotropy within the ab plane. However, being aware of a certain mosaicity of our single-crystal and a possible deviation when mounting the crystal, we take such a conclusion with caution. We are also aware of the fact that for the case of a magnetic
280
F.R. de Boer et al. / Properties of UPdSn and UAuSn
unit cell of the orthorhombic symmetry, reported in ref. [7], the magnetic response along crystallographically identical directions may be different, and the situation can be further obscured by the possible existence of magnetic domains. Neutron diffraction on a UPdSn single crystal is desirable to solve this problem. The c-axis is undoubtedly the hard-magnetization direction. The magnetization curve for B llc consists of three linear parts separated by anomalies at 3 T (an increase of the M(B) slope) and 14T (a small metamagnetic-like anomaly). The origin of these anomalies is not clear at the moment. The maximum moment of 0.6P.B/f.u. is reached in 35 T. The magnetic anisotropy field B a is generally approximated by the field of intersect of the M(B) curves along the easy- and hard-magnetization axes. For UPdSn this estimate yields B a = l l 0 T . The comparison of the single-crystal results with the magnetization measurement on UPdSn in powder form [4], obtained from the polycrystalline piece used for the other experiments, shows that the data obtained on powder free to be oriented by the applied field mimic very well the easy-axis magnetization. Only the slightly lower value (by 10%) of the maximum magnetization in 35 T and a correspondingly higher slope of the M(B) curve at 35 T (lack of saturation) are signs of imperfect alignment of the grains and/or some fraction of multicrystalline powder particles. UAuSn displays a pronounced maximum in the M/B(T) dependence (fig. 5). This maximum is located at 36K when measured in magnetic fields ~<2T. When applying higher fields, the maximum is partially suppressed, rounded and shifted to lower temperatures. This amounts in approximately 1 K shift for B = 6 T. These facts may support the idea of essentially antiferromagnetic ordering in UAuSn at temperatures lower than 36K. However, complicated magnetic history effects, which have not been studied thoroughly up to now, modify the low temperature behaviour to a limited extent. Also the fact that the temperature dependence of the susceptibility deviates from the Curie-Weiss law already below 80K, means that UAuSn is not a
3.00 350 I M/B (10-9m3/mol) 4°° ~2T 2.50
300 I ~ ~ T 250 200[
2.00 --~
ZE
1500
1.50
20
- ~;°o ~ o "l~o 40 60 T~K~
80 .,¢"~
1.00
0.50 0.00 0
50
100
150
200
250
300
T (K) Fig. 5. Temperature dependence of the inverse magnetic susceptibility (M/B in the magnetic field of 1 T) of a UAuSn powder sample in the paramagnetic state (T > 40). The solid line represents the fit according to eq. (2). Inset: Low temperature (T < 80 K) part of M / B vs. T curves measured in magnetic fields of 2 and 6 T.
typical antiferromagnet. In the ultimate case, the randomness introduced by an atomic disorder can lead to a cluster glass with prevailing antiferromagnetic interactions. Thus the maximum in x(T) does not need to be strictly connected with any magnetic phase transition in this case. New samples of UAuSn, which are better specified in the metallurgical sense, are necessary for future studies. The high-temperature susceptibility behaviour (T > 8 0 K ) can be fitted by a modified CurieWeiss law: C X
op)
+ x0.
(2)
The temperature-independent susceptibility X0 has a very small value (similar to UPdSn polycrystal) of X0 = 4.5 × 10 -9 m3/mol (other parameters can be found in table 1). This situation contrasts with the behaviour of the hexagonal UTX compounds of the ZrNiAl-structure group [3, 4]. Most of them, when measured in polycrystalline form, display considerable curvature of the 1/x(T) curves. These curves can approximately be fitted by the modified Curie-Weiss law (2), but the values of X0 are one order of mag-
F.R. de Boer et al. / Properties of UPdSn and UAuSn
nitude higher than those found for polycrystalline UPdSn and UAuSn. Closer inspection of the susceptibility data obtained on available single crystals (URuAI, UNiAI, UNiGa) shows that for these compounds the values of X0 are negligibly small [8-10] for B along any particular crystallographic direction. Therefore we believe that the large values of X0 obtained for polycrystals can be ascribed to the presence of a strong magnetic anisotropy becoming manifest also in the paramagnetic state. In a material with random grain orientation, the relative contribution of favourably oriented grains is low in the uniaxial case at high temperatures. At temperatures near Op, the relative contribution of these grains becomes dominant which leads to the curvature of 1/ x(r). The less pronounced curvature, measured for UPdSn and UAuSn, points thus to lower magnetic anisotropy or higher multiplicity of the easy-magnetization direction (which has actually been proved by the measurements on the UPdSn single crystal). Note that also the susceptibility data obtained on a powder material displaying high magnetic anisotropy yield values of the effective moment which are reduced with respect to the intrinsic values derived from single-crystal measurements. The UAuSn magnetization curves at 4.2K (fig. 6) are characterized by a very broad S-shape with an inflection point around 10 T and a weak tendency to saturation in higher fields. A mag1.5
UAuSn 4.2K free powder
1.0
o• 0.5
0.0
•
y
•
• o fixedpowder
10
20
30
40
B (T)
Fig. 6. Magnetizationcurves measured at 4.2 K in magnetic fields up to 35T on powders of UAuSn, free to orient in magnetic field and fixed in random orientation. The solid lines represent the measurement on the fixed powder in continuouslyvarying (up and down) magneticfield.
281
netization of 1.15/zB/f.u. is reached for oriented powder in 35 T, but this value is still far below the saturation magnetization, as the differential susceptibility d M / d B in this field is still considerably high. Note that the linear extrapolation of M versus 1 / B to 1 / B = 0 yields the value of 1.55/zB/f.u. The virtually featureless magnetization curve (exhibiting, however, small but measurable hysteresis in fields up to 15 T) may be associated with some kind of disorder of the spin system. In this stage of investigation, we cannot distinguish whether the small ferromagnetic component of 0.02tzB/f.u. is an intrinsic effect, possibly related to magnetic history phenomena seen in susceptibility measurements, or whether it is due to a spurious phase. The ratio Mrnd/Mor in 35 T for UAuSn (0.81) is similar to that found for UPdSn (0.78) which may point to similar anisotropy conditions.
4. l lgSn M6ssbauer effect studies
llgSn M6ssbauer spectra were taken on finepowder samples at various temperatures between 5 and 300K. A standard constant-acceleration spectrometer was used. The obtained spectra were fitted with a computer simulation including isomer shift IS (with respect to LaSnO3), quadrupole splitting QS and magnetic hyperfine fields Bhf. The experimental line width was 0.5 mms -~. Representative examples of 119Sn M6ssbauer spectra obtained on UPdSn are shown in fig. 7. It may be concluded that Zeeman splitting shows up in the spectra at temperatures lower than 40K and gradually increases with decreasing temperature. The full lines through the data points in fig. 7 represent the computer fits. The hyperfine parameters corresponding to the fit of the 15K spectrum are I S = 2 . 0 m m / s , Q S = 0 . 1 m m / s and B m = 5 . 0 T . Note that two subspectra (one of them with Bhf = 0) are observed in a certain temperature region (3040 K). The spectra consist of only one spectrum above 40 K (paramagnetic r a n g e - Bhf = 0) and below 30 K (antiferromagnetic range - Bh~ > 0). The single value of the magnetic hyperfine field recorded at low temperatures pertinent to all Sn
282
F.R. de Boer et al. / Properties o f UPdSn and UAuSn ,
300 K
100
o
8O 45K
>
60
#e~
Y=
4o g. t 20
....
/
/
: " " ' ÷ 30K
i
i
10
20
'
30
40
50
;
0
60
T (K) Fig. 8. Temperature dependence of the magnetic hyperfine field on Hgsn in UPdSn and of the contribution to the integral intensity of the subspectrum with Bhf = 0 (paramagnetic fraction). The solid lines are guides to the eye.
18 -
L 0
5. Electrical resistivity
L 8
Velocity (mm/s)
~-
Fig. 7. H~M6ssbauer spectra for UPdSn at different temperatures. The solid lines represent computer fits.
nuclei supports the idea that UPdSn is an ordered ternary compound. The temperature dependence of the hyperfine field shown in fig. 8. reveals that magnetic ordering in UPdSn commences at about 40 K. This means that the first maximum in the x(T) plots is representative of the N6el temperature. Qualitatively different M6ssbauer spectra were obtained for UAuSn. A broad spectrum with poorly resolved features were recorded at 15 K yielding a mean value of hyperfine field /~hf= 2.83 T. This result allows the following possible interpretations: (a) a complex antiferromagnetic structure producing different values of Bhf a t the Sn sites, (b) magnetic state of asperomagnetic or spinglass type leading to a statistical distribution Bhf,
(c) no magnetic ordering but spin fluctuations with a characteristic time longer than the time scale (10 -9 s) of the M6ssbauer effect.
The electrical resistivity was measured on barshaped UPdSn and UAuSn bulk samples by a conventional AC four-probe method in the temperature range from 4.2 to 300K. The p(T) curves are given in fig. 9. A high concentration of internal cracks hampered the determination of the geometrical factor, so that only relative values of resistivity can be displayed. A very rough estimate gives 10300K 2000 Ixft cm for UPdSn, and =300 ixl2 cm for UAuSn, which are values not very different from those given in ref. [1]. The flat o(T) and the negative dp/dT developing gradually at low T (especially below 80 K) found for UAuSn can be understood as a lack of any coherence which occurs in compounds with a strong scattering of conduction electrons. Although the understanding of the electrical resistivity behaviour in narrow-band actinide compounds is still quite unsatisfactory, it is probable that variations of the strength of the coupling of conduction electrons to scatterers like charge and spin fluctuations (variations of the effective mass of quasiparticles at EF) determine primarily the shape of the p(T) curves. The electron-phonon scattering becomes of =
F.R. de Boer et al. / Properties of UPdSn and UAuSn
283
3000 UAu~n 2500
2000
2000
7.
-Z k. v
1500
1500
1000 1000 500 500
T tK)
i
o
L 0
0 50
100
10
150 T (K)
20
30
200
40
50 250
60 300
Fig. 9. T e m p e r a t u r e dependence of the relative resistance p of U A u S n and UPdSn. Inset: The low-temperature part of the p(T) curve for UPdSn.
minor importance for compounds with resistivities of hundreds of txf~cm. In this context, the behaviour of UAuSn is not irregular when taking into account the Au-Sn sublattice disorder. A similar situation has been found in numerous disordered systems like U(Pt, Pd)3 [11] or (U, Th)2Znl7 [12] or CePd3+ x [13]. In the case of UAuSn this effect could thus obscure the impact of magnetic ordering on the p(T) dependence. An alternative model can be based on the assumption that the low-temperature increase of p(T) is reflecting mostly an antiferromagnetic ordering, which affects the resistivity in a more conventional way via the elastic scattering of conduction electrons on localized moments [14]. The lack of any sharp anomaly can then be explained by a possible disorder (randomness) in the system of magnetic moments, or by a lack of any long-range magnetic ordering. The electrical resistivity of UPdSn (fig. 9) shows, in contrast to UAuSn, a significant decrease with decreasing T at low temperatures. There is, however, no sharp anomaly observed at the magnetic ordering temperature. Instead, a broad knee spread between 40 and 60K is formed (note that x(T) commences to deviate from the Curie-Weiss law below 60K). The magnetic transitions connected with the x(T)
anomalies at 28 and 38 K show up in the temperature derivative of the electrical resistivity as a maximum at 30K and a sudden change of slope at 41 K. At higher temperatures, a nearly linear increase with low d p / d T slope can be followed up to =230 K with a relatively abrupt flattening observed above this temperature. The nature of this high-temperature anomaly remains unclear. Our measurements are, however, in this point well reproducing the results in ref. [1].
6. Specific heat
An adiabatic technique was used for specificheat measurements in the temperature range from 1.2 to 35 K in magnetic fields of 0 and 5 T [15]. Additional measurements at higher temperatures were performed with the transientheat-pulse technique [16]. The thermal sampleto-bath time constants were typically of the order of 1-50s. Internal thermalization times were found to be smaller than 0.5 s. The heat capacity was determined by the evaluation of the initial temperature rise, the time constant of the exponential temperature decay and a separate measurement of the thermal resistance. The results from both methods agreed by better than
F.R. de Boer et al. / Properties o f UPdSn and UAuSn
284
5%. The heat capacity of the addenda was estim a t e d and was corrected for if found to be non-negligible. The absolute accuracy of the m e t h o d is approximately 10%. The specific-heat behaviour (figs. 10 and 11) underlines the rather different character of U P d S n and U A u S n at low T. For UPdSn, C / T reaches remarkably low values around 7 m J / m o l K 2 at 2 K. Extrapolation to zero temperature from the interval 2 - 8 K, where linear behaviour of C / T versus T 2 is found, provides - / = 5 m J / m o l K 2. This value is in a good agreement with y = 4.3 m J / m o l K 2 reported in refs. [1, 2]. Such a low value has only one analogy a m o n g U-intermetallics, namely the proposed localized 5f-electron c o m p o u n d U P d 3, having a value of y of approximately the same magnitude [17]. The C / T versus T 2 plot shows an abrupt change of slope around 8 K, which makes the linear part abnormally short. The anomaly around 8 K may be associated with the magnetic part of the specific heat, because it is this t e m p e r a t u r e where specific heat measured in 5 T commences to deviate considerably towards higher values from the zero-field data (not seen in fig. 10). The magnetic transitions are relatively very broad, one being manifest only as a shoulder at T = 27 K, whereas the magnetic ordering tempera1.0 UPdSn 0.8
• ."
.
0,6
:%iI "/ ...,"
j 0.0
01f 0
0
I
6o
20
.U.Y ~'
i; 20 40
"Bv°Ti T I 40
60
80
1.0
v
v
v
v v
g•
UAuSn
v
0.8 o•
200
0.6
7"-.~,
C/T (mJ/mol K 2)
-6 E
18o
.,
t
L)
0.4!
160
¢ j
140
0.2
120 100
0.0
'¢
B=0T
~
~,*~""
B= 5T 20
20
40 40
T 2 (K2) 60
80 60
T (K) Fig. 11. T e m p e r a t u r e d e p e n d e n c e of the specific heat of U A u S n p l o t t e d in the r e p r e s e n t a t i o n C~ T vs. T m e a s u r e d by the a d i a b a t i c m e t h o d (circles) and by the t r a n s i e n t - h e a t - p u l s e
technique (triangles) in zero magnetic field. Inset: the C/T vs. T 2 plots at low temperatures for B = 0 and 5 T. ture is reflected in the m a x i m u m around 38 K. As no suitable non-magnetic " b a c k g r o u n d " compound is available, it is very difficult to estimate the magnetic-entropy change. The solid curve in fig. 10, corresponding to a D e b y e temperature O D = 220 K estimated from the slope of the low t e m p e r a t u r e part, results in A S = 1.5 Rln2 at 45 K. Comparing this value with 0.1 Rln2 reported for the heavy-fermion antiferromagnet UNiA1 [10], we can claim that despite the large uncertainty of our estimation the magnetic entropy of UPdSn is of the order of magnitude which is expected for a local-moment system. For U A u S n , C / T versus T 2 is linear between 5 and 14 K yielding y = 80 m J / m o l K 2. An upturn below 5 K, which is partially suppressed in 5 T, points to y = 110 m J / m o l K 2. However, as it is a field-sensitive effect we cannot exclude an extrinsic origin of this feature. Only a very broad m a x i m u m in C / T versus T was observed at 35 K, the t e m p e r a t u r e of the susceptibility maximum.
6O
T (K)
Fig. 10. Temperature dependence of the zero-field specific heat of UPdSn plotted in the representation C/T vs. T. The full line represents an estimation of the non-magnetic part (see text). Inset: the C/T vs. T 2 plot at low temperatures for B =0 and 5T.
7. Discussion
Although UPdSn and U A u S n both display magnetic order they differ qualitatively in several
F.R. de Boer et al. / Properties o f UPdSn and UAuSn
aspects. The basic difference consists in the character of the 5f states. Let us suppose the 3,-coefficient to be the primary key distinguishing the presence of 5f states at the Fermi level. Principally, band-like behaviour of 5f states, i.e. 5f character of the states at E F can be expected if 3' is enhanced and has values falling at least in the range 10-20 m J / m o l K 2, which is typical for pure light actinides. The existence of localized 5f states separated from E F can be then assumed if 3' is below 10 m J / m o l K 2. The boundary remains, however, rather fuzzy, because UPd 3 (3' = 5 m J/ molK 2 [17]) is a well-documented but still singular case among U intermetallics. According to this criterion, UPdSn should be taken as the second metallic system with localized 5f states. Correspondingly, the high 3,-values obtained for U A u S n would indicate the formation of a 5f band. We are aware that high 3' values can speculatively also be attained in, e.g., an Anderson lattice. In this case, it is not the presence, but the proximity of 5f states to E F that guarantees a high 3,-value, provided that the intra-ionic Coulomb interaction U and the 5f-hybridization with conduction-electron states are sufficiently strong. Whether such a regime occurs for U intermetallics is, however, still an open question. On the other hand, one can imagine a situation where, e.g., the magnetic sub-band splitting or the formation of a gap due to antiferromagnetic ordering can lead to a considerable reduction of the density of states at E F for a 5f band of any width. T o shed more light on this, high-resolution UPS experiments on UPdSn are under way. However, the influence of an antiferromagnetic gap can be, however, excluded in view of the simple p(T) dependence (fig. 9). The question arises, whether the striking difference between UPdSn and UAuSn is directly connected with the difference in interuranium spacing, which is somewhat larger in UPdSn. The values of du_ u around 360 pm are not much higher than the Hill limit [18], but the arrangement of the U atoms into a nearly one-dimensional network can lead either to higher sensitivity of the 5f bandwidth to the interuranium spacing, or to a shift of the effective Hill limit to lower values due to the fact that each U atom
285
has only 2 U nearest neighbours. Because we expect the strength of the 5f-ligand hybridization to be the dominating factor for the character of the 5f states [4], the difference in behaviour between UPdSn and UAuSn can be due also to differences in the degree of hybridization between the U 5f states and the Pd 4d or Au 5d states, respectively. Although the 4d states in metallic Pd are not filled completely in contrast to the 5d states of Au, the former are pushed down towards higher binding energies (to - 4 eV for 1 : 1 : 1 stoichiometry) and the 4d band becomes much narrower in compounds with the more electropositive U [19]. This reduces a possible energy overlap with 5f states and the 5f-4d hybridization may therefore be very weak. The arrangement of the U atoms in the crystal structure plays a key role also in the geometry of the magnetic ordering. For example, U T X compounds crystallizing in the hexagonal ZrNiAIstructure type exclusively have uniaxial anisotropy with the hexagonal axis being the easymagnetization axis [4]. As the values of the anisotropy fields amount to hundreds of teslas and hence exceed by one order of magnitude the anisotropy fields in the isostructural rare-earth compounds [20], it does not seem justified to use a conventional description of the anisotropy energy in terms of crystal-field theory. A tentative application of the Anderson Hamiltonian with an effective interaction of the CoqblinSchrieffer type and a quantitative analysis of concomitant hybridization-induced anisotropic interaction between local moments [21], leads to correct conclusions about the easy directions of the magnetic moments. In this description, parallel moments oriented perpendicular to the interionic axis are favoured. The uniaxial anisotropy of the hexagonal compounds U T X is in agreement with the strongest interaction (ferromagnetic as a rule) occurring within the basal-plane layers containing U and transition-metal atoms [5]. Analogously, in the compounds crystallizing in the orthorhombic structure (CeCu2-structure type), where the U atoms are positioned along zig-zag chains, the easy-magnetization direction is perpendicular to the chain [22]. The cases of UPdSn and U A u S n are expected to be similar.
286
F.R. de Boer et al. / Properties of UPdSn and UAuSn
U atoms in the Cain: structure or its modification form a network of one-dimensional chains, the separation of the chains being larger than 450 pm. Such a situation should provide a good possibility for the easy-plane anisotropy with the moments within the basal plane. Indeed, the values of M r , d / M o r , for both compounds very close to 0.79, as expected for an easy-plane system, support this idea. Single-crystal measurements show that the c-axis is indeed the hardmagnetization direction, but the a- and b-axes need not be equivalent. A rather complex type of magnetic structure of UPdSn is suggested on the basis of neutron diffraction [7] assuming a standard U form factor [23]. Primarily, it was shown that there are two different antiferromagnetic phases. The high-temperature phase (phase I), stable between approximately 27 and 38 K, has magnetic moments perpendicular to a and tilted from b towards c by =35 ° . In the low-temperature phase (phase II), the tilting towards c increases to =38 ° and, moreover, tilting from b appears. The components of moments in the a b plane are ordered parallel within the atomic chains (parallel to c) in both phases. The tendency of the U moments to couple ferromagnetically within the chains may be the source of the positive value of Op found in all compounds summarized in table 1 except for UPdSn where Op is small but negative. The fact that the lowest 00 value is reached for UPdSn may be related to the largest U - U spacing occurring in this compound. The antiferromagnetic ordering may then be attributed to an antiferromagnetic interaction between the chains for all compounds containing Sn, whereas in UPdSb it is ferromagnetic. In UAuSn, the atomic disorder in the A u - S n sublattice may introduce some randomness of the magnetic interactions and consequently lack of periodic ordering of the U magnetic moments.
netically ordered below 40K. Specific-heat studies specify the ordering temperature as T N = 38 K. The change of magnetic structure around 28 K, detected by neutron diffraction [7] is also documented in the temperature dependence of the magnetization. Magnetic moments of 1.81.9/XB/U were estimated from magnetization measurements in high magnetic fields. The magnetic anisotropy field equals 110 T which is estimated from the magnetic isotherms at 4 . 2 K measured with the field applied in the basal plane and along the c-axis, the latter being the hard-magnetization axis. The value of the 3' coefficient in UPdSn is very low and is reminiscent of that of UPd 3. Microscopic evidence is, however, necessary to establish the character of the 5f states. The difference between UPdSn and U A u S n probably is manifest already on the crystallographic level. While UPdSn is an ordered compound, there are indications from several experiments that there is a random occupation of the atomic Au and Sn sites in UAuSn, which leads to a certain degree of magnetic disorder. This has been corroborated by the precise X-ray diffraction analysis, that has shown that UAuSn is disordered ternary system with the Caln2-type of structure. The high value 3' = 8 0 m J / m o l K 2 points to a conventional band-like character of the 5f electron states in UAuSn.
Acknowledgements This work is part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie ( F O M ) " . Part of the work of V.S. has been kindly supported by the Alexander von Humboldt Foundation.
References 8. Conclusions We have prepared polycrystalline samples of UPdSn and UAuSn and a single crystal of UPdSn. Magnetic measurements and M6ssbauer spectroscopy show that UPdSn is antiferromag-
[1] T.T.M. Palstra, G.J. Nieuwenhuys, R.F.M. Vlastuin, J. van den Berg and J.A. Mydosh, J. Magn. Magn. Mater. 67 (1987) 331. [2] T.T.M. Palstra, G.J. Nieuwenhuys, J.A. Mydosh and K.H.J. Buschow, J. Magn. Magn. Mater. 54-57 (1986) 549. [3] V. Sechovsky, L. Havela, F.R. de Boer, J.J.M. Franse,
F.R. de Boer et al. / Properties o f UPdSn and UAuSn
[4]
[5]
[6]
[7]
[8] [9] [10]
[11] [12] [13]
P.A. Veenhuizen, J. Sebek, J. Stehno and A.V. Andreev, Physica B 142 (1986) 283. V. Sechovsky and L. Havela, in: Ferromagnetic Materials, Vol. 4, eds. E.P. Wohlfarth and K.H.J. Buschow (North-Holland, Amsterdam, 1988) p. 309. V. Sechovsky, L. Havela, P. Nozar, E. Briick, F.R. de Boer, A.A. Menovsky, K.H.J. Buschow and A.V. Andreev, Physica B 163 (1990) 103. H. Fujii, K. Kawanaka, T. Takabatake, E. Sugiura, K. Sugiyama and M. Date, J. Magn. Magn. Mater. 87 (1990) 235. R.A. Robinson, A.C. Lawson, K.H.J. Buschow, F.R. de Boer, V. Sechovsky and R.B. Von Dreele, J. Magn. Magn. Mater. 98 (1991) 147. P.A. Veenhuizen, F.R. de Boer, A.A, Menovsky, V, Sechovsky and L. Havela, J. de Phys. (1988) C8-485. L. Havela, V. Sechovsky, L. Jirman, F.R. de Boer and E. Briick, J. Appl. Phys. 69 (1991) 4813. L. Havela, V. Sechovsky, P. Nozar, E. Br/ick, F.R. de Boer, J.C.P. Klaasse, A.A. Menovsky, J.M. Fournier, M. Wulff, E. Sugiura, M. Ono, M. Date and A. Yamagishi, Physica B 163 (1990) 313. R. Verhoef, A. de Visser, A. Menovsky, A.J. Riemersma and J . J . M . Franse, Physica B 142 (1986) 11. J.O. Willis, Z. Fisk, G.R. Stewart and H.R. Ott, J. Magn. Magn. Mater. 54-57 (1986) 395. M.J. Besnus, J.P. Kappler and A. Meyer, J. Phys. F 13 (1983) 597.
287
[14] R.J. Elliott and F.A. Wedgwood, Proc. Phys. Soc. 81 (1963) 846. [15] R. Elenbaas, Thesis, University of Amsterdam (1980). [16] J.J. De Yoreo, W. Knak, M. Meissner and R.O. Pohl, Phys. Rev. B 32 (1986) 8828. V. Vaziri, Diplomarbeit, TU Berlin (1990). [17] K. Andres, D. Davidov, P. Dernier, F. Hsu, W.A. Reed and D.J. Nieuwenhuys, Solid State Commun. 28 (1978) 405. [18] H.H. Hill, in: Plutonium 1970 and other Actinides, ed. W.N. Miner, (Met. Soc. AIME, New York, 1970) p. 2. [19] J.C. Fuggle, F.U. HiUebrecht, R. Zeller, Z. Zolnierek, P.A. Bennet and Ch. Freiburg, Phys. Rev. B 27 (1982) 2145. [20] H. Fujii, M. Nagasawa, H. Kawanaka, T. Inoue and T. Takabatake, Physica B 165 & 166 (1990) 435. [21] B.R. Cooper, R. Siemann, D. Yang, P. Thayamballi and A. Banerjea, in: Handbook on the Physics and Chemistry of the Actinides, Vol. 2, eds. A.J. Freeman and G.H. Lander (North-Holland, Amsterdam, 1985) p. 435. [22] E. Br/ick, A.A. Menovsky, F.R. de Boer, K.H.J. Buschow, V. Sechovsky, L. Havela and P. Nozar, Proc. 20 ~mesJourn6es des Actinides, Prague, 1990, p. 37. [23] A.J. Freeman, J.P. Desclaux, G.H. Lander and J. Faber, Phys. Rev. B 13 (1976) 1168.
Physica B 176 (1992) 275-287 North-Holland
Magnetic, electrical, and specific-heat properties of UPdSn and UAuSn F(R. de B o e r a, E. Br/Jck a'l, H. N a k o t t e a, A.V. A n d r e e v a'2, V. Sechovsky b, L. H a v e l a b, P. N o z a r b, C.J.M. Denissen c, K . H . J . Buschow c, B. Vaziri d, M. Meissner d, H. Maletta e and P. Rogl f aVan der Waals -Zeeman Laboratorium, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands bDepartment of Metal Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czechoslovakia ~Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands dTechnische Universitiit, Berlin, Germany ~IFF KFA, D-5170 Jiilich, Germany fInstitut fiir Physikalische Chemie der Universitiit Wien, Wiihringerstrasse 42, A-I090 Wien, Austria Received 26 June 1991 Revised manuscript received 13 October 1991
UPdSn orders antiferromagnetically below 40 K and undergoes another magnetic phase transition at about 27 K, which is connected with a re-arrangement of the antiferromagnetic structure. The magnetic properties of UPdSn are strongly anisotropic with the c-axis as the hard-magnetization direction. For UAuSn, the maximum at 36 K in the x(T) curve may also indicate the onset of antiferromagnetism. However, the very broad anomaly in the specific heat, the poorly resolved "gSn M6ssbauer spectra and the magnetic history phenomena at lower temperatures do not point to long-range magnetic order. The possibility of a frozen non-periodic arrangement of U magnetic moments is discussed in connection with atomic disorder within the A u - S n sublattice. The distinction between the electron properties of UAuSn and UPdSn is reflected in the different values of the 3' coefficient of the low-temperature specific heat, which is remarkably small for UPdSn (5 mJ/mol K 2) in contrast to UAuSn (80 mJ/mol K2). A possible localization of the 5f states in UPdSn is envisaged.
I. Introduction
UPdSn and UAuSn belong to the large family of ternary UTX compounds of uranium with a transition (T) and a non-transition (X) element [1-4]. The compounds with X = Sn and T = Co, Ru, Rh, Ir crystallize in the ordered hexagonal structure of the ZrNiAl-type. Investigating UTSn compounds with even later d-metals, we observe a tendency to form either the cubic MgAgAs-type structure (UNiSn and one of the two reported modifications of UPtSn) or the hexagonal Caln2-type structure (UPdSn and ~On leave from Ural State University, Sverdlovsk, USSR. 2 Present address Center for materials Research, Stanford University, Stanford, California.
UAuSn). In this article we concentrate on the magnetic and related properties of the latter two compounds. The development of the electronic properties of the UTX compounds is strongly influenced by the varying degree of hybridization of the U 5f-electron states with valence-band states of ligands. As the d states of the transition metal ions are gradually filled, the hybridization, which affects the localization of the 5f states, becomes weaker due to the reduced 5f-d degeneracy. For the compounds with the ZrNiAI structure, which have been studied relatively extensively, we can thus follow the development from itinerant systems with a broad, strongly hybridized 5f-d band, to the situation where the 5f-band is narrowing, which leads to formation of local 5f
0921-4526/92/$05.00 (~) 1992- Elsevier Science Publishers B.V. All rights reserved
F.R. de Boer et al. / Properties of UPdSn and UAuSn
276
magnetic moments [3-5]. An analogous development has been observed within the group of UTX compounds with the CeCu 2 (TiNiSi)-type structure [5]. The enhanced y-values (characterizing the electronic contribution to the specific heat) observed for all compounds of these two groups illustrate that the more or less narrow 5f band remains pinned at E v and that real localization of the 5f states connected with a shift of 5f states from E F is not achieved in these systems. Our motivation for investigating compounds with the Caln2-type structure was to follow features of 5f-electron localization to a higher degree than can be achieved within the ZrNiA1structure group. We can suppose that, at least in first approximation, the crystal structure is favourable for such a study. Each U atom has only two nearest uranium neighbours with an interatomic separation of 360-365 pm (dr_ U = c / 2 ) along the c-axis. The distance between U atoms within the basal plane is equal to the lattice parameter a ranging from 460 to 472 pm. UPdSn and UAuSn have already been studied by Palstra et al. [1, 2]. Both compounds were reported as antiferromagnets, with T N = 29 K for UPdSn and 35 K for UAuSn. In this paper we report results of measurements of the magnetic susceptibility, the electrical resistivity, the specific heat in magnetic fields up to 5 T, the high-field magnetization at 4.2 K in fields up to
35T and the l~9Sn M6ssbauer effect at various temperatures.
2. Sample preparation and structure analysis Polycrystalline samples of UPdSn and UAuSn were prepared by arc melting appropriate amounts of at least 99.9% purity metals under argon gas. In the case of UPdSn, we have succeeded in growing a single crystal of approx. I cm 3 by means of the tri-arc Czochralski technique. X-ray diffraction patterns were consistent with the Caln2-type structure with the lattice parameters given in table 1. A small amount of impurity (probably around 5% USn3) was found in UAuSn. We have prepared also samples of UCuSn, another compound with the Caln2-type of structure. Because of the metallurgical difficulties (fast decomposition), only preliminary experimental data could be taken and this compound is not the subject of this paper. For comparison, however, the rough data have been included into table 1. A neutron diffraction study has indicated that an ordered ternary modification of Cain 2 (GaGeLi-structure type, space group P63mc) is the most plausible structure of UPdSn [7] with Pd and Sn occupying somewhat different positions. As the existence of atomic ordering within
Table 1 Lattice parameters a and c, magnetic-transition temperatures, Curie-Weiss parameters fgp, /~o,, and Xo obtained from fits (* - r e p r e s e n t the fit to the corrected gO(T) data) and the linear coefficient of the specific heat y for U A u S n and UPdSn. For comparison, also data for the antiferromagnet U C u S n and the ferromagnet U P d S b are given. U C u S n I denotes preliminary m e a s u r e m e n t s on our sample, U C u S n II values taken from ref. [6]. Data on UPdSb have been taken from ref. [1] except for the high-field magnetization done by ourselves. M~a, represents the saturated m o m e n t obtained by m e a n s of the m e t h o d m e n t i o n e d in the text. In cases where this extrapolation was not feasible only the magnetization in 35 T is given as the lower limit. comp. UPdSn polycr. a,b axis c axis * UAuSn UCuSn I U C u S n II UPdSb
a
c
~p [K]
10 9 X XII
3'
Msat
[pm]
TN, Tc [K]
~'/'eff
[pm]
[/xB/f.u.]
[m3/mol]
[mJ/molK2l
[jz./f.u. l
460.8
731.0
27 (38)
471.7 452.7 454.5 458.7
720.8 721.9 724.1 721.5
36 22 60 65
-8 -2.5 -60 -113 12
3.1 3.31 2.9 3.31 2.7 3.1 3.2 2.9
2.1 0 4.5 0 4.5
25 70
5
80 70 53 62
1.8
1.55 >1.65 >1.75 >1.63
F.R. de Boer et al. / Properties of UPdSn and UAuSn
277
Table 2 A t o m i c and thermal parameters for UPdSn. Space group: P63mc-C~v, No. 186; origin at 3 ml on 63mc. Unit-cell dimensions at 295 K: a = 0.46165 n m , c = 0.73205 nm, V = 0.1351 n m ~, c/a = 1.586. Density: p~ = 11.513 M g m -3. Linear absorption: p.(Mo K , , A 0 . 7 1 0 7 3 ) = 7 2 . 3 7 m m -~. T h e anisotropic thermal factors are expressed as: T=expl(-2~r2(Ulth2a*2+ Uz2kZb*2+ U3flZc*2+ U~2hka*b* + U~3hla*c* + U23klb*c*) × 10--')l, by symmetry U H = U22, U~3 = U23 = 0 ; the anisotropic secondary extinction (Zachariasen) was g = 3.86(33) x 10 -s. Residual values: R v. = 0.0478, R w = 0.0384, R G = 0.0464, G O F = 4.11. Atom
U Pd Sn
Site
2a 2b 2b
A t o m parameters x
y
z
0.0 i/3 2/3
0.0 2/3 1/3
I/4 0.4301(12) 0.5247(9)
the In sublattice of the Cain 2 structure can be very important for the electronic properties, we have performed a more profound X-ray diffraction study of a small single-crystal of UPdSn obtained from polycrystalline material by mechanical fragmentation. X-ray intensity data were collected on an automatic STOE four-circle diffractometer in one hemisphere of the reciprocal space up to the limit of sin 0/A = 8.1 nm -1 using monochromatic Mo K~I radiation. A set of 137 symmetry independent reflections was obtained by averaging symmetry equivalent reflections out of a total number of 1232 recorded intensities. All observed intensities (131 for ]F0] >3o'(F0) ) were used in the structure refinement. An empirical absorption correction was applied using q,-scans of three independent reflections. The results, summarized in table 2, are in very good agreement with ref. [7], and prove unambiguously that UPdSn is an ordered ternary compound. Similar analysis performed on UAuSn shows that the diversification of the In sites of the Cain 2 structure does not occur here and that Au and Sn randomly occupy the equivalent In sites.
3. Magnetic properties The temperature dependence of the magnetization in the temperature range 1.6-300 K was measured by means of a pendulum magnetometer in fields up to 1.3T and with a Faraday balance in fields up to 6 T. The measurements were performed on samples consisting of finepowder particles fixed in random orientation by
occ.
UH(=U22 )
U33
U~2
1 1 1
1.21(6) 1.69(15) 1.10(9)
1.29(9) 2.32(29) 1.65(29)
0.60(3) 0.85(8) 0.55(4)
glue. The magnetization of the UPdSn single crystal was measured also in the pendulum magnetometer, with the magnetic field applied along the various crystallographic axes. The magnetization at 4.2K was studied in magnetic fields up to 35 T in the High Field Installation at the University of Amsterdam. In order to derive the influence of the magnetocrystalline anisotropy from measurements on polycrystals, the following two types of finepowder samples were used: (a) loose powder, free to be orientated by the applied magnetic field, and (b) randomly-oriented powder, fixed by frozen alcohol. The magnetization data obtained in the first case (Mor) are believed to represent the magnetic response in the easy magnetization direction, while in the latter c a s e (Mrnd) we observe the behaviour of an "ideal" polycrystal. When interpreting such data, we are aware of the limitations due to possibly not perfectly singlecrystalline grains and incomplete orientation by the magnetic field. Direct comparison of powder data with measurements on a single crystal for UPdSn show that the free-powder magnetization is indeed very similar (about 10% lower) to that of the single crystal in the easy-magnetization direction. As can be seen in fig. 1, the magnetic susceptibility of UPdSn is strongly anisotropic. Measuring with the magnetic field B oriented along the basal plane, we observe two distinct maxima at 28 and 38 K. Nearly equivalent behaviour is found for fields along the a and b axis (in the orthorhombic notation). For B parallel to the
F.R. de Boer et al. / Properties o f UPdSn and UAuSn
278
500
a
500
' a
'
400i
400
200
~ crystal ]~
0
\'~0 " ~ " ""~.~ 0
10
20
30
40
;
t
i
i
i
50
100
150
200
250
5£
300
T (K) Fig. 1. Temperature dependence of the magnetization susceptibility (M/B vs. T plot) of the UPdSn single crystal in the a-, b- and c-directions and powder sample measured in a magnetic field of 1 T. The data denoted by s represent a simulation of the polycrystal data by an average of single-crystal results (see the text). Inset: details of the anomalies. hexagonal c-axis, the susceptibility is much w e a k e r and the lower m a x i m u m appears only in the form of a shoulder. In the t e m p e r a t u r e range between 20 and 40 K, and especially around the lower m a x i m u m , M/B in the a and b directions is rather field-dependent, as apparent from fig. 2, where a gradual upturn develops already around B = 1 T. This effect means that the lower maxim u m is more pronounced in higher fields, and the m e a s u r e m e n t s in fields of several teslas display the u p p e r anomaly only as a weak shoulder. This has led to the original claim that magnetic ordering takes place only at T - - 2 8 K [1]. The magnetization for B Nc grows linearly in fields up to 1.3T. In fig. 1, we also compare M/B obtained on the powder sample with that obtained on the basis of the single-crystal data as an average of the contributions from the three crystallographic axes. Very good agreement is found except for the range form 20 to 50 K. The field d e v e l o p m e n t of M/B for higher fields is d o c u m e n t e d in fig. 3, where the measurements p e r f o r m e d on powder in B = 1, 2, and 4 T are compared• A strong non-linearity in M versus B at low temperatures appears in fields B below 4T.
In the t e m p e r a t u r e range from 50 to 300 K, where the magnetization is proportional to the magnetic field, the susceptibilities (X = M/B) for B[]a, b are the same within the experimental error, as expected for the hexagonal compound. T h e y are well described by the Curie-Weiss law: I). I 0
0.()~
h "J"
30 K
0.()I
T
1(I I,, A" ~'
().(~'2 A
:'~0 I(
•
0.(10 ().7
! .()
L.?~
1~ i T ) F i g . 2. M a g n e t i z a t i o n c u r v e s m e a s u r e d o n U P d S n at 30 a n d 4 0 K in d i f f e r e n t c r y s t a l l o g r a p h i c d i r e c t i o n s . T h e solid lines a r e g u i d e s to t h e e y e .
F.R. de Boer et al. / Properties o f UPdSn and UAuSn 400
~
~
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279
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Fig. 4. Magnetization curves m e a s u r e d at 4.2 K in magnetic fields up to 35 T on a U P d S n single crystal with the magnetic field oriented along the principal crystallographic directions (using the orthorhombic notation).
60
Fig. 3. The low temperature ( T < 6 0 K ) part of M / B vs. T curves m e a s u r e d in magnetic fields of 1, 2 and 4 T. The solid lines are guides to the eye,
x
10
(1)
with Op = - 2 . 5 K and C = 1.75 × 10 -s m3/molK, from which the effective moment IXeff = 3.31/.q3/ U can be obtained. The gO(T) data can be fitted by the Curie-Weiss law ( O p = - 6 0 K and txeff = 2.9/.%/U) if an additive temperature-independent term X0 = 3.4 × 10 -9 m3/mol is assumed. Alternatively, this type of behaviour may be understood as a parasitic contribution due to the projection of the easy-axis magnetization connected with either a slight mosaicity of the crystal or a small error in the crystal orientation. The corrected gC(T) data (allowing a deviation of less than 2 ° in the crystal orientation) then can be tentatively fitted to (1) yielding 8p around - 1 1 0 K where the same value of /&eft is used as obtained for the a and b directions. The results of high-field magnetization measurements performed at 4 . 2 K on the UPdSn single-crystal (fig. 4) prove the enormous magnetic anisotropy. The magnetization curves for Blla and Bllb are very similar. The magnetization is low and proportional to the magnetic field below 3 T. The field of 3 T, where dM/dB increases abruptly, can be taken as the field where a moment-reorientation commences. We cannot,
however, distinguish where the transition terminates, because a smooth field dependence of the magnetization gradually tending towards saturation is observed up to the highest field applied. Intuitively, we can attribute this type of behaviour to a non-collinear antiferromagnetic ground state as suggested by the neutron-diffraction measurement [7]. The magnetization processes may consist of a spin flop retaining the non-collinearity of moments in the initial stage of the transition (in fields close to 3 T ) and subsequent rotation of the moments towards parallel alignment in high fields. The magnetization in 35 T, yielding 1.7 and 1 . 6 ~ J f . u . for a and b, respectively, is already close to the saturation value. More precisely, the saturation magnetization M0 can be estimated from the extrapolation of M versus 1/B which is found to be linear above 10T. This procedure leads to M 0 = 1.9 and 1.8~B/f.u. for a and b, respectively, which is close to the value of ( 2 . 0 5 ± 0 . 1 3 ) ~ B / U , obtained from the neutron-diffraction experiment [7]. The difference between the results obtained for B]la and BHb may be an indication of anisotropy within the ab plane. However, being aware of a certain mosaicity of our single-crystal and a possible deviation when mounting the crystal, we take such a conclusion with caution. We are also aware of the fact that for the case of a magnetic
280
F.R. de Boer et al. / Properties of UPdSn and UAuSn
unit cell of the orthorhombic symmetry, reported in ref. [7], the magnetic response along crystallographically identical directions may be different, and the situation can be further obscured by the possible existence of magnetic domains. Neutron diffraction on a UPdSn single crystal is desirable to solve this problem. The c-axis is undoubtedly the hard-magnetization direction. The magnetization curve for B llc consists of three linear parts separated by anomalies at 3 T (an increase of the M(B) slope) and 14T (a small metamagnetic-like anomaly). The origin of these anomalies is not clear at the moment. The maximum moment of 0.6P.B/f.u. is reached in 35 T. The magnetic anisotropy field B a is generally approximated by the field of intersect of the M(B) curves along the easy- and hard-magnetization axes. For UPdSn this estimate yields B a = l l 0 T . The comparison of the single-crystal results with the magnetization measurement on UPdSn in powder form [4], obtained from the polycrystalline piece used for the other experiments, shows that the data obtained on powder free to be oriented by the applied field mimic very well the easy-axis magnetization. Only the slightly lower value (by 10%) of the maximum magnetization in 35 T and a correspondingly higher slope of the M(B) curve at 35 T (lack of saturation) are signs of imperfect alignment of the grains and/or some fraction of multicrystalline powder particles. UAuSn displays a pronounced maximum in the M/B(T) dependence (fig. 5). This maximum is located at 36K when measured in magnetic fields ~<2T. When applying higher fields, the maximum is partially suppressed, rounded and shifted to lower temperatures. This amounts in approximately 1 K shift for B = 6 T. These facts may support the idea of essentially antiferromagnetic ordering in UAuSn at temperatures lower than 36K. However, complicated magnetic history effects, which have not been studied thoroughly up to now, modify the low temperature behaviour to a limited extent. Also the fact that the temperature dependence of the susceptibility deviates from the Curie-Weiss law already below 80K, means that UAuSn is not a
3.00 350 I M/B (10-9m3/mol) 4°° ~2T 2.50
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150
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T (K) Fig. 5. Temperature dependence of the inverse magnetic susceptibility (M/B in the magnetic field of 1 T) of a UAuSn powder sample in the paramagnetic state (T > 40). The solid line represents the fit according to eq. (2). Inset: Low temperature (T < 80 K) part of M / B vs. T curves measured in magnetic fields of 2 and 6 T.
typical antiferromagnet. In the ultimate case, the randomness introduced by an atomic disorder can lead to a cluster glass with prevailing antiferromagnetic interactions. Thus the maximum in x(T) does not need to be strictly connected with any magnetic phase transition in this case. New samples of UAuSn, which are better specified in the metallurgical sense, are necessary for future studies. The high-temperature susceptibility behaviour (T > 8 0 K ) can be fitted by a modified CurieWeiss law: C X
op)
+ x0.
(2)
The temperature-independent susceptibility X0 has a very small value (similar to UPdSn polycrystal) of X0 = 4.5 × 10 -9 m3/mol (other parameters can be found in table 1). This situation contrasts with the behaviour of the hexagonal UTX compounds of the ZrNiAl-structure group [3, 4]. Most of them, when measured in polycrystalline form, display considerable curvature of the 1/x(T) curves. These curves can approximately be fitted by the modified Curie-Weiss law (2), but the values of X0 are one order of mag-
F.R. de Boer et al. / Properties of UPdSn and UAuSn
nitude higher than those found for polycrystalline UPdSn and UAuSn. Closer inspection of the susceptibility data obtained on available single crystals (URuAI, UNiAI, UNiGa) shows that for these compounds the values of X0 are negligibly small [8-10] for B along any particular crystallographic direction. Therefore we believe that the large values of X0 obtained for polycrystals can be ascribed to the presence of a strong magnetic anisotropy becoming manifest also in the paramagnetic state. In a material with random grain orientation, the relative contribution of favourably oriented grains is low in the uniaxial case at high temperatures. At temperatures near Op, the relative contribution of these grains becomes dominant which leads to the curvature of 1/ x(r). The less pronounced curvature, measured for UPdSn and UAuSn, points thus to lower magnetic anisotropy or higher multiplicity of the easy-magnetization direction (which has actually been proved by the measurements on the UPdSn single crystal). Note that also the susceptibility data obtained on a powder material displaying high magnetic anisotropy yield values of the effective moment which are reduced with respect to the intrinsic values derived from single-crystal measurements. The UAuSn magnetization curves at 4.2K (fig. 6) are characterized by a very broad S-shape with an inflection point around 10 T and a weak tendency to saturation in higher fields. A mag1.5
UAuSn 4.2K free powder
1.0
o• 0.5
0.0
•
y
•
• o fixedpowder
10
20
30
40
B (T)
Fig. 6. Magnetizationcurves measured at 4.2 K in magnetic fields up to 35T on powders of UAuSn, free to orient in magnetic field and fixed in random orientation. The solid lines represent the measurement on the fixed powder in continuouslyvarying (up and down) magneticfield.
281
netization of 1.15/zB/f.u. is reached for oriented powder in 35 T, but this value is still far below the saturation magnetization, as the differential susceptibility d M / d B in this field is still considerably high. Note that the linear extrapolation of M versus 1 / B to 1 / B = 0 yields the value of 1.55/zB/f.u. The virtually featureless magnetization curve (exhibiting, however, small but measurable hysteresis in fields up to 15 T) may be associated with some kind of disorder of the spin system. In this stage of investigation, we cannot distinguish whether the small ferromagnetic component of 0.02tzB/f.u. is an intrinsic effect, possibly related to magnetic history phenomena seen in susceptibility measurements, or whether it is due to a spurious phase. The ratio Mrnd/Mor in 35 T for UAuSn (0.81) is similar to that found for UPdSn (0.78) which may point to similar anisotropy conditions.
4. l lgSn M6ssbauer effect studies
llgSn M6ssbauer spectra were taken on finepowder samples at various temperatures between 5 and 300K. A standard constant-acceleration spectrometer was used. The obtained spectra were fitted with a computer simulation including isomer shift IS (with respect to LaSnO3), quadrupole splitting QS and magnetic hyperfine fields Bhf. The experimental line width was 0.5 mms -~. Representative examples of 119Sn M6ssbauer spectra obtained on UPdSn are shown in fig. 7. It may be concluded that Zeeman splitting shows up in the spectra at temperatures lower than 40K and gradually increases with decreasing temperature. The full lines through the data points in fig. 7 represent the computer fits. The hyperfine parameters corresponding to the fit of the 15K spectrum are I S = 2 . 0 m m / s , Q S = 0 . 1 m m / s and B m = 5 . 0 T . Note that two subspectra (one of them with Bhf = 0) are observed in a certain temperature region (3040 K). The spectra consist of only one spectrum above 40 K (paramagnetic r a n g e - Bhf = 0) and below 30 K (antiferromagnetic range - Bh~ > 0). The single value of the magnetic hyperfine field recorded at low temperatures pertinent to all Sn
282
F.R. de Boer et al. / Properties o f UPdSn and UAuSn ,
300 K
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30
40
50
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60
T (K) Fig. 8. Temperature dependence of the magnetic hyperfine field on Hgsn in UPdSn and of the contribution to the integral intensity of the subspectrum with Bhf = 0 (paramagnetic fraction). The solid lines are guides to the eye.
18 -
L 0
5. Electrical resistivity
L 8
Velocity (mm/s)
~-
Fig. 7. H~M6ssbauer spectra for UPdSn at different temperatures. The solid lines represent computer fits.
nuclei supports the idea that UPdSn is an ordered ternary compound. The temperature dependence of the hyperfine field shown in fig. 8. reveals that magnetic ordering in UPdSn commences at about 40 K. This means that the first maximum in the x(T) plots is representative of the N6el temperature. Qualitatively different M6ssbauer spectra were obtained for UAuSn. A broad spectrum with poorly resolved features were recorded at 15 K yielding a mean value of hyperfine field /~hf= 2.83 T. This result allows the following possible interpretations: (a) a complex antiferromagnetic structure producing different values of Bhf a t the Sn sites, (b) magnetic state of asperomagnetic or spinglass type leading to a statistical distribution Bhf,
(c) no magnetic ordering but spin fluctuations with a characteristic time longer than the time scale (10 -9 s) of the M6ssbauer effect.
The electrical resistivity was measured on barshaped UPdSn and UAuSn bulk samples by a conventional AC four-probe method in the temperature range from 4.2 to 300K. The p(T) curves are given in fig. 9. A high concentration of internal cracks hampered the determination of the geometrical factor, so that only relative values of resistivity can be displayed. A very rough estimate gives 10300K 2000 Ixft cm for UPdSn, and =300 ixl2 cm for UAuSn, which are values not very different from those given in ref. [1]. The flat o(T) and the negative dp/dT developing gradually at low T (especially below 80 K) found for UAuSn can be understood as a lack of any coherence which occurs in compounds with a strong scattering of conduction electrons. Although the understanding of the electrical resistivity behaviour in narrow-band actinide compounds is still quite unsatisfactory, it is probable that variations of the strength of the coupling of conduction electrons to scatterers like charge and spin fluctuations (variations of the effective mass of quasiparticles at EF) determine primarily the shape of the p(T) curves. The electron-phonon scattering becomes of =
F.R. de Boer et al. / Properties of UPdSn and UAuSn
283
3000 UAu~n 2500
2000
2000
7.
-Z k. v
1500
1500
1000 1000 500 500
T tK)
i
o
L 0
0 50
100
10
150 T (K)
20
30
200
40
50 250
60 300
Fig. 9. T e m p e r a t u r e dependence of the relative resistance p of U A u S n and UPdSn. Inset: The low-temperature part of the p(T) curve for UPdSn.
minor importance for compounds with resistivities of hundreds of txf~cm. In this context, the behaviour of UAuSn is not irregular when taking into account the Au-Sn sublattice disorder. A similar situation has been found in numerous disordered systems like U(Pt, Pd)3 [11] or (U, Th)2Znl7 [12] or CePd3+ x [13]. In the case of UAuSn this effect could thus obscure the impact of magnetic ordering on the p(T) dependence. An alternative model can be based on the assumption that the low-temperature increase of p(T) is reflecting mostly an antiferromagnetic ordering, which affects the resistivity in a more conventional way via the elastic scattering of conduction electrons on localized moments [14]. The lack of any sharp anomaly can then be explained by a possible disorder (randomness) in the system of magnetic moments, or by a lack of any long-range magnetic ordering. The electrical resistivity of UPdSn (fig. 9) shows, in contrast to UAuSn, a significant decrease with decreasing T at low temperatures. There is, however, no sharp anomaly observed at the magnetic ordering temperature. Instead, a broad knee spread between 40 and 60K is formed (note that x(T) commences to deviate from the Curie-Weiss law below 60K). The magnetic transitions connected with the x(T)
anomalies at 28 and 38 K show up in the temperature derivative of the electrical resistivity as a maximum at 30K and a sudden change of slope at 41 K. At higher temperatures, a nearly linear increase with low d p / d T slope can be followed up to =230 K with a relatively abrupt flattening observed above this temperature. The nature of this high-temperature anomaly remains unclear. Our measurements are, however, in this point well reproducing the results in ref. [1].
6. Specific heat
An adiabatic technique was used for specificheat measurements in the temperature range from 1.2 to 35 K in magnetic fields of 0 and 5 T [15]. Additional measurements at higher temperatures were performed with the transientheat-pulse technique [16]. The thermal sampleto-bath time constants were typically of the order of 1-50s. Internal thermalization times were found to be smaller than 0.5 s. The heat capacity was determined by the evaluation of the initial temperature rise, the time constant of the exponential temperature decay and a separate measurement of the thermal resistance. The results from both methods agreed by better than
F.R. de Boer et al. / Properties o f UPdSn and UAuSn
284
5%. The heat capacity of the addenda was estim a t e d and was corrected for if found to be non-negligible. The absolute accuracy of the m e t h o d is approximately 10%. The specific-heat behaviour (figs. 10 and 11) underlines the rather different character of U P d S n and U A u S n at low T. For UPdSn, C / T reaches remarkably low values around 7 m J / m o l K 2 at 2 K. Extrapolation to zero temperature from the interval 2 - 8 K, where linear behaviour of C / T versus T 2 is found, provides - / = 5 m J / m o l K 2. This value is in a good agreement with y = 4.3 m J / m o l K 2 reported in refs. [1, 2]. Such a low value has only one analogy a m o n g U-intermetallics, namely the proposed localized 5f-electron c o m p o u n d U P d 3, having a value of y of approximately the same magnitude [17]. The C / T versus T 2 plot shows an abrupt change of slope around 8 K, which makes the linear part abnormally short. The anomaly around 8 K may be associated with the magnetic part of the specific heat, because it is this t e m p e r a t u r e where specific heat measured in 5 T commences to deviate considerably towards higher values from the zero-field data (not seen in fig. 10). The magnetic transitions are relatively very broad, one being manifest only as a shoulder at T = 27 K, whereas the magnetic ordering tempera1.0 UPdSn 0.8
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technique (triangles) in zero magnetic field. Inset: the C/T vs. T 2 plots at low temperatures for B = 0 and 5 T. ture is reflected in the m a x i m u m around 38 K. As no suitable non-magnetic " b a c k g r o u n d " compound is available, it is very difficult to estimate the magnetic-entropy change. The solid curve in fig. 10, corresponding to a D e b y e temperature O D = 220 K estimated from the slope of the low t e m p e r a t u r e part, results in A S = 1.5 Rln2 at 45 K. Comparing this value with 0.1 Rln2 reported for the heavy-fermion antiferromagnet UNiA1 [10], we can claim that despite the large uncertainty of our estimation the magnetic entropy of UPdSn is of the order of magnitude which is expected for a local-moment system. For U A u S n , C / T versus T 2 is linear between 5 and 14 K yielding y = 80 m J / m o l K 2. An upturn below 5 K, which is partially suppressed in 5 T, points to y = 110 m J / m o l K 2. However, as it is a field-sensitive effect we cannot exclude an extrinsic origin of this feature. Only a very broad m a x i m u m in C / T versus T was observed at 35 K, the t e m p e r a t u r e of the susceptibility maximum.
6O
T (K)
Fig. 10. Temperature dependence of the zero-field specific heat of UPdSn plotted in the representation C/T vs. T. The full line represents an estimation of the non-magnetic part (see text). Inset: the C/T vs. T 2 plot at low temperatures for B =0 and 5T.
7. Discussion
Although UPdSn and U A u S n both display magnetic order they differ qualitatively in several
F.R. de Boer et al. / Properties o f UPdSn and UAuSn
aspects. The basic difference consists in the character of the 5f states. Let us suppose the 3,-coefficient to be the primary key distinguishing the presence of 5f states at the Fermi level. Principally, band-like behaviour of 5f states, i.e. 5f character of the states at E F can be expected if 3' is enhanced and has values falling at least in the range 10-20 m J / m o l K 2, which is typical for pure light actinides. The existence of localized 5f states separated from E F can be then assumed if 3' is below 10 m J / m o l K 2. The boundary remains, however, rather fuzzy, because UPd 3 (3' = 5 m J/ molK 2 [17]) is a well-documented but still singular case among U intermetallics. According to this criterion, UPdSn should be taken as the second metallic system with localized 5f states. Correspondingly, the high 3,-values obtained for U A u S n would indicate the formation of a 5f band. We are aware that high 3' values can speculatively also be attained in, e.g., an Anderson lattice. In this case, it is not the presence, but the proximity of 5f states to E F that guarantees a high 3,-value, provided that the intra-ionic Coulomb interaction U and the 5f-hybridization with conduction-electron states are sufficiently strong. Whether such a regime occurs for U intermetallics is, however, still an open question. On the other hand, one can imagine a situation where, e.g., the magnetic sub-band splitting or the formation of a gap due to antiferromagnetic ordering can lead to a considerable reduction of the density of states at E F for a 5f band of any width. T o shed more light on this, high-resolution UPS experiments on UPdSn are under way. However, the influence of an antiferromagnetic gap can be, however, excluded in view of the simple p(T) dependence (fig. 9). The question arises, whether the striking difference between UPdSn and UAuSn is directly connected with the difference in interuranium spacing, which is somewhat larger in UPdSn. The values of du_ u around 360 pm are not much higher than the Hill limit [18], but the arrangement of the U atoms into a nearly one-dimensional network can lead either to higher sensitivity of the 5f bandwidth to the interuranium spacing, or to a shift of the effective Hill limit to lower values due to the fact that each U atom
285
has only 2 U nearest neighbours. Because we expect the strength of the 5f-ligand hybridization to be the dominating factor for the character of the 5f states [4], the difference in behaviour between UPdSn and UAuSn can be due also to differences in the degree of hybridization between the U 5f states and the Pd 4d or Au 5d states, respectively. Although the 4d states in metallic Pd are not filled completely in contrast to the 5d states of Au, the former are pushed down towards higher binding energies (to - 4 eV for 1 : 1 : 1 stoichiometry) and the 4d band becomes much narrower in compounds with the more electropositive U [19]. This reduces a possible energy overlap with 5f states and the 5f-4d hybridization may therefore be very weak. The arrangement of the U atoms in the crystal structure plays a key role also in the geometry of the magnetic ordering. For example, U T X compounds crystallizing in the hexagonal ZrNiAIstructure type exclusively have uniaxial anisotropy with the hexagonal axis being the easymagnetization axis [4]. As the values of the anisotropy fields amount to hundreds of teslas and hence exceed by one order of magnitude the anisotropy fields in the isostructural rare-earth compounds [20], it does not seem justified to use a conventional description of the anisotropy energy in terms of crystal-field theory. A tentative application of the Anderson Hamiltonian with an effective interaction of the CoqblinSchrieffer type and a quantitative analysis of concomitant hybridization-induced anisotropic interaction between local moments [21], leads to correct conclusions about the easy directions of the magnetic moments. In this description, parallel moments oriented perpendicular to the interionic axis are favoured. The uniaxial anisotropy of the hexagonal compounds U T X is in agreement with the strongest interaction (ferromagnetic as a rule) occurring within the basal-plane layers containing U and transition-metal atoms [5]. Analogously, in the compounds crystallizing in the orthorhombic structure (CeCu2-structure type), where the U atoms are positioned along zig-zag chains, the easy-magnetization direction is perpendicular to the chain [22]. The cases of UPdSn and U A u S n are expected to be similar.
286
F.R. de Boer et al. / Properties of UPdSn and UAuSn
U atoms in the Cain: structure or its modification form a network of one-dimensional chains, the separation of the chains being larger than 450 pm. Such a situation should provide a good possibility for the easy-plane anisotropy with the moments within the basal plane. Indeed, the values of M r , d / M o r , for both compounds very close to 0.79, as expected for an easy-plane system, support this idea. Single-crystal measurements show that the c-axis is indeed the hardmagnetization direction, but the a- and b-axes need not be equivalent. A rather complex type of magnetic structure of UPdSn is suggested on the basis of neutron diffraction [7] assuming a standard U form factor [23]. Primarily, it was shown that there are two different antiferromagnetic phases. The high-temperature phase (phase I), stable between approximately 27 and 38 K, has magnetic moments perpendicular to a and tilted from b towards c by =35 ° . In the low-temperature phase (phase II), the tilting towards c increases to =38 ° and, moreover, tilting from b appears. The components of moments in the a b plane are ordered parallel within the atomic chains (parallel to c) in both phases. The tendency of the U moments to couple ferromagnetically within the chains may be the source of the positive value of Op found in all compounds summarized in table 1 except for UPdSn where Op is small but negative. The fact that the lowest 00 value is reached for UPdSn may be related to the largest U - U spacing occurring in this compound. The antiferromagnetic ordering may then be attributed to an antiferromagnetic interaction between the chains for all compounds containing Sn, whereas in UPdSb it is ferromagnetic. In UAuSn, the atomic disorder in the A u - S n sublattice may introduce some randomness of the magnetic interactions and consequently lack of periodic ordering of the U magnetic moments.
netically ordered below 40K. Specific-heat studies specify the ordering temperature as T N = 38 K. The change of magnetic structure around 28 K, detected by neutron diffraction [7] is also documented in the temperature dependence of the magnetization. Magnetic moments of 1.81.9/XB/U were estimated from magnetization measurements in high magnetic fields. The magnetic anisotropy field equals 110 T which is estimated from the magnetic isotherms at 4 . 2 K measured with the field applied in the basal plane and along the c-axis, the latter being the hard-magnetization axis. The value of the 3' coefficient in UPdSn is very low and is reminiscent of that of UPd 3. Microscopic evidence is, however, necessary to establish the character of the 5f states. The difference between UPdSn and U A u S n probably is manifest already on the crystallographic level. While UPdSn is an ordered compound, there are indications from several experiments that there is a random occupation of the atomic Au and Sn sites in UAuSn, which leads to a certain degree of magnetic disorder. This has been corroborated by the precise X-ray diffraction analysis, that has shown that UAuSn is disordered ternary system with the Caln2-type of structure. The high value 3' = 8 0 m J / m o l K 2 points to a conventional band-like character of the 5f electron states in UAuSn.
Acknowledgements This work is part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie ( F O M ) " . Part of the work of V.S. has been kindly supported by the Alexander von Humboldt Foundation.
References 8. Conclusions We have prepared polycrystalline samples of UPdSn and UAuSn and a single crystal of UPdSn. Magnetic measurements and M6ssbauer spectroscopy show that UPdSn is antiferromag-
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F.R. de Boer et al. / Properties o f UPdSn and UAuSn
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[5]
[6]
[7]
[8] [9] [10]
[11] [12] [13]
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