This document is Gregory Daly's final year project report on multiferroic manganites for his degree at the University of Warwick. The project aims to discover if doping compounds of Sm1−xLuxMnO3 with Lu can induce multiferroic behavior, and if so how the properties are affected by external magnetic fields. The report summarizes the magnetic, dielectric and structural properties found for doping levels from 0 to 1, including the observation of multiferroic behavior at a doping of x=0.2. It also reviews the relevant theory on multiferroics, magnetic interactions and ordering.

1. The University of Warwick
Final year project
Multiferroic Manganites
Author:
Gregory Daly
Supervisor:
Dr.Geetha Balakrishnan
November 18, 2014

2. Abstract
We reported on the magnetic, dielectric and structural properties of Sm1−xLuxMnO3
for Lu doping levels 0 ≤ x ≤ 1. We were able to successfully induce multiferroic
behaviour in Sm1−xLuxMnO3 for a doping of x=0.2, which was also found to be the
solubility limit of Sm1−xLuxMnO3 for doping. This showed an additional magnetic
transition at ≈ 22 K with a coincident transition in the dielectric behaviour. Below
x=0.2 spin canting and suppression of the large magnetic moment of SmMnO3 were
also observed. X-ray powder diffraction of Sm1−xLuxMnO3 showed a decrease in
the Mn-O-Mn bond angle towards the structure of TbMnO3, suggesting that this
multiferroic will behave similarly to TbMnO3. LuMnO3, x=1, was found to have a
magnetic and dielectric transition at ≈ 90 K as expected from published data, but
also exhibited a large lambda type peak at ∼ 245 K.
1 Introduction
1.1 Project Aims
In recent years interest in the field of multiferroics has seen a resurgence[1]. This is mainly
due to the recent discovery that the polarization of the bulk material can be altered by
the application of magnetic fields [2, 3]. In this research, we have endeavoured to discover
if the series of doped compounds, Sm1−xLuxMnO3, have a multiferroic phase and if these
are affected by the application of external magnetic fields. For the doped compounds
that show multiferroic behaviour, we will conduct structural studies to determine if the
phase changes are related to the Mn-O-Mn bond angle of the crystal structure; as has
been shown in other rare-earth perovskite manganites[2, 4].
1.2 Theory of Multiferroics
A multiferroic is defined as a material that has two or more of the three ferroic types of
behaviour, ferroelectricity, ferromagnetism and ferroelasticity, occurring simultaneously in
the same phase[5]. This ferroic behaviour also extends to antiferromagnetic, ferrimagnetic
and ferrielectic materials.
Certain rare-earth perovskite manganites show antiferromagnetic ordering coupled
with ferroelectric behaviour and it has been shown that this can be induced in others by
1

3. doping[1, 2, 3, 4]. Hence, I will try and restrict my discussions to these pertinent ferroic
properties.
1.2.1 Ferromagnetic and Ferroelectric Ordering
Ferromagnetism is a phenomenon that creates a spontaneous magnetic moment in a bulk
material, even in the absence of an applied field[6]. If we consider a paramagnet with
concentration N ions of spin S with an interaction causing the spins to align parallel to
each other, the material is a ferromagnet; we call this postulated interaction the exchange
field, BE[6]. If we assume that each magnetic atom experiences a field proportional to
the average magnetization, M, of all other spins, the mean-field approximation, then[6]:
BE = λM (1)
where λ = Tc
C
and Tc and C are the Curie temperature and the Curie constant respectively.
The Curie temperature represents that point at which the thermal excitations have more
energy than BE and no spontaneous magnetization exists[6].
An antiferromagnet is defined as a material where the spins are ordered antiparallel
so that there is zero net momentum, below the N´eel temperature, TN [6], which defines
a similar point to Tc. This is a special kind of ferrimagnetism, whereby the two sublat-
tices have equal and opposite saturation magnetizations, CA = CB[6]. Hence, the N´eel
temperature in the mean field approximation is defined as:
TN = µC (2)
where µ is the magnetic moment. The susceptibility in the paramagnetic phase,
χ =
2C
T + TN
(3)
where χ is the susceptibility, is very similar in form to the Currie-Weiss law[6],
χ =
C
T + Tc
(4)
However, below the N´eel temperature, it takes a very different form and is heavily influ-
enced by the structure, alignment of the spins and the direction of the applied field[6].
2

4. For the applied magnetic field, Ba, perpendicular to the spin axis:
χ⊥ =
2Mϕ
Ba
=
1
µ
(5)
where 2ϕ is the angle the spins make with each other and M is the magnetization. If Ba
is parallel to the spins the magnetic energy is not altered. If the two spin systems make
equal angles with the applied field, then at T = 0 K, χ = 0[6].
There are also numerous different types of antiferromagnet, which occur due to the
different possible ways of arranging an equal number of up and down spin states on a
lattice[7]. Only A and E type are shown here as the materials studied are only known to
exist in these two forms.
(a) type A (b) type E
Figure 1: A and E type antifer-
romagnetic order, the two possible
spin states are marked + and -
Ferroelectricity is similar in some ways to ferromag-
netism, in that below a certain temperature, the material
can undergo a phase change where a spontaneous dielec-
tric polarization appears in the crystal. The new crys-
tal structure, after the phase change, displaces the centres
of negative and positive charge away from each other, giving rise to the spontaneous
polarization[6]. Ferroelectricity is a relatively newly discovered phenomenon, but it can
generally be described by Landau Theory, an explanation of which can be found in [6].
1.2.2 Magnetic Interactions
All magnetic ordering in crystal structures occurs via exchange interactions. These govern
the long range magnetic order via electrostatic interactions that minimise the energy of
the electrons in a crystal[7]. The origin of this is based in quantum mechanics, but the
important result obtained is the exchange integral,
J =
ES − ET
2
= ψ∗
a(r1)ψ∗
b (r2) ˆHψa(r1)ψb(r2)dr1dr2 (6)
where, ES and ET are the energy of the singlet and triplet states respectively; r1 and r2
are the spatial coordinates of two electrons; ψa(r1) and ψb(r2) are the wave functions of the
two electrons, with a joint state ψa(r1)ψb(r2); and ˆH is the Hamiltonian of the system[7].
Generalising to a many body system is far from trivial, but the above probably applies
between all neighbouring atoms and is expressed in the Hamiltonian of the Heisenberg
3

5. model,
ˆH = −
ij
JijSi.Sj (7)
where Jij is the exchange integral between the ith
and jth
spins and Si and Sj are the
spins of the ith
and jth
electrons.
The kinds of magnetic exchange that are currently believed to be involved in the prop-
erties of multiferroic rare-earth perovskite manganites are superexchange, double exchange
and the Dzyaloshinsky-Moriya interaction[8, 9]. Hence, I will restrict my discussion to
these.
Figure 2: Superexchange in a
magnetic oxide. The arrows show
the spins of the four electrons and
how they are distributed over the
transition metal (M) and oxygen
(O) atoms. M is assumed to have
a single unpaired electron, making
it magnetic. Taken from [7]
Superexchange can be defined as an indirect exchange
interaction between non-neighbouring magnetic ions which
is mediated by a non-magnetic ion placed in between the
magnetic ions[7]. As can be seen in Figure 2, the valent
magnetic electrons in the transition metal, in the case of
this study, Manganese, can in the antiferromagnetic phase
delocalise over the whole structure, thus lowering their ki-
netic energy[7]. This preference of the antiferromagnetic
phase over the ferromagnetic is due to the Pauli exclusion
principle, as the magnetic electrons would be forbidden
from delocalising and occupying the same orbitals in a fer-
romagnetic phase. Since superexchange involves both the
orbitals of the magnetic transition metal and oxygen it is a
second-order process. The exchange integral for superex-
change is dominated by a kinetic energy term which varies
with the degree of overlap of the orbitals and so is strongly
correlated to the M-O-M bond angle[7].
Double exchange is a ferromagnetic exchange which can occur if the magnetic ion can
show mixed valency, most importantly, in this case, that Manganese can exist as either
Mn3+
or Mn4+
. If we look at Figure 3, we can see the mechanism of the double exchange
clearly, if an Mn3+
ion is placed next to an Mn4+
ion then the eg electron can jump onto
the neighbouring site as there is a vacancy of the same spin. However, due to Hund’s first
rule, if the neighbouring atoms are antiferromagnetically aligned this is not energetically
favourable. Hence, the neighbouring ions adopt a ferromagnetic structure as it decreases
the kinetic energy of the eg electron and reduces the energy of the material[7].
4

6. The last exchange interaction that we will consider is the Dzyaloshinsky-Moriya in-
teraction. This is a spin orbit interaction, similar to superexchange. Here the excited
state is not connected to oxygen, but arises due to the spin-orbit interaction in one of the
magnetic ions[7]. The exchange interaction occurs between the excited state of one ion
and the ground state of the other.
When this acts between two spins, S1 and S2, it alters the Hamiltonian of the system,
adding a new term,
ˆHDM = D.S1 × S2 (8)
Figure 3: Double exchange mech-
anism gives ferromagnetic coupling
between Mn3+
and Mn4+
ions par-
ticipating in electron transfer. The
single-centre exchange interaction
favours hopping if (a) neighbouring
ions are ferromagnetically aligned
and not if (b) neighbouring ions
are antiferromagnetically aligned.
Taken from [7]
In general D is non-zero and will lie parallel or perpendic-
ular to the line connecting the two spins, depending upon
the symmetry[7]. The interaction tries to force S1 and
S2 to be at right angles in a plane perpendicular to D in
an orientation that gives negative energy. This tends to
produces a slight ferromagnetic component perpendicular
to the spin-axes of the antiferromagnet, due to the small
canting of the spins[7].
Above Tc, materials can enter either a paramagnetic or
diamagnetic phase, having a positive and negative mag-
netic susceptibility respectively. This magnetization arises
from the magnetic moment of a free atom in three princi-
pal ways: the electron spin, the orbital angular momentum
of electrons about a nucleus and the change in the orbital
moment induced by the applied magnetic field[6], the lat-
ter giving diamagnetism. Since Manganese and Samarium
are both paramagnetic ions, we will only discuss param-
agnetism here. The magnetic moment of an atom or ion
in free space is,
µ = −gµBJ (9)
where J is the sum of the orbital, L, and spin, S, angular momenta[6], µB is the Bohr
magneton and g is given by the Land´e equation[6],
g = 1 +
J(J + 1) + S(S + 1) − L(L + 1)
2J(J + 1)
. (10)
5

7. From this it can be derived that,
M
B
∼=
NAJ(J + 1)g2
µ2
B
3kBT
=
NAp2
µ2
B
3kBT
=
C
T
(11)
where NA is Avagadro’s number, kB is the Boltzmann’s constant, T is the temperature
of the system, C is the Curie constant and p is the effective number of Bohr magnetons,
defined as[6],
p ≡ g[J(J + 1)]
1
2 . (12)
From these two equations, we can measure the combined p of Sm3+
and Mn3+
in
Sm1−xLuxMnO3 and calculate the theoretical p for Sm3+
and Mn3+
.
1.2.3 The Crystal Structure of Orthorhombic Perovskites
Compounds of the form ReMnO3, where Re=La-Ho, typically adopt an orthorhombically
distorted perovskite structure, space group Pbnm[2, 10]. In this form, the central Mn
atom is surrounded by an octahedron of oxygen atoms. It is the interaction of the Mn
and O atoms, particularly, the Mn-O-Mn bond angle which allows for the appearance of
multiferroism[2, 4]. Due to the presence of Mn3+
ions, we expect the MnO6
octahedra to
exhibit Jahn-Teller distortions. In Mn3+
there is a single electron in the eg level which
can be lowered in energy by splitting the energy level and the t2g level below it. The
reduction in energy is balanced by the energy cost of the distortion. This process results
in the MnO6 octahedra being elongated in the z direction, an increase in the lattice
parameter c[7]. This can be represented phenomenologically by the following argument
from [7], we assume that the distortion of the MnO6 octahedra can be quantified by the
parameter Q, which denotes the distance of distortion along an appropriate normal mode
coordinate[7]. The energy cost of the distortion is quadratic in Q and given by,
E(Q) =
1
2
Mω2
Q2
(13)
where M and ω are the mass of the anion and the angular frequency respectively. In this
form, the minimum energy of the system is where there is no distortion. Any distortion
would raise and lower the energy of orbitals. If these orbitals are all completely full or
empty then E(Q) remains unchanged. However, any partially filled orbitals could have
a significant impact on E(Q)[7]. The electronic energy dependence on Q is in reality
extremely complex, but can be expressed as a Taylor expansion and assuming that the
6

8. distortion is small, we can linearise the expression[7]. This gives an energy of a given
orbital to be AQ or −AQ, where A is a suitable constant, for the raising and lowering of
the electronic energy, thereby giving us E(Q) as,
E(Q) = ±AQ +
1
2
Mω2
Q2
(14)
By considering only one of the solutions to the above, the minimum energy of the orbital,
∂E
∂Q
, gives a value of Q,
Q0 =
A
Mω2
(15)
and minimum energy,
Emin = −
A2
2Mω2
(16)
which is less than zero. Hence, by spontaneously distorting the system reduces its energy.
Figure 4: Cubic perovskite struc-
ture. The small Mn cation (in
black) is at the center of an octa-
hedron of oxygen anions (in gray).
The large Re cations (white) oc-
cupy the unit cell corners. Taken
from [11].
Moving from La-Ho in ReMnO3, the Mn-O-Mn bond
angle decreases[2] and the MnO6 octahedron becomes
distorted[4]. As the Mn-O-Mn bond angle decreases in
the structure, the properties of the crystal change and
it adopts different types of antiferromagnetic structures,
some of which also exhibit ferroelectric properties[2] (see
Figure 5).
It is also possible to induce this change in the Mn-
O-Mn bond angle by doping the rare earth manganites,
which have larger Mn-O-Mn bond angles, with smaller
ions[4, 10]. This enables us, in theory, to create a continu-
ous version of the undoped phase diagram (see Figure 5), which has been partially done in
(J. Hemberger et al., Phys. Rev. B, Vol. 75, 035118, 2007). Here, Eu1−xYxMnO3 single
crystals were grown for x = 0−0.5. These exhibited significant changes in the: Mn-O-Mn
bond angle, the lattice volume, V , and the orthorhombic distortion parameter, = (b−a)
(a+b)
for increasing values of x and went through several antiferromagnetic and ferroelectric
phases[4]. Through doped studies, where we can vary many of the different crystal pa-
rameters, we will be able to verify which parameters induce multiferroic behaviour and
other phase changes. This information will help us in determining the mechanism by
which these novel phenomena occur.
7

9. 1.2.4 The Origin of Multiferroism in Orthorhombic Perovskites
Most forms of magnetic ordering require high level of symmetry within a structure to
maximise the energy of the exchange field between adjacent spins[6]. This allows the
magnetic order to exist throughout the structure without it being suppressed by thermal
excitations at all temperatures above 0 K. However, ferroelectric ordering requires a loss of
symmetry, as the centres of negative and positive charge have to separate in the crystal[11].
These competing symmetry requirements are believed to be one of the reasons for the
rarity of multiferroics[11]. Nevertheless, this does determine some of the ways in which
multiferroism can arise.
Figure 5: Magnetic phase diagram for RMnO3 as a
function of Mn-O-Mn bond angle . Open and closed
triangles denote the N´eel and lock-in transition tem-
peratures, respectively. Left upper inset: Schematic
view of the reciprocal space at a phase with modu-
lated magnetic and crystallographic structure. Open
and closed circles represent nuclear Bragg and su-
perlattice reflections, respectively. Crosses give lo-
cations of magnetic scattering. Right upper inset:
Temperature profiles of the wave numbers of modu-
lated crystallographic (l) or magnetic (m) structures.
The arrows indicate the lock-in transition tempera-
tures. Left and right lower insets show schematic
illustrations of the A-type and the E-type AF struc-
tures, re- spectively. The commensurate AF state
(gray area) was proved to be ferroelectric by the
present study. Taken from [2].
It is currently believed that the mag-
netic ordering in a multiferroic perovskite
manganite is a long range incommensu-
rate longitudinally modulated antiferro-
magnetic ordering[2, 9, 11].
The incommensurate (IC) frustrated
spin structure of this ordering is believed
to create the spontaneous ferroelectric po-
larization that is seen[4]. How these order-
ings are created by the crystal structure
and how it gives rise to the magnetoelec-
tric ordering seen, is still a matter of great
debate, but I will try and describe some
of the current ideas that appear to fit the
experimental data.
In considering these phenomena, we
cannot restrict ourselves to discussing only
nearest neighbour interactions (NN), as the
experimental evidence has shown that this
is a long range type of ordering. We must also consider multiple kinds of exchange in-
teraction to account for the complex ordering, particularly the spiral ordering seen in
TbMnO3[8].
The most recent studies have looked at the roles of next nearest neighbour interac-
tions (NNN), the double exchange model (DE), super exchange model (SE), Jahn-Teller
8

10. distortions and interactions (JT)[8] and the possible role of the Dzyaloshinsky-Moriya
interaction (DM) [9].
From the 2D results of [8], DE and NNSE were able to account for the existence of
A and E type antiferromagnetic (AF) ordering (see Figure 1) , but not the spiral phase
of the IC-AF and C-AF of TbMnO3. To fully account for the existence of the magnetic
phases, the NNNSE was required. However, this only provided a qualitative description.
JT distortions helped to account for the insulating nature of the crystals.
While the above results were able to explain the structure to some extent, they did
not account for the coupling of the ferroelectricity and IC magnetism. It was initially
thought that coupling originated from the competition between the DE and SE with the
DM[9]. The DM explained why the polarization, P, was always perpendicular to the wave
vector, k, as DM allowed for P to be independent of the spin structure and only involved
interactions between spins induced by symmetry-breaking ionic displacements[9].
1.2.5 TbMnO3
The first multiferroic rare earth manganite to be discovered was TbMnO3 and it is also
the most widely studied of all of the rare earth manganites. TbMnO3 has a multiferroic
transition at Tlock = 28 K[12] and a second long-range ordering at ∼ 7 K[12]. It has been
deduced in numerous studies that below the first transition TbMnO3 adopts a type of
spiral magnetic ordering[12]. This long range symmetry breaking is believed to be created
by competition between nearest neighbour and further than nearest neighbour magnetic
interactions[12] and allows for the existence of a ferroelectric ordering. Although there has
been much debate over the structure of TbMnO3, it is currently believed that it has an
elliptically modulated cycloidal spiral magnetic structure[12]. One of the most interesting,
and potentially most useful properties of TbMnO3, is that the cycloidal ordering allows
for the rapid switching of the polarization of the material by the application of a magnetic
field[1, 12]. Furthermore, though doping, other rare earth manganites can also adopt this
ordering and behaviour[1, 4].
2 The Experimental Methods and Equipment
Since TbMnO3 was discovered to be a multiferroic there has been much research in mul-
tiferroism in the series of compoundsReMnO3[2]. Although only Eu-Ho are found to
naturally have multiferroic phases, it has been shown that through doping the other rare-
9

11. earths, Nd, Sd and Eu, can be distorted into the structure of TbMnO3 and adopt its
multiferroic properties [4, 10]. SmMnO3 is a low temperature A-type antiferromagnet[2]
as both the Sm and Mn are magnetic, Lu on the other hand is a non-magnetic ion and
LuMnO3 is a high temperature ferroelectric[13, 14]. Since other studies have shown that
by doping other rare earth manganites with similar non-magnetic atoms multiferroism
could be induced[4, 10], we believed that this was a very good candidate for a doped
multiferroic.
2.1 Sample Synthesis
We created our polycrystalline samples of Sm1−xLuxMnO3 by mixing Sm2O3, Lu2O3 and
MnO2 stoichiometrically and using the conventional solid state reaction method[4, 10, 15].
The samples were weighed on a balance that listed a mass in grammes to 4 d.p. and great
care was taken to ensure that there was no debris on the balance when the sample mixtures
were weighed. The solid state reaction method used was the following: a 12 hour heating
at 1100 ◦
C, a 24 hour heating at 1400 ◦
C and a final 24 hour sintering at 1400 ◦
C. Between
each stage the powdered samples were reground.
2.2 X-Ray Diffraction
The samples were checked for impurity phases by x-ray powder diffraction using CuKα
radiation. The scans were taken on a Philips x-ray generator and diffractometer. In x-ray
diffraction, the incident x-ray is absorbed by the electron cloud of an atom. The electron
cloud then emits an x-ray of the same frequency. At most angles incident to the lattice
planes, the x-rays produced by the atoms will destructively interfere and no x-rays will
be emitted from the lattice. However, for certain angles of incidence and lattice spacings,
constructive interference will occur and an x-ray will be emitted from the lattice. The
wavelength of the x-ray, λ, the interplanar spacing, d, and the angle of incidence of the
x-ray, θ, are all related by Bragg’s Law for λ ≤ 2d:
2dsinθ = nλ (17)
Using the above, we were able to compare the d-spacings of our peaks to those of published
data for SmMnO3 and LuMnO3, check that the peaks matched those of SmMnO3 and
contain no impurity phases of LuMnO3.
10

12. A Bruker D5005 was also used to take long high resolution x-ray scans which were
then used for Reitveld analysis. The analysis was done using Topas Accademic v.4.1 and
crystallographic data files from ICSD-WWW through the CDS website as a starting point
for the refinement. The Reitveld refinement was used to find the pertinent bond angles
in the structure: the Mn-O-Mn bond angles between MnO6 octahedra. In the Rietveld
refinement, we gave the background fitting only 6 parameters to vary and allowed for a
zero error to be accounted for. However, these had to be checked to ensure that they
were not masking any peaks in the data. The refinement of the lattice parameters was
conducted first, as it had the smallest capacity to provide a fit to the data that bore no
relation to reality, followed by each of the atomic positions individually. This was done
without any thermal parameters. Particular care had to be taken with the refinement of
the oxygen positions, as the x-ray scans would be inherently unable to accurately locate
them. Once the atomic positions had been refined to realistic values, i.e. not 20 ± 100 m
from that crystal, we allowed the thermal parameters to vary slightly. This was left until
the end as it is possible for the program to create a fit simply with unrealistic thermal
parameters.
2.3 Measuring the Magnetic Susceptibility and Dielectric
Constant
The magnetic susceptibility was calculated from measurements of the long moment in a
SQUID (Superconducting Quantum Interference Device) magnetometer. The basis of a
SQUID is two superconductors separated by two parallel Josephson junctions, where a
DC biasing current is passed through them. The Cooper pairs in the superconductor are
able to tunnel through the Josephson junction, a thin layer of insulating materials, with
remarkable effects. The effect that is used in SQUID magnetometers is described in detail
in (Kittel, Solid State Physics, Wiley). In short, it is that the maximum supercurrent
shows interference effects as a function of the magnetic field intensity for a dc magnetic
field[6].
This dc magnetic field is generated by the sample as follows: An even number of pick-
up coils are placed in a magnetic field, B, generated by a superconducting magnet. The
coils are wound in opposite directions and the sample is slowly moved through them. The
magnetic moment of the sample generates a current in the coils, in opposite directions in
each coil to compensate for external magnetic field variations. The current in the coils
11

13. generates a magnetic field that is picked up by the SQUID, which accurately measures
the small changes in the magnetic field caused by the movement of the sample[16]. The
magnetic susceptibility, χ, is obtained by normalising for the number of moles of sample
present and the applied field B.
The taking of measurements for the dielectric constant was by a far simpler method.
A thin platelet of sample was spluttered with gold on the top and bottom and painted
with silver dag to make a good electrical contact. This was attached to a probe and
placed in a cryomagnet, which in this case was the Quantum Design PPMS (Physical
Properties Measuring System). An AC current was passed to the contacts on the sample
and the capacitance of the sample was measured. In this situation, the sample acts like a
dielectric in between a parallel plate capacitor. The area, A, and thickness of the sample,
t, are also measured and the dielectric constant, , calculated by this simple formula[17]:
= C
t
A
. (18)
The measurements of the magnetic susceptibility and dielectric constant provide us with
information about any kind of regular magnetic and electric ordering in the crystals. In
particular, we are able to see sudden changes in χ and due to phase changes in the
crystal. If the changes in χ and occur at the same temperature it is highly probable
that the magnetic and electric ordering have become coupled and formed a multiferroic.
The magnetic susceptibility of the x = 0, 0.1 and 0.2 samples was measured between
10 and 300 K, warmed and cooled in a 100 Oe field and cooled in a 5000 Oe, and for
LuMnO3 between 10-400K, warmed and cooled in a 1000 Oe and 20000 Oe field. The
mass of the sample was determined using a balance that gave readings in grammes to
6.d.p and readings were averaged.
The dielectric constant of the x = 0, 0.1 and 0.2 samples was measured between 10 and
300K with a more detailed scan between 10 and 60K, warmed and cooled in 0 field and
cooled in a 90000 Oe field and for LuMnO3 between 10 and 300K warmed and cooled in 0
field, 20000 Oe and 90000 Oe. The thickness and area was measured using a micrometer
screw gauge and averaged over multiple readings.
12

14. 3 Results and Discussions
Early on in the project, it became apparent that unlike doping studies with Yttrium, [4]
and [10], we would not be able to create a wide range of Lutetium doped SmMnO3 despite
them having the same valent electronic configuration and similar crystal ionic radii, 0.85
◦
A
and 0.893
◦
A[18], for Lutetium and Yttrium.
At doping levels above x = 0.2 significant impurity phases of LuMnO3 were seen in
the x-ray spectra and even in the high resolution x-ray diffraction patterns, there were
small amounts of the impurity phase in the x = 0.2 composition. The x = 0.25, 0.3 and
0.4 were all given extra heating to try and force the dopants into the crystal structure,
but this failed and no further experiments were conducted with these compositions.
Figure 6: X-ray diffraction patterns of all of
the samples created in the project. Each line
is offset above the next by 100 counts.
The x = 0.2 sample successfully formed a
multiferroic material with a phase transition at
22 K which appears to couple both the magnetic
and electric ordering of the material. With the
data taken, however, we can determine very little
about the behaviour of this multiferroic. Other
than simply assuming that it behaves similarly
to TbMnO3 or other doped rare-earth mangan-
ites. We can, however, compare the phase transitions and TN to those of other rare-earth
manganites. SmMnO3 has a TN ≈ 60 K, for EuMnO3, TN ≈ 50 K and for TbMnO3,
tN ≈ 40 K[19], the SmMnO3 sample exhibited a magnetic phase transition at ≈ 60 K in
agreement with this result. However, both of the doped samples, x = 0.1 and 0.2 have a
TN ≈ 50 K, where x = 0.1 is just above 50 K and x = 0.2 just below 50 K, suggesting
that their magnetic structure has been shifted towards that of EuMnO3 and TbMnO3.
The dielectric constant and magnetic susceptibility of x = 0.2 also showed very similar
behaviour to Sm0.6Y0.4MnO3 and Eu0.5Y0.5MnO3 in [10] and [4] respectively. This again
suggests that this particular phase has adopted the cycloidal structure of TbMnO3 and
its magnetoelectric properties.
13

15. (a) x = 0.1 (b) x = 0.2, measurements of the were taken at 0 T
Figure 7: The magnetic susceptibility and the dielectric constant from 10-60K of Sm1−xLuxMnO3
The magnetic moment of the Samarium also does not appear to have been suppressed
completely in the x = 0.1 composition, since it is only suppressed in the field cooled
measurement. This is most likely the reason it was unable to form a multiferroic, since
the strong magnetization would have negated any possible bulk polarization. The field
cooled measurement also exhibited signs of spin canting in a small sinusoidal wave pattern
below TN . This suggests that the superexchange interaction may have become much
weaker due to the further deviation of the Mn-O-Mn bond angle from 180◦
and that the
Dzyaloshinsky-Moriya interaction is starting to dominate in the antiferromagnetic phase,
hence creating the canted spins.
Although we were only able to conduct x-ray powder diffraction patterns on our sam-
ples, we were able to see if there had been any kind of structural shift as a result of the
doping and check this against those of other rare-earth manganites.
Table 1: Main Lattice Parameters (
◦
A) and Selected Angles (deg) for Orthorhombic Sm1−xLuxMnO3
and TbMnO3
x = 0 x = 0.1 x = 0.2 TbMnO3
a 5.36219(2) 5.3483(1) 5.3299(1) 5.2949(7)
b 5.8275(2) 5.8363(2) 5.8372(2) 5.8329(7)
c 7.4853(2) 7.4693(2) 7.4475(2) 7.4050(9)
Mn-O1-Mn (x2) 148.8(95) 144.3(8) 146.62(7) 146.5(8)
Mn-O2-Mn (x4) 149.6(1) 149.6(5) 143.6(9) 144.76(6)
Mn-O-Mn 149.1(6) 146.1(6) 145.6(6) 145.9(6)
14

16. The data for the refinement of TbMnO3 was provided by Dan O‘Flynn of The Uni-
versity of Warwick. All of the parameters and their associated errors were given by the
Reitveld refinement in Topas Accademic v4.1. All of the structures resolved were or-
thorhombic with a space group of Pbnm. We can clearly see that coincident with the
changes in the magnetoelectric behaviour of Sm1−xLuxMnO3 is a structural shift and a
reduction in the Mn-O-Mn bond angle towards that of TbMnO3. However, due to the
inherent inability of x-rays to locate smaller atoms, in this case oxygen, accurately, I do
not believe that this data can tell us much more than that there has been a structural
shift towards a structure similar to that of TbMnO3 and that the errors given by Topas
were far more generous than they were in reality.
For the sake of completeness, we also created a small amount of pure LuMnO3 to look
at its magnetoelectric properties over similar temperature ranges as Sm1−xLuxMnO3.
LuMnO3 is known to be a high temperature ferroelectric, with an associated phase tran-
sition at TFE ≈ 900 K[13], which we were unable to look at, and a low temperature
magnetic ordering at TN ≈ 100 K[13] which was measured. A magnetic phase transition
was identified at TN = 90K, see Figure 8, which is in agreement with the published data
in [13]. However, this study only looked at the dielectric constant up to 200 K, above
which we have identified a lambda-type peak at 245 K with no change in the magnetic
susceptibility in this region. Due to the strength of the peak, I do not think that it is
likely to be due to any impurity phases; although I cannot at this time rule this out. With
only this data and no published data on this temperature region of LuMnO3, I currently
unable to draw any conclusions as to the nature of this peak or any phase transition it
may be associated with.
Figure 8: The magnetic susceptibility and the di-
electric constant from 2-300K of LuMnO3
In all cases our measurements of the
magnetic susceptibility of Sm1−xLuxMnO3
and LuMnO3 extended past their Cur-
rie temperatures into their paramagnetic
phases. This data was plotted as 1
/χ
against T and fitted to the Curie-Weiss re-
lation (see Equation 4). The gradient of
this fit gave a value for 1
/C which was used
in equation 11 to calculate p2
. This was
compared to theoretical values of p in [6]
and [7], which were calculated using equation 12. It must also be noted that the value of
15

17. p2
measured is actually equivalent to p2
Sm3+ + p2
Mn3+ .
Table 2: The theoretical and experimental values of p for Sm3+
and Mn3+
from [6], the theoretical
value of p for x=0 was calculated from these and all other other experimental values were measured in
the above experiments.
Ion/Compound p(calc) p(exp)
Sm3+
[6] 0.84 1.5
Mn3+
[6] 4.90 4.9
LuMnO3 - 4.75
x=0 4.97 5.08
x=0.1 - 5.14
x=0.2 - 5.16
The discrepancy between the experimental and calculated values of p for the x=0
sample is most likely due to the presence of other manganese oxides with Mn2+ ions
which have a higher effective moment, p = 5.92[6]. Since our polycrystalline samples
were not grown in a highly oxygenated environment, a small amount of these other oxides
would be expected to form and their concentration would be too low to be seen by x-ray
powder diffraction.
4 Conclusions
In this project we have successfully synthesised a new multiferroic material based on the
doping of a rare earth manganite. Furthermore, we have shown that it has a coincident,
and almost certainly coupled, phase transition in its magnetic and electric behaviour
at 22 K. We have also shown that this material behaves as expected above TC in its
paramagnetic phase and has an effective moment reasonably close to that of its undoped
form. Our structural study has also shown that the doping induced a structural distortion
in the crystal structure as expected from previous studies of doping rare earth manganites.
However, the x-ray scan was inherently unable to resolve that structure to a high degree.
To fully understand this new multiferroic we will need to conduct further studies on its
magnetoelectric behaviour, namely pyroelectric measurements and if it is possible to grow
a single crystal, measurements of the magnetic susceptibility and dielectric constant along
the crystallographic axes to determine the behavioural dependence upon crystal orienta-
tion. To investigate the nature of the phase transition into a multiferroic state, a study of
the specific heat capacity in the region of the transition would have to be conducted and
16

18. possibly an x-ray or neutron diffraction pattern as the material is being cooled through
the transition. Finally to accurately resolve the structure of the multiferroic phase, a
neutron study would have to be conducted on a single crystal of a non-neutron absorbing
isotope of samarium to determine if it has adopted the cycloidally ordered structure of
TbMnO3.
The high temperature ferroelectric, LuMnO3, was also investigated and a lambda type
peak was seen at 245 K, which has not been reported in any published data that I have
found to date. To fully determine the nature of this peak, we would firstly have to create
a new sample to ensure that this was not simply the result of an impurity. If it is still
present, then the specific heat should be measured around this peak to try and identify
any phase transitions linked to this. If any interesting behaviour is revealed, a neutron or
x-ray study, cooling through the transition, to determine the structural changes associated
with this peak should be conducted.
Acknowledgements
I would like to Dr.Geetha Balakrishnan for the idea of carrying out this doping study
and for continuously guiding us through this project; Dan O’Flynn for showing us how
to use the SQUID and PPMS and for putting up with a pair of undergrads eating up
his lab time; Dr Martin Lees for reminding us that we actually need to have a field to
take measurements in a SQUID; Dr Dave Walker for showing us how to use the Bruker
D5005 and TOPAS and finally the group’s technician, Tom Orton, for keeping everything
running and fixing everything that broke so we could actually do our experiments.
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