Field dependence of the hyperfine splitting of holmium in holmium hydroxide

Abstract

The hyperfine splitting of 1 6 5 H ~ in holmium hydroxide has been studied by spinecho NMR at liquid-helium temperatures in fields up to 8 T. The behaviour of the dipolar splitting in fields below 0.5 T confirms that the hyperfine parameters are not thermally averaged and that the NMR signals arise solely from ions in the electronic ground state. The field dependence of the hyperfine splitting is not accurately described by crystal-field parameters derived from magnetic susceptibility measurements on Ho(OH),, but is in close agreement with calculations based on parameters derived from optical spectroscopy of Ho3+ in Y(OH)3. The following quantities are derived from our measurements: spontaneous magnetisation and longitudinal susceptibility of Ho(OH), at T = 0: M O = (1.181 2 0,001) MA m-' and XI, = 0.0146 ? 0.0005; ratio of nuclear to electronic anti-shielding factors for Ho3+ in the hydroxide: yN/yE = 149 t 15. Ho(OH), 0.6255 0.3545 OS667 2.54 1.14 * 0.02 <0.025 0.13 * 0.04 Er(OH), 0.6232 0.3518 0.5645 Y(OH), 0.6241 0.3539 0.5671 Christensen et a/ (1967).After Catanese and Meissner (1973). The saturation magnetisation and susceptibilities, measured at 1.1 K, have been converted into SI units. holmium in Y(OH)3 (Bunbury et a1 1986).The lanthanide ions in the hydroxides are closely spaced along the c direction; the spacing in the basal plane is much larger (see table 1). Thus the ions belonging to alternate hexagonal planes form chains of practically contiguous neighbours: to a first approximation, we may picture the lanthanide sub-lattice in terms of one-dimensional arrays of weakly interacting but strongly anisotropic moments. The nature of the interaction between the lanthanide ions has been discussed by Wolf et a1 (1968), Cochrane et a1 (1971), Skjeltorp et a1 (1973), Catanese et a1 (1973), Catanese and Meissner (1973), Cone and Wolf (1978) and Kahle et a1 (1986). The interaction is predominantly dipolar, but there is a significant exchange term and a small electric multipolar contribution. Spontaneous magnetic order, where it occurs at all, does so only at temperatures below 4 K. Crystal-field splittings for non-S-state ions in the hydroxides are of the order of 500 K, so the inter-ionic interaction is much weaker than the crystal-field interaction.The sign of the crystal-field anisotropy in the hydroxides of terbium, dysprosium and holmium is such that the c axis is the preferred direction of magnetisation. Tb3+ and Ho3+, though non-Kramers ions, have crystal-field ground states that are magnetic doublets and so behave in a similar manner to the Kramers ion Dy3+. All three compounds have strongly uniaxial properties at low temperatures, and exhibit Ising-like ferromagnetic order in the liquid-helium range (Wolf et a1 1968, Catanese et a1 1973.In I we showed that zero-field hyperfine splitting of 1 6 5 H ~ in the ferromagnetic phase of holmium hydroxide agrees well with calculations based on optically derived crystalfield parameters. The field dependence of the hyperfine splitting, to be described in the pres...

Anisotropy in RFe2 Intermetallics: An NMR Study

“…The theory of the hyperfine splitting in rare-earth compounds is described in detail in McCausland and Makenzie (1979), Bunbury et al (1989) and Li et al (1996) whose notation we shall follow. The hyperfine splitting of the electronic states is described to first order by the effective nuclear spin Hamiltonian where I is the nuclear spin, t a a t and t P are respectively the dipolar and the quadrupolar hyperfine parameters.…”

“…Preliminary computations have shown that in the exchange dominated RFe 2 compounds second order contributions to the hyperfine parameters are at most 0.05%. Therefore, the second order terms (Bunbury et al 1989) have been neglected in the present work. Because of the strong hyperfine coupling in Ho 3+ , Tb 3+ and Tm 3+ the total dipolar hyperfine constant is dominated by the dipolar intraionic term + + B B B can be regarded as independent of the applied field.…”

The field dependence of the hyperfine splitting of terbium in

“…The theory for the hyperfine interaction of rare-earth ions in solids is described in detail by McCausland and Mackenzie (1979). See also Dormann (1991) and Bunbury et al (1989Bunbury et al ( , 1995. In sections 2.2 and 2.3 below, we review the main points of the theory which are relevant to the present work.…”

“…The free-ion hyperfine coupling constants a 0 and P 0 , together with other relevant constants pertaining to the Tb 3+ ion and the 159 Tb nucleus, are given in appendix A. Explicit expressions for the second-order terms can be found in Bunbury et al (1989). The term in I 3 z in H N arises not from the octupolar moment of the nucleus, which is negligible, but from cross-terms between the dipolar and quadrupolar terms in second-order perturbation theory.…”

“…Comparison between the value of P t measured from a single NMR spectrum and computation is not straightforward because the sign of P t cannot be obtained from the spectrum (Abragam 1961) and also because P , the extra-ionic contribution, is not known. However, given an accurate set of crystal-field parameters, P and the sign of P t can be obtained from the field dependence of |P t | and P (Bunbury et al 1989) provided that the changes in |P t | with the applied field are large compared to the experimental uncertainties. Since P = P t − P is independent of the applied field one expects the graph of |P t | − P against field to be horizontal if P t > 0 and, conversely, the graph of −|P t | − P against field to be horizontal if P t < 0.…”