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Anisotropies of the electrical resistivity and Hall effect in UAsSe
Journal of
ALLOYS AND COMPOUNDS ELSEVIER
Journal of Alloys and Compounds 219 (1995) 248-251
Anisotropies of the electrical resistivity and Hall effect in UAsSe Z. Henkie, R. Fabrowski, A. Wojakowski IV.. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 937, 50-950 Wroctaw 2, Poland
Abstract
We show that anisotropy of the resistivity in UAsSe proves that its total resistivity contains both an isotropic spin disorder component (controlled by RKKY exchange interaction) and an anisotropic single impurity Kondo-like (TK=50 K) component. They are present in both paramagnetic and ordered states. This uniaxial and collinear ferromagnet (below 113 K) exhibits high magnetocrystalline anisotropy. Examination of the Hall effect in the paramagnetic phase (up to 430 K) showed that the isotropic normal Hall coefficient Ro = - 8 . 8 × 10 -4 cm 3 C-1 (0.47 e - fu-1 in the single band model) is accompanied by a highly anisotropic spontaneous Hall coefficient. This is equal to 0.78 and 3.0 cm 3 C-a for Rsac and Rs"b (magnetic field along the c or b axis) respectively. Keywords: Anisotropies; Electrical resistivity; Hall effect
1. Introduction
2. Experimental details
UAsSe crystallizes in the tetragonal PbFCl-type structure [1]. This structure consists of layers stacked in the c direction with sequence A s - U - S e - S e - U - A s . UAsSe shows collinear ferromagnetism [2] with ordering temperature Tc = 113 K and a very high magnetocrystalline anisotropy constant 107 erg g-1 [3]. Over 20 years ago some of us [4] reported that the temperature coefficient of in-basal plane resistivity pa(Z) outside the range 0.5T~ and Tc is negative. This result was confirmed by Schoenes et al. [5]. They also examined the isostructural thorium compound ThAsSe which is a diamagnetic conductor. Its resistivity increases when the temperature decreases from 300 K to 100 K. Simultaneously, the Hall carrier concentration decreases from 0.6 e - fu -~ to 0.08 e - fu -1 [5]. UAsSe shows an enhanced electronic specific heat (3,=41 mJ mo1-1 K -2 [6]) and the same type of p(T) behaviour as observed for CeNiSn [7] and Ua_xCexRu2Si2 [8,9]. The first compound belongs to the pseudogap system while the second is a heavy fermion compound. The latter system has recently attracted much attention and we were curious to see whether similar physics can be applied to UAsSe. Therefore, we started with an extensive study of electron transport properties. Preliminary results are given in [10], and are completed here by quantitative analysis of the resistivity anisotropy and measurements of the Hall coefficient anisotropy in the paramagnetic phase.
Plate-like single crystals of UAsSe, of thickness up to 0.5 mm along the c axis and other dimensions up to 10 mm, were grown by chemical vapour transport. Details of resistivity measurements are given in [10]. The effective Hall coefficient *R was determined by a d.c. method with two Hall voltage electrodes. Two samples with very similar dimensions cut out of the same crystal (To = 106.0 K) were examined to ensure the same accuracy of measurements. Ag electrodes were attached to the specimen with In using a soldering iron. The parameter */Ub was determined for a sample with dimensions 1.1 × 0.16 × 0.34 mm 3 along the axbxc crystal axes which were parallel to the electrical current i, the magnetic field H, and the Hall voltage UH respectively. For determination of */Uc the sample had dimensions 1.1 ×0.14 x 0.36 mm 3 along the axcxb axes, i.e. along the i, H and UH directions respectively. The dimensions were determined by a conventional optical microscope. The Hall voltage was read as a function of time when the magnetic field was switched repeatedly between -T-1.9 T every 30 s. Each period consisted of a 15 s interval for field switching and stabilization and a 15 s interval for collecting five UH data. Determination of the time dependence of UH at constant current increased the accuracy of the Hall coefficient determination. The UH measurements were taken for both directions of current through the sample.
0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)05057-0
Z. Henkie et aL / Journal of Alloys and Compounds 219 (1995) 248-251
3. Results and discussion 6
3.1. The Hall effect
/~
The *R data are collected in Fig. 1. Data from Ref. [10] (samples 9 and 10) are also included for reference. These data were obtained from crystals with regular plate form and well formed natural faces. Their thickness was determined by measuring the weight and surface of the plate. The Hall coefficient measured under a magnetic field consists of two parts: the normal Hall coefficient Ro and an anomalous contribution. Ro is inversely proportional to the carrier concentration. The anomalous contribution is due to scattering of the carriers by the magnetic system. We assume that for the paramagnetic state of UAsSe the standard procedure for evaluation is applicable: *R=Ro+4~'Rs*K
*K=
¢w 1 + 47rNKv
(1)
Here *K(T) is the effective susceptibility, Rs the spontaneous Hall coefficient and N the demagnetization factor. We assume (after Refs. [3,11]) that the volume susceptibility of examined samples ~ is described by the Curie-Weiss relation ¢ ~ = C J ( T - * @ ) where Cv=0.0378 emu K cm -3 [11] was used for all samples. The Weiss constant w@ is the best value giving a linear fit of the *R vs. *K (*K=CJ(T-Wr)+47rNCO) dependence. Good linearity of */P~ vs. *~( dependence for all samples was found when the relation Tc + 20 =*@~ - 4"rrNC~was obeyed. The value w~gb= - 41 K provides linearity of the *R"b(*d') dependence. The linear extrapolations shown in Fig. 2 determine both Ro and R,. The * / ~ vs. *K~ data for samples 9 and 10 agree with each other quite well. The Curie temperatures differ by 2%. These *R"c data would also agree well 10
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i
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o
¢.3
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-11J
-12 U'HIIc-0xisj ~ l l b - * R °b.
8 ~"
@a A ÷ 0 A ÷ $6~
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a
÷*~*%@~'~ 0100
7
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I
I
200
300
a
a
a
oo . .
4~)0
T[K] Fig. 1. Temperature dependence of the effective Hall coefficient *R for samples characterized by T¢= 107.0 K and 104.8 K (samples 9 and 10 respectively), and 106.0 K (samples 11 and 12).
249
o,omp,.9
/
• ~o.,pl, 10
/C.,.,o~
+ sample 11
oAf~tK
•N =
Cv T_ 8.4~.NCv
/
"~2
0
4~*% Fig. 2. Effective Hall coefficient *R vs. effective susceptibility 4~-*K (see text).
with the data for sample 11, characterized by intermediate To, if multiplied by 1.22. This factor presumably accounts for inaccuracy of the thickness measurement of samples 11 and 12. Therefore we increased Ro and Rs by 22%. We conclude that the normal Hall coefficient of UAsSe is isotropic and equal to Ro = - 8.8 × 10 -4 cm 3 C-1. Thus, the carrier concentration is 0.47 e - fu -1 in the single band model. The spontaneous Hall coefficient is very anisotropic and equal to 0.78 and 3.0 cm 3 C- 1 for Rs"c and Rs=brespectively. Rsab is presumably underestimated as the fitted value of w@b= _ 41 K does not approach the value of wOb ------ 402 K anticipated from susceptibility measurements [11]. The accuracy of alignment of UH and H with the crystal axes seems rather poor owing to the small sample dimensions. 3.2. Resistivity We analyse the results of resistivity measurements given in Ref. [10]. Resistivity tensors are given along the a axis 0e(T), and along the c axis pc(T), for a UAsSe crystal characterized by Tc = 102.0 K. Fig. 3 shows pC(T)-p=(T)=Ap(T) vs. temperature (lower curve). These data are also plotted on coordinates [(Ap(T)-constant)/T, T - l lOg T]. The pc(T)-pa(T)= Ap(T) subtraction eliminates the isotropic component. This procedure removes the resistivity anomaly shown by both resistivity tensors at the ferromagnetic transition (see Fig. 6). If the negative slope of dp/dT for UAsSe were due to thermal activation of electrons through a forbidden gap, then all the resistivity components should show an anomaly at To. This is because of the expected shrink in the gap edge due to ferromagnetic ordering [12]. However, this is not the case and we propose another interpretation. The upper line in Fig. 3 is described by the formula Ap(T) = constant - CK log T+ Cp, T
(2)
Z. Henkie et al. / Journal of Alloys and Compounds 219 (1995) 248-251
250
0.01
Log(T) / T [Log(K)/K ] 0.03
10,
i
0.05 0
,
"~ i ---..._
,
S
,
1[, .':: U:ingp~i UAsSe : ' / ! - : : - - : - : ............ -'using Ln = /[ PKAr / / ,/J~'/ ./ . . . . . tu~'2
b
.~
i--
...'/.s'
...... UAs,
30K/
•~
Z7
-20
0
:
.........................
0 2
0
200 T[K]
..........
400
•
T/Tc,N
~
Fig. 3. Dependence of p C ( T ) - I f ( T ) = A p ( T ) vs. temperature (lower curve) and ( A p - l 1 7 5 ) / T vs. T -~ log(T) (upper curve) for crystal characterized by T¢= 102.0 K.
Fig. 5. R K K Y interaction controlled spin-disorder resistivity of UAsSe derived using both experimental pK(T) ( . . . . . ) and Arai's formula ( - - ) vs. T/T¢. The basal-plane resistivity for UAs2 and UP2 [17] vs. T/7~ is given for comparison.
p -• 1.0
-
P k ............
0.8
Pph
. . . . .
Ps
.......
Or
.........
~ 0.6 k-
E~o.4
>
0,2
'... ,,,i
10-1
. . . . .
,.,t
. . . . . . . .
10o T/TK
i
. . . .
Fig. 4. Kondo resistivity normalized to its value at 0 K vs. T/TK as predicted by Arai's formula (Eq. (3)) ( - - ) and our value derived experimentally for UAsSe ( . . . . . ).
where CK and Cph are coefficients. It allows us to assume that the anisotropic components are the Kondo resistivity pK and the phonon resistivity Pph- The isotropic component will be denoted p~(T). Deviation of Ap(T) from a logarithmic dependence at low temperatures can be described in terms of a single impurity behaviour in the Kondo limit of the Anderson model [13]. We use Arai's formula [14] for a quantitative description of pK(T) over the whole temperature range (Fig. 4)
(3)
where a(T) is a universal function of T/TK and is given by the solution of [a(T) - TL/T] ln{[1 + a2(T)]U2T/TL} - 7r In 2 = 0
/ ~ (1
2
101
I~(T)/pK(0) = {1 + 0r2/3)[a(T)]-2}-,
"'-,
(4)
where TL = Tx/0.624 [13]. The phonon component is described by the generalized Bloch-Grfineisen formula [15,16] written as
0
0
200 T[K]
400
Fig. 6. Total resistivity tensors along the c-axis ptc and along the a,axis pta for U A s S e and their components: Kondo Pr, phonon Pph, RKKY exchange controlled spin disorder p~ and residual p,.
p,..(T) = G.(T/e.)%(T/OD) J,(x) =
f
(e ~- 1)(1 - e - 0
(5)
o
We take n = 3 as we expect the band structure features of UAsSe will be closer to those of transition metals than to those of simple metals ( n = 5 ) . The Debye temperature OD=233 K is taken from specific heat measurements [6]. Ap(T) is described using a linear combination of Eqs. (3) (5). It allows us to split Ap(T) into two parts which give the temperature dependences of pK(T) and pp.(T). This p K e x P ( T ) / p K ( 0 ) determined experimentally from the best fit pK(0)= 6 6 0 / . ~ cm and TK = 40 K is compared
Z. Henla'e et al. / Journal of Alloys and Compounds 219 (1995) 248-251
in Fig. 4 with pKAr(T)/pK(0)given by Arai's formula (3). To determine the contribution of px(T) to the p,a(T) tensor we created a linear combination of pK(T) and Ppn(T) that describes the temperature dependence of this tensor above 120 K: pta(T)=xpK(T)+ypph(T)+ constant. We have assumed that p ~ ( T ) = x p K ( T ) and ppha(T) =ypph(T) and p ~ ( T ) + pr~ = pa(T) - pK~(T) -- Ppha(IV) between 2 and 443 K. This procedure could be done using either pK¢*P(T) or pKA~(T). TO determine the residual resistivity we have assumed that p~(2)= 0 for the case when p,a(T) is determined using pK~xp(T). The determined p,~(T) is normalized to its value at T¢, i.e. p,~(T)/p~(T~). Fig. 5 shows p~a(T) vs. the reduced temperature T/Tc. The same procedure was applied to the resistivity tensor along the c-axis. All the determined resistivity components are collected in Fig. 6. 4. Discussion It is interesting that Ps for UAsSe shows thermal behaviour very similar to the in-plane resistivity of uranium dipnictides. To show this, the basal plane resistivity of UAs2 and UP2 are presented in Fig. 5. The high temperature limit of the spin disorder resistivity psa(300) = 158/zl-I cm for UAsSe can be compared with pa(300) = 160 /zO cm for the basal plane resistivity of UAs2 [17]. The observed similarity is satisfying, if we take into account that all uncertainties, both experimental and due to assumptions on the temperature dependences, are cumulated in the derived psa(T). UPz and UAs2 are antiferromagnets with magnetic moments perpendicular to the basal plane. The basal plane residual resistivity is very low; RRR=p(300)/ p(4.2) > 200. This resistivity behaves in fact very much as is expected for the spin disorder resistivity of a ferromagnet with RKKY exchange interaction [17]. The residual resistivity increases as we come to ternaries. The RRR equals 1.8 and 2.8 for UAsS and UAsTe respectively [4]. At the other end of this class of compounds,/3-US2 is a paramagnetic semiconductor with forbidden gap at approximately 1.2 eV [18]. However, the/~-UYY' compounds (Y and Y' are chalcogen atoms) show a transition to a ferromagnetically ordered metallic state [19]. We think that this might be connected with possible disorder in occupation of Y and Y' positions in the structure. The magneto-optical Kerr effect shows the presence of an f band at the Fermi energy (filled with nearly three electrons) and hence p--f hybridization in UAsSe. However, the number of charge carriers nc is estimated to be less than 0.3 e - fu -1 [20]. Our Hall effect examination shows that nc = 0.47 is rather at the lower limit. It can be compared with 1.2 and 0.53 e - fu -1 (from the Hall effect) for UP/and USb2 [21] respectively. An even higher number of conduction electrons is deduced from positron annihilation experiments, 2.0,
251
2.5 and 1.6 + 0.4 for UP2, U S b 2 and UAsSe respectively [22]. The latter study also shows a lower anisotropy of the Fermi surface geometry in the ternaries than in the dipnictides. Various methods show different numbers of charge carriers but the expected difference in the number of charge carriers between UAsSe and some dipnictides is not well documented by either pdT) or Hall coefficient data. Thus the main feature that distinguishes the transport properties of UAsSe from those of the dipnictides is the high incoherent Kondo-like scattering present in excess of the RKKY exchange controlled spin disorder scattering in both paramagnetie and ordered states. The Kondo-like scattering is most probably induced by anion disorder which may result from strong hybridization. Acknowledgment This work was supported by the Committee for Scientific Research, Grant no. KBN-2 P302 173 06. References [11 F. Hulliger, J. Less-Common Met., 16 (1968) 113. [2] J. Leciejewicz and A. Zygmunt, Phys. Status Solidi A, 13 (1972) 657. [3] K.P. Bielov, A.S. Dmitrievski, A. Zygmunt, R.Z. Levitin and W. Trzebiatowski, Zh. Eksp. Teor. Fiz., 64 (1973) 582. [4] A. Wojakowski, Z. Henkie and Z. Kletowski, Phys. Status Solidi A, 14 (1972) 517. [5] J. Schoenes, W. Bacsa and F. Hulliger, Solid State Commun., 68 (1988) 287. [6] A. Blaise, R. Lagnier, A. Wojakowski, A. Zygmunt and M.J. Mortimer, J. Low Temp. Phys., 41 (1980) 61. [7] T. Takabatake, M. Nagasawa, H. Fujii, G. Kido, K. Sugiyama, K. Senda, K. Kindo and M. Date, Physica B, 177 (1992) 177. [8] M. Mihalik, A. deVisser, K. Bakker, L.T. Tai, A.A. Menovsky, R.W.A. Hendrix, T.J. Gortenmulder, S. Matas and N. Sato, Physica B, 186-188 (1993) 507. [9] M.B. Maple et al., Phys. Rev. Lett., 56 (1986) 185. [10] Z. Henkie, R. Fabrowski and A. Wojakowski, Acta Phys. Polon. A, 85 (1994) 249. [11] Z. Henkie, R. Fabrowski, A. Wojakowski and A.J. Zaleski, J. Magn. Magn. Mater., 140-144 (1995) in press. [12] S. Alexander, J.S. Helman and I. Balberg, Phys. Rev. B, 13 (1976) 304. [13] H.L. Neal and D.J. Collins, Phys. Rev. B, 48 (1993) 4299. [14] T. Arai, J. Appl. Phys., 57 (1985) 3161. [15] G. Grimvall, in E.P. Wohlfart (ed.), Selected Topics in Solid State Physics, Vol. 16, North-Holland, Amsterdam, 1981, p. 219. [16] J. Pierre, S. Auffret, J.A. Chroboczek and T.T.A. Nguyen, J. Phys. Condens. Matter, 6 (1994) 79. [17] Z. Henkie and Z. Kletowski, Acta Phys. Polon. A, 42 (1972) 405. [18] W. Suski, T. Gibifiski, A. Wojakowski and A. Czopnik, Phys. Status Solidi A, 9 (1972) 653. [19] R. Tro6, D. Kaczorowski, L. Shlyk, M. Potel and H. No61, J. Phys. Chem. Solids, 55 (1994) 815. [20] W. Reim, J. Magn. Magn. Mater., 58 (1986) 1. [21] Z. Henkie, P. Wi~niewski, R. Fabrowski and R. Maglanka, Solid State Commun., 79 (1991) 1025. [22] B. Rosenfeld, E. Debowska, Z. Henkie, A. Wojakowski and A. Zygmunt, Acta Phys. Polon. A, 51 (1977) 275.
ALLOYS AND COMPOUNDS ELSEVIER
Journal of Alloys and Compounds 219 (1995) 248-251
Anisotropies of the electrical resistivity and Hall effect in UAsSe Z. Henkie, R. Fabrowski, A. Wojakowski IV.. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 937, 50-950 Wroctaw 2, Poland
Abstract
We show that anisotropy of the resistivity in UAsSe proves that its total resistivity contains both an isotropic spin disorder component (controlled by RKKY exchange interaction) and an anisotropic single impurity Kondo-like (TK=50 K) component. They are present in both paramagnetic and ordered states. This uniaxial and collinear ferromagnet (below 113 K) exhibits high magnetocrystalline anisotropy. Examination of the Hall effect in the paramagnetic phase (up to 430 K) showed that the isotropic normal Hall coefficient Ro = - 8 . 8 × 10 -4 cm 3 C-1 (0.47 e - fu-1 in the single band model) is accompanied by a highly anisotropic spontaneous Hall coefficient. This is equal to 0.78 and 3.0 cm 3 C-a for Rsac and Rs"b (magnetic field along the c or b axis) respectively. Keywords: Anisotropies; Electrical resistivity; Hall effect
1. Introduction
2. Experimental details
UAsSe crystallizes in the tetragonal PbFCl-type structure [1]. This structure consists of layers stacked in the c direction with sequence A s - U - S e - S e - U - A s . UAsSe shows collinear ferromagnetism [2] with ordering temperature Tc = 113 K and a very high magnetocrystalline anisotropy constant 107 erg g-1 [3]. Over 20 years ago some of us [4] reported that the temperature coefficient of in-basal plane resistivity pa(Z) outside the range 0.5T~ and Tc is negative. This result was confirmed by Schoenes et al. [5]. They also examined the isostructural thorium compound ThAsSe which is a diamagnetic conductor. Its resistivity increases when the temperature decreases from 300 K to 100 K. Simultaneously, the Hall carrier concentration decreases from 0.6 e - fu -~ to 0.08 e - fu -1 [5]. UAsSe shows an enhanced electronic specific heat (3,=41 mJ mo1-1 K -2 [6]) and the same type of p(T) behaviour as observed for CeNiSn [7] and Ua_xCexRu2Si2 [8,9]. The first compound belongs to the pseudogap system while the second is a heavy fermion compound. The latter system has recently attracted much attention and we were curious to see whether similar physics can be applied to UAsSe. Therefore, we started with an extensive study of electron transport properties. Preliminary results are given in [10], and are completed here by quantitative analysis of the resistivity anisotropy and measurements of the Hall coefficient anisotropy in the paramagnetic phase.
Plate-like single crystals of UAsSe, of thickness up to 0.5 mm along the c axis and other dimensions up to 10 mm, were grown by chemical vapour transport. Details of resistivity measurements are given in [10]. The effective Hall coefficient *R was determined by a d.c. method with two Hall voltage electrodes. Two samples with very similar dimensions cut out of the same crystal (To = 106.0 K) were examined to ensure the same accuracy of measurements. Ag electrodes were attached to the specimen with In using a soldering iron. The parameter */Ub was determined for a sample with dimensions 1.1 × 0.16 × 0.34 mm 3 along the axbxc crystal axes which were parallel to the electrical current i, the magnetic field H, and the Hall voltage UH respectively. For determination of */Uc the sample had dimensions 1.1 ×0.14 x 0.36 mm 3 along the axcxb axes, i.e. along the i, H and UH directions respectively. The dimensions were determined by a conventional optical microscope. The Hall voltage was read as a function of time when the magnetic field was switched repeatedly between -T-1.9 T every 30 s. Each period consisted of a 15 s interval for field switching and stabilization and a 15 s interval for collecting five UH data. Determination of the time dependence of UH at constant current increased the accuracy of the Hall coefficient determination. The UH measurements were taken for both directions of current through the sample.
0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)05057-0
Z. Henkie et aL / Journal of Alloys and Compounds 219 (1995) 248-251
3. Results and discussion 6
3.1. The Hall effect
/~
The *R data are collected in Fig. 1. Data from Ref. [10] (samples 9 and 10) are also included for reference. These data were obtained from crystals with regular plate form and well formed natural faces. Their thickness was determined by measuring the weight and surface of the plate. The Hall coefficient measured under a magnetic field consists of two parts: the normal Hall coefficient Ro and an anomalous contribution. Ro is inversely proportional to the carrier concentration. The anomalous contribution is due to scattering of the carriers by the magnetic system. We assume that for the paramagnetic state of UAsSe the standard procedure for evaluation is applicable: *R=Ro+4~'Rs*K
*K=
¢w 1 + 47rNKv
(1)
Here *K(T) is the effective susceptibility, Rs the spontaneous Hall coefficient and N the demagnetization factor. We assume (after Refs. [3,11]) that the volume susceptibility of examined samples ~ is described by the Curie-Weiss relation ¢ ~ = C J ( T - * @ ) where Cv=0.0378 emu K cm -3 [11] was used for all samples. The Weiss constant w@ is the best value giving a linear fit of the *R vs. *K (*K=CJ(T-Wr)+47rNCO) dependence. Good linearity of */P~ vs. *~( dependence for all samples was found when the relation Tc + 20 =*@~ - 4"rrNC~was obeyed. The value w~gb= - 41 K provides linearity of the *R"b(*d') dependence. The linear extrapolations shown in Fig. 2 determine both Ro and R,. The * / ~ vs. *K~ data for samples 9 and 10 agree with each other quite well. The Curie temperatures differ by 2%. These *R"c data would also agree well 10
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I
200
300
a
a
a
oo . .
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T[K] Fig. 1. Temperature dependence of the effective Hall coefficient *R for samples characterized by T¢= 107.0 K and 104.8 K (samples 9 and 10 respectively), and 106.0 K (samples 11 and 12).
249
o,omp,.9
/
• ~o.,pl, 10
/C.,.,o~
+ sample 11
oAf~tK
•N =
Cv T_ 8.4~.NCv
/
"~2
0
4~*% Fig. 2. Effective Hall coefficient *R vs. effective susceptibility 4~-*K (see text).
with the data for sample 11, characterized by intermediate To, if multiplied by 1.22. This factor presumably accounts for inaccuracy of the thickness measurement of samples 11 and 12. Therefore we increased Ro and Rs by 22%. We conclude that the normal Hall coefficient of UAsSe is isotropic and equal to Ro = - 8.8 × 10 -4 cm 3 C-1. Thus, the carrier concentration is 0.47 e - fu -1 in the single band model. The spontaneous Hall coefficient is very anisotropic and equal to 0.78 and 3.0 cm 3 C- 1 for Rs"c and Rs=brespectively. Rsab is presumably underestimated as the fitted value of w@b= _ 41 K does not approach the value of wOb ------ 402 K anticipated from susceptibility measurements [11]. The accuracy of alignment of UH and H with the crystal axes seems rather poor owing to the small sample dimensions. 3.2. Resistivity We analyse the results of resistivity measurements given in Ref. [10]. Resistivity tensors are given along the a axis 0e(T), and along the c axis pc(T), for a UAsSe crystal characterized by Tc = 102.0 K. Fig. 3 shows pC(T)-p=(T)=Ap(T) vs. temperature (lower curve). These data are also plotted on coordinates [(Ap(T)-constant)/T, T - l lOg T]. The pc(T)-pa(T)= Ap(T) subtraction eliminates the isotropic component. This procedure removes the resistivity anomaly shown by both resistivity tensors at the ferromagnetic transition (see Fig. 6). If the negative slope of dp/dT for UAsSe were due to thermal activation of electrons through a forbidden gap, then all the resistivity components should show an anomaly at To. This is because of the expected shrink in the gap edge due to ferromagnetic ordering [12]. However, this is not the case and we propose another interpretation. The upper line in Fig. 3 is described by the formula Ap(T) = constant - CK log T+ Cp, T
(2)
Z. Henkie et al. / Journal of Alloys and Compounds 219 (1995) 248-251
250
0.01
Log(T) / T [Log(K)/K ] 0.03
10,
i
0.05 0
,
"~ i ---..._
,
S
,
1[, .':: U:ingp~i UAsSe : ' / ! - : : - - : - : ............ -'using Ln = /[ PKAr / / ,/J~'/ ./ . . . . . tu~'2
b
.~
i--
...'/.s'
...... UAs,
30K/
•~
Z7
-20
0
:
.........................
0 2
0
200 T[K]
..........
400
•
T/Tc,N
~
Fig. 3. Dependence of p C ( T ) - I f ( T ) = A p ( T ) vs. temperature (lower curve) and ( A p - l 1 7 5 ) / T vs. T -~ log(T) (upper curve) for crystal characterized by T¢= 102.0 K.
Fig. 5. R K K Y interaction controlled spin-disorder resistivity of UAsSe derived using both experimental pK(T) ( . . . . . ) and Arai's formula ( - - ) vs. T/T¢. The basal-plane resistivity for UAs2 and UP2 [17] vs. T/7~ is given for comparison.
p -• 1.0
-
P k ............
0.8
Pph
. . . . .
Ps
.......
Or
.........
~ 0.6 k-
E~o.4
>
0,2
'... ,,,i
10-1
. . . . .
,.,t
. . . . . . . .
10o T/TK
i
. . . .
Fig. 4. Kondo resistivity normalized to its value at 0 K vs. T/TK as predicted by Arai's formula (Eq. (3)) ( - - ) and our value derived experimentally for UAsSe ( . . . . . ).
where CK and Cph are coefficients. It allows us to assume that the anisotropic components are the Kondo resistivity pK and the phonon resistivity Pph- The isotropic component will be denoted p~(T). Deviation of Ap(T) from a logarithmic dependence at low temperatures can be described in terms of a single impurity behaviour in the Kondo limit of the Anderson model [13]. We use Arai's formula [14] for a quantitative description of pK(T) over the whole temperature range (Fig. 4)
(3)
where a(T) is a universal function of T/TK and is given by the solution of [a(T) - TL/T] ln{[1 + a2(T)]U2T/TL} - 7r In 2 = 0
/ ~ (1
2
101
I~(T)/pK(0) = {1 + 0r2/3)[a(T)]-2}-,
"'-,
(4)
where TL = Tx/0.624 [13]. The phonon component is described by the generalized Bloch-Grfineisen formula [15,16] written as
0
0
200 T[K]
400
Fig. 6. Total resistivity tensors along the c-axis ptc and along the a,axis pta for U A s S e and their components: Kondo Pr, phonon Pph, RKKY exchange controlled spin disorder p~ and residual p,.
p,..(T) = G.(T/e.)%(T/OD) J,(x) =
f
(e ~- 1)(1 - e - 0
(5)
o
We take n = 3 as we expect the band structure features of UAsSe will be closer to those of transition metals than to those of simple metals ( n = 5 ) . The Debye temperature OD=233 K is taken from specific heat measurements [6]. Ap(T) is described using a linear combination of Eqs. (3) (5). It allows us to split Ap(T) into two parts which give the temperature dependences of pK(T) and pp.(T). This p K e x P ( T ) / p K ( 0 ) determined experimentally from the best fit pK(0)= 6 6 0 / . ~ cm and TK = 40 K is compared
Z. Henla'e et al. / Journal of Alloys and Compounds 219 (1995) 248-251
in Fig. 4 with pKAr(T)/pK(0)given by Arai's formula (3). To determine the contribution of px(T) to the p,a(T) tensor we created a linear combination of pK(T) and Ppn(T) that describes the temperature dependence of this tensor above 120 K: pta(T)=xpK(T)+ypph(T)+ constant. We have assumed that p ~ ( T ) = x p K ( T ) and ppha(T) =ypph(T) and p ~ ( T ) + pr~ = pa(T) - pK~(T) -- Ppha(IV) between 2 and 443 K. This procedure could be done using either pK¢*P(T) or pKA~(T). TO determine the residual resistivity we have assumed that p~(2)= 0 for the case when p,a(T) is determined using pK~xp(T). The determined p,~(T) is normalized to its value at T¢, i.e. p,~(T)/p~(T~). Fig. 5 shows p~a(T) vs. the reduced temperature T/Tc. The same procedure was applied to the resistivity tensor along the c-axis. All the determined resistivity components are collected in Fig. 6. 4. Discussion It is interesting that Ps for UAsSe shows thermal behaviour very similar to the in-plane resistivity of uranium dipnictides. To show this, the basal plane resistivity of UAs2 and UP2 are presented in Fig. 5. The high temperature limit of the spin disorder resistivity psa(300) = 158/zl-I cm for UAsSe can be compared with pa(300) = 160 /zO cm for the basal plane resistivity of UAs2 [17]. The observed similarity is satisfying, if we take into account that all uncertainties, both experimental and due to assumptions on the temperature dependences, are cumulated in the derived psa(T). UPz and UAs2 are antiferromagnets with magnetic moments perpendicular to the basal plane. The basal plane residual resistivity is very low; RRR=p(300)/ p(4.2) > 200. This resistivity behaves in fact very much as is expected for the spin disorder resistivity of a ferromagnet with RKKY exchange interaction [17]. The residual resistivity increases as we come to ternaries. The RRR equals 1.8 and 2.8 for UAsS and UAsTe respectively [4]. At the other end of this class of compounds,/3-US2 is a paramagnetic semiconductor with forbidden gap at approximately 1.2 eV [18]. However, the/~-UYY' compounds (Y and Y' are chalcogen atoms) show a transition to a ferromagnetically ordered metallic state [19]. We think that this might be connected with possible disorder in occupation of Y and Y' positions in the structure. The magneto-optical Kerr effect shows the presence of an f band at the Fermi energy (filled with nearly three electrons) and hence p--f hybridization in UAsSe. However, the number of charge carriers nc is estimated to be less than 0.3 e - fu -1 [20]. Our Hall effect examination shows that nc = 0.47 is rather at the lower limit. It can be compared with 1.2 and 0.53 e - fu -1 (from the Hall effect) for UP/and USb2 [21] respectively. An even higher number of conduction electrons is deduced from positron annihilation experiments, 2.0,
251
2.5 and 1.6 + 0.4 for UP2, U S b 2 and UAsSe respectively [22]. The latter study also shows a lower anisotropy of the Fermi surface geometry in the ternaries than in the dipnictides. Various methods show different numbers of charge carriers but the expected difference in the number of charge carriers between UAsSe and some dipnictides is not well documented by either pdT) or Hall coefficient data. Thus the main feature that distinguishes the transport properties of UAsSe from those of the dipnictides is the high incoherent Kondo-like scattering present in excess of the RKKY exchange controlled spin disorder scattering in both paramagnetie and ordered states. The Kondo-like scattering is most probably induced by anion disorder which may result from strong hybridization. Acknowledgment This work was supported by the Committee for Scientific Research, Grant no. KBN-2 P302 173 06. References [11 F. Hulliger, J. Less-Common Met., 16 (1968) 113. [2] J. Leciejewicz and A. Zygmunt, Phys. Status Solidi A, 13 (1972) 657. [3] K.P. Bielov, A.S. Dmitrievski, A. Zygmunt, R.Z. Levitin and W. Trzebiatowski, Zh. Eksp. Teor. Fiz., 64 (1973) 582. [4] A. Wojakowski, Z. Henkie and Z. Kletowski, Phys. Status Solidi A, 14 (1972) 517. [5] J. Schoenes, W. Bacsa and F. Hulliger, Solid State Commun., 68 (1988) 287. [6] A. Blaise, R. Lagnier, A. Wojakowski, A. Zygmunt and M.J. Mortimer, J. Low Temp. Phys., 41 (1980) 61. [7] T. Takabatake, M. Nagasawa, H. Fujii, G. Kido, K. Sugiyama, K. Senda, K. Kindo and M. Date, Physica B, 177 (1992) 177. [8] M. Mihalik, A. deVisser, K. Bakker, L.T. Tai, A.A. Menovsky, R.W.A. Hendrix, T.J. Gortenmulder, S. Matas and N. Sato, Physica B, 186-188 (1993) 507. [9] M.B. Maple et al., Phys. Rev. Lett., 56 (1986) 185. [10] Z. Henkie, R. Fabrowski and A. Wojakowski, Acta Phys. Polon. A, 85 (1994) 249. [11] Z. Henkie, R. Fabrowski, A. Wojakowski and A.J. Zaleski, J. Magn. Magn. Mater., 140-144 (1995) in press. [12] S. Alexander, J.S. Helman and I. Balberg, Phys. Rev. B, 13 (1976) 304. [13] H.L. Neal and D.J. Collins, Phys. Rev. B, 48 (1993) 4299. [14] T. Arai, J. Appl. Phys., 57 (1985) 3161. [15] G. Grimvall, in E.P. Wohlfart (ed.), Selected Topics in Solid State Physics, Vol. 16, North-Holland, Amsterdam, 1981, p. 219. [16] J. Pierre, S. Auffret, J.A. Chroboczek and T.T.A. Nguyen, J. Phys. Condens. Matter, 6 (1994) 79. [17] Z. Henkie and Z. Kletowski, Acta Phys. Polon. A, 42 (1972) 405. [18] W. Suski, T. Gibifiski, A. Wojakowski and A. Czopnik, Phys. Status Solidi A, 9 (1972) 653. [19] R. Tro6, D. Kaczorowski, L. Shlyk, M. Potel and H. No61, J. Phys. Chem. Solids, 55 (1994) 815. [20] W. Reim, J. Magn. Magn. Mater., 58 (1986) 1. [21] Z. Henkie, P. Wi~niewski, R. Fabrowski and R. Maglanka, Solid State Commun., 79 (1991) 1025. [22] B. Rosenfeld, E. Debowska, Z. Henkie, A. Wojakowski and A. Zygmunt, Acta Phys. Polon. A, 51 (1977) 275.