Evolution of magnetic properties in the solid solution UCo1−xPdxGe

Author’s Accepted Manuscript Evolution of magnetic properties in the solid solution UCo1−xPdxGe D. Gralak, A.J. Zaleski, V.H. Tran

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S0022-4596(16)30285-7 http://dx.doi.org/10.1016/j.jssc.2016.07.025 YJSSC19472

To appear in: Journal of Solid State Chemistry Received date: 3 February 2016 Revised date: 15 June 2016 Accepted date: 24 July 2016 Cite this article as: D. Gralak, A.J. Zaleski and V.H. Tran, Evolution of magnetic properties in the solid solution UCo1−xPdxGe, Journal of Solid State Chemistry, http://dx.doi.org/10.1016/j.jssc.2016.07.025 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Evolution of magnetic properties in the solid solution UCo1−x Pdx Ge D.Gralak, A.J. Zaleski, and V.H. Tran Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P. O. Box 1410, 50-422 Wroclaw, Poland

Abstract We have investigated the evolution of magnetic properties in pseudo-ternary UCo1−x Pdx Ge (x = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9) intermetallics by measurements of ac-magnetic susceptibility and dc-magnetization. The measured samples have been prepared by arc-melting and characterized by powder X-ray diffraction and X-ray energy-dispersive electron spectroscopy technique. Rietveld refinements of the X-ray patterns indicate that the pseudo-ternaries crystallize in the orthorhombic TiNiSi-type structure with Pnma space group as the parent UCoGe and UPdGe compounds do. The magnetic measurements reveal that in addition to an increase in 5f -electron localization degree with increasing Pd concentration, an interesting magnetic phase diagram, which is more complex than that expected from the gradual change in magnetic ground state due to the substitution. Three compositional ranges with different magnetic properties have been established; the coexistence of spin-glass and itinerant-electron ferromagnetic orderings for x ≤ 0.3, antiferromagnetic order occurs in the range 0.4 ≤ x ≤ 0.7, and a complex ferromagnetic structure of more localized 5f moments takes place in x ≥ 0.8. The evolution of magnetic ground states in UCo1−x Pdx Ge is discussed in terms of interplay between cooperative magnetic interactions. We consider also implications of increasing conduction electrons upon the Pd substitution in Ruderman-Kittel-Kasuya-Yosida interactions, which would give rise to the evolution of magnetic properties in UCo1−x Pdx Ge pseudo-ternaries. PACS numbers:

1

I.

INTRODUCTION

Among the most interesting are intermetallic U-based systems, in which one observes exotic phenomena or one modifies their physical properties with an precise adjustment of chemical compositions. One of them is just the series of equiatomic ternaries with the chemical formula UTM, where T is a d - electron transition metal and M = Si or Ge [1, 2]. Based on systematic studies of U-based intermetallics, it has been established that magnetic ground state properties are determined by the localized/delocalized duality of 5f electrons, of which the nature depends mainly on strength of the 5f-spd hybridization [1]. In the UTM series, the degree of localization becomes higher when the number of d -electrons is increased. Thereby, the 5f -electrons in compounds containing Fe or Ru are certainly itinerant, and ground state is nonmagnetic. On the other hand, the 5f-electrons in ternaries consisting of Ni, Rh, Pd or Pt are more localized and these compounds order magnetically at low temperatures [1, 2]. In principle, one follows the evolution of magnetic ground state with a trivial substitution, e.g., substituting any of U, T or M for one another element but keeping the same crystal structure. It has been shown by Chevalier et al. [3] that in the URh1−x Irx Ge system a transition from a ferromagnetic to an antiferromagnetic ground state takes place near x = 0.45 - 0.50. In other solid solution systems, even more exciting properties can be found because of the possibility of observing a deviation from Fermi-liquid theory, e.g., a non-Fermi liquid behaviour apparently occurs in the vicinity of magnetic quantum critical point; where Curie temperature in URu1−x Rhx Ge [4, 5], UCo1−x Fex Ge [6], UCo1−x Rux Ge [7] or N´eel temperature in URu1−x Pdx Ge [8] is presumably suppressed to 0 at a critical concentration xcr . In the continuing course of searching for new phenomena, which arise from the coexistence or interplay between various cooperative interactions, we undertook measurements of magnetic properties on pseudoternary UCo1−x Pdx Ge system. UCoGe is ferromagnetic below ∼ 3 K and becomes superconducting below 0.7 - 0.8 K [9, 10]. On the other hand, UPdGe displays typical Kondo lattice behaviour in its electrical resistivity [11], and undergoes two successive phase transitions; an antiferromagnetic at 50 K and a ferromagnetic below 30 K [2]. The successive phase transitions have been confirmed by neutron diffraction experiments, where complicated spin structure was reported between 28 and 50 K [12, 13], and a simple ferromagnetic structure below 28 K with magnetic moments pointed along the

2

orthorhombic b-axis [14]. Because of ferromagnetic ground state in both the parent UCoGe and UPdGe compounds, the substitution of Co by Pd should not be expected to alter the ferromagnetic ground state. However, owing to the presence of the Kondo and antiferromagnetic interactions in UPdGe, we hope to introduce competing antiferromagnetic correlations in UCo1−x Pdx Ge, and in jointing increasing localization of the 5f electrons we anticipate to observe an anomaly in the evolution of magnetic properties upon the substitution. In this paper, we report X-ray diffraction data, ac magnetic susceptibility and dc magnetization for the pseudoternary UCo1−x Pdx Ge system. To the best of our knowledge, no data on magnetic properties of the UCo1−x Pdx Ge system are reported so far.

II.

EXPERIMENTAL DETAILS

Polycrystalline samples of UCo1−x Pdx Ge with x = 0.1 - 0.9 were prepared using the standard arc-melting technique. The purity of elements was U: 99.8%, Co: 99.99 %, Pd: 99.9 %, Ge: 99.999 %. Mass losses during the preparation were less than 0.1 % for these samples. The elemental compositions of a few controlled specimens (x = 0.1, 0.3, 0.5, 0.7 and 0.9) were done utilizing a scanning electron microscope FEI Nova NanoSEM 230 equipped with Xray energy-dispersive spectrometer (EDX). The atomic percentages of ingredients obtained from EDX spectra are very close to the theoretical values of the starting compositions. The quality of the samples was also examined by means of powder X - ray diffraction (XRD) at room temperature, utilizing an X0 Pert PRO diffractometer and monochromatized CuKα radiation (λ = 0.15406 nm). The diffraction patterns over the 2θ range of 10 - 90 deg. were recorded with a scan speed of 2 deg/min. The X - ray diffraction data were quantitatively analysed using the Rietveld method with the help of the FULLPROF software [15]. The ac susceptibility was measured with an Oxford Instrument susceptometer. An ac driving field amplitude of 795.77 A/m and frequencies f = 100 Hz, 1 kHz and 10 kHz were applied. The dc - magnetization (M ), measurements were made with a Quantum Design MPMS magnetometer in the temperature range 2 - 400 K and in magnetic fields µ0 H up to 5 T. From the magnetization values, magnetic susceptibility (χ(T )) is calculated using the relation χ(T ) ≡ M (T )/µ0 H. Zero-field cooling (ZFC) and field cooling (FC) measurements of isofield magnetization were carried out for x = 0.1, 0.2 and 0.3.

3

512/006/033 125

131/314 413/420 323/421 502/511

105

022

400 303 401 204/222 123/313 321

013/020

202/211

103 301

100

112

EXPERIMENTAL RESULTS AND ANALYSIS

002 102 111 201

III.

x = 0.9 x = 0.8

3

Intensities (10 a. u.)

80

x = 0.7

UCo1-xPdxGe

60 x = 0.6 x = 0.5

40 x = 0.4

x = 0.3

20 x = 0.2

x = 0.1

0 20

30

40

50

60

70

80

2θ (º) FIG. 1: X-ray powder patterns for studied UCo1−x Pdx Ge samples. The open circles are the experimental data and solid lines are the theoretical patterns. To improve the clarity of figure the background data of x = 0.2 - 0.9 have been shifted upward. Miller indices are denoted for strongest Bragg peaks of x = 0.9.

In Fig. 1 we show the X-ray powder diffraction patterns of studied UCo1−x Pdx Ge samples in the angle range 2θ = 20 - 80◦ . We recognize that positions of the Bragg peaks steadily shift down to lower angles with increasing Pd-contents, meaning that the substitution increases unit cell volume of samples. The peaks in XRD patterns are sharp and narrow, suggesting considerable homogeneity of the studied samples. Assuming the TiNiSi-type structure (space group Pnma) we are able to index all observed Bragg reflections, indicative 4

of single-phase materials within the resolution of powder X-ray diffraction technique. To analyse the experimental X-ray data in more detail we have refined following quantities: a scale factor, the pseudo-Voigt profile shape parameters, the instrument zero-point, a peak full width at half maximum (FWHM) function, the lattice parameters and atomic coordinates of all atoms located at the Wyckoff position 4c (x, 0.25, z ). The background was evaluated using twelve-parameter polynomial function. We obtained in the final refinements Bragg Rb -factor values less than 10% and profile Rf -factor less than 8 %. The theoretical patterns (solid lines), compared to the experimental data (open circles) are shown in Fig.

3

0.76

UCo1-xPdxGe

0.74

c-axis

0.23

(b)

0.22 0.21 0.0 0.2 0.4 0.6 0.8 1.0

0.72

Pd concentration x 0.70

0.36

a-axis

dU-U, dU-T (nm)

a, b, c (nm)

V (nm )

1. The obtained unit cell parameters are given in Table I.

0.68 0.44 0.42

b-axis (a)

0.40

0.0 0.2 0.4 0.6 0.8 1.0

dU-U

0.35 0.31 0.30

(c)

dU-T

0.29 0.28

0.0 0.2 0.4 0.6 0.8 1.0

Pd concentration x

Pd concentration x

FIG. 2: The Pd concentration dependencies of (a) the lattice parameters a(x), b(x), c(x), (b) unit cell volume V(x) and (c) distances between nearest U-U dU −U (x) and U-T atoms dU −T (x) in UCo1−x Pdx Ge.

Lattice parameters and unit cell volume as a function of Pd-concentration in UCo1−x Pdx Ge are shown in Fig. 2 (a) and (b), respectively. On the whole, concentration dependencies of the lattice parameters are linearly dependent on the substituted Pd content thus the Vegard rule [16] would be obeyed. Nonetheless, closer inspection of the figure divulges small positive departure in a(x)-parameter but negative departure in c(x). 5

6

0.69805

0.70005

0.70072

0.70347

0.70418

0.6

0.7

0.8

0.9

0.69308

0.3

0.5

0.69083

0.2

0.69609

0.68781

0.1

0.4

a (nm)

x

0.43474

0.43382

0.43255

0.43104

0.42959

4.27817

0.42588

0.42452

0.42261

b(nm)

0.75599

0.75168

0.74794

0.74417

0.74043

0.7346

0.73271

0.72947

0.72703

c(nm)

-0.0026

-0.0024

-0.0028

-0.0044

-0.0046

-0.0048

-0.0042

-0.0031

-0.0021

xU

0.2038

0.2031

0.2033

0.2047

0.2067

0.2048

0.2037

0.2047

0.2055

zU

0.1779

0.1891

0.1907

0.1925

0.2039

0.2048

0.1895

0.1965

0.2092

xT

0.5824

0.5823

0.5807

0.5859

0.5850

0.5822

0.5925

0.5756

0.5820

zT

0.7794

0.7815

0.7855

0.7891

0.8082

0.7832

0.7881

0.7870

0.7989

xGe

0.5813

0.5979

0.6045

0.5813

0.5947

0.6055

0.5906

0.6042

0.5936

zGe

TABLE I: Lattice parameters a, b and c, and atomic coordinates of atoms at Wyckoff position 4c (x, 0.25, y) in UCo1−x Pdx Ge. The lattice parameters are given with an accuracy ≥ 0.00005 nm, while the atomic coordinates 0.0002.

We suspect that the changes in the lattice parameters are affected by enlarged displacements caused by atomic disorders. The expansion of V through solid solution series is about 10% and it is in good agreement with the expectation due to the difference in covalent radius between palladium (rP d = 0.13 nm) and cobalt (rCo = 0.118 nm) [17]. The increase in unit cell parameters in UCo1−x Pdx Ge points to an enlargement of interatomic distances upon the Pd-substitution (see Fig.2 (c)), where the shortest distance between uranium atoms dU −U and between uranium and transition atoms dT −U are shown. The dU −U p and dU −T distances were calculated by: dU −U = (0.5a)2 + ((0.5 − 2 ∗ zU ) ∗ c)2 and dU −T = p ((0.5 + xU − xT ) ∗ a)2 + ((zU + zT − 0.5) ∗ c)2 , respectively. The Pd-concentration dependences of dU −U and dU −T imply weaker orbital overlap, in particular, between those of f-d orbitals. TABLE II: TC , [TN ], (T0 ) denote the Curie, N´eel and freezing temperature, respectively. The parameters: χ0 , Θp and µef f are obtained from fitting the inverse magnetic susceptibility data to mCW law in temperature range 100 - 400 K.

T C ,[T N ], (T0 )

χ0 ·10−8

Θp

µef f

(± 0.5 K)

(± 0.02 m3 /mol)

(± 1 K)

(± 0.05 µB /U atom)

0.0a

3

-

-2

1.7

0.1

21, (20.3)

1.21

-16.8

2.10

0.2

22.8, (21.1)

1.04

-13

2.32

0.3

18, (17)

1.22

6.7

2.38

0.4

[19]

0.93

9.5

2.52

0.5

[27]

1.08

13.3

2.60

0.6

[31]

0.87

18.7

2.70

0.7

9, [29]

0.71

25

2.73

0.8

31

0.39

23

2.90

0.9

39

0.50

25

2.81

1.0b

30, [50]

-

28

2.90

x

a b

Data from Refs.[9, 10] Data from Ref.[2] Fig. 3 displays the temperature dependence of the inverse magnetic susceptibility of

UCo1−x Pdx Ge measured in a magnetic field of 0.5 T. To analyse the data we used a modified Curie-Weiss (mCW) law: χ(T ) = χ0 +NA µ2ef f /[3kB (T −Θp )], where χ0 is a temperature independent susceptibility, µef f is an effective moment, Θp is a paramagnetic Curie temper7

700 UCo

1-x

Pd Ge x

H = 0.5 T

600

0

400

(10

5

3

mol/m )

500

300

200

x =

100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

100

200

300

400

T (K)

FIG. 3: The temperature dependence of the inverse magnetic susceptibility of UCo1−x Pdx Ge in a magnetic field of 0.5 T. The solid lines are the best fits of the mCW law in temperature range 100 - 400 K.

ature, NA and kB are the Avogadro number and Boltzmann constant, respectively. At low temperatures due to development of long-range magnetic order, the inverse magnetic susceptibility exhibits either a downward or upward deviation from the mCW law curvature. For this reason, a satisfactory fit of mCW law to the data was obtained for temperatures above 100 K. The results of the fit as solid lines are shown in Fig. 3 and the fitting parameters are listed in Table II. Owing to texture effects, absolute values of the reported parameters should be taken with caution. Nevertheless, one considers change in magnetic parameters across the solid solution series since crystallographic texture affects alike all samples. Looking at the Table we see that diminution in the temperature independent susceptibility χ0 values accompanies a gradual increase of the effective moments µef f . The change in both χ0 and µef f upon the substitution is quite consistent. This may indicate an increasing degree of the 5f electron localization, from a more itinerant electron magnetism in low Pd-content compounds to a more localized character in rich Pd-content ones. A convincing explanation 8

of this behaviour might be a reduction in the f-d hybridization, as expected from a rapid increase in the U-T distance, as well as a shifting down of 5f -level with respect to the Fermi level due to the d -band filling associated with less charge transfer from the U to the d -band states. We notice the sign change of the paramagnetic Curie temperatures from negative to positive around x = 0.25. As we show below, the sign of Θp does not reflect literally any type of magnetic order. Because Θp is a measure of the average magnetic interaction strength, thus the observed sign of Θp indicates only which type of magnetic interactions dominates at high temperatures. In Fig. 4 we show the ac-susceptibility data of UCo1−x Pdx Ge for x = 0.1, 0.2 and 0.3. A characteristic behaviour is that both real χ0 (T ) and imaginary χ00 (T ) components of the ac-susceptibility do exhibit an intense peak. Assuming Tf to be the position of χ0 (T )maximum, we found Tf = 20.95, 21.75 and 18.98 ± 0.05 K, respectively for x = 0.1, 0.2 and 0.3 at 100 Hz. It is observed that these maxima move to higher temperatures with increasing frequencies, thus indicating the presence of a relaxation process in these alloys. We estimated relative shift in Tf per decade of frequency: δTf = ∆Tf /(Tf ∆log10 f ) to be 0.019, 0.022 and 0.025 in x = 0.1, 0.2 and 0.3, respectively. The observed values make a pitch for spin-glass type behaviour, since they are the same order of magnitude to δTf = 0.004 - 0.018 reported for the canonical spin-glass (SG) systems [18]. In order to characterize the dynamic behaviour of the alloys, we analyzed the frequency dependence of Tf using the phenomenological Vogel - Fulcher law [19]:  −Ea , f = f0 exp kB (Tf − T0 ) 

(1)

where f0 is the attempt frequency of the clusters, Ea is the activation energy, and T0 is the characteristic freezing temperature. For analyzing the data, we have plotted lnf vs. 1/(Tf − T0 ), and choosing T0 value to obtain a straight line. The slope of this line gives magnitude of Ea /kB , and the intercept is lnf0 . For x = 0.1, 0.2 and 0.3 alloys we obtained T0 = 20.3, 21.15 and 17.0 K, Ea /kB = 5.46, 4.47 and 9.43 K, lnf0 [Hz] = 12.98, 12.05 and 14.22, respectively. From the latter values we estimated relaxation time τ0 = 1/(2πf0 ) = 3.67×10−7 , 9.30 ×10−7 and 1.06×10−7 s, respectively. Furthermore, using the equation of critical slowing down [20]: τ =τ

∗



−zν Tf −1 , Tg 9

(2)

50

100

40

100 UCo0.8Pd0.2Ge

(a)

80

30

60

20

40

10

20

0 25

0 40

20

40 20 0 50 100 Hz 1 kHz 10 kHz

30

-5

20

0

20

10

5 16

20

T (K)

24

0 16

100 Hz 1 khz 10 kHz

40

15 10

(c)

60

30

3

χ'' (10 m /kg)

100 kHz 1000 kHz 10 kHz

UCo0.7Pd0.3Ge

80

(b)

-5

3

χ' (10 m /kg)

UCo0.9Pd0.1Ge

10 20

24

T (K)

0

16

20

24

T (K)

FIG. 4: Temperature and frequency dependencies of the ac-magnetic susceptibility measured in an ac-magnetic field of 975.77 A/m for UCo1−x Pdx Ge with x = 0.1 0.3.

where τ ∗ is atomic spin flip time or the shortest relaxation time available to the system, Tg is the static freezing temperature, z is dynamic critical exponent and ν is the critical exponent of the correlation length, we obtained τ ∗ = 1.43×10−9 , 1.29×10−9 and 1.43×10−9 s, Tg = 20.72, 21.58 and 17.65 K, and zν = 3.09, 2.42 and 3.50 for x = 0.1, 0.2 and 0.3, respectively. We recognize that both τ0 ∼ 10−7 s and τ ∗ ∼ 10−9 s are at least of an order of magnitude higher than those reported for spin glasses, i.e., 10−10 - 10−13 s [18]. Our finding of a large relaxation time announces that the dynamic behaviour found in the low Pd-content alloys may be due to superspin-glassis properties having typical values of relaxation time 10−7 10−9 s [21–23]. Moreover, the studied x = 0.1, 0.2 and 0.3 alloys exhibit Ea /(kB Ts ) = 0.2 0.6, which quite low as compared to Ea /(kB Ts ) = 1.2 - 12 usually found in spin glasses [24]. The difference in dynamic behaviour from classical spin-glasses implies the coexistence of spin glass and ferromagnetic orderings in the studied alloys. Owing to similarity of the M(T) curves between x = 0.1, 0.2 and 0.3, we discuss only the M(T) data for x = 0.2 as the representative example. Fig. 5 (a) presents several iso-field

10

0.15

0.30 0.005 T 0.01 T 0.02 T 0.05 T 0.1 T 0.5 T 1T

(a)

0.25

UCo0.8Pd0.2Ge

0.10

µ0H (T)

M ( µΒ)

0.20

(b)

0.15 0.10 0.05

Tir

TC

0.05

0.00

Tir

TC

-0.05 0

5

10 15 20 25 30 35

T (K)

0.00

12

16

20

24

T (K)

FIG. 5: (a) The temperature dependence of the magnetization measured in several magnetic fields. Temperature Tir and TC are denoted by arrows. (b) The dependencies between applied fields and Tir and TC in UCo0.8 Pd0.2 Ge compound. The dashed line presents the theoretical AlmeidaThouless line.

M(T) curves of x = 0.2 collected in ZFC (open symbols) and FC (closed symbols) modes. From the M(T) data obtained in a low field of 0.005 T we determined value of TC = 22.8 K taking as the inflection point of the M(T) curve. In the same manner, TC of the x = 0.1 and x = 0.3 alloys were determined from dc-magnetization, and they are about 1 K larger than Tf . The most relevant result is the pronounced effect of magnetic fields on the M(T) curves. Upon increasing magnetic fields, broad maximum of the ZFC-M(T)-curve moves to lower temperatures and no longer detected by our measurement in fields higher than 1 T. The field dependence of ZFC-M(T)-maximum can be understood in terms of a magnetocrystalline anisotropy effect, which normally exists in 5f -electron intermetallic compounds. However, due to spin-glass properties detected by the ac-susceptibility measurements one should compare ZFC and FC magnetization. For x = 0.2, an irreversible magnetization appears at Tir just above the maximum. We mark this temperature by an arrow for data collected in 0.005 and 0.5 T. In 5 (b) we plot field dependence of Tir . The data can be

11

modelled by a relation µ0 H = Hir,0 [1 − Tir /Tir,0 ]a , where Hir,0 = 0.4 T, Tir,0 = 22 K and a = 3/2. The value of Tir,0 agrees well with the freezing temperature Tf deduced from the ac susceptibility measurement. The exponent a was taken as the mean-field value predicted by Almeida and Thouless for spin-glass materials [25]. It is worthwhile noticing that an application of fields below 0.5 T practically does not alter position of the inflection point of the M(T) curve (see Fig. 5 (b)) but upon larger field strengths TC strongly shifts towards higher temperatures, i.e., TC reaches as high as 23.1, 24.0 K and 25.5 K in fields of 0.5, 1 and 2.5 T, respectively. Obviously, this behaviour is the hallmark of ferromagnetic material.

0.35

0.25

UCo0.8Pd0.2Ge 3

0.30 (a)

M0 (µB), χ1 (µB/T), χ3 (µB/T )

(b)

M ( µ B)

0.25 0.20 0.15 0.10 2K 15 K 20 K 25 K 30 K 40 K

0.05 0.00

0

1

2 3 4 µ0H (T)

10 K 17.5 K 22.5 K 27 K 35 K 45 K

0.20

M0 χ1 χ3

0.15

Fit

0.10 0.05 0.00

5

0

10

20

30

40

50

T (K)

FIG. 6: (a) Isotherms of UCo0.8 Pd0.2 Ge in magnetic fields up to 5 T. The solid lines are fits of data to Eqs. 3, 4a and 4b. (b) Spontaneous magnetization M0 (µB ), linear susceptibility χ1 (µB /T ) and nonlinear susceptibility χ3 (µB /T 3 ) derived from the fitting. Solid line for χ3 data shows the fit with the relation χ3 (T ) ∝ (T − Tf )−γ with Tf = 22.5 ± 0.5 K and γ = 2.9 ± 0.2 K.

The isotherms of UCo0.8 Pd0.2 Ge measured in fields up to 5 T are shown in Fig. 6 (a). The considered compound characterizes by a small spontaneous magnetic moment of 0.26 µB at T = 2 K. In addition, we see that no saturation could be achieved up to 5 T, and the magnetization in this field is only 0.36 µB , being decidedly lower than any theoretical 12

value for localized uranium ions. Therefore, the magnetization data would further prove an itinerant electron magnetism in this Pd-substituted alloy. The ferromagnetic ordering and the Curie temperature may be confirmed by detailed analysing the magnetization data. We recall that for spin-glasses, the magnetization, at temperatures above and below Tf , expressed in terms of linear and nonlinear susceptibilities is expected to follow similar formula [26–28]: M (T, H) = χ1 (T )H − χ3 (T )H 3 + χ5 (T )H 5 ...,

(3)

where χ1 (T ) is the linear susceptibility while χ2n+1 , n ≥ 1 are nonlinear. On the other hand, for ferromagnets the magnetization curves above and below Tc have different forms of temperature and field dependencies [29, 30]: ( M (H, T ) =

M0 (T ) + χ1 (T )H + χ2 (T )H 2 + χ3 (T )H 3 ...

(T < TC )

(4a)

χ1 (T )H − χ3 (T )H 3 + χ5 (T )H 5 + ...

(T > TC )

(4b)

We have attempted to fit experimental data with Eqs. 3, 4a and 4b. It turns out that the data below Tf , TC have failed to fit with Eq. 3. Instead, the experimental data can be well fitted by 4a and 4b, thus suggesting a dominance of the ferromagnetic state over the spin-glass one in UCo0.8 Pd0.2 Ge. In Fig. 6 (b) we show temperature dependencies of spontaneous magnetization M0 , linear susceptibility χ1 and nonlinear susceptibility χ3 derived from fitting data with Eqs. 3, 4a and 4b. Though χ3 (T ) displays a power-law critical divergence of the relation χ3 (T ) ∼ (T − Tf )−γ , γ > 0, predicted for spin-glasses for T > Tf [36, 37], the figure strongly manifests the ferromagnetic behaviour of the sample, for which both χ1 and χ3 do have a divergence in the critical region and also by contrast to spin glasses, which should exhibit a crossover in χ1 (T ) at Tf and a lack of M0 (T ). The Arrott plot M 2 vs µ0 H/M of UCo0.8 Pd0.2 Ge is shown in Fig. 7. The relation between magnetization and magnetic field strength in the temperature range nearby to Curie point [31]: M2 =

a 1H − t bM b

(5)

where a and b are constants, and t = (T − TC )/TC , put forward that the M 2 versus H/M curves should be linear. The intercept of the curves for T < TC on the M 2 axis is the square of the spontaneous magnetization Ms while the intercept for T > TC on the H/M axis corresponds to inverse of the zero-field susceptibility 0T - χ−1 . At the critical temperature 13

T=2K

25 K 27 K

2

-2

22.5 K

8

30 K

4 35 K

0

0

5

(b) UCo0.8Pd0.2Ge

0.20

15 K 17.5 K 20 K TC ∼ 22 K

2

M (10 µB )

12

10 K

10 15 20 µ0H/M (T/µB)

25

Ms (µB), 0T-χ (10 µB/T)

(a)

0.15

0.10

0.05

0.00

0

10

20

30

40

50

T (K)

FIG. 7: (a) Arrott plot M 2 vs µ0 H/M of UCo0.8 Pd0.2 Ge. b) spontaneous magnetization Ms from the high-field limit and zero-field susceptibility from the low-field limit of the Arrott plot as a function of temperature.

TC the Arrott plot passes through the origin. For the studied x = 0.2 the Arrott plot provides TC ∼ 22 ± 0.5 K, in good agreement with low-field magnetization (22.8 K) data. However, one may remark that the M 2 vs µ0 H/M curves show a deviation from linearity at low fields. Such a feature is observed in system, where magnetic domain reorientation survives [32] or there exists a random anisotropy or random field [33]. Therefore, spontanous magnetization Ms is deduced from the linear part of the Arrot plot (high-field limit). We also estimated 0T - χ from the data in low fields. The obtained Ms and 0T - χ values are shown in Fig. 7 (b) and substantiate the ferromagnetic phase transition at TC ∼ 22 K. The real and imaginary components of ac-susceptibility for x = 0.4, 0.5, 0.6 and 0.7 at 1 kHz are shown in Fig. 8 (a). A comparison to those of x ≤ 0.3 reveals that χac -values of the 0.4 ≤ x ≤ 0.7 alloys are about 90 times lower. It is important to recall that the real component χ0 (T ) is proportional to the slope of magnetization M(H) curve and the imaginary component χ00 (T ) is a measure of the energy loss. A small χac -values in 0.4 ≤ x ≤ 0.7 imply that magnetic moments form quite stiffness arrangement, hence domain-wall motion and 14

12

10 T

6

8

x = 0.4

T

3

x =

N

3

0.4

6

0

0.5

6

m /kg)

m /kg)

(b)

9

N

' (10

-6

(a)

T

N

0.6 0.7

4

x = 0.5

3

4 T

2 100 Hz

(10

-6

N

0

UCo

1-x

x

10 kHz

6

x = 0.6

2

2 f = 1 kHz

0 9

-6

'' (10

1 kHz

8

4

Pd Ge

3

m /kg)

ac

2

0

6

1

x = 0.7

3 0

20

40

60

80

T (K)

0 0

20

40

60

80

T (K)

FIG. 8: (a) Temperature dependence of the real and imaginary components of ac-magnetic susceptibility measured at a frequency of 1 kHz for UCo1−x Pdx Ge with x = 0.4 - 0.7. (b) ac-susceptibility of the alloys at several frequencies as a function of temperature.

moment rotation supplying contribution to dissipative magnetic process are negligible. Such a state plausibly occurs in antiferromagnetic materials, and improbably in ferromagnets or spin-glasses. To support this explanation, we rely also on ac-susceptibility measurements p at several frequencies. The ac-susceptibility is calculated by χac = (χ0 )2 + (χ00 )2 and is shown in 8 (b). It is clear that the relative shift in χac (T ) maximum is less than 0.003, thus there practically is absence of relaxation process. Therefore, we may assume the anomalies of χac (T ) of the 0.4 ≤ x ≤ 0.7 samples to be a result of a long-range antiferromagnetic ordering and the N´eel temperature TN to be the position of χ0 (T ) maximum. It appears that TN varies with x and has its maximum value of 31 K at x = 0.6. A remark should be added that spin arrangements in x = 0.4 and 0.7 compounds seem to be complex, due to not only a larger ferromagnetic share, which reflects a more energy loss, visible in the imaginary χ00 (T ) component (see the bottom panel of Fig. 8 (b)) but also the presence of a knee in the χ0 (T ) curves below TN . The ambiguous magnetic state in these alloys is presumably due to the fact that they situate at the border between ferro- and antiferromagnetic phases. The low-temperature dc-magnetic susceptibility χ(T ) of UCo1−x Pdx Ge (0.4 ≤ x ≤ 0.7) measured in a field of 0.5 T is presented in Fig. 9. Only the χ(T ) curves of x = 0.5 15

12

9 x =

0.5 0.6 0.7

(10

-7

3

m /mol)

0.4

6

3

0

H = 0.5 T

1 1.8

20

40

60

80

(K)

FIG. 9: Magnetic susceptibility χ of the UCo1−x Pdx Ge samples, 0.4 ≤ x ≤ 0.7at a field of 0.5 T as a function of temperature.

and 0.6 show a peak, which is consistent with the behaviour due to a transition from a paramagnetic to a long-range-ordered antiferromagnetic state. The observed peak in the χ(T ) curves is shifted to lower temperatures with increasing field (not shown here), and can strengthen antiferromagnetic ordering in these alloys. For the χ(T ) curve of x = 0.4 there is a rounded maximum around 15 K, and for that of x = 0.7 an unexpected peak occurs at 9 K. These anomalies hint spin reorientation or multiple phase transitions. Therefore, to definitively settle the magnetic ground state and magnetic ordering temperatures, some more sophisticated measurements of physical properties will be necessary. Fig. 10 shows magnetization M(H) of x = 0.4 - 0.7 samples in fields up to 5 T. Except for x = 0.4, the remaining alloys exhibit the magnetization behaviour of a typical antiferromagnet, namely, in the initial M(H) curves at 2 K there is a linear dependence of M(H) in low fields and upward curvature in high fields. The return M(H) curves reveal narrow magnetic hysteresis loop associated with the magnetization irreversibility. This small hysteresis loss agrees with low χ00 values found in the samples. The upward curvature and magnetic hysteresis of the magnetization in these samples vanish as temperature approaches TN , thus may express a support for an antiferromagnetic behaviour. For x = 0.4, the magnetization data are qualitatively similar to the case of materials with short-range magnetic interac-

16

tions, though a linear field dependence of the magnetization curve in fields up to 1 T is characteristic of antiferromagnets or paramagnets. (a)

Ge

0.2

25 K

0.1

B

)

)

0.4

)

0.3

M (

0.2

0.1

0.0

M (

0.2

M (

B

5 K

)

Pd

0.6

B

UCo

0.3

(b)

0.2

M (

0.3

0

0.1

1

2 0

3

4

5

H (T)

5 K

0.1

15 K

0.0 0

1

2 0

3

4

UCo

5

Pd

0.5

Ge

0.5

H (T)

0.0

0.0 (c)

0.3

(d)

0.3

0.3

10 K

0.2

UCo

Pd

0.3

)

0.1

Ge

0.7

0.2

B

M (

0.2

1

2 0

3

4

5

0

H (T)

0.3

0.1

M (

0.1

1

2

3

4

5

5 K 30 K

)

0

M (

0.0

M (

B

)

)

5 K

0.2

40 K

0.1

UCo

Pd

0.4

Ge

0.6

0.0

0.0

0.0 0

1

2

3

4

5

0

1

2

3

4

5

FIG. 10: Magnetization M(H) of x = 0.4 - 0.7 samples measured at 2 K in fields up to 5 T. The insets show isotherms collected in higher temperatures.

In Fig. 11 (a) we plot the temperature dependence of the ac susceptibility of the x = 0.8 and 0.9 samples. Sharp peaks are observed at TC = 31 K and 39 K, respectively. These peaks are due to a ferromagnetic ordering because of enormous values of both the real and imaginary ac-susceptibility components at the ac-suceptibility maxima and the absence of frequency dependence in ac-susceptibility data (see Fig. 11 (b)). Further support on the ferromagnetic state in these compositions comes from the dc-magnetization data shown in Fig. 12 (a) and (b) for x = 0.8 and 0.9, respectively. Clearly, the temperature where the inflection point of the M(T) curves sets in, identified with the Curie temperature, agrees well with TC deduced from the ac-susceptibility measurements. Evidently, TC of these samples (as an inflection point of M(T)) moves to higher temperatures as strength of the applied magnetic field increases. Compared to ferromagnetic x = 0.1 - 0.3 alloys, the x = 0.8 and 0.9 samples exhibit much larger values of magnetization at 2 K, which attains about 0.8 µB /at. U at 5 T. This unveiling manifests that the 5f electrons in the Pd-rich compositions are more localized. 17

150

120

T

C

T

C

(a)

(b)

90

90

m

3

kg)

120

x = 0.8

m /kg)

60 f = 1 kHz

3

'

(

60

30

30

100 Hz

120

0 40

1 kHz 10 kHz

x =

3

m /kg)

ac

(

0 150

90

0.8

x = 0.9

0.9

60

(

20 ''

30 0

15

30

45

60

0 20

30

40

50

60

T (K)

T (K)

FIG. 11: (a) Temperature dependence of the real and imaginary components of ac-magnetic susceptibility measured at 1 kHz for x = 0.8 and x = 0.9. (b) Temperature dependence of the ac-magnetic susceptibility of x =0.8 and at several frequencies.

The isothermal magnetization of x = 0.8 and 0.9 and their Arrott plots for temperatures near TC are displayed in Fig. 13. Both samples exhibit discontinuous jump in the M(H) curves at µ0 H ∼ 1 T, which is much higher than those in x = 0.1 - 0.3. This feature argues huge magnetocrystalline anisotropy of the ferromagnetic state, strengthening in favour of localized 5f electrons. From the high-field range of the Arrott plot, TC is estimated to be 34 K and 42 K, for x = 0.8 and 0.9, respictively. However, due to strongly nonlinearity of the Arrott curves, the determination of TC is questionable. Possible reasons are among others, i) inhomogeneity of ferromagnetic phase, likewise at the hand of coexisting antiferromagnetic interactions, which cause the negative curvature of the M 2 vs µ0 H/M dependencies, ii) the behaviour of system deviates from long-range mean-field theory prediction.

IV.

DISCUSSION AND SUMMARY

Our measurements of ac-susceptibility and dc-magnetization of the pseudoternary UCo1−x Pdx Ge system reveal some new information about the equiatomic ternary UTM intermetallics. Besides the fact that the substitution of Co by Pd in UCoGe causes a grad18

0.8

(a)

1 T

0.6

0.3 T

M

(

B

)

2 T

0.4

0.1 T

0.05 T

0.2

TC

0.01 T

0.0 0

10

T

20

30

40

(K) (b)

0.8 1.5 T

3 T

)

0.6

(

M

0.05 T

0.1 T

0.4

0.5 T

0.2

0.01 T

TC

0.0 0

10

20

T

30

40

50

(K)

FIG. 12: Temperature dependence of the magnetization in several fields for (a) x = 0.8 and (b) x = 0.9.

ual localization of the 5f electrons, which is reflected by the decrease in the temperatureindependent susceptibility, the increase in the magnetic moments of uranium ions and magnetocrystalline anisotropy, we have found several worthwhile features, which will be discussed along the proposed magnetic phase diagram (Fig. 14). First of all the studied system exhibits a rich variety of magnetic phases, depending on the substituted Pd concentration. We observe that with increasing the Pd content, there occurs coexistence of itinerant-electron ferromagnetic and spin-glass orderings, then antiferromagnetic state, and finally in the rich Pd content compounds the uranium moments of a more local character order ferromagnetically interspersed with an antiferromagnetic component. The coexistence of SG and ferromagnetic orderings seems to be contradicting. Nevertheless, such a situation was already considered theoretically [38–41] and observed in numerous intermetallic compounds [42–46]. A simple explanation of such a variety of magnetic phases with reantrant ferromagnetism

19

0.8

0.8

(c)

(a)

0.6

(

)

Pd

0.8

Ge

T = 20 K

2

0.4

0.4

M

M (

0.2

)

0.6

UCo

0.2

2 K

25 K

30 K

35 K

37 K

40 K

45 K

50 K

0.2 40 K

0.0

0.0 (b)

(d)

0.8

0.8

UCo

0.1

Pd

0.9

Ge

)

)

0.4

0.6

M

2

(

B

0.6

M (

T = 25 K

2 K

0.2

0.0

40 K

41.5 K

43.5 K

45 K

47.5 K

50 K

55 K

0.4

0.2 47.5 K

0.0 0

1

2

3

4

5

0

2

4

/M (T/

6

8

)

B

FIG. 13: Isothermal dc-magnetization measured in fields up to 5 T at several temperatures for (a) x = 0.8 and (b) x = 0.9. Arrott plot of (c) UCo0.2 Pd0.8 Ge from the isotherms measured (from top to down) at T = 20, 25, 27.5, 30, 33, 35, 37 and 40 K and (d) UCo0.1 Pd0.9 Ge from the isotherms measured (from top to down) at T = 25, 30, 40, 41.5, 43.5, 45 and 47.5 K.

may be based on assumption of competition between ferromagnetic and antiferromagnetic interactions, which presumably survive between the nearest U-U and next-nearest U-U moments. The final magnetic ground state (ferromagnetic or antiferromagnetic) is dependent on the interaction type that prevails. The effect of competitive interactions in itinerant-electron systems was theoretically investigated by Moriya and Usami [47]. The authors considered strengths of the coupling between staggered MQ and uniform M0 components of the magnetizations and have predicted that when the coupling between MQ and MO is strong then a pure and stable magnetic (ferro-, or antiferromagnetic) state sets in. Conversely, when this coupling is weak there will be coexistent ferromagnetic and antiferromagnetic states. If the scenario of competitive ferromagnetic and antiferromagnetic interactions is applicable for UCo1−x Pdx Ge, one may account for not only successive magnetic phase transitions but also the incompatibility in the sign between θp and magnetic state for x ≤ 0.7, as well as possibly coexisting antiferromagnetic interaction in ferromagnetic state of x ≥ 0.8. Obviously, one cannot exclude possible input of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in the investigated alloys. Because of the fact that increase of the conduction electrons concentration ne associated with the increasing Pd content certainly modifies the Fermi wave

20

vector kF = (3π 2 ne )1/3 and Fermi energy EF , thus could give rise to alter RKKY exchange, J2 EF

which is given via IRKKY ∝

FRKKY , where J is the exchange cofficient, the oscillatory

4 function FRKKY = [2kF Rij cos(2kF Rij ) − sin(2kF Rij )]/Rij , and Rij are distances between

magnetic ions. However, to support this explanation, additional measurements of the Fermi wave vector will be needed. Another observation worth noting is that maximum of phase transition temperature Tord,max in each magnetic regime, i.e., 22, 31 and 39 K in x = 0.2, 0.6 and 0.9 samples, respectively, evidently increases upon the Pd substitution. The proportion of Tord,max vs x postulates a strengthening of exchange interactions between the magnetic uranium ions. This picture is quite consistent with the Pd-concentration dependence of magnetic effective moment and spontaneous magnetization. 60

50

UCo

Pd Ge

1-x

x

III 40

AF

30

I

T

N

T

ord

(K)

II

T

C

F

20

AF

10

0 0.0

?

F + SG

0.2

0.4

0.6

0.8

1.0

Concentration x

FIG. 14: Tentative magnetic phase diagram of the UCo1−x Pdx Ge system. Depending on the concentration x, three different magnetic regimes are detected: I - Itinerant-electron ferromagnetic coexisted with spin glass state, II - Antiferromagnetic, III - Complex ferromagnetic of localized 5f - electron moments. The solid lines connecting the experimental points serve to guide the eyes and hatching lines indicate the crossover regimes, yet unexplored magnetic properties.

The last feature of the diagram that seems to be interesting is the electron-concentration induced antiferromagnetism in between ferromagnetic regimes. The magnetic order different to those of the parent compounds and dome-shape structure of the new phase were previously 21

observed in several U-based solid solutions, e.g., URu1−x Pdx Ge [8], UFe1−x Nix Al [48] and URu1−x Pdx Ga [49]. The common behaviour found in these systems suggests that other contributions, for instance, the competition between the Kondo and spd-f hybridization effects could also be of importance in the studied here UCo1−x Pdx Ge system. However, further investigations are required to clarify this issue, since there remains lack of detailed knowledge about any change in both the density of states DOS at the Fermi level EF and the shift of the 5f band relative to EF . In summary, we have synthesized pseudoternary UCo1−x Pdx Ge (x = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9) alloys, crystallizing in the orthorhombic TiNiSi-type structure. We measured magnetic properties of the system and have found a rich variety of magnetic phases depending on the doped Pd concentration. The composition dependence of magnetic ground states indicates a significant modification of the magnetic interactions between magnetic uranium ions as well as between 5f and conduction electrons. Our discussions suggest that besides the interplay of different cooperative interactions, which play a crucial role, there is change in electron concentrations, giving a rise to RKKY and would also account for the complexity of the magnetic ground states. Finally, we would like to admit, however, that there remain some issues to be clarified in future studies. Among them are i) to settle definitive magnetic ground states for specific alloys, e.g., for x = 0.4 and 0.7, ii) to determine concentration dependencies of kF and DOS. We hope that investigations using sophisticated techniques, e.g., neutron diffraction, XPS or X-ray magnetic circular dichroism could be helpful. ACKNOWLEDGMENTS The

authors

acknowledge

for

the

financial

support

from

the

project

2011/01/B/ST3/04553 of the National Science Centre of Poland.

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25