PHYSICAL REVIEW B 97, 235147 (2018)
Interplay of covalency, spin-orbit coupling, and geometric frustration in the d
3.5
system Ba
3
LiIr
2
O
9
Jayita Chakraborty
*
Department of Physics, Indian Institute of Science Education and Research Bhopal, Bhauri, Bhopal 462066, India
(Received 21 February 2018; revised manuscript received 14 May 2018; published 27 June 2018)
The electronic and magnetic properties of d
3.5
iridate Ba
3
LiIr
2
O
9
have been studied using first-principles
electronic structure calculations. The results of the calculations reveal that the system lies in an intermediate
spin-orbit coupling (SOC) regime. There is strong covalency of Ir-5d and O-2p orbitals. SOC, together with
covalency, conspires to reduce the magnetic moment at the Ir site. By calculating the hopping interactions and
exchange interactions, it is found that there is strong antiferromagnetic intradimer coupling within an Ir
2
O
9
unit and
other antiferromagnetic interdimer interactions make the system frustrated. The anisotropic magnetic interactions
are also calculated. The calculations reveal that the magnitude of the Dzyaloshinskii-Moriya interactions parameter
is small for this system. The magnetocrystalline anisotropy energy is large for this system and the easy axis lies
on the ab plane.
DOI: 10.1103/PhysRevB.97.235147
I. INTRODUCTION
The interplay of strong spin-orbit coupling, electron-
electron correlation, and crystal-field splitting have recently
attracted much attention both theoretically and experimen-
tally [1,2]. Iridium oxides offer an excellent playground for
such an interplay and exhibit intriguing phenomena. Many ex-
otic phases like novel Mott insulating states, spin-liquid states,
orbital oriented exchange coupling in Kitaev-type models,
topological Mott insulators, Weyl semimetals, and topological
magnetic insulators with axionic excitations have been found
in these materials [3–6]. As a result, both experimental and
theoretical efforts have been undertaken to investigate novel
spin-orbit physics in various 5d systems. Iridates with 4+ (5d
5
)
and 5+ (5d
4
) oxidation state of Ir have been much explored and
found to exhibit interesting phenomena [7–10]. Realization
of J
eff
= 1/2 and J
eff
= 0 states are observed with d
5
and
d
4
valence states of Ir respectively [3,11]. However, iridates
with the higher oxidation state of Ir are hardly studied. The
hexavalent systems (6+ oxidation state, d
3
configuration) are
generally assumed to possess spin-only S =
3
2
ground states
with quenched orbital angular momentum according to the
usual L-S coupling scheme. This scenario is however not true
in the presence of strong spin-orbit coupling (SOC). Interesting
spin-orbit driven magnetism is found in 4d
3
and 5d
3
based
transition-metal oxides [12–14].
The 6H triple perovskite iridates with the general formula
Ba
3
MIr
2
O
9
attracted much attention because the valency of
Ir can be tailored by nonmagnetic M atom [11,15,16]. The
spin-orbital liquid state is found for Ba
3
ZnIr
2
O
9
[11]. The
fractional valence state of Ir (d
4.5
) is also found in these triple
perovskite systems. Spin-orbit driven magnetism is found
for Ba
3
YIr
2
O
9
and Ba
3
InIr
2
O
9
[15,16]. Another 6H -triple
perovskite Ba
3
LiIr
2
O
9
is synthesized by Kim et al., where
Ir is in a fractional oxidation state of +5.5 [17]. The magnetic
*
jayita@iiserb.ac.in
moments determined from the temperature dependence of the
magnetic susceptibility are low for this compound and the value
of magnetic moment at an Ir site is much smaller than the spin
only value. The spin-orbit coupling may play an important
role in this system. It is expected that the iridates with the
higher oxidation state of Ir have strong covalency with Ir-5d
and O-2p states. Zero-field-cooled (ZFC) and field cooled (FC)
data for magnetic susceptibility diverge at 75 K, suggesting the
presence of the frustration in this system [17]. The combined
effect of strong covalency, geometric frustration, and spin-orbit
coupling may lead to intriguing phases in this material. In
spite of all the work that has been done on 5-d
4
, 5-d
4.5
, and
5-d
5
iridates, there has been very little progress in iridates
containing Ir with higher oxidation states. In Ba
3
LiIr
2
O
9
, Ir
is in the fractional oxidation state of 5.5 (i.e., 5-d
3.5
state). In
this context, first-principles electronic structure calculations
based on density functional theory (DFT) are important for
investigating the effect of covalency, geometric frustration, and
spin-orbit coupling in this material.
In this paper, the electronic and magnetic properties of
Ba
3
LiIr
2
O
9
are studied using first-principles calculations
within the framework of density functional theory. The aim of
this study is to understand the cross coupling between spin, ge-
ometric frustration, covalency, and spin-orbit interaction in this
d
3.5
iridate. The nature of magnetism in Ba
3
LiIr
2
O
9
is studied
by determining the magnitude of the relevant magnetic inter-
actions including the isotropic exchange, the Dzyaloshinskii-
Moriya (DM) coupling, and the magnetocrystalline anisotropy,
by projecting the total energies for different magnetically
constrained spin configurations onto a spin Hamiltonian. The
possible spin model of Ba
3
LiIr
2
O
9
is proposed here.
II. CRYSTAL STRUCTURE AND METHOD
Ba
3
LiIr
2
O
9
crystallizes in a 6H -perovskite-type structure
with space group P 63/mmc. The unit cell, as depicted in Fig. 1,
contains two formula units. Ir is in the octahedral environment
with oxygen atoms. Each distorted IrO
6
octahedron shares
2469-9950/2018/97(23)/235147(6) 235147-1 ©2018 American Physical Society