Magnetotransport and magnetocaloric effects in intermetallic compounds - Chapter 6 Electrical-transport properties of GdT2Si2 compounds

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Magnetotransport and magnetocaloric effects in intermetallic compounds

Duijn, H.G.M.

Publication date

2000

Link to publication

Citation for published version (APA):

Duijn, H. G. M. (2000). Magnetotransport and magnetocaloric effects in intermetallic

compounds.

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Chapterr 6

Electrical-transportt properties

off GdT

₂

SÏ2 compounds

6.11 Introduction

Inn section 2.2.2, we discussed two origins of spin-polarised transport in bulk intermetallicc compounds. It may arise from band-structure effects as well as from magnetic interactions.. In the former case the spin-dependent-scattering probability is due to a different densityy of possible final states for the spin-up and spin-down electrons, while in the latter case itt is due to a difference in the scattering amplitudes. In any case, the electrical-transport propertiess are intimately linked with the magnetic structure and the magnetic properties of the intermetallicc compounds. Moreover, since the electrical resistivity as well as the magnetic propertiess are dominated by the electronic structure, investigation of the mutual influence of bothh properties may contribute to the basic understanding of the solid-state properties, especiallyy the electronic structure [6.1].

Onee of the many series of intermetallic compounds that have attracted much attention iss the series of ternary compounds with the general chemical formula RT2X2, where R is a rare-earthh element, T is a 3d, Ad or 5d element, and X is Si or Ge. During the last two decades, aa few hundred of these RT2X2 compounds have been studied extensively by means of a varietyy experimental techniques. The RT2X2 series exhibit prolific physical properties, like superconductivityy and heavy-fermion behaviour, and have a variety of magnetic structures. Forr a review of the magnetic properties of RT2X2 compounds we refer to Szytula and Leciejewiczz [6.2], and Szytula [6.3]. The present chapter is devoted to GdT2Si2 compounds, withh T = Cu, Ru, Rh, Pd, Ag, Os, Ir, Pt, Au, and the related compound GdGe2Al2. The Gd sublatticee of these compounds orders antiferromagnetically at low temperatures, and can be alignedd ferromagnetically by application of a magnetic field of the order of 10 T. The T sublatticee does not carry a (large) magnetic moment. We have carried out resistivity measurementss as a function of both temperature and magnetic field. The results are compared withh the results of magnetisation measurements performed by Tung et al. [6.4].

Mostt GdT2Si2 compounds crystallise in the body-centred tetragonal ThCr2Si2-type of structuree (space group I Almmm). A schematic drawing of the structure is given in figure 6.1. Thee Gd atoms occupy only a single crystallographic site (2a, position (0, 0, 0)). The structure

Chapterr 6 cann be described in terms of successive layers off atoms that vary along the c axis as —R— X—T—X—R—.. The compound GdPt2Si2 formss an exception, as it crystallises in the relatedd CaBe2Ge2-type of structure (space groupp P Alnmrn). This structure basically is characterisedd by a different stacking order of thee R, T and X layers. In both crystal structures,, the ratio of the lattice parameters clacla equals about 2.5, thus one may expect anisotropyy of the physical properties. In the basall plane the smallest Gd-Gd distance is aboutt 4 A, while between these planes it is aboutt 6 A. Hence, the pair-wise exchange interactionss between the Gd moments in GdT2Si22 compounds are expected to depend stronglyy on the orientation of the pairs under consideration.. Due to the s-character of the 4/ electronicc shell of Gd, crystalline-electric-field effectss are not expected to play an important role.. Thus, in GdT2Si2 compounds the (anisotropic)) magnetic properties are determinedd by exchange interactions.

Tungg et al. [6.4] have analysed the magneticc properties of GdT2Si2 compounds using a model that takes into account nearest and next-nearestt neighbour exchange interactions. In general, these exchange interactions depend ratherr erratically on the lattice parameters and the volume. They concluded that in some cases additionall exchange interactions cannot be neglected, the competition among the several interactionss leading to complex magnetic behaviour. Then, a relatively small anisotropy producedd by an electric-field gradient may influence the magnetic properties of GdT2Si2 compounds. .

Fromm Mössbauer studies [6.5] a general trend in the electric-field gradient VK is found. Uponn filling of the transition-metal band in GdT2Si2, VH at the Gd nuclei changes from stronglyy negative to zero or even becomes positive. Band-structure calculations [6.6] have shownn that Vu is determined to a large extent by the asphericity of the 6p and 5d shells. As the

/^-electronn density close to the nucleus is much larger than the J-electron density, VK mainly originatess from the p electrons. The behaviour of VH has been explained in terms of hybridisationn of the Gd p and d states on the one hand, and the T-metal d states on the other handd [6.6]. The centres of the Gd 6p and 5d bands are situated above the Fermi level, whereas thee centres of the d band of the T atom are situated below the Fermi level and lower in energy whenn going towards the end of each T series. This implies that the hybridisation between the Figuree 6.1. Schematic drawing of GdT2Si2

Gdd valence states and the T-atom d states, which leads to the formation of bonding orbital s withh large density of states at the Gd and T atoms, becomes weaker towards the end of each transition-metall series. As the p electrons take part in both hybridisation and electrical conductivity,, a larger anisotropy in electrical conductivity is expected for the compounds of earlyy transition-metals. Indeed, for the compound GdRu2Si2 anisotropic magnetic properties havee been reported [6.7]. Later on in this chapter, we will describe the results of magnetoresistancee measurements on GdOs2Si2 in terms of anisotropic magnetic interactions, similarr to those of GdRu2Si2. However, as we have performed electrical-resistivity measurementss on polycrystalline samples, a solid study of the anisotropic magnetic properties iss not possible.

6.22 Experimental

Forr electrical-resistivity measurements, polycrystalline samples with dimensions 1 x 1 x 44 mm3 were cut from batches used previously by Tung et al. [6.4] for magnetisation measurements.. These batches were prepared by arc-melting the pure starting materials of at leastt 99.9 at.% purity in a Ti-gettered atmosphere, followed by annealing in evacuated quartz ampouless for several weeks at 800 °C. The annealed samples were investigated by means of X-rayy diffraction and were found to be single phase. The contacts were welded on the samples ass described in section 3.3. The temperature dependence of the electrical resistivity was measuredd between 4.2 and 300 K in a home-built equipment. The electrical resistance in magneticc fields up to 5 T was measured with a home-built insert placed in a Quantum Design MPMSS cryostat. In both equipments, a standard four-point ac-technique was used to measure thee electrical resistivity. The magnetoresistance was measured in magnetic fields up to 38 T in thee high-Field installation at the University of Amsterdam, by means of a four-point dc-method. .

Thee field dependence of the magnetisation at 4.2 K was measured by Tung et al. [6.4] eitherr up to 20 or 35 T in the high-field installation at the University of Nijmegen or at the Universityy of Amsterdam, respectively. The measurements were performed on fine powder samples,, consisting of particles that are free to rotate in the sample holder.

6.33 Results and discussion

Inn this section, for each compound we describe the obtained electrical-resistivity curves.. The results are compared with the magnetisation measurements of Tung et al. [6.4]. Furthermore,, the obtained results are discussed in relation to the magnetic structure if known. Thee transition temperatures and magnetic structures are presented in table 6.1. Some general conclusionss are given in section 6.4.

Chapterr 6 Compound d GdCu2Si2 2 GdRu2Si2 2 GdRh2Si2 2 GdPd2Si2 2 GdAg2Si2 2 GdOs2Si2 2 GdIr2Si2 2 GdPt2Si2 2 GdAu2Si2 2 GdGe2Al2 2 TN(K) ) Res s 10.7(3) ) 44.2(5) ) 95(3) ) 15(1) ) 16.6(2) ) 26.2(5) ) 78(1) ) 9.6(2) ) 10(1) ) 20(1) ) TN(K) ) Tungg [6.4] 13 3 45.4 4 106 6 16.5 5 15.7 7 28.5 5 82.4 4 9.3 3 14.7 7 19.7 7 TN(K) ) MaxM M 13(1) ) 42(2) ) 106(5) ) 18.3(10) ) 17(2) ) 29(2) ) 82.7(10) ) 9-7(5) ) 14.2(10) ) 21(2) ) TN(K) ) Maxx dM/dT 9(1) ) 40(2)* * 100(5) ) 15(2)* * 17(2)* * 26(2) ) 78(1) ) 9(1)* * 11(2) ) 19(2)* * T„(K) ) Res s — — 36.3(5) ) 22(1)? ? 10;; 12 9(1) ) — — 14(1)? ? 6.7(2) ) — — ? ? T0(K) ) Mag g — — 36(2) ) 17? ? 10(2) ) 8(1) ) — — 15(1)? ? 6.5(5) ) — — 12(2)? ? Typee of ordering g F-L F-L S-M M F-L L F-L L S-M M F-L L F-L L S-M M F-L L F-L L

Tablee 6.1. Néel temperatures TN and spin-reorientation temperatures T0 of GdT2Si2 compounds obtainedd from electrical-resistivity and magnetisation measurements. The various methods to determinee the ordering temperatures are explained in the text. Temperatures marked with * were difficultt to determine. Last column: type of behaviour near the ordering temperature. F-L: Fisher and Langerr type [6.9]; S-M: Suezaki and Mori type [6.15].

temperaturee curves. In all cases, the samples show metallic behaviour, i.e.: dp/dT>0 above 1000 K. The obtained values of the room-temperature resistivity are rather high (55 to 8000 u.£2cm), which we attribute to cracks in the samples. As the reported room-temperature resistivityy of RT2X2 compounds is typically lower than 100 u,Qcm, we have normalised the resistivityy curves to their room-temperature value. Around the ordering temperature, magnetic interactionss give rise to various kinds of resistivity behaviour. In the absence of a general modell for determining the ordering temperature from the resistivity, there is some ambiguity inn choosing TN. We have considered the measured curve for each compound separately, taking intoo account the behaviour of the temperature derivative described with the critical exponents ass discussed in section 2.2.3. As seen in table 6.1, the ordering temperatures reported by Tung ett al. [6.4] are systematically higher than those obtained from resistivity. However, the determinationn of TN from magnetisation measurements has some ambiguity, too. The commonlyy used method is taking TN as the temperature where M(T) has a maximum. Alternatively,, TN can be defined as the temperature where dM/dT has a maximum [6.8]. The resultss of both methods are also given in table 6.1. For the GdT2Si2 compounds with T = Ru, Pd,, Ag and Pt, and for GdGeiAb, the determination of TN is complicated as these compounds havee an additional magnetic transition close to the ordering temperature. Generally, the latter definitionn of TN is in better agreement with the results of resistivity measurements. At the lowestt temperatures, there is often a considerable temperature dependence of the electrical resistivityy due to magnetic interactions. Therefore, we have not determined the residual resistancee ratio's.

Second,, the magnetoresistance curves obtained in the Amsterdam high-field installationn have substantial noise, especially at high fields. Therefore, the obtained data have

0.50 0 0.455 -fc-COO 0 . 4 0 CT> CT> C\] ] 0.35 5 0.30 0 0.25 5 ;; o --ii i i | i i i i | r i

~j\~j\

;

// 1

GdCuu Si

Figuree 6.2. Temperature dependence of the normalised electrical resistivity of GdCu2Si2 at low temperatures.. Top inset: Temperature derivative of the electrical resistivity at low temperatures. Bottomm inset: Electrical resistivity versus temperature for 4.2 < T < 300 K.

beenn averaged, resulting in the curves presented in the figures to follow. Still, considerable noisee is present in the magnetoresistance curves. Additionally, field pulses with zero measuringg current through the samples still yielded a significant induction voltage, that is roughlyy linear in field. The magnetoresi stance curves have been corrected for this contribution,, yielding, for example, a correction of 30 % in the magnetoresi stance at 20 T of thee compound GdGe2Al2. Thus, the accuracy in the absolute values of the magnetoresistance iss limited, and the curves mainly reflect the qualitative behaviour of the magnetoresistance.

GdCu2Si2 2

Thee temperature dependence of the electrical resistivity of GdCu2Si2 is given in figure 6.2.. With decreasing temperature, the resistivity shows a strong decrease at the ordering temperaturee arising from magnetic correlations. Hence, the temperature derivative of the electricall resistivity given in the top inset of figure 6.2, shows a pronounced maximum. Accordingg to the theory of Fisher and Langer [6.9], that states that the anomalous behaviour of thee electrical resistivity near the ordering temperature is determined largely by short-range ratherr than by long-range spin fluctuations, dp/dT has a sharp peak at the ordering temperature.. Hence, we determined the magnetic ordering temperature of GdCu2Si2 to be TNN = 10.7(3) K, which is somewhat lower than the value of 13 K reported by Tung et al. [6.4] derivedd from magnetisation measurements. Note that originally Fisher and Langer derived theirr theory for ferromagnetic compounds. However, neutron-diffraction experiments demonstratedd that the compound GdCu2Si2 orders antiferromagnetically with q = (1/2, 0, 1/2),

0.15 5 0.10 0 .Q. .

"o. .

< <

B(T) )

Figuree 6.3. Left axis: Magnetoresistance of polycrystalline GdCuiSi2 at 4.2 K for magnetic fields appliedd along the measuring current. Right axis: Magnetisation of free-powder of GdCu2Si2 taken fromm Tung et al. [6.4].

thee magnetic moment of 7.2(4) Ha/Gd pointing along the [010] direction [6.10]. The electrical resistivityy of GdCu2Si2 has been reported previously by Sampathkumaran and Das [6.11], and Barandiarann et al. [6.10]. The latter group obtained a room-temperature resistivity of 20 |jX2cm andd a Néel temperature of 12.5 K, TN being defined as the point where the temperature derivativee of the electrical resistivity changes slope. We would denote this method rather as a definitionn of a sort of 'onset' temperature of the ordering. As can be seen in the top inset of figuree 6.2, our results yield a similar value for the 'onset' temperature as that obtained by Barandiarann et al. [6.10].

Thee magnetoresistance (p(B)-p(0))/p(0) = Ap/p of GdCu2Si2 measured at 4.2 K in fieldss up to 18 T is given in figure 6.3. The curve is compared with the results of a magnetisationn measurement performed by Tung et al. [6.4], With increasing field, the magnetoresistancee approximately linearly increases to a value of 14 % at 14.5 T. Next, a considerablee reduction of the resistivity of 5 % is observed, which corresponds to the antiferromagneticc to ferromagnetic transition, showing up as a kink in magnetisation. The measuredd magnetoresistance curve exhibits pronounced behaviour, and theoretical models thatt link the magnetoresistance with the magnetisation like that of Van Peski-Tinbergen et al. (sectionn 2.2.3) fail to describe the observed behaviour. One might attribute the decrease of the resistivityy at the antiferromagnetic to ferromagnetic transition to vanishing superzone boundariess at the Fermi surface. However, then one should also expect an upturn in the temperaturee dependence of the resistivity around the ordering temperature, which is clearly absentt in figure 6.2.

CO O

O) )

CM M

a. a.

T(K) )

Figuree 6.4. Temperature dependence of the normalised electrical resistivity of GdRu2Si2 at low

temperatures.. Top inset: Temperature derivative of the electrical resistivity at low temperatures. Bottomm inset: Electrical resistivity versus temperature for 4.2 < T < 300 K.

GdRu2Si2 2

Thee temperature dependence of the electrical resistivity of GdRu2Si2 is given in figure 6.4.. Around TN, the resistivity is characterised by a distinct upturn. The ordering temperature cann be determined with two different approaches. De Gennes and Friedel [6.12] have predictedd a cusp-like peak in the resistivity arising from long-range spin fluctuations of the magnetisationn near the ordering temperature. The ordering temperature corresponds to the maximumm change in resistivity below the peak. This yields for GdRu2Si2 TN = 36.3(5) K (see

insett figure 6.4). For example, the resistivity behaviour of UNiGa around the ordering temperaturee is explained similarly [6.13]. However, as discussed by Alexander et al. [6.14] thee approach of De Gennes and Friedel is more appropriate for semiconductors and less applicablee to metals. Furthermore, the obtained ordering temperature is rather low compared too the results of magnetisation measurements (TN = 45.4 K). Alternatively, the upturn may be attributedd to the opening of a gap at the Fermi-surface arising from superzone boundaries. Then,, according to the approach of Suezaki and Mori [6.15], TN corresponds to the temperaturee at which the temperature derivative of the electrical resistivity diverges negatively.. Associating this divergence with the minimum in the top inset of figure 6.4, this yieldss TN = 44.2(5) K, which is more consistent with the results of magnetisation measurements.. Furthermore, Gamier et al. [6.7] have reported two magnetic transitions as a functionn of temperature, determined as the maxima in magnetisation: TN = 47 K, To = 40 K. Hence,, we attribute the transition temperature obtained by the first approach to the spin-reorientationn temperature TQ.

Chapterr 6

Q. .

< <

B(T) )

Figuree 6.5. Left axis: Magnetoresistance of polycrystalline GdRu2Si2 at 4.2 K for magnetic fields appliedd along the measuring current. Right axis: Magnetisation of free-powder of GdRu2Si2 taken fromm Tung et al. [6.4]. Inset: Field derivative of the magnetoresistance. The arrows indicate transitions. .

Althoughh the magnetic structures in the different states are not known, they can be anticipatedd to be (incommensurate) helimagnetic structures, in agreement with the other compoundss in the RRu2Si2 series. Czjzek et al. [6.16] have concluded from Mössbauer spectroscopyy that the magnetic ordering is definitely not collinear. Then, upon application of a magneticc field, the helimagnetic structure is expected to transform to a fan structure, and at highh fields to a forced ferromagnetic state.

Thee magnetoresistance and magnetisation of GdRu2Si2 measured at 4.2 K in fields up too 15 T are given in figure 6.5. The magnetisation displays a field-induced transition at about 22 T and levels off at 9 T. The corresponding magnetoresistance shows complicated behaviour beloww 5 T. The saturation of the magnetisation corresponds with a large reduction in resistancee of 3 5 % between 5 and 10 T. Taking the extrema in the derivative of the magnetoresistancee as transition fields, one can designate four transitions in the magnetoresistancee (inset figure 6.5). To further investigate these transitions, the magnetoresistancee up to 5 T was measured at several temperatures (figure 6.6). The resulting phasee diagram is given in the inset of figure 6.6.

Fromm magnetisation measurements on a single-crystalline sample of GdRu2Si2, Gamierr et al. [6.7] have constructed magnetic phase diagrams for the field applied along the a andd the c axis. At low temperatures, they have found three field-induced transitions, whereas wee have observed four. However, the magnetic phase diagrams constructed by Gamier et al. [6.7]] exhibit anisotropic behaviour. At 5 K, for B // a axis the field-induced transitions are observedd at 2, 4 and 10.5 T, whereas for B // c axis they are observed at 2, 2.3 and 9 T. As in

Figuree 6.6. Magnetoresistance of polycrystalline GdRu2Si2 at several temperatures for magnetic fields appliedd along the measuring current. Inset: Magnetic phase diagram of GdRu2Si2 constructed from magnetoresistance. .

magnetoresistancee experiments on polycrystalline samples one measures an average of both axes,, we conclude that in the phase diagram of GdRu2Si2 we have constructed (inset figure 6.6),, the two phase lines cutting off the field axis at 2.5 and 4 T correspond to the same, anisotropic,, phase transition. The fact that both transitions show up in a similar way in magnetoresistancee and have a comparable size (figure 6.5), supports this assertion. In contrast, thee phase transition at 9 to 10.5 T is not distinguishable in magnetoresistance, as it correspondss to a reduction in resistance of 35 % over a broad field regime. Again, one may envisagee this reduction in resistance as being due to the removal of superzone boundaries at thee Fermi surface.

GdRh2Si2 2

Thee compound GdRh2Si2 and its iso-electronic equivalents GdCo2Si2 and GdIr2Si2 orderr at relatively high temperatures, which is due to a relatively strong next-nearest neighbourr exchange interaction in these compounds [6.4]. The temperature dependence of the

0.7 7 co o O) ) C\J J 0.55 -0.3 3 0.1 1 _,, s 3 3* 3* Q. . T3 3

.. (

^na ^na

5

^^f-^^f-^^^^ ^^f-^^f-^^^^

// GdRh Si

T(K) )

Figuree 6.7. Temperature dependence of the normalised electrical resistivity of GdRh2Si2 at low

temperatures.. Top inset: Temperature derivative of the electrical resistivity at low temperatures. Bottomm inset: Electrical resistivity versus temperature for 4.2 < T < 300 K.

0.35 5

Figuree 6.8. Temperature dependence of the normalised electrical resistivity of GdPd2Si2 at low

temperatures.. Top inset: Temperature derivative of the electrical resistivity at low temperatures. Bottomm inset: Electrical resistivity versus temperature for 4.2 < T < 300 K.

TT r -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r a.a. 0.0' ' ' ' ' 00 100 200 300-JJ I I I I I I I I I I • » \ I I I I I I I I I I 00 5 10 T / I X, 15 20 25 II (K)

Figuree 6.9. Temperature dependence of the normalised electrical resistivity of GdAg2Si2 measured at

loww temperatures in 0 and 5 T. Top inset: Temperature derivative of the electrical resistivity measured inn 0 T at low temperatures. Bottom inset: Electrical resistivity versus temperature measured in 0 T for 4 . 2 < T < 3 0 0 K . .

electricall resistivity of GdRh2Si2 is given in figure 6.7. Taking the maximum in the temperaturee derivative of the resistivity as the ordering temperature, we obtain TN = 95(3) K (topp inset figure 6.7). However, the weakness of the maximum compared to the noise yields a limitedd accuracy. Czjzek et al. [6.16] reported, beside a Néel temperature of 106 K, a cusp in thee dc susceptibility at 17 K, which they attribute to a magnetic phase transition. The kink in thee temperature derivative of the electrical resistivity at To = 22(1) K, may be related to this transition. .

GdPd2Si2 2

Thee temperature dependence of the electrical resistivity of GdPd2Si2 is given in figure 6.8.. The temperature derivative of the electrical resistivity shows maxima at 10.3(2) K and

12.2(2)) K. We associate the Néel temperature with the shoulder in the derivative at 15(1) K. Tungg et al. [6.4] obtained TN = 16.5 K from magnetisation measurements. For GdPd2Si2, no temperature-inducedd magnetic phase transitions have been reported in literature. However, the resultss of our electrical-resistance measurements indicate that there are magnetic phase transitionss as a function of temperature.

GdAg2Si2 2

Thee temperature dependence of the electrical resistivity of GdAg2Si2 is given in figure 6.9.. Magnetic ordering is observed at TN = 16.6(2) K as a sharp minimum in the temperature derivativee of the electrical resistance, that can be attributed to the appearance of a gap at the

Chapterr 6 Fermii level. Furthermore, at about 9 K a magnetic phase transition is present, the considerable hysteresiss observed indicates that the transition is of first order. The electrical resistivity measuredd in 5 T also shows an increase at the ordering temperature, but does not show the transitionn at 9 K. The temperature dependence of the electrical resistivity of GdAg2Si2 in 0 andd 5 T has also been reported by Mallik and Sampathkumaran [6.17]. Their results agree withh ours, except that they find a decrease of TN upon application of a magnetic field, whereas wee find a small increase. As the error in temperature of our B = 5 T curve amounts about 2 K, wee cannot decide on an increase or decrease of TN based on our data.

Thee magnetoresistance and magnetisation of GdAg2Si2 measured at 4.2 K in fields up too 38 T are given in figure 6.10. At 3.5 and 10.5 T, the magnetisation shows a field-induced transition.. These field-induced transitions are observed in magnetoresistance as a large increasee of 30 % and a decrease of 4 %, respectively. To the kink in magnetisation at 23.5 T correspondss a reduction of magnetoresistance of 20 %. Note that the magnetoresistance betweenn 25 and 40 T is approximately linear and extrapolates to zero at zero field.

Thee magnetoresistance measured at 5 T in the high-field installation is about 20 %, whereass an effect of 80 % is deduced from the resistivity curves given in figure 6.9. However, thee measurements have been performed with B 1 i and B // i, respectively. Yet, it is doubtful whetherr the difference in measuring configuration can explain the observed difference. Moreover,, the larger effect is expected for B 1 i, which is in contrast to our findings. The resultss of magnetoresistance measurements up to 5 T for B // i at several temperatures are givenn in figure 6.11. The magnetoresistance effect at 5 K in 5 T is almost 70 %. Mallik and Sampathkumarann [6.17] have reported a comparable effect of 75 % for B // i, corroborating thee magnetoresistance given in figures 6.9 and 6.11. On the other hand, the magnetoresistance measurementss performed in the high-field installation cannot be rejected either, as results obtainedd on other compounds compare well (cf. for example figure 6.5 with figure 6.6).

Att 20 K, the magnetoresistance is proportional to B2 65 (solid line in the inset of figure 6.11),, which is slightly larger than the quadratic behaviour expected in the paramagnetic state (seee section 2.2.3). From the transitions observed in the (magneto)resistance, we have constructedd the (tentative) phase diagram given in the bottom inset of figure 6.10. The dashed lineslines represent the measured trajectories. The solid lines connect the transition points that showw up in a similar way in the (magneto)resistance, and serve as guides to the eye. Besides thee paramagnetic and forced-ferromagnetic states, one can distinguish at least two magnetic states,, denoted by Ml and M2. The distinction between M2 and a possible third magnetic statee M3 is less obvious, and additional measurements are needed to refine the magnetic phase diagramm of GdAg2Si2.

GdOs2Si2 2

Thee temperature dependence of the electrical resistivity of GdOs2Si2 is given in figure 6.12.. The ordering is characterised by a reduction of electrical resistivity as described by the theoryy of Fisher and Langer [6.9]. Hence, the ordering temperature has been taken as the maximumm of the first derivative (see inset figure 6.12), yielding TN = 26.2(5) K.

20 0

B(T) )

Figuree 6.10. Left axis: Magnetoresistance of polycrystalline GdAg2Si2 at 4.2 K for magnetic fields

appliedd perpendicular to the measuring current. Right axis: Magnetisation of free-powder of GdAg2Si2

takenn from Tung et al. [6.4]. Right inset: Field derivative of the magnetoresistance. The arrows indicatee transitions. Bottom inset: Tentative phase diagram of GdAg2Si2. For further information see

text. .

Figuree 6.11. Magnetoresistance of polycrystalline GdAg2Si2 measured at 5, 12 and 20 K (inset) in

Chapterr 6 0.30 0 0.25 5 COO 0.20 C\L L . Q . . OO 0.15 0.10 0 0.05 5 - II 1 1 1-_{1 r- - 11 1 1} r-Q. . T3 3

GdOss Si

T(K) )

Figuree 6.12. Temperature dependence of the normalised electrical resistivity of GdOs2Si2 at low

temperatures.. Top inset: Temperature derivative of the electrical resistivity at low temperatures. Bottomm inset: Electrical resistivity versus temperature for 4.2 < T < 300 K.

0.10 0

Figuree 6.13. Left axis: Magnetoresistance of polycrystalline GdOs2Si2 at 5 K for magnetic fields

appliedd along the measuring current. Right axis: Magnetisation of polycrystalline GdOs2Si2. Inset:

TT ' 1 ' 1 r

Figuree 6.14. Magnetoresistance of polycrystalline GdOs?Si2 at several temperatures for increasing magneticc fields applied along the measuring current. Inset: Magnetic phase diagram of GdOs2Si2

constructedd from magnetoresistance.

Thee magnetoresistance and magnetisation of GdOs2Si2 measured at 5 K in fields up to 55 T are given in figure 6.13. The magnetisation, in this case measured on a bulk polycrystallinee sample, displays several transitions and an anomalous hysteresis. The magnetisationn curves measured at several temperatures up to 25 K show qualitatively similar behaviour.. The magnetisation curve measured at 5 K displays a small step at 4.8 T. With increasingg temperature, the field at which the step occurs, decreases to 2.5 T at 25 K. At 30 K andd higher temperatures, the hysteresis in magnetisation has disappeared. The magnetisation curvee at 4.2 K of GdOs2Si2 powder that was free to rotate, that has been measured by Tung et

al.. [6.4], shows an almost linear increase with saturation at 6.5 T. Hence, it is likely that the anomalouss magnetic behaviour arises from metastable states that are stabilised by domain walls. .

Chapterr 6

Figuree 6.15. Temperature dependence of the normalised electrical resistivity of GdIr2Si2 at low temperatures.. Top inset: Temperature derivative of the electrical resistivity at low temperatures. Bottomm inset: Electrical resistivity versus temperature for 4.2 < T < 300 K.

Thee magnetoresistance curve given in figure 6.13 shows even more exotic behaviour thann the magnetisation. From the field-derivative of the magnetoresistance, four transitions are obtainedd (see inset figure 6.13). A fifth transition at 6.5 T which corresponds to the saturation off magnetisation falls outside the measured field interval. To probe the various transitions, magnetoresistancee curves have been measured at several temperatures up to 100 K. The resultss are shown in figure 6.14. For clarity, only the curves measured with increasing field are given.. The curve measured at 5 K shows hysteresis in the transition at 2 T. With increasing temperature,, the hysteresis becomes smaller, but persists up to 16 K. The obtained phase diagramm is given in the inset of figure 6.14. The phase line at low fields and low temperatures cann be followed up to 13 K. It is not clear in which way it extrapolates to higher temperatures. Thee magnetoresistance curves and corresponding magnetic phase diagram of GdOs2Si2 (figure 6.14)) show large similarities to those of GdRu2Si2 (figure 6.6). Note that Os and Ru (and Fe) aree in the same column of the periodic system (i.e.: the elements are iso-electronic). The two compoundss are reported to exhibit anomalous behaviour in Mössbauer spectroscopy [6.16], Furthermore,, the compounds GdOs2Si2, GdRu2Si2 and GdFe2Si2 have paramagnetic Curie temperaturess that are positive, whereas for all other GdT2Si2 compounds negative values have beenn found [6.4]. Hence, both compounds have complicated magnetic structures, that are likelyy to be related. On the other hand, the phase diagrams have some differences, too. For example,, the phase line at low fields and low temperatures for GdOs2Si2 is absent for GdRu2Si2.. Furthermore, for GdRu2Si2 we discussed that the phase diagram appears to be more complicatedd due to anisotropy. Whether this also applies to GdOs2Si2 is not clear at the moment. .

0.38 8 0.36 6

ST T

p p

'S S

T(K) )

Figuree 6.16. Temperature dependence of the normalised electrical resistivity of GdPt2Si2 at low temperatures.. Top inset: Temperature derivative of the electrical resistivity at low temperatures. Bottomm inset: Electrical resistivity versus temperature for 4.2 < T < 300 K.

GdIr2Si2 2

Thee temperature dependence of the electrical resistivity of GdIr2Si2 is given in figure 6.15.. The resistivity and hence also the temperature derivative of the resistivity (inset figure 6.15)) looks similar to the related (iso-electronic) compound GdRh2Si2 (figure 6.7). Again, the maximumm in dp/dT has been taken as the ordering temperature, yielding TN = 7 8 ( 1 ) K .

Furthermore,, similar to GdRh2Si2, at low temperatures there might be an additional magnetic phasee transition, the kink in dp/dT at 14(1) K being even weaker for GdIr2Si2.

GdPt2Si2 2

Thee temperature dependence of the electrical resistivity of GdPt2Si2 is given in figure 6.16.. The behaviour is similar to that of GdAg2Si2. With decreasing temperature, ordering is observedd at TN = 9.6(2) K as a strong increase of resistivity, that is attributed to the appearancee of a gap at the Fermi level. Furthermore, at 6.7(2) K an additional magnetic phase transitionn is present, that is characterised by a decrease in resistivity of about 6 %. The electricall resistivity of GdPt2Si2 has also been reported by Sampathkumaran and Das [6.11], andd is in agreement with our findings. Upon application of a magnetic field of 5 T, they have foundd a reduction of TN from 10 to 8 K. Furthermore, in 5 T the additional magnetic phase transitionn is not observed in the resistivity down to 4.2 K.

Thee magnetoresistance and magnetisation of GdPt2Si2 measured at 4.2 K in fields up too 20 T are given in figure 6.17. At 2.7(2) T, a field-induced transition is observed as an increasee in resistance of 5 %. The saturation of the magnetisation is accompanied by a large

Chapterr 6 Q. .

"a. .

B(T) )

Figuree 6.17. Left axis: Magnetoresistance of polycrystalline GdPt2Si2 at 4.2 K for magnetic fields appliedd along the measuring current. Right axis: Magnetisation of free-powder of GdPt2Si2 taken from Tungg et al. [6.4]. Right inset: Field derivative of the magnetoresistance. The arrows indicate transitions.. Bottom inset: Tentative phase diagram of GdPt2Si2. : present work. : literature data [6.11;; 6.18].

reductionn of the resistance of about 25 %, the minimum in dp/dB occurring at 7.7(3) T (right insett figure 6.17). From the transitions observed in the (magneto)resistance we have constructedd the (tentative) phase diagram given in the bottom inset of figure 6.17. The magneticc structures in the two ordered states at 0 T have been determined by means of neutron diffractionn by Gignoux et al. [6.18]. For the high-temperature ordered state, they obtained a collinearr sine-wave modulated structure with wave vector q = (1/3, 1/3, 1/2), the magnetic momentss lying along the [110] direction. The low-temperature magnetic structure is characterisedd by a collinear structure with the same wave vector, the magnetic moments in this casee lying along the [100] direction. The two magnetic structures are denoted in the phase diagramm (bottom inset of figure 6.17) by AF1 and AF2, respectively. Thus, the magnetic groundd state of GdPt2Si2 is an antiferromagnetic structure, that modifies into a sine-modulated antiferromagneticc structure upon application of a magnetic field and/or upon increasing temperature.. The latter structure is accompanied by a gap at the Fermi surface, giving rise to a high'' electrical resistance. At even higher fields or temperatures, the magnetic state is forced intoo a ferromagnetic or paramagnetic state, yielding a reduction of the resistivity compared to thee sine-modulated state.

GdAu2Si2 2

Thee temperature dependence of the electrical resistivity of GdAu2Si2 is given in figure 6.18.. Taking the maximum in the temperature derivative of the resistivity as the ordering

0.69 9 CO O CD D C\J J 0.68 8 ^^ 0.67 -0.66 6 i i i I * I * i_ 00 100 200J(K)300 —II 1 1 1 1 1 1 I ' 100 15

T(K) )

Figuree 6.18. Temperature dependence of the normalised electrical resistivity of GdAu2Si2 at low

temperatures.. Top inset: Temperature derivative of the electrical resistivity at low temperatures. Bottomm inset: Electrical resistivity versus temperature for 4.2 < T < 300 K.

temperature,, we obtain TN= 1 0 ( 1 ) K (inset figure 6.18). The weakness of the maximum

comparedd to the noise yields a limited accuracy of TN.

Thee magnetoresistance and magnetisation of GdAu2Si2 measured at 4.2 K in fields up too 36 T are given in figure 6.19. The magnetisation increases approximately linearly up to aboutt 25 T and then levels off to a value of 6.5 u.e/f.u.. The corresponding magnetoresi stance decreasess monotonously to -10.9 % and also remains constant. As both magnetisation and magnetoresii stance display rather simple behaviour, we have performed a fit of the magnetoresistancee using a model often applied for multilayered systems [6.19]. The linear increasee of the magnetisation observed in GdAu2Si2 is due to a gradual bending of the magneticc moments from the antiferromagnetic configuration towards the applied magnetic field,, yielding a 'forced' ferromagnetic structure above 25 T. The magnetisation M is given by thee expression

MM = M„, cos 9 (6.1) )

wheree Msat is the saturation magnetisation (6.51 u,e/f.u.) and 0 is the angle between the

magnetisationn and the applied magnetic field [6.20]. It has been shown [6.21] that the resistivityy of multilayered systems depends on the angle cp between the magnetisation in the successivee ferromagnetic layers as

Chapterr 6 0.00 0 -0.04 4 Q. . < < -0.08 8 -0.12 2 - ii 1 1 1 1 1 -44 ^ DO O 0 0 40 0 20 0

B(T) )

Figuree 6.19. Left axis: Magnetoresistance of polycrystalline GdAu2Si2 at 4.2 K for magnetic fields appliedd along the measuring current (solid line). The dashed line is a fit of the magnetoresistance as explainedd in the text. Right axis: Magnetisation of powdered GdAu2Si2 taken from Tung et al. [6.4]. whenn the conduction electrons are submitted to spin-dependent scattering. AMR is the differencee in resistance between the ferromagnetic and the antiferromagnetic state. Note that p((p=180°)) corresponds to p(B=0 T). Combining equations 6.1 and 6.2, given that (p = 28, yieldss for the magnetoresistance

App = p ( B ) - p ( B = 0 T ) PP ' p(B = 0T)

A, , M M

p(B=0T) ) M. . (6.3) )

Thee magnetoresistance calculated with equation 6.3 taking AMR / P ( B = 0 T ) = 10.9 % is

depictedd as the dashed line in figure 6.19. The calculated curve is in reasonable agreement withh the measured curve. In the presence of potential barriers, the angular dependence of the magnetoresistancee may be much more complicated than the simple expression 6.3 [6.22],

Notee that the calculated magnetoresistance is obtained from the magnetisation measuredd on a powder that was free to rotate, while the magnetoresistance is measured on a bulkk polycrystalline sample. The magnetisation of a bulk piece is similar to that of a free-powderr sample when the system has negligible anisotropy. Since in GdAu2Si2 we are dealing withh a spherical ƒ shell of Gd, and since the 5d band of Au is completely filled, the assumption off negligible anisotropy seems reasonable. Moreover, the electric-field gradient VK almost vanishess for GdAu2Si2 [6.6].

Sincee expression 6.3 is derived for multilayered systems, one might argue about its applicabilityy to bulk antiferromagnetic systems. As discussed in section 2.2.3, De Gennes and

0.6 6

2**

0.5

C\J--g0.4 4

T(K) )

Figuree 6.20. Temperature dependence of the normalised electrical resistivity of GdGe2Al2 at low

temperatures.. Top inset: Temperature derivative of the electrical resistivity at low temperatures. Bottomm inset: Electrical resistivity versus temperature for 4.2 < T < 300 K.

Friedell [6.12] have obtained a similar expression for the magnetoresistance of a bulk magnetic systemm in the paramagnetic state (cf. equation 2.25). The reduction of the conduction-electron scatteringg is due to the gradual alignment of the magnetic moments upon application of a magneticc field. From symmetry considerations, one can derive that the magnetoresistance shouldd go with even powers of M at low magnetic fields. Noting this, one can reverse the argumentation.. The magnetisation of GdAu2Si2 is reasonably described with equation 6.1, whichh corresponds to a gradual bending of the magnetic moments towards the applied magneticc field. The magnetoresistance in the magnetically ordered state is, to a certain extent, properlyy described with an M2 term, solely. Then, one can interpret the magnetoresistance as beingg described by equation 6.2.

GdGe2Al2 2

Thee compound GdGe2Al2 crystallises in the hexagonal CaCr2Si2-type of structure. For

moree information on the structural properties of GdGe2Al2, we refer to Tung et al. [6.4]. The temperaturee dependence of the electrical resistivity of GdGe2Al2 is given in figure 6.20. Takingg the maximum in the temperature derivative of the resistivity as the ordering temperature,, we obtain TN = 20(1) K (inset figure 6.20). The weakness of the maximum comparedd to the noise yields a limited accuracy of TN. At low temperatures, the resistivity doess not tend to saturate yet, but shows convex behaviour. Accordingly, the temperature dependencee of the magnetisation seems to display two transitions, too.

Thee magnetoresistance and magnetisation of GdGe2Al2 measured at 4.2 K in fields up too 20 T are given in figure 6.21. Similar to GdAu2Si2 the magnetisation increases

Chapterr 6

ii—i—'—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—I—i—'—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—I 8

00 5 10 15 20

B(T) )

Figuree 6.21. Left axis: Magnetoresistance of polycrystalline GdGe2Al2 at 4.2 K for magnetic fields appliedd along the measuring current. Right axis: Magnetisation of free-powder of GdGe2Al2 taken fromm Tung et a!. [6.4], Inset: Field derivative of the magnetoresistance. The arrows indicate transitions. .

approximatelyy linearly until it reaches saturation. The magnetoresistance of GdGe2Al2, however,, displays three field-induced transitions (inset figure 6.22). The transition at 9 T showingg in magnetoresistance as a reduction of 20 % is associated with the fading of a gap at thee Fermi surface. Thus, based on both the temperature dependence and the field dependence off the electrical resistivity, we conclude that GdGe2Al2 has more than one magnetic state.

6.44 Conclusions

Thee temperature dependence of the resistivity arising from magnetic interactions in the compoundss GdT2Si2 generally follows the behaviour schematically depicted in figure 2.5. Aroundd TN, the resistivity is in principle dominated by short-range interactions among the magneticc moments, as described by the theory of Fisher and Langer [6.9], The compounds GdRu2Si2,, GdAg2Si2 and GdPt2Si2 show a maximum in resistivity around TN- This behaviour iss attributed to the opening of a gap at the Fermi level due to the formation of superzone boundariess arising from the antiferromagnetic structure. Although all GdT2Si2 compounds orderr antiferromagnetically, the formation of a gap at the Fermi level seems to happen accidentally.. One should realise, however, that the superzone boundaries occur at positions in thee Brillouin zone that are principally determined by the wave vector of the antiferromagnetic structure,, and the wave vector varies for the different GdT2Si2 compounds. Additionally, the positionn of the Fermi level in the energy bands shifts substantially as a function of T, as with

eachh subsequent element one electron is added to the system. Furthermore, among other things,, volume effects and hybridisation processes influence the band structure. Therefore, in ourr opinion, with the element T in GdT2Si2, the Fermi level shifts through the band structure andd may accidentally coincide with a superzone boundary caused by the antiferromagnetic structure.. In chapter 7, we will explain the observed resistance effects in the RMn6Ge6 compoundss with R = rare-earth element, in a similar way.

Thee distinction made in table 6.1 between the Fisher-Langer type and the Suezaki-Morii type of behaviour of the resistivity at TN is not decisive. Since we have performed the resistivityy measurements on polycrystalline GdT2Si2 samples, the measured curves represent ann average of the resistivity over the various directions. As the gap at the Fermi level is often anisotropic,, the characteristic maximum in resistivity around TN, may have become blurred [6.23]. .

Mostt of the GdT2Si2 compounds exhibit magnetic phase transitions as a function of temperaturee due to competing magnetic interactions. Also, various field-induced transitions aree observed in the field dependence of the electrical resistivity. The effects in the magnetoresistancee can often be attributed to the removal or opening of gaps at the Fermi level (orr to reconstruction of the band structure) yielding large magnetoresistance effects up to 700 %. Often the effect of field-induced transitions shows up more pronounced in the magnetoresistancee than in the magnetisation. Hence, measurement of the magnetoresistance provess to be a valuable technique, as it often serves as a sort of 'magnifying glass' for determiningg transition fields.

Asidee from the various field-induced transitions, there appear to be two trends in the magnetoresistancee on going from the antiferromagnetic to the forced ferromagnetic state. One trendd is reflected best by the compound GdAu2Si2. Upon application of a magnetic field, the magneticc moments gradually bend towards the magnetic field, yielding a linear magnetisation. Correspondingly,, the magnetoresistance decreases continuously until the magnetisation levels off.. The compounds GdRu2Si2, GdPt2Si2 show this behaviour, too. Another trend in magnetoresistancee is observed for the compounds GdCu2Si2, GdAg2Si2 and GdGe2Al2- Here again,, the magnetisation more or less increases linearly and levels off when the magnetic momentss are aligned along the magnetic field. For these compounds, the magnetoresistance hass a more or less pronounced step corresponding to the saturation of the magnetisation.

Inn section 2.2.2, we have discussed spin-polarised transport in bulk intermetallic compounds.. The spin polarisation may arise from band-structure effects as well as from magneticc interactions. The description of the magnetoresistance with equation 6.2 can be takenn as an example of the latter. Still, the magnetoresistance effect which most likely can be attributedd to the removal of superzone boundaries at the Fermi level, shows up in two differentt ways. This difference is clearly seen by comparing the magnetoresistance curves of GdAg2Si22 (figure 6.10) and GdPt2Si2 (figure 6.17). Note that for these compounds the magnetisationn around the antiferromagnetic to forced-ferromagnetic transition behaves differently,, too. Therefore, whether or not the two sorts of magnetoresistance effects observed inn GdT2Si2 compounds have a different origin or that the difference arises for example from

preferentiall orientation in the polycrystalline samples remains an open question, at the moment.. Obviously, magnetoresistance and magnetisation measurements on single-crystalline sampless will elucidate this point. Furthermore, study of single-crystalline samples of GdT2Si2

willl prove interesting to further investigate the anisotropic magnetic properties observed in somee of these Gd-based compounds.

References s

[6.1]] K. Schroder, Handbook of electrical resistivities of binary metallic alloys (CRC Press, Boca Raton,, Florida, 1983)

[6.2]] A. Szytula and J. Leciejewicz, Magnetic properties of ternary intermetallic compounds of the RT2X22 type, Chapter 83 of Handbook on the physics and chemistry of rare earths, Vol. 12,

eds.. K.A. Gschneidner, Jr. and L. Eyring (North-Holland, Amsterdam, 1989)

[6.3]] A. Szytula, Magnetic properties of ternary intermetallic rare-earth compounds, Chapter 2 of Handbookk of magnetic materials, Vol. 6, ed. K.H.J. Buschow (North-Holland, Amsterdam,

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[6.4]] L.D. Tung, J.J.M. Franse, K.H.J. Buschow, P.E. Brommer and N.P. Thuy, J. Alloys Compnds. 2600 (1997) 35; L.D. Tung, Antiferromagnetism in some compounds of rare earth with non-magneticc other elements (rare earth = Gd or Ce), Thesis, University of Amsterdam (1998) [6.5]] M.W. Dirken, R.C. Thiel, K.H.J. Buschow, J. Less-Common Met. 147 (1989) 97; M.E.

Dirken,, A l55Gd Mössbauer study on the origin of the electric field gradient, Thesis, Universityy of Leiden (1991)

[6.6]] R. Coehoorn, K.H.J. Buschow, M.W. Dirken and R.C. Thiel, Phys. Rev. B 42 (1990) 4645 [6.7]] A. Gamier, D. Gignoux, N. Iwata, D. Schmitt, T. Shigeoka and F.Y. Zhang, J. Magn. Magn.

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[6.8]] M.E. Fisher, Phil. Mag. 7 (1962) 1731

[6.9]] M.E. Fisher, and J.S. Langer, Phys. Rev. B 20 (1968) 665

[6.10]] J.M. Barandiaran, D. Gignoux, D. Schmitt, J.C. Gomez-Sal, J. Rodriguez Fernandez, P. Chieuxx and J. Schweizer, J. Magn. Map. Mater. 73 (1988) 233

[6.11]] E.V. Sampathkumaran and I. Das, Phys. Rev. B 51 (1995) 8631 [6.12]] P.G. De Gennes and J. Friedel, J. Phys. Chem. Solids 4 (1958) 71

[6.13]] E.H. Brück, Hybridization in Cerium and Uranium intermetallic compounds, Thesis, Universityy of Amsterdam (1991)

[6.14]] S. Alexander, J.S. Helman and I. Balberg, Phys. Rev. B 13 (1976) 304 [6.15]] Y. Suezaki and H. Mori, Prog. Theor. Phys. 41 (1969) 1177

[6.16]] G. Czjzek, V. Oestreich, H. Schmidt, K. Latka and K Tomala, J. Magn. Magn. Mater. 79 (1989)42 2

[6.17]] R. Mallik and E.V. Sampathkumaran, Phys. Rev. B 58 (1998) 9178

[6.18]] D. Gignoux, P. Morin and D. Schmitt, J. Magn. Magn. Mater. 102 (1991) 33

[6.19]] B. Dieny, V.S. Speriosu, S.S.P. Parkin, B.A. Gurney, D.R. Wilhoit and D. Mauri, Phys. Rev. BB 43 (1991) 1297; B. Dieny J. Magn. Magn. Mater. 136 (1994) 335

[6.20]] S. V. Tyablikov, Methods in the quantum theory of magnetism (Plenum Press, New York, 1967) )

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[6.23]] For a comparison of resistance of single-crystalline and polycrystalline rare-earth metals see: R.S.. Tebble and D.J. Craik, Magnetic materials (John Wiley & Sons, London, 1969)