Magnetotransport and magnetocaloric effects in intermetallic compounds - Chapter 7 Electrical-transport properties of RMn6Ge6 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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RMneGe66 compounds 133 3

Chapterr 7

Electrical-transportt properties

off RMn

6

Ge

6

compounds

7.11 Introduction

Thee discovery of the giant magnetoresistance (GMR) effect in magnetic multilayers hass led to a revival of the research of intermetallic compounds by means of electrical-resistivityy measurements. It is generally agreed upon that the GMR effect in multilayers has its originn in spin-dependent scattering of the conduction electrons both at the interfaces and in the bulkk of the multilayers. Analogously, in several antiferromagnetic intermetallic compounds, a largee reduction of the resistivity is observed when the antiferromagnetic structure is transformedd into a ferromagnetic state upon application of a magnetic field. As the reduction inn resistivity is comparable to or even larger than that in multilayers, one often denotes these largee resistance effects in intermetallic compounds as 'giant', too. However, the scattering mechanismm causing the GMR effect in intermetallic compounds may be of different origin thann that in multilayers. As we discussed in section 2.2, among other things, spin-fluctuations andd band-structure effects like the formation of superzone boundaries at the Fermi energy may havee a distinct effect on the electrical-transport properties.

AA discussion on possible origins of the GMR effect in UTX compounds is given by Nakottee [7.1]. Although he concludes that the origin of the spin-dependent scattering in these compoundss remains unclear, there appears to be a relation between the size of the magnetic unitt cell and the observed magnetoresistance effect. Havela et al. [7.2] and Prokes [7.3] proposee that a necessary condition for the occurrence of a large magnetoresistance effect is a strongg exchange interaction between the 5/ electrons and the conduction electrons, that is inducedd by hybridisation.

Inn this chapter, we investigate the relation between (the complexity of) the magnetic structuree and the observed resistance effects in RMnóGeö intermetallic compounds, with RR = Sc, Y, Gd, Tb, Dy, Ho, Er, Tm, Lu. In the last decade, the magnetic properties of RMn6Ge66 compounds have been extensively investigated by means of neutron-diffraction

experimentss and magnetisation measurements [7.4; 7.5; 7.6]. RMn^Geo compounds have high magnetic-orderingg temperatures (400 to 520 K) and possess complex magnetic structures due too the existence of magnetic moments on the R and Mn sublattices that interact in a complex

Figuree 7.1. Schematic drawing of RMn6Ge6 crystallising in the hexagonal HfFe6Ge6-type of structure.

way.. Furthermore, most of the compounds undergo spin-reorientation transitions upon loweringg of the temperature. In the following section, a short overview is given of the magneticc properties of the RMn6Ge6 compounds as determined by others. Next, the results of electrical-resistivityy measurements are presented. The chapter is concluded with a discussion off the obtained results.

7.22 Magnetic properties

RMn6Ge66 compounds with R = Sc, Y, Gd, Tb, Dy, Ho, Er, Tm, Lu, crystallise in the

hexagonall HfFe6Ge6-type of structure (space group No. 191; P 6/mmm). A schematic drawing

off the structure is shown in figure 7.1. This relatively simple structure can be described as beingg built up of alternating layers containing R and Mn atoms, respectively. Whereas the R atomss build hexagonal planes (H), the Mn atoms build Kagomé lattices (K), stacked along the

cc axis with the sequence ...KHK—KHK...[7.7]. The Ge atoms occupy three in-equivalent

latticee sites. The room-temperature values of the lattice parameters are approximately

aa ~ 5.2 A and c = 8.1 A, the exact value depending on the actual R atom.

Below,, we will briefly describe the common features of the magnetic structures of severall RMnóGe^ compounds. They are also summarised in table 7.1. For a detailed descriptionn of the magnetic structures of each compound, we refer to several papers of Schobinger-Papamantelloss et al. [7.5].

Thee RMnöGeö compounds order at temperatures between 420 and 520 K. The RMn6Ge66 compounds with non-magnetic R (R = Y, Sc, Lu) order antiferromagnetically with

wavee vector q = (0, 0, 1/2), the Mn moments being directed along the c axis. With decreasing temperature,, YMn6Ge6 displays at Ts r=80K a spin reorientation from a collinear

antiferromagneticc structure to a conical antiferromagnetic structure. The compounds ScMn6Ge66 and LuMnöGeö remain simply antiferromagnetically ordered down to low temperatures. .

RMn6Ge66 compounds 135 5 Compound d ScMn6Ge6 6 YMn6Ge6 6 GdMn^Gej j TbMn^Geö ö DyMn6Ge6 6 HoMn6Ge6 6 ErMn^Geo o TmMn6Ge6 6 LuMnfiGe6 6 T„rdd (K) 516 6 473 3 463 3 427 7 423 3 466 6 475 5 482 2 509 9 TsrMagg (K) — — 80 0 200 0 100 0 60 0 200 0 100 0 40 0 — — Magneticc structure (loww temperature) A F / / c c Conee AF AF(?) ) Ferroo spiral Ferroo spiral Skewedd spiral Skewedd spiral Skewedd spiral A F / / c c Magneticc structure (highh temperature) A F / / c c A F / / c c Ferri i Spirall J. c Spirall JL c A F / / c c A F / / c c A F / / c c A F / / c c

Tablee 7.1. Magnetic properties of RMn6Ge6 compounds [7.4; 7.5; 7.6] Tord and TsrMae are the ordering

temperaturee and the spin-reorientation temperature determined from magnetisation. For a further descriptionn of the magnetic structures, see text and figure 7.2.

RR (z=0) ^ ^ ^ ,Mnn (z=+l/4) Mnn (z=-l/4) d d ^ ^ ^ ^ ^ ^ e e ^ ^ ^ ^ ^ ^

Figuree 7.2a. Schematic representation of the magnetic-moment arrangement below the spin-reorientationn temperature. It consists of two layers of Mn moments at z = +l/4 and z = - l / 4 , respectively,, and a layer of R moments at z = 0.

b.. Spiral spin structure. Each arrow represents the basic moment arrangement given in a. c.. Ferromagnetic spiral spin structure.

d.. Skewed spiral spin structure.

Att the magnetic ordering temperature, the compounds HoMn6Ge6, ErMn6Ge6 and

TmMn6Ge66 develop a magnetic structure similar to that of the RMn6Ge6 compounds with

non-magneticc R. Again, the Mn sublattice orders antiferromagnetically with wave vector qq = (0, 0, 1/2), the Mn moments being directed along the c axis. With decreasing temperature, thee Ho, Er and Tm sublattices develop a magnetic moment. Due to the coupling between the RR and the Mn sublattices and due to a change in Mn—Mn interaction, spin reorientations take placee typically below 200 K. The basic magnetic moment configuration is then constructed fromm two layers of Mn moments and one layer of R moments, as depicted in figure 7.2a. In thiss basic arrangement, the moments are confined to the basal plane, the direction within the basall plane spirals along the caxis (figure 7.2b). The periodicity is characterised by a magneticc wave vector or a spiral turn angle that is often incommensurate, yielding a large magneticc unit cell. Furthermore, the basic moment arrangement can make a canting angle with thee c axis, resulting in a so-called skewed spiral (figure 7.2d). Moreover, magnetic structures aree observed with an additional wave vector, resulting in even more complicated structures likee a ferromagnetic spiral (figure 7.2c) and an antiferromagnetic skewed spiral (figure 7.2e).

Thee compounds TbMn6Ge6 and DyMn6Ge6 behave differently than the RMn6Ge6

compoundss described above, as for these compounds the R sublattice carries a magnetic momentt already at the ordering temperature. Hence, these compounds order already at high temperaturess in a simple spiral structure. Below the spin-reorientation temperature, they undergoo a transition to a ferromagnetic spiral structure. Also the Gd sublattice in the compoundd GdMn6Ge6 has a magnetic moment already at high temperatures, resulting in this

casee in a ferrimagnetic structure. Below Tsr = 200 K, the Mn moments appear to order

antiferromagnetically,, while the moment configuration at the Gd sublattice is not resolved, yet. .

7.33 Results

Polycrystallinee samples of RMn6Ge6 compounds were obtained from the same batches

usedd by Brabers et al. [7.6] for magnetisation measurements and by Schobinger-Papamantelloss et al. [7.5] for neutron-diffraction experiments. The samples were cut by means off spark erosion into bars with typical dimensions of 1 x 1 x 4 mm3 suitable for electrical-resistivityy measurements. The contacts were prepared by soldering Cu wire with Pb-based alloyy as a solder and using saturated ZnCl2 solution as a flux. As optical inspection of the

sampless revealed the presence of microscopic cavities, the measured resistivity curves have beenn normalised to their room-temperature value. The obtained room-temperature resistivity rangess from 350 to 500 ui2cm, values that are rather high for intermetallic compounds.

Thee temperature dependence of the electrical resistivity between 5 and 300 K of RMnöGe66 is shown in figure 7.3. All samples show metallic behaviour, the residual resistance

ratioo p(291K)/p(5K) ranging from 6 to 44 (table 7.2). As presented in section 2.2.3, in the low-temperaturee regime one expects a T4 dependence of the electrical resistivity due to spin

RMriöGeöö compounds 137 7

TT 1 1 ( 1 1 1 1 1 1 r

Figuree 7.3. Temperature dependence of the normalised electrical resistivity of RMn6Ge6 compounds.

wavess in an antiferromagnet, while in a ferromagnet one expects a T dependence. Hence, the low-temperaturee part (5 < T < 30 to 40 K) of the resistivity curves has been fitted with the relationn p ( T ) « Ta. The resulting powers a are given in table 7.2. As the values of a vary betweenn 2.2 and 3.6, there is no indication of well-defined spin waves in this system with localisedd magnetic moments. The observed anomalies in resistivity are related to spin-reorientationn transitions. For the compounds TmMn6Ge6 and HoMnöGeö, the resistivity curves

showw hysteresis, indicating that for these compounds the spin-reorientation transition is of first-orderr (insets figure 7.3). The resistivity curve of TbMn6Ge6 has been measured only at

decreasingg temperature. Hence, we cannot determine the order of the spin-reorientation transitionn in this compound. No spin reorientation is detected in the resistivity curves of the YMn6Ge6,, GdMn6Ge6 and DyMn6Ge6 compounds.

Forr GdMn6Ge6, the spin-reorientation temperature has been determined indirectly from

magnetoresistancee measurements. The magnetoresistance curves have been compared with the resultss of magnetisation measurements on a fixed powder presented in figure 7.4. At 300 K,

-0.088 —l

00 1 B ( T ) 2 3 Figuree 7.4. Magnetisation of a fixed powdered sample and magnetoresistance of GdMn6Ge6.

Compound d ScMn6Ge6 6 YMn6Ge6 6 GdMn6Ge6 6 TbMn6Ge6 6 DyMn6Ge6 6 HoMn6Ge6 6 ErMn6Ge6 6 TmMn6Ge6 6 LuMn6Ge6 6 p(291K)/p(5K) ) 5.9 9 11.3 3 12.6 6 9.3 3 20.6 6 14.5 5 43.3 3 43.9 9 9.8 8 a a 2.5 5 2.2 2 2.5 5 2.4 4 3 3 3.5 5 3.6 6 3.6 6 2.6 6 TsrRess (K) — — — — -2100 (mr) 95 5 — — 200 0 90 0 40 0 — —

Tablee 7.2. Information on RMn6Ge6 compounds obtained from electrical-resistivity measurements.

p(291K)/p(5K)) is the residual resistance ratio, a has been obtained by fitting the low-temperature resistivityy curves (5 < T < 30 to 40 K) to the relation p(T) °= T". TsrRes is the spin-reorientation

temperaturee determined from resistivity. For GdMn6Ge6, TsrRcs is determined from magnetoresistance

RMn6Ge66 compounds 139 9 CD D !gg 0.00 'S S £ - 0 . 0 1 1 x s ;; -0.02

Intermediatee T

"" t

Mn: Antiferro *

O »

Gd:: ? \ v

\}J\}J T=125K^

GdMnn Ge

Ferri i

T(K) )

Figuree 7.5. Magnetic phase diagram of GdMn6Ge6. The data points have been determined as the

minimaa in the field-derivative of the magnetoresistance as depicted by the arrows in the inset.

thee magnetisation saturates at a value of 5.5 u,B/f.u.. Assuming the Mn moments to be approximatelyy 2 |XB and the Gd moments to be 7 U,B, this corresponds to a ferrimagnetic alignmentt of the Mn and Gd magnetic moments. At 300 K, the magnetoresistance decreases approximatelyy linearly, the effect being less than 1 % at 3 T. Below Tsr = 200 K, the Mn

momentss appear to order antiferromagnetically, while the moment configuration of the Gd sublatticee has not been resolved [7.6]. The magnetisation curves measured at 125 and 5 K, showw a induced transition towards a ferrimagnetic moment alignment. With the field-inducedd transition corresponds a negative magnetoresistance behaviour. The curve at 5 K, has aa pronounced increase of 1 % at low field. We attribute this to the Pb-based contacts, that becomee superconducting below approximately 7 K. Upon application of a magnetic field of 0.088 T, the contacts are driven into the normal state, yielding a somewhat larger measured resistivity.. The field-derivative of the magnetoresistance at 125 K is given in the inset of figuree 7.5. The magnetoresistance curve shows two field-induced transitions, which are determinedd as the minima in the field-derivative of the magnetoresistance. The resulting phase diagramm is given in figure 7.5. From the phase diagram we deduce a spin-reorientation temperaturee of about 210 K, which is in agreement with the results of Brabers et al. [7.6]. Basedd on magnetisation measurements, Rösch et al. [7.8] have constructed a similar phase diagramm for GdMn6Ge6. The magnetic-moment configuration in the so-called intermediate phasee remains unclear, but its origin may be found in the development of an ordered magnetic momentt at the Gd sublattice. Furthermore, Rösch et al. have calculated that at approximately 433 T the ferrimagnetic state is forced to a ferromagnetic one.

0.02 2 0.00 0 .CL L "o. . < < -0.02 2 -0.04 4 22

B(T)

Figuree 7.6. Magnetoresistance of TbMn6Ge6 for B // i.

Thee results of magnetoresistance measurements up to 5 T on TbMn6Ge6 are given in

figuree 7.6. At 10 K, there is a small positive magnetoresistance effect. At 100 K, just above thee spin-reorientation temperature Tsr = 95 K, the magnetoresistance is negative and has a

tendencyy to saturate. The magnetoresistance amounts to -4 % in 5 T, an effect that is comparablee to the temperature-induced change in resistivity when going through the spin reorientation.. Finally, at 300 K the magnetoresistance has decreased considerably, the effect beingg only -0.5 % at 5 T.

Thee electrical resistivity of ErMn6Ge6 as a function of temperature from 5 to 400 K is

givenn in figure 7.7. ErMn6Ge6 exhibits anomalous behaviour, showing a huge change of slope

att the spin-reorientation temperature Tsr = 90 K and showing hysteretic behaviour between 90

andd about 160 K (top inset figure 7.7). Here, we should note that ErMn6Ge6 orders in a

skewedd spiral spin structure below Tsr = 90 K. In the transition region 90 to 160 K, a

decouplingg of the Mn and Er sublattices sets in, and the magnetic ordering can be described as aa superposition of a skewed spiral with an additional antiferromagnetic component on the Mn sublatticee (cf. figure 7.2e). Above 170 K, the magnetic ordering is described by an antiferromagneticc arrangement of the Mn magnetic moments [7.5]. Furthermore, the electrical resistivityy of ErMn6Ge6 has a maximum at about 360 K. This behaviour can be qualitatively

describedd by the theory for the resistance in helical magnetic structures as discussed by Elliott andd Wedgwood [7.9]. A discussion will be given in the next section. The results of magnetoresistancee measurements up to 5 T on ErMngGe6 are given in the bottom inset of figuree 7.7. The observed positive magnetoresistance at low temperatures modifies into negativee behaviour between 100 and 150 K. To further investigate the spin reorientation in

RMnöGe66 compounds 141 1

T(K) )

Figuree 7.7. Temperature dependence of the normalised electrical resistivity of ErMn6Ge6. The top

insett shows the temperature derivative of the electrical resistivity. The bottom inset shows the magnetoresistancee of ErMn6Ge6 measured at several temperatures for B // i.

ErMneGe6,, the specific heat was measured between 4 and 180 K. As depicted in figure 7.8,

thee spin reorientation shows up as a large peak at about 95 K, suggesting that the spin-reorientationn transition in ErMnöGeö is of first order. A plot of C/T versus T at low temperaturess is given in the inset of figure 7.8. A fit of the data with formula 5.3 yields an electronicc contribution to the specific heat y= 110 mJ/mol K2, and a Debye temperature 9DD = 102 K. An estimate of y expected for ErMn6Ge6 yields a value comparable to the

measuredd y. The obtained value of the Debye temperature is rather low. However, it has limitedd validity, as there may still be a substantial magnetic contribution to the specific heat.

7.44 Discussion

Thee behaviour of the electrical resistance of ErMnöGeö can be qualitatively described withh the theory for the resistance in antiferromagnetic or spiral-spin structures as discussed by Elliottt and Wedgwood [7.9]. Since the periodicity of these magnetic structures is different fromm that of the crystallographic structure, the conduction electrons experience an exchange interactionn with a periodicity different from that of the lattice. This introduces so-called superzonee boundaries in the Brillouin zone and distorts the Fermi surface, possibly leading to aa distinct effect in electrical resistivity. In this way, the high-resistance state of ErMn6Ge6 abovee Tsr = 900 K may be interpreted as being due to the formation of superzone boundaries at

3 3 ^ 2 2 O O

£ £

5i i

T(K) )

Figuree 7.8. Temperature dependence of C/T of the compound ErMn6Ge6. The inset shows a fit of C/T

versuss T " at low temperatures.

thee Fermi energy, associated with an additional periodicity, caused by the antiferromagneticallyy ordered Mn sublattice. The spiral spin structure, which sets in below

1600 K, apparently has only a moderate effect on the electrical resistivity. The results of magnetoresistancee measurements are in accordance with this picture. In the gap-state, the magnetoresistancee tends to be negative, i.e.: upon application of a magnetic field, the magneticc moments are eventually forced to align ferromagnetically, resulting in a closing of thee gap and a reduction of the resistivity. The magnetic field needed to induce this field-inducedd transition is, however, larger than 5 T. Hence, the magnetoresistance measurement up too 5 T show only the onset of the closing of the gap. From the temperature dependence of the resistivity,, we can estimate the size of the magnetoresistance effect at the field-induced transitionn by extrapolating the resistivity below Tsr to higher temperatures. In this way, a

possiblee magnetoresistance effect of 50 % is obtained at 200 K. This procedure is very speculative,, however. Magnetoresistance measurements in high magnetic fields must be performedd to verify the magnetoresistance effect in ErMngGe6.

Superzonee boundaries occur at positions in the Brillouin zone that are principally determinedd by the wave vector of the antiferromagnetic structure. The RMn6Ge6 compounds

thatt order antiferromagnetically at high temperature (R = Sc, Y, Ho, Er, Tm and Lu), all have thee same wave vector: q = (0, 0, 1/2). Hence, at first glance, for all these compounds one may expectt a distinct effect in resistivity. However, as the conductivity is determined by the conductionn electrons that are around the Fermi level, a necessary condition for the occurrence off a distinct effect in resistivity is that the superzone boundaries occur at the Fermi surface.

RMnöGeöö compounds 143 3 Generally,, the position of the Fermi level in the energy bands shifts substantially as a function off R or transition-metal element [7.10]. Furthermore, among other things, volume effects and hybridisationn processes influence the band structure. Therefore, in our opinion, with variable RR in RMnóGeö the Fermi level shifts through the band structure, and may accidentally coincidee with a superzone boundary caused by the antiferromagnetic structure. In RMn6Ge6 compoundss this apparently is the case for R = Er. In this picture, the measured anomalies at Tsrr in the resistivity of the compounds HoMn6Ge6 and TmMn6Ge6 then may also originate

fromm superzone boundaries at the Fermi surface. Note that in the periodic system Ho and Tm aree the neighbouring elements of Er. Then one also understands why the RMn6Ge6

compoundss with R = Sc, Y and Lu lack an anomaly at Tsr, although they have the same

magneticc structure at high temperature as the compounds with R = Ho, Er and Tm.

Thee Dy and Tb compounds both undergo a spin reorientation, at which the magnetic momentss develop a canting out of the basal plane below Tsr. At TST, a resistance effect is

observed,, however, only in TbMnóGee. This may be understood if one considers the temperaturee dependence of the wave vector q [7.5], For TbMn6Ge6, q is discontinuous at Tsr

andd the resistivity exhibits an anomaly. For DyMnöGe6, the temperature dependence of q is continuouss and no anomaly in the resistivity is observed at Tsr.

Onee should keep in mind that the above-given reasoning is far from evident. To be moree decisive about the presence or absence of superzone boundaries in the various RMnöGeé compounds,, band-structure calculations are needed. However, as these calculations are difficult,, other techniques that are more accessible, could prove to be useful. For example, measurementss of the temperature dependence of the electrical resistivity should be extended too 550 K, to study the resistance effect at the ordering temperature. Furthermore, measurementss of the magnetoresistance in high fields at temperatures in the various magnetic statess may prove to be elucidative.

Summarising,, in RMnöGee compounds there are in principle only moderate (magneto)resistancee effects arising from magnetic interactions. As the R and Mn magnetic momentss are thought to be well localised, we attribute this to the only limited interaction betweenn the electrons carrying a magnetic moment and the conduction electrons. The opposite iss the case in UTX compounds. Here, considerable magnetoresistance effects are observed due too hybridisation effects. Nevertheless, both in RMnöGeö and in UTX compounds considerable (magneto)resistancee effects may arise due to formation of superzone boundaries at the Fermi surfacee resulting from magnetic structures. In RMn6Gee compounds, this situation is met for

References s

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[7.3]] K. Prokes\ Magnetism in uranium intermetallic compounds, Thesis, University of Amsterdamm (1997)

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[7.6]] J.H.VJ. Brabers, V.H.M. Duijn, F.R. de Boer and K.H.J. Buschow, J. Alloys Compds. 1988 (1993) 127; J.H.VJ. Brabers, Competing interactions in R-3d intermetallics, Thesis,, University of Amsterdam (1995)

[7.7]] G. Venturini, B. Chafik El Idrissi, B. Malaman and D. Fruchart, J. Less-Common Met. 1755 (1991) 143

[7.8]] P. Rosch, M.T. Kelmen, B. Pilawa, E. Dormann and K.H.J. Buschow, J. Magn. Magn. Mater.. 164 (1996) 175

[7.9]] RJ. Elliott and F.A. Wedgwood, Proc. Phys. Soc. 81 (1963) 846

[7.10]] Cf. band structures of UNiAl, UCoAl and UFeAl: M.S.S. Brooks and B. Johansson, Densityy functional theory of the ground state magnetic properties, Chapter 3 of Handbookk of magnetic materials, Vol. 7, ed. K.H.J. Buschow (North-Holland, Amsterdam,, 1993)