Spin-Orbit Electric Field Gradient in Cubic Ferromagnets: Strong Magnetization-Direction Dependence of the Field Gradient Distribution

Abstract

[2,3]. For the system AuFe the EFG could also be detected with spin echo measurements on 197 AuFe [8,9].In principle, the EFG in a cubic ferromagnet can arise from magnetostriction and from unquenched local moments. As the observed EFG's are much larger than an EFG due to magnetostriction could be, it was early adopted that the main source is the unquenched orbital momentum [13][14][15]. From theoretical calculations Demangeat [13] postulated that EFG's originating from an unquenched orbital momentum should strongly depend on the direction of magnetization with respect to the crystallographic axes. Based on experimental results of NMR measurements on 191,193 Ir in Fe single crystals [5] and NMR on orientated nuclei (NMR-ON) measurements on 192 Ir in a Ni single crystal [4] it was concluded, however, that such a dependence does not exist. Another theoretical approach was considered by Gehring and Williams [15]. In the general framework of their model, the EFG may, depending on the relative sizes of spin-orbit coupling, the crystal field, and the exchange splitting, depend on the direction of the magnetization with respect to the crystal axes, or not. Led by the experiments suggesting the EFG to be invariant, they concluded that the effects of the crystal field can be neglected, which leads to an invariant EFG.Recent NMR-ON and modulated adiabatic fast passage on oriented nuclei (MAPON) measurements on Z 77 188 Ir in an Fe single crystal showed a strong dependence of the EFG on the direction of magnetization with respect to the crystallographic axes [11]. In these experiments no special attention was directed to the widths of the EFG distributions, as there was no theoretical hint that the EFG width could be directional dependent. The measured ratio, G ͓͑100͔͒ ͞G ͓͑111͔͒1.5͑5͒, showed, however, that the width could be larger for M k ͓100͔ than for M k ͓111͔. On the other hand, these data were not conclusive because of the too large statistical error. Thus, it was concluded that the EFG is sharp and that the distribution is introduced by the nonperfect surface quality of the used single crystal.

Spin-orbit induced noncubic charge distribution in cubic ferromagnets. II. Tight-binding analysis

“…In contrast, the respective SO-EFG's are of the order of 10 15 V/cm 2 and 10 16 V/cm 2 . 7 Thus, the magnetostriction seems to be not an important contribution to the noncubic charge distribution. This conclusion was already drawn in Ref.…”

Spin-orbit induced noncubic charge distribution in cubic ferromagnets. I. Electric field gradient measurements on5dimpurities in Fe and Ni

“…The measurements on PtFe were reported in Ref. 23, the measurements on the 5d impurities in Co͑fcc͒ in Ref. 24.…”