Supplementary data for
Spin-phonon coupling in Gd(Co1/2Mn1/2)O3 perovskite
R. X. Silva, H. Reichlova, X. Marti, D. A. B. Barbosa, M. W. Lufaso, B. S. Araujo, A. P. Ayala and C.
W. A. Paschoal
In this file, supplementary data are given in order to show detailed informations about the XRPD
analysis, group theory predictions of optical-active phonons, GF Wilson’s matrix analysis calculations and
phonons pictures.
A) Structural analysis based on refining of XRPD data of GCMO.
Table S1 - Data collection and refinement details for the GCMO sample.
Crystallographic and refining properties
Data
Space Group; Z
Pnma (no. 62); 2
Lattice parameters, Å
a=5.60503(5), b=7,55299(8) , c= 5,30460(5)
Temperature, K
298(1)
Density (calculated), g/cm3
7.7563
Cell Volume (calculated), Å3
224.569(4)
λ, Å
1.540560 (Cukα)
Prolife function
Thompson-Cox-Hastings pseudo-Voigt * Axial
divergence asymmetry
Cagglioti parameters (U, V, W)
χ2, Rp, Rwp, Rexp
ICSD collection code of the cif file used in
the refinement procedure.
0.0066, -0.018, 0.011
1.55, 9.53, 13.1 , 10.5
023562
Table S2 – Refined atomic coordinates in the orthorhombic structure of the GCMO sample.
Coordinates
Ion
Site
Symmetry
x
y
z
Gd3+
4c
Csxz
0.06629(19)
1/4
-0.0158(3)
(Co, Mn)3+
4b
Ci
0
0
1/2
1O
4c
Csxz
0.4697(19)
1/4
0.098(2)
2O'
8b
C1
0.3023(16)
0.0474(11)
-0.3027(15)
Table S3 - Calculated bond distances in A and B sites for the GCMO sample.
Label
Bond Distance, Å
Gd1--O1
2.281(11)
Gd1--O1
2.340(11)
Gd1--O2 (×2)
2.336(9)
Gd1--O2 (×2)
Label
Bond Distance, Å
Co1/Mn1--O1†
1.966(3)
Co1/Mn1--O2†
1.983(8)
Co1/Mn1--O2†
2.023(9)
2.620(9)
Gd1--O2 (×2)
2.531(8)
Gd1--O1 (×2)
3.135(11)
Gd1--O1 (×2)
3.3980(11)
Gd1--O2 (×2)
3.488(8)
Table S4 - Calculated valence sums for the GCMO sample.
Ion
Bond Valence Sum, v.u.
Gd3+
3.13
Co3+
2.31
Mn3+
3.22
O1(2-)
1.99
O2(2-)
1.85
B) Group prediction of Optical-active modes in GCMO
Table S5 - Modes distribution in the perovskite crystalline structure belonging to the
orthorhombic space group 𝑃𝑛𝑚𝑎. [1]
Ion
Site Symmetry
Distribution of modes
Gd3+
4c
Csxz
2𝐴𝑔 ⊕ 𝐴𝑢 ⊕ 𝐵1𝑔 ⊕ 2𝐵1𝑢 ⊕ 2𝐵2𝑔 ⊕ 𝐵2𝑢 ⊕ 𝐵3𝑔 ⊕ 2𝐵3𝑢
(Co, Mn)3+
4b
Ci
3𝐴𝑢 ⊕ 3𝐵1𝑢 ⊕ 3𝐵2𝑢 ⊕ 3𝐵3𝑢
O1
4c
Csxz
2𝐴𝑔 ⊕ 𝐴𝑢 ⊕ 𝐵1𝑔 ⊕ 2𝐵1𝑢 ⊕ 2𝐵2𝑔 ⊕ 𝐵2𝑢 ⊕ 𝐵3𝑔 ⊕ 2𝐵3𝑢
O2
8d
C1
3𝐴𝑔 ⊕ 3𝐴𝑢 ⊕ 3𝐵1𝑔 ⊕ 3𝐵1𝑢 ⊕ 3𝐵2𝑔 ⊕ 3𝐵2𝑢 ⊕ 3𝐵3𝑔 ⊕ 3𝐵3𝑢
All modes
7𝐴𝑔 ⊕ 8𝐴𝑢 ⊕ 5𝐵1𝑔 ⊕ 10𝐵1𝑢 ⊕ 7𝐵2𝑔 ⊕ 8𝐵2𝑢 ⊕ 5𝐵3𝑔 ⊕ 10𝐵3𝑢
Acoustic/Silent
𝐵1𝑢 ⊕ 𝐵2𝑢 ⊕ 𝐵3𝑢 / 8𝐴𝑢
Raman
7𝐴𝑔 ⊕ 5𝐵1𝑔 ⊕ 7𝐵2𝑔 ⊕ 5𝐵3𝑔 = 24 Raman active modes
Infravermelho
9𝐵1𝑢 ⊕ 7𝐵2𝑢 ⊕ 9𝐵3𝑢 = 25 IR active modes
C) Lattice dynamics - GF Wilson Matrix analysis
The lattice dynamic calculations of the normal modes of GCMO were performed with basis on
the GF matrix Wilson’s method. In this method, in order to obtain the force constants from the
vibrational frequencies, the material has been treated as a system of point masses connected by springs
obeying Hooke’s law. Thus, the system can be taken as harmonic and the secular equation is given as
|𝐺𝐹 − 𝐸𝜆| = 0
where 𝐹 is a matrix of force constants connected to the vibration potential energies, which arises from
the interaction between the atoms and hence provides valuable information about the nature of
interatomic forces; 𝐺 is a matrix related to the kinetic energies, which depends on the masses of the
individual atoms and their geometrical arrangement; 𝐸 is an unit matrix and 𝜆 is the eigenvalue
connected to the frequency through the follow equation
𝑙 = 4𝑝2 𝑐 2 𝑢2
where 𝑐 is the light velocity.
To determine the force constant set that gives the best description of the structural and
vibrational of GCMO data, we started from reported data of Iliev et al [2]. The initial force constants
were modified in order to model the observed phonons. The final force constant values are given in the
Table S6.
Table S6 - Interatomic force constant values obtained in this work. No off-diagonal interaction terms
were applied.
Force constant
K1
K2
K3
K4
K5
K6
K7
F1
F2
F3
F4
F5
F6
Between atoms
Gd -O (1)
Gd -O (1)
Gd -O (2)
Gd -O (2)
Co/Mn - O (1)
Co/Mn - O (2)
Co/Mn - O (2)
O(1) - O(2)
O(1) - O(2)
O(1) - O(2)
O(1) - O(2)
O(2) - O(2)
O(2) - O(2)
Distance (Å)
2.2814
2.3403
2.3362
2.5313
1.9658
1.9835
2.0235
2.7654
2.7821
2.8032
2.8759
2.8091
2.8577
Force constant values (N/cm)
1.261
0.886
0.733
0.465
0.412
0.185
0.210
0.445
0.198
0.221
0.494
0.524
0.667
D) Atomic motions in the Raman-active modes
Next figures show the atomic motion in each observed Raman-active phonons.
(a)
(b)
Calculated at 624 and 334 cm-1.
Figure S1 - (a) In-phase and (b) out-of-phase (Mn/Co)O6 octahedral stretching modes. The motions of Gd
and O1 atoms are restricted by the site symmetry (𝑪𝒙𝒛
𝑺 ) within the xz plane for the Ag and B2g modes,
and along the y axis for the B1g and B3g modes.
(a)
(b)
Calculated at 494 and 381 cm-1.
Figure S2 – (a) Out-of-phase octahedral bendings and (b) O2 antistretching with the Ag symetries.
(a)
(b)
Calculated at 540 and 463.1 cm-1.
Figure S3 – (a) In-phase octahedral bendings with the B2g symetries. (b) Out-of-phase bending with Ag
symetries and O1 along the x axis.
Calculated at 439.5 cm-1.
Figure S4 – Out-of-phase octahedra tilt along the x axes bendings with the B2g symmetries.
Calculated at 295.6 and 255.6 cm-1.
Figure S5 - In-phase octahedra tilt along the b axes with the Ag symetries. In this phonon the RE and O1
ions also moves in the plane xz In-phase
Calculated at 277.9 cm-1
Figure S6 – Octahedra out-of-phase rotation along the b axes, whose symmetry is B1g. In this phonon RE
and O1 ions moves along the b axes.