EPR study of Er 3 ¿ crystal-field and 165 Ho 3¿ -Er 3¿ interactions in single crystals of Ho x Y 1 Àx VO 4 „ x Ä 0.02 – 1.00… Sushil K. Misra and Serguei I. Andronenko Physics Department, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, Canada H3G1M8 ~Received 5 September 2000; published 15 August 2001! Liquid-helium temperature electron paramagnetic resonance ~EPR! spectra of the Er 31 ion in single crystals of Ho x Y 12x VO 4 ( x 50.02– 1.0) are exploited to reveal the influence of the crystal-field and Er 31 -Ho 31 inter- actions. The Er 31 g value at 4 K in the lightly doped samples ( x ,0.3) was here successfully accounted for by the estimated crystal-field parameters ~cm 21 !: B 2 0 52108.0, B 4 0 540.0, B 6 0 5240.0, B 4 4 52949.0, B 6 4 526.0, while that in the concentrated paramagnetic samples ~x 50.9, 1.0! by the parameters ~cm 21 !: B 2 0 52114.8, B 4 0 546.9, B 6 0 5243.8, B 4 4 52971.4, B 6 4 591.9. The shift of the Er 31 g value in the paramagnetic Ho x Y 12x VO 4 crystals ~x 50.9, 1.0! from that in the diamagnetic YVO 4 crystal has been analyzed to estimate the value of the parameter g ~522.2 cm 21 ! describing the diagonal element of the symmetric tensor representing Ho 31 -Er 31 interactions. The unresolved EPR linewidth of the Er 31 ion is accounted for by the indirect superhyperfine interaction ( A i ) of the Er 31 ion with the surrounding 165 Ho nuclei, estimating A i 50.0026 cm 21 . In addition, the absolute value of the parameter «, an off-diagonal element of the antisymmetric tensor describing Ho 31 -Er 31 interactions, has been estimated to be u « u 50.029 cm 21 . DOI: 10.1103/PhysRevB.64.094435 PACS number~s!: 76.30.Kg, 75.20.2g I. INTRODUCTION Recently, single crystals of HoVO 4 have been investigated extensively by various techniques, including x-ray diffraction, 1,2 powder neutron diffraction, 3 magnetic properties, 1,4–6 and electron paramagnetic resonance ~EPR!. 7 As for the Gd 31 ion, influence of the Ho 31 ion on EPR linewidth and shift of the g value of the Gd 31 ion in HoVO 4 was investigated by Mehran et al. 8 EPR studies of the Er 31 ion in the diamagnetic host YVO 4 were performed by Ranon, 9 while Misra et al. 10 investigated hyperfine splitting of the Er 31 ion in YVO 4 single crystals. It is the purpose of this paper to interpret previously reported x-band EPR data, in conjunction with some additional experimental data re- ported here, on the Er 31 ion in doped Ho x Y 1 2x VO 4 ( x 50.02– 0.25) compounds in order to understand Er 31 -Ho 31 interactions in these hosts. Mehran et al. 8 proposed a model to take into account magnetic interactions between the Gd 31 ion and the Van Vleck Ho 31 ions. However, the rare-earth ion Gd 31 considered by them was isotropic, being an S-state ion, whereas the impurity rare-earth ion considered here is the Kramers ion Er 31 , which is highly anisotropic. Extension of the model of Mehran et al. 8 as attempted here is thus not straightforward. Section II provides relevant details of the structures of YVO 4 and HoVO 4 crystals, along with Er 31 EPR spectra in Ho x Y 1 2x VO 4 . Details of the estimation of Er 31 crystal-field parameters to describe precisely the ob- served Er 31 EPR spectrum in the lightly doped ( x ,0.3) and concentrated hosts ~x 50.9, 1.0! are given in Sec. III. The analysis of the shift of the Er 31 g value in the paramagnetic HoVO 4 crystal from that in the isostructural diamagnetic crystal YVO 4 due the Er 31 -Ho 3 interactions leading to esti- mation of the element g of the Ho 31 -Er 31 symmetric inter- action tensor is described in Sec. IV. An interpretation of the Er 31 EPR linewidth in Ho x Y 1 2x VO 4 based on induced superhyperfine interaction between the Er 31 ion and 165 Ho nucleus and estimation of the magnitude of the off-diagonal element « of the antisymmetric tensor describing Er 31 -Ho 31 interactions are given in Sec. V. Concluding remarks are made in Sec. VI. II. CRYSTAL STRUCTURE AND EPR DATA A. Crystal structure Pure YVO 4 , HoVO 4 and mixed Ho x Y 1 2x VO 4 (0 ,x ,1) crystals belong to the tetragonal space group D 4 h 19 . 11 The rare-earth ions possess the local site symmetry D 2 d . The structural parameters a and c at 290 K are: for YVO 4 , a 57.1193 Å and c 56.2892 Å; 11 the parameters u and w, which determine the positions of the oxygen ions, have the values u 50.185 and w 50.325; 12 for HoVO 4 , a 57.1237 Å and c 56.2890 Å. 11 At low temperatures, there occur changes in the parameters a, c, u, w in HoVO 4 due to the influence of the electronic quadrupole moment of the Ho 31 ion. Specifically, the measured values as reported are: a 57.1194 Å, c 56.2815 Å at 12 K, 2 while u 50.186 and w 50.328 at 4.2 K. 13 For the diamagnetic YVO 4 crystal, the temperature dependence of the parameters a and c has been reported only above 290 K. 14 Assuming the same relative changes with temperature of a and c in YVO 4 as those in GdVO 4 , where there is no influence of magnetoelastic inter- actions on the crystal structure similar to YVO 4 , one obtains: a 57.1186 Å and c 56.2815 Å for YVO 4 at 12 K. Thus the parameters a and c for YVO 4 and for HoVO 4 turn out to be only slightly different from each other at 12 K. B. Experimental data Spectra. EPR spectra of the Er 31 ion in samples with x 50.02, 0.3, and 0.9, observed at 9.615 GHz ~4.2 K!, 8.609 GHz ~5K!, and 8.885 GHz ~5K! for the orientation of the magnetic field B i c axis are shown in Figs. 1, 2, and 3, re- spectively. There are two isotopes of Er 31 : 166 Er with zero PHYSICAL REVIEW B, VOLUME 64, 094435 0163-1829/2001/64~9!/094435~8!/$20.00 ©2001 The American Physical Society 64 094435-1