In a galaxy far, far away someone is enjoying this view, while
we sit here waiting for the talk to begin...
Ferromagnetic order found at 298 K in
(Sn0.995Cr0.005)Te and is SnTe metallic ?
C. P. Opeil1, J. C. Lashley2, R. K. Schulze2, B. Mihaila2,
P. B. Littlewood3,
E. Rotenberg4, A. Bostwick4
R. D. Field2, D. J. Safarik2,
T. Durakiewicz2, J. E. Gubernatis2, J. L. Smith2,
1Boston
College, Physics Department, Chestnut Hill, MA 02467 USA
2Los Alamos National Laboratory, Los Alamos, NM 87545 USA
3Cavendish Laboratory, Cambridge University, JJ Thomson Ave, Cambridge, UK
4Advanced Light Source, Lawrence Berkeley National Lab., Berkeley, CA, USA
Work sponsored by: Department of Energy and Boston College Trustees
Brief Outline:
*** Ferromagnetic ordering appears in (Sn0.995Cr0.005)Te at 298 K
*** Structural phase transition observed at 98 K via dilatometry
*** Phase transition at 98 K is polar & ferro-elastic not ferroelectric
*** TEM images at 298 K show modulated cubic structure, rather
than heretofore accepted rocksalt (cubic) structure.
*** ARPES on undoped SnTe confirms metallic behavior (gap-less)
not semiconductoring behavior in the low-temperature phase
We will show that SnTe is polar and the low-temperature phase is
metallic therefore it cannot be ferroelectric: one cannot observe a
dielectric hysteresis loop because of conduction arising from free
carriers. a second-order transition with strain must be accompanied
by some other internal symmetry change. One possible change is
the spontaneous development of a symmetry represented by a
polar (vector) order parameter, P. In the present case, this polar
order parameter is the static displacement associated with the
optical phonon.
"... structure to a low-temperature rhombohedral crystal structure.
Associated with the structural change is a relative shift of the sublattices
along the [111] direction, to produce a low-temperature phase with
ferroelectric symmetry. However, there is no direct measurement of the
ferroelectric moment, since it is evidently screened out by the free
carriers always present in these small-gap materials. A sequence of ..."
"... structure to a low-temperature rhombohedral crystal structure.
Associated with the structural change is a relative shift of the sublattices
along the [111] direction, to produce a low-temperature phase with
ferroelectric symmetry. However, there is no direct measurement of the
ferroelectric moment, since it is evidently screened out by the free
carriers always present in these small-gap materials. A sequence of ..."
Why Chromium Doping ?
24
Cr
Chromium
51.9961
At. radius of Cr = 128 pm
At. radius of Sn = 145 pm
Period Number: 4
Group Number: VIB
Oxidation States: +6, +3, +2
Electron Shell Configuration:
1s2
2s22p6
3s23p63d5
4s1
!"
"
1/chi
(Oe Mol-Cr/emu)
Curie-Weiss analysis and Valence determination:
"
In this plot of 1/! vs T the Curie-Weiss region is only in the temperature range for T > 300 K.
The parameters from a fit to the data above this region gives the Weiss constant TW = 290 K
indicating ferromagnetic ordering. The effective number of Bohr magnetons from the analysis
above the ordering region is p = 3.3. For paramagnetic Cr2+ p = 4.9 and for Cr3+ p = 3.8. Thus p
= 3.3 is not unreasonable, and indicates the Cr is in the +3 valence state.
agrees with Inoue et al., J. Phys. Soc. Jpn. 50 (1981) 1222.
M (emu/mole)
QD-VSM measurements indicate ferromagnetic PT and hysteresis:
warming
cooling
diamagnetic
M vs. T: Note the two hysteretic regions, one around 98 K (upper left) supporting the
ferroelastic transition, the second ferromagnetic is shown to the right. Above 300 K
(up to 1100 K), the Cr-doped SnTe remains diamagnetic.
Dilatometry: This technique measures the length change in a sample over changes in temperature and magnetic 5ield (5-­‐350 K, 0-­‐9 T). This dilatometer made of OFHC copper utilizes a capacitive technique that compares a capacitor gap to the expansion or contraction of a sample. Further design details of this dilatometer can be found in G. Schmiedeshoff, et al., Rev. of Sci. Inst. 77, 123907 (2006) see below. This technique enables measurement of linear and volumetric coef5icients of expansion, Grüenisen parameters and indications of sudden changes in crystal symmetry. ΔL = α L ΔT
sample space
Dilatometry measurements:
capacitor gap
sample
Dilatometry measurements:
Sn0.995Cr0.005Te
1.2
H=0T
1.0
H=9T
ΔL
! L (µm)
0.8
0.6
0.4
0.2
0.0
0
20
40
60
80
T (K)
100
120
140
160
Dilatometry measurements:
Sn0.995Cr0.005Te
1.2
H=0T
1.0
H=9T
ΔL
! L (µm)
0.8
0.6
0.4
0.2
Ferro-elastic transition
0.0
0
20
40
60
80
T (K)
100
120
140
160
Spontaneous Strain:
Red curve is Salje fit.
Spontaneous Strain:
Red curve is Salje fit.
Curve saturates below 45 K
Landau theory predicts
quantum mechanical fluctuations
Quantum saturation in order
parameter in Bosonic systems
is simpler than Fermionic.
Remaining Fermions (electrons)
drive the structural transition.
Linear dependence in Tc vs n is
Dirac point.
Solid black lines show
Salje's fit to experimental data
Resonant Ultrasound Measurement Probe and Sample:
Resonant Ultrasound Measurements on (Sn0.995Cr0.005)Te and SnTe:
Room Temp
SnTe single crystal
NaCl structure
a = 0.640 nm
evidence of incommensurate structure
Extra periodicity:
macroscopic view:
Cubic
microscopic view:
Incommensurate,
modulated, not cubic
Photoemission,
Electrons and Gaps
Fundamentals of Photoemission:
The big three names:
Photoelectric
effect
H. Hertz
Observed
P.E.E. first
in 1887
A. Einstein
Nobel 21
K. Siegbahn
Nobel 81
ARPES: Angle
Resolved
Photoemission
Spectroscopy
!
Brillouin
zone
orientation
!
[100]
kX
kZ
Z
2meEkinetic
2
h
θ to specify k-vector to
probe, and then vary polar
φ to collect DOS at various
kII and observe dispersion
of bands along k-vector
surface normal
e-
Ekinetic = h" # e$ # Ebinding
kII =
ARPES - choose azimuthal
analyzer
φ
α-U(001) surface
" sin#
θ
[001]
kY
[010]
(100) plane
Energy Levels or Bands
1s2, 2s2, 2p6, 3s2, 3p6,
4s2, 4p6....6d, 7f
Outer shell
Valence band
Fermi
Energy
N
Inner shell
or energy band
Outer shell
Valence band
Energy Levels or Bands
Fermi Energy
What happens at
the Fermi energy
determines the type
of energy gap.
1s2, 2s2, 2p6, 3s2, 3p6,
4s2, 4p6....6d, 7f
As distance changes
from the nucleus,
electron energy and
density change until the
Fermi energy is
reached.
N
Inner shell
or energy band
Energy Levels or Bands
Fermi Energy
What happens at
the Fermi energy
determines the type
of gap.
1s2, 2s2, 2p6, 3s2, 3p6,
4s2, 4p6....6d, 7f
Just before the Fermi
Energy we can have
three kinds of gaps,
Band Gaps:
1) No Gap
2) Full Gap
3) Pseudo-Gap
Think of a Gap as the
ability for outer
electrons to reach the
Fermi Energy.
Inner shell
or energy band
Outer shell
Valence band
N
Density of states
Densities of States and
Gaps
No Gap
Density of states
Energy (eV)
Fermi Energy
Gap between last
energy state and the
FE
Energy (eV)
Fermi Energy
Photoemission: ARPES at 20 K on SnTe
L-point
kx vs ky
Calculation
E vs k
Data
Selected Data
Photoemission: ARPES at 20 K on SnTe
L-point
kx vs ky
Calculation
E vs k
Data
Data
Conclusions:
At the L point in T = 0 limit, ARPES (at 20 K) shows no gap therefore the
low-temperature phase is a metal (this result settles an old problem). The
phase is polar (metallic) and not ferroelectric because one cannot put an
electric field on the metal.
All band calculations predict a gap there: except calculations by Rabi
et al. where fully relativistic show a gap whereas non-relativistic
calculations do not.
Can quantum fluctuations drive the truncated-cone Dirac behavior and
apparent critical behavior? One would need to look for critical scattering.
With gratitude for my collaborators:
R. K. Schulze, J. L. Smith, J. E. Gubernatis,
B. Mihaila, R. D. Field, D. J. Safarik, T. Durakiewicz,
P. B. Littlewood, E. Rotenberg, A. Bostwick, J. "Captain" Lashley
Special thanks to Dr. Madalina Furis and the
Department of Physics at
Thank you for your kind attention.