Orbital Magnetic Moments of the High-Spin Co²⁺ Ions at Axially-Elongated Octahedral Sites: Unquenched as Reported from Experiment or Quenched as Predicted by Theory?

Abstract

Neutron diffraction studies on magnetic solids composed of axially elongated CoO4X2 (X = Cl, Br, S, Se) octahedra show that the ordered magnetic moments of their high-spin Co2+ (d7, S = 3/2) ions are greater than 3 μB, i.e., the spin moment expected for S = 3/2 ions, and increase almost linearly from 3.22 to 4.45 μB as the bond-length ratio r Co–X/r Co–O increases from 1.347 to 1.659 where r Co–X and r Co–O are the Co–X and Co–O bond lengths, respectively. These observations imply that the orbital moments of the Co2+ ions increase linearly from 0.22 to 1.45 μB with increasing the r Co–X/r Co–O ratio from 1.347 to 1.659. We probed this implication by examining the condition for unquenched orbital moment and also by evaluating the magnetic moments of the Co2+ ions based on DFT+U+SOC calculations for those systems of the CoO4X2 octahedra. Our work shows that the orbital moments of the Co2+ ions are essentially quenched and, hence, that the observations of the neutron diffraction studies are not explained by the current theory of magnetic moments. This discrepancy between experiment and theory urges one to check the foundations of the current theory of magnetic moments as well as the current method of neutron diffraction refinements for ordered magnetic structures.

Unusually High Magnetic Moments Reported for the High-Spin Co2+ Ions at Axially Elongated CoO4X2 (X = Cl, Br, S, Se) Octahedral Sites: Overestimated Magnetic Moments Caused by Underestimated Magnetic Form Factors

“…Let us examine the moment distribution ρ­( r ) in an axially elongated CoO 4 X 2 octahedron (Figure a), for which the d-states of the Co 2+ ion are split as ( xz , yz ) < xy < 3 z 2 – r 2 < x 2 – y 2 . , Thus, the electron configuration appropriate for the Co 2+ ion is given by ( xz ↑, yz ↑) 2 ( xy ↑) 1 (3 z 2 – r 2 ↑) 1 ( x 2 – y 2 ↑) 1 ( xz ↓, yz ↓) 2 (Figure b). , In this configuration, the xz and yz states are not magnetic orbitals because their up-spin and down-spin states are both occupied. The 3 z 2 – r 2 , xy , and x 2 – y 2 states are each singly occupied so they are the magnetic orbitals of CoO 4 X 2 .…”

“…2,5 Thus, the electron configuration appropriate for the Co 2+ ion is given by (xz↑,yz↑) 2 (xy↑) 1 (3z 2 −r 2 ↑) 1 (x 2 − y 2 ↑) 1 (xz↓,yz↓) 2 (Figure 1b). 2,5 In this configuration, the xz and yz states are not magnetic orbitals because their up-spin and down-spin states are both occupied. The 3z 2 −r 2 , xy, and x 2 −y 2 states are each singly occupied so they are the magnetic orbitals of CoO 4 X 2 .…”

“…4 These two observations are striking because the orbital moments of the Co 2+ ions are quenched in the axially elongated octahedral sites so that their magnetic moments should not exceed the spin-only value of 3 μ B , as confirmed from our DFT + U + SOC calculations and theoretical analyses. 5 Thus, it is natural to ask if the unusually large moment μ obs resulted from the use of an underestimated magnetic form factor F(q) 0 based on calculations using atomic wave functions of an isolated Co 2+ ion and also if the true form factor F(q) of the Co 2+ ion in the CoO 4 X 2 octahedron increases with the bond-length ratio R.…”

Spin–Orbital States and Strong Antiferromagnetism of Layered Eu2SrFe2O6 and Sr3Fe2O4Cl2

“…Therefore, the experimental perpendicular magnetic moment of 2.82 μ B itself seems to contain inconsistent information, and it was already deemed a contrast to the in-plane magnetization of Eu 2 SrFe 2 O 6 in another very recent experimental work which leaves this issue open. A similar issue appeared recently for several cobaltates containing the HS Co 2+ ions at the axially elongated octahedral sites: a large orbital moment as reported from experiment but a small in-plane orbital moment as predicted by theory. All of these issues may be settled by a further study.…”

Temperature- and Field-Induced Transformation of the Magnetic State in Co2.5Ge0.5BO5

“…This value is slightly larger than the spin-only one (μ eff S = 3.87μ B ), indicating some contribution from the orbital moment, which is typical of octahedrally coordinated Co 2+ ions. 49,50 The negative sign of θ av = −77.4 ± 1.9 K testifies to the dominant antiferromagnetic exchange interactions between Co 2+ ions. The Curie−Weiss temperature for Co 2.5 Ge 0.5 BO 5 was found to be the more negative (largest modulus) among other tetravalent-substituted ludwigites.…”