DSpace at VNU: Magnetic properties of Tb1-xYx(Co0.85Si0.15)(2) compounds

Journal of Magnetism and Magnetic Materials 262 (2003) 472–478 Magnetic properties of Tb1ÀxYx(Co0.85Si0.15)2 compounds P.E Brommera,*, N.H Ducb b a Van der Waals-Zeeman Institute, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands Cryogenic Laboratory, Faculty of Physics, Vietnam National University, 334 Nguyen Trai Road, Thanh xuan, Hanoi, Viet Nam Abstract A series of Tb1ÀxYx(Co0.85Si0.15)2 compounds was prepared for x ¼ 0; 0.2, 0.4, 0.6, and 0.8 The Curie temperatures were determined by AC susceptibility measurements and the temperature dependence of the magnetisation was measured in an applied field of 0.2 T Magnetisation curves were determined at 4.2 K in applied fields up to 10 T In the curves obtained for the compounds with xo0:8; a clear hysteresis was found at low fields (up to T) and at moderate fields (2–8 T) The anomaly at lower fields is ascribed to freezing-in phenomena and domain wall pinning The same effects may cause the observed splitting of field-cooled and zero-field-cooled magnetisation vs temperature curves in an applied field of 30 mT The behaviour of the anomaly at moderate fields as a function of the Tb concentration is discussed in a two-subsystem molecular-field model The anomaly is tentatively ascribed to a metamagnetic transition in the Tb subsystem r 2003 Elsevier Science B.V All rights reserved PACS: 75.10; 75.50.Gg Keywords: Laves phase; (Tb, Y)(Co, Si)2; Molecular-field model; Hysteresis Introduction The study of magnetic and transport properties of the cubic Laves phase RCo2 (R=rare earths) intermetallic compounds is of great interest due to the peculiar nature of their 3d(Co) magnetism The Co-subsystem appears to be close to the critical condition for the appearance of magnetism and exhibits itinerant-electron metamagnetism (IEMM) The present state of theory and experiment for RCo2 compounds were reviewed by Duc and Goto [1] and Duc and Brommer [2] The *Corresponding author Tel.: +31-020-525-5737; fax: +31020-525-5788 E-mail address: brommer@science.uva.nl (P.E Brommer) magnetic instability causes not only IEMM, but also many other striking properties such as an enhanced magnetic susceptibility, a huge electronic specific-heat constant, spin fluctuations and a volume anomaly Substitution of Al for Co does lower the metamagnetic-transition field, and eventually stabilises a weakly ferromagnetic structure that still may exhibit metamagnetism Brommer et al [3] described the magnetisation process of Tm0.25Y0.75(Co0.88Al0.12)2 as a sequence of a reverse metamagnetic transition (Co going from a high-spin to a low-spin state), the familiar rotation of the moments in the two-sublattice model, and then again the metamagnetic transition to the Co high-spin state Kowalczyk et al [4] added to this picture magnetic anomalies due to 0304-8853/03/$ - see front matter r 2003 Elsevier Science B.V All rights reserved doi:10.1016/S0304-8853(03)00080-5 P.E Brommer, N.H Duc / Journal of Magnetism and Magnetic Materials 262 (2003) 472–478 50 x = 0.0 40 M [Am2/kg] 0.4 30 0.6 20 0.8 10 0 100 200 300 T [K] Fig Temperature dependence of the magnetisation at B ¼ 0:2 T for Tb1ÀxYx(Co0.85Si0.15)2 compounds 25 FC 20 15 10 ZFC Experimental technique Tb1-xYx(Co0.85Si0.15)2 0.2 M (arb unit) ‘‘freezing-in’’ phenomena and domain wall pinning The importance of the volume (lattice parameter) was also stressed [2,5] In order to study this volume effect, experiments were performed on the effect of substitution in some series of R(Co1ÀxMx)2 compounds (with M=Al, Si, Cu,y) The Al-substitution revealed that the volume has a major influence [6] The Si-substitution, however, leads to a series of compounds with invariable cell parameter, and the observed modification of the magnetic properties was ascribed to 3d–p hybridisation effects [7] In their study of field-induced non-collinear magnetic structures in (Lu1ÀyTmy)(Co0.88Al0.12)2, Brommer et al [8] observed a first-order metamagnetic transition (with a large hysteresis) for y ¼ 0:6: The origin of this transition is not clear, and could be a transition of the Co system or a transition of the Tm moments, in the crystalline electric field (CEF) The present paper deals with similar field-induced magnetic transitions in a series of Tb1ÀxYx(Co0.85Si0.15)2 compounds The fact that the transitions occur at different Tb contents allows a more thorough discussion, based on a simple molecular-field model 473 50 100 150 200 250 300 T (K) The samples were prepared by melting stoichiometric mixtures of rare earth (and yttrium) (4N8), Co and Si (5 N) in an induction furnace under argon atmosphere The melted buttons were wrapped in Ta foil, sealed under argon in silica tubes and annealed at 950 C X-ray analysis shows the presence of one (C15) phase only The magnetisation was measured using an induction method in fields up to 10 T, at the Laboratoire Louis Ne! el (Grenoble) The magneto-thermal experiments, field-cooling (FC) and zero-fieldcooling (ZFC) measurements were carried out by means of an extraction magnetometer Results In Fig we present the temperature dependence of the magnetisation of the Tb1ÀxYx(Co0.85Si0.15)2 Fig ZFC (filled markers) and FC (open markers) magnetisation curves of Tb0.8Y0.2(Co0.85Si0.15)2 compounds Data obtained at increasing temperature in a field of 30 mT compounds in an applied magnetic field of 0.2 T Typical ZFC and FC magnetisation curves measured in an applied field of 30 mT are presented in Fig for the sample with x ¼ 0:2: Obviously, ‘‘freezing-in’’ phenomena occur like those mentioned in the introduction The Curie temperatures (TC ) were determined from AC susceptibility data (not shown here) The results are listed in Table and plotted in Fig For comparison, the TC data of some (Tb1ÀxYx)Co2 compounds [9,10] are included Fig presents the magnetisation curves measured at 4.2 K for the Tb1ÀxYx(Co0.85Si0.15)2 compounds The total magnetic moment at 10 T and the Co moment, deduced P.E Brommer, N.H Duc / Journal of Magnetism and Magnetic Materials 262 (2003) 472–478 474 Table The Curie temperature (TC ), the total magnetic moment (Mtot ) in a field of 10 T, and the corresponding magnetic moment per Co (mCo ), derived by taking mTb ¼ 8:4 mB /Tb after Voiron [11], for the Tb1ÀxYx(Co0.85Si0.15)2 compounds Tb1-xYx(Co0.85Si0.15)2 x = 0.0 TC (K) Mtot (mB/f.u.) mCo (mB) 1.0 0.8 0.6 0.4 0.2 230 210 190 150 75 6.65 5.3 3.8 2.25 0.94 1.03 0.835 0.73 0.65 0.43 M [µB /f.u.] x 0.2 0.4 0.6 0.8 240 Tb1-xYx(Co0.85Si0.15)2 200 10 B [T] Fig Magnetisation curves at T ¼ 4:2 K for Tb1ÀxYx(Co0.85Si0.15)2 compounds The up- and down-arrows indicate the fields Bup;c and Bdwn;c ; respectively (see main text) 160 Tb1-xYxCo2 TC [K] 120 80 40 0 0.2 0.4 0.6 0.8 x Fig Y-concentration dependence of the Curie temperature of Tb1ÀxYx(Co0.85Si0.15)2 (this work), and of (Tb1ÀxYx)Co2 (J: [9], +[10]) The solid lines are guides to the eye The dashed line stresses the linear concentration dependence for the lowest two Tb concentrations effects were ascribed to domain structure, possibly influenced by anisotropy and so on (ii) at moderate fields (2–8 T), in the magnetisation curve, a transition with a large hysteresis is observed for the higher Tb concentrations As mentioned in Section 1, these anomalies show a systematic dependence on the Tb concentration, offering for the first time an opportunity for a more detailed analysis to be presented in the following section The anomaly at moderate fields using Voiron’s estimate for the Tb moment mTb ¼ 8:4 mTb [11], are listed in Table In the magnetisation curves, one may distinguish two kinds of ‘anomalies’: (i) At low fields (up to or T) there appears to be some hysteresis, presumably corresponding to the differences between FC and ZFC magnetisation vs temperature curves mentioned above A similar low-field hysteresis is observed in Dy(Co0.8Al0.2)2 [12] and in DyCo2 [4], together with a time-dependent remanence and a similar splitting of FC and ZFC curves These ‘‘spin-glass-like’’ In the two-subsystem (RT) molecular-field model (see e.g Ref [2]), a stable structure cannot exist whenever the product of the differential susceptibilities wT (of the T-subsystem) and wR (of the R-subsystem) increases to such values that 12wT wR n2RT changes sign Here, nRT is the RT molecular-field parameter, negative for the antiferromagnetic Tb–Co coupling A simple example is the transition caused by a rather sharp, metamagnetic transition (MMT) in either subsystem: the susceptibility of either the T-subsystem or the R-subsystem reaches a critical large value An P.E Brommer, N.H Duc / Journal of Magnetism and Magnetic Materials 262 (2003) 472–478 MMT in the (Co,Si) T-subsystem would occur at a certain value of the effective field exerted on it, BT ẳ nRT MR ỵ B; where MR is the magnetic moment of the (Tb) R-subsystem B is the applied field, taken to be positive With the substitution of Y for Tb, the reduction of |nRT MR |, the molecular field exerted by the Tb moments, can be estimated to be of the order of mB (the saturation moment of a Tb ion) times |nRT |, and thus, with the low estimate jnRT j ¼ 14 T f:u:=mB ([2,3]), is expected to be larger than 100 T Since this reduction is in any case much larger than the (compensating) observed reduction of the applied field at the anomaly (see Fig 4), we can exclude the possibility that the anomaly is caused by a MMT in the (Co,Si)-subsystem Next, we consider the case that the anomaly is triggered by a MMT in the Tb subsystem, presumably a (single-ion) CEF effect We assume that the CEF parameters are the same, regardless of the Y substitution, but inclusive of a possible spread due to variations in the local environment (e.g in the number of Si neighbours) For a given set of parameters, the anomaly should occur at a fixed value BTb;c of the effective field acting on the Tb moments, i.e of BTb ẳ nRT MT ỵ nRR MR ỵ B: Here, nRR is the Tb–Tb molecularfield parameter At the MMT, the Tb moment may jump from mTb;low up to mTb;hi ¼ mTb;low þ DmTb : The lower value is associated with the transition at (Bup;c ; Mup;c ) in the curve obtained with increasing field, the other with that at (Bdwn;c ; Mdwn;c ) obtained with decreasing field A sharp transition (MMT) in one subsystem may correspond to a wide hysteresis in the total magnetisation In order to demonstrate this, we assume that, in the neighbourhood of the anomaly, the T-sublattice magnetisation can be approximated by MT x; BT ị ẳ MT x; 0ị ỵ wT xịBT : After some manipulation, we nd Bup;c Bdwn;c ẳ xịNTb DmTb ẵnRR ỵ n2RT wT xị= ẵ1 ỵ nRT wT xị; 1aị Mup;c Mdwn;c ẳ xịNTb DmTb ẵ1 ỵ 2nRT nRR ịwT xị= ẵ1 ỵ nRT wT ðxފ: ð1bÞ 475 Here, NTb is the number of Tb atoms per chosen unit (NTb ¼ 1/f.u.) For the data displayed in Fig 4, we identify the (first) occurrence of a change in slope of the (lower) magnetisation curve with the onset of the MMT, determining characteristic values (Bup;c ; Mup;c ) (see up-arrows) Assuming that the ‘‘wings’’ of the hysteresis are due to a spread in the local MMT fields (of the individual Tb moments), Bup;c À Bdwn;c can be identified with the shift of the ‘‘down’’ curve with respect to the ‘‘up’’ curve Then, at Bdwn;c (see down-arrows), Mdwn;c can be estimated by extrapolating the upper (down) curve It can be seen that Bup;c À Bdwn;c is of the order of T Accurate values for Mup;c À Mdwn;c cannot be given, but they are rather small, of the order of 0.1 mB/f.u The observed hysteresis width does not clearly decrease with decreasing Tb content From Eqs (1a) and (1b), we conclude that this behaviour is possible only in case the factor nRR ỵ n2RT wT ị=1 þ nRT wT Þ plays an important role For a more quantitative approach, we first try to estimate wT ; nRT and nRR : Such estimates are usually derived by considering the observed TC values (Fig 2) and by applying that in the meanfield approximation, in the absence of crystal field effects, TC is given by [1,2,6] TC ¼ ð1 xịNTb CTb ẵn2RT wT TC ị ỵ nRR : ð2Þ Here, CTb is the Curie constant for a single ‘‘free’’ Tb (CTb ¼ 21:16 K mB/T), and wT ðTC Þ is the initial susceptibility of the (Co,Si) T-subsystem at TC Usually, one estimates wT ðTC Þ as the susceptibility of the corresponding (paramagnetic) Y-compound wYðCo;SiÞ ðTC Þ: Duc and Oanh [7] applied this method to various R(Co,Si)2 compounds, using the susceptibility values for Y(Co1ÀySiy)2 reported by Miller et al [13], and concluded that nRT would decrease with increasing Si content For the Tb(Co1ÀySiy)2 compounds, this conclusion was based on the observation that TC appears to be almost independent of the Si concentration y (up to y ¼ 0:08), whereas the substitution of Si for Co in Y(Co1ÀySiy)2 does initially enhance the susceptibility wYCo;Siị TC ị: For y ẳ 0:17; however, the susceptibility of Y(Co0.83Si0.17)2 at 230 K appears to be lowered again down to about the value for P.E Brommer, N.H Duc / Journal of Magnetism and Magnetic Materials 262 (2003) 472–478 YCo2 Estimating from Ref [13] wT ð230 Kị ẳ 4:2 103 emu=mol ẳ 0:0075 mB =T f.u., we find: jnRT j ¼ 38 T f.u./mB (with nRR ¼ 0), for both TbCo2 and Tb(Co0.85Si0.15)2 We note also that, on the basis of Eq (2), for both TC curves in Fig the deviation from linearity should be determined by the behaviour of the initial T-susceptibility as a function of temperature Calculated wT ðTC Þ vs TC curves (not given here) show qualitatively similar trends as the wYðCo;SiÞ ðTÞ curves reported in Ref [13] The quantitative deviations, however, prohibit using the susceptibility values of Y(Co0.83Si0.17)2 as wT ðTC Þ for our Tb1ÀxYx(Co0.85Si0.15)2 system Consequently, the just derived |nRT | value can only be regarded as indicating the order of magnitude of the RTinteraction Notice also that in Ref [13] the initial susceptibility appears to increase by about a factor two at low temperatures Finally, in view of Eq (2), it is reasonable to assume jnRR jon2RT wT ðTC ÞE10 Tf:u:=mB : A second estimate can be obtained by constructing the magnetisation curve of the T-subsystem by guessing some characteristic value for the Tbmoment Indeed, for given mTb and Tb content (1 À x), the total magnetic moment, Mðx; BÞ; can be decomposed in the R and T components MR ðx; BÞ and MT ðx; BÞ; yielding also mCo x; Bị; by applying MR x; Bị ẳ xịNTb mTb ; 3aị mCo x; Bị ẳ MT x; Bị=NCo ẳ ẵMx; Bị MR x; Bị=NCo : ð3bÞ Here, NCo is the number of Co atoms per chosen unit (NCo ¼ 1:7/f.u.) At the point (B; Mðx; BÞ), the effective field acting on an R (i.e Tb) moment and that acting on the T-subsystem are given by BTb x; Bị ẳ nRT MT x; Bị ỵ nRR MR x; Bị ỵ B; 4aị BT x; Bị ẳ nRT MR x; Bị ỵ B: 4bị Fig shows the Co-moment mCo ; calculated from Eqs (3a) and (3b) at some characteristic points, as a function of the effective field BT ; derived from Eq (4b) with nRT ¼ À38 T f.u./mB We assumed mTb;low ¼ 7:2 mB at any point (Bup;c ; Mup;c ) In Fig 4, the fields Bup;c are indicated by up-arrows By adopting Voiron’s estimate mTb ¼ 8:4 mB [11] at B ¼ 10 T, the Co moment in an applied field of 10 T were calculated from the observed Mx; B ẳ 10 Tị values (see Table 1) The upward curvature of the (mCo ; BT ) plot in Fig is contrary to the expectation that the Co moment would become saturated The constructed curve, however, appears to be very sensitive for small changes in e.g., the concentration x: Again, it appears to be impossible to derive exact values Nevertheless, we estimate the differential susceptibility wT to have values up to about 0.005 mB/T f.u., i.e nRT wT E À 0:2; and n2RT wT E8 T f.u./mB Then, for a hysteresis width Bup;c À Bdwn;c E2 T (see Fig 4, x ¼ 0:8), we estimate, taking nRR ¼ 0; from Eq (1a): DmTb ¼ 0:3 mB, and then from Eq (1b): Mdwn;c À Mup;c E0:16 mB/f.u Within the accuracy of the measurements and the necessary extrapolation, this is a not-unreasonable value For a given magnetisation curve of the Tsubsystem, it is possible to decompose the total 1.6 µCo [µB/Co] 476 1.2 0.8 0.4 0 100 200 300 BT [T] 400 500 Fig The magnetic moment of the T-subsystem (per Co atom) as a function of the effective field BT : J: from the points (Bup;c ; Mup;c ) indicated in Fig 4, taking mTb;low ¼ 7:2 mB ; +: from the magnetisation data at Bapp ¼ 10 T, taking mTb ¼ 8:4 mTb (see Table 1); &: the point (0,0) is added because the T-subsystem is supposed to be paramagnetic P.E Brommer, N.H Duc / Journal of Magnetism and Magnetic Materials 262 (2003) 472–478 10 µ Tb [µB /Tb] 10 µTb [µB /Tb] magnetic moment M in the contributions MT and MR by iteration: choosing a start value for MT ; MR is known (as M À MT ), and so is BT for given nRT (Eq (4b)), whence a new MT value is obtained by interpolation of the data shown in Fig For any choice of nRR ; also BTb can be determined (Eq (4a)) The resulting magnetisation curves for the Tb-subsystem are shown in Fig for nRR ¼ 0: The shift to lower fields of these curves with decreasing Tb content corresponds to the remarkable decrease of Bup;c apparent in Fig Since both the total R moment and (the absolute value of) the Co moment decrease with decreasing Tb content, the molecular field exerted on the Tb moments by the (Co,Si)-system also decreases Assuming that the molecular-field parameters nRT and nRR are constant (independent of the Tb content), the only way to compensate this decrease is an increase of the term nRR MR ðxÞ by choosing negative nRR values For the present choice nRT ¼ À38 T f.u./mB, one finds that nRR values around À3 T f.u./mB are necessary for this 477 0 20 40 60 BTb [T] 80 100 Fig Same as Fig 6, now for nRR ¼ À3: compensation (see Fig 7) A really satisfactory fitting would result in a unique magnetisation curve of a ‘‘single Tb ion’’ Since such a satisfactory fitting was not found, this estimate, again, must be regarded as a qualitative result only Moreover, the value of (nRR ỵ n2RT wT ) is decreased too, with the present choice of parameter values from n2RT wT E8 T f.u./mB down to T f.u./mB, thereby affecting the estimates given above, but still not leading to unacceptable values Further, more detailed consideration of the influence of various assumptions (e.g the nature of the ‘‘wings’’ of the hysteresis, the occurrence of a sharp MMT, the single-ion treatment of the Tb moment) is necessary for a final conclusion Concluding remarks 0 20 40 60 BTb [T] 80 100 Fig The magnetic moment of the R-subsystem (per Tb atom) of Tb1ÀxYx(Co0.85Si0.15)2 derived for nRT ¼ À38 T f.u./ mB and nRR ¼ from the experimental data shown in Fig The magnetisation of the (Co,Si) T-subsystem is obtained by interpolation of the data shown in Fig W: x ¼ 0; up; X: x ¼ 0; down; B: x ¼ 0:2; up; E: x ¼ 0:2; down; &: x ¼ 0:4; up; ’: x ¼ 0:4; down; +: x ¼ 0:6; up;  : x ¼ 0:8; up Solid line: Brillouin curve for free Tb3+ ions, at 4.2 K We have shown how to combine results for different concentrations x in order to construct, if possible, eventually a unique magnetisation curve for a ‘‘single’’ Tb moment: mTb as a function of the effective field BTb : In the present case, a perfect fitting was not found Nevertheless, in view of the qualitative nature of the present analysis, we feel to have demonstrated the possibility that the observed anomalies at moderate fields are caused by instability in the Tb subsystem 478 P.E Brommer, N.H Duc / Journal of Magnetism and Magnetic Materials 262 (2003) 472–478 The obtained negative value of nRR may be puzzling, because one usually adopts a positive value for this parameter in the Laves-phase RT compounds It may be connected to the relatively high Si content in the (Co,Si) sublattice, although we cannot exclude the possibility that it is merely an artefact of our analysis The apparent deviation of the results for x ¼ 0:8 may be due to the fact that the analysis is based on an extrapolation of the magnetisation curve of the T-subsystem (i.e adding the point corresponding to B ¼ 10 T with mTb ¼ 8:4 mB) In fact, we find that reasonable fitting results can be obtained by either assuming relatively large Co moments here (as in the present analysis, see Fig 5), or just relatively low values and a sharp increase at about 50 T (not shown) In other words, we cannot exclude the occurrence of a MMT from a ‘‘low-spin’’ to a ‘‘highspin’’ state in the (Co,Si) subsystem for this Si concentration Moreover, the vertical slope of the curves for x ¼ 0:2; 0.4 and 0.6 in Fig 7, would indicate a sharp transition in the Tb subsystem Although this phenomenon may be an artefact of the analysis (related to the adopted values of the Co magnetic moment in low effective fields), the anomalies observed at low fields would occur just in the neighbourhood of such a transition, pointing to an alternative explanation Further analysis is necessary to answer this question Acknowledgements We would like to acknowledge the support by the State Program for Natural Scientific Researches of Vietnam, within project 420.301 References [1] N.H Duc, T Goto, in: K.A Gschneidner Jr., L Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol 26, North-Holland, Amsterdam, 1999, p 338 [2] N.H Duc, P.E Brommer, in: K.H.J Buschow (Ed.), Handbook of Magnetic Materials, Vol 12, North-Holland, Amsterdam, 1999, p 259 (Chapter 3) [3] P.E Brommer, I.S Dubenko, J.J.M Franse, F Kayzel, N.P Kolmakova, R.Z Levitin, A.S Markosyan, A.Yu Sokolov, Physica A 189 (1993) 253 [4] A Kowalczyk, J Baszynski, A Szajek, J Kovac, I Skorvanek, J Magn Magn Mater 152 (1996) L279 [5] S Khmelevsky, P Mohn, J Phys.: Condens Matter 12 (2000) 9453 [6] N.H Duc, T.D Hien, P.E Brommer, J.J.M Franse, J Magn Magn Mater 104–107 (1992) 1252 [7] N.H Duc, T.K Oanh, J Phys.: Condens Matter (1997) 1585 [8] P.E Brommer, I.S Dubenko, J.J.M Franse, R.Z Levitin, A.S Markosyan, R.J Radwan˜ski, V.V Snegirev, A.Yu Sokolov, Physica B 183 (1993) 363 [9] J.J.M Franse, T.D Hien, N.H.K Ngan, N.H Duc, J Magn Magn Mater 39 (1983) 275 [10] R Kuentzler, A Tari, J Magn Magn Mater 61 (1986) 29 [11] J Voiron, Thesis, Grenoble, 1973 [12] N.H Duc, private communication [13] D Michels, J Timlin, T Mihalisin, J Appl Phys 67 (1990) 5289  ... magnetisation curves of Tb0.8Y0.2(Co0.85Si0.15)2 compounds Data obtained at increasing temperature in a field of 30 mT compounds in an applied magnetic field of 0.2 T Typical ZFC and FC magnetisation curves... leads to a series of compounds with invariable cell parameter, and the observed modification of the magnetic properties was ascribed to 3d–p hybridisation effects [7] In their study of field-induced... detailed consideration of the influence of various assumptions (e.g the nature of the ‘‘wings’’ of the hysteresis, the occurrence of a sharp MMT, the single-ion treatment of the Tb moment) is necessary