Raman- and infrared-active phonons in superconducting and nonsuperconducting rare-earth
transition-metal borocarbides from full-potential calculations
P. Ravindran,* A. Kjekshus, and H. Fjellva
˚
g
Department of Chemistry, University of Oslo, Box 1033, Blindern, N-0315, Oslo, Norway
P. Puschnig and C. Ambrosch-Draxl
Institut fu ¨r Theoretische Physik, University Graz, Universita ¨tsplatz 5, A-8010 Graz, Austria
L. Nordstro
¨
m and B. Johansson
Condensed Matter Theory Group, Department of Physics, Uppsala University, Box 530, 75121, Uppsala, Sweden
Received 24 July 2002; published 14 March 2003
Ab initio frozen-phonon calculations were performed for superconducting YNi
2
B
2
C and LuNi
2
B
2
C and
nonsuperconducting LaNi
2
B
2
C and YCo
2
B
2
C to establish the phonon frequencies for all Raman- and IR-
infrared-active optical q =0 modes using the generalized-gradient-corrected full-potential linear augmented
plane-wave method. From a series of atomic force calculations the shape of the phonon potential is established.
Our calculated Raman-active phonon frequencies are found to be in very good agreement with the available
Raman-scattering measurements. In the case of IR-active phonons, to our best knowledge, there are no experi-
mental frequencies available and our theoretical study is the first report for these series. The Raman-scattering
intensities for all Raman-active modes of YNi
2
B
2
C are determined allowing a detailed comparison between
theoretical and experimental Raman spectra. The changes in the electronic structure introduced by the phonon
modes are also analyzed. Although the calculated electronic structure of these materials has three-dimensional
character we found a large anisotropy in the optical dielectric function due to the layered nature of the crystal
structure.
DOI: 10.1103/PhysRevB.67.104507 PACS numbers: 74.70.Ad, 74.25.Gz, 74.25.Jb
I. INTRODUCTION
The discovery
1
of superconductivity in the Y-Ni-B-C sys-
tem and its coexistence with magnetism in quaternary
transition-metal T borocarbides with the formula R Ni
2
B
2
C
( R =Y, Ho, Er, Tm or LuRef. 2 has stimulated consider-
able research activity. The layered R -T boride carbides
RT
2
B
2
C show a rich variety of phenomena: superconductiv-
ity with elevated T
c
;
1–3
exotic magnetic behavior such as
helical magnetism;
4
heavy Fermion behavior;
5,6
cascades of
field-induced magnetic phase transitions;
7
mixed-valence
states;
8,9
a striking manifestation of the interplay between
magnetism and superconductivity, such as reentrance and
coexistence;
2– 4,7,10,11
anisotropic upper critical fields; angular
dependence of in-plane magnetization;
12
hexagonal-to-
square vortex lattice transition;
13–15
and phonon softening at
a finite wave vector where strong Fermi-surface nesting is
suggested.
16–20
The superconducting mechanism and the pairing symme-
try of RT
2
B
2
C have been extensively studied over the past
few years. There are many experimental observations of
strong electron-phonon interaction, while considerable doubt
has been expressed regarding the adequacy of a solely con-
ventional electron-phonon EP mechanism to account for
such high T
c
. The presence of the light elements boron and
carbon, which is expected to result in high phonon frequen-
cies, opened the door for speculation that some exotic pair-
ing mechanism is responsible for the relatively high transi-
tion temperatures. For example, recent measurements of the
microwave surface impedance in the vortex state suggest that
low-energy quasiparticles may have d-wave dispersion.
21
The residual absorption in the superconducting gap SG
seen by Raman spectroscopy
22
and the upward curvature of
the critical field vs temperature
23,24
are difficult to explain
within BCS theory. The absence of a Hebel-Slichter peak,
the temperature to the third power dependence of the nuclear
relaxation rate,
25
and the direct measurement of the SG by
photoemission spectroscopy
26
suggest the existence of nodes
in the SG.
However, band-structure calculations,
27–30
the T
c
vs
relation,
31
and the variation in superconducting transition
temperature with nonmagnetic impurities
32,33
suggest strong
EP interaction as a possible origin for the superconductivity.
Also, the good agreement between transport and critical-field
properties based on Eliashberg theory
24,34
as well as s-wave-
like tunneling spectra
35
support the above viewpoint. Fur-
thermore, the observation
36
of the de Haas-van Alphen effect
indicates that the superconducting state evolves from the
Fermi-liquid ground state. While it is generally believed that
EP interaction is the underlying mechanism for superconduc-
tivity in these systems, the responsible phonons are claimed
to be either of a high-frequency (B-A
1 g
near 830 cm
-1
)
Ref. 37 or low-energy soft-mode nature.
18,27,38
Hence, it is
important to fully characterize the lattice-dynamical proper-
ties of superconducting as well as nonsuperconducting boro-
carbides for understanding the superconducting mechanism.
Among the R Ni
2
B
2
C superconductors the nonmagnetic
compounds with R =Lu and Y exhibit
2,3
the highest transi-
tion temperatures, T
c
=16.5 and 15.5 K, respectively. In ad-
dition, electronic band-structure calculations
27,29,39
suggest
that these materials are conventional superconductors with a
PHYSICAL REVIEW B 67, 104507 2003
0163-1829/2003/6710/10450711/$20.00 ©2003 The American Physical Society 67 104507-1