- Email: [email protected]
Electrical resistivity and magnetic properties of the ternary compounds Ho2TGe2; T=Ru, Os
Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
Electrical resistivity and magnetic properties of the ternary compounds Ho TGe ; T"Ru, Os 2 2 K. Hiebl!,*, O. Sologub" ! Institut fu( r Physikal. Chemie der Universita( t Wien, Wa( hringerstra}e 42, A-1090 Wien, Austria " Department of Inorg. Chemistry, L+viv University, Kyryla i Mefodia ul. 6, 290005 L+viv, Ukraine Received 4 February 1997; received in revised form 15 April 1997
Abstract We have performed an investigation of the magnetic properties of the new compounds Ho (Ru,Os)Ge , which 2 2 crystallize in the monoclinic structure-type Sc CoSi (space-group B2/m), using an AC susceptometer. Both compounds 2 2 undergo possibly antiferromagnetic transitions at ¹ +40 K; subsequent spin-reorientations towards a ferromagnetic N spin alignment occur at temperatures below 20 K. From isothermal (¹"5 K) magnetization measurements versus external field (k H"0—3 T) an ordered moment of 5.2 l has been derived for both samples. In the paramagnetic region 0 B effective moments close to the ideal free Ho3` ion moment (k "10.6 l ) were deduced, the h values being positive. The %&& B 1 temperature dependence of the electrical resistivity reveals pronounced changes of slope at the ordering temperatures ¹ and ¹ . The maxima of do/d¹ versus ¹ are in agreement with magnetic data above. For the paramagnetic region N C a deflection of the generally linear o—¹ plot of nonmagnetic metallic systems is observed, which could be attributed to the influence of the crystalline field split levels of the seventeenfold degenerate Ho3` ground-state 5I . Not knowing the exact 8 4-f level scheme, we use a single spacing (d) crystal-field model for an order of magnitude estimate. The results of the negative magnetoresistivity data are due to the reduced spin disorder scattering in the ordered state. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 61.10; 72.15; 75.20; 75.30 Keywords: Magnetic properties; Electrical resistivity; Magnetoresistivity
1. Introduction In recent years, a great amount of research work has been dedicated to the ternary compounds
* Corresponding author: Tel.: #43 1 31367 2504; fax: #43 1 310 45 97; e-mail: [email protected].
M—T—X, where M is a rare-earth or an actinide ion, T a transition metal and X is Al, Ga, In, Si, Ge, Sn, P, As and Sb, respectively. Phase equilibria and structural chemistry data show a wide variety of stoichiometric compositions crystallizing in a manifold of distinct structure types [1,2]. Concerning the physical properties, these systems became a fantastic playground for many research
0304-8853/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 0 6 6 - 3
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
57
groups, since a lot of interesting phenomena are exhibited. Among these phenomena are, e.g., reentrant superconductivity [3], complex magnetic structures [4,5], heavy-fermion behavior [6], valence fluctuations and Kondo lattice formation [7] or magnetoresistance anomalies [8]. Holmium is the ion bearing the largest effective moment among the rare-earth elements and therefore plays an important role in the interplay of RE3` magnetism and 4d, 5d element superconductivity. Thus, the investigation of the magnetic properties and the electrical resistivity of two new compounds with composition 2 : 1 : 2 became the subject of the present paper.
to 3 T. Measurements of the electrical resistivity were done with a general four probe Lake-Shore AC resistivity option ( f"133 Hz, i"10 mA) in the temperature range 4.2—300 K and in applied magnetic fields up to 1 T. The alloy buttons were cut by diamond saw (Bu¨hler Isomet) into barshaped samples with the dimensions of ca. 1] 1]5 mm3. Electrical contacts were made using commercial silver paint and 25 l Cu wires. All calculations concerning the magnetic and electrical resistivity data were performed using the program TableCurve 2D (Jandel Corp.) and the goodness-of-fit coefficient r2 was in any case better than 0.993.
2. Experimental details
3. Results and discussion
Sample preparation was performed by arc melting under argon ingots of the elements of 99.9 mass% minimum purity, each alloy button with a total weight of ca. 1 g. For further details of heat treatment and on X-ray powder techniques concerning structural characterization, the reader is kindly referred to an article recently published on a related series of compounds [9]. Both compounds were found to crystallize in a monoclinic cell with the structure type of Sc CoSi , space2 2 group B2/m [10]. Unit cell parameters are listed in Table 1. The magnetic properties were studied by use of a Faraday balance, SUS-10, in the temperature range 80—500 K in external fields up to 1.3 T, a Lake-Shore AC susceptometer, AC 7000 ( f"133 Hz and H "1 mT) for temperatures AC 4.2 K(¹(100 K as well as a SHE-SQUID magnetometer at ¹"5 K and 35 K as well as fields up
3.1. Magnetism Generally, we observe that the magnetic properties of both compounds Ho RuGe and Ho OsGe 2 2 2 2 are quite alike. Fig. 1 shows the paramagnetic region and the susceptibility clearly obeys linear dependence of temperature due to the Curie—Weiss law for ¹'80 K. The data were fitted using the formula C s" #s , 0 ¹!h 1
(1)
where C is the Curie constant, h the paramagnetic 1 Curie temperature and s denotes temperature-in0 dependent contributions such as core diamagnetism, Landau diamagnetism and Pauli paramagnetism. The results are listed in Table 1 and the derived
Table 1 Crystallographic and magnetic data of Ho TGe ; T"Ru, Os 2 2 Compound
Lattice parameters, nm
k %&& (l ) B
h 1 (K)
¹ N (K)
¹ C (K)
p (l ) B
a
b
c
Ho RuGe 2 2
1.06732(5)
0.4249(7)
10.7
13.4
40.7
7.5
5.2
Ho OsGe 2 2
1.0691(2)
1.020(1) c"118.0(1)° 1.0050(2) c"118.07(1)°
0.42618(7)
10.5
15.0
39.6
12.9
5.2
58
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
Fig. 1. Reciprocal gram susceptibility versus temperature for Ho TGe symbols: measured data, solid line: calculated data (Eq. (1)). 2 2
Fig. 2. AC susceptibility versus temperature for Ho TGe . 2 2
value for the effective moment k thereby was %&& found to agree well with the theoretical value of the tripositive Ho3` free ion moment. The values of v are of &10~5 cm3/mole and therefore negli0 gible. Fig. 2 reveals the temperature plot of the AC susceptibility. Two pronounced maxima of the real
part s@ are encountered around 40 K and below 20 K for both samples, indicating two consecutive magnetic transitions. Certainly the lower transition is stemming from a parallel spin alignment of reduced moments (ferromagnet). This is confirmed from the isothermal magnetization, M versus magnetic field curve (see Fig. 3). The values of M tend
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
59
Fig. 3. Isothermal magnetization versus applied field at ¹"5 K and ¹"35 K for Ho TGe . 2 2
to saturate in applied fields k H'2.0 T at 0 ¹"5 K, which is, however, close to the Curie points. At lower temperatures we can expect the M curves to saturate at much lower fields indic(H) ating a rather weak magnetocrystalline anisotropy for these samples. The magnetization of both compounds reaches values of 99 and 89 Am2/kg in high field, and hence an ordered moment k of 5.2 l can 4 B be derived. The values of the remanent magnetization as can be seen from Fig. 3 are rather small (&10% of M ), leading to a remanent mo(H/3T) ment of 0.5 and 0.7 l , respectively. Assuming that B our measurements performed on polycrystalline bulk specimens represent the response of a randomly oriented fixed powder, a maximal value k of 4 &1gJ"5 l , which is smaller than the observed 2 B value above, can be expected in case of uniaxial anisotropy and is therefore excluded. Thus, it is suggested that the anisotropy in Ho TGe 2 2 is rather of the easy plane type. A possible model which could explain the observed result is that both holmium moments residing on the two nonequivalent crystallographic positions slightly point out of the plane in an opposite manner (canted ferromagnet). The magnetic transition associated with the cusp-like peak at +40 K is possibly due to an
antiferromagnetic spin alignment. The holmium atoms are located at sites of the B -point symmetry 2 and do form ‘sheets’ parallel to the ac plane and hence we could expect the formation of rather complex noncollinear magnetic structures in the Ho TGe compounds, crystallizing in a monoclinic 2 2 structure type with low symmetry. A simple model to describe the observed magnetic behavior could be the following: The magnetic moments within one layer are coupled parallel whereas the intraplane coupling is antiparallel or almost antiparallel. In other words, the canting angle a of the two holmium sublattices is close to 180°. The positive values of h as well as the small upturn 1 in the imaginary part sA (see Fig. 2), which is generally not observed in pure collinear antiferromagnets, support such a simple model. The additional assumption that the canting angle a depends on both the applied field and the temperature (see the weak nonlinear dependency of M versus H at 35 K) is an indication that spin reorientation gradually sets in below the ‘Ne´el-type’ ordering temperature (spin-glass like behavior). Such a ‘spin-glass like’ state might occur as the result of competing ferro- and antiferromagnetic interactions as observed earlier in UCu Ge [11]. 2 2
60
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
3.2. Electrical resistivity
magnetically ordered systems is expected to fulfill the equation
In Fig. 4, the temperature dependence of the electrical resistivity o is shown for Ho TGe . If (T) 2 2 we assume the validity of Matthiesen’s rule, the total resistivity of magnetic materials can be written as
o "o !o "A¹a. (3) .!'(T) (T) 0 For an isotropic ferromagnet a is supposed to be close to factor 2 [12], whereas for ferromagnetic spirals or an antiferromagnet a can vary between 3 and 4 [13]. We have fitted our experimental data for the various restricted temperature ranges according to Eq. (3). The derived parameters are in reasonable accord with theory and have been listed in Table 2. Hence it is concluded that only electron scattering by spin waves is present and, as is often the case for anisotropic ferromagnets [14], an energy gap in the spin wave energy spectrum is not formed for the ferromagnetic state of Ho TGe . 2 2
o "o #o #o , (2) (T) 0 .!'(T) 1)(T) where o is the residual resistivity mainly arising 0 from the impurity scattering of the conduction electrons and o is the contribution of the resistivity 1)(T) due to phonon interactions. At low temperatures o is almost temperature-independent. o , on 1) .!'(T) the other hand, is the temperature-dependent socalled spin disorder resistivity. This part of o for (T)
Fig. 4. Temperature dependence of the electrical resistivity o for Ho TGe . Inset: do/d¹ versus ¹ plot. (T) 2 2
Table 2 Data of electrical resistivity for Ho TGe ; T"Ru, Os 2 2 Compound
(do/d¹) .!9 (K)
Temp. range (K)
o 0 (l) cm)
A (l)/Ka)
a
d (K)
o CF(=) (l) cm)
Ho RuGe 2 2
10 41 12.5 40
4.2—7.5 17—37 4.2—9 17—37
295 315 457 469
0.093 0.001 0.15 0.009
1.99 3.00 1.99 2.34
164
51.5
192
58.4
Ho OsGe 2 2
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
From the observed singularities in the derivative curves do /d¹, we were able to confirm the order(T) ing temperatures (see inset Fig. 4 and Table 2). These values are practically identical with the one’s found by AC susceptibility measurements above. We note that a value for a"2.3 in case of Ho OsGe is small for an antiferromagnetic 2 2 ground state. Hence, the possibility of spin-glass behavior must not be excluded a priori (see also magnetism). In the paramagnetic phase o for Ho TGe (T) 2 2 reveals an almost linear decrease when the temperature is lowered from 300 to +200 K, owing from a dominant electron phonon scattering process. Upon lowering the temperature further downwards o decreases more rapidly. In the paramagnetic (T) state, it is the influence of the crystal field on the resistivity, which makes the spin disorder resistivity temperature-dependent. Unfortunately, we have failed to produce the isostructural homologue of nonmagnetic La TGe in order to get an approx2 2 imate absolute value of o . Instead we tried to get 1) a rough estimate of the o by graphical extrapola.!' tion. The slope of the linear part of the high temperature (¹'200 K) of o is comparable with the (T) slope of the pure o [15]. Linear extrapolation 1)(T)
61
from just above the upper ordering temperature cuts the o-axis and gives an approximate value for o . Hence shifting the linear o contribution 41$ 1) through that point and subsequent subtraction of o give *o curves shown in Fig. 5, the values of *o (T) are of course arbitrary units. The so obtained resistivity *o shows a pronounced rise up to +150 and +200 K, respectively, and finally passes through shallow maxima. We associate the extra contribution up to the above mentioned temperatures with the possible interaction of conduction electrons and the crystalline field split levels of the 5I 8 seventeenfold degenerate Ho3` ground state in Ho TGe . Not knowing the exact 4f level scheme, 2 2 we use a single spacing, d, crystal-field model [16] for an order of magnitude estimate. A least-squares fit according to the equation 1 *o"o "o CF(T) CF(=)cosh2(d/2k¹)
(4)
provides a good description of the experimental data up to +250 K, as shown by solid line in Fig. 5, and leads to a crystal-field splitting of the first excited ‘multiplet’ of 164 and 192 K, respectively.
Fig. 5. Temperature dependence of the crystalline field split contribution of the resistivity *o after subtracting the residual phonon and spin disorder resistivity for Ho TGe . Thick line: extrapolated data, thin line: calculation according Eq. (4). 2 2
62
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
3.3. Magnetoresistivity The results of the magnetoresistivity defined as o !o (T,0) *o " (T,B) (T,B) o (T,0)
(5)
which was investigated in fields up to 1 T are presented in Figs. 6—8. As shown in Fig. 6, the magnetoresistivity in the ferromagnetic state is, as for any ferromagnetic system, negative for both compounds. In case of Ho RuGe *o/o is zero in low 2 2 field and decreases linearly with change of slope at B"0.4 T reaching a value of !1.5% at B"1 T. For Ho OsGe we observe a sharp drop of *o/o in 2 2 low field (B(0.1 T) and above it tends to level of reaching a saturation value of !2.5% at B"1 T. Having in mind that the negative *o/o is due to the effect that the external magnetic fields act on the magnetic moments reducing their thermal fluctuation, as a consequence, the resistivity decreases in applied magnetic fields. It is inferred that the magnetocrystalline anisotropy thereby is somewhat stronger in Ho RuGe . 2 2 In Fig. 7, the temperature dependence of the resistivity o is shown in zero field and B"1 T (T) and Fig. 8 reveals the temperature dependence of
Fig. 6. Magnetoresistivity *o/o versus magnetic field for Ho TGe at ¹"5 K. 2 2
the magnetoresistivity for both compounds at B"1 T. *o/o is negative for the whole temperature range and becomes zero way above the higher ordering temperatures, which we attribute to short-range order phenomena. At the magnetic transition temperatures *o/o curves exhibit minima
Fig. 7. Temperature dependence of o in zero field and B"1 T for Ho TGe . 2 2
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
63
Fig. 8. Temperature dependence of the magnetoresistivity for Ho TGe measured in B"1 T. 2 2
associated with spin disorder scattering at ¹ or C ¹ , as well. The discrepancies of the position of the N lower minima and the ¹ values observed above is C obviously due to the dependence of the Curie temperature on the magnetic field. The marked reduction of the magnetoresistivity in the temperature range between the two ordering points is again an indication for a weakening of *o/o caused by a spin disorder scattering due to the strong random magnetic structure of a spin-glass like state [11].
small exponential factor a in case of Ho OsGe , 2 2 remain and are an indication for spin-glass like behavior. In the paramagnetic region for both compounds, an important contribution to the total resistivity due to a possible interaction of the conduction electrons with crystalline field split energy levels is encountered. The magnetoresistivity is negative as expected for magnetically ordered systems and reduced between ¹ and ¹ owing from N C a random spin structure caused by the competing ferro- and antiferromagnetic interactions.
4. Conclusions Acknowledgements We have measured the magnetic AC susceptibility, magnetization versus field, the electrical resistivity and magnetoresistivity for the compounds Ho RuGe and Ho OsGe . Both samples show 2 2 2 2 two magnetic transitions. The ordering at the lower transition temperature is certainly due to ferromagnetic spin alignment. The transition at the upper temperature is at this stage not quite clear. Some arguments are in favor of an antiferromagnetic ground state with possibly a rather complex magnetic structure. A few contradictions, e.g. the kink in the imaginary part of the AC susceptibility, weak nonlinear magnetization just below ¹ and the N
This research has been sponsored in part by the Austrian Science Foundation FWF under grant P8218. K.H. is grateful to the Austrian—French Scientific Program PICS-134 for a one month stay in Rennes, France. Thanks are due to Dr. H. Noe¨l for the use of the SQUID. References [1] E. Parthe´, B. Chabot, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 6, Elsevier, Amsterdam, 1984, p. 113.
64
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
[2] E. Gladyshevsky, O. Bodak, V.K. Pecharski, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 13, Elsevier, Amsterdam, 1990, p. 1. [3] D.C. Johnston, H.F. Braun, in: M.B. Maple, ". Fischer (Eds.), Topics in Current Physics — Superconductivity in Ternary Compounds II, Springer, Berlin, 1982, p. 11. [4] A. Szytula, J. Leciejewicz, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 12, Elsevier, Amsterdam, 1989, p. 133. [5] V. Sechovsky, L. Havela, in: E.P. Wohlfahrt, K.H.J. Buschow (Eds.), Handbook of Magnetic Materials, vol. 4, North Holland, Amsterdam, 1988, p. 309. [6] N. Grewe, F. Steglich, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 14, Elsevier, Amsterdam, 1991, p. 343.
[7] M. Lo¨wenhaupt, K.H. Fischer, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 16, Elsevier, Amsterdam, 1993, p. 1. [8] E.V. Sampathkumaran, P.L. Paulose, R. Mallik, Phys. Rev. B 54 (6) (1996) R3710. [9] O. Sologub, K. Hiebl, P. Rogl, O. Bodak, J. Alloys Comp. 227 (1995) 37. [10] O. Sologub, K. Hiebl, P. Rogl, H. Noe¨l, J. Alloys Comp. 245 (1996) L13. [11] A.K. Nigam, S.B. Roy, Girish Chandra, Phys. Rev. B 49 (2) (1994)-II 1127. [12] T. Kasuya, Prog. Theor. Phys. 22 (2) (1959) 227. [13] Y. Suezaki, H. Mori, Phys. Lett. 28A (1) (1968) 70. [14] A.R. Mackintosh, Phys. Lett. 4 (2) (1963) 140. [15] E. Gratz, M.J. Zuckermann, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 5, Elsevier, Amsterdam, 1982, p. 137. [16] T. Van Peski-Tinbergen, A.S. Dekker, Physica 29 (1963) 917.
Electrical resistivity and magnetic properties of the ternary compounds Ho TGe ; T"Ru, Os 2 2 K. Hiebl!,*, O. Sologub" ! Institut fu( r Physikal. Chemie der Universita( t Wien, Wa( hringerstra}e 42, A-1090 Wien, Austria " Department of Inorg. Chemistry, L+viv University, Kyryla i Mefodia ul. 6, 290005 L+viv, Ukraine Received 4 February 1997; received in revised form 15 April 1997
Abstract We have performed an investigation of the magnetic properties of the new compounds Ho (Ru,Os)Ge , which 2 2 crystallize in the monoclinic structure-type Sc CoSi (space-group B2/m), using an AC susceptometer. Both compounds 2 2 undergo possibly antiferromagnetic transitions at ¹ +40 K; subsequent spin-reorientations towards a ferromagnetic N spin alignment occur at temperatures below 20 K. From isothermal (¹"5 K) magnetization measurements versus external field (k H"0—3 T) an ordered moment of 5.2 l has been derived for both samples. In the paramagnetic region 0 B effective moments close to the ideal free Ho3` ion moment (k "10.6 l ) were deduced, the h values being positive. The %&& B 1 temperature dependence of the electrical resistivity reveals pronounced changes of slope at the ordering temperatures ¹ and ¹ . The maxima of do/d¹ versus ¹ are in agreement with magnetic data above. For the paramagnetic region N C a deflection of the generally linear o—¹ plot of nonmagnetic metallic systems is observed, which could be attributed to the influence of the crystalline field split levels of the seventeenfold degenerate Ho3` ground-state 5I . Not knowing the exact 8 4-f level scheme, we use a single spacing (d) crystal-field model for an order of magnitude estimate. The results of the negative magnetoresistivity data are due to the reduced spin disorder scattering in the ordered state. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 61.10; 72.15; 75.20; 75.30 Keywords: Magnetic properties; Electrical resistivity; Magnetoresistivity
1. Introduction In recent years, a great amount of research work has been dedicated to the ternary compounds
* Corresponding author: Tel.: #43 1 31367 2504; fax: #43 1 310 45 97; e-mail: [email protected].
M—T—X, where M is a rare-earth or an actinide ion, T a transition metal and X is Al, Ga, In, Si, Ge, Sn, P, As and Sb, respectively. Phase equilibria and structural chemistry data show a wide variety of stoichiometric compositions crystallizing in a manifold of distinct structure types [1,2]. Concerning the physical properties, these systems became a fantastic playground for many research
0304-8853/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 0 6 6 - 3
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
57
groups, since a lot of interesting phenomena are exhibited. Among these phenomena are, e.g., reentrant superconductivity [3], complex magnetic structures [4,5], heavy-fermion behavior [6], valence fluctuations and Kondo lattice formation [7] or magnetoresistance anomalies [8]. Holmium is the ion bearing the largest effective moment among the rare-earth elements and therefore plays an important role in the interplay of RE3` magnetism and 4d, 5d element superconductivity. Thus, the investigation of the magnetic properties and the electrical resistivity of two new compounds with composition 2 : 1 : 2 became the subject of the present paper.
to 3 T. Measurements of the electrical resistivity were done with a general four probe Lake-Shore AC resistivity option ( f"133 Hz, i"10 mA) in the temperature range 4.2—300 K and in applied magnetic fields up to 1 T. The alloy buttons were cut by diamond saw (Bu¨hler Isomet) into barshaped samples with the dimensions of ca. 1] 1]5 mm3. Electrical contacts were made using commercial silver paint and 25 l Cu wires. All calculations concerning the magnetic and electrical resistivity data were performed using the program TableCurve 2D (Jandel Corp.) and the goodness-of-fit coefficient r2 was in any case better than 0.993.
2. Experimental details
3. Results and discussion
Sample preparation was performed by arc melting under argon ingots of the elements of 99.9 mass% minimum purity, each alloy button with a total weight of ca. 1 g. For further details of heat treatment and on X-ray powder techniques concerning structural characterization, the reader is kindly referred to an article recently published on a related series of compounds [9]. Both compounds were found to crystallize in a monoclinic cell with the structure type of Sc CoSi , space2 2 group B2/m [10]. Unit cell parameters are listed in Table 1. The magnetic properties were studied by use of a Faraday balance, SUS-10, in the temperature range 80—500 K in external fields up to 1.3 T, a Lake-Shore AC susceptometer, AC 7000 ( f"133 Hz and H "1 mT) for temperatures AC 4.2 K(¹(100 K as well as a SHE-SQUID magnetometer at ¹"5 K and 35 K as well as fields up
3.1. Magnetism Generally, we observe that the magnetic properties of both compounds Ho RuGe and Ho OsGe 2 2 2 2 are quite alike. Fig. 1 shows the paramagnetic region and the susceptibility clearly obeys linear dependence of temperature due to the Curie—Weiss law for ¹'80 K. The data were fitted using the formula C s" #s , 0 ¹!h 1
(1)
where C is the Curie constant, h the paramagnetic 1 Curie temperature and s denotes temperature-in0 dependent contributions such as core diamagnetism, Landau diamagnetism and Pauli paramagnetism. The results are listed in Table 1 and the derived
Table 1 Crystallographic and magnetic data of Ho TGe ; T"Ru, Os 2 2 Compound
Lattice parameters, nm
k %&& (l ) B
h 1 (K)
¹ N (K)
¹ C (K)
p (l ) B
a
b
c
Ho RuGe 2 2
1.06732(5)
0.4249(7)
10.7
13.4
40.7
7.5
5.2
Ho OsGe 2 2
1.0691(2)
1.020(1) c"118.0(1)° 1.0050(2) c"118.07(1)°
0.42618(7)
10.5
15.0
39.6
12.9
5.2
58
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
Fig. 1. Reciprocal gram susceptibility versus temperature for Ho TGe symbols: measured data, solid line: calculated data (Eq. (1)). 2 2
Fig. 2. AC susceptibility versus temperature for Ho TGe . 2 2
value for the effective moment k thereby was %&& found to agree well with the theoretical value of the tripositive Ho3` free ion moment. The values of v are of &10~5 cm3/mole and therefore negli0 gible. Fig. 2 reveals the temperature plot of the AC susceptibility. Two pronounced maxima of the real
part s@ are encountered around 40 K and below 20 K for both samples, indicating two consecutive magnetic transitions. Certainly the lower transition is stemming from a parallel spin alignment of reduced moments (ferromagnet). This is confirmed from the isothermal magnetization, M versus magnetic field curve (see Fig. 3). The values of M tend
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
59
Fig. 3. Isothermal magnetization versus applied field at ¹"5 K and ¹"35 K for Ho TGe . 2 2
to saturate in applied fields k H'2.0 T at 0 ¹"5 K, which is, however, close to the Curie points. At lower temperatures we can expect the M curves to saturate at much lower fields indic(H) ating a rather weak magnetocrystalline anisotropy for these samples. The magnetization of both compounds reaches values of 99 and 89 Am2/kg in high field, and hence an ordered moment k of 5.2 l can 4 B be derived. The values of the remanent magnetization as can be seen from Fig. 3 are rather small (&10% of M ), leading to a remanent mo(H/3T) ment of 0.5 and 0.7 l , respectively. Assuming that B our measurements performed on polycrystalline bulk specimens represent the response of a randomly oriented fixed powder, a maximal value k of 4 &1gJ"5 l , which is smaller than the observed 2 B value above, can be expected in case of uniaxial anisotropy and is therefore excluded. Thus, it is suggested that the anisotropy in Ho TGe 2 2 is rather of the easy plane type. A possible model which could explain the observed result is that both holmium moments residing on the two nonequivalent crystallographic positions slightly point out of the plane in an opposite manner (canted ferromagnet). The magnetic transition associated with the cusp-like peak at +40 K is possibly due to an
antiferromagnetic spin alignment. The holmium atoms are located at sites of the B -point symmetry 2 and do form ‘sheets’ parallel to the ac plane and hence we could expect the formation of rather complex noncollinear magnetic structures in the Ho TGe compounds, crystallizing in a monoclinic 2 2 structure type with low symmetry. A simple model to describe the observed magnetic behavior could be the following: The magnetic moments within one layer are coupled parallel whereas the intraplane coupling is antiparallel or almost antiparallel. In other words, the canting angle a of the two holmium sublattices is close to 180°. The positive values of h as well as the small upturn 1 in the imaginary part sA (see Fig. 2), which is generally not observed in pure collinear antiferromagnets, support such a simple model. The additional assumption that the canting angle a depends on both the applied field and the temperature (see the weak nonlinear dependency of M versus H at 35 K) is an indication that spin reorientation gradually sets in below the ‘Ne´el-type’ ordering temperature (spin-glass like behavior). Such a ‘spin-glass like’ state might occur as the result of competing ferro- and antiferromagnetic interactions as observed earlier in UCu Ge [11]. 2 2
60
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
3.2. Electrical resistivity
magnetically ordered systems is expected to fulfill the equation
In Fig. 4, the temperature dependence of the electrical resistivity o is shown for Ho TGe . If (T) 2 2 we assume the validity of Matthiesen’s rule, the total resistivity of magnetic materials can be written as
o "o !o "A¹a. (3) .!'(T) (T) 0 For an isotropic ferromagnet a is supposed to be close to factor 2 [12], whereas for ferromagnetic spirals or an antiferromagnet a can vary between 3 and 4 [13]. We have fitted our experimental data for the various restricted temperature ranges according to Eq. (3). The derived parameters are in reasonable accord with theory and have been listed in Table 2. Hence it is concluded that only electron scattering by spin waves is present and, as is often the case for anisotropic ferromagnets [14], an energy gap in the spin wave energy spectrum is not formed for the ferromagnetic state of Ho TGe . 2 2
o "o #o #o , (2) (T) 0 .!'(T) 1)(T) where o is the residual resistivity mainly arising 0 from the impurity scattering of the conduction electrons and o is the contribution of the resistivity 1)(T) due to phonon interactions. At low temperatures o is almost temperature-independent. o , on 1) .!'(T) the other hand, is the temperature-dependent socalled spin disorder resistivity. This part of o for (T)
Fig. 4. Temperature dependence of the electrical resistivity o for Ho TGe . Inset: do/d¹ versus ¹ plot. (T) 2 2
Table 2 Data of electrical resistivity for Ho TGe ; T"Ru, Os 2 2 Compound
(do/d¹) .!9 (K)
Temp. range (K)
o 0 (l) cm)
A (l)/Ka)
a
d (K)
o CF(=) (l) cm)
Ho RuGe 2 2
10 41 12.5 40
4.2—7.5 17—37 4.2—9 17—37
295 315 457 469
0.093 0.001 0.15 0.009
1.99 3.00 1.99 2.34
164
51.5
192
58.4
Ho OsGe 2 2
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
From the observed singularities in the derivative curves do /d¹, we were able to confirm the order(T) ing temperatures (see inset Fig. 4 and Table 2). These values are practically identical with the one’s found by AC susceptibility measurements above. We note that a value for a"2.3 in case of Ho OsGe is small for an antiferromagnetic 2 2 ground state. Hence, the possibility of spin-glass behavior must not be excluded a priori (see also magnetism). In the paramagnetic phase o for Ho TGe (T) 2 2 reveals an almost linear decrease when the temperature is lowered from 300 to +200 K, owing from a dominant electron phonon scattering process. Upon lowering the temperature further downwards o decreases more rapidly. In the paramagnetic (T) state, it is the influence of the crystal field on the resistivity, which makes the spin disorder resistivity temperature-dependent. Unfortunately, we have failed to produce the isostructural homologue of nonmagnetic La TGe in order to get an approx2 2 imate absolute value of o . Instead we tried to get 1) a rough estimate of the o by graphical extrapola.!' tion. The slope of the linear part of the high temperature (¹'200 K) of o is comparable with the (T) slope of the pure o [15]. Linear extrapolation 1)(T)
61
from just above the upper ordering temperature cuts the o-axis and gives an approximate value for o . Hence shifting the linear o contribution 41$ 1) through that point and subsequent subtraction of o give *o curves shown in Fig. 5, the values of *o (T) are of course arbitrary units. The so obtained resistivity *o shows a pronounced rise up to +150 and +200 K, respectively, and finally passes through shallow maxima. We associate the extra contribution up to the above mentioned temperatures with the possible interaction of conduction electrons and the crystalline field split levels of the 5I 8 seventeenfold degenerate Ho3` ground state in Ho TGe . Not knowing the exact 4f level scheme, 2 2 we use a single spacing, d, crystal-field model [16] for an order of magnitude estimate. A least-squares fit according to the equation 1 *o"o "o CF(T) CF(=)cosh2(d/2k¹)
(4)
provides a good description of the experimental data up to +250 K, as shown by solid line in Fig. 5, and leads to a crystal-field splitting of the first excited ‘multiplet’ of 164 and 192 K, respectively.
Fig. 5. Temperature dependence of the crystalline field split contribution of the resistivity *o after subtracting the residual phonon and spin disorder resistivity for Ho TGe . Thick line: extrapolated data, thin line: calculation according Eq. (4). 2 2
62
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
3.3. Magnetoresistivity The results of the magnetoresistivity defined as o !o (T,0) *o " (T,B) (T,B) o (T,0)
(5)
which was investigated in fields up to 1 T are presented in Figs. 6—8. As shown in Fig. 6, the magnetoresistivity in the ferromagnetic state is, as for any ferromagnetic system, negative for both compounds. In case of Ho RuGe *o/o is zero in low 2 2 field and decreases linearly with change of slope at B"0.4 T reaching a value of !1.5% at B"1 T. For Ho OsGe we observe a sharp drop of *o/o in 2 2 low field (B(0.1 T) and above it tends to level of reaching a saturation value of !2.5% at B"1 T. Having in mind that the negative *o/o is due to the effect that the external magnetic fields act on the magnetic moments reducing their thermal fluctuation, as a consequence, the resistivity decreases in applied magnetic fields. It is inferred that the magnetocrystalline anisotropy thereby is somewhat stronger in Ho RuGe . 2 2 In Fig. 7, the temperature dependence of the resistivity o is shown in zero field and B"1 T (T) and Fig. 8 reveals the temperature dependence of
Fig. 6. Magnetoresistivity *o/o versus magnetic field for Ho TGe at ¹"5 K. 2 2
the magnetoresistivity for both compounds at B"1 T. *o/o is negative for the whole temperature range and becomes zero way above the higher ordering temperatures, which we attribute to short-range order phenomena. At the magnetic transition temperatures *o/o curves exhibit minima
Fig. 7. Temperature dependence of o in zero field and B"1 T for Ho TGe . 2 2
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
63
Fig. 8. Temperature dependence of the magnetoresistivity for Ho TGe measured in B"1 T. 2 2
associated with spin disorder scattering at ¹ or C ¹ , as well. The discrepancies of the position of the N lower minima and the ¹ values observed above is C obviously due to the dependence of the Curie temperature on the magnetic field. The marked reduction of the magnetoresistivity in the temperature range between the two ordering points is again an indication for a weakening of *o/o caused by a spin disorder scattering due to the strong random magnetic structure of a spin-glass like state [11].
small exponential factor a in case of Ho OsGe , 2 2 remain and are an indication for spin-glass like behavior. In the paramagnetic region for both compounds, an important contribution to the total resistivity due to a possible interaction of the conduction electrons with crystalline field split energy levels is encountered. The magnetoresistivity is negative as expected for magnetically ordered systems and reduced between ¹ and ¹ owing from N C a random spin structure caused by the competing ferro- and antiferromagnetic interactions.
4. Conclusions Acknowledgements We have measured the magnetic AC susceptibility, magnetization versus field, the electrical resistivity and magnetoresistivity for the compounds Ho RuGe and Ho OsGe . Both samples show 2 2 2 2 two magnetic transitions. The ordering at the lower transition temperature is certainly due to ferromagnetic spin alignment. The transition at the upper temperature is at this stage not quite clear. Some arguments are in favor of an antiferromagnetic ground state with possibly a rather complex magnetic structure. A few contradictions, e.g. the kink in the imaginary part of the AC susceptibility, weak nonlinear magnetization just below ¹ and the N
This research has been sponsored in part by the Austrian Science Foundation FWF under grant P8218. K.H. is grateful to the Austrian—French Scientific Program PICS-134 for a one month stay in Rennes, France. Thanks are due to Dr. H. Noe¨l for the use of the SQUID. References [1] E. Parthe´, B. Chabot, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 6, Elsevier, Amsterdam, 1984, p. 113.
64
K. Hiebl, O. Sologub / Journal of Magnetism and Magnetic Materials 186 (1998) 56—64
[2] E. Gladyshevsky, O. Bodak, V.K. Pecharski, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 13, Elsevier, Amsterdam, 1990, p. 1. [3] D.C. Johnston, H.F. Braun, in: M.B. Maple, ". Fischer (Eds.), Topics in Current Physics — Superconductivity in Ternary Compounds II, Springer, Berlin, 1982, p. 11. [4] A. Szytula, J. Leciejewicz, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 12, Elsevier, Amsterdam, 1989, p. 133. [5] V. Sechovsky, L. Havela, in: E.P. Wohlfahrt, K.H.J. Buschow (Eds.), Handbook of Magnetic Materials, vol. 4, North Holland, Amsterdam, 1988, p. 309. [6] N. Grewe, F. Steglich, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 14, Elsevier, Amsterdam, 1991, p. 343.
[7] M. Lo¨wenhaupt, K.H. Fischer, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 16, Elsevier, Amsterdam, 1993, p. 1. [8] E.V. Sampathkumaran, P.L. Paulose, R. Mallik, Phys. Rev. B 54 (6) (1996) R3710. [9] O. Sologub, K. Hiebl, P. Rogl, O. Bodak, J. Alloys Comp. 227 (1995) 37. [10] O. Sologub, K. Hiebl, P. Rogl, H. Noe¨l, J. Alloys Comp. 245 (1996) L13. [11] A.K. Nigam, S.B. Roy, Girish Chandra, Phys. Rev. B 49 (2) (1994)-II 1127. [12] T. Kasuya, Prog. Theor. Phys. 22 (2) (1959) 227. [13] Y. Suezaki, H. Mori, Phys. Lett. 28A (1) (1968) 70. [14] A.R. Mackintosh, Phys. Lett. 4 (2) (1963) 140. [15] E. Gratz, M.J. Zuckermann, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 5, Elsevier, Amsterdam, 1982, p. 137. [16] T. Van Peski-Tinbergen, A.S. Dekker, Physica 29 (1963) 917.