An ab initio study of the magnetic properties of strontium hexaferrite

Abstract

The magnetic properties of $${\text{SrFe}}_{12}{\text{O}}_{19}$$ SrFe 12 O 19 , a paradigmatic hexaferrite for permanent magnet applications, have been addressed in detail combining density functional theory including spin–orbit coupling and a Hubbard U term with Monte Carlo simulations. This multiscale approach allows to estimate the Néel temperature of the material from ab initio exchange constants, and to determine the influence of different computational conditions on the magnetic properties by direct comparison versus available experimental data. It is found that the dominant influence arises from the choice of the Hubbard U term, with a value in the 2–3 eV range as the most adequate to quantitatively reproduce the two most relevant magnetic properties of this material, namely: its large perpendicular magnetocrystalline anisotropy and its elevated Néel temperature.

Effects of Ca–Gd co‐substitution on the structural, magnetic, and dielectric properties of M‐type strontium hexaferrite

“…42 Therefore, the Fe-O-Fe bond length is influenced by changes in the spin state of the Fe atoms, which will result in the lattice parameters variation. 41 This nonmonotonic trend in cell parameters is also observed in other studies. 23,42 According to Verstegen and Stevels, 43 the presence of an M-type structure can be expected if the c/a ratio is observed to be lower than 3.98.…”

“…It is known that for Gd substitution, the [12k] configuration has the lowest followed by the 2a and 4f 2 42 . Therefore, the Fe–O–Fe bond length is influenced by changes in the spin state of the Fe atoms, which will result in the lattice parameters variation 41 . This non‐monotonic trend in cell parameters is also observed in other studies 23,42 …”

Microscopic mechanism of ferroelectric properties in barium hexaferrites

“…In particular, the Dudarev's approach [29] was used, in which set U = 3.6 eV on Fe atoms according to Ref. [30,31]. In the process of geometry optimization, the lattice constants and positions of ions were optimized with included U correction.…”

Influence of substitutional defects on the structural and magnetic properties of barium hexaferrites

“…One strategy to improve different properties of BFO revolves around the concept of atomic substitutions or doping, which involves replacing specific atoms in the BFO structure with different ones, thereby altering the material's properties. Recently, extensive experimental studies have been conducted with a focus on investigating the impact of different atomic substitutions in M-type barium (BFO) and strontium hexaferrite (SFO) [9][10][11][12][13][14][15][16][17]. Specifically, the effects of titanium (Ti) [18][19][20], aluminum (Al) [21][22][23], indium (In) [24][25][26][27], scandium (Sc) [28], and neodymium (Nd) [29] substitutions have been rigorously explored.…”

“…Where E 0 is the total energy of the most stable spin configuration a = E 0, i and E j correspond to the total energy of spin configurations where the spin of sublattices i or j has been flipped with respect to a = 0, and E ij is the total energy of spin configuration where both sublattices i and j have been flipped. More calculation details of the exchange parameters can be found in references [11,15,43].…”