1

Magnetic Phase Transition and Spin Wave Excitations in the Colossal 

Magnetoresistive Manganites: An Experiment Using the BT7 Triple-Axis 

Spectrometer

Yang Zhao, Zhijun Xu, William Ratcliff, and Jeffrey Lynn

NIST Center for Neutron Research

OBJECTIVES: The summer school participants will use elastic scattering to measure the ferromagnetic order 

parameter and transition temperature, and inelastic neutron scattering measurements to study the spin wave 

excitations in the perovskite La0.7Sr0.3MnO3. This system will allow us to demonstrate the versatility and power 

of triple-axis spectrometry in studying the static and dynamic properties of condensed matter systems.

I. Introduction to the system

The improved modern-day material synthesis 

techniques for oxide materials were developed in part 

in the quest to fabricate high temperature 

superconductors, and has enabled researchers to revisit 

other systems such as the LaMnO3 class of materials. 

The crystal structure of these materials is based on the 

cubic perovskite system, where the Mn ion is 

surrounded by six oxygen ion with octahedral 

symmetry, with the La ions on a simple cubic lattice 

as shown in Fig. 1. LaMnO3 is an antiferromagnetic 

insulator (TN=140 K), but the properties can be 

changed by substituting 2+ cations such as Ca, Sr, and 

Ba for La3+. Doping La1-xAxMnO3 in the range 

0.2<x<0.5 produces an isotropic, metallic ferromagnet 

at low temperature. The magnetic ordering (Curie) 

temperature is accompanied by a metal-insulator 

transition, with can then be controlled by the

application of a magnetic field. The effect on the 

resistivity can be enormous—several orders-ofmagnitude—which would be ideal for device 

applications such as for sensors and for read/write 

heads in magnetic storage media, where information is 

stored in the form of bits which are read by magnetic 

read heads. These magnetic read/write heads work by 

exhibiting a small change in their electrical resistivity 

as they pass over a magnetic bit. This change in the 

resistivity when the magnetic field changes is called 

magnetoresistance (MR) and materials evincing it are 

called magnetoresistive. Most materials have 

negligible MR, while the magnetoresistance is 

typically only a few percent in select metals and 

semiconductors. One favorable material is Permalloy, 

an alloy of iron and nickel, and this material was used 

for many years as read/write heads in disk media. The 

current generation of read/write heads in hard drives is

based on multilayer thin film technology, which 

amplifies the magnetoresistive effect (≈20 %) and is 

termed giant magnetoresistance (GMR). The 

manganites, on the other hand, possess colossal 

magnetoresistance (CMR), as compared to the much 

smaller MR or GMR observed previously.

The basic physics behind this colossal change in

resistivity is this insulator-to-metal transition, which 

often is first-order in nature and results in electronic 

phase separation (in which two electronic phases are 

spatially distinct) between a ferromagnetic metallic 

and a paramagnetic insulating states. The particular 

material that we will examine is La0.7Sr0.3MnO3, where 

doped holes induce ferromagnetism and metallic 

conductivity. Let us first briefly discuss how doping 

the system leads to metallic conductivity [1].

Fig. 1. A unit cell of a cubic perovskite ABO3 structure The 

yellow, red, and blue spheres are La, Mn, and O sites, 

respectively.
2

Fig. 2. (a) Cubic and tetragonal crystal field splitting of 3d 

orbitals in Mn3+. (b) A simple representation of 

ferromagnetic coupling via double exchange.

In a crystal, the wave functions of electrons on 

neighboring atoms mix and their energy levels expand 

into bands of allowed energies. Because electrons 

follow the Pauli Exclusion principle, they cannot 

occupy the same states simultaneously. Thus, the 

electrons fill the available states up to an energy 

known as the Fermi energy, EF. In metals, electrons 

near EF are still free to move because there are 

unoccupied states available in the band. An insulator 

(like LaMnO3) is the case when all the available states 

are filled with electrons.

The manganites of interest here have crystal 

structures derived from cubic perovskite lattices (see 

Fig. 1), in which each Mn cation is surrounded by six 

oxygen ions which form an octahedron around it. For 

La3+Mn3+O-2

3, the Mn3+ ion has four d-electrons. In 

this cubic crystal environment, the energy levels of the 

d-electrons split into three degenerate orbitals

(designated t2g) and two degenerate eg orbitals, as 

shown in Fig. 2(a). Strong Hund's rule coupling 

(related to the minimization of Coulomb repulsion of 

the electrons on a given atom, while satisfying the 

Pauli exclusion principle) results in the spins of the 3d 

electrons needing to be aligned. As a result, three 

electrons with parallel spins occupy the lowest lying 

t2g orbital, and form a localized magnetic moment with 

S=3/2. The fourth electron occupies the doubly 

degenerate eg level. This electron must also have its 

spin aligned with the spins in the t2g orbitals because 

of the same strong Hund’s rule coupling. There are 

still six d orbitals that are unoccupied—another 3 t2g

orbitals and two eg orbitals where the spins would be

in the reverse direction, but these are very high in 

energy (compared to the thermal energies kT of 

interest) because of the Hund’s rule coupling and are 

out of the picture.

Note that the occupied eg is doubly degenerate, 

which makes Mn3+ a Jahn-Teller (JT) active ion. That 

is, the system may be able to lower its energy by 

allowing a distortion of the oxygen environment. Such 

a distortion breaks the degeneracy of the eg orbitals, 

with one orbital becoming lower in energy and the 

other higher than in the degenerate case (Fig. 2(a)). 

Since there is only one electron occupying the eg level, 

it can always lower its energy (at the cost of the elastic 

energy of the distortion). Therefore all these Mn3+

oxides exhibit small distortions away from the ideal 

cubic structure, but are still insulating.

As we replace La3+ cations with Sr2+ cations, we 

change the Mn3+ ions into Mn4+ ions, where the eg

orbital is unoccupied. This allows the eg electrons the 

possibility to hop to an adjacent unoccupied site. As 

the carrier concentration is varied, the system's 

physical properties change as shown in Fig. 3 [2]. The 

ferromagnetic order and metallic conductivity first 

show up at x≈0.1 and at x≈0.15, respectively. When 

the Sr concentration reaches x≈0.3, the ferromagnetic 

transition temperature, TC, becomes maximum and the 

system is a good metal.

Now, we've suggested how the system becomes 

metallic with doping, but the question remains, why 

does it become ferromagnetic (that is, why do the spins 

on different Mn sites spontaneously align in the same 

direction?). While there are various causes of 

magnetism in materials, the dominant factor for the 

manganites is known as double exchange. Here, there

is a “virtual process” in which the eg electrons are 

allowed to hop from site to site through an oxygen 

orbital. If you imagine that the eg electron is hoping 

from an occupied Mn3+ site to an unoccupied

Fig. 3. (a) Resistivity of La1-xSrxMnO3 as a function of 

temperature. The arrows indicate critical temperatures for 

magnetic transitions. (b) The phase diagram of the La1-

xSrxMnO3 system. The abbreviations F, P, CN, M, and I 

stand for ferromagnetic, paramagnetic, spin-canted 

antiferromagnetic, metallic and insulating, respectively [2].
3

Mn4+ site, and back again, the probability of hoping 

will depend on the relative orientation of spins on the 

two sites (see Fig. 2(b)). In fact, because of the strong 

Hund's rule coupling, as the spin moves from the Mn3+

site to the Mn4+ site, it must be aligned with the t2g

“core” spins on both sites. Therefore ferromagnetism 

evolves from the system by maximizing the 

probability of hopping. This is the physical basis 

behind the double-exchange model for the manganites.

II. THE BT-7 TRIPLE-AXIS SPECTROMETER

The basics of neutron scattering and the flexibility 

of triple-axis spectrometer is covered in a separate 

experiment handout, so here we only give a brief 

overview of the BT-7 triple-axis spectrometer [3]. The 

instrument (Fig. 4) has the choice of either a copper 

[Cu(220)] or pyrolytic graphite [PG(002)] doublyfocusing monochromator, providing a continuous 

incident neutron energy range from 5 to 500 meV. The 

400 cm2 reflecting area for each monochromator 

yields as much as an order-of-magnitude gain of 

neutrons onto the sample over earlier instruments, 

with available fluxes well into the 108 n/cm2/s range. 

Generally speaking, neutron scatFig. 4 The BT-7 triple-axis spectrometer with the polarized 

beam system installed.

tering is a flux-limited technique, and every 

experimenter wants higher count rates and better 

resolution. Unfortunately these are contradictory 

requirements, and the experimenter must carefully 

balance these to successfully measure the quantity of 

interest with sufficient resolution in the beam time 

available. It is therefore highly desirable to have a

wide range of choices of instrumental parameters in 

order to optimize the resolution and intensity of the 

instrument.

The sample stage of the instrument includes two 

coaxial rotary tables, one for sample rotation and one 

for the independent rotation of magnetic field coils, 

and a computer controlled sample goniometer and 

elevator. Polarized He3 cells are available to provide 

neutron polarization capability with either 

monochromator and the standard PG analyzer system.

The BT-7 spectrometer is designed to be used with 

interchangeable customized analyzer/detection 

systems (Fig. 4). The analyzer system currently 

available has various detectors and related collimators 

housed in a shield that is supported on air pads, as 

shown in Fig. 5. The analyzer system has a multi-strip 

PG(002) analyzer array that can be used in a 

horizontally focused mode, or in a flat configuration 

either with a linear position-sensitive detector (PSD) 

or with conventional Söller collimators. All options 

can be selected and interchanged through the 

instrument control program (ICE) without any 

mechanical changes or user intervention. A separate 

diffraction detector is provided in front of the analyzer 

for Bragg peak 

Fig. 5. Schematic of the BT-7 detector/analyzer system.

Question: (1) Based on the picture described in Fig.3, 

explain how magnetic field reduces the resistivity in CMR

materials. (2) In Fig. 3(b), what would you suggest is the 

hole doping concentration that is potentially useful for a 

CMR read/write head application, and why?
4

measurements, and a series of 11 detectors imbedded 

in the shielding behind the analyzer continuously 

monitor the neutron flux entering the analyzer system. 

These detectors can also be used for measurements of 

the instantaneous correlation function, for example, or 

with a radial collimator to determine a diffraction 

pattern over a limited angular range. The PSD can also 

be used with a radial collimator to determine the 

diffraction pattern or instantaneous correlation 

function, with higher resolution.

General Specifications for BT-7: 

• PG filter in reactor beam, remotely insertable 

and tunable.

• Double focusing PG(002) (d=3.35416 Å) or 

Cu(220) (d=1.273 Å) monochromator crystals

• Flat PG or horizontally focused PG (13 blades, 2 

cm wide each)

• Built-in guide fields, and insertable spin rotators, 

He3 polarizers

• Monochromator take-off angles 2θ from 16 to 

75 degrees

• Variable incident energy from 5.0 to 500 meV

• Scattering angles from 0 to 120 degrees

• Söller slit collimation of 10′, 25′, 50′, 80′and 

open at most positions.

• Radial collimators are available before and after 

the analyzer.

• Computer controlled vertical or horizontal guide 

field at sample position.

III. EXPERIMENT AND ANALYSIS

Simple ferromagnetic spin-waves

Perhaps one of the simplest microscopic models of 

magnetism starts from the Heisenberg Hamiltonian. It 

is generally applicable to systems in which the spins 

are localized on atomic sites, and where the spin 

interactions are mediated by direct overlap of their

atomic wave-functions, or through intermediaries such 

as oxygen (superexchange) or through conduction 

electrons (indirect, or Ruderman-Kittel-KosuyaYosida (RKKY) exchange). The resulting magnetism 

originates from a combination of the Coulomb 

repulsion and the Pauli exclusion principle. In this 

model, the interaction energy between two 

neighboring spins is simply 

S1 S2 E = −J ⋅ (1)

where J is the exchange constant representing the 

strength of magnetic exchange, and Si is a vector 

operator of the ith spin. If J is positive, then a lower 

energy occurs when the moments are parallel, while if 

J is negative then the spins will align antiparallel to 

lower their energies. To get the total energy of the 

system we simply sum over all the spins in the system:

Si Sj

i j

J i j

H = − ∑ ⋅ , , 2

1 (2)

where the sum is over all spins in the system. 

Typically the exchange for nearest-neighbors spins 

dominates the energetics and the ground state is either 

a ferromagnet (all spins parallel) or an 

antiferromagnetic (nearest neighbor spins 

antiparallel). More complicated spin arrangements 

(See Fig. 6(a)) certainly can and do occur in many 

systems. Typically the exchange energies are taken as 

fitting parameters to be determined experimentally, 

and due to its simplicity this model is often used as a 

starting point to fit data regardless of the underlying 

physics of the magnetism. 

But given the ground state of the system, how do 

we make a magnetic excitation? One of the simplest 

excitations we could imagine is to simply flip the 

direction of one of the spins. However, the energy cost 

of this would be very large (12J for a cubic lattice), in 

fact, this is the highest energy excitation you can 

make. A much lower energy excitation can be 

achieved if this single spin reversal is shared among 

many spins. Classically, if we allow the spins to 

precess about their axes, then a spin-wave can be 

thought of as a constant phase difference between the 

precession rates of neighboring spins (see Fig. 6(b)).

Question: (1) What are the advantages of using a

position-sensitive detector? (2) What is the best 

instrumental configuration if the spin-wave 

excitations above 40 meV were to be measured on 

BT-7?

Question: where did the factor of 1⁄2 come from in 

Eq. (2)?
5

Fig. 6(a) Examples of simple magnetic ordering patterns. 

(b) Classical representation (side and top views) of spin 

wave excitation in a one-dimensional ferromagnet.

The measured spin wave dispersion relation at low 

temperatures for La0.85Sr0.15MnO3 [4], which is similar 

to the sample we are going to study [5], is shown in 

Fig. 7. We can see that the energy of the spin waves 

at small reduced wave vector q (long spin wave 

wavelength) is very small, while at the zone boundary, 

the excitation energy rises to a relatively high energy 

of 55 meV (short wavelength excitations mean that the 

excitation is shared by fewer spins and that 

neighboring spins are out of phase to a much greater 

extent, thus requiring more energy to excite). 

Assuming nearest-neighbor exchange only, the 

solution to the spin wave excitation energies for our 

simple Hamiltonian gives the following spin wave 

dispersion relation:





 



 = 2 8 sin2 qa E SJ SW (3)

where a is the lattice parameter (nearest-neighbor 

distance). Because of time restrictions, we will be 

focusing on the small-q spin wave excitations in this 

experiment, where we may expand the sine function in 

the dispersion relation to obtain the approximate 

expression 

2 2 ESW = 2JSa q . (4)

Note that we have E → 0 as q → 0 , which is the 

definition of an isotropic ferromagnet; with 

q = 2π λ , q=0 corresponds to infinite wavelength, 

i.e. a uniform rotation of the entire spin system, which 

for an isotropic system costs no energy by definition. 

More generally, we should also include the possibility 

of magnetic anisotropy in the system, because in real 

spin systems the moments prefer to point along one 

particular crystallographic direction. This is 

represented by the gap parameter, ∆. This particular 

direction is called the magnetic easy axis, and 

represents the energy required to rotate the spins away 

from this easy direction. Then for a completely 

isotropic system, ∆≡0. A "soft" ferromagnet is one 

where ∆ is small, which judging from Fig. 7 is the case 

for the present system. For a “hard” or “permanent”

magnet, such as on your refrigerator, this costs a lot of 

energy, and ∆ will be large.

Fig. 7. Measured spin wave dispersion relations in 

La0.85Sr0.15MnO3. The wave vectors are based on the 

orthorhombic representation [4].

Temperature Dependent Properties

For a ferromagnet, the ordered magnetic moment 

on each atomic site (or equivalently, the bulk 

magnetization) is a maximum at low T, in the ground 

state, while it vanishes (by definition) at the ordering 

temperature, TC. How do we get from the state with 

maximum magnetization to one where it vanishes? By 

thermally exciting spin waves—each spin wave we 

create lowers the magnetization by 1 μB. As we 

approach the ordering temperature, the magnetization 

is expected to follow a power law:

Question: What kind of magnet is your 

refrigerator, hard, soft, or non-magnetic?
6

β















 − ∝

C

C

T

T T

M (T) (5)

where the critical exponent β≈0.3 for this type of 

magnet.

The magnetization, or sublattice magnetization for 

an antiferromagnet, can be directly determined in a 

neutron measurement. The integrated intensity for a 

magnetic Bragg reflection is given (for a simple 

collinear magnetic structure) by [6] 

( )[ ] 2

2 ^ ^ 24 2 0.54 10 1 B M FM I CA cm 



 



 = × − ⋅ − θ τ

(6)

where the neutron-electron coupling constant is 

0.54×10-24cm2

, 

^

τ and ^

M are unit vectors in the 

direction of the reciprocal lattice vector τ and the spin 

direction, M, respectively, and the orientation factor 

<...> must be evaluated for all possible domains. C is 

an instrumental constant which includes the resolution 

of the measurement, and A(θ) is an angular factor 

which depends on the method of measurement. The 

magnetic structure factor F, is given by

( ) j j W i

j

j

z

j MF f e e τ r τ − ⋅ = ∑ μ (7)

where <...> is the thermal average of the aligned 

magnetic moment of the magnetic ion at the jth site at 

position rj, Wj is the Debye Waller factor for the jth

atom, f(τ) is the magnetic form factor (Fourier 

transform of the magnetization density), and the sum 

extends over all magnetic atoms in the unit cell. We 

see from these expressions that neutrons are sensitive 

to the location of magnetic atoms and the spatial 

distribution of their magnetic electrons; the 

temperature, field,... dependence of the thermal 

average of the ordered moment, which is directly 

related to the order parameter for the magnetic phase. 

An example of the magnetic scattering is given in Fig. 

8 [7]. Note that the magnetic intensity is proportional 

to the square of the ordered moment.

We should also expect the spin wave spectrum to 

change with temperature. Mean field theory simply

Fig. 8. Temperature dependence of the integrated intensity 

of the ferromagnetic (1 0 0) peak for La0.8Ca0.2MnO3 [7].

replaces S with the thermal average value, which 

(within a constant) is the magnetization. From Eq. (3) 

we can then expect the spin waves to lower their 

energies, or renormalize, with T. Generally, we can 

write the spin wave dispersion relation in the small q 

regime as a Taylor series in q:

( ) ( ) ( ) ... 2 4 Espinwaves = ∆ T + D T q + E T q + (8)

where D is the spin-wave “stiffness” parameter, and 

the rest of the terms are higher order terms in a Taylor 

expansion. The quantitative value of the stiffness 

parameter D depends on the details of the interactions 

and the nature of the magnetism, such as whether the 

magnetic electrons are localized or itinerant, or the 

structure is amorphous or crystalline, but the general 

from of the spin wave dispersion relation is the same 

for all isotropic ferromagnets. As T→TC, D(T) 

follows M(T) in mean field theory, while more 

generally in the critical regime just below magnetic 

ordering temperature TC, D(T) should follow a power 

law given by

ν ′−β















 − ∝

C

C

T

T T D(T) (9)

where ν′ (≈2/3) is the critical exponent for the 

correlation length below TC. Fig. 9 shows examples 

of spin waves measurements, and Fig. 10 shows the 

renormalization of the spin waves energies with 

temperature.

Question: What do you mean, “this type of 

magnet”? What controls the value of β?
7

Fig. 9. Constant-Q scans revealing spin wave excitations 

for La0.7Sr0.3MnO3 (a) at T = 300 K, for several wave 

vectors, and (b) Q = (0 0 0.965), for several temperatures 

[5].

At elevated temperatures, there will also be many 

spin waves in the system, and collisions between the 

spin waves will result in decays of normal modes and

consequently finite intrinsic lifetimes for the spin 

waves. The intrinsic linewidths of the spin wave 

excitations in the long wavelength regime are expected 

to follow:

2

4 ( , ) ln 





























 Γ ∝

ESW

kT

q T q T . (10)

Fig. 11 shows an example of spin wave linewidth 

measurements. Finally, we can determine the number 

of spin waves that are thermally populated at each 

energy, which is directly related to the observed 

intensity of the spin waves in an inelastic neutron 

scattering experiment. These are boson excitations 

(bosons are particles in which there are no restrictions 

on the number of particles existing in the same state), 

and should obey the Bose-Einstein population factor:

1

1 ( ) / − = SW ESW kT

e

n E . (11)

A neutron can annihilate a spin wave excitation in the 

sample and gain energy; the probability for this 

process to occur is directly proportional to the number 

of spin waves n(E) at the spin wave energy ESW. A 

neutron can also create a spin wave in the system, 

while losing energy. The probability for this process 

is proportional to 1+n(E), where the 1 comes

Fig. 10. (a) Low energy spin wave dispersion measured at 

two different temperatures and (b) the temperature 

dependence of the spin wave stiffness constant of 

La0.85Sr0.15MnO3 [4].

from the fact that it is always possible to create a spin 

wave excitation, even at T = 0. This is something that 

we should also be able to extract from the 

experimental data.

Experimental Planning and Setup

When planning neutron scattering experiments, it 

is important to have as much understanding as possible 

of the basic properties of the material. For instance, 

understanding of the crystallographic information, 

such as lattice parameters, is imperative. In the case 

of single crystal samples, it is also important to have 

some idea about the direction of principal crystal axes. 

For an effective investigation, 
8

Fig. 11. Intrinsic spin wave linewidths. (a) At low 

temperatures there should be no intrinsic linewidth in the 

localized model, while the very large linewidths indicate 

magnon—electron damping in this metallic system. (b) At 

small wave vectors the linewidths follow the expected 

theoretical form (Eq. 10), but at larger wave vectors there 

are intrinsic linewidths that don’t have a thermal origin [4].

measurements of bulk properties such as the magnetic 

susceptibility, heat capacity and resistivity, can serve 

as an invaluable guide. All NCNR facility users 

should avail themselves of any existing data, be it their 

own, or published elsewhere, that could help them 

make more efficient use of their beam time. 

Crystallographically, La0.7Sr0.3MnO3 belongs to a 

space group R3c with the lattice parameters 

a=b=5.5084Å, c=13.3717Å, α=β=90°, and γ =120°. 

This hexagonal geometry is equivalent to a 

rhombohedral one with a=b=c=3.8835 Å and 

α=β=γ=90.344°. Since this is close to cubic 

symmetry, for convenience we will carry out the 

measurements based on the cubic notation.

Fig. 3(b) shows the ferromagnetic transition 

temperatures, TC, of La1-xSrxMnO3 as a function of x. 

La0.7Sr0.3MnO3 has TC ≈ 350 K [5]. Therefore, we 

need sample environment equipment that can control 

higher than room temperature in order to study the 

ferromagnetic transition.

The primary goal of this experiment is to measure 

the spin excitation spectrum in the ferromagnetically 

ordered phase and understand its temperaturedependent behavior. A ≈4 gram single crystal sample 

of La0.7Sr0.3MnO3 has been sealed inside an aluminum 

container. Aluminum is among the most commonly 

used materials for sample containers because it is 

relatively transparent to neutrons, easy to machine, 

and is a good thermal conductor. The container has 

been mounted inside a He closed-cycle 

refrigerator/furnace that can be controlled between 30 

- 600 K, and placed on top of the goniometer (or 

sample) table. The measurement will be done in the 

temperature range between 30 and 400 K.

Our measurements will proceed as following. 

(Some data sets may be taken in advance and 

distributed.) (1) First, we will measure the integrated 

intensity of (1 0 0) Bragg peak as a function of 

temperature in the range 250-400 K. To properly 

obtain integrated intensities, one needs to perform 

both transverse (θ) and longitudinal (θ:2θ) scans. 

From this, we will be able to extract TC of the sample. 

(2) Second, we will measure the spin wave spectrum 

up to E ≈ 10 meV by scanning the incident energy at 

several Q points. From the measured data we can 

obtain the spin wave dispersion, which can be fit to 

extract the spin wave stiffness parameter, D(T). The 

spin wave data may be taken at a few selected 

temperatures, and the collection of data can be used to 

show how D changes as a function of temperature. 

Question: (1) La0.7Sr0.3MnO3 orders 

ferromagnetically below TC = 350 K. (1) Where in 

reciprocal space do we expect to find the magnetic 

Bragg peaks? (2) Where will the low energy spin 

wave excitations be located? (3) How will the spin 

dynamics differ between above and below TC?
9

Intensity of the quasielastic peak for La0.85Sr0.15MnO3 at (0 

0 1.15) as a function of temperature [4].

(3) Third, we will measure the quasielastic intensity at 

a certain Q close to (1 0 0) over a temperature range 

going through TC, such as is shown in Fig. 12. The 

measurement will also be done by scanning the 

incident energy. By analyzing the integrated 

intensities and the linewidths of the quasielastic peaks 

as a function of temperature, we will be able to gain 

insights into the spin dynamics in the vicinity of the 

transition.

Data and Analysis

Fig. 8 shows the temperature dependence of the 

integrated intensity of (1 0 0) Bragg peak observed 

from La0.8Ca0.2MnO3 [7]. There is an intensity 

increase observed below TC = 181 K, which follows a 

power law behavior. This intensity increase comes 

from ferromagnetic order on Mn sites. The sample we 

are going to study, La0.7Sr0.3MnO3, will show TC at a 

different temperature, but the data should look similar. 

Knowing that spin waves are fluctuations of ordered 

spins around the average moment, one should expect 

to observe the low energy spin excitation spectrum in 

the vicinity of this reflection. The (1 0 0) position is 

particularly advantageous, since it is the smallest wave 

vector where ferromagnetic intensity is observed. 

This is because the magnetic scattering intensity 

generally decreases at higher momentum transfer due 

to spatial distribution of unpaired electron density, as 

indicated in Eq. (7).

The energy scan data we are going to obtain will 

be similar to what is shown in Fig. 9. Constant-Q 

scans typically show as many as three peaks: a central 

(quasi)elastic peak and an inelastic spin wave peak on 

each side of positive (neutron energy loss—spin wave 

creation) and negative (neutron energy gain—spin 

wave annihilation) energy transfer. Fig. 9(a) shows 

that the spin wave energy increases as we move away 

from the ferromagnetic (0 0 1) peak. The temperature 

dependence of D is demonstrated by the data shown in 

Fig. 9(b). Although the lineshape of triple-axis data is 

a complex function of various parameters, one can 

approximately extract the energy values by fitting with 

Gaussian (if the intrinsic linewidth is small) or 

Lorentzian (if the intrinsic spin wave linewidth is 

large) functions. A series of energy values obtained at 

various momentum transfers can be used to obtain the 

dispersion relation. The dispersion relation in an 

isotropic ferromagnet can be conveniently expressed 

by Eqs. (3,4), where the temperature dependent spin 

stiffness constant is denoted as D(T). Fig. 10(a) shows 

results obtained from La0.85Sr0.15MnO3 at two different 

temperatures, and the obtained D(T) is plotted in Fig. 

10(b). The quantitative values of the stiffness constant 

D depend on the details of the interactions and the 

nature of the magnetism, but the general form of the 

spin wave dispersion relation is the same for all 

Heisenberg ferromagnets.

Finally, the integrated intensities of the 

quasielastic central peaks are obtained and the result 

will be similar to what is shown in Fig. 12. These data 

were obtained slightly away from the ferromagnetic 

zone center (q=0), since otherwise the counts will be 

swamped by the intense nuclear and 

Question: (1) A θ scan may show multiple peaks 

instead of a single Gaussian.

What could be the reason if it does? (2) Although 

it is not the case for the (1 0 0) peak in 

La0.7Sr0.3MnO3, what would it mean if a θ:2θ

scan shows multiple peaks?

Question: Why does the ferromagnetic peak 

position coincide with the nuclear peak, say, at (1 

0 0)? How about antiferromagnets?
10

Fig. 13. An energy scan through the spin wave excitations 

in La0.7Sr0.3MnO3 using polarized neutron incident on the 

sample, and analyzing the polarization state of the scattered 

neutrons. Spin wave scattering can reverse, or “flip” the 

neutron spin, while spin diffusion may not. The data here 

were taken for both spin-flip and non-spin-flip channels, 

and the difference in intensities shows that the inelastic 

signal is due to the expected spin wave scattering, while the 

quasielastic peaks in the non-spin-flip scattering is due to 

spin diffusion, while the elastic (resolution-limited) peak is 

from magnetic clusters (polarons [8-11]) and nuclear 

scattering. 

magnetic Bragg scattering. In the paramagnetic phase 

the central peak slowly gains intensity as we lower the 

temperature and approach TC, and quickly 

drops in intensity below TC. The intensity above TC

comes from paramagnetic spin fluctuations, while that 

below TC it is mostly from spin waves, which quickly 

move to higher energies and out of the range of these 

quasielastic measurements. The intrinsic linewidths

(Fig. 11), if available, provide a determination of the 

lifetimes of the magnetic excitations.

Polarized Neutron Scattering

Finally, we remark about the use of polarized 

neutrons. We have previously learned that neutrons 

interact either with nuclei or with unpaired electrons. 

While it is useful to have more than one type of 

neutron-sample interaction, it can also be a source of 

confusion. Therefore, it becomes an important issue 

how to discriminate magnetic scattering from nuclear 

scattering. There are several experimental clues to 

identify the origin of the scattering. Magnetic 

scattering follows a magnetic form factor [Eq. (7)], so 

the intensity decreases with increasing Q, while 

phonon scattering generally increases as Q2

. The 

temperature dependence also can identify whether the 

scattering is spin wave (qualitatively changing 

character above the ordering temperature) or phonon. 

If these trends are not definitive, however, then the 

most powerful and unambiguous method of neutron 

polarization analysis can be employed. This takes 

advantage of the fact that a neutron can reverse its spin 

direction when the origin of the scattering is magnetic 

(magnetic Bragg peaks, spin waves, critical scattering, 

etc.), while the scattering is always non-spin-flip for 

coherent nuclear scattering (structural Bragg peaks, 

phonons, etc). Since the neutron polarization analysis 

involves many experimental complexities and requires 

multiple measurements that are time consuming, we 

will not perform this during the summer school. 

Nevertheless, the data shown in Fig. 13, which were 

previously taken with this technique, powerfully 

confirm that the scattering we observe in 

La0.7Sr0.3MnO3 is truly magnetic in nature. The 

present manganite class of materials continues to be 

under active investigation [12].

IV. Summary

Neutron scattering can be used to make a complete 

determination of the magnetic properties of a system. 

In order of the complexity of the measurement that 

needs to be carried out, the magnetic order parameter 

is typically the easiest quantity to measure, since the 

scattering is strong and localized at a point in 

reciprocal space. The magnetic structure and spin 

direction(s) can be determined by measuring a series 

of magnetic Bragg peaks, and the magnetic form 

factor—Fourier transform of the magnetization 

density—can be determined with more effort. 

Inelastic scattering, on the other hand, is spread 

throughout the (three dimensional) Brillouin zone, and 
11

is thus much weaker in any particular measurement 

and requires larger samples and considerably more 

effort. However, it leads to the determination of the 

fundamental exchange interactions of the systems. 

Further effort still is needed to determine spin wave 

linewidths, critical scattering and exponents, and the 

general nature of paramagnetic fluctuations. But 

neutron scattering has the capability of making a 

complete determination of the nature and origin of the 

magnetism of any class of materials. The present 

workshop has focused on this magnetic system, but 

neutron scattering can be employed equally well in the 

investigation of crystal structures and lattice 

dynamics. 

V. References

[1] For reviews, see for example, N. Nagaosa, and Y. 

Tokura, Science 288, 462 (2000); E. Dagotto, 

Science 309, 257 (2005); Nanoscale Phase 

Separation and Colossal Magnetoresistance,

Springer, Berlin, (2002).

[2] Insulator-metal transition and giant 

magnetoresistance in La1-xSrxMnO3, A. 

Urushibara, Y. Moritomo, T. Arima, A. 

Asamitsu, G. Kido, and Y. Tokura, Phys. Rev. 

B51, 14103 (1995).

[3] Double Focusing Thermal Triple Axis 

Spectrometer at the NCNR, J. W. Lynn, Y. Chen, 

S. Chang, Y. Zhao, S. Chi, W. Ratcliff, II, B. G. 

Ueland, and R. W. Erwin, Journal of Research of 

NIST 117, 61-79 (2012).

[4] Structure and Spin Dynamics of La0.85Sr0.15MnO3, 

L. Vasiliu-Doloc, J. W. Lynn, A. H. Moudden, 

A. M. de Leon-Guevara, and A. Revcolevschi,

Phys. Rev. B58, 14913 (1998).

[5] Spin Dynamics of Strongly Doped La1-xSrxMnO3, 

L. Vasiliu-Doloc, J. W. Lynn, Y. M. Mukovskii, 

A. A. Arsenov, and D. A. Shulyatev, J. Appl. 

Phys. 83, 7342 (1998).

[6] Magnetic Neutron Scattering, J. W. Lynn, J. 

Appl. Phys. 75, 6806 (1994).

[7] First-order Nature of the Ferromagnetic Phase 

Transition in (La-Ca)MnO3 near optimal doping, 

C. P. Adams, J. W. Lynn, V. N. Smolyaninova, 

A. Biswas, R. L. Greene, W. Ratcliff, II, S-W. 

Cheong, Y. M. Mukovski, and D. A. Shulyatev, 

Phys. Rev. B70, 134414 (2004).

[8] Charge Ordering and Polaron Formation in the 

Magnetoresistive Oxide La0.7Ca0.3MnO3, C. P. 

Adams, J. W. Lynn, Y. M. Mukovskii, A. A. 

Arsenov, and D. A. Shulyatev, Phys. Rev. Lett. 

85, 3954 (2000).

[9] Charge Correlations in the Magnetoresistive 

Oxide La0.7Ca0.3MnO3, J. W. Lynn, C. P. Adams, 

Y. M. Mukovskii, A. A. Arsenov, and D. A. 

Shulyatev, J. Appl. Phys. 89, 6846 (2001).

[10] Order and Dynamics of Intrinsic Nanoscale 

Inhomogeneities in Manganites, J. W. Lynn, D. 

N. Argyriou, Y. Ren, Y. Chen, Y. M. Mukovskii, 

and D. A. Shulyatev, Phys. Rev. B 76, 014437 

(2007).

[11] Polaron Formation in the Optimally Doped 

Ferromagnetic Manganites La0.7Sr0.3MnO3 and 

La0.7Ba0.3MnO3, Y. Chen, B. G. Ueland, J. W. 

Lynn, G. L. Bychkov, S. N. Barilo, and Y. M. 

Mukovskii, Phys. Rev. B 78, 212301 (2008).

[12] See, for example, Evolution of Spin-Wave 

Excitations in Ferromagnetic Metallic 

Manganites, F. Ye, P. Dai, J. A. Fernandez-Baca, 

H. Sha, J. W. Lynn, H. Kawano-Furukawa, Y. 

Tomioka, Y. Tokura, and J. Zhang, Phys. Rev. 

Lett. 96, 047204 (2006); Quantized Spin Waves 

in the Metallic State of Magnetoresistive 

Manganites, S. Petit, M. Hennion, F. Moussa, D. 

Lamago, A. Ivanov, Y. M. Mukovskii, and D. 

Shulyatev, Phys. Rev. Lett. 102, 207201 (2009); 

Damping and softening of transverse acoustic 

phonons in colossal magnetoresistive 

La0.7Ca0.3MnO3, Joel S. Helton, Yang Zhao, 

Dmitry A. Shulyatev, and Jeffrey W. Lynn, Phys. 

Rev. B 99, 024407 (2019).