Magnetic and transport properties of selected YbxGd1−xNi5 intermetallics

Intermetallics 32 (2013) 384e393

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Magnetic and transport properties of selected YbxGd1
xNi5 intermetallics _ Anna Bajorek*, Grazyna Che1kowska, Artur Chrobak A. Chełkowski Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 April 2012 Received in revised form 16 July 2012 Accepted 6 August 2012 Available online 15 October 2012

We report the magnetic and transport properties of the YbxGd1
xNi5 (x  0.5) intermetallic compounds. According to the X-ray diffraction (XRD) this series crystallize in the hexagonal CaCu5-type structure. The magnetic properties in the studied system strongly depends on Yb concentration. Moreover, the socalled field cooledezero field cooled (FCeZFC) curves reveal an unexpected existence of a negative magnetization M in a certain temperature range. The M(T) dependences exhibit two compensation points in which the value of M equals zero. The origin of the observed behaviour may be due to the possible switching effect in spin (M4fS) and orbital (M4fL) moment within 4f sublattice. Near the compensation points where the opposing contribution from 4f local magnetic moments are nearly equals the conduction electron polarization become significant. Additionally, the observed exchange bias in the vicinity of the compensation point can be attributed to the anisotropy between the coupling within spin (M4fS) and orbital (M4fL) moments. The observed unique behaviour is the most evident in the case of x ¼ 0.4 ytterbium concentration. The transport properties confirm the results obtained by the magnetic studies. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: A. Rare-earth intermetallics A. Magnetic intermetallics B. Magnetic properties B. Electrical resistance and other electrical properties

1. Introduction The RNi5 compounds (R e rare earth) have been intensively studied in recent decades [1e12]. The highest value of the Curie temperature (TC) was evidenced for the GdNi5 compound which exhibits magnetic ordering below about TC ¼ 30 K [1e5]. This kind of behaviour is connected with a negative polarization of the Ni3d band by Gd5d band but also with the filling of Ni3d band and its splitting [2,3,5,8], which leads to reduction of the magnetic moment e.g. for the YxGd1
xNi5 series with increasing of Y concentration [2,4,8]. Newly obtained series of the YbxGd1
xNi5 compounds (x  0.5) exhibit quite interesting properties [5,13]. The whole system crystallizes in the hexagonal CaCu5 type of crystal structure. The Yb/Gd substitution causes the increase in c(x) lattice parameter in the full range of studied concentrations. This kind of change is connected with different ionic radii for gadolinium and ytterbium ions. The deviation from the linear change of a(x) and V(x) for x > 0.4 may be related to intermediate valence of Yb ions. However, the next evidence of mostly trivalent state of Yb ions is the gradual decrease in the residual resistivity value (ro) due to Yb3þ ions which have smaller ionic radius of than Yb2þ. The XPS valence band near by the Fermi level for the whole series are

* Corresponding author. E-mail address: [email protected] (A. Bajorek). 0966-9795/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.intermet.2012.08.018

dominated by Ni3d states. The multiplet structure in the valence bands is typical for Yb3þ states. Moreover, the valence of Yb ions is confirmed by the Yb4d core level spectrum which is rather characteristic for Yb3þ structure. Quite interesting and unusual behaviour has been evidenced in M(T) curves measured in the field e cooled (FC) as well as in the zero field e cooled mode (ZFC). Under a certain conditions M(T) indicates a negative value. The origin of this behaviour seems to be complicated and probably depends on several factors. In the recent years a similar phenomenon was observed in the various intermetallic compounds reported in [15e23]. As it was previously reported the negative value of M(T) especially in the low temperature range can be associated to the field induced magnetic switching within 4f sublattice and conduction electrons polarization [17e20,23]. Usually in 4f metallic compounds the 4f spins are coupled to the spins of conduction electrons via indirect RudermaneKitteleKasuyaeYosida (RKKY) interactions. This type of interaction exhibits either ferromagnetic or antiferromagnetic 4f arrangement depending on the rare earth element. Moreover the limited substitution of R element by another one from the opposite half of the 4f-series in the case of ferromagnetic system may lead to the zero-magnetization [17e20,23]. Such a behaviour is closely related to the RKKY interaction which favours ferromagnetic coupling of R elements if they belong to the light (J ¼ L
S) or heavy (J ¼ L þ S) 4f series. This coupling is responsible for the formation of 4f-magnetic moment. As it was

A. Bajorek et al. / Intermetallics 32 (2013) 384e393

previously reported in the case of R1
xR0 xAl2 systems where Relight rare earth, R0 eheavy rare earth or R1
xR0 xCu4Pd [17e20,23] the R and R0 moments are arranged antiferromagnetically. For some x concentrations and low applied magnetic field a ferrimagnetic behaviour with characteristic compensation point Tcomp between R and R0 local magnetic moments was observed [17e20]. Nonetheless a small contribution to the total magnetic moment from the conduction electron polarization (CEP) was also noticed. It is well known that applying a higher value of the external magnetic field may lead to reversal within 4f moments in the vicinity of Tcomp. Then, such a change involves a modification of CEP sign. Moreover this field-induced flipping effect is associated with an asymmetric shift in the magnetization hysteresis loops which is so-called an exchange bias phenomenon. Previously, this kind of effect was only observed in the thin films [17,25] but in the recent years was also observed for some bulk systems [17e23]. The value of the exchange bias field (HEB) as well as the coercive field (HC) changes across Tcomp. Because our YbxGd1
xNi5 system (x  0.5) exhibits a negative M(T) dependence in the low applied magnetic field thus, in a present paper we wanted highlight a relation between such a phenomenon and the exchange bias field. Moreover, the electrical resistivity as well as the specific heat study are presented. 2. Experimental Polycrystalline samples of the YbxGd1
xNi5 series with x ¼ 0.0, 0.2, 0.4, 0.5 have been prepared by arc melting from high purity elements under argon atmosphere. The purity of materials used for preparing samples were 99.99% for Ni and Yb and 99.9% for Gd. The crystal structures of all samples has been checked by means of Xray diffraction using Siemens D5000 diffractometer. The magnetic properties of YbxGd1
xNi5 compounds have been measured with the use of SQUID magnetometer (MPMS XL7 Quantum Design). All measurements have been performed in the 2 Ke400 K temperature range up to 7 T magnetic field. The socalled AC magnetization measurements were curried out in the condition of f ¼ 1 kHz and HAC ¼ 3 Oe. The magnetocaloric effect (MCE) has been estimated from the family of the magnetic isotherms. The electrical resistivity r(T) has been measured quasi-continuously at a slowly changing temperature (4.2 Ke300 K) by a standard four e probe technique. The specific heat measurements have been performed by using PPMS platform in the temperature range 1 Ke300 K and at the zero applied magnetic field. 3. Results and discussion 3.1. The FC e ZFC measurements The latter performed measurements [13] indicates that the temperature dependence of magnetization M(T) for the newly obtained YbxGd1
xNi5 series with x  0.5 exhibits strong dependence on the applied magnetic field as well as the on the way of measurements that is if the samples are cooled with (FC) or without the applied magnetic field (ZFC). Additionally, for all examined samples the AC measurements were carried out. The values of the temperature of magnetic phase transition (Tmag1) were estimated from AC as well as DC measurements at 1000 Oe as the maximum of jdM/dTj [13]. Thus, for the whole series Tmag1 decreases significantly from 33 K to 16 K with increasing of Yb content fromx ¼ 0.0 tox ¼ 0.5 respectively(see Table 1). Quite peculiar behaviour has been observed in M(T) dependences at low applied magnetic field (3 Oe  Happl  500 Oe). Thus, in the ordered state Yb e rich compounds (x  0.2) exhibit

385

Table 1 The magnetic parameters for the YbxGd1
xNi5 compounds. x

Tmag1 [K]

MS [mB/f.u]

Tmin [K] at M(T) e FC

Tcomp1 [K]

Tcomp2 [K]

jDSmj [J/kg K] at 1 T

jDSmj [J/kg K] at 7 T

0.0 0.2 0.4

33 28 20

6.52 5.72 4.66

e 55  5 35  4 (<100 Oe) 48  2 (100 Oe) 28  3

e 42  6 21  2 (<100 Oe) 39  1 (100 Oe) 18  2

e 97  4 75  1

3.17 3.51 2.31

12.73 19.98 9.12

69  1 (100 Oe) 51  3

2.23

10.29

0.5

16

4.36

a remarkable thermomagnetic irreversibility (see Fig. 1aed). In the field e cooled conditions (FC) and higher magnetic field (Happl  250 Oe) the magnetization rises rapidly with lowering the temperature and is almost saturated at the lowest T. In the zerofield cooled conditions (ZFC) the M(T) behaviour is totally different and the magnetization indicates smaller values at lower temperatures. Around temperature of the magnetic phase transition (Tmag1) both curves overlap each other. In the studied system the MFCeZFC difference is obviously higher in doped compounds than in the GdNi5. So, the thermomagnetic irreversibility arises from the anisotropy is caused by R ions. The gadolinium ion is described by the orbital momentum L ¼ 0 which gives a negligible magnetic anisotropy. In the case of trivalent ytterbium ion the orbital momentum is L ¼ 3 and the influence of the anisotropy cannot be neglected. The difference in FCeZFC curves can be also understood as the domain-wall pinning effect and as the temperature dependence of coercivity (HC). During FC process the initial magnetic state of sample is obviously quite different than in ZFC process. In the zero applied magnetic field (Happl) the magnetic domains are already oriented along the Happl direction after cooling the sample below Tmag1. The domain walls move easier when the temperature increases and in the FC conditions the magnetization is larger than in the ZFC mode. In the ZFC process the magnetic domains are oriented in random directions when the sample is cooled through Tmag1. After cooling, when the small filed is applied at the lower temperatures the magnetization is small because a quite high coercivity at this temperature. As the increase of the temperature the coercivity is reduced and the magnetic domain walls motion becomes easier. In a consequence an increase of the magnetization is observed. The coercivity is the measure of the anisotropy according to the relation: MFC
MZFC z MFCHC/(Happl þ HC) [26]. If the applied magnetic field is higher and significantly exceeds the coercivity, then the thermoremanent effect will disappear. Here we have observed such an effect even at 0.05 T, but MFC
MZFC difference is quite small (w0.2 emu/g). Thus, a significant thermoremanent effect has been observed below 100 Oe which is in close relation to HC. The strong thermomagnetic dependence has been evidenced for Yb-rich compounds (x  0.2) in the low temperature range. In the case of x ¼ 0.2 this effect is weaker than for the other doped compounds. At a certain conditions M(T) indicates minimum at Tmin and two compensation points Tcomp1 w 42  6 K and Tcomp2 w 97  4 K depending on the Happl. Moreover, at low applied magnetic field [13] and in FC mode M(T) indicates a negative value at Tmin at about 40e100 K temperature range (Table 1). This negative value can be rather ascribed to the interaction between two ore more opposite aligned magnetic sublattices than to the superconductivity of the investigated compounds. The minimum is followed by maximum at Tmax visible between 100 Ke130 K. The negative magnetization depends on the magnetic field and on the

386

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Fig. 1. The temperature dependence M(T) at different applied magnetic fields in the YbxGd1
xNi5 series: (a) x ¼ 0.0; (b) x ¼ 0.2; (c) x ¼ 0.4; (d) x ¼ 0.5. Inserts show the negative M(T) at low temperature range.

way of measurements e cooling the sample with (FC) or without (ZFC) magnetic field. With increasing Happl the minimum is still observed and moves upward into higher temperatures where becomes saturated. At a certain Happl the negative magnetization changes to positive. The series of successive M(T) measurements at different applied magnetic field allow estimating the value of Happl where the M(T) minimum at Tmin equals zero or almost zero. It turned out that the highest value is obviously observed for x ¼ 0.4 and equals about 210 Oe. For higher Happl the observed minimum is smaller and totally vanishes at 1000 Oe [13]. It is worth to mention that in ZFC condition such a minimum is also observed. However, it has a positive value and is much smaller. For x ¼ 0.5 yterrbium content the MFC
MZFC dependence becomes weaker. The negative MFC(T) value vanishes around Happl z 70 Oe and for higher applied fields (Happl > 100 Oe) we do not observe minima neither at Tmin nor at Tmax. At the same time we have observed the increase of the intensity of states near by the EF [5]. It could be a trace of divalent Yb states. Thus, if we have an intermediate valence the image of the magnetism differs from x ¼ 0.4 compounds. It is worth to notice that Tcomp1 as well as Tcomp2 move into higher values with the increase of Happl. After crossing the certain Happl these two minima vanish and we observe only one compensation point which is denoted as Tmin. It is also important that an additional phase transition is observed at Tmag2 w 145 K  10 K. This transition is much weaker that the previous one and can be only observed at a certain lower

applied magnetic field Happl  500 Oe. The origin of Tmag2 may be related to the magnetic arrangement within 4f sublattice which becomes more visible in certain conditions such as low Happl. The negative M(T) value has been already observed in some intermetallic compounds which contains rare earth atoms with a modulated magnetic structure such as Sm, Ho, Tb, Yb [14e20,23]. However, despite an efforts to explain the mechanisms responsible for the negative M(T) there are still a lot of lacks and no convincing explanation of a negative signal in M(T) has been proposed. For example, in the YbFe4Al8 compound [14] the negative signal in FC is a result of forming a complicated magnetic structure by Fe as well as the rare earth atom. As it was reported by the authors, even a small magnetic field during field-cooled conditions can create a small magnetic moment on the R atom which can be arranged in a different phase than iron moment. At low temperatures the Yb moment dominates on the transition metal and a negative M(T) is observed. When a stronger field is applied the ReT phase relation can be change and the negative signal in M(T) disappears. This signal is attributed to the hysteretic effect. The latter studies performed for RAl2 compounds indicate quite peculiar behaviour of M(T) dependence which is attributed to the unique properties of the magnetic R ion (R ¼ Gd3þ, Sm3þ, Nd3þ or Ho3þ) [17e19,23]. Thus in the case of Sm3þ it has been shown that magnetism depends on the small separation between the J levels. Such an effect leads to the thermally induced mixing of J multiplets and as a consequence different temperature dependences of 4f-spin (M4fS) and 4f-orbital (M4fL) parts of total magnetization (M) [23]. Additionally the interaction with the conduction electrons by

A. Bajorek et al. / Intermetallics 32 (2013) 384e393

polarization (CEP) has an influence of interesting M(T) curves. So, if M4fS magnetization is almost equal to M4fL one and coupled antiferromagnetically then M is usually small and contribution of magnetization of conduction electron (MCE) becomes significant. The appropriate applied magnetic field has a strong influence on M(T) dependence in such systems. In our case the situation seems to be much more complicated. In the initial GdNi5 compound the negative Ni3d band polarization by Gd5d band is observed [4,8]. As a consequence the total magnetic moment in this compound is smaller than for free Gd3þ what is in accordance with band structure calculation [8]. It seems to be that such observed interesting magnetic properties can be caused by a statistical Yb/Gd substitution which leads to crystallographic disorder in the unit cell. Probably the inhomogeneous distribution of the magnetic moment especially under the FC mode and two or more magnetic sublattices have a considerable influence on the observed effects. Under certain favourable conditions, the frustration of the magnetic interaction between these sublattices causes an appearance of negative M(T) value. Additionally, a decrease of the temperature of the main magnetic phase transition (Tmag1) from 33 K to 16 K has been observed. Obviously, the total magnetic moment also decreases from 6.52 mB/f.u. (x ¼ 0.0) to 4.36 mB/f.u. (x ¼ 0.5) which confirms the opposite arrangement of the magnetic moment in 4f and 3d sublattice [13]. The main contribution to the M(T) comes from the (Gd/Yb)Ni5 phase which gives the ferrimagnetic phase transition below 30 K. The unusual behaviour of M(T) in the temperature range

387

Tmag1 < T < Tmag2 may be related to the magnetic behaviour of Gd/ Yb sublattice on the molecular level. The appropriate Happl favours such an arrangement within 4f sublattice than 4fe4f interaction between 4f-orbital and 4f-spin moments as well as CEP leads to the emergence of negative M(T) values and different Tcomp. In some bulk intermetallics such a negative M(T) is usually accompanied by an exchange-bias phenomenon [15,18,19,21,23]. 3.2. The hysteresis loops The interesting behaviour of the sets of FC e ZFC curves has been the cause to measure the hysteresis loops. The applied magnetic field was cycling between 1500 Oe. Fig. 2 shows M(H) curves at four chosen temperatures 2 K, 50 K, 100 K and 150 K. By analysing of M(H) loops one can notice a small shift. This shift is most known as the exchange bias (EB) phenomenon. This effect is usually observed when the sample is cooled in the presence of an applied magnetic field. Thus, EB is due to the anisotropy caused by the coupling of the ferromagnet (FM) to antiferromaget (AFM) at the interface in the thin films and is mostly discussed in relation to the pinning of the ferromagnetic moments in two layers below TN [17,25]. In this case the occurrence of a positive EB is observed. However the presence of a such phenomena was also evidenced in the bulk compounds e.g. Ni50Mn35In15 Heusler alloy [17,22] where EB behaviour has been evidenced in the low temperature range at martensitic state, Laves phases [17e19,23] or some oxides [17]. In the first group EB is associated with the coupling of the FM to the

Fig. 2. The hysteresis loops measured at 2 K, 50 K, 100 K and 150 K for the YbxGd1
xNi5 series: (a) x ¼ 0.2; (b) x ¼ 0.4; (c) x ¼ 0.5. An arrow marks the hysteresis at 2 K depicted on an additional axis.

388

A. Bajorek et al. / Intermetallics 32 (2013) 384e393

AFM at the interface of AFM and FM grains. Such a structure causes a unidirectional anisotropy when the sample is cooled at the magnetic field. In the bulk intermetallic compounds e.g. Nd0.75Ho0.25Al2 or some samarium compounds [17e20] it was proved that the EB phenomena and the change within its sign in the vicinity of Tcomp is correlated to the reversal orientation in conduction electron polarization (CEP) in relation to the external applied magnetic field. In the intermetallic compounds with different R atoms it is possible to observe the compensation point at a certain temperature. Such an effect gives “net-zero” magnetization within R sublattice and it was previously observed in the systems with nonmagnetic element such as R1
xR0 xAl2 [17e19,23] but also in e.g. the R(Fe1
xTx)3 series [1,24] where the compensation point which is typical for ferrimagnetic compounds with two magnetic sublattices. In the first 1:2 series the EB phenomena was discovered and described in the vicinity of Tcomp and with relation to the CEP [17e 19]. At the compensation point the magnetic moment coming from R sublattice is almost compensated and therefore the CEP plays a significant role. So the polarization of the conduction electrons is sensitive to the mutual arrangement of the magnetic moments within the R sublattice in the presence of the applied magnetic field (Happl). Thus, both R moments are aligned opposite one to each other and high enough Happl causes different CEP e (MReMR) exchange coupling in T < Tcomp as well as Tcomp < T < TC ranges. The negative EB was observed in T < Tcomp [17e19,23]. The temperature variations of the EB field (HEB) and the coercivity (HC) obtained from the hysteresis loops in the YbxGd1
xNi5 series are presented in the Fig. 3. The HEB and HC fields have been calculated from the hysteresis loops as the change HEB ¼ (HCþ þ HC
)/2 and HC ¼ (HCþ
HC
)/2 respectively. Both parameters indicate the oscillating behaviour with the change of the temperature. The most visible change has been evidenced at low temperature range below 100 K. The HEB changes its sign from the negative to the positive for

x > 0.2 and approaches zero around 76 K, 63 K for x ¼ 0.4 and 0.5 respectively. The highest value of EB has been noticed for x ¼ 0.4 ytterbium concentration (see Fig. 3a). Moreover, for the same concentration we have observed the biggest change in the FC e ZFC curves and the highest negative value of M(T) (see Fig. 1c). However, in our case the EB is smaller in comparison to the Ni50Mn35In15 alloy as well as to Nd0.75Ho0.25Al2 and Sm0.975Gd0.025Cu4Pd. In latter two compounds EB approaches 400 Oe and þ500 Oe respectively [18,20]. While we have obtained the higher value of EB only
67 Oe and þ30 Oe in the case of 40% of ytterbium concentration. It is worth to notice that HEB reverses its sign in the temperature range where HC values reach the minimal level this is w78 K and w62 K for x ¼ 0.4 and 0.5 respectively. Thus in the studied YbxGd1
xNi5 especially for higher Yb content x  0.5 the orientation of 4f moments within 4f sublattice and its relation to conduction electron may lead to different magnetic arrangement below and above Tcomp where the reversal of the HEB sign has been observed. 3.3. The magnetocaloric effect MCE The magnetocaloric effect (MCE) represents the isothermal entropy change or the adiabatic temperature change by applying or removing an external magnetic field [30e36]. The interaction between magnetic sublattice and applied magnetic field causes the arrangements of unpaired 4f or 3d electrons with the field. When the magnetic field is switched off the magnetic moments come back to the chaotic orientation. The magnetizatione demagnetization process is reflected in the change of the magnetic entropy. The MCE can be evaluated from the magnetic entropy change DSm(T,H) according to the formula:






DSm T; H ¼

ZH   vM dH’ vT H’

(1)

0

and can be calculated from a family of magnetic isotherms measured at different temperatures. The value of DSm(T,H) at T ¼ TC and Dm0H ¼ 1 T for GdNi5 is close to the previously reported [37]. However is a little bit higher that for GdNi3 compound (1.53 J/kg K) [24]. At Dm0H ¼ 7 T the magnetic entropy change value for GdNi5 equals 12.73 J/kg K and is little bit lower than previously obtained for GdNi2 at the same applied field (w14 J/kg K) [37] and much higher than for GdNi3 compound (7.21 J/kg K) [24]. The DSm(T,H) curves for the YbxGd1
xNi5 compounds (x  0.5) are presented as a function of temperature at magnetic field change Dm0H ¼ 1 T (Fig. 4a) and as a function of magnetic field up to 7 T at temperatures Tmag1 (Fig. 4b). The maximum entropy change at Dm0H ¼ 1 T is observed for the x ¼ 0.2 ytterbium concentration (3.51 J/kg K) and decreases with the increasing Yb content to 2.23 J/kg K for x ¼ 0.5. For all investigated samples the increase in applied magnetic field causes an increase in DSm(T,H). The highest value of DSm(T,H) was observed at Dm0H ¼ 7 T for the Yb0.2Gd0.8Ni5 compound (19.98 J/kg K) and the lowest for x ¼ 0.4 (9.12 J/kg K). The higher values of MCE in doped compounds is typical in systems with higher number of 4f electrons [37]. 3.4. Electrical resistivity

Fig. 3. The exchange bias HEB (a) and coercivity HC (b) fields in the YbxGd1
xNi5 series (x ¼ 0.2, 0.4, 0.5).

The temperature dependence of electrical resistance has been measured for the whole YbxGd1
xNi5 (x  0.5) series. The increase of Yb content in YbxGd1
xNi5 alloys causes the decrease of Tmag1 value (see Table 2) obtained from the plots of R/R(273) versus T (see Fig. 5a). This kind of behaviour is confirmed also by magnetic measurements at higher magnetic field (0.1 T).

A. Bajorek et al. / Intermetallics 32 (2013) 384e393

Fig. 4. (a) Temperature dependence of DSm(T, m0H ¼ 1 T) of the YbxGd1
xNi5 compounds. (b) Field dependence of DSm(T ¼ Tc, H) of the YbxGd1
xNi5 compounds.

The electrical resistivity has been measured on a bar-shaped samples using a standard four probe technique. Knowing the dimensions of samples we were able to obtain the thermal variation of electrical resistivity r(T) besides x ¼ 0.2. The sample with

389

Fig. 5. (a) The electrical resistance R/R(273) in the YbxGd1
xNi5 series. (b) As an example the temperature dependence of the electrical resistivity r(T) in GdNi5 compound fitted by the use of the BlocheGrüneisen relation (3). Inset represents fitting with the use of (4) formula.

this concentration had a lot of microcracks and was too brittle for cutting. The r(T) dependence for YbxGd1
xNi5 series shows a typical metallic behaviour in opposite to thermal dependence of electrical

Table 2 The electrical resistivity parameters for the YbxGd1
xNi5 compounds. x

0.0 0.2 0.4 0.5

Tmag1 [K]

33.7 24.3 18.8 13.3

r0 [mU cm] 27.38 e 12.5 9.25

T < Tmag1

Tmag1 < T < 100 K

a [mU cm/K5]

b [mU cm/K3]

c [mU cm/K2]

n

7.98  10
8 e 7.98  10
7 7.94  10
7

1.04  10
4 e 3.65  10
4 7.64  10
4

4.46  10
3 e 10.6  10
3 14.3  10
2

2.05 e e e

D

Tmag1 < T < 300 K

A [mU cm/K]

B [mU cm/K2]

r0 [mU cm]

QD [K]

[meV]

r0 [mU cm]

R [mU cm/K]

K [mU cm/K3]

e e 1.45 1.07

35.1 e 12.3 9.21

5.78  10
2 e 4.5  10
3 6.56  10
3

1.94  10
4 e 1.88  10
4 1.29  10
4

37.3 e 12.5 9.4

528.6 e 288.7 289.8

0.408 e 0.032 0.027

8.2  10
8 e 1.83  10
8 0.078  10
8

390

A. Bajorek et al. / Intermetallics 32 (2013) 384e393

Table 3 The specific heat parameters for the YbxGd1
xNi5 compounds. x

0.0 0.2 0.4 0.5

Tmag1 [K]

T > Tmag1

31.9 27.2 21.6 16.3

59.4 83.6 83.0 115.2

g [mJ/mol K2]

QD [K]

   

335.8 316.1 313.5 333.6

0.6 1.1 1.3 0.9

QE [K]

   

3.0 4.1 4.0 2.7

252.6 229.2 225.4 254.0

   

3.7 5.3 5.3 5.1

Smag [J/mol at Tmag

Smag [% of Rln8] at Tmag

13.9 10.9 8.2 6.7

80 63 48 39

resistivity for Yb(Cu, Al)5 compounds where logarithmic dependence typical for Kondo scattering and crystal field effects was found [41]. According to the Matthiesen’s rule the thermal dependence of resistivity is ascribed by the equation:




 r T ¼ ro þ rph T þ rmag T

(2)

in which the first term represents a residual resistivity, second the phonon contribution due to the interaction of conduction electrons with thermally excited phonons and the third consists of spindisorder contribution which is caused by the scattering of the conduction electrons on 4f moments and contribution correlated with spin fluctuations. The observed value of residual resistivity obtained experimentally at 4.2 K decreases with increasing Yb concentration from ro ¼ 27.28 mU cm (x ¼ 0.0) to ro ¼ 9.25 mU cm (x ¼ 0.5) (see Table 2). The highest value of ro observed for GdNi5 compound can be correlated with some microcracks detected by SEM image (not shown here). The decrease of ro value with increasing of Yb concentration is correlated with different sizes of ionic radii for A) and Gd3þ (1.02 A) ions. The change of ro value with Yb/ Yb3þ (0.94  Gd substitution can suggest that Yb ions can occur in trivalent state A) is smaller than because the value of ionic radius for Yb3þ (0.94  A). Yb2þ (1.13  The behaviour of r(T) above Tmag up to 300 K can be fitted (as an example see Fig. 5b) using modified BlocheGrüneisen relation:

rðTÞ ¼ ro þ 4RQD



T

QD

5

T= Z QD

0

x5 dx
KT 3 ðex
1Þð1
ex Þ

(3)

where R is a constant and last term describes interband processes connected with electron scattering on sed bands according to Mott’s theory. The method used to fit the experimental value of the electrical resistivity by Equation (3) is the standard least squares method. The fitting procedure has been performed by using Mathematica computer program through minimization of the sum of squared residuals. The residual in such fitting procedure is the difference between the experimental data and obtained by an Equation (3). Such a theoretical fit was used many times in RT5 compounds [27,28]. The magnitude of K constant in Equation (3) equation and its sign depends on the density of states at the Fermi level (EF) and its curvature. Such a parameter describes the scattering of the conduction electrons into the narrow d band near EF. The least-squares fitting procedure yields the values of ro, R, K and QD which are presented in Table 2. The Gd/Yb substitution causes the change within all estimated parameters. Thus, it has been found that the residual resistivity is similar to experimental one and R parameter varies from 0.408 mU cm/K to 0.027 mU cm/K for x ¼ 0.0 and 0.5 respectively. Quite interesting behaviour has been noticed for the Mott’s coefficient K, which decreases from 82.2  10
8 mU cm/K3 to 0.078  10
8 mU cm/K for x ¼ 0.0 and

x ¼ 0.5 but exhibits a negative
1.84  10
8 mU cm/K value for x ¼ 0.4. For such a concentration the valence band near by EF indicates the largest intensity of states around 1.45e0.9 eV binding energy range [5]. The values of QD obtained from fitting for both doped compounds is almost the same (Table 2). In the paramagnetic range r(T) show almost linear behaviour what is connected with electron e phonon scattering. In the case of GdNi5 compound due to the large amount of microcracks the whole values obtained from the r(T)fitting may be higher. The low-temperature resistivity between 20 K and 100 K can be approximated by a T2 dependence which is correlated with spin fluctuations. The fitting using

r ¼ ro þ AT þ BT 2

(4)

formula gives better results than BlocheGrüneisen relation in this temperature range (inserts to Fig. 6aec). Such a square dependence probably may indicate the contribution of spin fluctuations. In many RNi4X compounds the main contribution to r(T) dependence below Tmag1 is connected with scattering on the spin wave excitations and is represented by rm w T2 dependence [27,28]. For compounds where R ¼ Nd, Sm the magnetic part of electrical resistivity in low temperatures is strongly dependent on magnetic anisotropy which causes a gap D in the magnon spectrum. As it was reported before [28] in the case of GdNi4X compounds the magnetic anisotropy can be negligible. Analysing the r(T) curve below Tmag1 we have to take into account the phonon contribution (rph w T5) and the scattering of s electrons to free d states (rsd w T3). Therefore, the following expression has been used only for the pure GdNi5 compound:

r ¼ ro þ aT 5
bT 3 þ cT n

(5)

The obtained n parameter is close to 2 which indicates the scattering on the spin waves (magnons). In the case compounds with x  0.4 the resistivity below Tmag1 can be rather fitted by using the equation:



r ¼ ro þ aT 5
bT 3 þ cT 2 exp
d=T



(6)

where a, b, c are constants and parameter d is proportional to the energy gap (d ¼ D/2kB). The all obtained parameters are presented in Table 2. The a parameter is almost stable in the all studied samples. At the same time the value of energy gap D in the spin waves spectra indicates the higher value for x ¼ 0.4. This change is caused by using additional energy which is needed to reverse the localized spins opposite to the anisotropy field. It is worth to mention that for this Yb concentration we have observed the most pronounced negative M(T) in the presence of low applied magnetic field. 3.5. The specific heat Fig. 6a shows the temperature dependence of the specific heat C(T). Inset represents C(T) in the low temperature range. A welldefined l-type anomaly has been observed only at Tmag1 like in the case of some RNi5 compounds [38e40]. The values of Tmag1(x) are in a good agreement with those obtained from the magnetic measurements (see Table 3). Below the anomaly at Tmag1 an upturn of the C/T versus T2 has been observed for x ¼ 0.4 and x ¼ 0.5 (see Fig. 6b). This effect is much more higher in the case of x ¼ 0.5. Additionally below 3 K a trace of extra peak has been found. Such a discontinuity in many Yb compounds is attributed to the presence of an extra Yb2O3 phase

A. Bajorek et al. / Intermetallics 32 (2013) 384e393

391

Fig. 6. (a) The temperature dependence of the specific heat C(T) in the YbxGd1
xNi5 series fitted according to (8) equation. Inset represents C(T) in the low temperature range. (b) C/T versus T2 in the YbxGd1
xNi5 series. Inset shows C/T versus T2 for x ¼ 0.4 and 0.5 Yb concentration. (c) The magnetic part of the specific heat Cmag(T) in the YbxGd1
xNi5 series obtained by (10) formula. (d) The magnetic entropy Smag versus temperature in the YbxGd1
xNi5 series obtained with the use of (11) equation.

which exhibit antifferomagnetic arrangement around 2 K [44]. In order to explain the origin of a such behaviour the C(T) dependence has been measured carefully once again below 10 K to 1 K (see inset to Fig. 6c). Notice that around 4 K2 there is clearly visible a peak which may be associated to the antiferromagnetic phase transition in Yb2O3. Those measurements confirms the increase in the C/T for x ¼ 0.5 ytterbium concentration. This increase in may Yb compounds points to the heavy fermion behaviour and indicate a Kondo interaction usually in the presence of CEF splitting, especially when the electronic specific heat coefficient is high enough [41,42]. Such enhancement of g coefficient in the low temperature specific heat dependence usually is characteristic for the mixedvalent compounds [42]. To get the magnetic contribution Cm(T) to the specific heat the electronic and phonon contributions have to be subtracted. There are two possibilities to estimate Cm(T). The first can be performed by using the nonmagnetic analogue and the second is based on the optimal fit the experimental data by using the standard formula:



Ctheor ¼ Cel þ Cph ¼ gT þ 9nR

T

QD

3 QZD =T 0

x4 expðxÞ ½expðxÞ
12

dx

(7)

where Cel represents the electronic contribution and g is the electronic specific heat coefficient, Cph represents the lattice contribution and n is the number of the atoms in the formula unit, QD is the Debye temperature [50]. At higher temperatures the specific heat

can take value over the DulongePetit limit (3nR) and some correction coefficient has to be taking into account [45e47,51]. In our case the best fitting has been obtained by using the expression:

      Ctheor ¼ Cel þ Cph ¼ gT þ 1
k CD T þ kCE T

(8)

where the phonon contribution to C(T) consists of both the Debye CD(T) as well as Einstein CE(T) functions:


 CD T ¼ 9nR



T

QD

3 QZD =T 0

x4 expðxÞ ½expðxÞ
12

dx

(9)


2      3 
 QE QE QE
1 exp exp CE T ¼ 3nR T T T as well as the k parameter which is correlated to the oscillator correction coefficient. The estimated values of g, QD and QE are presented in Table 2. One can see that the increase of yterrbium concentration is reflected in the increase of g from 59.4 [mJ/mol K2] (x ¼ 0.0) to 115.2 [mJ/mol K2] (x ¼ 0.5). It was previously reported that in the GdNi5 compound g ¼ 36 [mJ/mol K2] and QD ¼ 296  2 K. This values were obtained under the assumption that Cph(T) is described only by Debeye function [39]. In second experiment performed for the whole RNi5

392

A. Bajorek et al. / Intermetallics 32 (2013) 384e393

series it was shown that for the whole series g reaches value 32  2 [mJ/mol K2] [40]. In our case g values are higher than obtained by fitting by Debye function (9) and higher than obtained from the electronic structure calculation [43]. Such a quite large g coefficients probably are not related to the heavy fermion behaviour but are an evidence of an additional contribution to C(T) e.g. such as spin fluctuations near Tmag1, influence of the CEF in Yb-rich compounds. However, an enhanced g may and an upturn in C/T dependence (x ¼ 0.5) be an indication of a mixed-valent state of ytterbium ions as shown by the highest intensity of states near by the EF for such Yb content [5]. One can notice that with Gd/Yb substitution g increases. It is obvious because usually some ytterbium compounds exhibits quite large value of electronic specific heat coefficient e.g. in the YbPdSn compound g ¼ 68 [mJ/mol K2] [44], in the Yb(Cu1
xAlx)5 series the highest value of g was observed for x ¼ 0.7 and equals g ¼ 120 [mJ/ mol K2] [29,41] and in the YbXCu4 series where g reaches even 230 [mJ/mol K2] for X ¼ Zn [42]. In contrary in some Yb-compounds the electronic specific heat coefficient is quite small e.g. in the YbNi4Cu equals 10 [mJ/mol K2] and this compound is not ordered magnetically to 2 K [45], for YbNi4Si g ¼ 25 [mJ/mol K2] e two valence state with domination of Yb3þ [46]. The magnetic part of C(T) as well as the magnetic entropy (Smag) are related to the energy levels of the magnetic ions. Fig. 6c presents the temperature variation of the magnetic contribution to C(T) after fitting with the use of (8) formula and subtracting as:

Cmag ¼ Cexp
Ctheor

(10)

The hump at T < Tmag usually arises from the Schottky like anomaly in the ordered state involving (2J þ 1) e fold degenerate multiplet. For Gd compounds because their 8S7/2 states with zero orbital moment, the ground state multiplet (J ¼ 7/2) is not influenced by the crystal electric filed (CEF). However, in the case of Yb3þ (2F7/2 multiplet) in the hexagonal symmetry (CaCu5 crystal structure) CEF splits 4f level with J ¼ 7/2 into four doublets (n ¼ 8). So, when the Gd/Yb substitution increases the CEF starts to be significant. It is worth to mention that in our case the whole fitting procedure can be influenced by an impurity of Yb2O3 phase and the obtained parameters may be a bit disrupted. The integration of the Cmag/T versus T dependence leads to the temperature dependence of the magnetic entropy Smag(T) according to the relation:


 Smag T ¼

ZT

Cmag ðTÞ dT T

(11)

0

The magnetic entropy described as Smag ¼ Rln(2J þ 1) where J is a quantum number and R is a molar gas constant, should reach its full value at high temperature. For Gd compounds J ¼ 7/2 because the orbital moment S equals zero and the ground state is not influenced by CEF. Thus, the full Smag for such compounds equals 17.3 [J/mol K] but in fact the experimental Smag in some gadolinium compounds above Tmag reaches at least 80e90% of Rln8 [48,49] and even 0% as in the case of GdInCu4 system [37]. In our case at Tmag1 the value of Smag decreases from 13.9 [J/mol K] (x ¼ 0.0) to 6.7 [J/ mol K] (x ¼ 0.5) (see Fig. 6d) which corresponds respectively to 80% and 39% of full Rln8. It is worth noticing that above Tmag1 the magnetic entropy attains almost 84% (x ¼ 0.0) and 47% (x ¼ 0.5) of the full Smag. Thus, probably the short-range magnetic correlations within 4f sublattice can be still present above Tmag1 and may have an influence on the magnetization which indicate an unusual behaviour.

4. Summary and conclusions To summarize, here we have presented highlights results of our studies on magnetic and transport properties in the polycrystalline YbxGd1
xNi5 series (x  0.5). All obtained results can be concluded as follows: a) The value of the temperature of main magnetic phase transition Tmag1 decreases from 33  3 K (x ¼ 0.0) to 13  3 K (x ¼ 0.5). The transition at Tmag1 has been confirmed by all performed measurements and it may be related to the well known magnetic transition typical for CaCu5-type of structure with magnetic 3d-transition element. So, the magnetic structure in the studied system can be recognized as ferrimagnetic. The observed decrease within Tmag1 as well as the saturation magnetization MS is a result of Gd/Yb substitution due to the lower ytterbium contribution to the total magnetization. b) An unusual M(T) dependence related to the negative magnetization values has been observed in the Tmag1 < T < Tmag2 temperature range. Such a behaviour may be caused by the field-induced reversal of the arrangement of local Gd/Yb magnetic moments as well as CEP. At a certain Tcomp the 4forbital and 4f-spin contribution to the total magnetization is compensated and then CEP plays an important role. Such an effect is closely related to the exchange bias phenomenon. Here, this effect can be highlighted and it has been observed for the first time in the case of heavy 4f elements and may be associated with. c) The hysteresis loops indicate an exchange bias phenomena for Yb-rich compounds. Additionally, the HEB changes its sign across Tcomp in correlation with the coercivity HC. It can be a result of an interplay between self-compensation of tiny Yb3þ local moments and the competition between of the magnetic moment associated with Gd3þ as well as doped Yb3þ ions including tiny CEP which also takes part in a such competition. The exchange bias as well as and the accompanying negative M(T) value is present in certain applied magnetic field which are lower than HC. Nevertheless observed phenomena are much more weaker than the main contribution to the total magnetization which is derived from the R(4f)eNi(3d) interactions. The possible field-induced switching effect of spin and orbital moment within 4f sublattice in relation to the CEP can have a useful application as the material in spin-resolved nanodevices. d) The change of magnetic entropy (DSm(T ¼ TC, m0H ¼ 1 T) for the studied YbxGd1
xNi5 compounds decreases with increasing Yb concentration from 3.17 J/kg K (x ¼ 0) to 2.23 J/kg K (x ¼ 0.5). This behaviour can be explained by an increase in a magnetic disorder in 4f magnetic sublattice. e) The electrical resistivity in the vicinity of Tmag1 is proportional to T2 which indicates the contribution of the spin fluctuation. In the higher T the r(T) dependence is well defined by the Bloche Grüneisen relation. The value of the residual resistivity (ro) obtained from r(T) fitting is close to the experimental one. The gradual decrease of ro(x) with Gd/Yb substitution may point to the trivalent state of ytterbium ion which has a lower ionic radius than divalent one. For ytterbium doped samples the estimated energy gap in the magnon spectrum adopts the highest value for x ¼ 0.4. f) The temperature dependence of the specific heat above Tmag1 is mostly influenced by phonons which on this temperature give larger contribution than electrons. Thus, the electronic specific heat coefficient increases upon Gd/Yb substitution from 59.4 [mJ/mol K2] (x ¼ 0.0) to 115.2 [mJ/mol K2] (x ¼ 0.5). The g coefficient is proportional to the density of states on the Fermi

A. Bajorek et al. / Intermetallics 32 (2013) 384e393

level. Thus, such an increase within g can be probably associated with the change in the electronic structure. Thus, an enhanced value of g for higher Yb concentration may be an indication of the mixed valence of ytterbium ions. The value of the magnetic entropy estimated from the Cmag(T) at Tmag1 attains at most 80% (x ¼ 0.0) of the total entropy Smag ¼ Rln8. Such an effect is typical for Gd-like compounds and is due to the magnetic correlations which reduces the expected value of Smag. The Gd/Yb is reflected in the decrease of the magnetic entropy to 39% of Rln8 at Tmag1 (x ¼ 0.5). It is due to the influence of CEF. Acknowledgements  We thank prof. dr hab. A. Slebarski, dr J. Goraus and mgr M. Fija1kowski for performing the PPMS measurements. References [1] Buschow KHJ. Rep Prog Phys 1977;40:1169. [2] Burzo E, Che1kowski A, Kirchmayr HR. Landolt Börnstein handbook, vol. III. Berlin: Springer; 1990. 19d2. [3] Coldea M, Chiuzbaian SG, Neumann M, Todoran D, Demeter M, Tetean R, et al. Acta Physica Polonica 2000;98:629. [4] Gignoux D, Givord D, Moral A del. Sol State Comm 1976;19:891. [5] Bajorek A, Che1kowska G. Acta Physica Polonica A 2009;115:188. [6] Burzo E, Pop V, Costina I. J Magn Magn Matter 1996;157/158:615. [7] Nesbitt EA, Williams HJ, Wernick HJ, Sherwood RC. J Appl Phys 1962;33:1674. [8] Bajorek A, Stysiak D, Che1kowska G, Deniszczyk J, Borgie1 W, Neumann M. Mater Sci e Poland 2006;24:867. [9] Balkis Ameen K, Bhatia ML. J Alloys Compd 2002;347:165. [10] Fremy MA, Gignoux D. J Less-Comm Metals 1985;106:251. [11] Palenzona A, Cirafici S. J Less-Comm Metals 1973;33:361. [12] He J, Tsujii N, Nakanishi M, Yoshimura K, Kosuge K. J Alloys Compd 1996;240:261. [13] Bajorek A, Che1kowska G, Chrobak A. J Phys Conf Ser 2010;200:032005.  ski T. Acta Physica Polonica A 2006; [14] Andrzejewski B, Kowalczyk A, Tolin 109:561. [15] Suski W. Mater Sci e Poland 2007;25:333. [16] Drzyzga M, Szade J. J Alloys Compd 2001;321:27. [17] Giri S, Patra M, Majumdar S. J Phys: Condens Matter 2011;23:073201. [18] Kulkarni PD, Thamizhavel A, Rakhecha VC, Nigam AK, Paulose PL, Ramakrishnan S, et al. Euro Phys Lett 2009;86:47003. [19] Venkatesh S, Vaidya U, Rakhecha VCh, Ramakrishnan S, Grover AK. J Phys: Condens Matter 2010;22:496002.

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