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Spin reorientation in UFe2 upon non-magnetic substitution in the uranium sublattice
Journal of Alloys and Compounds 337 (2002) 18–24
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Spin reorientation in UFe 2 upon non-magnetic substitution in the uranium sublattice a, b A.V. Andreev *, R.Z. Levitin b
a Institute of Physics ASCR, Na Slovance 2, 182 21 Prague 8, Czech Republic Moscow State University, Faculty of Physics, Vorob’ evy Gory, 119899 Moscow, Russia
Received 11 October 2001; accepted 18 October 2001
Abstract The spin reorientation from the k111l to the k100l easy-magnetization axis as a consequence of the competition between the cubic magnetocrystalline anisotropy constant K 01 and the magnetoelastic contribution to the magnetic anisotropy DK me was predicted and 1 observed upon magnetic dilution of the uranium sublattice of UFe 2 . The total K1 5K 01 1DK me was determined from the magnetization 1 measurements on single crystals of UFe 2 and U 0.8 Lu 0.2 Fe 2 as 20.21 and 0.15 MJ / m 3 (at 4.2 K), respectively. The individual values of K 10 and DK 1me in UFe 2 were found as 1.03 and 21.24 MJ / m 3 , respectively, which shows that the low magnetic anisotropy of UFe 2 is a result of the mutual cancellation of rather large K 01 and DK me 1 . The change of the anisotropy type is accompanied by the disappearance of spontaneous magnetostriction distortion in U 0.8 Lu 0.2 Fe 2 . 2002 Elsevier Science B.V. All rights reserved. Keywords: Actinide compound; Transition metal compound; Magnetically ordered materials; Anisotropy; Magnetic measurements
1. Introduction and motivation The Laves phase UFe 2 crystallizing in the cubic MgCu 2 structure has in many respects a special position in the magnetism of actinides. It was the first actinide-containing compound found to be magnetically ordered [1] and still attracts large attention. Many studies of UFe 2 have been performed on single crystals which can be grown relatively easily by different methods. UFe 2 is a ferromagnet with Curie temperature T C varying from 158 to 195 K and spontaneous molecular magnetic moment mm from 0.96 to 1.36 m B per formula unit. As it was shown in Ref. [2], this difference is due to existence of a homogeneity range that was not taken into account in early works, and the stoichiometric composition UFe 2 corresponds to T C (165 K and mm (1.1 m B . For a long time, ferromagnetism in UFe 2 was attributed exclusively to Fe, whereas the U atoms do not carry a magnetic moment. The strong argument for such an opinion is the very short interuranium spacing in UFe 2 , d U – U 5305 pm. This is much smaller than the Hill limit 340 pm, the critical d U – U value above which the U atoms can carry a magnetic moment *Corresponding author. KFES MFF UK, Ke Karlovu 5, 12116 Prague 2, Czech Republic. Tel.: 1420-2-2191-1352; fax: 1420-2-2191-1351. E-mail address: [email protected] (A.V. Andreev).
[3]. The reduction of the Fe magnetic moment mFe and T C in UFe 2 in comparison with isostructural rare-earth compounds RFe 2 (where mFe reaches 1.5 m B and T C .500 K [4]) was attributed to an additional filling of the 3d band of Fe by uranium 5f and 6d electrons. Early neutron-diffraction studies confirmed the negligible magnetic moment on the uranium sites [5,6]. From this viewpoint, the discovery of giant anisotropic magnetostriction in UFe 2 [7] was rather unexpected because it was in complete disagreement with the nonmagnetic state of U. Below T C , the cube angle a decreases by 10 min, i.e. UFe 2 undergoes a rhombohedral distortion ´ 5cos a (Fig. 1). The magnetostrictive origin of this distortion was confirmed by strain-gauge measurements in magnetic field. The magnetostriction of a cubic crystal is described by
l 5 l0 1 3 / 2 l100 (a x2 b x2 1 a y2 b y2 1 a z2 b z2 2 1 / 3) 1 3 l111 (ax ay bx by 1 ay az by bz 1 ax az bx bz ).
(1)
Here ai are the cosines of the magnetic moment direction, bi are the cosines of the strain measurement direction, li are the magnetostriction constants. l0 is the isotropic strain which does not depend on the orientation of magnetic moment and is equal to the related difference between the experimental and extrapolated curves in Fig.
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01911-9
A.V. Andreev, R.Z. Levitin / Journal of Alloys and Compounds 337 (2002) 18 – 24
Fig. 1. Top: the temperature dependence of lattice parameter a of UFe 2 . The dotted line represents the phonon contribution with Debye temperature QD 5190 K. Bottom: the deviation of the cube angle a from p / 2 in UFe 2 . The right-hand scale shows the corresponding values of the rhombohedral distortion ´ 5cos a.
1. In UFe 2 , l0 reaches 4.8310 24 which corresponds to the spontaneous volume magnetostriction vs 51.45310 23 . l111 describes the rhombohedral distortion occurring when the magnetic moment is directed (spontaneously or by magnetic field) along the k111l axis. In the case of easy k111l axis, like in UFe 2 , l111 5 ´. The l100 constant, describing the tetragonal distortion when magnetic moment is along the k100l axis, is found by strain-gauge measurements to be 2310 24 at low temperatures, e.g. is negligible compared to the l111 value (2.9310 23 , Fig. 1) [7]. Since the Fe sublattice can provide a two-orders of magnitude smaller magnetostriction (as known from magnetostriction measurements of RFe 2 with non-magnetic R [8]), the observed l111 value was a strong evidence for the uranium contribution to the magnetic properties of UFe 2 . The absolute value of l111 of UFe 2 exceeds that of RFe 2 for some magnetic R (Er, Ho) and is comparable with the maximum observed for R5Tb ( l111 (5310 23 [4,8]). In order to reconcile the giant magnetostriction of UFe 2 with the negligible magnetic moment on uranium sites, a mutual cancellation of noticeable spin ( mS ) and orbital ( mL ) moments was proposed in [7] similar to the state of the Sm 31 ion in some compounds [9]. Later such a cancellation was obtained from band-structure calculations (absolute values of mS and mL are about 0.5 m B [10]) and then confirmed by many modern methods of investigation
19
of the electronic structure: polarized neutron diffraction [11,12], X-ray magnetic circular dichroism [13], magnetic Compton scattering [14]. Results of the experimental studies [11–14] are in very good agreement and give mS 5 2(0.20–0.22) m B and mL 50.21–0.23 m B . The total mU (0.01 m B is ferromagnetically coupled with 2mFe (1.2 mB . The compensation of spin and orbital moments of uranium in UFe 2 that attracted so much attention, is not, however, the only very special feature of UFe 2 . The anisotropic magnetostriction and the magnetic anisotropy have the same origin and are either both strong (like in RFe 2 with anisotropic R ions) or both weak (like in RFe 2 with non-magnetic R5Y, Lu or isotropic Gd). The giant magnetostriction (.10 23 ) corresponds to the absolute value of the first anisotropy constant K1 of an order of magnitude up to 10 MJ / m 3 [4,15]. UFe 2 with giant magnetostriction is, however, a low-anisotropic ferromagnet, K1 is only 20.1 MJ / m 3 , e.g. by at least one order of magnitude lower than could by expected [7,16]. Generally, a combination of the low anisotropy and high magnetostriction can be reached, but only in solid solutions of the R 912x R 99 x Fe 2 type where the rare earth ions R9 and R0 have the same sign of magnetostriction and different signs of anisotropy [4]. In UFe 2 , only one type of magnetostrictive ion is present, and another mechanism explaining the reduced anisotropy should be found. In [7], we have solved the problem by the assumption that a large intrinsic cubic magnetocrystalline anisotropy described by the positive K 01 constant is overcome by the negative magnetoelastic contribution to the anisotropy DK me [15] 1 K1 5 K 10 1 DK 1me
(2)
2 2 DK me 1 5 (9 / 4) [(c 11 2 c 12 )l 100 2 2c 44 l 111 ],
(3)
where c ij are the elastic constants. Since in UFe 2 l111 4 2 l100 , DK 1me (2(9 / 2)c 44 l 111 (20.8 MJ / m 3 (c 44 523 10 2 0 3 10 N / m [7]) and K 1 is estimated as 0.7 MJ / m which is already not in so large a contradiction with giant magnetostriction. Thus, UFe 2 is believed to have two compensations of large terms, the spin and orbital moments of uranium and the intrinsic and magnetoelastic contributions to the magnetic anisotropy. Each of these cases is rather interesting and unusual, but the simultaneous appearance of such phenomena in the same compound makes from UFe 2 a unique magnetic matter. The former compensation is studied in great detail whereas the latter one is not. Both the low anisotropy and the strong magnetoelasticity in UFe 2 were confirmed by many studies, but their direct correlation still needs more clear evidence. One of the 0 me methods is destroying the delicate balance of K 1 and DK 1 by dilution of the U sublattice, e.g. by non-magnetic Lu. For our study, we selected 20% dilution. In any models, 0 either single- or two-ion, K 1 and l111 have the same
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A.V. Andreev, R.Z. Levitin / Journal of Alloys and Compounds 337 (2002) 18 – 24
behavior upon dilution. Since according to (3) 2 me DK me decreases with dilution considerably 1 ~ l 111 , DK 1 0 faster than K 1 . Using for UFe 2 K 10 50.7 MJ / m 3 and 3 DK me from [7] and the single-ion (i.e. 1 5 20.8 MJ / m linear) approach, we estimated for 20% dilution K 10 50.6 3 MJ / m 3 and DK me 1 5 20.55 MJ / m . The total K 1 (0.05 3 MJ / m becomes positive, which means that the k100l axis becomes the easy magnetization direction. The same result (positive K1 at 20% dilution) can be obtained also in a two-ion approach. Therefore, if our explanation of low anisotropy of UFe 2 is right, we should observe different types of anisotropy in UFe 2 and U 0.80 Lu 0.20 Fe 2 . In the present paper we have checked this prediction.
2. Experimental The UFe 2 and U 0.8 Lu 0.2 Fe 2 samples were spark-erosion cut perpendicular to the k100l, k110l and k111l axes from single crystals prepared by a modified Czochralski method. First, 10-g precursors were melted under a protective high-purity Ar atmosphere from stoichiometric amounts of the elementary metals (U and Lu of 3N purity, Fe 4N) on a rotating copper water-cooled bottom in a tetra-arc furnace with tungsten electrodes. Then the crystals were pulled out with a pulling speed of 10 mm / h using a tungsten wire as a seed. The check of crystal quality as well as its orientation for cutting was done using the X-ray Laue method. The phase purity and the lattice parameters of the samples were determined by standard X-ray diffraction on a powder sample prepared from a part of the crystal. The low-temperature (at T55 K) search for a spontaneous magnetostrictive distortion was performed by profile analysis of the (642) reflection in Co Ka radiation. The magnetization was measured along the k100l, k110l and k111l axes in the temperature range 4.2–300 K in a vibrating sample magnetometer with a superconducting coil providing fields up to 14 T. The values of mm and T C were determined from the Belov–Arrott plots of the magnetization isotherms.
Table 1 Structural and magnetic characteristics of UFe 2 and U 0.8 Lu 0.2 Fe 2
a at 300 K (pm) a at 5 K (pm) ´ at 5 K (10 23 ) mm at 4.2 K (m B ) Easy axis T C (K) K1 at 4.2 K (MJ / m 3 ) K 01 at 4.2 K (MJ / m 3 ) 3 DK me 1 at 4.2 K (MJ / m ) a
UFe 2
U 0.8 Lu 0.2 Fe 2
705.8 704.3 2.9 1.09 k111l 168 20.21 1.03 a 21.24 a
708.9 707.7 0 1.59 k100l 290 0.15 0.66 a 20.51 a
In the two-ion approach.
stoichiometry. A comparison with the crystals used in Refs. [7,16] for anisotropy and magnetostriction studies, presented in the inset in Fig. 2, points to a much better quality of the new crystal. The easy-magnetization curve saturates completely at 0.2 T in the new crystal which is comparable with the demagnetization field of the sample ((0.15 T), whereas only 70% of the saturation was reached at this field in the previous crystal. In this case, a 0.8 T is needed for complete saturation evidently because of considerable residual stresses. Also, the enhanced mm value (1.16 m B ) indicates a deviation from the 1:2 stoichiometry in this crystal. The energy of magnetic anisotropy for a cubic crystal is described in a two anisotropy-constant approximation by formula Ea 5 K1 (a x2 a 2y 1 a 2x a 2z 1 a 2y a 2z ) 1 K2 a 2x a 2y a 2z ,
(4)
where ai are the cosines of the magnetic moment direction.
3. Results and discussion The X-ray phase analysis showed that the crystals do not contain extraneous phases. The room-temperature lattice parameter of UFe 2 a5705.8 pm is in good agreement with literature. The larger a value (708.9 pm) of U 0.8 Lu 0.2 Fe 2 is due to the larger atomic radius of Lu compared to U. All structural and magnetic characteristics of both compounds studied are listed in Table 1. Magnetization curves of the UFe 2 crystal along the principal axes at 4.2 K presented in Fig. 2 confirm that the k111l axis is the easy-magnetization direction and the k100l is the hardest direction. The value of mm 51.09 m B (as well as T C 5168 K) corresponds well to the 1:2
Fig. 2. Magnetization curves of the UFe 2 crystal along the principal axes at 4.2 K. The inset shows the k111l curves for the crystals used in the present work and in Ref. [7].
A.V. Andreev, R.Z. Levitin / Journal of Alloys and Compounds 337 (2002) 18 – 24
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In particular, E100 50, E110 5K1 / 4 and E111 5K1 / 31K2 / 27. Therefore, K1 5 4 DE110
(5a)
K2 5 27 DE111 –36 DE110 ,
(5b)
where DE110 5E100 –E110 (the area between the k100l and k110l curves in Fig. 2) and DE111 5E100 –E111 (the area between the k100l and k111l curves). The values of K1 and K2 determined in this way are equal to 20.21 and 0.22 MJ / m 3 , respectively. These results differ quantitatively from those of Ref. [16]. The absolute value of K1 is larger by a factor of 2 and that of K2 by a factor of 4 than previously obtained. We attribute the difference first of all to an evidently non-stoichiometric composition of the crystal of Ref. [16]. Then, the above-mentioned different quality of crystals can also affect the results as well as the different methods of anisotropy measurement (by torque anisometer in Ref. [16]). We consider the new results as more reliable. It is worth to mention that the K2 value depends very much not only on the hard-direction curve like K1 , but also on the easy-direction curve and, consequently, on the quality of the crystal. For this reason, K2 is determined with much larger error. This does not affect K1 . If we neglect K2 , the K1 value determined from DE111 is 3 equal to 20.19 MJ / m , only |10% different from the value determined from DE110 according to (5a). In any case, the result obtained does not change the conclusion of Ref. [7] about a low total anisotropy of UFe 2 and almost does not influence the K 01 value estimated from formulas 2 and 3 (0.6 MJ / m 3 instead of 0.7 MJ / m 3 in [7]). Fig. 3 illustrates the temperature evolution of the magnetization curves of UFe 2 . It shows a monotonous decrease of the anisotropy with increasing the temperature. A detailed study of temperature dependence of the anisotropy and a search for a possible spontaneous spinreorientation in the vicinity of T C is in progress and the results will be published elsewhere. Magnetization curves of the U 0.8 Lu 0.2 Fe 2 crystal along the principal axes at 4.2 K presented in Fig. 4 show another type of the magnetic anisotropy with respect to UFe 2 . The k111l axis becomes the hardest-magnetization direction, whereas the k100l axis is now the easy-magnetization direction. Calculation of the anisotropy constants, especially of K2 , from the curves of Fig. 4 faces the problem of the shape of the easy-magnetization curve. If we use the experimental k100l curve from Fig. 4, K1 50.15 MJ / m 3 and K2 50.01. However, the easy-direction curve in the U 0.8 Lu 0.2 Fe 2 crystal is clearly not as good as in UFe 2 . It resembles the easy-axis curve of the crystal from Ref. [7] (see inset in Fig. 2) and is evidently influenced by residual stress in the crystal. If we use the same shape of easy-direction curve as for the UFe 2 crystal, K1 50.18 MJ / m 3 and K2 5 20.11 MJ / m 3 . One can see that K2 is much more sensitive to the procedure of the determination. In the further discussion we will consider only K1 . The
Fig. 3. Magnetization curves of the UFe 2 crystal along the principal axes at elevated temperatures.
Fig. 4. Magnetization curves of the U 0.8 Lu 0.2 Fe 2 crystal along the principal axes at 4.2 K.
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temperature evolution of the magnetization curves of the U 0.8 Lu 0.2 Fe 2 crystal is shown in Fig. 5. As in UFe 2 , the anisotropy weakens with increasing temperature. A more detailed study of temperature dependence of the anisotropy is in progress. The mechanism responsible for the magnetocrystalline anisotropy in the RFe 2 intermetallics with well localized 4f states is their interaction with the crystalline electric field. It has a single-ion character. The mostly delocalized 5f states in intermetallics of light actinides, being involved in the anisotropic covalent bonding, imply an essentially different, two-ion (5f–5f) interaction via 5f-ligand hybridization, which plays a major role in the anisotropy [17]. (The strong spin–orbit interaction is a necessary prerequisite in both cases.) With the experimental K1 values for UFe 2 and U 0.8 Lu 0.2 Fe 2 , we can estimate K 01 and DK me 1 in UFe 2 . The linear approach, which corresponds to the single-ion mechanism of magnetic anisotropy, gives K 01 5 1.78 MJ / m 3 and DK 1me 5 21.99 MJ / m 3 . The quadratic approach, corresponding to the two-ion mechanism, gives K 10 51.03 MJ / m 3 and DK 1me 5 21.24 MJ / m 3 . The latter result is considerably closer to K 10 50.6 MJ / m 3 and DK 1me 5 20.8 MJ / m 3 obtained above by another method (from formulas (2) and (3)). This could be considered as a proof for the two-ion mechanism of anisotropy in UFe 2 .
Fig. 5. Magnetization curves of the U 0.8 Lu 0.2 Fe 2 crystal along the principal axes at elevated temperatures.
However, we understand that several factors neglected in these estimates reduce the reliability of this conclusion: (a) non-negligible difference in the lattice parameter a (see Table 1); (b) different state of the Fe sublattice in UFe 2 and U 0.8 Lu 0.2 Fe 2 reflected in the considerably higher mm and T C in the latter case; (c) possible change of state of the 5f electrons due to points (a) and (b); (d) the Fe-sublattice contribution to the magnetic anisotropy. It is expected to be small in comparison with K 01 and DK me 1 , but could be comparable with their sum. In this respect it is worth ¨ mentioning the results obtained by Fe 57 Mossbauer effect measurements in the U 12x Zr x Fe 2 system [18]. The Zr atoms like the Lu ones do not carry a magnetic moment. It was found that the spectra of the terminal compounds and most of the solid solutions are well described by the assumption of an k111l easy axis, whereas the compositions with x50.5 and 0.6 exhibit k100l as easy axis. We can explain the first spin reorientation the this system (between x50.4 and 0.5) as originating from the competi0 me tion of K 1 and DK 1 , as in the present work. The difference in concentration of the spin reorientation may be attributed to a different effective valence of Lu (3) and Zr (4). However, the reentrant reorientation back to the k111l easy axis needs the third term in K1 which starts to dominate at low U content. This is evidently the Fe sublattice contribution. Figs. 6 and 7 gives a comparison of the 300 and 5 K profiles of the (642) line of the powder-diffraction pattern of UFe 2 and U 0.8 Lu 0.2 Fe 2 , respectively. In the case of UFe 2 , the rhombohedral distortion should lead to a splitting of the low-temperature (642) line into four lines of ] ] ] equal intensities, (642), (642), (642) and (642). The calculated splitting that fits well the experimental profile is shown at the bottom of Fig. 6. The corresponding lattice parameter a5704.3 pm and the rhombohedral distortion ´ (in this case of the k111l easy axis equal to the magnetostriction constant l111 )52.9310 23 are in good agreement with previous single-crystal results [7] (see Fig. 1). In U 0.8 Lu 0.2 Fe 2 , the situation is qualitatively different. There is practically no change in the line profile above and below T C . The l111 constant is believed to be still very high, but due to the k100l easy axis it cannot manifest itself in the spontaneous distortion. It can be determined only by direct magnetostriction measurement in a field, which is in progress. Instead of the rhombohedral, a tetragonal distortion described by the l100 constant should exist in the substituted compound and the (642) line should be split ] ] ] into three lines of equal intensities, (642), (642) and (642). If it is not seen experimentally, we can deduce from the threshold sensitivity of the X-ray powder diffraction in respect to distortion that l100 in U 0.8 Lu 0.2 Fe 2 does not reach a value higher than 3310 24 . l100 in UFe 2 (2310 24 ) and evidently in U 0.8 Lu 0.2 Fe 2 is indeed below this limit. Thus, the disappearance of the spontaneous distortion confirms the change of the easy-magnetization axis from k111l to k100l.
A.V. Andreev, R.Z. Levitin / Journal of Alloys and Compounds 337 (2002) 18 – 24
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Fig. 6. Profiles of the (642) line of the X-ray powder-diffraction pattern of UFe 2 at 5 and 300 K. Calculated splitting into four lines (thin lines) due to the rhombohedral distortion is shown for the 5 K pattern. The arrows show positions of Ka 1 maximum for the split lines.
Fig. 7. Profiles of the (642) line of the X-ray powder-diffraction pattern of U 0.8 Lu 0.2 Fe 2 at 5 and 300 K.
4. Conclusions
Acknowledgements
The spin reorientation from the tetra-axial (the k111l easy magnetization direction) to the tri-axial (the k100l easy magnetization direction) magnetic anisotropy as a consequence of the competition between the cubic magnetocrystalline anisotropy constant K 01 and the magnetoelastic contribution to the magnetic anisotropy DK me was 1 predicted to occur upon non-magnetic substitution in the uranium sublattice of UFe 2 . It was actually observed by magnetization measurements on single crystals of UFe 2 and U 0.8 Lu 0.2 Fe 2 and confirmed by the fact that the large spontaneous magnetostriction distortion in UFe 2 disappears in U 0.8 Lu 0.2 Fe 2 . The total K1 5K 01 1DK me 1 was found to be 20.21 and 0.15 MJ / m 3 at 4.2 K in UFe 2 and U 0.8 Lu 0.2 Fe 2 , respectively. From these data, the individual values of K 01 and DK me 1 in UFe 2 were found in the two-ion approach as 1.03 and 21.24 MJ / m 3 , respectively. This confirms the conclusion that the low magnetic anisotropy of UFe 2 is a result of the mutual cancellation of rather large contributions.
The authors thank Dr. Y. Homma, Dr. D. Rafaja, Mr. N. Izmaylov and Mr. D. Filippov for the help in experiments and calculations. The work is a part of research program of the Joint Laboratory for Magnetic Studies of the Charles University and Academy of Sciences of the Czech Republic. It was supported by grants [202 / 99 / 0184 of the Grant Agency of the Czech Republic and A1010018 of the Grant Agency of the Academy of Sciences of the Czech Republic.
References [1] P. Gordon, Thesis, Massachusetts Institute of Technology (1949); cited in: V. Sechovsky, L. Havela, in: E.P. Wohlfarth, K.H.J. Buschow (Eds.), Ferromagnetic Materials, Vol. 4, Elsevier, Amsterdam, 1988, p. 309. [2] A.T. Aldred, J. Magn. Magn. Mater. 10 (1979) 42. [3] H.H. Hill, in: W.N. Miner (Ed.), Plutonium and Other Actinides, Nucl. Met. Series, Vol. 17, AIME, 1970, p. 2.
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[4] A.E. Clark, in: E.P. Wohlfarth (Ed.), Ferromagnetic Materials, Vol. 1, Elsevier, Amsterdam, 1980, p. 531, and Refs. therein. [5] M. Yessik, J. Appl. Phys. 40 (1969) 1133. [6] G.H. Lander, A.T. Aldred, B.D. Dunlap, G.K. Shenoy, Physica B 86–88 (1977) 152. [7] Y.F. Popov, R.Z. Levitin, A.V. Deryagin, M. Zeleny, A.V. Andreev, Sov. Phys. JETP 51 (1980) 1223. [8] A.V. Andreev, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 8, Elsevier, Amsterdam, 1995, p. 59, and Refs. therein. [9] N.M. Kolacheva, R.Z. Levitin, L.P. Shlyakhina, Fiz. Tverd. Tela (Soviet Phys. Solid State) (In Russian) 19 (1977) 970. [10] M.S.S. Brooks, O. Eriksson, B. Johansson, J.J.M. Franse, P.H. Frings, J. Phys. F. 18 (1988) L33. [11] M. Wulff, G.H. Lander, B. Lebech, A. Delapalme, Phys. Rev. B 39 (1989) 4719.
[12] B. Lebech, M. Wulff, G.H. Lander, J. Rebizant, J.C. Spirlet, A. Delapalme, J. Phys.: Condens. Matter 1 (1989) 10229. [13] M. Finazzi, P. Sainctavit, A.M. Dias, J.P. Kappler, G. Kril, J.P. ´ Sanchez, P. Dalmas de Reotier, A. Yaouanc, A. Rogalev, J. Goulon, Phys. Rev. B 55 (1997) 3010. [14] P.K. Lawson, M.J. Cooper, M.A.G. Dixon, D.N. Timms, E. Zukowski, F. Itoh, H. Sakurai, Phys. Rev. B 56 (1997) 3239. [15] K.P. Belov, G.A. Kataev, R.Z. Levitin, S.A. Nikitin, V.I. Sokolov, Sov. Phys. Uspekhi 26 (1983) 518. [16] A.V. Andreev, A.V. Deryagin, R.Z. Levitin, A.S. Markosyan, M. Zeleny, Phys. Stat. Sol. (a) 52 (1979) K13. [17] V. Sechovsky, L. Havela, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 11, Elsevier, Amsterdam, 1998, p. 1, and Refs. therein. [18] V. Sechovsky, G. Wiesinger, J. Toul, Physica B 102 (1980) 212.
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www.elsevier.com / locate / jallcom
Spin reorientation in UFe 2 upon non-magnetic substitution in the uranium sublattice a, b A.V. Andreev *, R.Z. Levitin b
a Institute of Physics ASCR, Na Slovance 2, 182 21 Prague 8, Czech Republic Moscow State University, Faculty of Physics, Vorob’ evy Gory, 119899 Moscow, Russia
Received 11 October 2001; accepted 18 October 2001
Abstract The spin reorientation from the k111l to the k100l easy-magnetization axis as a consequence of the competition between the cubic magnetocrystalline anisotropy constant K 01 and the magnetoelastic contribution to the magnetic anisotropy DK me was predicted and 1 observed upon magnetic dilution of the uranium sublattice of UFe 2 . The total K1 5K 01 1DK me was determined from the magnetization 1 measurements on single crystals of UFe 2 and U 0.8 Lu 0.2 Fe 2 as 20.21 and 0.15 MJ / m 3 (at 4.2 K), respectively. The individual values of K 10 and DK 1me in UFe 2 were found as 1.03 and 21.24 MJ / m 3 , respectively, which shows that the low magnetic anisotropy of UFe 2 is a result of the mutual cancellation of rather large K 01 and DK me 1 . The change of the anisotropy type is accompanied by the disappearance of spontaneous magnetostriction distortion in U 0.8 Lu 0.2 Fe 2 . 2002 Elsevier Science B.V. All rights reserved. Keywords: Actinide compound; Transition metal compound; Magnetically ordered materials; Anisotropy; Magnetic measurements
1. Introduction and motivation The Laves phase UFe 2 crystallizing in the cubic MgCu 2 structure has in many respects a special position in the magnetism of actinides. It was the first actinide-containing compound found to be magnetically ordered [1] and still attracts large attention. Many studies of UFe 2 have been performed on single crystals which can be grown relatively easily by different methods. UFe 2 is a ferromagnet with Curie temperature T C varying from 158 to 195 K and spontaneous molecular magnetic moment mm from 0.96 to 1.36 m B per formula unit. As it was shown in Ref. [2], this difference is due to existence of a homogeneity range that was not taken into account in early works, and the stoichiometric composition UFe 2 corresponds to T C (165 K and mm (1.1 m B . For a long time, ferromagnetism in UFe 2 was attributed exclusively to Fe, whereas the U atoms do not carry a magnetic moment. The strong argument for such an opinion is the very short interuranium spacing in UFe 2 , d U – U 5305 pm. This is much smaller than the Hill limit 340 pm, the critical d U – U value above which the U atoms can carry a magnetic moment *Corresponding author. KFES MFF UK, Ke Karlovu 5, 12116 Prague 2, Czech Republic. Tel.: 1420-2-2191-1352; fax: 1420-2-2191-1351. E-mail address: [email protected] (A.V. Andreev).
[3]. The reduction of the Fe magnetic moment mFe and T C in UFe 2 in comparison with isostructural rare-earth compounds RFe 2 (where mFe reaches 1.5 m B and T C .500 K [4]) was attributed to an additional filling of the 3d band of Fe by uranium 5f and 6d electrons. Early neutron-diffraction studies confirmed the negligible magnetic moment on the uranium sites [5,6]. From this viewpoint, the discovery of giant anisotropic magnetostriction in UFe 2 [7] was rather unexpected because it was in complete disagreement with the nonmagnetic state of U. Below T C , the cube angle a decreases by 10 min, i.e. UFe 2 undergoes a rhombohedral distortion ´ 5cos a (Fig. 1). The magnetostrictive origin of this distortion was confirmed by strain-gauge measurements in magnetic field. The magnetostriction of a cubic crystal is described by
l 5 l0 1 3 / 2 l100 (a x2 b x2 1 a y2 b y2 1 a z2 b z2 2 1 / 3) 1 3 l111 (ax ay bx by 1 ay az by bz 1 ax az bx bz ).
(1)
Here ai are the cosines of the magnetic moment direction, bi are the cosines of the strain measurement direction, li are the magnetostriction constants. l0 is the isotropic strain which does not depend on the orientation of magnetic moment and is equal to the related difference between the experimental and extrapolated curves in Fig.
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01911-9
A.V. Andreev, R.Z. Levitin / Journal of Alloys and Compounds 337 (2002) 18 – 24
Fig. 1. Top: the temperature dependence of lattice parameter a of UFe 2 . The dotted line represents the phonon contribution with Debye temperature QD 5190 K. Bottom: the deviation of the cube angle a from p / 2 in UFe 2 . The right-hand scale shows the corresponding values of the rhombohedral distortion ´ 5cos a.
1. In UFe 2 , l0 reaches 4.8310 24 which corresponds to the spontaneous volume magnetostriction vs 51.45310 23 . l111 describes the rhombohedral distortion occurring when the magnetic moment is directed (spontaneously or by magnetic field) along the k111l axis. In the case of easy k111l axis, like in UFe 2 , l111 5 ´. The l100 constant, describing the tetragonal distortion when magnetic moment is along the k100l axis, is found by strain-gauge measurements to be 2310 24 at low temperatures, e.g. is negligible compared to the l111 value (2.9310 23 , Fig. 1) [7]. Since the Fe sublattice can provide a two-orders of magnitude smaller magnetostriction (as known from magnetostriction measurements of RFe 2 with non-magnetic R [8]), the observed l111 value was a strong evidence for the uranium contribution to the magnetic properties of UFe 2 . The absolute value of l111 of UFe 2 exceeds that of RFe 2 for some magnetic R (Er, Ho) and is comparable with the maximum observed for R5Tb ( l111 (5310 23 [4,8]). In order to reconcile the giant magnetostriction of UFe 2 with the negligible magnetic moment on uranium sites, a mutual cancellation of noticeable spin ( mS ) and orbital ( mL ) moments was proposed in [7] similar to the state of the Sm 31 ion in some compounds [9]. Later such a cancellation was obtained from band-structure calculations (absolute values of mS and mL are about 0.5 m B [10]) and then confirmed by many modern methods of investigation
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of the electronic structure: polarized neutron diffraction [11,12], X-ray magnetic circular dichroism [13], magnetic Compton scattering [14]. Results of the experimental studies [11–14] are in very good agreement and give mS 5 2(0.20–0.22) m B and mL 50.21–0.23 m B . The total mU (0.01 m B is ferromagnetically coupled with 2mFe (1.2 mB . The compensation of spin and orbital moments of uranium in UFe 2 that attracted so much attention, is not, however, the only very special feature of UFe 2 . The anisotropic magnetostriction and the magnetic anisotropy have the same origin and are either both strong (like in RFe 2 with anisotropic R ions) or both weak (like in RFe 2 with non-magnetic R5Y, Lu or isotropic Gd). The giant magnetostriction (.10 23 ) corresponds to the absolute value of the first anisotropy constant K1 of an order of magnitude up to 10 MJ / m 3 [4,15]. UFe 2 with giant magnetostriction is, however, a low-anisotropic ferromagnet, K1 is only 20.1 MJ / m 3 , e.g. by at least one order of magnitude lower than could by expected [7,16]. Generally, a combination of the low anisotropy and high magnetostriction can be reached, but only in solid solutions of the R 912x R 99 x Fe 2 type where the rare earth ions R9 and R0 have the same sign of magnetostriction and different signs of anisotropy [4]. In UFe 2 , only one type of magnetostrictive ion is present, and another mechanism explaining the reduced anisotropy should be found. In [7], we have solved the problem by the assumption that a large intrinsic cubic magnetocrystalline anisotropy described by the positive K 01 constant is overcome by the negative magnetoelastic contribution to the anisotropy DK me [15] 1 K1 5 K 10 1 DK 1me
(2)
2 2 DK me 1 5 (9 / 4) [(c 11 2 c 12 )l 100 2 2c 44 l 111 ],
(3)
where c ij are the elastic constants. Since in UFe 2 l111 4 2 l100 , DK 1me (2(9 / 2)c 44 l 111 (20.8 MJ / m 3 (c 44 523 10 2 0 3 10 N / m [7]) and K 1 is estimated as 0.7 MJ / m which is already not in so large a contradiction with giant magnetostriction. Thus, UFe 2 is believed to have two compensations of large terms, the spin and orbital moments of uranium and the intrinsic and magnetoelastic contributions to the magnetic anisotropy. Each of these cases is rather interesting and unusual, but the simultaneous appearance of such phenomena in the same compound makes from UFe 2 a unique magnetic matter. The former compensation is studied in great detail whereas the latter one is not. Both the low anisotropy and the strong magnetoelasticity in UFe 2 were confirmed by many studies, but their direct correlation still needs more clear evidence. One of the 0 me methods is destroying the delicate balance of K 1 and DK 1 by dilution of the U sublattice, e.g. by non-magnetic Lu. For our study, we selected 20% dilution. In any models, 0 either single- or two-ion, K 1 and l111 have the same
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A.V. Andreev, R.Z. Levitin / Journal of Alloys and Compounds 337 (2002) 18 – 24
behavior upon dilution. Since according to (3) 2 me DK me decreases with dilution considerably 1 ~ l 111 , DK 1 0 faster than K 1 . Using for UFe 2 K 10 50.7 MJ / m 3 and 3 DK me from [7] and the single-ion (i.e. 1 5 20.8 MJ / m linear) approach, we estimated for 20% dilution K 10 50.6 3 MJ / m 3 and DK me 1 5 20.55 MJ / m . The total K 1 (0.05 3 MJ / m becomes positive, which means that the k100l axis becomes the easy magnetization direction. The same result (positive K1 at 20% dilution) can be obtained also in a two-ion approach. Therefore, if our explanation of low anisotropy of UFe 2 is right, we should observe different types of anisotropy in UFe 2 and U 0.80 Lu 0.20 Fe 2 . In the present paper we have checked this prediction.
2. Experimental The UFe 2 and U 0.8 Lu 0.2 Fe 2 samples were spark-erosion cut perpendicular to the k100l, k110l and k111l axes from single crystals prepared by a modified Czochralski method. First, 10-g precursors were melted under a protective high-purity Ar atmosphere from stoichiometric amounts of the elementary metals (U and Lu of 3N purity, Fe 4N) on a rotating copper water-cooled bottom in a tetra-arc furnace with tungsten electrodes. Then the crystals were pulled out with a pulling speed of 10 mm / h using a tungsten wire as a seed. The check of crystal quality as well as its orientation for cutting was done using the X-ray Laue method. The phase purity and the lattice parameters of the samples were determined by standard X-ray diffraction on a powder sample prepared from a part of the crystal. The low-temperature (at T55 K) search for a spontaneous magnetostrictive distortion was performed by profile analysis of the (642) reflection in Co Ka radiation. The magnetization was measured along the k100l, k110l and k111l axes in the temperature range 4.2–300 K in a vibrating sample magnetometer with a superconducting coil providing fields up to 14 T. The values of mm and T C were determined from the Belov–Arrott plots of the magnetization isotherms.
Table 1 Structural and magnetic characteristics of UFe 2 and U 0.8 Lu 0.2 Fe 2
a at 300 K (pm) a at 5 K (pm) ´ at 5 K (10 23 ) mm at 4.2 K (m B ) Easy axis T C (K) K1 at 4.2 K (MJ / m 3 ) K 01 at 4.2 K (MJ / m 3 ) 3 DK me 1 at 4.2 K (MJ / m ) a
UFe 2
U 0.8 Lu 0.2 Fe 2
705.8 704.3 2.9 1.09 k111l 168 20.21 1.03 a 21.24 a
708.9 707.7 0 1.59 k100l 290 0.15 0.66 a 20.51 a
In the two-ion approach.
stoichiometry. A comparison with the crystals used in Refs. [7,16] for anisotropy and magnetostriction studies, presented in the inset in Fig. 2, points to a much better quality of the new crystal. The easy-magnetization curve saturates completely at 0.2 T in the new crystal which is comparable with the demagnetization field of the sample ((0.15 T), whereas only 70% of the saturation was reached at this field in the previous crystal. In this case, a 0.8 T is needed for complete saturation evidently because of considerable residual stresses. Also, the enhanced mm value (1.16 m B ) indicates a deviation from the 1:2 stoichiometry in this crystal. The energy of magnetic anisotropy for a cubic crystal is described in a two anisotropy-constant approximation by formula Ea 5 K1 (a x2 a 2y 1 a 2x a 2z 1 a 2y a 2z ) 1 K2 a 2x a 2y a 2z ,
(4)
where ai are the cosines of the magnetic moment direction.
3. Results and discussion The X-ray phase analysis showed that the crystals do not contain extraneous phases. The room-temperature lattice parameter of UFe 2 a5705.8 pm is in good agreement with literature. The larger a value (708.9 pm) of U 0.8 Lu 0.2 Fe 2 is due to the larger atomic radius of Lu compared to U. All structural and magnetic characteristics of both compounds studied are listed in Table 1. Magnetization curves of the UFe 2 crystal along the principal axes at 4.2 K presented in Fig. 2 confirm that the k111l axis is the easy-magnetization direction and the k100l is the hardest direction. The value of mm 51.09 m B (as well as T C 5168 K) corresponds well to the 1:2
Fig. 2. Magnetization curves of the UFe 2 crystal along the principal axes at 4.2 K. The inset shows the k111l curves for the crystals used in the present work and in Ref. [7].
A.V. Andreev, R.Z. Levitin / Journal of Alloys and Compounds 337 (2002) 18 – 24
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In particular, E100 50, E110 5K1 / 4 and E111 5K1 / 31K2 / 27. Therefore, K1 5 4 DE110
(5a)
K2 5 27 DE111 –36 DE110 ,
(5b)
where DE110 5E100 –E110 (the area between the k100l and k110l curves in Fig. 2) and DE111 5E100 –E111 (the area between the k100l and k111l curves). The values of K1 and K2 determined in this way are equal to 20.21 and 0.22 MJ / m 3 , respectively. These results differ quantitatively from those of Ref. [16]. The absolute value of K1 is larger by a factor of 2 and that of K2 by a factor of 4 than previously obtained. We attribute the difference first of all to an evidently non-stoichiometric composition of the crystal of Ref. [16]. Then, the above-mentioned different quality of crystals can also affect the results as well as the different methods of anisotropy measurement (by torque anisometer in Ref. [16]). We consider the new results as more reliable. It is worth to mention that the K2 value depends very much not only on the hard-direction curve like K1 , but also on the easy-direction curve and, consequently, on the quality of the crystal. For this reason, K2 is determined with much larger error. This does not affect K1 . If we neglect K2 , the K1 value determined from DE111 is 3 equal to 20.19 MJ / m , only |10% different from the value determined from DE110 according to (5a). In any case, the result obtained does not change the conclusion of Ref. [7] about a low total anisotropy of UFe 2 and almost does not influence the K 01 value estimated from formulas 2 and 3 (0.6 MJ / m 3 instead of 0.7 MJ / m 3 in [7]). Fig. 3 illustrates the temperature evolution of the magnetization curves of UFe 2 . It shows a monotonous decrease of the anisotropy with increasing the temperature. A detailed study of temperature dependence of the anisotropy and a search for a possible spontaneous spinreorientation in the vicinity of T C is in progress and the results will be published elsewhere. Magnetization curves of the U 0.8 Lu 0.2 Fe 2 crystal along the principal axes at 4.2 K presented in Fig. 4 show another type of the magnetic anisotropy with respect to UFe 2 . The k111l axis becomes the hardest-magnetization direction, whereas the k100l axis is now the easy-magnetization direction. Calculation of the anisotropy constants, especially of K2 , from the curves of Fig. 4 faces the problem of the shape of the easy-magnetization curve. If we use the experimental k100l curve from Fig. 4, K1 50.15 MJ / m 3 and K2 50.01. However, the easy-direction curve in the U 0.8 Lu 0.2 Fe 2 crystal is clearly not as good as in UFe 2 . It resembles the easy-axis curve of the crystal from Ref. [7] (see inset in Fig. 2) and is evidently influenced by residual stress in the crystal. If we use the same shape of easy-direction curve as for the UFe 2 crystal, K1 50.18 MJ / m 3 and K2 5 20.11 MJ / m 3 . One can see that K2 is much more sensitive to the procedure of the determination. In the further discussion we will consider only K1 . The
Fig. 3. Magnetization curves of the UFe 2 crystal along the principal axes at elevated temperatures.
Fig. 4. Magnetization curves of the U 0.8 Lu 0.2 Fe 2 crystal along the principal axes at 4.2 K.
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temperature evolution of the magnetization curves of the U 0.8 Lu 0.2 Fe 2 crystal is shown in Fig. 5. As in UFe 2 , the anisotropy weakens with increasing temperature. A more detailed study of temperature dependence of the anisotropy is in progress. The mechanism responsible for the magnetocrystalline anisotropy in the RFe 2 intermetallics with well localized 4f states is their interaction with the crystalline electric field. It has a single-ion character. The mostly delocalized 5f states in intermetallics of light actinides, being involved in the anisotropic covalent bonding, imply an essentially different, two-ion (5f–5f) interaction via 5f-ligand hybridization, which plays a major role in the anisotropy [17]. (The strong spin–orbit interaction is a necessary prerequisite in both cases.) With the experimental K1 values for UFe 2 and U 0.8 Lu 0.2 Fe 2 , we can estimate K 01 and DK me 1 in UFe 2 . The linear approach, which corresponds to the single-ion mechanism of magnetic anisotropy, gives K 01 5 1.78 MJ / m 3 and DK 1me 5 21.99 MJ / m 3 . The quadratic approach, corresponding to the two-ion mechanism, gives K 10 51.03 MJ / m 3 and DK 1me 5 21.24 MJ / m 3 . The latter result is considerably closer to K 10 50.6 MJ / m 3 and DK 1me 5 20.8 MJ / m 3 obtained above by another method (from formulas (2) and (3)). This could be considered as a proof for the two-ion mechanism of anisotropy in UFe 2 .
Fig. 5. Magnetization curves of the U 0.8 Lu 0.2 Fe 2 crystal along the principal axes at elevated temperatures.
However, we understand that several factors neglected in these estimates reduce the reliability of this conclusion: (a) non-negligible difference in the lattice parameter a (see Table 1); (b) different state of the Fe sublattice in UFe 2 and U 0.8 Lu 0.2 Fe 2 reflected in the considerably higher mm and T C in the latter case; (c) possible change of state of the 5f electrons due to points (a) and (b); (d) the Fe-sublattice contribution to the magnetic anisotropy. It is expected to be small in comparison with K 01 and DK me 1 , but could be comparable with their sum. In this respect it is worth ¨ mentioning the results obtained by Fe 57 Mossbauer effect measurements in the U 12x Zr x Fe 2 system [18]. The Zr atoms like the Lu ones do not carry a magnetic moment. It was found that the spectra of the terminal compounds and most of the solid solutions are well described by the assumption of an k111l easy axis, whereas the compositions with x50.5 and 0.6 exhibit k100l as easy axis. We can explain the first spin reorientation the this system (between x50.4 and 0.5) as originating from the competi0 me tion of K 1 and DK 1 , as in the present work. The difference in concentration of the spin reorientation may be attributed to a different effective valence of Lu (3) and Zr (4). However, the reentrant reorientation back to the k111l easy axis needs the third term in K1 which starts to dominate at low U content. This is evidently the Fe sublattice contribution. Figs. 6 and 7 gives a comparison of the 300 and 5 K profiles of the (642) line of the powder-diffraction pattern of UFe 2 and U 0.8 Lu 0.2 Fe 2 , respectively. In the case of UFe 2 , the rhombohedral distortion should lead to a splitting of the low-temperature (642) line into four lines of ] ] ] equal intensities, (642), (642), (642) and (642). The calculated splitting that fits well the experimental profile is shown at the bottom of Fig. 6. The corresponding lattice parameter a5704.3 pm and the rhombohedral distortion ´ (in this case of the k111l easy axis equal to the magnetostriction constant l111 )52.9310 23 are in good agreement with previous single-crystal results [7] (see Fig. 1). In U 0.8 Lu 0.2 Fe 2 , the situation is qualitatively different. There is practically no change in the line profile above and below T C . The l111 constant is believed to be still very high, but due to the k100l easy axis it cannot manifest itself in the spontaneous distortion. It can be determined only by direct magnetostriction measurement in a field, which is in progress. Instead of the rhombohedral, a tetragonal distortion described by the l100 constant should exist in the substituted compound and the (642) line should be split ] ] ] into three lines of equal intensities, (642), (642) and (642). If it is not seen experimentally, we can deduce from the threshold sensitivity of the X-ray powder diffraction in respect to distortion that l100 in U 0.8 Lu 0.2 Fe 2 does not reach a value higher than 3310 24 . l100 in UFe 2 (2310 24 ) and evidently in U 0.8 Lu 0.2 Fe 2 is indeed below this limit. Thus, the disappearance of the spontaneous distortion confirms the change of the easy-magnetization axis from k111l to k100l.
A.V. Andreev, R.Z. Levitin / Journal of Alloys and Compounds 337 (2002) 18 – 24
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Fig. 6. Profiles of the (642) line of the X-ray powder-diffraction pattern of UFe 2 at 5 and 300 K. Calculated splitting into four lines (thin lines) due to the rhombohedral distortion is shown for the 5 K pattern. The arrows show positions of Ka 1 maximum for the split lines.
Fig. 7. Profiles of the (642) line of the X-ray powder-diffraction pattern of U 0.8 Lu 0.2 Fe 2 at 5 and 300 K.
4. Conclusions
Acknowledgements
The spin reorientation from the tetra-axial (the k111l easy magnetization direction) to the tri-axial (the k100l easy magnetization direction) magnetic anisotropy as a consequence of the competition between the cubic magnetocrystalline anisotropy constant K 01 and the magnetoelastic contribution to the magnetic anisotropy DK me was 1 predicted to occur upon non-magnetic substitution in the uranium sublattice of UFe 2 . It was actually observed by magnetization measurements on single crystals of UFe 2 and U 0.8 Lu 0.2 Fe 2 and confirmed by the fact that the large spontaneous magnetostriction distortion in UFe 2 disappears in U 0.8 Lu 0.2 Fe 2 . The total K1 5K 01 1DK me 1 was found to be 20.21 and 0.15 MJ / m 3 at 4.2 K in UFe 2 and U 0.8 Lu 0.2 Fe 2 , respectively. From these data, the individual values of K 01 and DK me 1 in UFe 2 were found in the two-ion approach as 1.03 and 21.24 MJ / m 3 , respectively. This confirms the conclusion that the low magnetic anisotropy of UFe 2 is a result of the mutual cancellation of rather large contributions.
The authors thank Dr. Y. Homma, Dr. D. Rafaja, Mr. N. Izmaylov and Mr. D. Filippov for the help in experiments and calculations. The work is a part of research program of the Joint Laboratory for Magnetic Studies of the Charles University and Academy of Sciences of the Czech Republic. It was supported by grants [202 / 99 / 0184 of the Grant Agency of the Czech Republic and A1010018 of the Grant Agency of the Academy of Sciences of the Czech Republic.
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