- Email: [email protected]
Influence of cobalt vacancies and nickel substitution on the magnetic properties of TiCo2Sn Heusler-type compound
Journal of Magnetism and Magnetic Materials 128 (1993) 93-100 North-Holland
Influence of cobalt vacancies and nickel substitution on the magnetic properties of TiCo2Sn Heusler-type compound J. Pierre
a, R.V. Skolozdra b and Yu.V. Stadnyk b
a Laboratoire L. N~el, CNRS, 166X, 38042 Grenoble, France b Department of Inorganic Chemistry, Yvan Franko University, 290005 Lviv, Ukraine Received 4 March 1993
The magnetic properties of the cubic compounds TiCoxSn (1 < x < 2) and TiCoxNi2_xSn (0 < x < 2) have been studied. Paramagnetic, ferromagnetic moments, Curie temperatures increase with Co content. The ratio of paramagnetic to ferromagnetic moment, the discrepancy between the paramagnetic temperature and the ferromagnetic Curie point are accounted for by the itinerant ferromagnetism model. A peculiar variation of the magnetic moment versus temperature and versus composition in the TiCoxSn series may be explained by induced magnetism on the Co atom located in the less occupied Co sublattice.
1. Introduction
Heusler-type compounds are well-known ternary compounds of the MM~X type, where M belongs to the transition metal series, M' to the end of these series, and X is a nonmagnetic metal or nonmetallic element. Many of Mn, Fe and Co compounds show ferromagnetic properties. The properties of Mn-based Heusler compounds may often be accounted for in terms of localized moments [1-3], due to the half-filled 3d shell which is a particularly stable configuration that reduces charge fluctuations [4,5]. Conversely, for MCoEX compounds, where M = Ti, Zr, Hf . . . . . the magnitudes of the Curie temperature and ordered moment vary much with substitutions in M, M' and X sublattices [1,6], providing an example of itinerant magnetism with strong spin fluctuations. Among these phases, MCoESn compounds (M = Ti, Hf, Zr) are ferromagnets with a Curie temperature above room temperature [1], whereas Correspondence to: Dr J. Pierre, Laboratoire L. N6el, CNRS, 166X, 38042 Grenoble, France.
corresponding Ni compounds are Pauli paramagnets. By varying the C o / N i ratio in these compounds, it is possible to lower the Curie point and to pass progressively to the paramagnetic regime. Another possibility is to lower the Co concentration in these compounds, keeping the initial cubic symmetry [7]. One of the two Co sites remains fully occupied, whereas vacancies progressively replace Co in the other, ending in the composition MCOlSn , which has the MgAgAs cubic structure. Lattice parameters are not much changed by the lowering of Co concentration. The magnetic properties of some TiCoxSn compounds have been previously studied [7] between 77 and 900 K. The Curie point and the ordered moment by Co atom were found to decrease strongly with decreasing Co content. We focus in the following on the magnetic properties of solid solutions of the type TiCoxSn and TiCoxNi2_xSn. Our aim is to study the formation and coupling of magnetic moments in these solid solutions, particularly through the variation of the paramagnetic moment /~p, ordered moment /'/'sat and their ratio versus the Curie point.
0304-8853/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
J. Pierre et al. / Magneticproperties of TiCo2Sn Heusler-type compound
94
2. Preparation and crystallographic properties
3. Magnetic properties
These samples were prepared under polycrystalline form, using an arc furnace, and annealed at 650°C for at least one month. Some compounds were also annealed at 800°C, and no significant variations in crystallographic and magnetic properties were observed due to the difference in annealing temperatures. Thus the samples seem to have reached a sufficient homogeneity, an important feature for the discussion of their magnetic properties. All compounds show after annealing one single cubic phase, the lattice parameters are given in table 1. For CO-Ni compounds, the parameter slightly increases as function of Ni concentration. In the TicoxSn series, the lattice parameter decreases slightly with Co concentration down to Xco = 1.6, and remains more or less constant for smaller CO concentrations. A precise X-ray study of the structure corresponding to the nominal composition TicoSn shows that Co and Sn atoms partly occupy the vacancy position. A M6ssbauer study of Sn gamma resonance also shows the occurrence of two different hyperfine fields [8]. Thus the precise formula for the stable compound should be written as: TiCol(COySnz)Sn, instead of TiCo_Sn. The atomic fractions y and z are less than 0.1. This additional occupation of the vacancy site probably begins for Xco less than 1.6, which helps to understand why the lattice parameter does not change for lower Co concentrations.
Magnetic properties were studied between 1.5 and 600 K, using a superconducting coil magnetometer and fields up to 7 T. Arrott-Belov plots (M 2 versus H / M ) were used to determine the spontaneous magnetisation, or the initial paramagnetic susceptibility in the vicinity of the Curie point. In the following, M is the magnetisation per formula unit, a n d / z is the value of the local moment; we derive the value for the paramagnetic moment /Xp assuming the local moment relation:
Table 1 Crystallographic properties of Co/Ni Heusler compounds. The standard deviation for all parameters is about 0.003 ,A Compound
a (.A)
Compound
a (,A)
TiCo2Sn TiCOL9Sn TiCoLsSn TiCOLTSn TiCoL6Sn TiCox.4Sn TiCOl.ESn TiCoSn
6.067 6.065 6.051 6.033 6.040 5.999 5.993 5.997
TiCoL9Ni0.1Sn TiCol.8Ni0.zSn TiCOl.TNi0.3Sn TiCol.6Ni0.4Sn TiCol.4Ni0.6Sn TiCol.2Ni0.aSn TiCo0.aNiL2Sn TiNi2Sn
6.066 6.058 6.065 6.072 6.074 6.076 6.077 6.097
2 2 CM = NlzBl.~p/3kn(T - Op).
For TiCoxNiE_xSn solutions, the value given for the moment in the ferromagnetic state/~f(T) and in the paramagnetic state/% is the mean value of the moments borne by the two C o / N i atoms. 3.1. Stoichiometric compounds For TiCo2Sn, the observed saturation magnetisation per Co atom at 0 K, /~sat=/x(0)= 0.98/~ a, and the Curie temperature Tc = 370 K are in good agreement with data from Ziebeck and Webster [1], which give 1.03~a and 359 K. The temperature dependence of magnetisation near the Curie temperature follows M ( T ) = A . (Tc - T ) ~, where the critical exponent has the value a = 0.495-1-0.01, equal to the mean field value 0.5. For T lower than 150 K, M(T) -M(O) varies as T 2<+ 0.05). For TiCoSn, M(0) reaches 0.357~B, and Tc is 135 K, in good agreement with Skolozdra et al. [9], Kuentzler et al. [10], which give respectively 0.35~B, 135 K and 0.32/x B, 143 K. The critical exponent near Tc is found to be 0.475 + 0.01, again close to 0.5. For T lower than 110 K, M ( T ) -M(O) also varies as T 2. The paramagnetic susceptibility for TiNi2Sn is nearly constant between 100 and 600 K (X = 5.2 X 10 - 4 emu/mol). 3.2. TiCoxSn systems For these non-stoichiometric solutions, the Curie point and saturation moment increase with
J. Pierre et aL / Magneticproperties of TiCo2Sn Heusler-type compound
95
500
400
o
E D
E Q}
300
v X
200
100
150
200
250
300
350
400
450
500
Temperature [K) Fig. l. Reciprocal suceptibility for TiCoxSn compounds.
Co concentration, in agreement with Skolozdra et al. [71. Fo r temperatures well above the Curie point, a Curie-Weiss law is obeyed, both Curie constants per formula unit or per Co ion increase with Co concentration (fig. 1). We derive (table 2) a value
for the paramagnetic moment /% assuming the local moment relation as defined above. For low Co concentrations, the reciprocal susceptibility has a nonlinear behaviour and shows a positive curvature near the Curie temperature. The ferromagnetic Curie point Tc is thus lower
1.0 '
2
'
'
200
300
.80 c ol E
L
tO n3
.60
:g
.40
• 20
0
100
T e m p e r a t u r e (K] Fig. 2. Spontaneous magnetisation for TiCo~Sn compounds.
400
J. P/erre et aL
96
/ Magneticproperties of TiCo2Sn Heusler-type compound
Table 2 Magnetic properties of TiCoxSn compounds, as functions of Co concentration./~p and//'sat are the moments per Co atom Xco Ia 1 1.2 1.4 1.6 1.7 b 1.8 1.9 2.0 2.0 c
@p(K)
P~p(/~s)
~t,~t(/z B)
TC (K)
/%//~sat
158 193 245 285
1.35 1.41 1.43 1.49 1.51 1.75 1.82 1.96
0.32 0.357 0.401 0.483 0.529 0.680 0.829 0.929 0.98 1.03
135 134 150 180 240 218 320 364 370 359
3.78 3.62 2.96 2.52 2.22 2.11 1.96 1.98
325 364 370
magnetisation which remains up to the paramagnetic Curie-Weiss temperature defined by hightemperature data, the temperature dependence of this magnetisation being anomalous. Conversely, the spontaneous magnetisation deduced from high field data ( H larger than 1 T) has a quite normal temperature dependence (fig. 2), excepted for some compositions, and vanishes at the Curie point given in table 2. A first explanation of this behaviour may be the occurrence of fluctuations of Co concentration throughout the sample, which give rise to strong variations of the Curie point. Small parts of the sample would keep a spontaneous magnetisation above the Curie point of the main part. A second explanation may be the occurrence of spin fluctuations in the range of temperature close to Tc, which are quenched by the application of external field. In the following we refer to susceptibility and magnetisation values deduced from the high-field data, which are given in table 2 and figs. 1 and 2.
a Kuentzler et al. [10]. b Skolozdra et al. [7]. c Ziebeck et al. [1].
than the paramagnetic temperature Op. This behaviour is already predicted by theoretical models for itinerant magnets. Some difficulties are encountered in the analysis for compounds with x between 1.2 and 1.6, where the largest difference occurs between Tc and Op. In this composition range, the ArrottBelov plots are nonlinear for temperatures in the vicinity of the Curie point. Data obtained in small fields (smaller than 0.5 T) give a spontaneous
600
i
3.3. Solid solutions between TiCo2Sn and TiNi2Sn The same analysis as before was performed for TiCoxNi2_xSn solutions. These systems show a
i
,
i
300 Temperature
400 (K)
500 o
E
400 E o X
300
200
iO0
0 0
~100
200
Fig. 3. Reciprocal suceptibility for TiCoxNi2_xSn compounds.
3. Pierre et aL / Magnetic properties of TiCo2Sn Heusler-type compound
ferromagnetic moments are calculated for one C o / N i atom.
Table 3 Magnetic properties of TiCoxNi2_xSn compounds, as function of Co concentration. /zp and /~sat are the moments per (Co/Ni) atom
Xco @p(K) 2.0 1.9 1.8 1.7 1.6 1.4 1.2 0.8
~p (JttB)
370 1.96 325 1.66 300 1.62 266 1.53 221 ~ 1.45 115 1.5 71 1.31 Not Curie-Weiss
/'/'sat (]'tB)
r C (K)
~£p/btsat
0.98 0.82 0.763 0.63 0.436 0.166 0 0
370 320 290 230 165 53 0 0
1.98 2.02 2.13 2.42 2.67 9.0
4. Discussion
For both series, the magnitudes of Tc, Op,/J'sat and/~p increase with Co concentration (figs. 4-6). A more rapid drop of ferromagnetic and paramagnetic Curie temperatures is observed for CoNi solid solutions than for TiCoxSn compounds; in particular, Tc drops to zero for Xco smaller than 1.4 in the first series. This may be ascribed to the filling of 3d band, which decreases the density of 3d states and is more efficient in reducing the moment and Curie temperature than simply replacing Co by vacancies. In the latter case, the local density of 3d states on Co is less variable with Co concentration; hence the more gentle reductions in Op and Tc. In agreement with the general trend for other itinerant systems, ~eff/]./,sat decreases as function of the Curie temperature, as described by Rhodes and Wohlfarth for Fe, Ni, Co alloys [14]. The classical explanation is that the effective paramagnetic moment is related to the band
Curie-Weiss behaviour at high enough temperatures for cobalt concentrations larger than 1.2, they order ferromagnetically for x > 1.4. The compounds with x = 0.8 and 1.2 remain paramagnetic down to 1.5 K. Reciprocal susceptibilities are given in fig. 3. Again, for Xco between 1.7 and 1.2, Arrott's plots are not linear in the vicinity of Tc. The magnetisation, paramagnetic moment and Curie temperature are derived using the linear part of Arrott's plots for fields larger than 1 T, and are summarized in table 3. The paramagnetic and
400
,
,
,
350
o
,//'/ / /
/
<3)
oo .~
15o
loo
,
..~.~
~I~: /
/
/4- TC
/
/° P ,
Co x N i2_ x
?
,
,
5O 1.2
97
1.4
1.6 1.8 2 X CO Fig. 4. Paramagnetic and ferromagnetic Curie temperatures versus Co content in the two series.
98
J. Pierre
et al. / Magnetic properties of TiCo2Sn Heusler-type compound ;
C
I
I
I
I . 80
E
o rn
i . 150 O.
I .40
.20
I
1.2
I
I
I .4
i .6 x
I
1.8
Co
Fig. 5. Mean paramagnetic moment of Co in TiCoxSn compounds.
structure and to local correlations, whereas Tc and ordered moment vary much more rapidly together with the band splitting, due to intersite interactions [13]. It is interesting to point that the /~¢ff//Zsat ratio for these Heusler compounds fall nearly exactly on the Rhodes-Wohlfarth curve for F e - C o - N i alloys. An anomalous thermal dependence of the spontaneous magnetisation is observed for i
TiCoxSn compounds with x = 1.4, 1.6 (fig. 2). This behaviour may be attributed first to concentration fluctuations in the sample, which give rise to important variations in the Curie temperature in this concentration range. But the long annealing time should provide a good homogeneity of the samples. We may also quote a possible chemical disorder on the partially occupied site of Co, or the i
i
i
2.0
c I:D
1.6
H to m
1.2
.80
.40
0
I
I
I
I
1.2
:1.4
1.6
1.B
X
2
CO
Fig. 6. Magnetisation per formula unit, and per Co atom extrapolated at 0 K in TiCoxSn compounds.
J. Pierre et al. / Magnetic properties of TiCo2Sn Heusler-type compound
occurrence of different moments on the two Co sites leading to ferrimagnetism. We recall that previous M6ssbauer experiments [8] performed on TiColSn have revealed the existence of two different hyperfine fields for Sn, which probably indicates the presence of Sn on the minority site of Co. However, the same behaviour is also observed in TiCOl.6Ni0.4Sn solution, where only C o / N i substitution is expected. Some possible preferential order may exist between the two sites in this case. The peculiar variation of the magnetisation is possibly related to a sudden increase of the resuiting moment on one sublattice as function of the exchange field. Such kind of metamagnetism for the Co bands is well known in compounds such as RCo 2 [11] and ThCo5 [12]. In the case of ThCos, two different Co sites exist as in the present case, which bear different moments in low fields, since the local Stoner's criterion for ferromagnetism is not fulfilled for one site. The ThCo 5 compound also shows a tremendous increased in Co moment for a slight variation of composition [12]. Thus the present behaviour may perhaps be explained in the same manner; the filled Co sublattice orders magnetically at Tc, whereas the other incomplete sublattice experiences an induced moment due to the exchange field from the first site, giving rise to the anomalous increase in magnetisation below Tc. /-~efe and //'sat both increase as function of Co content in the two series. For TiCo~Sn paramagnetic, saturation moment and Curie temperature show rapid increases in the range x = 1.6-1.9, indicating a strong change in the density of states or magnetic moment of 3d electrons in this concentration range. This together with the anomalous temperature variation of magnetisation pointed out above suggests an increase in the local moment, at least on one site, due to the increased intersite correlations in the band. In the TiCo~Sn series, Tc varies roughly as 0.84 M 0"63, o r as /'/'sat M being the magnetisation per formula unit, and /'/'sat the mean Co moment. Generally, the Curie point of weak ferromagnets is expected to vary more or less as M 2 [13]. This ,
99
anomalously low power also indicates that the mean magnetic moment increases much with Co concentration, whereas the Curie temperature is ruled by the moments on the most occupied site and interactions between them. Conversely, the Curie temperature of TicoxNi2_~Sn series varies as
. 1.05 /.Lsa t .
For concentrated CO systems, Tc and Op are nearly equal, whereas they strongly differ in both series for low Co concentrations. This behaviour is often observed in the case of amplitude spin fluctuations; in these cases, a break appears in the 1/X versus T curve, at a temperature T*. According to theories for itinerant magnetism [13], this temperature is that at which the local amplitude of longitudinal spin fluctuations saturates. In the present case, spin fluctuations may occur mainly on the less occupied Co sublattice. The largest difference between Tc and Op occurs for TiCo0.8Ni0.2Sn, which does not order and has a positive Op = 71 K. It may be considered as a 3d analog of rare earth heavy-fermion systems.
5. Conclusions The reduction of Co concentration in TiCo2Sn through Ni substitution or vacancy creation demonstrates the classical features of itinerant magnetism in these series. The study of both series of compounds helps to separate the influence of pure magnetic dilution from the filling of 3d band by an extra electron. Some peculiar features occur, concerning in particular the temperature dependence of magnetisation in some intermediate solutions; this behaviour may indicate an induced magnetism of Co 3d bands on the less occupied sublattice. Neutron diffraction will be valuable to measure the magnetic moments on the two different sites of Co in TiCoxSn, in order to see whether there is some difference between them, and to obtain information on a possible preferential order of Co and Ni on the two sites. For TiCoSn compound, the MgAgAs structure leads to the fact that the Co site is no longer an inversion center. It has been shown [15] that for some 3d compounds belonging to this structure,
100
Z Pierre et al. / Magnetic properties of TiCo2Sn Heusler-type compound
such as NiMnSb, the lack of an inversion center can lead to strongly different spin-up and spindown subbands in the ferromagnetic state, and even in some cases to half-metallic ferromagnetism, that is, the occurrence of a gap at the Fermi energy for the spin-down subband. In the present case, this possibility is enhanced by the fact that TiNiSn itself has a very low density of states and may be a nonmagnetic semiconductor with a small gap [16,10]. Single-crystal growth and polarised neutron studies will be undertaken to check this point in the present compounds; magnetotransport experiments are also under way for these systems.
Acknowledgements We thank C1. Lacroix for a critical reading of the manuscript.
References [1] K.R.A. Ziebeck and P.J. Webster, J. Phys. Chem. Solids 35 (1974) 1.
[2] A. Hamzic, R. Asomoza and I.A. Campbell, J. Plays F: Metal Phys. 11 (1981) 1441. [3] J. Kiibler, A.R. Williams and C.B. Sommers, Phys. Rev. B 28 (1983) 1745. [4] A.M. Oles, Phys. Rev. B 23 (1981) 271. [5] F. Gautier, in: Magnetism of Metals and Alloys, ed. M. Cyrot (North-Holland, Amsterdam, 1982) p. 1. [6] S. Jha, S. Yehia, C. Mitros, A. Lahamer, G.M. Julian, and R.A. Dunlap, J. Physique 49, C 8 (1988) 137. [7] R.V. Skolozdra, Yu.V. Stadnyk, Yu.K. Gorelenko and E.E. Terletskaya, Sov. Phys.-Solid State 32 (1990) 1536. [8] S.I. Yuschuk, S.A. Yur'ev, R.V. Skolozdra and Yu.V. Stadnyk, 2nd Mtg Nuclear Spectrosopy Studies of Hyperfine Interactions (Grozny, USSR, 1987), p. 47. [9] R.V. Skolozdra, Yu.V. Stadnyk and O.E. Starodynova, Ukr. Phys. J. 31 (1986) 1258. [10] R. Kuentzler, R. Clad, G. Schmerber, and Y. Dossmann, J. Magn. Magn. Mater. 104-107 (1992) 1976. [11] D. Bloch, D.M. Edwards, M. Shimizu and J. Voiron, J. Phys. F: Metal Phys. 5 (1975) 1217. [12] D. Givord, J. Laforest and R. Lemaire, J. Appl. Phys. 50 (1979) 7489. [13] T. Moriya, J. Magn. Magn. Mater. 14 (1979) 1. [14] P. Rhodes and E.P. Wohlfarth, Proc. R. Soc. 273 (1963) 247. [15] R.A. de Groot, F.M. Mueller, P.G. van Engen and K.H.J. Buschow, Phys. Rev. Letters 50 (1983) 2024. R.A. de Groot and K.H.J. Buschow, J. Magn. Magn. Mater. 54-57 (1986) 1377. [16] F.G. Aliev, V.V. Kozyrkov, V.V. Moshchalkov, R.V. Skolozdra and K. Durczewski, Z. Phys. B 80 (1990) 353.
Influence of cobalt vacancies and nickel substitution on the magnetic properties of TiCo2Sn Heusler-type compound J. Pierre
a, R.V. Skolozdra b and Yu.V. Stadnyk b
a Laboratoire L. N~el, CNRS, 166X, 38042 Grenoble, France b Department of Inorganic Chemistry, Yvan Franko University, 290005 Lviv, Ukraine Received 4 March 1993
The magnetic properties of the cubic compounds TiCoxSn (1 < x < 2) and TiCoxNi2_xSn (0 < x < 2) have been studied. Paramagnetic, ferromagnetic moments, Curie temperatures increase with Co content. The ratio of paramagnetic to ferromagnetic moment, the discrepancy between the paramagnetic temperature and the ferromagnetic Curie point are accounted for by the itinerant ferromagnetism model. A peculiar variation of the magnetic moment versus temperature and versus composition in the TiCoxSn series may be explained by induced magnetism on the Co atom located in the less occupied Co sublattice.
1. Introduction
Heusler-type compounds are well-known ternary compounds of the MM~X type, where M belongs to the transition metal series, M' to the end of these series, and X is a nonmagnetic metal or nonmetallic element. Many of Mn, Fe and Co compounds show ferromagnetic properties. The properties of Mn-based Heusler compounds may often be accounted for in terms of localized moments [1-3], due to the half-filled 3d shell which is a particularly stable configuration that reduces charge fluctuations [4,5]. Conversely, for MCoEX compounds, where M = Ti, Zr, Hf . . . . . the magnitudes of the Curie temperature and ordered moment vary much with substitutions in M, M' and X sublattices [1,6], providing an example of itinerant magnetism with strong spin fluctuations. Among these phases, MCoESn compounds (M = Ti, Hf, Zr) are ferromagnets with a Curie temperature above room temperature [1], whereas Correspondence to: Dr J. Pierre, Laboratoire L. N6el, CNRS, 166X, 38042 Grenoble, France.
corresponding Ni compounds are Pauli paramagnets. By varying the C o / N i ratio in these compounds, it is possible to lower the Curie point and to pass progressively to the paramagnetic regime. Another possibility is to lower the Co concentration in these compounds, keeping the initial cubic symmetry [7]. One of the two Co sites remains fully occupied, whereas vacancies progressively replace Co in the other, ending in the composition MCOlSn , which has the MgAgAs cubic structure. Lattice parameters are not much changed by the lowering of Co concentration. The magnetic properties of some TiCoxSn compounds have been previously studied [7] between 77 and 900 K. The Curie point and the ordered moment by Co atom were found to decrease strongly with decreasing Co content. We focus in the following on the magnetic properties of solid solutions of the type TiCoxSn and TiCoxNi2_xSn. Our aim is to study the formation and coupling of magnetic moments in these solid solutions, particularly through the variation of the paramagnetic moment /~p, ordered moment /'/'sat and their ratio versus the Curie point.
0304-8853/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
J. Pierre et al. / Magneticproperties of TiCo2Sn Heusler-type compound
94
2. Preparation and crystallographic properties
3. Magnetic properties
These samples were prepared under polycrystalline form, using an arc furnace, and annealed at 650°C for at least one month. Some compounds were also annealed at 800°C, and no significant variations in crystallographic and magnetic properties were observed due to the difference in annealing temperatures. Thus the samples seem to have reached a sufficient homogeneity, an important feature for the discussion of their magnetic properties. All compounds show after annealing one single cubic phase, the lattice parameters are given in table 1. For CO-Ni compounds, the parameter slightly increases as function of Ni concentration. In the TicoxSn series, the lattice parameter decreases slightly with Co concentration down to Xco = 1.6, and remains more or less constant for smaller CO concentrations. A precise X-ray study of the structure corresponding to the nominal composition TicoSn shows that Co and Sn atoms partly occupy the vacancy position. A M6ssbauer study of Sn gamma resonance also shows the occurrence of two different hyperfine fields [8]. Thus the precise formula for the stable compound should be written as: TiCol(COySnz)Sn, instead of TiCo_Sn. The atomic fractions y and z are less than 0.1. This additional occupation of the vacancy site probably begins for Xco less than 1.6, which helps to understand why the lattice parameter does not change for lower Co concentrations.
Magnetic properties were studied between 1.5 and 600 K, using a superconducting coil magnetometer and fields up to 7 T. Arrott-Belov plots (M 2 versus H / M ) were used to determine the spontaneous magnetisation, or the initial paramagnetic susceptibility in the vicinity of the Curie point. In the following, M is the magnetisation per formula unit, a n d / z is the value of the local moment; we derive the value for the paramagnetic moment /Xp assuming the local moment relation:
Table 1 Crystallographic properties of Co/Ni Heusler compounds. The standard deviation for all parameters is about 0.003 ,A Compound
a (.A)
Compound
a (,A)
TiCo2Sn TiCOL9Sn TiCoLsSn TiCOLTSn TiCoL6Sn TiCox.4Sn TiCOl.ESn TiCoSn
6.067 6.065 6.051 6.033 6.040 5.999 5.993 5.997
TiCoL9Ni0.1Sn TiCol.8Ni0.zSn TiCOl.TNi0.3Sn TiCol.6Ni0.4Sn TiCol.4Ni0.6Sn TiCol.2Ni0.aSn TiCo0.aNiL2Sn TiNi2Sn
6.066 6.058 6.065 6.072 6.074 6.076 6.077 6.097
2 2 CM = NlzBl.~p/3kn(T - Op).
For TiCoxNiE_xSn solutions, the value given for the moment in the ferromagnetic state/~f(T) and in the paramagnetic state/% is the mean value of the moments borne by the two C o / N i atoms. 3.1. Stoichiometric compounds For TiCo2Sn, the observed saturation magnetisation per Co atom at 0 K, /~sat=/x(0)= 0.98/~ a, and the Curie temperature Tc = 370 K are in good agreement with data from Ziebeck and Webster [1], which give 1.03~a and 359 K. The temperature dependence of magnetisation near the Curie temperature follows M ( T ) = A . (Tc - T ) ~, where the critical exponent has the value a = 0.495-1-0.01, equal to the mean field value 0.5. For T lower than 150 K, M(T) -M(O) varies as T 2<+ 0.05). For TiCoSn, M(0) reaches 0.357~B, and Tc is 135 K, in good agreement with Skolozdra et al. [9], Kuentzler et al. [10], which give respectively 0.35~B, 135 K and 0.32/x B, 143 K. The critical exponent near Tc is found to be 0.475 + 0.01, again close to 0.5. For T lower than 110 K, M ( T ) -M(O) also varies as T 2. The paramagnetic susceptibility for TiNi2Sn is nearly constant between 100 and 600 K (X = 5.2 X 10 - 4 emu/mol). 3.2. TiCoxSn systems For these non-stoichiometric solutions, the Curie point and saturation moment increase with
J. Pierre et aL / Magneticproperties of TiCo2Sn Heusler-type compound
95
500
400
o
E D
E Q}
300
v X
200
100
150
200
250
300
350
400
450
500
Temperature [K) Fig. l. Reciprocal suceptibility for TiCoxSn compounds.
Co concentration, in agreement with Skolozdra et al. [71. Fo r temperatures well above the Curie point, a Curie-Weiss law is obeyed, both Curie constants per formula unit or per Co ion increase with Co concentration (fig. 1). We derive (table 2) a value
for the paramagnetic moment /% assuming the local moment relation as defined above. For low Co concentrations, the reciprocal susceptibility has a nonlinear behaviour and shows a positive curvature near the Curie temperature. The ferromagnetic Curie point Tc is thus lower
1.0 '
2
'
'
200
300
.80 c ol E
L
tO n3
.60
:g
.40
• 20
0
100
T e m p e r a t u r e (K] Fig. 2. Spontaneous magnetisation for TiCo~Sn compounds.
400
J. P/erre et aL
96
/ Magneticproperties of TiCo2Sn Heusler-type compound
Table 2 Magnetic properties of TiCoxSn compounds, as functions of Co concentration./~p and//'sat are the moments per Co atom Xco Ia 1 1.2 1.4 1.6 1.7 b 1.8 1.9 2.0 2.0 c
@p(K)
P~p(/~s)
~t,~t(/z B)
TC (K)
/%//~sat
158 193 245 285
1.35 1.41 1.43 1.49 1.51 1.75 1.82 1.96
0.32 0.357 0.401 0.483 0.529 0.680 0.829 0.929 0.98 1.03
135 134 150 180 240 218 320 364 370 359
3.78 3.62 2.96 2.52 2.22 2.11 1.96 1.98
325 364 370
magnetisation which remains up to the paramagnetic Curie-Weiss temperature defined by hightemperature data, the temperature dependence of this magnetisation being anomalous. Conversely, the spontaneous magnetisation deduced from high field data ( H larger than 1 T) has a quite normal temperature dependence (fig. 2), excepted for some compositions, and vanishes at the Curie point given in table 2. A first explanation of this behaviour may be the occurrence of fluctuations of Co concentration throughout the sample, which give rise to strong variations of the Curie point. Small parts of the sample would keep a spontaneous magnetisation above the Curie point of the main part. A second explanation may be the occurrence of spin fluctuations in the range of temperature close to Tc, which are quenched by the application of external field. In the following we refer to susceptibility and magnetisation values deduced from the high-field data, which are given in table 2 and figs. 1 and 2.
a Kuentzler et al. [10]. b Skolozdra et al. [7]. c Ziebeck et al. [1].
than the paramagnetic temperature Op. This behaviour is already predicted by theoretical models for itinerant magnets. Some difficulties are encountered in the analysis for compounds with x between 1.2 and 1.6, where the largest difference occurs between Tc and Op. In this composition range, the ArrottBelov plots are nonlinear for temperatures in the vicinity of the Curie point. Data obtained in small fields (smaller than 0.5 T) give a spontaneous
600
i
3.3. Solid solutions between TiCo2Sn and TiNi2Sn The same analysis as before was performed for TiCoxNi2_xSn solutions. These systems show a
i
,
i
300 Temperature
400 (K)
500 o
E
400 E o X
300
200
iO0
0 0
~100
200
Fig. 3. Reciprocal suceptibility for TiCoxNi2_xSn compounds.
3. Pierre et aL / Magnetic properties of TiCo2Sn Heusler-type compound
ferromagnetic moments are calculated for one C o / N i atom.
Table 3 Magnetic properties of TiCoxNi2_xSn compounds, as function of Co concentration. /zp and /~sat are the moments per (Co/Ni) atom
Xco @p(K) 2.0 1.9 1.8 1.7 1.6 1.4 1.2 0.8
~p (JttB)
370 1.96 325 1.66 300 1.62 266 1.53 221 ~ 1.45 115 1.5 71 1.31 Not Curie-Weiss
/'/'sat (]'tB)
r C (K)
~£p/btsat
0.98 0.82 0.763 0.63 0.436 0.166 0 0
370 320 290 230 165 53 0 0
1.98 2.02 2.13 2.42 2.67 9.0
4. Discussion
For both series, the magnitudes of Tc, Op,/J'sat and/~p increase with Co concentration (figs. 4-6). A more rapid drop of ferromagnetic and paramagnetic Curie temperatures is observed for CoNi solid solutions than for TiCoxSn compounds; in particular, Tc drops to zero for Xco smaller than 1.4 in the first series. This may be ascribed to the filling of 3d band, which decreases the density of 3d states and is more efficient in reducing the moment and Curie temperature than simply replacing Co by vacancies. In the latter case, the local density of 3d states on Co is less variable with Co concentration; hence the more gentle reductions in Op and Tc. In agreement with the general trend for other itinerant systems, ~eff/]./,sat decreases as function of the Curie temperature, as described by Rhodes and Wohlfarth for Fe, Ni, Co alloys [14]. The classical explanation is that the effective paramagnetic moment is related to the band
Curie-Weiss behaviour at high enough temperatures for cobalt concentrations larger than 1.2, they order ferromagnetically for x > 1.4. The compounds with x = 0.8 and 1.2 remain paramagnetic down to 1.5 K. Reciprocal susceptibilities are given in fig. 3. Again, for Xco between 1.7 and 1.2, Arrott's plots are not linear in the vicinity of Tc. The magnetisation, paramagnetic moment and Curie temperature are derived using the linear part of Arrott's plots for fields larger than 1 T, and are summarized in table 3. The paramagnetic and
400
,
,
,
350
o
,//'/ / /
/
<3)
oo .~
15o
loo
,
..~.~
~I~: /
/
/4- TC
/
/° P ,
Co x N i2_ x
?
,
,
5O 1.2
97
1.4
1.6 1.8 2 X CO Fig. 4. Paramagnetic and ferromagnetic Curie temperatures versus Co content in the two series.
98
J. Pierre
et al. / Magnetic properties of TiCo2Sn Heusler-type compound ;
C
I
I
I
I . 80
E
o rn
i . 150 O.
I .40
.20
I
1.2
I
I
I .4
i .6 x
I
1.8
Co
Fig. 5. Mean paramagnetic moment of Co in TiCoxSn compounds.
structure and to local correlations, whereas Tc and ordered moment vary much more rapidly together with the band splitting, due to intersite interactions [13]. It is interesting to point that the /~¢ff//Zsat ratio for these Heusler compounds fall nearly exactly on the Rhodes-Wohlfarth curve for F e - C o - N i alloys. An anomalous thermal dependence of the spontaneous magnetisation is observed for i
TiCoxSn compounds with x = 1.4, 1.6 (fig. 2). This behaviour may be attributed first to concentration fluctuations in the sample, which give rise to important variations in the Curie temperature in this concentration range. But the long annealing time should provide a good homogeneity of the samples. We may also quote a possible chemical disorder on the partially occupied site of Co, or the i
i
i
2.0
c I:D
1.6
H to m
1.2
.80
.40
0
I
I
I
I
1.2
:1.4
1.6
1.B
X
2
CO
Fig. 6. Magnetisation per formula unit, and per Co atom extrapolated at 0 K in TiCoxSn compounds.
J. Pierre et al. / Magnetic properties of TiCo2Sn Heusler-type compound
occurrence of different moments on the two Co sites leading to ferrimagnetism. We recall that previous M6ssbauer experiments [8] performed on TiColSn have revealed the existence of two different hyperfine fields for Sn, which probably indicates the presence of Sn on the minority site of Co. However, the same behaviour is also observed in TiCOl.6Ni0.4Sn solution, where only C o / N i substitution is expected. Some possible preferential order may exist between the two sites in this case. The peculiar variation of the magnetisation is possibly related to a sudden increase of the resuiting moment on one sublattice as function of the exchange field. Such kind of metamagnetism for the Co bands is well known in compounds such as RCo 2 [11] and ThCo5 [12]. In the case of ThCos, two different Co sites exist as in the present case, which bear different moments in low fields, since the local Stoner's criterion for ferromagnetism is not fulfilled for one site. The ThCo 5 compound also shows a tremendous increased in Co moment for a slight variation of composition [12]. Thus the present behaviour may perhaps be explained in the same manner; the filled Co sublattice orders magnetically at Tc, whereas the other incomplete sublattice experiences an induced moment due to the exchange field from the first site, giving rise to the anomalous increase in magnetisation below Tc. /-~efe and //'sat both increase as function of Co content in the two series. For TiCo~Sn paramagnetic, saturation moment and Curie temperature show rapid increases in the range x = 1.6-1.9, indicating a strong change in the density of states or magnetic moment of 3d electrons in this concentration range. This together with the anomalous temperature variation of magnetisation pointed out above suggests an increase in the local moment, at least on one site, due to the increased intersite correlations in the band. In the TiCo~Sn series, Tc varies roughly as 0.84 M 0"63, o r as /'/'sat M being the magnetisation per formula unit, and /'/'sat the mean Co moment. Generally, the Curie point of weak ferromagnets is expected to vary more or less as M 2 [13]. This ,
99
anomalously low power also indicates that the mean magnetic moment increases much with Co concentration, whereas the Curie temperature is ruled by the moments on the most occupied site and interactions between them. Conversely, the Curie temperature of TicoxNi2_~Sn series varies as
. 1.05 /.Lsa t .
For concentrated CO systems, Tc and Op are nearly equal, whereas they strongly differ in both series for low Co concentrations. This behaviour is often observed in the case of amplitude spin fluctuations; in these cases, a break appears in the 1/X versus T curve, at a temperature T*. According to theories for itinerant magnetism [13], this temperature is that at which the local amplitude of longitudinal spin fluctuations saturates. In the present case, spin fluctuations may occur mainly on the less occupied Co sublattice. The largest difference between Tc and Op occurs for TiCo0.8Ni0.2Sn, which does not order and has a positive Op = 71 K. It may be considered as a 3d analog of rare earth heavy-fermion systems.
5. Conclusions The reduction of Co concentration in TiCo2Sn through Ni substitution or vacancy creation demonstrates the classical features of itinerant magnetism in these series. The study of both series of compounds helps to separate the influence of pure magnetic dilution from the filling of 3d band by an extra electron. Some peculiar features occur, concerning in particular the temperature dependence of magnetisation in some intermediate solutions; this behaviour may indicate an induced magnetism of Co 3d bands on the less occupied sublattice. Neutron diffraction will be valuable to measure the magnetic moments on the two different sites of Co in TiCoxSn, in order to see whether there is some difference between them, and to obtain information on a possible preferential order of Co and Ni on the two sites. For TiCoSn compound, the MgAgAs structure leads to the fact that the Co site is no longer an inversion center. It has been shown [15] that for some 3d compounds belonging to this structure,
100
Z Pierre et al. / Magnetic properties of TiCo2Sn Heusler-type compound
such as NiMnSb, the lack of an inversion center can lead to strongly different spin-up and spindown subbands in the ferromagnetic state, and even in some cases to half-metallic ferromagnetism, that is, the occurrence of a gap at the Fermi energy for the spin-down subband. In the present case, this possibility is enhanced by the fact that TiNiSn itself has a very low density of states and may be a nonmagnetic semiconductor with a small gap [16,10]. Single-crystal growth and polarised neutron studies will be undertaken to check this point in the present compounds; magnetotransport experiments are also under way for these systems.
Acknowledgements We thank C1. Lacroix for a critical reading of the manuscript.
References [1] K.R.A. Ziebeck and P.J. Webster, J. Phys. Chem. Solids 35 (1974) 1.
[2] A. Hamzic, R. Asomoza and I.A. Campbell, J. Plays F: Metal Phys. 11 (1981) 1441. [3] J. Kiibler, A.R. Williams and C.B. Sommers, Phys. Rev. B 28 (1983) 1745. [4] A.M. Oles, Phys. Rev. B 23 (1981) 271. [5] F. Gautier, in: Magnetism of Metals and Alloys, ed. M. Cyrot (North-Holland, Amsterdam, 1982) p. 1. [6] S. Jha, S. Yehia, C. Mitros, A. Lahamer, G.M. Julian, and R.A. Dunlap, J. Physique 49, C 8 (1988) 137. [7] R.V. Skolozdra, Yu.V. Stadnyk, Yu.K. Gorelenko and E.E. Terletskaya, Sov. Phys.-Solid State 32 (1990) 1536. [8] S.I. Yuschuk, S.A. Yur'ev, R.V. Skolozdra and Yu.V. Stadnyk, 2nd Mtg Nuclear Spectrosopy Studies of Hyperfine Interactions (Grozny, USSR, 1987), p. 47. [9] R.V. Skolozdra, Yu.V. Stadnyk and O.E. Starodynova, Ukr. Phys. J. 31 (1986) 1258. [10] R. Kuentzler, R. Clad, G. Schmerber, and Y. Dossmann, J. Magn. Magn. Mater. 104-107 (1992) 1976. [11] D. Bloch, D.M. Edwards, M. Shimizu and J. Voiron, J. Phys. F: Metal Phys. 5 (1975) 1217. [12] D. Givord, J. Laforest and R. Lemaire, J. Appl. Phys. 50 (1979) 7489. [13] T. Moriya, J. Magn. Magn. Mater. 14 (1979) 1. [14] P. Rhodes and E.P. Wohlfarth, Proc. R. Soc. 273 (1963) 247. [15] R.A. de Groot, F.M. Mueller, P.G. van Engen and K.H.J. Buschow, Phys. Rev. Letters 50 (1983) 2024. R.A. de Groot and K.H.J. Buschow, J. Magn. Magn. Mater. 54-57 (1986) 1377. [16] F.G. Aliev, V.V. Kozyrkov, V.V. Moshchalkov, R.V. Skolozdra and K. Durczewski, Z. Phys. B 80 (1990) 353.