The magnetostriction of Tb, Dy and Ho revisited

Abstract

In this paper we present re-analyses of magnetostriction measurements earlier performed in terbium, dysprosium and holmium single crystals. In the framework of the standard theory of single-ion crystal-electric-field and two-ion exchange magnetostrictions, we explain the thermal variation of the anisotropic saturation magnetostriction within the basal plane by considering high-order terms in the magnetoelastic energy. Using complementary basal-plane magnetic anisotropy measurements, we have been able to obtain the second- and fourth-order magnetoelastic coupling parameters associated with the orthorhombic distortion of the hexagonal plane for the above-mentioned three heavy rare earths.

Spin-flop transition driven by competing magnetoelastic anisotropy terms in a spin-spiral antiferromagnet

“…Figure 1 shows the α-MS modes in bulk Ho for μ 0 H = 3 T. It is observed that ε α1 and ε α2 attain larger values at low temperature than the symmetry-breaking γ -striction in Ho. In particular, this latter attains a smaller value in Ho than in its spin-spiral counterparts, Tb and Dy (i.e., ε γ 1 ∼1.3×10 −3 for the former against ∼5.7×10 −3 and ∼5.3×10 −3 for the latter [28], respectively). More particularly, a comparative analysis of the α-MS modes reveals that ε α2 is almost 80% larger in Ho than in Dy, whereas that ε α1 attains a value that is about 20% bigger in Dy than in Ho (not shown here); furthermore, the ratio ε α2 /ε α1 in Ho indicates a clear asymmetry between the α strictions, being considerably larger ε α2 ; however, this α and γ in hexagonal symmetry [25].…”

“…Thus, if we consider that M [28] (notice that experimentally the γ MS in Ho is finely modeled by utilizing a few low-rank MEL constants [28]), which means that K 6,γ 6,mel > 0, we can conclude that the γ -MEL anisotropy term tends to align M along the b direction, competing with K 6 6 [28]. On the other hand, from inspecting Eq.…”

“…First, we should consider the sign of the symmetric MS modes at high field (as observed in Fig. 1, we notice that ε α1 ,ε α2 >0 and ε γ 1 <0) and that of the α-MEL (see Table I) and γ -MEL [28] constants. In addition, we must bear in mind that the symmetric MS modes in single-crystal Ho are monotonic functions of the temperature (see Fig.…”

“…To this end, the relationships for ε α1 ,ε α2 [given in Eq. (1)] and ε γ 1 [28] will be inserted into Eq. (8), which after retaining only α-MEL constants up to l = 2,4, and considering that c α = c α1 c α2 − c 2 α3 ≈ c α1 c α2 , enables us to provide a further simplified relationship, leading to…”

“…Additionally, the outcome of this study shows that, in contrast to the general wisdom that states that the magnetostriction (MS) in heavy rare earth metals is primarily of crystal-field origin [16,17,26,27], α-striction modes are significantly contributed by exchange terms. Generally, two-ion MEL contributions are neglected and when these are brought into the analysis tend to be considerably smaller than single-ion counterparts [28].…”