Multiple pressure-induced transitions in HgCr2S4
Ilias Efthimiopoulos1#, Alexander Yaresko2, Vladimir. Tsurkan3,4, Joachim Deisenhofer3, Alois
Loidl3, Changyong Park5, and Yuejian Wang1*
1
Department of Physics, Oakland University, Rochester, MI, 48309, USA
Max Planck Institute for Solid State Research, D-70569, Stuttgart, Germany
3
Experimental Physics 5, Center for Electronic Correlations and Magnetism, Institute of
Physics, University of Augsburg, D-86159 Augsburg, Germany
4
Institute of Applied Physics, Academy of Sciences of Moldova, MD 2028 Chisinau, Republic of
Moldova
5
High Pressure Collaborative Access Team, Geophysical Laboratory, Carnegie Institution of
Washington, Argonne, IL 60439, USA
2
Supplementary Material
FIG. S1: (a) XRD patterns of HgCr2S4 at selected pressures (T=300 K, λ=0.4246 Å). The various phases
are indicated by different colors: black for Fd-3m, red for I41/amd, blue for orthorhombic, and dark green
for HP3.. Asterisks mark the Bragg peaks of the Re gasket. Background has been subtracted for clarity.
(b) Expanded view of the HgCr2S4 XRD patterns between 22 GPa and 49 GPa in the 6o-7.5o 2θ range.
Notice the splitting of the (200) Bragg peak of the I41/amd phase at ~27 GPa, signaling the onset of the
orthorhombic distortion.
FIG. S2: Measured HgCr2S4 XRD pattern at 48.6 GPa (T=300 K, λ=0.4246 Å). The various colors of the
Bragg peak positions (vertical ticks) represent different structures: blue for the HgCr 2S4
orthorhombic phase (estimated values), green for Re, and red for Ne. The more intense features in
the diffractogram arise due to rhenium; the strongest Ne peak is located at ~13o1.
TABLE S1: List of the lattice constants for the various phases of HgCr2S4 for all pressures.
Phase
P (GPa)
a (Å)
b (Å)
c (Å)
Fd-3m
1.00E-04
0.7
1.7
3.6
5.6
7.5
8.1
8.63
10.16
12.8
14.3
16.23
18.1
10.2414
10.2069
10.1835
10.1196
10.0767
10.0080
9.9947
9.9820
9.9440
9.8883
9.8619
9.8387
9.8085
10.2414
10.2069
10.1835
10.1196
10.0767
10.0080
9.9947
9.9820
9.9440
9.8883
9.8619
9.8387
9.8085
10.2414
10.2069
10.1835
10.1196
10.0767
10.0080
9.9947
9.9820
9.9440
9.8883
9.8619
9.8387
9.8085
19.96
22.2
25.2
7.2997
7.2948
7.2732
7.2997
7.2948
7.2732
8.3981
8.2391
8.1049
26.8
30.1
32.2
33.96
36.5
7.3013
7.2893
7.2586
7.2188
7.2069
7.2023
7.1714
7.1394
7.0894
7.0473
8.0453
7.9141
7.8865
7.8731
7.8509
I41/amd
[Imma]
TABLE S2: Refined crystallographic data for the ambient-pressure Fd-3m phase, and the high-pressure
I41/amd and orthorhombic modifications of HgCr2S4. The SG Imma used for the refinement
of the orthorhombic phase is tentative and was selected due to the following reasons: (1) it is
a direct subgroup of SG I41/amd, and (2) it is a low-temperature modification of the related
ZnCr2S4 spinel2, which undergoes a similar sequence of structural transitions upon lowering
temperature.
Space Group
Fd-3m (227)
I41/amd (141)
[Imma (74)]
Pressure (GPa)
5.6
22.2
32.2
a (Å)
10.0767(1)
7.2948(1)
7.2586(24)
b (Å)
10.0767(1)
7.2948(1)
7.1394(10)
c (Å)
10.0767(1)
8.239(2)
7.8865(35)
c/a
1
1.13
1.087
c/b
1
1.13
1.105
V (Å )
1023.2
438.4
408.7
Z
8
4
4
Rp, wRp
0.0084, 0.0126
0.0127, 0.0172
0.0103, 0.0155
Hg
8a (0.125, 0.125, 0.125)
4a (0, 0.75, 0.125)
Cr
16d (0.5, 0.5, 0.5)
8d (0, 0, 0.5)
S
32e (u, u, u)
16h (0, y, z)
u=0.2621(5)
y=0.4448(20)
3
Atomic parameters
z=0.2335(10)
Cr-S bond length (Å)
2.403(5)
2.316(3) x 4 /Cr-S(2) // ab-plane
Hg-S bond length (Å)
2.393(8)
2.3996(20)
Cr-S-Cr bond angle (degrees)
95.7(4)
103.91(3) (along ab-plane)
2.232(10) x 2 /Cr-S(1) // c-axis
93.05(5) (along c-axis)
TABLE S3: Elastic parameters (volume VTr, the bulk modulus BTr, and the pressure derivative of bulk
modulus B’Tr) for the various phases of HgCr2S4 under pressure, as obtained by the fitting of
a Birch-Murnaghan EOS form3 to the measured P-V data. Each parameter is evaluated at the
transition pressure point PTr.
Phase
PTr (GPa)
-4
VTr/Z (Å3)
BTr (GPa)
B'Tr
133.7(4)
107(5)
4(fixed)
Fd-3m
10
I41/amd
20
111.8(2)
112(3)
4(fixed)
Orthorhombic
26.8
105.7(2)
142(10)
4(fixed)
TABLE S4: Assignment4, frequencies, pressure coefficients, and the mode Gruneisen parameters γ of the
Raman modes of HgCr2S4. The pressure depencence of the Raman-active modes is described
by the relation: ω(P)=ωTr+αPTr, where frequeny ωTr is in cm-1 and pressure PTr in GPa. The
Gruneisen parameters γ are determined from the relation: γ=(BTr/ωTr)x(∂ω/∂P), where
BTr=107 GPa (Fd-3m) and BTr=85 GPa (I41/amd, extrapolated).
Phase
Assignment
ωTr (cm-1)
∂ω/∂P (cm-1/GPa)
γ
Fd-3m
Eg
257.9
2.7
1.1
PTr=1 bar
F2g (2)
273
3.5
1.4
F2g (1)
404.9
3.8
1
I41/amd
-
290.5
0.3
0.1
PTr=12.6 GPa
-
296.4
0.8
0.2
FIG. S3: The ferromagnetic (FM) spin structure (left) and a non-collinear structure that gives zero
moment (ZM) in each Cr tetrahedron (right).
FIG. S4: Pressure dependence of the stabilization energies ΔE of the FM (blue) and ZM (red) spin
configurations assumed for both Fd-3m and I41/amd phases of HgCr2S4. The stabilization energy
is defined as ΔE=EM−E0, where EM and E0 are the total energies obtained from magnetic and nonspin-polarized calculations, respectively.
FIG. S5: The AFM I41/amd structure
FIG. S6: The pressure dependence of the difference E(q)-E(0), where E(0) is the energy of the FM
solution, calculated for the Fd-3m structure with the wave vector q varying along (qq0) and (00q)
lines. The values of qmin are 0.6 (0 GPa), 0.8 (5.6 GPa), 0.95 (10 GPa), and 1.05 (16.2 GPa) in
2π/a units.
References
1
R.J. Hemley, C.S. Zha, A.P. Jephcoat, H.K. Mao, L.W. Finger, and D.E. Cox, Phys. Rev. B 39, 11820
(1989).
2
F. Yokaichiya, A. Krimmel, V. Tsurkan, I. Margiolaki, P. Thompson, H.N. Bordallo, A. Buchsteiner, N.
Stuesser, D.N. Argyriou, and A. Loidl, Phys. Rev. B 79, 64423 (2009).
3
F. Birch, Phys. Rev. 71, 809 (1947).
4
A.K. Kushwaha, Commun. Theor. Phys. 50, 1422 (2008).