Supplemental Material for
Intrinsic dielectric properties of magnetodielectric La2CoMnO6
R. X. Silva, R. L. Moreira, R. M. Almeida, R. Paniago and C. W. A. Paschoal
In this file, supporting data are given in order to give detailed information about the XRPD
analysis and GF Wilson’s matrix calculations.
A) Structural analysis after refining XRPD data of LCMO.
Table S1 - Data collection and refinement details for the LCMO sample.
Crystallographic and refining properties
Data
Space Group; Z
5
P21/n (#14 or 𝐶2ℎ
); Z=2
Lattice parameters, Å
a = 5.5255(1) Å, b = 5.4847(1) Å, c = 7.7771(2) Å
Temperature, K
298(1)
Density (calculated), g/cm3
3
6.871
Cell Volume (calculated), Å
235.710±0.005
λ, Å
1.540560 (Cukα)
Prolife function
Thompson-Cox-Hastings pseudo-Voigt * Axial
divergence asymmetry
Cagglioti parameters:
Gaussian (U,P); Lorentz (X, Y)
χ2, Rp, Rwp
ICSD collection code of the .cif file used
in the refinement procedure.
(130.3, 4.72); (0.135, 14.7)
1.888, 5.23, 6.53
98240
Table S2 – Refined atomic coordinates in the monoclinic structure of the LCMO sample.
Coordinates
Ion
Site
Symmetry
x
Y
z
La
4e
C1
0.00210
0.02090
0.25200
Co
2c
Ci
0
½
0
Mn
2d
Ci
½
0
0
O(1)
4e
C1
0.27390
0.22570
0.03300
O(2)
4e
C1
0.27420
0.30370
0.47280
O(3)
4e
C1
0.56830
-0.00300
0.24750
B) Lattice dynamics - GF Wilson Matrix analysis
The lattice dynamic calculations of the normal modes of LCMO were performed based upon 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 into the harmonic approximation with the secular equation
|𝐺𝐹 − 𝐸𝜆| = 0 ,
where 𝐹 is a force constant matrix corresponding to the vibration potential energies that arise 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 velocity of the light.
To determine the force constant set that gives the best description of the structural and
vibrational of LCMO data, we started from reported data of Iliev et al1. The modeling was optimized by
applying a least square route to Raman spectroscopic data1,2. The initial force constants were modified
in order to model the observed phonons. The final force constant values are given in the Table S3.
Table S3 - Interatomic force constant values obtained in this work. No off-diagonal interaction terms
were applied.
Force constant
reference
K1
K2
K3
K4
K5
K6
K7
K8
K9
F1
F2
F3
F4
F5
F6
F7
F8
F9
F10
F11
F12
Considered bond
Distance (Å)
La - O (3)
La - O (2)
La - O (1)
Co - O (3)
Co - O (2)
Co - O (1)
Mn - O (3)
Mn - O (2)
Mn - O (1)
2.4186
2.4608
2.4959
2.0311
2.0144
2.0707
1.9350
1.9334
1.8836
2.8142
2.9617
2.8782
2.9227
2.8421
2.8790
2.6927
2.7058
2.6841
2.7167
2.7304
2.7403
O(1) - O(2)
O(1) - O(3)
O(2) - O(3)
O(1) - O(2)
O(1) - O(3)
O(2) - O(3)
Force constant value
(N/cm)
2.151
2.518
1.632
0.419
0.633
0.167
0.548
0.231
0.404
0.167
0.614
0.024
0.329
0.547
0.323
0.330
0.597
0.249
0.343
0.395
0.402
Table S4 - Assignment of the LCMO Raman-active modes based on the GF Wilson matrix analysis.
P21/n
Calculated Observed*
(cm-1)
(cm-1)
Symmetry
Calculated Observed*
(cm-1)
(cm-1)
Symmetry
636.9
31.7
Ag
Ag
Ag
Ag
Ag
Ag
Ag
Ag
Ag
Ag
Ag
23.7
Bg
Bg
Bg
Bg
Bg
Bg
Bg
Bg
Bg
Bg
Bg
16.4
Ag
17.7
Bg
650.2
645.0
633.2
596.6
493.1
498.0
425.0
422.0
387.9
387.0
328.3
267.7
209.2
84.5
260.0
640.0
610.7
548.1
537.8
485.7
404.5
549.0
483.0
408.0
368.3
207.3
176.0
170.0
84.9
99.0
Table S5 - Calculated infrared-active modes based on the GF Wilson matrix analysis.
P21/n
Calculated
(cm-1)
632.0
608.3
582.4
518.2
488.4
451.1
291.3
257.1
210.0
171.1
149.0
134.0
125.7
107.3
96.5
67.6
61.4
Symmetry
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Au
Calculated
(cm-1)
643.7
642.6
560.6
547.0
450.2
433.4
275.5
257.0
222.4
168.4
157.9
140.3
116.9
102.3
75.8
55.4
Symmetry
Bu
Bu
Bu
Bu
Bu
Bu
Bu
Bu
Bu
Bu
Bu
Bu
Bu
Bu
Bu
Bu
ObservedThis Work
ωj,TO (cm-1)
634.0
599.0
558.2
470.2
433.8
406.4
385.6
284.4
262.9
173.0
163.4
127.6
References
*,1
M. Iliev, M. Abrashev, A. Litvinchuk, V. Hadjiev, H. Guo, and A. Gupta, Phys. Rev. B 75, (2007).
*,2
K. Truong, J. Laverdière, M. Singh, S. Jandl, and P. Fournier, Phys. Rev. B 76, 132413 (2007).