Spin crossover and hyperfine interactions of iron in $(\mathrm{Mg},\mathrm{Fe}){\mathrm{CO}}_{3}$ ferromagnesite

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Spin crossover and hyperfine interactions of iron in $(Mg, Fe) {CO}_{3}$ ferromagnesite

Han Hsu and Sheng-Chieh Huang

Phys. Rev. B 94, 060404(R) – Published 8 August 2016

Abstract

Ferromagnesite, an iron-bearing carbonate stable up to 100–115 GPa, is believed to be the major carbon carrier in the earth's lower mantle and play a key role in the earth's deep carbon cycle. In this paper, we use the local density approximation plus self-consistent Hubbard $U$ (LDA+ $U_{sc}$ ) method to study the iron spin crossover in ferromagnesite with a wide range of iron concentration (12.5–100%). Our calculation shows that this mineral undergoes a crossover from the high-spin (HS) ( $S = 2$ ) to the low-spin (LS) ( $S = 0$ ) state at around 45–50 GPa, regardless of the iron concentration. The intermediate-spin ( $S = 1$ ) state is energetically unfavorable and not involved in spin crossover. The anomalous changes of volume, density, and bulk modulus accompanying the spin crossover obtained in our calculation are in great agreement with experiments. Our calculation also predicts that an abrupt change of the iron nuclear quadrupole splitting, from $≳ 2.8$ mm/s to $≲ 0.3$ mm/s, can be observed in Mössbauer spectra at 45–50 GPa as a signature of the HS-LS crossover.

Received 6 April 2016
Revised 16 June 2016

DOI:https://doi.org/10.1103/PhysRevB.94.060404

Physics Subject Headings (PhySH)

Magnetic phase transitions Pressure effects

Magnetic systems

DFT+U Hubbard model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Han Hsu^* and Sheng-Chieh Huang

Department of Physics, National Central University, Taoyuan City 32001, Taiwan

^*hanhsu@ncu.edu.tw

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Vol. 94, Iss. 6 — 1 August 2016

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Figure 1
Crystal structure of $({Mg}_{1 - x}, {Fe}_{x}) {CO}_{3}$ ferromagnesite. The orange, green, blue, and red spheres are Mg, Fe, C, and O atoms, respectively. (a) Ten-atom primitive cell of ${MgCO}_{3}$ magnesite ( $R \bar{3} c$ symmetry). (b) and (c) 40-atom supercells with $x = 0.125$ and 0.5, respectively.
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Figure 2
(a)–(c) The $3 d$ orbitals in a trigonally distorted crystal field ( $D_{3 d}$ symmetry). The black thick segments represent the Fe-O bonds; the [111] direction is aligned with the $z$ axis. (d) Sum of the three occupied orbitals [panels (b) and (c)] of the LS ${Fe}^{2 +}$ . (e) Sum of the two orbitals occupied by the monitory-spin electrons of the IS ${Fe}^{2 +}$ [panel (b)]. The minority-spin electron of the HS ${Fe}^{2 +}$ occupies the singlet [panel (c)].
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Figure 3
Electronic structures of high-spin and intermediate-spin $({Mg}_{0.875}, {Fe}_{0.125}) {CO}_{3}$ at $\sim 60$ GPa (40-atom supercell with $V = 274.47 Å^{3}$ ). (a) and (c) Total (gray shade) and projected density of states on each atomic site (lines) of the HS and IS states, respectively. (b) and (d) Integrated local density of states of the Fe peaks in (a) and (c), respectively (isosurface of $0.05 a . u .^{- 3}$ ). The Fe-O bond length $d_{Fe-O}$ and O-Fe-O bond angle $Θ$ are also indicated.
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Figure 4
Relative enthalpy $Δ H$ of IS and LS $({Mg}_{1 - x}, {Fe}_{x}) {CO}_{3}$ ferromagnesite with respect to the HS state. Calculations with (a) $U = 4$ eV and (b) self-consistent $U_{sc}$ are shown ( $U_{sc}^{(H S)} = 4.0, U_{sc}^{(I S)} = 5.7$ , and $U_{sc}^{(L S)} = 5.3$ eV). The solid, dashed, and dotted lines represent the HS, IS, and LS states, respectively; different linewidths represent different iron concentrations $x = 0.125$ , 0.5, and 1. For ${FeCO}_{3}$ siderite ( $x = 1$ ), the ground state is an AFM-ordered HS state; the FM-ordered HS state has a slightly higher enthalpy, as shown in (b).
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Figure 5
Spin crossover of $({Mg}_{1 - x}, {Fe}_{x}) {CO}_{3}$ ferromagnesite with various iron concentrations ( $x = 0.125$ , 0.65, and 1) and the accompanying volume reduction and elastic anomalies. (a)–(c) The fraction $n_{i}$ of spin state $i$ in the mixed-spin phase at $T = 300$ K. (d)–(f) Compression curves of each spin state and the mixed-spin phase. (g)–(i) Volume difference with respect to ${MgCO}_{3}$ magnesite ( $V_{M s}$ ). (j)–(l) Bulk modulus of each spin state and the mixed-spin phase. The black (dark solid), green (dashed), blue (dotted), and orange (light solid) lines are the HS, IS, LS, and mixed-spin states at $T = 300$ K, respectively; symbols are room-temperature measurements [26, 27, 28, 29, 30].
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Figure 6
Temperature effects on the spin crossover of $({Mg}_{1 - x}, {Fe}_{x}) {CO}_{3}$ ( $x = 0.5$ and 1.0) and accompanying volume and elastic anomalies. (a) and (b) The fraction of LS iron $n_{L S}$ in the mixed-spin phase at various temperatures. (c) and (d) Volume difference with respect to ${MgCO}_{3}$ magnesite $V_{M s}$ at various temperatures. (e) and (f) Bulk modulus of (Mg,Fe) ${CO}_{3}$ at various temperatures.
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Physical Review B

covering condensed matter and materials physics

Spin crossover and hyperfine interactions of iron in $(Mg, Fe) {CO}_{3}$ ferromagnesite

Han Hsu and Sheng-Chieh Huang

Phys. Rev. B 94, 060404(R) – Published 8 August 2016

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Physical Review B

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Spin crossover and hyperfine interactions of iron in (Mg,Fe)CO3 ferromagnesite

Han Hsu and Sheng-Chieh Huang

Phys. Rev. B 94, 060404(R) – Published 8 August 2016

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Spin crossover and hyperfine interactions of iron in $(Mg, Fe) {CO}_{3}$ ferromagnesite