Spin-orbit dilution effects on the magnetism of frustrated spinel Ge(Co1-xMgx)2O4

We investigated magnetic properties of spinel oxides Ge(Co1-xMgx)2O4 with x = 0 ~ 0.5 to study the spin-orbit dilution effects on the magnetism of spin-orbit frustrated spinel GeCo2O4. We discovered that the magnetic moment per single Co2+ ion is decreased with increasing nonmagnetic Mg2+ concentration, which indicates the spin-orbit decoupling caused by the spin-orbit dilution. Additionally, small-amount substitution of Mg2+ for Co2+ causes the rapid increase of the positive Weiss temperature indicating the enhancement of ferromagnetic interactions, while the Mg2+ substitution suppresses the antiferromagnetic ordering resulting in the appearance of spin glass behavior. The present results suggest that the spin-orbit dilution causes the spin-orbit decoupling and the reinforcement of ferromagnetic frustration in GeCo2O4.


Introduction
Geometrical frustration is a concept which provides an intriguing playground for condensed matter physics. Cubic spinels AB 2 O 4 with magnetic B ions have attracted much interest in light of the geometrical frustration which is inherent in the B-site sublattice of corner sharing tetrahedra (pyrochlore lattice). Cobaltite spinel GeCo 2 O 4 consists of magnetic Co 2+ ions (3d 7 ) with threefold degeneracy of t 2g orbitals on the octahedral B sites as shown in Fig. 1, and non-magnetic Ge 4+ ions on the tetrahedral A sites. Thus it is expected that this compound provides a rich field for the orbital physics in the magnetically frustrated system. GeCo 2 O 4 exhibits the occurrence of an antiferromagnetic transition at Néel temperature T N = 21.0 K accompanied with cubic-to-tetragonal structural elongation [1,2,3]. On the other hand, the magnetic susceptibility in the paramagnetic state exhibits Curie-Weiss behaviour with the positive Weiss temperature  W = 81.0 K indicating the dominant contribution of the ferromagnetic interactions [4]. For GeCo 2 O 4 , recent ultrasound velocity measurements and inelastic neutron scattering experiments suggested that this compound is a promising candidate for the spin-orbit-coupled frustrated system [5,6,7]. In this paper, we investigate structural and magnetic properties of the nonmagnetic-Mg-doped Ge(Co 1-x Mg x ) 2 O 4 to study the spin-orbit dilution effects on the magnetism of GeCo 2 O 4 .

Experimental
Polycrystalline samples of Ge(Co 1-x Mg x ) 2 O 4 (x = 0 ~ 0.5) were prepared by solid state reaction. Mixtures of stoichiometric amounts of GeO 2 , CoO, and MgO powders were sealed into evacuated quartz tube, and heated for 40 hours at 800 o C followed by 24 hours at 950 o C. The crystal structure of the samples was analyzed by powder X-ray diffraction (XRD) measurements at room temperature using Cu Kα radiation. The magnetic susceptibility measurements were carried out using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design Magnetic Property Measurement System (MPMS)) at temperatures from 3 K to 300 K with magnetic field of H = 1000 Oe in zero-field-cooled (ZFC) and field-cooled (FC) processes.   Fig. 3. As shown in Fig. 3 (a), all the samples exhibit Curie-Weiss behavior in the paramagnetic phase of ~30 K < T < 300 K. Additionally, the low-temperature magnetic susceptibilities shown in Fig. 3 (b) reveal that the antiferromagnetic transition is suppressed with increasing the nonmagnetic Mg concentration x up to x = 0.1, resulting in the appearance of the spin-glass-like behavior with the evolution of the irreversibility of magnetic susceptibility above x = 0.2.

Results and Discussion
On the basis of the magnetic susceptibilities shown in Fig. 3, Figs. 4 (a), (b), and (c) plot effective magnetic moment per Co atom p eff , Weiss temperature  W , and Néel temperature T N or spinglass transition temperature T SG as a function of Mg concentration x, respectively. Here, p eff and  W are obtained by fitting the experimental data in 250 K < T < 300 K to the linear Curie-Weiss law, and T SG is defined as the temperature below which the irreversibility in the magnetic susceptibility evolves. For GeCo 2 O 4 , the previous work of the measurements and analyses of the magnetic susceptibility and the specific heat claimed invalidity of the Curie-Weiss analysis of the magnetic susceptibility due to the dominant contribution of the low-lying crystal-field states compared to the magnetic correlations [8]. However, the recent inelastic neutron scattering experiments by using high-purity GeCo 2 O 4 single crystals revealed the dominant contribution of the ferromagnetic correlations compared to the crystalfield states [7], which is compatible with the positive  W obtained from the Curie-Weiss analysis [4].  Thus, in the present study, we discuss the Mg-doping effects on the magnetic susceptibility of GeCo 2 O 4 by utilizing the Curie-Weiss analysis, although we should take into account the contribution of the crystal-field states for the correct quantitative analysis. It is noted that the ultrasound velocity measurements in GeCo 2 O 4 suggested the possible generation of the "ferromagnetic" geometrical frustration of Kugel-Khomskii (KK)-type orbital-spin interaction between the nearest-neighbor Co 2+ ions [5]. The present results might suggest that the spinorbit dilution reinforces the orbital-spin frustration by the spin-orbit decoupling.

Summary
In summary, we investigated magnetic properties of the cobaltite spinel Ge(Co 1-x Mg x ) 2 O 4 with x = 0 ~ 0.5 to study the spin-orbit dilution effects on the magnetism of the spin-orbit frustrated spinel GeCo 2 O 4 . The magnetic susceptibilities in Ge(Co 1-x Mg x ) 2 O 4 suggest that the spin-orbit dilution causes the spin-orbit decoupling and the reinforcement of ferromagnetic frustration in GeCo 2 O 4 . Further experimental and theoretical works are expected to verify the orbital-spin frustration and its reinforcement by the spin-orbit dilution in GeCo 2 O 4 .

Acknowledgement
This work was partly supported by Grant-in-Aid for Scientific Research (C) (25400348) from MEXT of Japan, and by Nihon University College of Science and Technology Grants-in-Aid for Fundamental Science Research.