The University of Warwick

Final year project

Multiferroic Manganites

Author:

Gregory Daly

Supervisor:

Dr.Geetha Balakrishnan

November 18, 2014

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

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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 = TcC

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 Neel 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 Neel

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 Neel 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].

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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 possiblespin 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)Hψa(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 H 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

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model,

H = −∑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 amagnetic oxide. The arrows showthe spins of the four electrons andhow they are distributed over thetransition metal (M) and oxygen(O) atoms. M is assumed to havea single unpaired electron, makingit 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].

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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,

HDM = D.S1 × S2 (8)

Figure 3: Double exchange mech-anism gives ferromagnetic couplingbetween Mn3+ and Mn4+ ions par-ticipating in electron transfer. Thesingle-centre exchange interactionfavours hopping if (a) neighbouringions are ferromagnetically alignedand not if (b) neighbouring ionsare 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 Lande equation[6],

g = 1 +J(J + 1) + S(S + 1)− L(L+ 1)

2J(J + 1). (10)

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From this it can be derived that,

M

B∼=NAJ(J + 1)g2µ2

B

3kBT=NAp

2µ2B

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)]12 . (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

2Mω2Q2 (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

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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

2Mω2Q2 (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 (inblack) is at the center of an octa-hedron of oxygen anions (in gray).The large Re cations (white) oc-cupy the unit cell corners. Takenfrom [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, ε = (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.

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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 afunction of Mn-O-Mn bond angle . Open and closedtriangles denote the Neel and lock-in transition tem-peratures, respectively. Left upper inset: Schematicview of the reciprocal space at a phase with modu-lated magnetic and crystallographic structure. Openand 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 schematicillustrations 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 thepresent 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

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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-

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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.

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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

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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, ε, calculated by this simple formula[17]:

ε = Ct

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 ε due to phase changes in the

crystal. If the changes in χ and ε 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.

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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 ofthe samples created in the project. Each lineis 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.

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(a) x = 0.1 (b) x = 0.2, measurements of the ε 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

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

p2 measured is actually equivalent to p2Sm3+ + p2

Mn3+.

Table 2: The theoretical and experimental values of p for Sm3+ and Mn3+ from [6], the theoreticalvalue of p for x=0 was calculated from these and all other other experimental values were measured inthe above experiments.

Ion/Compound p(calc) p(exp)

Sm3+[6] 0.84 1.5Mn3+[6] 4.90 4.9LuMnO3 - 4.75x=0 4.97 5.08x=0.1 - 5.14x=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

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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