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Changes of the magnetic interactions in TlCo2Se2 upon metal substitution
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 303 (2006) 204–213 www.elsevier.com/locate/jmmm
Changes of the magnetic interactions in TlCo2Se2 upon metal substitution Sabina Ronnetega,, Marck-Willem Lumeyb, Richard Dronskowskib, Rolf Bergera a
Department of Materials Chemistry, Uppsala University, Box 538, SE-751 21 Uppsala, Sweden Institut fu¨r Anorganische Chemie, Rheinisch-Westfa¨lische Technische Hochschule, Landoltweg 1, D-52056, Aachen, Germany
b
Received 4 July 2005; received in revised form 23 September 2005 Available online 28 November 2005
Abstract Various solid solutions TlCo2xMexSe2 (Me ¼ Fe, Ni and Cu) have been investigated by neutron powder diffraction, supplemented by magnetometry. The incommensurate spin-helix running along the c-axis in tetragonal TlCo2Se2 prevails for low concentrations of copper and iron but changes pitch. In the copper case, only cobalt carries a magnetic moment. On nickel substitution, however, collinear antiferromagnetic coupling between the ferromagnetic layers occurs. The magnetic moment distribution between the two transition metals in the solid solution TlCo2xNixSe2 was tentatively probed with first principle calculations on fictive ordered TlCoNiSe2, modelled by two types of superstructures. Also the ternary mother compounds, Pauli paramagnetic TlNi2Se2 and antiferromagnetic TlCo2Se2, were investigated with the same LMTO method. r 2005 Elsevier B.V. All rights reserved. Keywords: Layered magnetic structure; Antiferromagnetism; ThCr2Si2 type; Incommensurate helix; TlCo2Se2
1. Introduction The incommensurate magnetic helix structure of antiferromagnetic TlCo2Se2 [1–3] was very unexpected and it is to our knowledge the only non-collinear magnetic structure found for cobalt. TlCo2Se2 belongs to the tetragonal ThCr2Si2 structure type (space group I4/mmm) [4]. The cobalt atoms form sheets that are separated by the large non-magnetic thallium and selenium atoms, which results in an enhanced two-dimensional layered structure. The intralayer coupling between the cobalt atoms is ferromagnetic, with the moments perpendicular to the c-axis. In contrast, the interlayer coupling is antiferromagnetic of a kind that creates a spin helix running along the c-axis. The closest distance between the cobalt atoms within the sheets (2.7 A˚) is quite near to that in pure cobalt metal (2.51 A˚). Now, what happens to the magnetic structure of TlCo2Se2, if these layers are altered by gradually introducing another transition metal? And how does the change in electron density affect the interlayer magnetic interactions Corresponding author. Tel.: +46184713764; fax: +4618513548.
E-mail address: [email protected] (S. Ronneteg). 0304-8853/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2005.11.010
and thereby also the helix? These are questions we try to answer with this study on TlCo2xMexSe2 (Me ¼ Fe, Ni and Cu). The magnetic properties have earlier been investigated globally for Ni [5] and Cu [1] substitution. The ternary compound TlNi2Se2 is Pauli paramagnetic [5]. In this case, substitution for cobalt results in adding delectrons to the 3d band operative in the magnetic layers. Nickel was found to enhance the antiferromagnetic coupling and the transition temperature reaches a maximum for x ¼ 0:5 at 142 K [5]. The possibility of a magnetic moment on nickel in TlCo2xNixSe2 is unclear and the problem was discussed in an earlier study by Newmark et al. [5]. Three ideas were addressed in their discussion: 1. Ni substitution leads to adding electrons to the 3d and (by hybridization) the valence band and therefore can influence the strength of the RKKY (Rudermann, Kittel, Kasuya, Yosida) interactions. 2. The nickel atom retains a magnetic moment while at the same time the magnetic moment on cobalt may change. 3. An increased 3d localization occurs, due to the substitution, and this enhances the cobalt magnetic moment.
ARTICLE IN PRESS S. Ronneteg et al. / Journal of Magnetism and Magnetic Materials 303 (2006) 204–213
First principles calculations (LMTO, Linear Muffin-Tin Orbital) have earlier been performed on ferromagnetic TlCo2S2 [6], but to calculate the helical structure of TlCo2Se2 is more difficult [3]. A more precise method was used in this investigation (APW+lo, Augmented planewave), but the interlayer interaction is harder to simulate. The ferromagnetic driving force in the layers is shown in both methods. Due to the uncertainty whether Ni exhibits a magnetic moment, a study of the electronic structure in TlCoNiSe2 and its mother compounds (TlCo2Se2 and TlNi2Se2) is presented here in the form of first principles calculations. The LMTO approach was used because the arrangement of the magnetic moments in the layers is of interest more than the interlayer interaction. Substitution with iron would also lead to a change in the electron density of the magnetic layers. Similar ternary iron phases exist, but only with vacancies, TlFe2xSe2. Some phases appear with ordering such that still the ThCr2Si2 subcell can be recognized [7]. Around x 0:4 antiferromagnetic ordering occurs (TN450 K) in a tetragonal pffiffiffi supercell with a0 ¼ a 5. TlCu2Se2 is Pauli paramagnetic [8] and has earlier been studied with first principles calculations [9,10]. Copper is proven to always be diamagnetic (3d10) together with the heavy chalcogens. Earlier studies of TlCo2xCuxSe2 showed the presence of orthorhombic distortion for 0.4pxo1.3 [1]—similar to that later found for KCu2Se2 [11]—and also incommensurate Co/Cu atomic ordering [12]. The Ne´el temperature decreases on copper substitution, the cobalt magnetic moments becoming diluted. In this article we present a study of TlCo2xMexSe2 (Me ¼ Fe, Ni and Cu) with neutron powder diffraction to investigate how the magnetic structure is affected by metal exchange. Moreover, the electronic structure was probed by calculation for TlCo2Se2, TlNi2Se2 and ordered TlCoNiSe2. 2. Methods 2.1. Synthesis Eight samples were synthesized: TlCo2xNixSe2 with x ¼ 0:25, 0.5 and 1.0; TlCo2xFexSe2 with x ¼ 0:2, 0.5 and 1.0, and TlCo2xCuxSe2 with x ¼ 0:1 and 0.2. All transition metals were etched in hydrochloric acid before use to remove superficial oxides. The materials purity was: Tl 99.999%; Se 99.999%; Co 99.8% (powder), 99.998% (ingots); Ni 99.995%; Fe 99.98% and Cu 99.98%. The quaternary nickel samples were synthesized directly from the elements and heat-treated in an evacuated pyrextube at 480 1C, first for 10 days and then reground and pressed into pellets. The pellets were sealed in a new pyrextube and heated at the same temperature for another week. For the manufacture of TlCo2xFexSe2, metal ingots of cobalt and iron were melted together using arc melting (no weight loss). This whole ingot was then put in a silica-tube together with TlSe and Se-shots. The tube was evacuated,
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sealed and heat-treated at 700 1C for 2–3 weeks. The sample was homogenized and kept at 700 1C for a week. TlCu2Se2 and TlCo2Se2 were first synthesized by mixing TlSe, Se-shots and Cu sheet-metal or Co-powder in an evacuated silica-tube heated at 400 1C and 600 1C, respectively. The ternary mother phases were then mixed together to form TlCo2xCuxSe2, kept at 600 1C for a week. 2.2. Diffraction All the samples were characterised by X-ray diffraction using a Guinier-Ha¨gg camera (CuKa1) and germanium ˚ [13] or silicon ða ¼ 5:431028 AÞ ˚ [14] ða ¼ 5:6570805 AÞ as internal standard. The powders were also studied with neutron diffraction at Studsvik, Sweden (NPD, ˚ in the temperature range 10–300 K. The l ¼ 1:471 A) refinements of the diffraction data were made with the Rietveld method using the FullProf program [15]. The parameters from the diffractograms measured over the magnetic transition temperature were refined describing the background by a polynomial expression. These refinements were made in the 2y interval 9.0–52.01. For data from below the transition temperature the refinements were made in the interval 2.0–52.01 and with manual background correction. The magnetic structures were refined with a magnetic moment only on the cobalt atom. In the nickel case this was done because of the uncertainty whether nickel really possesses a magnetic moment or not. Copper is diamagnetic and therefore does not exhibit a magnetic moment. Finally iron is only refined with very low concentration and it is impossible to know the magnetic moment on iron. 2.3. Magnetometry Only the three nickel-samples were investigated with a SQUID magnetometer (Quantum Design, MPMSXL). The applied field was fixed to 100 G for TlCo1.5Ni0.5Se2 and to 200 G for TlCo1.75Ni0.25Se2 and TlCoNiSe2. The temperature was scanned in the interval 10–300 K. Both zero-field cooled (ZFC) and field cooled (FC) procedures were used for all the three samples. Several attempts were made to measure the magnetic properties also of the iron solutions, both powder and crystals, but small impurities (probably Fe3O4) made the interpretation of the data impossible. SQUID data for TlCo2xCuxSe2 were already published by Broddefalk et al. [16]. 2.4. Calculation The program used for the calculations of the electronic structure was TB-LMTO 4.7 [17]. The approach for the calculations was the same as for the calculations on TlCo2S2 [6]. The exchange and correlation effects were treated in the generalized gradient approximation (GGA) as parameterized by Perdew and Wang [18]. The bonding character was studied with the Crystal Orbital Hamilton
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Population (COHP) [19] weighting approach. Note that the bonding state has a negative sign in COHP (opposite to that of COOP). One way of probing the stabilization of a magnetic structure is to look at the partial density-of-states (DOS) for the metal–metal bonding at the Fermi-level in the non-spin-polarized COHP. A high value of an antibonding character here can be a sign for a possibility to lower the total energy by spin-polarization [20] and thereby stabilize a ferromagnetic structure. Another analysis tool is ICOHP, the integral of the COHP, which serves as a measure of the strength of a chemical bond. Calculations were performed on TlCo2Se2, TlNi2Se2 and TlCoNiSe2. The calculations for non-magnetic and ferromagnetic situations in the first two compounds were made using the unit cell of space group I4/mmm. For the calculations of antiferromagnetic interactions between the layers in TlCo2Se2, space group P4mm was chosen [6]. Since random solid solutions such as TlCo2xNixSe2 cannot be treated easily in calculations, ordered situations must be chosen. No evidence for a superstructure was found in the diffraction data; this approach is only an approximation to make the calculations possible at all. The smallest system to be handled is then found for a 50% substitution. The first approximation was that every Co atom only had close Ni neighbours in the sheet and vice versa. To allow for antiferromagnetic interactions between the cobalt atoms within the same layer, the unit cell had to be doubled and lowered in symmetry. The space group then is Pmm2 (see atom positions in Table 1). The structure is illustrated in Fig. 1. The z ¼ 14 layer is exactly the same as for z ¼ 34. Non-magnetic, ferromagnetic as well as
Fig. 1. The superstructure described in Pmm2 used for one model calculation on TlCoNiSe2. All Ni atoms are surrounded by Co in the sheet, and vice versa. Both sheets in the unit cell are exactly the same.
Table 1 The atom positions for the TlCoNiSe2 super cell in space group Pmm2 and I 4¯ (cf. Figs. 1 and 2) Atom
Tl
I 4¯
Pmm2 Position
x; y; z
Position
x; y; z
1a 1b 2h
0, 0, 0
2d
1 2,
0,
3 4
2b
0, 0,
1 2
2a
0, 0, 0
4f
1 2,
0, 12, 0 1 3 1 2, 4, 2
Co
1c 1c 1d 1d
1 2, 1 2, 1 2, 1 2,
0, 14 0, 34 1 3 2, 4 1 1 2, 4
Ni
2g 2g
0, 34, 0, 34,
Se
1a 1a 1b 1b 2h 2h
0, 0, 0.35 0, 0, 0.65 0, 12, 0.35 0, 12, 0.65 1 1 2, 4, 0.85 1 3 2, 4, 0.15
1 4 3 4
0, 0.4
Fig. 2. The superstructure model described in I 4¯ used for calculations on TlCoNiSe2. All Ni atoms are also here surrounded by Co in the sheet. The difference compared to Fig. 1 is that in adjacent sheets Ni is now above Co and vice versa.
ARTICLE IN PRESS S. Ronneteg et al. / Journal of Magnetism and Magnetic Materials 303 (2006) 204–213
o P-0
o
o
P-A
o I-0
o
o
o
o
o
o
o
o
+
+
P-FCo +
P-FNi
o
o
+
+
I-F
+
o
o
+
+
+
+
+
+
o
o
o
+
+
o
o -
+ o
I-A
+
207
+
+
Fig. 4. Data from SQUID measurements on three compositions of TlCo2xNixSe2, recorded after two modes of cooling (fc, zfc). For x ¼ 1, a background signal of 25 106 emu/gG was subtracted from the data before the inverse susceptibility was calculated.
o
Fig. 3. The transition metal layers in the two models Pmm2 (left) and I 4¯ (right). o ¼ no net magnetic moment, 7 refer to opposite spin directions (spin polarization), all being initial conditions in the calculations. White and grey circles denote the two kinds of transition metal (cf. Figs. 1 and 2), Co and Ni.
antiferromagnetic calculations were performed using this model. Another model used implied the space group I 4¯ (see atom positions in Table 1) with the same cell size as the original unit cell (see Fig. 2). To account for the symmetry the origin is moved to ð12 0 14Þ and this allows two separate positions for the transition metals, cobalt and nickel. In this model only ferromagnetic calculations within the sheet can be made for any one transition metal. The cell parameters used in all calculations were based on the (sub)cell dimensions as taken from Newmark et al. [5]. The z-parameter of selenium was fixed at 0.35. All the starting positions for the calculations for TlCoNiSe2 are illustrated in Fig. 3. 3. Results 3.1. Magnetometry TlCo2xNixSe2 (x ¼ 0:25, 0.5 and 1.0) show an antiferromagnetic behaviour with a Ne´el temperature of 140, 140 and 95 K respectively. The susceptibility curves are illustrated in Fig. 4. All curves follow the Curie–Weiss law in the paramagnetic region. For x ¼ 1:0 a constant background magnetization was subtracted to obtain the straight line of the inverse. The effective magnetic moments
per formula unit were: 2.9 mB, 3.3 mB and 1.3 mB, respectively, and the corresponding y values obtained were 36(8) K, 6(15) K and 69(13) K. 3.2. Neutron powder diffraction For all the solid solutions, the only change observed in neutron powder diffraction on magnetic ordering was the appearance of very weak low-angle peaks. These peaks are drawn for all compositions in Fig. 5, where their global relation to the main is exemplified. 3.2.1. TlCo2xNixSe2 The results from the neutron powder refinements for TlCo1.75Ni0.25Se2, TlCo1.5Ni0.5Se2 and TlCoNiSe2 are shown in Table 2. An example of the fit is illustrated in Fig. 6. All the cell parameters are in good agreement with earlier published results of Newmark et al. [5]. Both the aand the c-axis decrease on lowering the temperature, but the a parameter flattens out just below the transition temperature. The same observation was made for the system TlCo2Se2xSx [1,2]. The interesting result is that the helix is destroyed for the compositions of Ni substitution investigated here. The crucial difference with the situation for x ¼ 0 was not previously realized [5] and neither was it anticipated in our study when choosing the compositions for the syntheses. The magnetic structure is collinear antiferromagnetic between the ferromagnetic layers. Consequently, the bct centring extinction condition is broken: the (0 0 1) reflection carries intensity and no satellites are present. The spins are still confined to the ab-plane, but powder diffraction cannot give information on the specific orientation further. The magnetic moment on the cobalt
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S. Ronneteg et al. / Journal of Magnetism and Magnetic Materials 303 (2006) 204–213 Table 2 Results from neutron powder diffraction of TlCo2xNixSe2 at different temperatures. Only cobalt was allowed to carry a magnetic moment TlCo2xNixSe2 x ¼ 0:0 [1] Temp (K) a (A˚) c (A˚) zSe Rcryst (%) mCo (mB) Rmag (%)
295 3.8443(1) 13.5723(7) 0.3525(1) 4.74 — —
70 3.8317(2) 13.4513(12) 0.3537(1) 2.34 0.32(2) 32.1
40 3.8314(2) 13.4401(9) 0.3537(1) 2.10 0.40(2) 16.5
10 3.8316(2) 13.4254(8) 0.3537(1) 1.76 0.46(2) 16.6
100 3.8329(1) 13.5285(4) 0.3538(2) 3.34 0.54(3) 8.39
50 3.8307(2) 13.5079(7) 0.3535(2) 3.76 0.69(2) 9.86
10 3.8300(2) 13.4973(6) 0.3535(2) 3.14 0.73(2) 12.70
160 3.8338(2) 13.5602(7) 0.3538(2) 3.87 — —
100 3.8286(2) 13.5532(6) 0.3545(2) 3.04 0.75(3) 9.28
10 3.8248(2) 13.5386(6) 0.3544(2) 2.60 0.92(2) 10.18
50 3.8269(2) 13.5281(7) 0.3548(2) 5.18 0.88(5) 16.9
10 3.8237(2) 13.5311(7) 0.3550(2) 5.08 1.01(5) 13.9
x ¼ 0:25 Temp (K) a (A˚) c (A˚) zSe Rcryst (%) mCo (mB) Rmag (%)
295 3.8449(2) 13.6020(8) 0.3529(3) 4.28 — — x ¼ 0:5
Temp (K) a (A˚) c (A˚) zSe Rcryst (%) mCo (mB) Rmag (%)
295 3.8436(2) 13.6083(7) 0.3535(2) 4.49 — — x ¼ 1:0
Temp (K) a (A˚) c (A˚) zSe Rcryst (%) mCo (mB) Rmag (%)
Fig. 5. The low-angle part of the neutron powder diffractograms recorded at 10 K for the different solid solutions TlCo2xMexSe2. The notation (0 0 1)7 indicates the satellite reflections (0 0 17qz).
atom is increasing with substitution by nickel (in the approximation that only Co exhibits a magnetic moment). 3.2.2. TlCo2xMxSe2 (M ¼ Fe and Cu) The neutron diffraction results are listed in Table 3. In TlCo2xFexSe2, a continuous cell volume change is observed for x ¼ 0.2, 0.5 and 1.0, well following Vegard’s rule. Analysis of the patterns showed that the helix still remains at x ¼ 0:2. However, for the other compositions no magnetic peaks are visible, neither was any extra intensity found on the nuclear peaks. For small amounts of copper in TlCo2xCuxSe2 (x ¼ 0:1 and 0.2), the tetragonal structures prevails and no
295 3.8471(2) 13.5698(8) 0.3545(3) 5.75 — —
orthorhombic distortion is seen. It seems that the substitution does not affect the kind of magnetic ordering drastically, a conclusion that is supported by the susceptibility measurements [1,16]. The diffraction patterns showed that the magnetic helix prevails in this region. Due to the very low intensities of the satellite peaks, the Rmag-values (Table 3) for the copper-phases are rather high. 3.3. Calculations 3.3.1. TlNi2Se2 The result from the non-magnetic calculation is illustrated in Fig. 7 with the DOS and the COHP over the shortest nickel-nickel bond (within the metal sheet). Spinpolarization was not energetically favourable in this structure which agrees with the Pauli paramagnetic character measured [5]. This can be rationalized by the
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quite small anti-bonding Ni–Ni interactions at the Fermi level. 3.3.2. TlCo2Se2 The calculations were performed in the same way as for ferromagnetic TlCo2S2 [6]. The differences between the ferromagnetic and the antiferromagnetic energies are quite small in line with the assumption that the short distance direct ferromagnetic coupling in the layer is by far the strongest interaction which lowers the energy. This holds for both TlCo2S2 and TlCo2Se2. Spin-polarization lowers the total energy and the density around the Fermi level decreases in the DOS-curve. The results are condensed in Table 4 and in Fig. 8a and b. 3.3.3. TlCoNiSe2 Four types of calculations were made in the superstructure Pmm2, non-magnetic (P-0), ferromagnetic coupling between cobalt atoms (P-FCo), ferromagnetic coupling between nickel atoms (P-FNi) and, finally, antiferromagnetic coupling within a layer between the cobalt atoms (P-A). In the space group I 4¯ (see Fig. 2)
Fig. 6. The results from the Rietveld refinements for TlCo1.75Ni0.25Se2 at 10 K. The fit is illustrated by the data points and full line as well as by their difference curve (bottom).
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calculations were possible with magnetic moment on both cobalt and nickel at the same time—this is the reason why this model was used, even though neutron diffraction showed that the I-centring has disappeared. Calculations were performed for both antiferromagnetic (I-A) and ferromagnetic coupling (I-F) between cobalt and nickel (cf. Fig. 3). The results from all the calculations are found in Table 5 and illustrated in Fig. 9a and b. 4. Discussion Let us start by discussing the COHP for the mother compounds in more detail: The structure of the TlNi2Se2, TlCo2Se2 and their intermediates is, except for minor differences, the same. Therefore in a first crude approximation, a rigid-band model can be considered here. Moving from TlNi2Se2 to TlCo2Se2, the total number of electrons is reduced. Therefore, the Fermi level is shifted down. This leads to the conclusion that the Fermi level of the intermediates and also TlCo2Se2 would be positioned in the metal–metal antibonding peak region and therefore possibly lead to spin polarization. On gradually substituting the cobalt atom in TlCo2Se2 by another transition metal, the magnetic structure changes. The magnetic helix prevails for small substitution ðxp0:2Þ by both iron and copper, in contrast to nickel substitution for cobalt. In that case the helix structure is obviously broken and the phase becomes ordinary antiferromagnetic. The reason for this large difference is not immediately evident. That the nickel case behaves differently is seen macroscopically in the trend regarding the c-axis parameter change on substitution (cf. Tables 2 and 3). The agreement with earlier published [5] transition temperatures for TlCo2xNixSe2 is very good, but there are large differences regarding the y-values. The background magnetization is found to increase with higher concentrations of nickel. This makes a determination of the slope of the inverse susceptibility very uncertain, with large systematic errors in both y and the effective paramagnetic moment. Newmark et al. [5] found a decreasing trend of
Table 3 Results from the neutron powder diffraction for TlCo2xMexSe2 (Me ¼ Cu and Fe) Only cobalt was allowed to carry a magnetic moment Sample
TlCo2xCuxSe2
Composition
x ¼ 0:1
Temp (K) a (A˚) c (A˚) zSe Rcryst (%) mCo (mB) qz Angle f (1) Rmag (%)
295 3.8432(4) 13.610(2) 0.3527(4) 3.61 — — — —
TlCo2xFexSe2 x ¼ 0:2 10 3.8330(1) 13.4750(6) 0.3536(3) 3.19 0.58(3) 0.376(3) 112.3(6) 23.76
295 3.8443(4) 13.621(2) 0.3526(5) 4.0 — — — —
x ¼ 0:2 10 3.8346(1) 13.5127(7) 0.3531(4) 5.02 0.32(4) 0.330(5) 120.6(9) 34.0
10 3.8344(2) 13.4788(7) 0.3540(2) 3.87 0.55(2) 0.388(2) 110.1(4) 17.46
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4
4
2
2
0
0 Energy (eV)
Energy (eV)
210
-2
-2
-4
-4
-6
-6
-8
-8 0
2
4
6
8
10
12
DOS
-1
0
1
2
-COHP
Fig. 7. The density-of states (DOS) for TlNi2Se2 and COHP for the Ni–Ni bonds in one layer. Both calculations are without allowing for spinpolarization. The black part of DOS indicates the contribution by Ni 3d. The zero level indicates the Fermi energy.
Table 4 Results from the LMTO-ASA calculations for TlCo2Se2. The values are normalised to the nonmagnetic calculation
Etot (kJ/mol) ICOHP (kJ/mol)a msat Tl (mB/atom) msat Co (mB/atom) msat Se (mB/atom) a
Ferromagnetic
Antiferromagnetic
3.8 0.16 0.1 0.92 0.06
2.3 2.3 0.00 70.79 70.06
Four identical Co–Co bonds in one sheet in the unit cell.
the y-values which even change sign, from positive to negative, at 0.25oxo0.5. However, their values suffer from non-linear relationships approximated by a Curie– Weiss line. Moreover, the background in their measurements varies considerably (but decreases with increasing nickel content), a sign that traces of another phase are present, not detected by diffraction. In a study of TlCo2Se2xSx [21], our results differed from those by Greaney et al. [22], again probably reflecting the sensitivity to synthesis conditions. These experimental factors are very difficult to control and interpret fully, and it would be preferable to use single-crystal material rather than powders. That also anisotropy is important is evident for instance from the single-crystal work on TlCo2Se2 [1] where the susceptibility peak values (near TN) differ by a factor of
more than two depending on field direction. Pronounced powder texture may thus also influence the outcome of measurements. The localization of magnetic moment (including a possible moment on nickel) and the Co/Ni ordering are factors of importance for the magnetic properties. TN increases from 95 K for x ¼ 0 in TlCo2xNixSe2 to 140 K for x ¼ 0:25 and x ¼ 0:5, and decreases again back to 95 K for x ¼ 1:0. At the same time the effective paramagnetic moment follows the same trend. The trend in ordering temperature indicates that the antiferromagnetic interactions are enhanced between the layers, as remarked by Newmark et al. [5]. The crucial question is whether there is any magnetic moment on the nickel atom in the solid solution, as there is none in the ternary nickel compound (or at xX1:75 in the solutions [5]). The fact that there is an enhancement of the effective paramagnetic moment on increasing the nickel content up to x ¼ 0:5 is another indicator that nickel does contribute—either directly or indirectly through enforcing localization. However, it is impossible to distinguish which transition metal possesses the magnetic moment in neutron powder refinements. To simplify the evaluation a magnetic moment was allowed only on the cobalt atoms. This resulted in an increase of the moment per cobalt atom on increasing the nickel content (Table 2), thus in line with the evolution of the effective paramagnetic moment values. This trend is not easily
ARTICLE IN PRESS S. Ronneteg et al. / Journal of Magnetism and Magnetic Materials 303 (2006) 204–213
α
4
211
β
Energy (eV)
2 0 -2
-4
-6
-8
0
2
(a)
4
6 8 DOS
10
4
2
0 2 DOS
4
0
2
4
6 8 DOS
10
minority majority
4
Energy (eV)
2
0
-2
-4
-6
-8 -1 (b)
0 1 -COHP
2
-1
0 1 -COHP
2
-1
0 1 -COHP
2
Fig. 8. (a) Density-of-states (DOS) with Co 3d projections in black for the non-magnetic, ferromagnetic and antiferromagnetic structure of TlCo2Se2. In the ferromagnetic picture the majority (a) and minority (b) are plotted separately. The energy is shifted so that the Fermi level lies at 0 eV. (b) Crystal orbital Hamilton population (COHP) of the Co–Co bond at 2.71 A˚ in TlCo2Se2 for non-magnetic, ferromagnetic and antiferromagnetic structure, respectively. Note that the –COHP is drawn, in correspondence with the conclusions from sign of COOP representations.
Table 5 Results from the calculations on TlCoNiSe2 Pmm2 and I 4¯ I 4¯
Pmm2 (see notations from Fig. 3)
P-FCo
P-FNi
P-A
I-F and I-A
Etot (kJ/mol) msat Tl (mB) msat Co (mB) msat Ni (mB) msat Se (mB)
4.2 0.13 1.59 0.58 0.15
4.3 0.13 1.59 0.58 0.15
0.8 0.02 71.38 0.0 70.11
4.4 0.13 1.60 0.58 0.15
understood. Some consistency concerning the increased total moment found from the neutron data would be obtained if nickel is allowed to carry a moment higher than
that of cobalt in the range xo1, for instance mCo ¼ 0:6 mB and mNi ¼ 0:9 mB . This assumption carries no theoretical support. The values of Table 2 may be translated into an average metal moment (Ni and Co both contributing) that increases slightly—from 0.64 mB to 0.69 mB—when changing the nickel content from x ¼ 0:25 to 0:5, but the trend collapses for x ¼ 1 (with the average of 0.50 mB). In fortunate cases, the cell parameter evolution upon dissolution can give a clue to the electron transfer, e.g. when substituting iron or manganese for copper in TlCu2Se2 [23]. There, in the same structure type as presented here, discontinuities of the slope of the c-axis vs. composition relationship have proven to be strong indicators of sudden changes in the band structure. A similar effect, probably reflecting the change in magnetic or structural conditions
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212
α
4
β
Energy (eV)
2 0 -2 -4 -6 -8 0
10
20 30 DOS
(a)
40
50
20
10
α
4
0 10 DOS
20
0
10
20 30 DOS
40
β
Energy (eV)
2 0 -2 -4 -6 -8 0 (b)
2
4
6 8 10 12 DOS
6 4 2 0 2 4 6 DOS
0
2
4
6 8 10 12 DOS
Fig. 9. (a) Density-of-states (DOS) for TlCoNiSe2 in the Pmm2 model (cf. Fig. 1). Designations as in Fig 8a. (b) The density-of-states (DOS) curve for TlCoNiSe2 in the I 4¯ model (cf. Fig. 2). Designations as in Fig. 8a. Note the similarity between the non-magnetic and ferromagnetic calculations of Fig. 9a.
was noted for TlCo2xCuxSe2 [1]. No clear indications of the same kind were found for TlCo2xNixSe2. Maybe fortuitous, the c-axis is smaller for x ¼ 2 than for x ¼ 0 in the nickel substitution case while larger for either iron and copper into TlCo2Se2, the latter two solutions showing the retention of the x ¼ 0 helical structure (for xp0:2). We cannot say whether these observations have a proper bearing on the difference in magnetic structure, and it is in retrospect very unfortunate that we cannot present data of TlCo2xNixSe2 for the range 0o xo0.25 where there is a definite change of magnetic structure, also reflected in the ordering temperature. The electronic structure was studied for TlCoNiSe2 in an attempt to answer the question about the possible Ni moment. LMTO calculations from four starting points (P-FCo, P-FNi, I-F and I-A of Fig. 3) showed an energy minimum around 4 kJ/mol for ferromagnetic coupling between nickel and cobalt atoms in the layer (Table 5).
There is a magnetic moment on both cobalt and nickel with a three times larger moment on cobalt. The antiferromagnetic calculation (P-A) resulted in less lowering of the energy and no magnetic moment on nickel. Unfortunately, it is not possible to distinguish which model best describes the true structure. It may be noted that the models with ferromagnetic interactions within the metal sheets lead to an increased cobalt moment as well as a moment on nickel, values that are not at all in line with the findings from neutron diffraction on the x ¼ 1 solution. We emphasize that the superstructure models are only crude approximations of the true situation, where the metal atoms most probably are disordered on the crystallographic site. Moreover, the calculations may not in all cases succeed in the modelling. As regards the moment values, as seen from Table 5, there is a hefty over-estimation of the spin moment of cobalt (experimentally 0.6 mB from a renewed neutron diffraction determination [24]).
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The DOS-curves of Figs. 7–9 may be compared on a qualitative basis. The two models of ordered TlCoNiSe2 of 9a and 9b give for the non-magnetic case, as expected, almost the same DOS which is found to be closely related to those of TlCo2Se2 and TlNi2Se2 on a rigid-band basis. One may speculate that, on nickel substitution, the addition of some electrons would increase the cobalt moment localization. However, as commented previously, the methods of calculation used here are not capable of taking care of long-range effects, and the DOS-curves of the magnetic states suffer from this inaccuracy.
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separately, while at low temperature tuning synchrotron radiation to respective transition element. Acknowledgements Financial support from the Swedish Foundation for Strategic Research (SSF/FRAM) and A˚ngpannefo¨reningen’s Foundation for Research and Development is thankfully acknowledged. We are also very grateful to Mr. Ha˚kan Rundlo¨f at the Studsvik nuclear reactor facility for recording the neutron powder diffraction data of all samples.
5. Conclusions The electronic calculations have been shown valuable in at least explaining the trends in global magnetic behaviour in the series TlCo2Se2–TlNi2Se2–TlCu2Se2, where we in the DOS find a strong support for a rigid-band view. Especially helpful is the COHP representation as a strong indicator for possible spin-polarization. Even though the level of sophistication of the LMTO method may be low to describe complicated spin structures, it mostly yields interesting information that correlates well with experiment and associates closely with the chemical expectations. We have here presented the experimental outcome of transition metal substitution in TlCo2Se2. Surprisingly, iron and copper that have, respectively, less and more electrons than cobalt yield the same kind of magnetic ordering: the incommensurate helix of the mother compound remains (for limited substitution). However, there is a drastic lowering of moment in the copper case since copper is diamagnetic. In both cases, a somewhat higher degree of substitution removes the moment and the phases seem to become Pauli paramagnetic. Although nickel does not carry any moment in TlNi2Se2, there are indications (also noted previously [5]) that the substitution for cobalt effectuates an enhancement of the total moment as well as the magnitude of the antiferromagnetic interactions (from TN), the latter resulting in a collinear arrangement at much higher ordering temperatures and with another structure than for cobalt alone. Neither experimentally nor by calculations have we found a rigid basis for a trustworthy analysis of the Ni moment in the solid solutions TlCo2xNixSe2 but face bewilderment. One possible way to solve the dilemma, but experimentally extremely demanding, would be to apply X-ray magnetic linear dichroism (XMLD) on single crystals of the solid solutions to determine the spin and orbital moments
References [1] R. Berger, M. Fritzsche, A. Broddefalk, P. Nordblad, B. Malaman, J. Alloys Compds. 343 (2002) 186. [2] S. Ronneteg, S. Felton, P. Nordblad, R. Berger, J. Magn. Magn. Mater. 299 (2005) 53. [3] R. Lizarraga, S. Ronneteg, R. Berger, A. Bergman, P. Mohn, O. Eriksson, L. Nordstro¨m, Phys. Rev. B 70 (2004) 024407. [4] Z. Ban, M. Sikirica, Acta Cryst. 18 (1965) 594. [5] A.R. Newmark, G. Huan, M. Greenblatt, M. Croft, Solid State Commun. 71 (1989) 1025. [6] S. Ronneteg, M.-W. Lumey, R. Dronskowski, U. Gelius, R. Berger, S. Felton, P. Nordblad, J. Solid State Chem. 177 (2004) 2977. [7] L. Ha¨ggstro¨m, A. Seidel, R. Berger, J. Magn. Magn. Mater. 98 (1991) 37. [8] R. Berger, C.F. van Bruggen, J. Less-Common Met. 99 (1984) 113. [9] M. Shirai, Synth. Metals 71 (1995) 1857. [10] G.V. Vajenine, R. Hoffmann, Inorg. Chem. 35 (1996) 451. [11] O. Tiedje, E.E. Krasovskii, W. Schattke, P. Stoll, C. Nather, W. Bensch, Phys. Rev. B 67 (2003) 134105. [12] L. Nore´n, R.L. Withers, R. Berger, J. Solid State Chem. 151 (2000) 260. [13] J.F.C. Baker, M. Hart, Acta Crystallogr. A 31 (1975) 364. [14] M. Deutsch, M. Hart, Phys. Rev. B 26 (1982) 5558. [15] J. Rodriguez-Carvajal, Physica B 192 (1993) 55. [16] A. Broddefalk, P. Nordblad, R. Berger, Physica B 284–288 (2000) 1317. [17] G. Krier, O. Jepsen, A. Burkhardt, O.K. Andersen, The TB-LMTOASA program, version 4.7, Stuttgart, Germany. [18] J.P. Perdew, in: A. Ziesch, A. Eschrig (Eds.), Electronic Structure of Solids, Akademie Verlag, Berlin, 1991 p. 11. [19] R. Dronskowski, P.E. Blo¨chl, J. Phys. Chem. 97 (1993) 8617. [20] G.A. Landrum, R. Dronskowski, Angew. Chem. Int. Ed. 39 (2000) 1560. [21] S. Ronneteg, R. Berger, R.Z. Levitin, E.A. Popova, R.M. Scherbov, A.N. Vasiliev, J. Magn. Magn. Mater. 281 (2004) 388. [22] M. Greaney, G. Huan, K.V. Ramanujachary, Z. Teweldemedhin, M. Greenblatt, Solid State Commun. 79 (1991) 803. [23] R. Berger, C.F. van Bruggen, J. Less-Common Metals 113 (1985) 291. [24] S.Ronneteg, R.Berger, G.Andre´. to be published.
Journal of Magnetism and Magnetic Materials 303 (2006) 204–213 www.elsevier.com/locate/jmmm
Changes of the magnetic interactions in TlCo2Se2 upon metal substitution Sabina Ronnetega,, Marck-Willem Lumeyb, Richard Dronskowskib, Rolf Bergera a
Department of Materials Chemistry, Uppsala University, Box 538, SE-751 21 Uppsala, Sweden Institut fu¨r Anorganische Chemie, Rheinisch-Westfa¨lische Technische Hochschule, Landoltweg 1, D-52056, Aachen, Germany
b
Received 4 July 2005; received in revised form 23 September 2005 Available online 28 November 2005
Abstract Various solid solutions TlCo2xMexSe2 (Me ¼ Fe, Ni and Cu) have been investigated by neutron powder diffraction, supplemented by magnetometry. The incommensurate spin-helix running along the c-axis in tetragonal TlCo2Se2 prevails for low concentrations of copper and iron but changes pitch. In the copper case, only cobalt carries a magnetic moment. On nickel substitution, however, collinear antiferromagnetic coupling between the ferromagnetic layers occurs. The magnetic moment distribution between the two transition metals in the solid solution TlCo2xNixSe2 was tentatively probed with first principle calculations on fictive ordered TlCoNiSe2, modelled by two types of superstructures. Also the ternary mother compounds, Pauli paramagnetic TlNi2Se2 and antiferromagnetic TlCo2Se2, were investigated with the same LMTO method. r 2005 Elsevier B.V. All rights reserved. Keywords: Layered magnetic structure; Antiferromagnetism; ThCr2Si2 type; Incommensurate helix; TlCo2Se2
1. Introduction The incommensurate magnetic helix structure of antiferromagnetic TlCo2Se2 [1–3] was very unexpected and it is to our knowledge the only non-collinear magnetic structure found for cobalt. TlCo2Se2 belongs to the tetragonal ThCr2Si2 structure type (space group I4/mmm) [4]. The cobalt atoms form sheets that are separated by the large non-magnetic thallium and selenium atoms, which results in an enhanced two-dimensional layered structure. The intralayer coupling between the cobalt atoms is ferromagnetic, with the moments perpendicular to the c-axis. In contrast, the interlayer coupling is antiferromagnetic of a kind that creates a spin helix running along the c-axis. The closest distance between the cobalt atoms within the sheets (2.7 A˚) is quite near to that in pure cobalt metal (2.51 A˚). Now, what happens to the magnetic structure of TlCo2Se2, if these layers are altered by gradually introducing another transition metal? And how does the change in electron density affect the interlayer magnetic interactions Corresponding author. Tel.: +46184713764; fax: +4618513548.
E-mail address: [email protected] (S. Ronneteg). 0304-8853/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2005.11.010
and thereby also the helix? These are questions we try to answer with this study on TlCo2xMexSe2 (Me ¼ Fe, Ni and Cu). The magnetic properties have earlier been investigated globally for Ni [5] and Cu [1] substitution. The ternary compound TlNi2Se2 is Pauli paramagnetic [5]. In this case, substitution for cobalt results in adding delectrons to the 3d band operative in the magnetic layers. Nickel was found to enhance the antiferromagnetic coupling and the transition temperature reaches a maximum for x ¼ 0:5 at 142 K [5]. The possibility of a magnetic moment on nickel in TlCo2xNixSe2 is unclear and the problem was discussed in an earlier study by Newmark et al. [5]. Three ideas were addressed in their discussion: 1. Ni substitution leads to adding electrons to the 3d and (by hybridization) the valence band and therefore can influence the strength of the RKKY (Rudermann, Kittel, Kasuya, Yosida) interactions. 2. The nickel atom retains a magnetic moment while at the same time the magnetic moment on cobalt may change. 3. An increased 3d localization occurs, due to the substitution, and this enhances the cobalt magnetic moment.
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First principles calculations (LMTO, Linear Muffin-Tin Orbital) have earlier been performed on ferromagnetic TlCo2S2 [6], but to calculate the helical structure of TlCo2Se2 is more difficult [3]. A more precise method was used in this investigation (APW+lo, Augmented planewave), but the interlayer interaction is harder to simulate. The ferromagnetic driving force in the layers is shown in both methods. Due to the uncertainty whether Ni exhibits a magnetic moment, a study of the electronic structure in TlCoNiSe2 and its mother compounds (TlCo2Se2 and TlNi2Se2) is presented here in the form of first principles calculations. The LMTO approach was used because the arrangement of the magnetic moments in the layers is of interest more than the interlayer interaction. Substitution with iron would also lead to a change in the electron density of the magnetic layers. Similar ternary iron phases exist, but only with vacancies, TlFe2xSe2. Some phases appear with ordering such that still the ThCr2Si2 subcell can be recognized [7]. Around x 0:4 antiferromagnetic ordering occurs (TN450 K) in a tetragonal pffiffiffi supercell with a0 ¼ a 5. TlCu2Se2 is Pauli paramagnetic [8] and has earlier been studied with first principles calculations [9,10]. Copper is proven to always be diamagnetic (3d10) together with the heavy chalcogens. Earlier studies of TlCo2xCuxSe2 showed the presence of orthorhombic distortion for 0.4pxo1.3 [1]—similar to that later found for KCu2Se2 [11]—and also incommensurate Co/Cu atomic ordering [12]. The Ne´el temperature decreases on copper substitution, the cobalt magnetic moments becoming diluted. In this article we present a study of TlCo2xMexSe2 (Me ¼ Fe, Ni and Cu) with neutron powder diffraction to investigate how the magnetic structure is affected by metal exchange. Moreover, the electronic structure was probed by calculation for TlCo2Se2, TlNi2Se2 and ordered TlCoNiSe2. 2. Methods 2.1. Synthesis Eight samples were synthesized: TlCo2xNixSe2 with x ¼ 0:25, 0.5 and 1.0; TlCo2xFexSe2 with x ¼ 0:2, 0.5 and 1.0, and TlCo2xCuxSe2 with x ¼ 0:1 and 0.2. All transition metals were etched in hydrochloric acid before use to remove superficial oxides. The materials purity was: Tl 99.999%; Se 99.999%; Co 99.8% (powder), 99.998% (ingots); Ni 99.995%; Fe 99.98% and Cu 99.98%. The quaternary nickel samples were synthesized directly from the elements and heat-treated in an evacuated pyrextube at 480 1C, first for 10 days and then reground and pressed into pellets. The pellets were sealed in a new pyrextube and heated at the same temperature for another week. For the manufacture of TlCo2xFexSe2, metal ingots of cobalt and iron were melted together using arc melting (no weight loss). This whole ingot was then put in a silica-tube together with TlSe and Se-shots. The tube was evacuated,
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sealed and heat-treated at 700 1C for 2–3 weeks. The sample was homogenized and kept at 700 1C for a week. TlCu2Se2 and TlCo2Se2 were first synthesized by mixing TlSe, Se-shots and Cu sheet-metal or Co-powder in an evacuated silica-tube heated at 400 1C and 600 1C, respectively. The ternary mother phases were then mixed together to form TlCo2xCuxSe2, kept at 600 1C for a week. 2.2. Diffraction All the samples were characterised by X-ray diffraction using a Guinier-Ha¨gg camera (CuKa1) and germanium ˚ [13] or silicon ða ¼ 5:431028 AÞ ˚ [14] ða ¼ 5:6570805 AÞ as internal standard. The powders were also studied with neutron diffraction at Studsvik, Sweden (NPD, ˚ in the temperature range 10–300 K. The l ¼ 1:471 A) refinements of the diffraction data were made with the Rietveld method using the FullProf program [15]. The parameters from the diffractograms measured over the magnetic transition temperature were refined describing the background by a polynomial expression. These refinements were made in the 2y interval 9.0–52.01. For data from below the transition temperature the refinements were made in the interval 2.0–52.01 and with manual background correction. The magnetic structures were refined with a magnetic moment only on the cobalt atom. In the nickel case this was done because of the uncertainty whether nickel really possesses a magnetic moment or not. Copper is diamagnetic and therefore does not exhibit a magnetic moment. Finally iron is only refined with very low concentration and it is impossible to know the magnetic moment on iron. 2.3. Magnetometry Only the three nickel-samples were investigated with a SQUID magnetometer (Quantum Design, MPMSXL). The applied field was fixed to 100 G for TlCo1.5Ni0.5Se2 and to 200 G for TlCo1.75Ni0.25Se2 and TlCoNiSe2. The temperature was scanned in the interval 10–300 K. Both zero-field cooled (ZFC) and field cooled (FC) procedures were used for all the three samples. Several attempts were made to measure the magnetic properties also of the iron solutions, both powder and crystals, but small impurities (probably Fe3O4) made the interpretation of the data impossible. SQUID data for TlCo2xCuxSe2 were already published by Broddefalk et al. [16]. 2.4. Calculation The program used for the calculations of the electronic structure was TB-LMTO 4.7 [17]. The approach for the calculations was the same as for the calculations on TlCo2S2 [6]. The exchange and correlation effects were treated in the generalized gradient approximation (GGA) as parameterized by Perdew and Wang [18]. The bonding character was studied with the Crystal Orbital Hamilton
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Population (COHP) [19] weighting approach. Note that the bonding state has a negative sign in COHP (opposite to that of COOP). One way of probing the stabilization of a magnetic structure is to look at the partial density-of-states (DOS) for the metal–metal bonding at the Fermi-level in the non-spin-polarized COHP. A high value of an antibonding character here can be a sign for a possibility to lower the total energy by spin-polarization [20] and thereby stabilize a ferromagnetic structure. Another analysis tool is ICOHP, the integral of the COHP, which serves as a measure of the strength of a chemical bond. Calculations were performed on TlCo2Se2, TlNi2Se2 and TlCoNiSe2. The calculations for non-magnetic and ferromagnetic situations in the first two compounds were made using the unit cell of space group I4/mmm. For the calculations of antiferromagnetic interactions between the layers in TlCo2Se2, space group P4mm was chosen [6]. Since random solid solutions such as TlCo2xNixSe2 cannot be treated easily in calculations, ordered situations must be chosen. No evidence for a superstructure was found in the diffraction data; this approach is only an approximation to make the calculations possible at all. The smallest system to be handled is then found for a 50% substitution. The first approximation was that every Co atom only had close Ni neighbours in the sheet and vice versa. To allow for antiferromagnetic interactions between the cobalt atoms within the same layer, the unit cell had to be doubled and lowered in symmetry. The space group then is Pmm2 (see atom positions in Table 1). The structure is illustrated in Fig. 1. The z ¼ 14 layer is exactly the same as for z ¼ 34. Non-magnetic, ferromagnetic as well as
Fig. 1. The superstructure described in Pmm2 used for one model calculation on TlCoNiSe2. All Ni atoms are surrounded by Co in the sheet, and vice versa. Both sheets in the unit cell are exactly the same.
Table 1 The atom positions for the TlCoNiSe2 super cell in space group Pmm2 and I 4¯ (cf. Figs. 1 and 2) Atom
Tl
I 4¯
Pmm2 Position
x; y; z
Position
x; y; z
1a 1b 2h
0, 0, 0
2d
1 2,
0,
3 4
2b
0, 0,
1 2
2a
0, 0, 0
4f
1 2,
0, 12, 0 1 3 1 2, 4, 2
Co
1c 1c 1d 1d
1 2, 1 2, 1 2, 1 2,
0, 14 0, 34 1 3 2, 4 1 1 2, 4
Ni
2g 2g
0, 34, 0, 34,
Se
1a 1a 1b 1b 2h 2h
0, 0, 0.35 0, 0, 0.65 0, 12, 0.35 0, 12, 0.65 1 1 2, 4, 0.85 1 3 2, 4, 0.15
1 4 3 4
0, 0.4
Fig. 2. The superstructure model described in I 4¯ used for calculations on TlCoNiSe2. All Ni atoms are also here surrounded by Co in the sheet. The difference compared to Fig. 1 is that in adjacent sheets Ni is now above Co and vice versa.
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o P-0
o
o
P-A
o I-0
o
o
o
o
o
o
o
o
+
+
P-FCo +
P-FNi
o
o
+
+
I-F
+
o
o
+
+
+
+
+
+
o
o
o
+
+
o
o -
+ o
I-A
+
207
+
+
Fig. 4. Data from SQUID measurements on three compositions of TlCo2xNixSe2, recorded after two modes of cooling (fc, zfc). For x ¼ 1, a background signal of 25 106 emu/gG was subtracted from the data before the inverse susceptibility was calculated.
o
Fig. 3. The transition metal layers in the two models Pmm2 (left) and I 4¯ (right). o ¼ no net magnetic moment, 7 refer to opposite spin directions (spin polarization), all being initial conditions in the calculations. White and grey circles denote the two kinds of transition metal (cf. Figs. 1 and 2), Co and Ni.
antiferromagnetic calculations were performed using this model. Another model used implied the space group I 4¯ (see atom positions in Table 1) with the same cell size as the original unit cell (see Fig. 2). To account for the symmetry the origin is moved to ð12 0 14Þ and this allows two separate positions for the transition metals, cobalt and nickel. In this model only ferromagnetic calculations within the sheet can be made for any one transition metal. The cell parameters used in all calculations were based on the (sub)cell dimensions as taken from Newmark et al. [5]. The z-parameter of selenium was fixed at 0.35. All the starting positions for the calculations for TlCoNiSe2 are illustrated in Fig. 3. 3. Results 3.1. Magnetometry TlCo2xNixSe2 (x ¼ 0:25, 0.5 and 1.0) show an antiferromagnetic behaviour with a Ne´el temperature of 140, 140 and 95 K respectively. The susceptibility curves are illustrated in Fig. 4. All curves follow the Curie–Weiss law in the paramagnetic region. For x ¼ 1:0 a constant background magnetization was subtracted to obtain the straight line of the inverse. The effective magnetic moments
per formula unit were: 2.9 mB, 3.3 mB and 1.3 mB, respectively, and the corresponding y values obtained were 36(8) K, 6(15) K and 69(13) K. 3.2. Neutron powder diffraction For all the solid solutions, the only change observed in neutron powder diffraction on magnetic ordering was the appearance of very weak low-angle peaks. These peaks are drawn for all compositions in Fig. 5, where their global relation to the main is exemplified. 3.2.1. TlCo2xNixSe2 The results from the neutron powder refinements for TlCo1.75Ni0.25Se2, TlCo1.5Ni0.5Se2 and TlCoNiSe2 are shown in Table 2. An example of the fit is illustrated in Fig. 6. All the cell parameters are in good agreement with earlier published results of Newmark et al. [5]. Both the aand the c-axis decrease on lowering the temperature, but the a parameter flattens out just below the transition temperature. The same observation was made for the system TlCo2Se2xSx [1,2]. The interesting result is that the helix is destroyed for the compositions of Ni substitution investigated here. The crucial difference with the situation for x ¼ 0 was not previously realized [5] and neither was it anticipated in our study when choosing the compositions for the syntheses. The magnetic structure is collinear antiferromagnetic between the ferromagnetic layers. Consequently, the bct centring extinction condition is broken: the (0 0 1) reflection carries intensity and no satellites are present. The spins are still confined to the ab-plane, but powder diffraction cannot give information on the specific orientation further. The magnetic moment on the cobalt
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S. Ronneteg et al. / Journal of Magnetism and Magnetic Materials 303 (2006) 204–213 Table 2 Results from neutron powder diffraction of TlCo2xNixSe2 at different temperatures. Only cobalt was allowed to carry a magnetic moment TlCo2xNixSe2 x ¼ 0:0 [1] Temp (K) a (A˚) c (A˚) zSe Rcryst (%) mCo (mB) Rmag (%)
295 3.8443(1) 13.5723(7) 0.3525(1) 4.74 — —
70 3.8317(2) 13.4513(12) 0.3537(1) 2.34 0.32(2) 32.1
40 3.8314(2) 13.4401(9) 0.3537(1) 2.10 0.40(2) 16.5
10 3.8316(2) 13.4254(8) 0.3537(1) 1.76 0.46(2) 16.6
100 3.8329(1) 13.5285(4) 0.3538(2) 3.34 0.54(3) 8.39
50 3.8307(2) 13.5079(7) 0.3535(2) 3.76 0.69(2) 9.86
10 3.8300(2) 13.4973(6) 0.3535(2) 3.14 0.73(2) 12.70
160 3.8338(2) 13.5602(7) 0.3538(2) 3.87 — —
100 3.8286(2) 13.5532(6) 0.3545(2) 3.04 0.75(3) 9.28
10 3.8248(2) 13.5386(6) 0.3544(2) 2.60 0.92(2) 10.18
50 3.8269(2) 13.5281(7) 0.3548(2) 5.18 0.88(5) 16.9
10 3.8237(2) 13.5311(7) 0.3550(2) 5.08 1.01(5) 13.9
x ¼ 0:25 Temp (K) a (A˚) c (A˚) zSe Rcryst (%) mCo (mB) Rmag (%)
295 3.8449(2) 13.6020(8) 0.3529(3) 4.28 — — x ¼ 0:5
Temp (K) a (A˚) c (A˚) zSe Rcryst (%) mCo (mB) Rmag (%)
295 3.8436(2) 13.6083(7) 0.3535(2) 4.49 — — x ¼ 1:0
Temp (K) a (A˚) c (A˚) zSe Rcryst (%) mCo (mB) Rmag (%)
Fig. 5. The low-angle part of the neutron powder diffractograms recorded at 10 K for the different solid solutions TlCo2xMexSe2. The notation (0 0 1)7 indicates the satellite reflections (0 0 17qz).
atom is increasing with substitution by nickel (in the approximation that only Co exhibits a magnetic moment). 3.2.2. TlCo2xMxSe2 (M ¼ Fe and Cu) The neutron diffraction results are listed in Table 3. In TlCo2xFexSe2, a continuous cell volume change is observed for x ¼ 0.2, 0.5 and 1.0, well following Vegard’s rule. Analysis of the patterns showed that the helix still remains at x ¼ 0:2. However, for the other compositions no magnetic peaks are visible, neither was any extra intensity found on the nuclear peaks. For small amounts of copper in TlCo2xCuxSe2 (x ¼ 0:1 and 0.2), the tetragonal structures prevails and no
295 3.8471(2) 13.5698(8) 0.3545(3) 5.75 — —
orthorhombic distortion is seen. It seems that the substitution does not affect the kind of magnetic ordering drastically, a conclusion that is supported by the susceptibility measurements [1,16]. The diffraction patterns showed that the magnetic helix prevails in this region. Due to the very low intensities of the satellite peaks, the Rmag-values (Table 3) for the copper-phases are rather high. 3.3. Calculations 3.3.1. TlNi2Se2 The result from the non-magnetic calculation is illustrated in Fig. 7 with the DOS and the COHP over the shortest nickel-nickel bond (within the metal sheet). Spinpolarization was not energetically favourable in this structure which agrees with the Pauli paramagnetic character measured [5]. This can be rationalized by the
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quite small anti-bonding Ni–Ni interactions at the Fermi level. 3.3.2. TlCo2Se2 The calculations were performed in the same way as for ferromagnetic TlCo2S2 [6]. The differences between the ferromagnetic and the antiferromagnetic energies are quite small in line with the assumption that the short distance direct ferromagnetic coupling in the layer is by far the strongest interaction which lowers the energy. This holds for both TlCo2S2 and TlCo2Se2. Spin-polarization lowers the total energy and the density around the Fermi level decreases in the DOS-curve. The results are condensed in Table 4 and in Fig. 8a and b. 3.3.3. TlCoNiSe2 Four types of calculations were made in the superstructure Pmm2, non-magnetic (P-0), ferromagnetic coupling between cobalt atoms (P-FCo), ferromagnetic coupling between nickel atoms (P-FNi) and, finally, antiferromagnetic coupling within a layer between the cobalt atoms (P-A). In the space group I 4¯ (see Fig. 2)
Fig. 6. The results from the Rietveld refinements for TlCo1.75Ni0.25Se2 at 10 K. The fit is illustrated by the data points and full line as well as by their difference curve (bottom).
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calculations were possible with magnetic moment on both cobalt and nickel at the same time—this is the reason why this model was used, even though neutron diffraction showed that the I-centring has disappeared. Calculations were performed for both antiferromagnetic (I-A) and ferromagnetic coupling (I-F) between cobalt and nickel (cf. Fig. 3). The results from all the calculations are found in Table 5 and illustrated in Fig. 9a and b. 4. Discussion Let us start by discussing the COHP for the mother compounds in more detail: The structure of the TlNi2Se2, TlCo2Se2 and their intermediates is, except for minor differences, the same. Therefore in a first crude approximation, a rigid-band model can be considered here. Moving from TlNi2Se2 to TlCo2Se2, the total number of electrons is reduced. Therefore, the Fermi level is shifted down. This leads to the conclusion that the Fermi level of the intermediates and also TlCo2Se2 would be positioned in the metal–metal antibonding peak region and therefore possibly lead to spin polarization. On gradually substituting the cobalt atom in TlCo2Se2 by another transition metal, the magnetic structure changes. The magnetic helix prevails for small substitution ðxp0:2Þ by both iron and copper, in contrast to nickel substitution for cobalt. In that case the helix structure is obviously broken and the phase becomes ordinary antiferromagnetic. The reason for this large difference is not immediately evident. That the nickel case behaves differently is seen macroscopically in the trend regarding the c-axis parameter change on substitution (cf. Tables 2 and 3). The agreement with earlier published [5] transition temperatures for TlCo2xNixSe2 is very good, but there are large differences regarding the y-values. The background magnetization is found to increase with higher concentrations of nickel. This makes a determination of the slope of the inverse susceptibility very uncertain, with large systematic errors in both y and the effective paramagnetic moment. Newmark et al. [5] found a decreasing trend of
Table 3 Results from the neutron powder diffraction for TlCo2xMexSe2 (Me ¼ Cu and Fe) Only cobalt was allowed to carry a magnetic moment Sample
TlCo2xCuxSe2
Composition
x ¼ 0:1
Temp (K) a (A˚) c (A˚) zSe Rcryst (%) mCo (mB) qz Angle f (1) Rmag (%)
295 3.8432(4) 13.610(2) 0.3527(4) 3.61 — — — —
TlCo2xFexSe2 x ¼ 0:2 10 3.8330(1) 13.4750(6) 0.3536(3) 3.19 0.58(3) 0.376(3) 112.3(6) 23.76
295 3.8443(4) 13.621(2) 0.3526(5) 4.0 — — — —
x ¼ 0:2 10 3.8346(1) 13.5127(7) 0.3531(4) 5.02 0.32(4) 0.330(5) 120.6(9) 34.0
10 3.8344(2) 13.4788(7) 0.3540(2) 3.87 0.55(2) 0.388(2) 110.1(4) 17.46
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4
4
2
2
0
0 Energy (eV)
Energy (eV)
210
-2
-2
-4
-4
-6
-6
-8
-8 0
2
4
6
8
10
12
DOS
-1
0
1
2
-COHP
Fig. 7. The density-of states (DOS) for TlNi2Se2 and COHP for the Ni–Ni bonds in one layer. Both calculations are without allowing for spinpolarization. The black part of DOS indicates the contribution by Ni 3d. The zero level indicates the Fermi energy.
Table 4 Results from the LMTO-ASA calculations for TlCo2Se2. The values are normalised to the nonmagnetic calculation
Etot (kJ/mol) ICOHP (kJ/mol)a msat Tl (mB/atom) msat Co (mB/atom) msat Se (mB/atom) a
Ferromagnetic
Antiferromagnetic
3.8 0.16 0.1 0.92 0.06
2.3 2.3 0.00 70.79 70.06
Four identical Co–Co bonds in one sheet in the unit cell.
the y-values which even change sign, from positive to negative, at 0.25oxo0.5. However, their values suffer from non-linear relationships approximated by a Curie– Weiss line. Moreover, the background in their measurements varies considerably (but decreases with increasing nickel content), a sign that traces of another phase are present, not detected by diffraction. In a study of TlCo2Se2xSx [21], our results differed from those by Greaney et al. [22], again probably reflecting the sensitivity to synthesis conditions. These experimental factors are very difficult to control and interpret fully, and it would be preferable to use single-crystal material rather than powders. That also anisotropy is important is evident for instance from the single-crystal work on TlCo2Se2 [1] where the susceptibility peak values (near TN) differ by a factor of
more than two depending on field direction. Pronounced powder texture may thus also influence the outcome of measurements. The localization of magnetic moment (including a possible moment on nickel) and the Co/Ni ordering are factors of importance for the magnetic properties. TN increases from 95 K for x ¼ 0 in TlCo2xNixSe2 to 140 K for x ¼ 0:25 and x ¼ 0:5, and decreases again back to 95 K for x ¼ 1:0. At the same time the effective paramagnetic moment follows the same trend. The trend in ordering temperature indicates that the antiferromagnetic interactions are enhanced between the layers, as remarked by Newmark et al. [5]. The crucial question is whether there is any magnetic moment on the nickel atom in the solid solution, as there is none in the ternary nickel compound (or at xX1:75 in the solutions [5]). The fact that there is an enhancement of the effective paramagnetic moment on increasing the nickel content up to x ¼ 0:5 is another indicator that nickel does contribute—either directly or indirectly through enforcing localization. However, it is impossible to distinguish which transition metal possesses the magnetic moment in neutron powder refinements. To simplify the evaluation a magnetic moment was allowed only on the cobalt atoms. This resulted in an increase of the moment per cobalt atom on increasing the nickel content (Table 2), thus in line with the evolution of the effective paramagnetic moment values. This trend is not easily
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α
4
211
β
Energy (eV)
2 0 -2
-4
-6
-8
0
2
(a)
4
6 8 DOS
10
4
2
0 2 DOS
4
0
2
4
6 8 DOS
10
minority majority
4
Energy (eV)
2
0
-2
-4
-6
-8 -1 (b)
0 1 -COHP
2
-1
0 1 -COHP
2
-1
0 1 -COHP
2
Fig. 8. (a) Density-of-states (DOS) with Co 3d projections in black for the non-magnetic, ferromagnetic and antiferromagnetic structure of TlCo2Se2. In the ferromagnetic picture the majority (a) and minority (b) are plotted separately. The energy is shifted so that the Fermi level lies at 0 eV. (b) Crystal orbital Hamilton population (COHP) of the Co–Co bond at 2.71 A˚ in TlCo2Se2 for non-magnetic, ferromagnetic and antiferromagnetic structure, respectively. Note that the –COHP is drawn, in correspondence with the conclusions from sign of COOP representations.
Table 5 Results from the calculations on TlCoNiSe2 Pmm2 and I 4¯ I 4¯
Pmm2 (see notations from Fig. 3)
P-FCo
P-FNi
P-A
I-F and I-A
Etot (kJ/mol) msat Tl (mB) msat Co (mB) msat Ni (mB) msat Se (mB)
4.2 0.13 1.59 0.58 0.15
4.3 0.13 1.59 0.58 0.15
0.8 0.02 71.38 0.0 70.11
4.4 0.13 1.60 0.58 0.15
understood. Some consistency concerning the increased total moment found from the neutron data would be obtained if nickel is allowed to carry a moment higher than
that of cobalt in the range xo1, for instance mCo ¼ 0:6 mB and mNi ¼ 0:9 mB . This assumption carries no theoretical support. The values of Table 2 may be translated into an average metal moment (Ni and Co both contributing) that increases slightly—from 0.64 mB to 0.69 mB—when changing the nickel content from x ¼ 0:25 to 0:5, but the trend collapses for x ¼ 1 (with the average of 0.50 mB). In fortunate cases, the cell parameter evolution upon dissolution can give a clue to the electron transfer, e.g. when substituting iron or manganese for copper in TlCu2Se2 [23]. There, in the same structure type as presented here, discontinuities of the slope of the c-axis vs. composition relationship have proven to be strong indicators of sudden changes in the band structure. A similar effect, probably reflecting the change in magnetic or structural conditions
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212
α
4
β
Energy (eV)
2 0 -2 -4 -6 -8 0
10
20 30 DOS
(a)
40
50
20
10
α
4
0 10 DOS
20
0
10
20 30 DOS
40
β
Energy (eV)
2 0 -2 -4 -6 -8 0 (b)
2
4
6 8 10 12 DOS
6 4 2 0 2 4 6 DOS
0
2
4
6 8 10 12 DOS
Fig. 9. (a) Density-of-states (DOS) for TlCoNiSe2 in the Pmm2 model (cf. Fig. 1). Designations as in Fig 8a. (b) The density-of-states (DOS) curve for TlCoNiSe2 in the I 4¯ model (cf. Fig. 2). Designations as in Fig. 8a. Note the similarity between the non-magnetic and ferromagnetic calculations of Fig. 9a.
was noted for TlCo2xCuxSe2 [1]. No clear indications of the same kind were found for TlCo2xNixSe2. Maybe fortuitous, the c-axis is smaller for x ¼ 2 than for x ¼ 0 in the nickel substitution case while larger for either iron and copper into TlCo2Se2, the latter two solutions showing the retention of the x ¼ 0 helical structure (for xp0:2). We cannot say whether these observations have a proper bearing on the difference in magnetic structure, and it is in retrospect very unfortunate that we cannot present data of TlCo2xNixSe2 for the range 0o xo0.25 where there is a definite change of magnetic structure, also reflected in the ordering temperature. The electronic structure was studied for TlCoNiSe2 in an attempt to answer the question about the possible Ni moment. LMTO calculations from four starting points (P-FCo, P-FNi, I-F and I-A of Fig. 3) showed an energy minimum around 4 kJ/mol for ferromagnetic coupling between nickel and cobalt atoms in the layer (Table 5).
There is a magnetic moment on both cobalt and nickel with a three times larger moment on cobalt. The antiferromagnetic calculation (P-A) resulted in less lowering of the energy and no magnetic moment on nickel. Unfortunately, it is not possible to distinguish which model best describes the true structure. It may be noted that the models with ferromagnetic interactions within the metal sheets lead to an increased cobalt moment as well as a moment on nickel, values that are not at all in line with the findings from neutron diffraction on the x ¼ 1 solution. We emphasize that the superstructure models are only crude approximations of the true situation, where the metal atoms most probably are disordered on the crystallographic site. Moreover, the calculations may not in all cases succeed in the modelling. As regards the moment values, as seen from Table 5, there is a hefty over-estimation of the spin moment of cobalt (experimentally 0.6 mB from a renewed neutron diffraction determination [24]).
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The DOS-curves of Figs. 7–9 may be compared on a qualitative basis. The two models of ordered TlCoNiSe2 of 9a and 9b give for the non-magnetic case, as expected, almost the same DOS which is found to be closely related to those of TlCo2Se2 and TlNi2Se2 on a rigid-band basis. One may speculate that, on nickel substitution, the addition of some electrons would increase the cobalt moment localization. However, as commented previously, the methods of calculation used here are not capable of taking care of long-range effects, and the DOS-curves of the magnetic states suffer from this inaccuracy.
213
separately, while at low temperature tuning synchrotron radiation to respective transition element. Acknowledgements Financial support from the Swedish Foundation for Strategic Research (SSF/FRAM) and A˚ngpannefo¨reningen’s Foundation for Research and Development is thankfully acknowledged. We are also very grateful to Mr. Ha˚kan Rundlo¨f at the Studsvik nuclear reactor facility for recording the neutron powder diffraction data of all samples.
5. Conclusions The electronic calculations have been shown valuable in at least explaining the trends in global magnetic behaviour in the series TlCo2Se2–TlNi2Se2–TlCu2Se2, where we in the DOS find a strong support for a rigid-band view. Especially helpful is the COHP representation as a strong indicator for possible spin-polarization. Even though the level of sophistication of the LMTO method may be low to describe complicated spin structures, it mostly yields interesting information that correlates well with experiment and associates closely with the chemical expectations. We have here presented the experimental outcome of transition metal substitution in TlCo2Se2. Surprisingly, iron and copper that have, respectively, less and more electrons than cobalt yield the same kind of magnetic ordering: the incommensurate helix of the mother compound remains (for limited substitution). However, there is a drastic lowering of moment in the copper case since copper is diamagnetic. In both cases, a somewhat higher degree of substitution removes the moment and the phases seem to become Pauli paramagnetic. Although nickel does not carry any moment in TlNi2Se2, there are indications (also noted previously [5]) that the substitution for cobalt effectuates an enhancement of the total moment as well as the magnitude of the antiferromagnetic interactions (from TN), the latter resulting in a collinear arrangement at much higher ordering temperatures and with another structure than for cobalt alone. Neither experimentally nor by calculations have we found a rigid basis for a trustworthy analysis of the Ni moment in the solid solutions TlCo2xNixSe2 but face bewilderment. One possible way to solve the dilemma, but experimentally extremely demanding, would be to apply X-ray magnetic linear dichroism (XMLD) on single crystals of the solid solutions to determine the spin and orbital moments
References [1] R. Berger, M. Fritzsche, A. Broddefalk, P. Nordblad, B. Malaman, J. Alloys Compds. 343 (2002) 186. [2] S. Ronneteg, S. Felton, P. Nordblad, R. Berger, J. Magn. Magn. Mater. 299 (2005) 53. [3] R. Lizarraga, S. Ronneteg, R. Berger, A. Bergman, P. Mohn, O. Eriksson, L. Nordstro¨m, Phys. Rev. B 70 (2004) 024407. [4] Z. Ban, M. Sikirica, Acta Cryst. 18 (1965) 594. [5] A.R. Newmark, G. Huan, M. Greenblatt, M. Croft, Solid State Commun. 71 (1989) 1025. [6] S. Ronneteg, M.-W. Lumey, R. Dronskowski, U. Gelius, R. Berger, S. Felton, P. Nordblad, J. Solid State Chem. 177 (2004) 2977. [7] L. Ha¨ggstro¨m, A. Seidel, R. Berger, J. Magn. Magn. Mater. 98 (1991) 37. [8] R. Berger, C.F. van Bruggen, J. Less-Common Met. 99 (1984) 113. [9] M. Shirai, Synth. Metals 71 (1995) 1857. [10] G.V. Vajenine, R. Hoffmann, Inorg. Chem. 35 (1996) 451. [11] O. Tiedje, E.E. Krasovskii, W. Schattke, P. Stoll, C. Nather, W. Bensch, Phys. Rev. B 67 (2003) 134105. [12] L. Nore´n, R.L. Withers, R. Berger, J. Solid State Chem. 151 (2000) 260. [13] J.F.C. Baker, M. Hart, Acta Crystallogr. A 31 (1975) 364. [14] M. Deutsch, M. Hart, Phys. Rev. B 26 (1982) 5558. [15] J. Rodriguez-Carvajal, Physica B 192 (1993) 55. [16] A. Broddefalk, P. Nordblad, R. Berger, Physica B 284–288 (2000) 1317. [17] G. Krier, O. Jepsen, A. Burkhardt, O.K. Andersen, The TB-LMTOASA program, version 4.7, Stuttgart, Germany. [18] J.P. Perdew, in: A. Ziesch, A. Eschrig (Eds.), Electronic Structure of Solids, Akademie Verlag, Berlin, 1991 p. 11. [19] R. Dronskowski, P.E. Blo¨chl, J. Phys. Chem. 97 (1993) 8617. [20] G.A. Landrum, R. Dronskowski, Angew. Chem. Int. Ed. 39 (2000) 1560. [21] S. Ronneteg, R. Berger, R.Z. Levitin, E.A. Popova, R.M. Scherbov, A.N. Vasiliev, J. Magn. Magn. Mater. 281 (2004) 388. [22] M. Greaney, G. Huan, K.V. Ramanujachary, Z. Teweldemedhin, M. Greenblatt, Solid State Commun. 79 (1991) 803. [23] R. Berger, C.F. van Bruggen, J. Less-Common Metals 113 (1985) 291. [24] S.Ronneteg, R.Berger, G.Andre´. to be published.