Anisotropic transport properties of U4Cu4P7

Z. Phys. B - Condensed Matter 88, 135 140 (1992)

Condensed ze,t c,,,tB Matter far Physik 9 Springer-Verlag 1992

Anisotropic transport properties of U4Cu4P 7 J. Schoenes, D. Kaczorowski*, and C. Beeli Laboratorium fiir Festk6rperphysik, ETH-H6nggerberg, CH-8093 Z/irich, Switzerland Received February 7, 1992 The electrical resistivity of U4 Cu4 P7 for the current flowing in the basal plane of this tetragonal antiferromagnetic compound has been measured from 2 to 1000 K. Contrary to the case where the current flows along the e axis, we find an increasing resistivity with increasing temperature over the whole temperature range. This ferromagnetic-like behavior in the basal plane and the antiferromagnetic-like behavior perpendicular to it, is explained with the complex magnetic structure of the compound. The Hall effect for B parallel to the c axis shows an antiferromagnetic-like temperature dependence. The ordinary part of the Hall effect in the paramagnetic phase gives in an one-band model a carrier concentration of 0.7 holes per uranium atom, which is quite unique in uranium compounds by its sign and which results from the presence of two kinds of uranium atoms with different bonding, valence, magnetic moment and exchange. Quantitative differences between various samples of U4 Cu4 P7 are related to a mixed-layer stacking polytype of U4Cu4P 7 and UCuP 2 units.

four inequivatent positions of which one is only half occupied. From susceptibility measurements it was concluded that U4Cu4P 7 orders antiferromagnetically at TN= 146 K [2]. The temperature dependence of the susceptibility shows a strongly anomalous behavior. For the field parallel to the c axis, Z II displays a pronounced maximum near T~v,but starts to increase again with decreasing temperature below about 80 K. For the field perpendicular to e, the susceptibility was reported to increase from 300 K down to 4 K with the same values below 80 K as ZII [2]. Above 190K ZIE can be fitted by the Curie-Weiss law, giving #~ff~ =2.87 gB per uranium atom and 0p~=84.5 K. To fit Z• above 160K, a modified Curie-Weiss law had to be used with the fitting parameters #,ff~ = 2.07 PB per uranium atom and 0pi = - 5 4 K. Until now the resistivity had only been measured in zero field for the current flowing along the c axis [2]. As we will discuss later the resistivity in this geometry is markedly different from that for the current flowing in the basal plane.

Experimental details Introduction Besides the better-known compounds UCuPa and UCu2Pz, uranium, copper and phosphorus also form a compound with the rare formula U4Cu4P7 [1J. It crystallizes in a tetragonat structure with space group I4/ mmm and lattice parameters a=3.803~ and c = 34.954 A. The long c axis can be thought as stacking of 4 UCuAs2-type unit cells with space group P4/nmm, the two upper unit cells being inverted compared to the t w o lower ones (see also Fig. 8). The uranium atoms occupy two inequivalent positions and the phosphorus * Permanent address: Institute for Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 937, PL59-950 Wroctaw, Poland

U4Cu4P7 crystals grown by an iodine transport reaction have generally the form of needles with the needle axis parallel to the crystallographic e axis. To perform the measurements to be reported here with the current direction perpendicular to c, three single crystals of U4Cu4P 7 were chosen which, in contrast to the general habitus, had grown in the form of platelets perpendicular to e. The typical edge length in the basal plane amounted to 3 mm and the thickness parallel to the c axis was reduced by mechanical polishing to 30-80 pm. For the resistivity and the Hall measurements between 2 and 300 K, four electrical contacts were attached near the edges of the samples 2 and 3 by ultrasonic welding of aluminum wires. For the resistivity measurements between 300 and 1000 K four tungsten contacts were pressed against the edges of the sample 1. To exclude that the differences observed for different samples are

136 due to the contacts, sample 3 was subsequently also contacted with pressure contacts and the resistivity measurement between 2 and 300 K was repeated. The results were found to be the same within the accuracy of the ac-van der Pauw method used. Fields up, to 10 T were generated with a split-coil superconducting magnet. The variable temperature of the sample was realized by exposing the sample to a controlled stream of He and regulating the temperature with an attached heating system. The accuracy of the temperature is ___1 K. F o r the measurements above room temperature the sample was encapsulated in a quartz ampoule with an inert gas and Ce turnings to avoid a deterioration of the sample. As we will see in detail in the section describing the results of the electron-transport measurements, samples 2 and 3 showed non negligible differences of the temperature dependence of the resistivity and the Hall effect. We have searched intensively for a poosible reason for this different behavior. As mentioned already above, an electrode effect could be excluded by making the resistivity measurement on the very same sample with welded and with pressure contacts. We also checked by changing the direction of current flow within the basal plane that there is no order-induced anisotropy in the basal plane. Another thought was that the result for sample 3 represents a linear combination of those found for sample 0 [-2] and 2. However, an X-ray analysis showed a perfect fourfold symmetry with no indication of a misorientation of some part of the crystal. Searching then for smaller compositional or structural differences, the samples 2 and 3 were studied with various electron microscopy methods. First, both crystals were investigated by scanning electron microscopy (SEM). Because these primary electron images displayed a dark band across the whole fragment of the crystal no. 3, the latter has additionally been investigated by transmission electron microscopy (TEM) and selected electron diffraction (SAD). For T E M investigations cleaved fragments in the shape of a wedge, with an angle of approximately 45 ~, were attached an a 2.3 mm copper ring with electrically conductive carbonglue. The crystal was oriented in such a way that the c axis was perpendicular to the beam direction and the margin of the wedge was approximately parallel to the c axis.

Fig. 1. a High-resolution electron micrograph of the lamellar region obtained in a [110] projection for U4Cu4P7 sample 3. b Schematic drawing of the individual layers of a

Results of the electron microscopy study The scanning electron microscopy images indicate that there exists in crystal no. 3 a lamellar region which has a composition different from the composition of the average crystal structure. This lamellar region is bounded by approximately parallel planes perpendicular to the e axis and extends through the whole single crystal. The lamella was found to have an average thickness of 1.5+_0.5 gm and to be located approximately 5 gm below one surface of the plate-like single crystal having a thickness of 32 ~tm. The T E M investigation of a wedge-shaped crystal fragment containing the above-mentioned lamella reveals a large number of planar stacking defects (Fig. 1 a).

Fig. 2. a [li0]-type electron diffraction pattern of U4Cu4Pv. Arrows indicate additional diffuse scattering intensity, b and e Line of reflections through (000) parallel to the e axis taken with a larger camera length than a. b has been obtained from a perfect crystal region, e from the lamellar region

The projection direction of this image corresponds to a [110] direction. Figure 1 b presents a schematic drawing of the individual layers. One recognizes 17.5_+0.1 wide layers which are interrupted by another layer type with an average width of 9.3 _+0.1 A. Therefore, the lamellar region corresponds to a mixed-layer stacking po-

137 lytype of the two units. The number of 17.5 A wide layers intercalated between two of the 9.3 i wide layers follows the scheme 6, 8, 3, 5, 6, 8, 3, 5,... over 11 periods i.e. over about 39% of the lamella. The [110] diffraction patterns shown in Fig. 2 have been obtained from a perfect crystal region (Fig. 2 a and b) as well as from a part of the lamellar region (Fig. 2c). The diameter of the region selected for the diffraction patterns was in all cases 0.52 gm. All diffraction patterns have been taken with the same crystal orientation. The orientation is not exactly parallel to the [110] axis, which explains the small differences in the intensity of the reflections which are centro-symmetric with respect to the (000) beam. Figure 2b and c, taken with the same camera length, show the line of reflection through the (000) reflection, which is parallel to the e axis. In contrast to Fig. 2b, additional scattering intensity (streaks and isolated satellite reflections) can be recognized between the main reflections in Fig. 2c. The streaks are due to stacking disorder present in the lamellar region and corroborate the defect structure observed in the transmission electron micrographs, whereas the satellite reflections are due to the regular stacking sequence mentioned above. The period of this regular stacking polytype corresponds to 422 A. The thickness of the additional layers of 9.3_+0.1 A is within the given accuracy equal to 1/2 of the c axis parameter of UCuP2(c = 18.523 ~), while the measured value of 17.5+0.1 A corresponds to 1/2 of the e axis parameter of U4CusPT(c= 34.954 A). Therefore, the additional layers have a c axis parameter which is 5% larger than the one of the main UsCu4P7 structure of the crystal. Consequently, the density of U atoms for these layers is approximately 5% smaller than in the main crystal structure. This explains the observation that the lamellar region shows a dark contrast in primary electron images made with the scanning electron microscope. Returning to Fig. 2a, we observe in [ll0]-type diffraction patterns additional lines of diffuse scattering which are parallel to the c axis and run through the positions: (89 - 89 0), @, - 3 , 0), ... (see arrows). Similarly, in [310]-type diffraction patterns streaks through (89 3, 0), ... do occur, while for the [120J-type orientations no diffuse scattering corresponding to streaks through (89 1, 0) were found. The additional diffuse scattering intensity has been observed in diffraction patterns of the lamellar region with stacking disorder and in perfect crystal regions. It can be interpreted as an incomplete disorderorder phase transition. The whole diffraction spectrum can be indexed with integer indices if a doubled cell in the [110] and the [ l i 0 ] directions is assumed. It is suggested here that the ordered structure has an ordered arrangement of the P atoms in the P(4) positions (see Fig. 8). Instead of 50% occupancies at (0, 89 88 and (89 0, 88 only one of these positions is occupied in the ordered phase, but with an occupancy of 100%. This results in a l/~ times larger cell parameter a but the symmetry of the ordered phase remains tetragonal.

Electron transport results Figure 3 displays our low temperature resistivity data for the current i flowing perpendicular to the c axis together with the curve for i parallel to c obtained previously [2]. In the following, we will call this latter sample No 0. All three samples show pronounced anomalies near Tu, which manifest themselves even more clearly in the derivatives ~p/c3T. For i • we find a narrow maximum at 136 K (Fig. 4). For i He c3p/c3T displays a minimum at 134 K [2]. We identify these peaks with the onset of antiferromagnetic order and derive TN=135 _+ 1 K. Indeed, an increase of p with decreasing temperature is quite common in antiferromagnets and is most beautifully seen in antiferromagnetic USb [3]. A decrease of p below the ordering temperature is more characteristic for ferromagnets and has, for example, been found in ferromagnetic US and USe [3]. As we will

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of measurements for two different samples of a same material. The change of sign of the Hall resistivity near 120 K is reminiscent of the behavior in antiferromagnetic USb [3] and is absent in the parent, but ferromagnetic compounds UCuP 2 1-5] and UCuAs2 [6]. A separation of the total Hall resistivity into an ordinary and an extraordinary part is possible for T > 150 K assuming the empirical relation

Fig. 6. Temperature dependence of the Hall effect for B IIe. The field is 2 T and the data are shown for the U4Cu4Pv samples 2 and 3

pn(B, T)= Ro(T)" B +4rcR="M(B, T)

discuss later the different behavior for different current directions manifests the spin structure of U4Cu4P 7. Below about 45 K the resistivity changes dramatically its slope. This is best seen for i 1[e for which Op/~Tchanges its sign from negative to positive values, but also shows up, with different intensity in our two samples 2 and 3 for i_l_c. Figure 5 displays the resistivity data up to 1000 K for i.Le. One recognizes that the part between 150 and 300 K which from Fig. 3 could be thought to correspond to the linear electron-phonon contribution gives an incorrect value. From a linear fit of p between 500 and 1000 K we derive cphI = (~p/0 T)• = 0.075 gf~cm/K, which is approximately the same value as derived for ille from the data between 240 and 300 K. The data for other uranium compounds are 0.092 g ~ c m / K for US [3] and 0.09 g ~ c m / K for URu2Si2 [4]. The Hall resistivity Pr~ =Rt~' B for sample 2 and 3 and a field B of 2 T parallel to e is shown in Fig. 6. As for the resistivity, quantitative deviations occur below about 100 K, while above this temperature the agreement is within the general reproducibility of this type

where Ro and R= are the ordinary and extraordinary Hall coefficients, respectively. Above 150 K the magnetization M is proportional to the susceptibility Z and Fig. 7 shows a plot of the Hall resistivity versus the susceptibility for temperatures from 150 to 300 K. The intersection of the fitted straight line with the ordinate gives Ro=0.56.10 -3 cm3/As. The slope of the straight line gives R==0.036 cm3/As. While the positive sign of R= agrees with the general finding in the paramagnetic phases of uranium compounds, the positive sign of R0 is uncommon. Indeed, out of a good dozen of uranium compounds that the authors have investigated and analyzed in terms of ordinary and extraordinary Hall contributions, U4Cu4P 7 is the first material to show a positive ordinary Hall effect. In an one-band model the value of R o corresponds to 0.72 holes per uranium atom (e+/U). In U C u P / t h e corresponding value is 0.06 e - / U [5]. The value for R= is roughly a factor 30 smaller than in the heavy fermions system UPt 3 [7] and URu2Si2 [4] and a factor 100 smaller than in UCuP2 [5]. While a factor of 10 compared to the latter material can be explained by the different carrier concentration, some other mechanism has to be inferred to account for the remaining discrepancy.

(1)

139 Table 1. Nearest-neighbor distancesin UCuPz and U 4 C n 4 P 7 calculated from the crystallographicdata in [1]. All values are in A

Discussion The very unusual electrical and magnetic properties of U4Cu4P7 can largely be explained by a close look at the particular crystallographic structure. To elucidate our arguments we show in Fig. 8 a projection of the structure of U4Cu4P7 on the x z plane. Atoms at y = 0 (or 1) are shown by thick lines, those at y = 1/2 by narrow lines. The position of the atoms are taken from [1], but the size of the atoms are drawn approximately proportional to the ionic radii of p3-, Cul+ and U 3§ For comparison UCuP2 is also shown on the same scale. Both structures consist of a stacking of layers containing only one kind of atoms. However, the surrounding of one element in different layers may be different and so one distinguishes, for example, two different phosphorus sites in UCuP2 denoted P(1) and P(2) and four different phosphorus sites in U4Cu4P7 denoted P(1), P(2), P(3) and P(4), respectively. In the representation of Fig. 8 one realizes immediately, that the half-occupation of the P (4) site drastically affects the distance of the U(2) atoms to the P(4) atoms, indicating changes in bonding, valence, magnetic moment and exchange. The ordinary part of the Hall effect manifest the changes of the first two quantities. Because the environment of the Cu and U(1) atoms in U4Cu4P7 is identical to the one of Cu

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and U in UCuP2, we assume that the Hall results for the latter material describe the contribution of the two U(1)CuP(3)P(2) blocks in U4Cu4P 7. In UCuPz the interatomic distance between P(1) sites is much smaller than between P(2) sites (see Table 1), suggesting a formal description of this compound as U4+Cul+P(1)2-p(2) 3-. In U4Cu4P7 the interatomic distances between P(3) sites, on one hand, and P(2) sites, on the other hand, is identical to that of P(1) and P(2) sites, respectively, in UCuP2, leading for the two U(1)CuP(3)P(2) blocks to a formal description as U(1)4+Cul+P(3)2-p(2) 3-. The layers with divalent phosphorus contain covalent bonding of each phosphorus atom with its four nearest neighbors. Electron-counting arguments would suggest that each pa- ion contributes one hole. The small electron concentration found in UCuP/, however, indicates that there exist a strong hybridization with the uranium 6d states leading to a dominance of n-type conduction. If the phosphorus atoms on the P(4) sites of UaCu4Pv remain divalent, charge neutrality of the corresponding block requires that uranium becomes trivalent, i.e. the formal description becomes U(2) 3 +Cu 1+ ~P(4) z-p(1) ~-. Yet, the half occupation of the P(4) sites reduces the number of nearest neighbors of each P(4) atom. In the ordered structure the P(4) atoms occupy only the corners of squares and the nearest neighbor distances is 3.80 ]k. Thus, from the inter-phosphorus distance and the local symmetry we conclude that phosphorus on the P(4) sites tends to become trivalent. The necessary one electron per occupied P(4) site is obviously not transferred completely from uranium on U(2) sites, as indicated by the p-type character of the Hall effect in U 4 C u 4 P 7, Thus, besides the different valence of some of the P atoms comparing UCuP2 and UgCu4PT, the valence of half of the uranium atoms has decreased to (3 + 5) + with 5 < 1. The smaller valence of U(2) suggest a higher moment for U(2) than the 1 gB per U observed in UCuP2 [8], which we anticipate also for U(1) in U 4 C u 4 P 7 . An idea of the moment to be expected for U(2) is given by the value of 1.9 g~ for uranium in UP [9]. A recent neutron scattering investigation [103 confirms this expectation and finds at 4.2K m l = l . 1 g~ and m z = 2 . 2 g B. These authors report also a (ml m2 n52 rhl r~l m2 m2 m~) stacking of (001) planes with m2 saturating below 100 K, but mt saturating only below 30 K. Obviously the large moment on U(2) and the strong indirect exchange via

140 P(4) dominates and leads to an antiferromagnetic ordering at 135 K. The U(1) atoms, as we know from UCuP2, would like to order ferromagnetically below 75 K. This ferromagnetic ordering is hindered in U4Cu4P7 by the antiferromagnetic coupling between nearest U(2) layers leading to ferromagnetically aligned blocks m2 ml ml m2 which couple antiferromagnetically among each other. Although the unit cell is not enlarged, this ordering reduces the symmetry (Fig. 8) and we observe an increase of the electrical resistivity below TN for the current flowing along c. In contrast, within each a b plane the symmetry is unchanged and the ferromagnetic ordering reduces the magnetic disorder scattering. Consequently, the resistivity decreases below TN for i• The development of the full moment of the U(1) sublattice below 30 K reduces the magnetic disorder scattering from this sublattice below 30 K and manifests itself in the decrease of the resistivity. For i[I e the effect is larger because the resistivity may be viewed as a serial circuit, while for i • it corresponds to a parallel circuit. The different behavior of the electrical resistivity of sample 2 and 3 can be explained by a combination of the above arguments with the results of the electron microscopy study. For i_l_c the resistivity of sample 3 is to be expected to correspond to parallel circuits of resistivities of the types of sample 2 (perfect U4Cu4PT) and UCuP2. This means that in sample 3 the resistivity shall first decrease less below TN= 135 K, until below approximately 75 K the UCuP2 blocks do also order. This is exactly what we observe in Fig. 3. To explain the difference in the Hall effect, we remind that the extraordinary Hall effect of a perfectly ordered magnet should be zero ( T ~ 0). In this sense one understands that the less perfect sample 3 has the larger extraordinary Hall effect and since this is the dominant part of the total Hall effect it is also true for the latter. We also note that the difference of the Hall curves between sample 3 and 2 has a similar temperature dependence as the Hall effect of UCuP2, but a different sign, in agreement with the opposite sign of the free carriers in U4CuaP 7 and UCuP2. As for the resistivity, the full ordering of ma below 30 K reduces the differences between the Hall effect of sample 2 and 3.

Conclusions U4CH4P 7 constitutes a complex system which can nicely be modeled with two magnetic subsystems consisting of uranium atoms with different bonding, valence, magnetic

moment and exchange. The large differences of the respective values allow a clear separation of the effects from the two subsystems and give a particular richness to the transport properties. The non-reproducibility of the transport properties for different samples led us to a detailed structure analysis, revealing that the regular stacking sequence of unit cells of the U4Cu4P 7 structure can be interrupted by single layers corresponding to one half of the unit cell of the UCuPz-type structure. In our sample we found a periodic stacking variance with 6, 8, 3 and 5 U4Cu4P? half cell units. This corresponds to a period of 422 A, which is remarkably long. The finding of this intergrowth of two structures raises also the question whether the anomalous rise of the susceptibility for T