Continuous Evolution of Eu2+/Eu3+ Mixed Valency Driven by Pressure and Temperature

Abstract

Continuous mixed valency involving Eu²⁺ and Eu³⁺ in Eu₄Bi₆Se₁₃ can be induced under applied pressure or at reduced temperatures. The monoclinic structure of Eu₄Bi₆Se₁₃, crystallizing in the P2₁/m space group (No. 11), features linear chains of Eu atoms aligned along the b-axis. Magnetic susceptibility measurements, conducted both parallel and perpendicular to the b-axis and analyzed using Curie-Weiss theory, alongside high-pressure partial fluorescence yield (PFY) data from X-ray absorption spectroscopy (XAS), indicate the material's propensity to adopt a mixed-valent state. Within this state, the trivalent Eu³⁺ configuration becomes increasingly favored as the pressure rises or the temperature decreases.

Figure 1

Crystal structure of Eu₄Bi₆Se₁₃ and high-pressure powder X-ray diffraction measurements. (a) Crystal structure of Eu₄Bi₆Se₁₃ showing the edge-share distorted BiSe₆ octahedra. (b) Powder X-ray diffraction (PXRD) data were obtained at 0.3 GPa. The inset shows the picture of crystals on the millimeter grid paper. (c) Powder X-ray diffraction patterns were collected at room temperature at various pressures of up to 9 GPa. (d) Lattice parameters comparison between single-crystal X-ray diffraction (SCXRD) and PXRD under high pressure.

Figure 2

Temperature-dependent mixed valency in Eu₄Bi₆Se₁₃ (a) Curie–Weiss (CW) fitting on the polycrystalline average susceptibility with the range of temperature 50 K–300 K calculated as χ = (2χ_⊥ + χ_∥)/3, where χ_⊥ and χ_∥ denote susceptibilities perpendicular and parallel to the crystallographic b-axis, respectively. The inset shows the linear fitting. (b) Effective moments compared with saturation moments at 1.8 K. The inset shows the field-dependent magnetization.

Figure 3

High-pressure partial fluorescence yield X-ray spectrometry (PYF-XAS) spectra and analysis. (a) PYF-XAS spectra at the L₃ edge in Eu₄Bi₆Se₁₃ with increasing pressure from 0.1 to 40.0 GPa along with a decompressed pressure of 2.2 GPa (marked with an asterisk). (b) Analysis of the PFY-XAS data at 0.1 GPa using two sets of Lorentzian and arctangent functions for Eu²⁺ and Eu³⁺.

Figure 4

Weight fraction and Eu valence as a function of pressure from PYF-XAS spectra analysis. (a) Pressure-dependent weight fraction; (b) Eu valence measured using PYF-XAS spectra analysis. The blue point presents the average valence from releasing pressure.

Figure 5

(a) Percentage of Eu³⁺ as a function of temperature at ambient pressure and as a function of pressure at room temperature fitted by CW fitting and field-dependent magnetization measurements at ambient pressure. The red symbols give the results from the CW fitting, and the blue symbol shows the Eu³⁺ ratio estimated using the saturation moment. The green line shows the exponential fitting. The right panel presents the Eu³⁺ ratio as a function of the pressure determined by PYF-XAS spectra at room temperature. The black symbols present the results from PYF-XAS. The color gradation indicates the change in the Eu³⁺ ratio. The arrows give the increase directions of the temperature and pressure. Volume change as (b) a function of temperature and (c) as a function of pressure with the pressure projected up to 47 GPa. The red solid line is Birch–Murnaghan fitting using P = 3B₀/2[(V₀/V)^7/3 – (V₀/V)^5/3]. The bulk modulus of B₀ is calculated to be 66.5 GPa.

Figure 6

Specific heat fitting and magnetic entropy calculation (inset).