PHYSICAL REVIEW B 87, 214418 (2013)
Incommensurability and spin dynamics in the low-temperature phases of Ni
3
V
2
O
8
G. Ehlers, A. A. Podlesnyak, and S. E. Hahn
Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6475, USA
R. S. Fishman
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6114, USA
O. Zaharko, M. Frontzek, and M. Kenzelmann
Laboratory for Neutron Scattering, Paul Scherrer Institute, CH-5232 Villigen, Switzerland
A. V. Pushkarev, S. V. Shiryaev, and S. Barilo
Institute of Solid State and Semiconductor Physics, Minsk 220 072, Belarus
(Received 26 April 2013; published 17 June 2013)
Magnetic order and low-energy spin dynamics in the zero field ground state of Ni
3
V
2
O
8
are revealed in elastic
and inelastic neutron scattering experiments. Neutron diffraction shows that below T = 2.3 K the Ni
2+
moments
(spin S = 1) order in a cycloid pattern with incommensurate wave vector k
ICM
= (0,1,τ ), where τ = 0.4030 ±
0.0004, which is superimposed on a commensurate antiferromagnetic spin arrangement with k
CM
= (0,0,0).
Three spin wave modes are discerned below E ∼ 3 meV in inelastic measurements and qualitatively described
by a model Hamiltonian that involves near neighbor exchange, local anisotropy, and a small biquadratic coupling
between the spine and cross-tie sites. Results from both elastic and inelastic scattering experiments suggest that
the two sublattices on spine and cross-tie sites are largely decoupled.
DOI: 10.1103/PhysRevB.87.214418 PACS number(s): 75.10.Hk, 75.25.−j, 78.70.Nx
I. INTRODUCTION
Many new multiferroic materials, in which both magnetic
and electric order parameters coexist, have emerged during
the last decade.
1–4
The study of these systems, and the new
phenomena associated with the coupling between ferroelectric
polarization and magnetic order, is driven by the immense
technological promise that new types of multifunctional
devices may be developed which are based on these materials,
for example, for information storage.
5
Ni
3
V
2
O
8
is a multiferroic system with an extremely rich
phase diagram. To date, many experimental and theoretical
studies of Ni
3
V
2
O
8
have been published in the literature, with
techniques including neutron scattering, nonresonant x-ray
magnetic scattering, specific heat, muon spin relaxation,
51
V
NMR, electric polarization, and magnetization.
6–18
Ni
3
V
2
O
8
undergoes a series of successive and complex phase transitions
when cooled in zero field, and four different magnetically
ordered phases have been identified below ∼9 K (which were
termed, in order of decreasing temperature, HTI, LTI, C, C
′
).
In the HTI and LTI phases, magnetic order is incommensurate,
with an ordering wave vector parallel to the H direction,
and a spin reorientation occurs at the transition between
the two phases.
10
The LTI phase shows spontaneous electric
polarization which sparked a lot of interest in this compound.
The paraelectric low-temperature C and C
′
phases have been
previously described as canted antiferromagnetic phases with
commensurate order but the main difference between the two
phases remained unclear.
8,13
Magneto-optical investigations and band structure calcu-
lations show that Ni
3
V
2
O
8
is a local moment insulator and
that each Ni
2+
ion carries spin S = 1 with 2 μ
B
local moment
as expected.
11
The Curie-Weiss temperature of Ni
3
V
2
O
8
is
W
∼−30 K,
6
and spontaneous magnetic order occurs at
T
N
∼ 9 K.
7
Thus, by a conventional estimate
19
the degree
of geometric frustration in this material is moderate, as
the ratio |
W
/T
N
|∼ 3 shows. However, the unusually large
number of distinct zero-field phases can still be attributed to
the interplay between the particular lattice geometry, which
features two distinct Ni sites unrelated by symmetry, and the
antiferromagnetic near neighbor interactions. The two sites
have been commonly referred to as “spine” (Wyckoff notation
8e) and “cross-tie” (4a) respectively, their atom positions in
the unit cell can be found in Table I.
In this paper the magnetic interactions in Ni
3
V
2
O
8
are being
studied with elastic and inelastic neutron scattering measure-
ments, and with supporting model calculations based on a
magnetic Hamiltonian that contains exchange and anisotropy
terms. Despite a large body of work, an understanding of
Ni
3
V
2
O
8
at this level has been missing so far. In particular,
the difference between the magnetic ordering patterns in the C
and C
′
phases can now be understood.
II. EXPERIMENT
Single crystals of Ni
3
V
2
O
8
were grown from a melt of
BaO/1.17·V
2
O
5
composition, which is between two eutectic
points on the BaO/V
2
O
5
phase diagram.
20
The starting
materials BaCO
3
, NiO, and V
2
O
5
(all in powder form and
of 99.99% purity) were mixed in molar ratio 1:1:1.5 and
placed in a platinum crucible. The mixture was calcined in
air at 900
◦
C. After homogenization of the melt at 1200
◦
C
for 8 h, the temperature in the furnace was decreased down
to approximately 900
◦
C. The remainder of the flux melt was
removed from the crucible and grown crystals were cooled
down to room temperature at the rate 50
◦
C/h for about 15 h.
Typical crystals were of deep dark gray color and had a
214418-1 1098-0121/2013/87(21)/214418(7) ©2013 American Physical Society