Ferrimagnetic ordering and spin entropy of field-dependent intermediate spins in ${\mathrm{Na}}_{0.82}{\mathrm{CoO}}_{2}$

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Ferrimagnetic ordering and spin entropy of field-dependent intermediate spins in ${Na}_{0.82} {CoO}_{2}$

G. J. Shu and F. C. Chou

Phys. Rev. B 93, 140402(R) – Published 5 April 2016

Abstract

The peculiar field-dependent magnetism of ${Na}_{0.82} {CoO}_{2}$ has been investigated through an analysis of its dc and ac spin susceptibilities. To account for the easily activated narrow $b_{2 g} − a_{1 g}$ gap of the crystal field for Co in the cobalt oxide layer, the spin-state transition of ${Co}^{3 +}$ ( $3 d^{6}$ ) between the low-spin (LS) state $b_{2 g}^{2} a_{1 g}^{0}$ of $S = 0$ and the intermediate-spin (IS) state $b_{2 g}^{1} a_{1 g}^{1}$ of $S = 1$ is thus seen as thermally activated and exhibits a Boltzmann distribution. The IS state of ${Co}^{3 +}$ within each $\sqrt{13} a$ hexagonal superlattice formed by the $S = 1 / 2$ state of the ${Co}^{4 +}$ ions appears randomly within each supercell and shows significant temperature and field dependence. The magnetic field is found to assist in pinning down the thermally activated state of ${Co}^{3 +}$ and swings the Boltzmann distribution weight toward a higher fraction of the IS state. The field dependence of the in-plane magnetic moment from the added number of $S = 1$ spins is used to explain the origin of $A$ -type antiferromagnetic (AF) ordering, particularly that the ferromagnetic (FM)-like behavior below $T_{N}$ at low field is actually a ferrimagnetic IS spin ordering of ${Co}^{3 +}$ .

Received 3 December 2015
Revised 12 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.140402

Physics Subject Headings (PhySH)

Ferrimagnetism Thermoelectric effects

Cobaltates

AC susceptibility measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

G. J. Shu¹ and F. C. Chou^1,2,3,*

¹Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan
²National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan
³Taiwan Consortium of Emergent Crystalline Materials, Ministry of Science and Technology, Taipei 10622, Taiwan

^*fcchou@ntu.edu.tw

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Vol. 93, Iss. 14 — 1 April 2016

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Figure 1
(a) Conventional view of the ${CoO}_{2}$ plane of ${Na}_{x} {CoO}_{2}$ as a layer of edge-sharing ${CoO}_{6}$ octahedra has been revised into weakly coupled edge-sharing ${CoO}_{2}$ chains. (b) The correct crystal field for Co has a square-planar shape with two apical oxygens that belong to the neighboring ${CoO}_{2}$ chains of weaker effective charge (see Ref. [17] for details). (c) The electronic configuration of ${Co}^{3 +}$ with $d^{6}$ sitting in the proposed CEF has a narrow $b_{2 g} − a_{1 g}$ gap with an LS state of $S = 0$ and an IS state of $S = 1$ .
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Figure 2
(a) Homogeneous spin susceptibilities ( $χ (T) = M / H$ ) of single-crystal ${Na}_{0.82} {CoO}_{2}$ measured at a low applied field of 0.01 T and a high field of 1 T shown in the inset. While the high-field measurement shows the typical $A$ -type antiferromagnetic transition of $T_{N} \sim 22$ K, the low-field measurement suggests a ferromagneticlike transition with thermal and field hysteresis in both orientations. (b) ac spin susceptibilities measured using an ac field of 5 Oe/10 Hz with zero applied field. The insets show the powder-average ( $\frac{2}{3} χ^{∥} + \frac{1}{3} χ^{⊥}$ ) data to extract $α (T)$ , and the $α (T)$ in an Arrhenius plot to suggest a thermal activation gap of $\sim 20$ meV.
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Figure 3
(a) The Curie constant and the fraction of ${Co}^{3 +}$ activated to the IS state at various fields $α (H)$ increase with the field toward saturation. (b) Field-dependent activation behavior suggests a gap of $\sim 2.6$ meV. The inset of (a) shows top and side views of a superlattice cell of $\sqrt{13} a$ , which correspond to the model of $α = 1 / 12 (\approx 0.083)$ and $1 / 24 (\approx 0.042)$ for one IS per one and two superlattice cells, respectively. The inset of (b) shows a schematic diagram extracted from a measurement under 1 T (see Ref. [17]) of the narrow $b_{2 g} − a_{1 g}$ gap in the Boltzmann distribution, where the gap size estimated from the zero-field measurement $\sim 20$ meV [see Fig. 2] is reduced to $\sim 17$ meV, as if the IS state level is shifted down by $\sim 2.6$ meV effectively through the work done by the field.
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Figure 4
(a) For $x = 0.71$ of hexagonal superlattice size $\sqrt{12} a$ without an IS state, where the blue arrows represent the localized spins of ${Co}^{4 +}$ ( $S = 1 / 2$ ) at the corners, and all spins are geometrically frustrated. (b)–(d) For $x = 0.82$ on a hexagonal superlattice of size $\sqrt{13} a$ with IS existence, the red arrows represent the excited IS spins of ${Co}^{3 +}$ ( $S = 1$ ) appear randomly among the 12 ${Co}^{3 +}$ ions per superlattice cell. (b) and (c) represent the ferrimagnetic ordering at zero and low field, respectively, and (d) illustrates the typical $A$ -AF ordering at high field before the occurrence of a spin-flop transition at $H_{sf}$ .
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Physical Review B

covering condensed matter and materials physics

Ferrimagnetic ordering and spin entropy of field-dependent intermediate spins in ${Na}_{0.82} {CoO}_{2}$

G. J. Shu and F. C. Chou

Phys. Rev. B 93, 140402(R) – Published 5 April 2016

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Physical Review B

covering condensed matter and materials physics

Ferrimagnetic ordering and spin entropy of field-dependent intermediate spins in Na0.82CoO2

G. J. Shu and F. C. Chou

Phys. Rev. B 93, 140402(R) – Published 5 April 2016

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Ferrimagnetic ordering and spin entropy of field-dependent intermediate spins in ${Na}_{0.82} {CoO}_{2}$