111Cd-time differential perturbed angular correlation study of pressure effect on the hyperfine quadrupole interaction in the UGe2 cubic phase

Journal of Alloys and Compounds 541 (2012) 234–237

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111

Cd-time differential perturbed angular correlation study of pressure effect on the hyperfine quadrupole interaction in the UGe2 cubic phase

A.V. Tsvyashchenko a,c,⇑, L.N. Fomicheva a, A. Velichkov b, A.V. Salamatin b, O.I. Kochetov b, G.K. Ryasny c, A.V Nikolaev c,e, M. Budzynski d, A.V. Spasskiy c a

Vereshchagin Institute for High Pressure Physics, RAS, 142190 Troitsk, Russia Joint Institute for Nuclear Research, P.O. Box 79, Moscow, Russia Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119234 Moscow, Russia d Institute of Physics, M. Curie-Sklodowska University, 20-031 Lublin, Poland e Frumkin Institute of Physical Chemistry and Electrochemistry, RAS, 119071 Moscow, Russia b c

a r t i c l e

i n f o

Article history: Received 23 April 2012 Received in revised form 5 July 2012 Accepted 6 July 2012 Available online 17 July 2012 Keywords: Actinide compounds High pressure synthesis Perturbed angular cc-correlation TDPAC Hyperfine quadrupole interaction Structural phase transition

a b s t r a c t The time differential perturbed angular cc-correlation method (TDPAC) has been used to study the hyperfine quadrupole interaction (HQI) of 111Cd probe nuclei introduced in the novel cubic phase of UGe2 (the AuCu3 crystal lattice). The HQI parameters have been measured as a function of pressure up to 8 GPa. At normal pressure the TDPAC spectrum is described by a single quadrupole frequency of 101.8 MHz. The quadrupole frequency increases with pressure to 118.4 MHz at 5.5 GPa. At a pressure of 7.0 GPa the TDPAC spectrum becomes complex and can be fit by two characteristic quadrupole frequencies: m1Q = 117 MHz and m2Q = 147 MHz. The appearance of the second quadrupole frequency of 111 Cd probe nuclei has been ascribed to a signal from 111Cd probes in U sites, which become effective due to a structural phase transition in UGe2. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction At normal pressure there are five different U–Ge binary intermetallic compounds U5Ge4, UGe, U3Ge5, UGe2, UGe3 [1–6], whose physical and chemical properties strongly depend on the U:Ge ratio. Interestingly, some of them are crystallized in lattices, which correspond to other compositions of the constituent elements. For example, U3Ge5, where the U/Ge ratio is 3:5, has the AlB2 hexagonal lattice [5], where the Al/B ratio is 1:2. These non-stoichiometric U–Ge compounds show unusual cooperative properties, which reflects their complex electronic structure. In particular, neutron-diffraction measurements have revealed that U3Ge5 is a ferromagnet with the Curie temperature Tc = 94 K and a uranium magnetic moment lU = 2.28 lB [5]. The UGe3 cubic phase is known to display a temperature-independent susceptibility of about 1.3  103 emu/mole [6]. Polarized neutrons study of UGe3 has detected the appearance of a positive induced magnetization density at Ge sites, which was attributed to a charge transfer from uranium to germanium and a strong hybridization between the 5f-electrons of uranium and 4p-electrons of germanium [7]. On the other hand, ⇑ Corresponding author. Tel.: +7 496 751 05 93; fax: +7 496 751 00 12. E-mail address: [email protected] (A.V. Tsvyashchenko). 0925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.07.036

UGe2, which has a layered orthorhombic structure of the ZrGa2 type at room temperature [1,2], is a band ferromagnetic superconductor [8,9] in the pressure range of 1.0–1.6 GPa with a pronounced hybridization anisotropy between 5f- and 4p-electrons [10,11]. U5Ge4 has the Ti5Ga4 hexagonal structure and shows the temperature-independent paramagnetic behavior down to 2 K [4]. In this study we report on our time differential perturbed angular cc-correlation (TDPAC) measurements for a cubic phase of UGe2. The phase has the AuCu3 crystal lattice and is metastable at room temperature. We have synthesized it at elevated pressures and found that it transforms to the stable UGe2 phase of the ZrGa2 structure upon heating [11]. However, at room temperature the cubic phase remains stable in a wide pressure range. Previously we have studied UGe2 in the ZrGa2 structure [11], and have found that the electric field gradient which is directly probed by TDPAC is sensitive to the hybridization between 5f-electrons of U and 4p-electrons of Ge. The nature of f-electron bonds continues to draw great attention of many theoretical studies because the bonding mechanism of f-electrons implies various correlation effects, which are not yet fully understood. It is therefore of much interest to investigate further the influence of high pressure on the hyperfine quadrupole interaction parameters and, consequently, on the peculiarities of the electronic structure of

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the 5f-electrons of uranium and 4p-electrons of germanium in the novel phase of UGe2. The TDPAC method which we use below belongs to instruments of nuclear spectroscopy where the electric field gradient (EFG) is measured [11–13] at nuclear probes introduced in sites of crystal lattice. As the probes 111In/111Cd nuclei were used. The electric field gradient measured through the hyperfine quadrupole interactions at 111In/111Cd nuclei as a function of pressure gives reach information about the physical properties and electron structure of the host (UGe2) crystal.

Fig. 1. The crystal structure of the cubic phase of UGe2 (AuCu3 type). Yellow (grey) and blue (dark) spheres represent U and Ge atoms, respectively.

2. Experiment The cubic phase of UGe2 was synthesized at a pressure of 8 GPa as described by Tsvyashchenko [14]. The measurements were carried out by the time-differential perturbed angular correlation method using the 171–245 keV c-ray cascade in 111Cd populated through the 2.8 day isotope 111In electron capture decay. The cascade proceeds via the 245 keV level with the half-life T1/2 = 84 ns, spin I = 5/2, and quadrupole moment Q = 0.83 b. The 111In activity was produced via the 109Ag (a, 2n) 111In reaction through irradiating a silver foil with the 32 MeV a–beam. The 111In–111Cd nuclear probes were introduced into the lattice of UGe2 by the high-pressure synthesis: the constituents (U and Ge) taken in proper amounts with an overall weight of about 500 mg were melted together with a small piece of the irradiated silver foil ( 0.5 mg) in a special chamber under pressure of 8 GPa [12]. The TDPAC measurements were carried out using a 4-detector spectrometer equipped with a small-size hydraulic four-arm press of the capacity up to 300 t [15]. As the samples were polycrystalline and paramagnetic at room temperature, the perturbation of the angular correlation can be described by the perturbation factor for the static electric quadrupole interaction [16]:

G22 ðt; mQ ; g; ^Þ ¼

X X pi ðs20 þ s2n cosðxn tÞ expð ^ xn t=2Þ i

ð1Þ

n

Here pi are the relative populations of nonequivalent sites of the probe nuclei; the hyperfine frequencies xn depend on the quadrupole coupling constant mQ ¼ eQV ZZ =h (the quadrupole frequency) and the asymmetry parameter g ¼ ðV xx  V yy Þ=V zz , where V ii ¼ @ 2 V=@i2 (i = x,y,z) are the principal-axis components of the EFG tensor. The coefficients s2n depend only on gð1 P g P 0Þ. For the nuclear spin I = 5/2 there are three transitions: n = 1, 2, 3. The exponential factor accounts for possible random lattice defects, and K is the relative half-width of the Lorentzian distribution. Here we restrict ourselves to the perturbation parameter of the second order since the unperturbed angular correlation coefficient A44  A22 ðA22 ¼ 0:18Þ. The perturbation factor G22(t) describing a nuclear spin precession due to the hyperfine interaction, was determined in a usual way from the angular TDPAC spectrum R(t), obtained by combining the delayed coincidence spectra measured at the angles of 90° and 180° between detectors, N(90°, t) and N(180°, t), through the expression

RðtÞ ¼ A22 Q 2 G22 ðtÞ

ð2Þ

Here Q2  0.80 is the solid-angle correction and

RðtÞ ¼ 2½Nð180 ; tÞ  Nð90 ; tÞ=½Nð180 ; tÞ þ 2Nð90 ; tÞ

ð3Þ

A 100 mg sample of UGe2 (the AuCu3 structure), doped with 111In was positioned inside a rock-salt ampoule that was used as a pressure-transmitting medium. The high pressure was generated in a calibrated ‘‘toroid’’-type device [17]. The calibration of the device was confirmed through measuring the EQI of 111Cd in 111In-doped metallic Zn at normal pressure and at nominal pressure of 3 GPa. The obtained values, mQ = 131 and 113 MHz, respectively, were in good agreement with those reported by da Jornada and Zawislak [18].

3. Results and discussion Our X-ray diffraction analysis of the UGe2 powdered samples synthesized at high pressures has shown that it can be described as a single phase of the0 AuCu3 cubic structure with the cubic lattice  space constant a = 4.193(4) Å A. The AuCu3 lattice with the Pm3m symmetry is shown in Fig. 1. Since the UGe2 composition differs from that implied by its AuCu3 lattice there must be germanium vacancies in the lattice. It is than natural to assume that the inserted probe 111Cd nuclei will occupy some of these Ge vacancies. Although indeed we have clear evidence of that from our experimental data, the whole situation is more complex. Below we will show that only about 2/3 of the 111Cd nuclei are at germanium sites while the remaining 1/3 of the probe nuclei are located at uranium sites, see Table 1. Such behavior of 111Cd probes can be explained by their tendency to avoid Ge sites. We have clearly observed it in our samples of UGe3 prepared under high pressure. Notice, that although UGe3 0 has the same AuCu3 cubic structure (a = 4.201(4) Å A according to our X-ray diffraction data), in contrast to UGe2 it does not allow for Ge vacancies in its lattice. (As a result we could not carry out TDPAC measurements for our samples of UGe3.) However, in USn2.9 with non-stoichiometric U:Sn composition and Sn vacancies, it was found that 111Cd probes did occupy Sn sites [19]. The resultant TDPAC spectrum was described by a single quadrupole frequency mQ = 89.9 MHz and the g = 0 asymmetry parameter. Thus, the existence of Ge vacancies in UGe2 facilitates their occupation by probe atoms, which enables our TDPAC experiments. Nevertheless, because of the 111Cd tendency to avoid Ge sites, some of 111 Cd probes are placed in U sites of the lattice. Before discussing our results we briefly describe the site symmetry of Ge and U in the AuCu3 lattice, see Fig. 1. The structure can be viewed as a framework of Ge6 octahedra sharing corners with the large U atoms in the interstitials between octahedra. The U site has the cubic Oh site symmetry with zero electric field gradient. Therefore, owing to the high site symmetry the 111Cd probes, which substitute U in the lattice, will not be effective in our TDPAC measurements. On the other hand, the Ge site has the D4h site symmetry with a principal 4-fold axis of symmetry. This site symmetry allows for a quadrupole electric component with a nonzero EFG and the g = 0 asymmetry parameter.

Table 1 Hyperfine quadrupole interaction parameters of 111Cd probe nuclei in the UGe2 cubic phase measured at various pressures. The second quadupolar frequency (m2Q ) appears at high pressure (P > 70 kbar) as a result of a structural phase transition of the UGe2 host lattice (see text for details). Here pi stands the relative population of nonequivalent 111Cd sites (i = 1,2), which we associate with 111Cd probes in Ge and U lattice sites, respectively. Vizz is EFG, the error of pi is about 10%. Pressure (kbar)

m1Q

Ambient pressure 30 55 70 75 77.5

102.0(5) 113(1) 118(2) 117(4) 117(2) 116(2)

(MHz)

g1

p1

V1zz (1021Vm2)

m2Q

0 0 0 0 0 0

0.67 0.62 0.64 0.58 0.67 0.62

5.10(3) 5.65(5) 5.90(10) 5.85(20) 5.85(10) 5.80(10)

– – – 147(5) 149(6) 151(3)

[MHz]

g2

p2

V2zz(1021Vm2)

– – – 0 0 0

– – – 0.30 0.22 0.22

– – – 7.35(25) 7.45(30) 7.55(15)

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Amplitude [a. u.]

R (t)

νQ = 101.8(6) MHz

111

-0.16

Cd in UGe2 , T=300 K

60

structure type AuCu3

-0.12

80

40

-0.08

20

-0.04 0

νQ = 104.3(5) MHz

111

Cd in UGe2 , T=220 K

-0.16

structure type AuCu3

-0.12

0 80 60

-0.08

40

-0.04

20

0

νQ = 105.7(7) MHz

111

Cd in UGe2 , T=160 K

-0.16

64

structure type AuCu3

-0.12

0 80

48

-0.08

32

-0.04

16

0 0

100

200

300 0

t [ns]

0

0.1 0.2 0.3 0.4 0.5

ω [Grad/s]

Fig. 2. TDPAC spectra R(t) (left panel) and their Fourier transforms (right panel), for 111 Cd in the UGe2 cubic phase (the AuCu3 lattice), measured at different temperatures at normal pressure. Right panel shows three quadrupole transition frequencies between energy levels of the 111Cd nucleus split by crystal electric field.

The TDPAC spectra R(t) measured at 111Cd probe nuclei in the UGe2 cubic phase according to Eq. (3), are reproduced in Figs. 2 and 3. Fig. 2 shows the evolution of R(t) with temperature, Fig. 3 with pressure. In Table 1 we give the extracted quadrupole

Amplitude [a. u.]

R(t)

frequency mQ, the asymmetry parameter g and the estimation of the 111Cd occupation of Ge and U sites at various pressures. First, we discuss the temperature evolution of R(t) (see Fig. 2). From these spectra we have determined the temperature dependence of the quadrupole frequency mQ, which characterizes the quadrupole transitions of the 111Cd nucleus. The temperature dependence of mQ is reproduced in Fig. 4 (g = 0 at all temperatures). It has been found that as temperature decreases from 300 to 100 K, mQ increases from 101.8 to 109 MHz. Previously, similar behavior was observed in USn2.9 [19]. Notice that here there is only single detected quadrupole frequency mQ which is due to the signal from the 111Cd probes at Ge sites, because the signal from the 111Cd nuclei at cubic U sites is silent (mQ = 0). The pressure TDPAC measurements of 111Cd probes inserted in cubic UGe2 shown in Fig. 3 were carried out at room temperature in the pressure range from atmospheric pressure to 8 GPa. The procedure is described in detail in [12] where it has been applied to YbAl2. It was found that the quadrupole frequency starting with a value of mQ = 102 MHz at normal conditions (see Table 1) increases monotonically with increasing pressure up to 5.5 GPa reaching mQ = 118.4 MHz. The estimated population of 111Cd probes in Ge sites does not exceed 70%. The other 111Cd nuclei located in U sites are inefficient, because uranium sites have cubic site symmetry which imposes zero electric field gradient. With further pressure increase (5.5–6.8 GPa), mQ does not change within experimental accuracy. At all pressures it was found that g = 0. When pressure exceeds 7.0 GPa the TDPAC spectrum R(t) is described by two quadrupole frequencies: m1Q and m2Q . The first frequency (m1Q =117 MHz) corresponds to the one observed previously, while the second one has a higher value m2Q =147 MHz (see Table 1 and Fig. 5). In contrast to m1Q which practically does not change upon further pressure increase, m2Q increases with pressure reaching 151 MHz at P = 7.75 GPa. We have also estimated that the population p2 of 111Cd nuclei responsible for the second signal amounts to 20–30%, see Table 1.

Amplitude (a. u.)

R (t)

80

-0.2

νQ = 102.0(6) MHz

111Cd in UGe , ambient pressure 2 structure type AuCu3

-0.15

60

-0.1

40

-0.05 0 -0.2

111Cd

-0.15

Cd in UGe2 , p=70 kbar structure type AuCu3

-0.15

νQ 2=147(5)MHz

80 60

-0.10

40

20

-0.05

20

0 80

0.00 -0.20

111

-0.15

structure type AuCu3

νQ = 113(1) MHz

in UGe2 , p = 30 kbar structure type AuCu3

νQ 1 = 117(4) MHz

111

-0.20

60

νQ 1 = 117(2) MHz

Cd in UGe2 , p=75 kbar

νQ 2=149(6)MHz

0 80 60

-0.1

40

-0.10

40

-0.05

20

-0.05

20

0 80

0.00 -0.20

111

-0.15

structure type AuCu3

0 -0.2

νQ = 118(2) MHz

111

Cd in UGe2 , p = 55 kbar structure type AuCu3

-0.15

64

νQ 1 = 116(2) MHz

Cd in UGe2 , p=77.5 kbar

νQ 2=151(3)MHz

48

-0.1

0 0

100

200

t [ns]

300 0

40

16

-0.05

20

0

0.00

0.1 0.2 0.3 0.4 0.5

ω [Grad/s]

60

-0.10

32

-0.05

0 80

0

0

50

100

t (ns)

150

200 0

0.1 0.2 0.3 0.4 0.5

ω (Grad/s)

Fig. 3. TDPAC spectra R(t) (left panel) and their Fourier transforms (right panel), for 111Cd in UGe2, measured at different pressures at room temperature. One can see the appearance of two sets of quadrupole nuclear transitions due to two different signals from 111Cd probes (see text for details).

A.V. Tsvyashchenko et al. / Journal of Alloys and Compounds 541 (2012) 234–237

trons of Cd is 1.3 times higher than in Ge sites. Since we have observed a discontinues jump of m2Q , the structural phase transition is likely of the first order.

115 111

Cd in UGe2

structure type AuCu3

νQ (MHz)

110

4. Conclusions

105

100

95 80

120

160

200

237

240

280

320

T (K) Fig. 4. Temperature evolution of quadrupole frequency (mQ = eQVzz/h) for the UGe2 cubic phase.

111

Cd in

We have applied the TDPAC spectroscopy to study the novel cubic phase of UGe2. The phase is synthesized at high pressure (about 8 GPa) but is stable at normal temperature. The phase has the AuCu3 cubic lattice (Fig. 1), although the 1:3 ratio of the constituent elements of AuCu3 apparently differs from that for UGe2. The TDPAC spectra at various temperatures and pressures can be rationalized by assuming that about 70% of 111Cd probe nuclei are located at Ge sites while 20–30% at U sites. Since the U sites have the cubic symmetry with zero EFG, the 111Cd probe nuclei at U sites are inefficient and the TDPAC spectrum is characterized by only one quadrupole frequency m1Q , which is due to 111Cd probes at Ge sites (Fig. 2). However, at pressures P > 7 GPa the second quadrupole frequency m2Q emerges in TDPAC spectrum, which is interpreted as due to 111Cd probes at U sites (see Fig. 3 and Table 1). The temperature and pressure evolution of quadrupole frequencies are shown in Figs. 4 and 5, respectively. The data indicate that at P  7 GPa UGe2 undergoes a structural phase transition which lowers the uranium site symmetry.

160 111Cd

Acknowledgments

in UGe2

structure type AuCu3

140

The authors are grateful to Prof S.M. Stishov for support of this work and for useful discussions. The work was supported by the Russian Foundation for Basic Research (grant No. 11-02-00029) and by special programs of the Department of Physical Science, Russian Academy of Sciences. The work at the Joint Institute for Nuclear Research was carried out under the auspices of a Polish representative in the JINR.

120

References

100

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νQ [MHz]

νQ2

νQ1 0

20

40

60

80

p [kbar] Fig. 5. Pressure evolution of quadrupole frequency (m1Q ) for 111Cd in UGe2. The second quadrupole frequency (m2Q ) appears at high pressure (P > 70 kbar) as a result of a phase transition of the UGe2 host lattice (see text for details).

[12] [13]

The appearance of two sets of quadrupole nuclear transitions in TDPAC spectrum (see Fig. 3) implies that now 111Cd nuclei probe two different electric field gradients. It can be explained only if we assume that 111Cd nuclei are in different environments. Therefore, 111Cd probes occupy different sites of the UGe2 lattice, that is Ge and U sites. The conclusion is fully confirmed by the population analysis of 111Cd nuclei. Furthermore, the appearance of the electric field gradient at 111Cd nuclei in U sites at P > 7 GPa signals that the U site symmetry is not cubic at these pressures. We thus conclude that at P  7 GPa UGe2 undergoes a structural phase transition which lowers the uranium site symmetry. The high value of m2Q ðm2Q > m1Q Þ is explained by contributions from valence 5f and 6d electrons of U which produce an appreciable EFG when the cubic symmetry is destroyed [11,12,20,21]. In terms of hybridization it means that the degree of mixing of the f-electrons with p-elec-

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[21]

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