Hyperfine interactions of 161Dy in dysprosium pyrogermanate at low temperature

J. Phys. Chem. Solids Vol. S6, No. I. pp. 3M8.

00223697(94)00118-9

EW

cOpyri@ Q 1995 Elswier Science Ltd Printed in Great Britsin. All rights reserved oozz-3697/95 $9.50 + 0.00

HYPERFINE INTERACTIONS OF “‘Dy IN DYSPROSIUM PYROGERMANATE AT LOW TEMPERATURE AJITA SENGUFTA

and D. GHOSH

Solid State Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India (Received 25 March 1994; accepted in revised form 6 July 1994) Ah&a&--A crystal field (CF) analysis of our previous experimental results on the magnetic susceptibility and anisotropies of Dy,Ge,O, (DyPG) single crystals has yielded very accurate values of the CF levels of the lowest 6H,,,, term. These results have been used to calculate the nuclear hypetline (HF) splittings of the energy levels corresponding to the ground (Is = 5/2) and excited (1, = 5/2) 25.6 keV nuclear manifolds of 16’Dyin DyPG. These HF splittings are found to be 0.086 and 0.112 cm-‘, respectively. The Mossbauer spectra at 4 K, which contain more lines that usual, are predicted. The nuclear HF field and specific heat are also calculated. The latter shows a peak at about 40 mK and follows a l/T* law between 30 and 5 K. KeyworL: D. crystal structure, D. Miissbauer effect, D. specific heat.

Nuclear HF interactions arise when the electric and magnetic moments of a RE nucleus interact with the electric and magnetic fields produced in an ionic crystal by the surrounding ions and by the atomic electrons of the ion containing the particular nucleus. Hence to calculate the nuclear HF splitting in dysprosium pyrogermanate (DyPG), a knowledge of the positions of the surrounding ions and a knowledge of the electronic state of the probe ion in its surrounding are prerequisites. These can be obtained indirectly but very accurately from the crystal field (CF) energy levels and CF parameters. These quantities were determined from a fit to our previous experimental measurements of magnetic susceptibilities and their anisotropies in single crystals of DyPG between 300 and 26 K with the corresponding theoretical expressions of Van Vleck (see Ref. [3]). Table 1 lists some of the important structural properties of this compound. The highly anisotropic g tensor of the ground CF level for DyPG makes the spin-lattice and spin-spin relaxation times at low temperature much larger; hence, the nuclear HF energy patterns for “‘Dy [4] are observable at low temperature. This feature has motivated the present work involving the calculations of the nuclear HF splittings, Mijssbauer spectral (MS) transitions and the low temperature HF nuclear specific heat for DyPG.

1. INTRODUCTION

All stable rare earth (RE) nuclei have low-lying excited states (generally below 90 keV), most of which are suitable for recoil-free resonance experiments. The width associated with these states is of the order of 10v7 eV, and the hyperfme (HF) interaction with the 4felectrons of the RE atoms is often so large that a completely resolved HF spectrum of the y-rays is observable. The results of such studies can provide valuable information about nuclear moments in the highly deformed nuclei and the electronic structure of RE ions in the crystals. Wickman and Nowik [l], Ofer et al. [2] and others were thus able to determine the internal magnetic field, the magnetic moment of the nuclear ground and first excited states and the quadrupole moment of the 16’Dy nucleus in different hosts. The present paper reports for the first time a theoretical analysis of the effect of nuclear HF interactions on the 16’Dy nucleus (odd isotope, relative abundance 18.88%) in a pyrogermanate host (Dy,Ge,07), which is reported to have interesting magnetic properties [3] due to its strong crystal field, causing the lowest level to be an isolated spin f system with non-zero and highly anisotropic g values. This system thus offers a special case in which the ground doublet possesses a rather different HF tensor from that observed earlier in Dy3+ compounds. 35

AJITA SENGUFTA and D. GHOSH

36

Table 1. Important structural properties of the 161Dynucleus in DyPG Space group of DyPG Symmetry of Dy’+ ion in the lattice CF splitting of the ground term gllI& First CF parameter B! Energy of the first excited nuclear state Transition Half life V~p,ll J >

The values Q, the Sternheimer

0: D,,

fit to the magnetic results [3]. The magnetic HF interaction can be observed at low temperature only, because any averaging process over the CF levels at elevated temperatures yields nearly equal contributions from all the states, thus leading to a vanishingly small net magnetic moment from the electronic states. However, a similar averaging process over the CF levels does not destroy the nuclear quadrupole interactions, and they can in fact, be observed over a wide range of temperatures. By assuming a very low temperature (~4 K) and the absence of an external magnetic field, the HF energy-level structure can be calculated using the Hamiltonian in eqn (1) and ISZm,m,) space. The allowed dipolar transitions (Am, = 0, + 1) give rise to MS whose angular intensity distribution Z,,,(e) (nuclear transitions from the different ground state levels h4, to the excited state levels M,,) is expressed by the following relation [7]:

610 cm-’ 1.293/10.301 -219.57 cm-’ 25.6 keV 5/2- --) 5/2+ 28.2 ns -2/32 5.7 10.34a:’ 0.726ai 2.6 barns 262

,”

state (cm-‘) -0.0036 -0.0286 -0.00063

A B P

For the first excited nuclear state (cm- ’) 0.0047 0.0372 -0.00062

A B P

z,(e) =I

2. THEORETICAL CONSIDERATIONS When the CF has axial symmetry (along z-axis), the total HF Hamiltonian becomes

=AS,z,+B(S,Z*+S,Z,)+P[3Z~-Z(Z+l)],

the

(1)

where S and Z refer to the electronic and nuclear spins, respectively, A and B are the components of the HF tensor d and the last term represents the quadrupole interaction involving the quadrupole moment Q. Generally in a RE ion with a non-zero f value in the ground term, the first term dominates. The quadrupole interaction parameter P has two parts, PI,, and P4, from lattice and 4f electronic contributions, respectively. Usually an average electric field gradient (EFG), arising from the individual CF levels weighted according to the corresponding Boltzmann factors, is used to estimate that temperature-dependent part P4, [S]. Due to the effects of Pqf, the HF energy level structure is also a sensitive function of temperature,

P = [-9e2Q/4Z(2Z

- 1)]

x [(l - &)& +4(1 - r,)@/3e2&

110: IV >
shielding factors

R,, ym and other constants [6] are listed in Table 1. B i is the CF parameter obtained from the parametric

(2)

((z1M,mlzlz’M,~)(2 [l + t(3m2 - 2)(3 cos* 0 - l)].

(3)

The magnetic HF energy can be represented as an interaction -g,p(,(Z . Be), where Z3,is the effective HF magnetic field. Generally this is of the order of IOO-800T for the RE ion, much greater than any external field. 3. RESULTS AND DISCUSSION For DyPG, the low temperature paramagnetic HF interactions involve only the ground Kramers doublet tiB, because the first excited level is 161 K above the ground level, for which g,, = 1.293 and g, = 10.301, I& = 0.025115/2, f 1l/2) + 0.999) 1S/2, + l/2) -0.021115/2,

r9/2).

(4)

We mention that most of the earlier results imply a somewhat restrictive magnetic character for the ground doublet of Dy compounds in which g,, is non-zero while g1 vanishes. Since g, is non-zero in DyPG, the HF spectra contain more lines and are thus more interesting. For the magnetic HF interaction, the relation between the HF constants and g tensor within such an anisotropic doublet is given by A/g,, = B/g, = A,/gJ[8]. For 16*Dy,A,,& is taken as - 109.5 MHz [9],

Hyperiine interactions of 16’Dyin Dy@,O,

37

Fig. I. Thermal variation of the quadrupolar interaction parameter (P) for the ground nuclear level of 16’Dyin DyPG.

and g, as 1.312, corrected for intermediate coupling [lo] for the present case. The calculated values of A, B and P for both the nuclear states are listed in Table 1, taking into consideration the fact that the ratios of the magnetic and quadrupole moments of the first excited and ground state of 16’Dy are - 1.21 + 0.02 and 0.98 f 0.03, respectively [l 11. Using standard methods [5] and eqn (2), P was computed for a temperature range of 30&l K. It reaches a constant value of -6.31 x 10-4cm-’ below 5 K (Fig. 1) and this was used to calculate the HF spectra for DyPG (Fig. 2) at 4 K. Inspection of Fig. 2 shows that the ground level (I = 5/2) splits into five doublets and two singlets that have a total splitting of 0.086~~~I. Similarly, the first excited nuclear level (I’ = 72) splits into five doublet and two singlets that have a total width of 0.112crni. The 19 allowed transitions are listed in Table 2, together with the relative energies and directional intensities; generally 16 MS lines are

Fig. 2. Hyperfine energy level scheme for the nuclear 5/2- --+ 5/2+ (25.6 keV) y transition of “‘Dy in DyPG.

Table 2. Predicted Mossbauer transitions for DyPG (I, = 5/2, I, = 5/2 and E, = 25.6 keV) Transitions m,-+m,

Relative energies at 4K (mm s-r)

l/2+ -112 l/2-+3/2 l/2-+ -l/2 -l/2+ l/2 -l/2--1 -312 -3/2+-I/2 -3/2-+ -512

-21.83 -13.17 140.12 - 20.95 132.22 - 26.72 105.07

-3/2--t -312 -3/2--l/2 -5/2+ -512 -5/2-+ -312 512-312 512-r 512 3/2-l/2 312-312 312-512 l/2-+ -l/2 l/2+3/2 l/2-+ -l/2

128.15 135.23 71.94 95.03 -110.91 -44.56 -138.39 -131.44 -65.09 -146.37 - 137.72 15.57

Relative intensities for crystal c-axis (II) c-axis (I) 27135 24135 27135 27135 24135 24135

27170 12135 27170 27170 12135 12135

317 204135

3114 27170 12135 15114 3114 3114 15114 12135 27170 3114 27170 12135 27170

0 317 317 204135 0 3s 27135 24135 27135

AJITA SENGUPTA and D. GHOSH

38

0

I

t

I

150.0

Tmx T (mK)

Fig. 3. Thermal variation of calculated hypertine specificheat C,/R from 1 mK to 30 K. Inset shows the constant value for C,,,‘Z*/Rfrom 5 to 30K.

observed [I, 4. The effective HF field was also calculated and found to be 556 T. The specific heat for DyPG at very low temperatures depends sensitively on the HF structure of the ground nuclear level. The nuclear specific heat C,, for i6iDy in DyPG was calculated for temperature between 1 mK and 30 K using the standard relation [12]. C,/R shows a maximum near 40 mK and follows an inverse T* rule (Fig. 3) in the higher temperature region (30-S K), with a value of the constant equal to 0.0025 K*, which is the same as that obtained from the expression given by Bleaney [13] for an Ising system C,,T*/R = (1/9)S(S + l)Z(Z + l)(A * + 2B*)

(5)

the low temperature experimental studies of the MS and specific heat.

REFERENCES Wickman H. H. and Nowik I., Phys. Rev. 142, 115 (1966). 2. Ofer S., Rakavy M., Segal E. and Kherrgin B., Pl?ys. Rev. A13t3, 241 (1966).

3. Sengupta A., Ghosh D. and Wanklyn B. M., Whys.Rev. B47, 8281 (1993).

4. Nowik I., Phys. Left. 15, 219 (1965). 5. Sengupta A., Bhattacharyya S. and Ghosh D., Phys. Left. A140, 261 (1989).

6. Karmakar S., J. Phys. Chem. Solids 46, 369 (1985). I. Golding R. M., Applied Wme Mechanics, p. 382. Van Nostrand, Princeton (1969).

8. Elliot R. J. and Steven K. W. H., Proc. R. Sot. A215, when the values of S = l/2 and Z = S/2 are substituted. This finding thus supports the fact that at low temperature DyPG behaves as an Ising spin f system. In summary, we find that the predicted MS contains more lines than is usual for Dy compounds due to a non-zero anisotropic g tensor of the ground CF doublet. It would therefore be of interest to carry out

437 (1952).

9. Bleaney B., Magnetic Reasonance Spectroscopy and HyperJne Interactions (Edited by K. A. Gschneidner, Jr and L. Ering), Vol. 11, p. 323. North-Holland, Amsterdam (1988). 10. Wyboume B. G., J. Chem. Phys. 36, 2301 (1962). 11. Nowik I. and Wickman H. H., Phys. Reu. A140, 869 (1965). 12. Dasgupta S., Saha M. and Ghosh D., J. Phys. Chem. Solids 45, 589 (1984).

13. Bleaney B., Phys. Rev. 78, 214 (1950).