Effect of R substitution in spin glass RFeTi₂O₇ compounds

Highlights

• RFeTi₂O₇ behave as insulating spin glasses (SG) combining 3d and 4f elements.

• Disorder in the Fe sublattice is driving the SG behavior modulated by the R presence.

• R³⁺ single ion anisotropy increases SG temperature and the coercive field.

• Uniaxial anisotropy of R³⁺ slows down spin dynamics and reduces spin fluctuations.

• Increase in the SG temperature correlates with the anisotropic RFe exchange interaction.

Abstract

Zirconolite oxides R³⁺Fe³⁺Ti₂O₇ (R rare earth element) are known to exhibit spin glass behaviour at low temperatures. Here we present a detailed study of these compounds for R = Eu, Gd, Dy, Ho, and Er, together with reviewed previous measurements on Sm, Tb, Tm, Yb and Lu, with the scope of determining the role played by the rare earth on their magnetic properties. They have been investigated using X-ray powder diffraction, and further characterized by magnetization, frequency dependent ac susceptibility and heat capacity measurements. RFeTi₂O₇ compounds are all isostructural showing orthorhombic structure, space group Pcnb at 300 K. Disorder of the magnetic ions in the RFeTi₂O₇ lattice induces spin glass behaviour at low temperatures, mainly due to the Fe sublattice. We show that magnetic rare earth ions participate in the spin glass state tuning its properties. The single ion anisotropy of the R³⁺ ions, excluding exchange interaction with other magnetic ions, has been calculated by ab initio methods, and expressed in terms of the g tensor of the ground doublet or quasi-doublet in Kramers (Sm, Dy, Er, Yb) and non-Kramers (Tb, Ho) ions, respectively, in an effective spin S* = 1/2 model. In the case of R with a singlet ground state (Eu, Tm) or a multiplet state (Gd), the ion is isotropic. We show that the relative increase in the spin-glass temperature $\mathrm{\Delta }{T}_{\mathit{SG}}^R/T_{\mathit{SG}}^{\mathit{Fe}}$ with respect to the LuFeTi₂O₇, where Lu is non-magnetic, correlates qualitatively with the product of the ratio g_z/g_J (R = Tb, Dy, Ho, and Er), or g_⊥/g_J (R = Sm), times the ratio of exchange interactions $\raisebox{1ex}{${\tilde{J}}_{R,Fe}$}\!\left/ \!\raisebox{-1ex}{$J_{Fe,Fe}$}\right.$ determined from the paramagnetic room temperature susceptibility measurements. Besides, for increasing anisotropy the spin glass transition dynamics slows down to values typical of cluster glass. The coercive field below the transition is increased in the same trend. This paper explains the effect of the R-Fe exchange interaction and R single ion anisotropy on the spin-glass behaviour of these compounds.

Introduction

The physics of spin glass systems has been a field of scientific interest in the last decades [1], [2], [3], [4], [5]. There is a large variety of materials showing spin glass behaviour or exhibiting spin-glass-like features, being the current experimental and theoretical research on this field of great interest. The study of new spin-glass materials and their behaviour may reveal fascinating physical properties.

In canonical spin glasses, a 3d transition metal magnetic impurity is dissolved in a nonmagnetic noble metal host. In these systems the interaction between localized moments is mediated by conduction electrons through the long-range isotropic so-called RKKY interaction. Most of the anisotropy in canonical spin-glasses comes from the much weaker Dzyloshinskii-Moriya interaction. On the contrary, insulating spin glasses contain high concentration of magnetic ions presenting short range interactions which can be isotropic or anisotropic [5]. Antiferromagnetic (AFM) superexchange interactions are dominant in the magnetic oxide spin glasses, with the exception of Eu²⁺ containing oxides, where FM interactions are predominant [6], [7]. The effect of single ion anisotropy has been addressed in a study of Fe phosphate glasses [8]. It was concluded that anisotropy tends to suppress fluctuations, giving rise to an increase of the freezing temperature.

Examples of insulating spin glasses containing either 3d metals or 4f rare earth ions are abundant [3], [5]. Numerous are the studies of spin-glass phase in transition-metal oxides, in manganites [9], [10], [11], cobaltites [12], and cuprates [13], [14], among others. Besides, spin glass behaviour is found in highly anisotropic 3d-metal heterometallic oxyborates like warwickites, which are naturally disordered materials [15]. Mixed crystals Eu_xSr_1-xS with Eu²⁺ rare earth ion are well-known examples of Heisenberg spin glasses [16]. However the number of studies of spin glasses containing both 3d and 4f ions is scarce [6]. The role of the presence of rare earth in spin glasses is important in binary metallic glasses [17], or in manganites [5], [18]. The R = Pr and Nd doping induces structural modifications, and magnetic anisotropy gives rise to anisotropic spin glasses [19], since their atomic radius varies along the series, affecting the interatomic distances and hence, their magnetic phases. Besides, spin glass behavior has also been found in other aluminoborates containing Fe and R, where a dependence on the freezing temperature was observed depending on the Fe/R ratio [6].

Within this framework, rare-earth zirconolite oxides with general chemical formula R³⁺Fe³⁺Ti₂O₇ (R-rare earth element) can serve as model materials for the study of disordered systems and spin glass magnetism. These compounds conjugate the possibility of cation substitution with the presence of crystal lattice disorder together with competing magnetic interactions [20], [21], [22], [23], [24].

The LuFeTi₂O₇ compound serves as reference example, where Lu is non-magnetic, to show characteristic spin glass behaviour. Dc magnetic susceptibility measured in zero-field cooled (ZFC) and field-cooled (FC) conditions deviate from each other below the freezing temperature T_f = 4.5 K, ac susceptibility is frequency dependent, and heat capacity presents a rounded bump at that temperature range. Combining these results with X-ray diffraction and Mössbauer spectroscopy it was argued that the spin glass behavior stems from the disorder of the Fe atoms located at the different crystallographic positions [20], [25].

The spin glass behaviour is maintained upon substitution of Lu by Sm [23], Gd [26], Tb [20], Dy [22], Tm [21], and Yb [24]. All of these compounds have similar magnetic spin glass behaviour, albeit dependent in detail on the rare-earth substitution. The purpose of this paper is to investigate the effect of the different magnetic rare earths on the spin glass behaviour of these series, depending on the R magnetic moment, and anisotropy. For this aim, besides the previously published results, we have carried out magnetic experiments and analysis of the new compounds with R = Eu, Er and Ho, and complemented the study on R = Gd and Dy. Within this study we analyse the role of rare earth ions, providing a plethora of anisotropy types, in the behaviour of insulating spin glasses combining transition metal and rare earth elements. The magnetization as a function of field, dc and ac susceptibilities, and heat capacity measurements have been performed to account for the effect of R substitution in the RFeTi₂O₇ compounds. Ab initio calculation of the R single ion anisotropy has been performed for each studied ion to aid in the analysis of the experimental results.