Magnetothermodynamic properties of frustrated pyrochlore Gd₂FeSbO₇ in cooperative two-sublattice molecular-field model

Highlights

• Antiferromagnetic superexchange interaction through Gd−O−Fe−O−Gd pathways.

• Fe sublattice exhibits a weak ferromagnetic transition at T_C ≈ 5 K.

• Moderately frustrated.

• Cooperative two-sublattice model describes magnetic and heat capacity of Gd₂FeSbO₇.

Abstract

The pyrochlore, Gd₂FeSbO₇, having general formula unit A₂B₂O₇, was chosen for magnetic and heat capacity study in this work due to presence of Fe³⁺ moments, whose 3d orbitals (3d⁵:$3t_{2g}^3{e}_g^2$) are half-filled and carry a large magnetic moment, at B site of the structure, and hence create additional Gd−O−Fe−O−Gd pathways, which result in strongly antiferromagnetic superexchange interactions among the Gd−Gd spins as well as for the Gd−Fe bonds. Gd₂FeSbO₇ behaves paramagnetic down to ~10 K with effective antiferromagnetic nearest-neighbour interactions resulting negative Curie-Weiss temperature, θ_CW = −12.62 K. Fe sublattice exhibits a weak ferromagnetic transition at T_C ≈ 5 K. The frustration index f = |θ_CW|/T_C becomes 2.5 indicative of moderate frustration, which may prevent Palmer-Chalker ground state configuration of Gd sublattice at lower temperature in the system. Heat capacity C_p exhibits a broad anomaly at ~3.1 K and calculated magnetic heat capacity C_m/T attains a peak at ~1 K, but is much weaker than for other pyrochlores Gd₂B₂O₇ (B = Sn, Ti, Ge, Pt) which are all found to order at 1 K or lower, thereby reflecting a short-range second-order transition in Gd₂FeSbO₇. The nature of transition was also verified by Arrott plot of magnetization. Finally the magneto-thermodynamic data were analyzed on the basis of a cooperative two-sublattice model taking account of intra-sublattice (Gd−Gd and Fe−Fe) and inter-sublattice (Gd−Fe) magnetic interactions, defined by three molecular-field parameters, λ_Gd−Gd = −0.71 T/μ_B, λ_Fe−Fe = 0.87 T/μ_B, and λ_Gd−Fe = −0.61 T/μ_B in presence of the easy-planer crystal-field anisotropy at Gd-site. Without Gd−Fe interaction, two independent interpenetrating Gd³⁺ and Fe³⁺Sb⁵⁺ sublattices can not precisely demonstrate the measured thermomagnetic properties of Gd₂FeSbO₇. This study thus revealed that 3d−4f magnetic interactions offer Gd₂FeSbO₇ a unique place in the series of gadolinium-based pyrochlores.

Introduction

Pyrochlore compounds, having general formula unit (f.u.) A₂B₂O₇ with A³⁺ a rare-earth (R) ion and B⁴⁺ a 3d, 4d or 5d transition metal ion, exhibit rich physics due to magnetic geometrical frustration [1], [2]. In cubic pyrochlore structure, larger A (16d) cations are coordinated to eight oxygen anions arranged in a distorted scalenohedron, involving six O (48f) anions and two O′ (8b) anions to construct A₂O′ chains. B (16c) cations are octahedrally coordinated to six O anions to yield a B₂O₆ network, as can be seen in Fig. 1(a). Therefore, the pyrochlore structures are often described as two interpenetrating networks of BO₆ octahedra and A₄O′ tetrahedra, and such network design is the origin of the frustrated properties of pyrochlore magnetic systems when A and/or B sites contain magnetic ions. Frustration of spin–spin interactions on the pyrochlore lattice structure gives rise to diverse magnetic ground states and properties, spanning from spin-ice, spin-glass, spin-liquid or cooperative paramagnetic ground states to Néel-like and Palmer-Chalker (PC) antiferromagnetic (AFM) state [2]. This diversity of magnetic phenomena arises due to interplay between different single-ion anisotropy caused by the crystal-field (CF), nearest-neighbour (n.n.) magnetic exchange and dipolar interactions realized at the magnetic A and B sites, depending on their relative strength and magnitudes.

Among the R-series, trivalent Gd demands a unique and interesting position. As a first approximation, 4f⁷ Gd³⁺ ion has zero orbital angular momentum (L = 0, S = J = 7/2) in ⁸S_7/2 ground state and hence should lead to isotropic magnetic properties. Gd-based compounds with non-magnetic B ions offer themselves as possible realization of the Heisenberg anisotropy on pyrochlore structure which classically possesses a disordered ground state [3], [4]. Palmer and Chalker [5] had shown that an isotropic Heisenberg antiferromagnet with long-range dipolar interactions would order into a four-sublattice Néel state with an ordering wave vector k = (0, 0, 0) which is referred to a PC state. To search for the PC state in real materials, a number of Gd₂B₂O₇ pyrochlores have been so far investigated with B = Ti, Sn, Zr, Hf, Pb, Ge, Pt [6], [7], [8], [9], [10], [11], [12]. Each of these compounds undergoes an AFM ordering transition at 1 K or below. For B = Sn, a strongly first-order state with AFM pairs of spins, perpendicular to each other, on each tetrahedron, was identified at 1.01 K as the PC state [8], [9]. In the Ti case, unlike the PC state observed for Gd₂Sn₂O₇ (GSO), two consecutive phase transitions to a partially ordered magnetic state, referred to as ‘1-k’ and ‘4-k’ structure, at T_N1 = 1.02 K and T_N2 = 0.74 K are observed [6], [7]. It still remains an open question [2] that whether these distinct properties of Gd₂Ti₂O₇ (GTO) were ascribed to remaining structural disorders or thermal fluctuations [13] or additional ‘magnetic degrees of freedom’ such as further- neighbour interactions or additional anisotropies in GTO [9]. To look into these additional perturbations, Gd₂Pt₂O₇ (GPO) has recently been investigated by Hallas et al. [11] and Li et al. [12]. GPO undergoes a strongly first-order AFM transition at T_N ≈ 1.6 K, which in many senses resembles to GSO, suggesting GPO as another candidate for the PC ground state [11], though its transition temperature is relatively higher than for other Gd-pyrochlores. It was proposed that the 5d orbitals of Gd³⁺ ions interact with the spatially more extended 5d valence shells of non-magnetic Pt⁴⁺ ions (5d⁶:$5t_{2g}^6{e}_g^0$ in a low-spin state within an octahedral coordination) via empty e_g orbitals and open additional superexchange (SE) pathways [11], [12]. The SE interactions through Gd−O−Pt−O−Gd path enhance AFM order and relieve magnetic frustration for GPO. However, detailed understanding of the SE pathways in Gd₂B₂O₇ demands more investigation if the B-sites contain magnetic ions.

Therefore, in order to explore SE pathways which interconnect the A-site and B-site magnetic sublattices in pyrochlores in a more comprehensive perspective, we replaced half of the nonmagnetic transition metal ions at B-sites in Gd₂B₂O₇ by a magnetic ion, e.g. Fe³⁺ (at B′ site) and half by another nonmagnetic Sb⁵⁺ ion (at B′′ site) such that the B-site (2B⁴⁺ = B′³⁺B′′⁵⁺) cationic arrangement satisfies the charge neutrality condition in Gd₂FeSbO₇ (GFS). Since Fe³⁺ ion is in high-spin S = 5/2 state (3d⁵: $3t_{2g}^3{e}_g^2$) in Gd₂FeSbO₇ as seen from previous Mössbauer spectral analysis for R₂FeSbO₇ samples [14], one may expect that not only e_g orbitals, but also half-filled t_2g orbitals of magnetic iron ions may participate in making SE paths between two Gd ions, involving 2p⁶ orbitals of intermediate O²⁻ ions. We took an initiative to measure the dc and ac magnetization, and heat capacity with and without external field for GFS and the obtained results were analyzed taking advantage of a cooperative two-sublattice molecular-field approximation with additional Gd−O−Fe path, drawn in Fig. 1(b). We have shown that this SE path relieves frustration in GFS and becomes an important factor in characterizing its magnetic properties. Thus in general, the present study has extended the family of Gd-based pyrochlores and may allow us to further explore their fascinating frustrated magneto-thermodynamic properties.