Orbital dilution effect in ferrimagnetic Fe_{1 −x}Mn_xCr₂O₄: competition between anharmonic lattice potential and spin–orbit coupling

Abstract

Magnetic and structural phase diagram in a spinel-type solid solution system Fe(1-x)Mn(x)Cr(2)O(4) has been investigated. The cubic-to-tetragonal transition temperature T(s 1) is gradually reduced by the substitution of Mn(2+) (3d(5)) for Jahn-Teller-active Fe(2+) (3d(6)) ions, implying the long-range nature of the ferroic interaction between orbitals. In the paramagnetic tetragonal phase for x < 0.5, the c parameter is shorter than a because of the anharmonicity of the elastic energy. The crystal structure further changes to orthorhombic at around the ferrimagnetic transition temperature T(N 1). T(s 1) and T(N 1) meet at x = 0.5, and Mn substitution of more than 0.5 gives rise to another tetragonal phase with a < c. The systematic change in crystal structure is discussed in terms of competition between the anharmonic lattice potential and the intra-atomic spin-orbit interaction at Fe(2+).

Orthorhombic distortion and orbital order in the vanadium spinelFeV2O4

“…To understand the origin of structural phase transitions, we investigated the detailed orbital states of both Fe 2+ and V 3+ ions in the LTO phase as well as other phases, and we performed normal (Q) mode analysis, which is related to the local distortions of the ligands [11,[24][25][26][27][28]. Figure 2 represents the distortions of the FeO 4 tetrahedron and the VO 6 octahedron in the two-dimensional Q 2 -Q 3 plane, where Q 2 and Q 3 correspond to orthorhombic and tetragonal distortions, respectively.…”

“…A negative Q 3 (θ = π related to the 3z 2 -r 2 type orbital) mode was observed at 115 K, and a positive Q 2 mode appeared at 100 K. Subsequently, at 60 K, the y 2 -z 2 orbitals are stabilized where θ = 2π/3. These behaviors are explained by the cooperative JT effect at T S1 and the relativistic spin-orbit (SO) coupling at T N1 of the Fe 2+ ions, which stabilize the 3z 2 -r 2 and y 2 -z 2 orbitals [11,25,27], respectively. Here, we introduce the deviation angle θ from θ = π (Fig.…”

Magnetic and structural phase transitions in the spinel compoundFe1+xCr2−xMa1, Garlea2, Rondinone3 et al. 2014Phys. Rev. B

“…Since the FeO 4 tetrahedra are generated from a cube where one Fe 2+ ion is located at the center of four O 2− ions that occupy two diagonal corners, the distortion modes can be represented, as discussed in Ref. [34], by a combination of 3d z 2 and 3d x 2 −y 2 , which are described by Q 2 and Q 3 , respectively, 34,50,51…”

“…Although the firstorder perturbation of spin-orbit coupling is absent, the second-order term λL·S breaks the degeneracy of the two e g orbitals and lowers the energy of the 3d x 2 −y 2 relative to the 3d z 2 orbital. 34,51,52 The second-order perturbation of the Hamiltonian H SO can be presented as,…”

“…Previously, a largely separate line of research has been devoted to the spin-lattice interaction which is related to the spin frustration and the cooperative Jahn-Teller distortion especially for the compounds involving orbitally active Asite cations. 17,[20][21][22]27,[31][32][33][34][35] However, very few materials have been studied from the view point of the coupling between frustration and Jahn-Teller effects by changing the orbital configuration of B-site cation. ions.…”