Spin wave and percolation studies in epitaxial La2/3Sr1/3MnO3 thin films grown by pulsed laser deposition

Author’s Accepted Manuscript

spin wave and percolation studies in epitaxial La _2/3 Sr _1/3 mno ₃ thin films grown by pulsed laser deposition

A. Ettayfi, R. Moubah, H. Hlil, S. Colis, M.

Lenertz, A. Dinia, H. Lassri

PII: S0304-8853(16)30143-3

DOI: http://dx.doi.org/10.1016/j.jmmm.2016.02.046 Reference: MAGMA61172

To appear in: Journal of Magnetism and Magnetic Materials Received date: 20 December 2015

Revised date: 20 January 2016 Accepted date: 15 February 2016

Cite this article as: A. Ettayfi, R. Moubah, H. Hlil, S. Colis, M. Lenertz, A.

Dinia and H. Lassri, spin wave and percolation studies in epitaxial La _2/3 Sr _1/3 mno ₃ thin films grown by pulsed laser deposition, Journal of

Magnetism and Magnetic Materials,

http://dx.doi.org/10.1016/j.jmmm.2016.02.046

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1

Spin wave and percolation studies in epitaxial La 2/3 Sr 1/3 MnO 3 thin films grown by pulsed laser deposition

A. Ettayfi

, R. Moubah

, H. Hlil

, S. Colis

, M. Lenertz

, A. Dinia

, H. Lassri

1

LPMMAT, faculté des Sciences Ain chock, Université Hassan II de Casablanca, B.P. 5366 Casablanca, Morocco

2

Institut Néel, CNRS, Université Joseph Fourier, BP 166, 38042 Grenoble Cedex 9, France

3

Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), UMR 7504 UDS- CNRS (UDS-ECPM), 23 rue du Loess, BP 43, F-67034 Strasbourg Cedex 2, France

*

Corresponding author: reda.moubah@hotmail.fr

Abstract

We investigate the magnetic and transport properties of high quality La

Sr

MnO

thin films grown by pulsed laser deposition. X-ray diffraction shows that the deposited films are epitaxial with the expected pseudo-cubic structure. Using the spin wave theory, the temperature dependence of magnetization curve was satisfactory modeled at low temperature, in which several fundamental magnetic parameters were obtained (spin wave stiffness, exchange constants, Fermi wave-vector, Mn-Mn interatomic distance). The transport properties were studied via the temperature dependence of electrical resistivity [ρ(T)], which shows a peak at Curie temperature due to metal to insulator transition. The percolation theory was used to simulate ρ(T) in both the ferromagnetic and paramagnetic phases. Reasonable agreement with the experimental data is reported.

Keywords: Spin wave theory, Percolation theory, epitaxial LSMO films, Magnetism,

Electrical properties

2

1. Introduction

La

Sr

MnO

(LSMO) has been extensively studied in recent years due to its particular physical properties, with high potential applications in spintronic devices [1], such as magnetic memory-storage cells or magnetic-field sensors. This compound exhibits some interesting properties, such as a half-metallic character, colossal magnetoresistance, and a high Curie temperature (T

= 370 K) [2,3,4,5]. In such systems, the magnetic interaction is described by the double-exchange mechanism between the Mn

and Mn

ions [6], where the coupling is induced by the electron hoping between two partially filled d shells. The existence of Mn

and Mn

mixed valence is essential to interpret both the ferromagnetism and metallic conductivity states. However, it was demonstrated that the double-exchange interaction alone cannot fully explain the magnetic interaction in LSMO. It was suggested that other mechanisms may influence the exchange interaction, such as the charge ordering, the size and the disorder at the cation sites [7,8], the oxygen vacancies [9] or the polarons effect induced by strong electron–phonon interaction originating from the Jahn–Teller distortion [10]. On the other hand, a relationship between electrical and magnetic properties has been demonstrated.

In fact, LSMO exhibits a metal-insulator transition, which is accompanied by a ferromagnetic

to paramagnetic transition evidencing the strong correlation between the magnetic and

transport properties. However, the simulation of the change of resistivity as a function of

temperature is limited by the metal-to-insulator transition. To be able to model ρ(T) in the

entire temperature window, Li et al. [11] have developed a percolation model based on phase

segregation, which we use in this present study. In order to better understand the properties

and exploit LSMO for applications a detailed fundamental understanding of the magnetic and

electrical properties is needed [12,13]. Here, we report on the magnetic and transport

3

properties of high quality LSMO thin films using spin wave and percolation theories, respectively. [14,15,16]

2. Experimental methods

LSMO thin films were deposited using pulsed laser deposition technique on SrTiO

(001) (STO) substrates [17]. The background pressure was about 10

mbar. Before deposition, the substrate was heated at 900 °C for 30 min to clean the surface. During growth, the substrate temperature was kept at 750 °C and the oxygen pressure at 0.5 mbar. A KrF excimer laser (l

= 248 nm), with a frequency of 10 Hz and an energy density of 1.5 J/cm

was used for ablation [18,19]. The film thicknesses were about 38 nm. The LSMO target was prepared via conventional solid state reaction technique using stoechiomteric mixture of La

O

, SrCO

, and MnCO

powders used as starting materials. The mixture was annealed at 1200 °C during 16 hours. Then, the obtained powder was pressed into a disk by applying a pressure of 600 bar, and sintered at 1450 °C during 16 hours in air. The crystalline structure was investigated by X-ray diffraction (XRD) using a Rigaku Smartlab (9 kW) diffractometer equipped with a monochromatic Cu Kα

source (l = 0.154056 nm) and a Ge(220) 2-bounce front monochromator. Magnetic measurements were carried out on a superconducting quantum interference device (SQUID) magnetometer. Electrical resistivity as a function of temperature was carried out using a four-probe method.

3. Results and discussion

4

Figure 1a shows the XRD pattern of a LSMO thin film grown on SrTiO3(001) substrate. Only the (0 k 2l) reflections of the rhombohedral LSMO phase

are observed suggesting that the film has a well defined texture. No spurious phases could be identified in the detection limit of the XRD technique. The average grain size along the growth axis was calculated using Debye-Scherrer formula:  = _g ^.. _{. !"} ^l _q where, G is the grain size, l is the wavelength of the x- ray source, g is the full width at half maximum (FWHM) of diffraction peaks. In order to determine the FWHM, the LSMO (036) peak was fitted to Gaussian function. The calculated grain size is found to be 25 ± 2 nm. In order to check if there is an in-plane structural relation between the substrate and the layer, f scans were performed for both the substrate and the layer. For this purpose the {2,0,2} and {1,1,3} plane families of STO and LSMO were analyzed, respectively. The choice of the {1,1,3} LSMO plane family is motivated by the fact that no STO peak can be found nearby. As expected the scan showed four peaks corresponding to the cubic (fourfold symmetry) structure of STO (fig. 1b). Although the symmetry of the LSMO structure is lower, four peaks are observed as well, suggesting the existence of at least two variants. It appears that there is an in-plane relation between the substrate and the layer, and therefore, LSMO is perfectly epitaxied on the STO substrate. This epitaxial relation can be written (for two LSMO variants) as [1±10]STO(001) ║ [2- 10]LSMO(012). This relation is compatible with the very small lattice mismatch of about 0.5% existing at the STO(001) / LSMO(012) interface and with the almost square lattice inside the LSMO(012) plane (angles of 90.4° and 89.6° instead of 90°).

i

Although the structure of LSMO is rhombohedral (R-3c), the crystalline structure of LSMO is often described

as pseudocubic. In this case the (024)LSMO peak in the rhombohedral notation corresponds to the (002)LSMO

peak in the pseudocubic notation.

5

The change of magnetization as a function of temperature of a LSMO thin film is shown in figure 2. The measurements were made upon warming the film after a zero field cooling (ZFC) mode starting from 4 K in a field of 500 Oe parallel to the [100]SrTiO

(001) direction.

The T

is found to be around 340 K. This value is lower than that reported for LSMO bulk samples ( ∼ 370 K). Song, et al. [20] have shown that T

depends sensitively on the deposition parameters such as the oxygen pressure during growth or the laser beam defocus on the LSMO target. Thus, the lower T

can be attributed to these parameters.

For ferromagnetic materials, the temperature dependence of magnetization follows Block’ s law (T

) which is associated with the thermal excitation of spin waves. Using spin wave theory, the change of magnetization as a function of temperature for ferromagnets can be written as:[21]

.

) 5 (

) ( ) 5

( BT

K M

T M K

M - =

(1)

Where B is the spin-wave constant and M(5K) is the magnetization at 5 K. Equation (1) is a good estimate of low temperature magnetization for ferromagnetic materials. The B parameter expressed in equation (1) is linked to the spin wave stiffness constant (D) by:[21]

2 / 3

4 ) 5 612 ( .

2 ÷

ø ç ö è

= æ

D µ K M

B gµ

p ⁽²⁾

Where g is the spectroscopic g-factor (g

= 2), k

is the Boltzmann’s constant and µ

is the Bohr magneton. The change of magnetization as a function of T

is displayed in figure 3.

The linear fit of the experimental data allows obtaining the B parameter using equation (1),

which is defined as the slope of the M versus T

curve. As can be observed, equation (1) fits

well the low temperature data. For temperatures higher than 180 K, (T

~ 2415 K) a

deviation from linearity is seen. The concept of spin wave theory assumes that the local

6

magnetic order fluctuates with increasing temperature. Thermally induced spin waves of long wavelengths are expected to dominate at low temperature as a result of the low energy excitations.[22,23] With the increase of temperature, the fluctuations increase giving rise to a deviation from linearity of the M versus T

curve.

On the basis of the obtained B values and using equation (2), the constant exchange stiffness D was deduced (Table 1). The relationship between D and T

has been studied by Katsuki and Wolhfarth [24] based on the itinerant electron model. Using the effective mass approximation, these authors have found the following correlation:[24]

2

6

C B

k T D p k

= (3)

Where k

is the Fermi wave-vector.

According to Heisenberg model, D can also be expressed by the following formula [25]:

) 1 ( 2

2

=

+

Mn C Mn Mn B

S T r

D k (4)

Where r

is the distance between nearest magnetic ions (Mn

, Mn

) and S

is the spin moment of Mn ions. Using equation (4), it is found that r

is about 3.99 ± 0.1 Å. This value is in a line with that deduced from the structural analysis using XRD technique: which is found to be r

≈ a ≈ 3.87 Ǻ. The good agreement with the experimental results can be considered as a validation of the approach used in this study.

From the coefficient D mentioned above, it is possible to calculate the exchange constant A

(Table I). The A parameter is linked to D by the following formula:[26]

7 g

D K K M

A = m

2 ) 5 ) (

5

( . (5)

With the use of the mean field theory, the exchange interaction between a Mn ion and its nearest neighbors can be expressed as:[27]

) 1 ( 2

3

= + S zS

T

J

k

(6)

We found that

Now, we describe the transport properties of LSMO thin films. Figure 4 shows the experimental temperature dependence of LSMO resistivity in the temperature range from 10 to 400 K. As can be observed, the behavior of ρ(T) is typical for manganites, showing a metal to insulator transition with a peak at T

= 348 K. We note that the magnitude of ρ(T) is smaller than that reported for bulk LSMO samples

which can be attributed to the growth conditions or the finite size effects. At low temperature, ferromagnetic phase, ρ(T) can be approximated using a formula which includes some scattering mechanisms:[29]

ρ

(T)=ρ

+AT

+BT

(7)

Where ρ

is the residual resistance, the term AT

is usually attributed to the mutual scattering of change in carriers, and BT

is a small contribution due to the electron-magnon scattering processes.

For temperatures higher than that of the metal-insulator transition (paramagnetic phase), ρ(T) can be expressed by the thermo-activated law using the following formula: [30]

k T

CT E

B p

PM

exp

r = (8)

ij

0,1

J » mRy

8

Where E

is the activation energy, and a is a constant. As shown in figure 4, ρ(T) is well fitted for both the low and high temperature regimes. From the fits, the obtained values of the parameters used in equations (7) and (8) are listed in table 2and table 3.

As mentioned above, the behavior of ρ(T) is well described by using equations (7) and (8).

However, in the vicinity of the metal to insulator transition, there is a divergence between the two models. This is due to the fact that the system should be considered as a phase foliated in a region of phase transition: the ferromagnetic conducting phase with a small fraction of the paramagnetic dielectric phase (below T

), and the paramagnetic insulating phase with a tiny portion of the ferromagnetic conducting phase, which is prevailing above T

. Therefore, in such a phase-foliated system, the metal-insulator transition is a percolation phase transition and ρ(T) can be described using percolation theory.[11] By assuming a percolation character of the metal to insulator transition, and considering that the competition between the ferromagnetic and paramagnetic regions plays a key role. The electrical resistivity can be expressed as: ρ (T)= ρ

*f+ ρ

*(1-f). Where f and (1-f) are the volume fractions of the ferromagnetic and paramagnetic phases, respectively. The volume fraction function of the two phases satisfies the Boltzman distribution:f = ^$

$%&'( (

) . Here, ∆U(T) is the difference in

energy between the ferromagnetic and paramagnetic states, which depends on temperature.

We note that ∆U(T) can be developed at the first order to ∆U(T) ~ U

(1- ₁ ¹

23

).

U

is considered as the energy difference at low temperature (T<< T

). Therefore, ρ (T) can be expressed in the whole temperature window using the following formula:[11]

ρ (T)=( ρ’

+A’T

+B’T

)f+ C’

T k

E

B

p

(1-f) (9)

9

From the fit, we can observe that equation (9) describes satisfactory the ρ(T) behavior in the whole temperature range, including the region of phase transition. The obtained parameter values used in formula (9) are all presented in table 4. These parameters are comparable to those found by Khlifi et al. [31] in bulk La

Ca

MnO

using the same percolation model.

Figure 5 displays the deduced temperature dependence of the ferromagnetic phase volume fraction (f) for LSMO thin films. One can notice that f is equal to 1 where the ferromagnetism is prevailing (low temperature), indicating the domination of the ferromagnetic fraction in the ferromagnetic region. With increasing temperature, the ferromagnetic phase volume fraction decreases, indicating that the paramagnetic contribution is increasing as the temperature is increased. These results highlight the applicability of the percolation model, which takes into account a transition from ferromagnetic to paramagnetic states when the temperature is elevated.

4. Conclusion

In summary, the magnetic and transport properties of epitaxial LSMO thin films were studied

experimentally and theoretically. The temperature dependence of magnetization was fitted

using spin wave theory. Several magnetic constants were extracted using simulations. The

extracted results are in agreement with those determined experimentally. The electrical

resistivity as a function of temperature was modeled in two separate regions: metallic and

insulating phases. However, these models diverge at metal-insulator transition. To overcome

this divergence, the electrical resistivity was simulated in the entire temperature window,

using a phenomenological percolation model. Finally, this study will be useful to understand

the magnetic and transport properties of LSMO compounds.

10

Fig. 1. (a) X-ray diffraction pattern of a 25-nm-thick LSMO film grown on SrTiO

(001) substrate. (b) f Scans of the STO {2,0,2} and LSMO {1,1,3} planes showing 90° periodicities for the monovariant STO and multivariant (a and b) LSMO

.

Fig. 2. Temperature dependence of normalized magnetization for LSMO thin films obtained at an applied magnetic field of 500 Oe. The magnetic field was parallel to the [100]SrTiO

(001) direction.

Fig. 3. Variation of magnetization as a functionof T

recorded by applying a field of 500 Oe (sphere symbols). Red solid lines display the corresponding linear fit obtained using spin wave theory.

Fig. 4. Change of resistivity as a function of temperature of LSMO thin films without applying a magnetic field, solid red, black and green lines are the fits obtained using equations (7),(8), and (9), respectively.

Fig. 5. Thermal variation of the simulated change of the ferromagnetic phase volume fraction for a LSMO thin film.

ii

Although at first glance the (113) and (-123) LSMO planes do not seem to be part of the same plane family,

this is indeed the case. In the four indices notation (hexagonal structure) these planes are (11-23) and (-12-13)

which are indeed part of the same plane family.

11

Table 1: Some magnetic parameters of LSMO film extracted from spin wave theory.

M (emu/cm

) at 5K B (10

K

) D (meV.Å

) at 5K A (10

erg/cm) at 5K k

(Å

)

600 6 83.6 21.6 0.36

Table 2: Deduced parameters from the fit of r (T) using equation (7) for the ferromagnetic phase.

Equation ρ

(T)=ρ

+AT

+BT

Parameters Values

FM ρ

[Ω.cm] 3.11 10

FM A[Ω.cm/K

] 7.95 10

FM B[Ω.cm/K

] 1.14 10

Table 3: Deduced parameters from the fit of r (T) using equation (8) for the paramagnetic region.

Equation

T k CT E

B p

PM

exp

r =

Parameters Values

PM C[Ω.cm/K] 3 10

PM E

/ k

[K] 606.12

12

Table 4: Deduced parameters from the fit of r (T) using equation (9) for the percolation theory:

Equation ρ (T )= ^{( 4}

′

%6’1

%8’1

)

$%&'(

($:

) + ^&'(

,-/+5

;$:

<∗?’1 &'(

$%&'(

($:

)

parameters Values

Pe rc olation t h eor y

ρ'

[Ω.cm] 2 10

A’[Ω.cm/K

] 3.3 10

B’[Ω.cm/K

] -1.9 10

C’[Ω.cm/K] 1.76 10

E

/k

[K] 1856

U

/k

[K] -3900

13

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Highlights

Ø The magnetic and transport properties of epitaxial La

Sr

MnO

thin films are investigated.

Ø The M(T) curve was modeled at low temperature, and several magnetic parameters were obtained using spin wave theory.

Ø The percolation theory was used to simulate ρ(T) in both the ferromagnetic and

paramagnetic phases.

20 40 60 80 10

10

10

10

10

10

10

10

In te nsit y ( cp s)

2 q an gle (° )

LS MO (0 12 )

Sr

3

TiO (0 01 )

LS MO (0 24 )

Sr

3

TiO (0 02 )

LS MO (0 36 Sr )

3

TiO (0 03 )

(a ) (b ) 0 60 120 180 240 300 360

10

10

10

10

10

10

LS MO (-1 23 ) b

LS MO (-1 23 ) a Sr

3

TiO (-2 0-2 )

Sr

3

TiO (-2 02 )

Sr

3

TiO (0 22 )

LS MO (1 13 ) b

LS MO (1 13 ) a

In te nsit y ( cp s)

f an gle (° )

Sr

3

TiO (2 02 )

90 ° 45 °

Figure

0 10 0 20 0 30 0 40 0

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

M(T )/M (5 K)

T (K )

Figure

0 10 00 20 00 30 00 40 00 50 00 60 00 70 00 0. 0

0. 2

0. 4

0. 6

0. 8

1. 0 Ex pe rim en tal da ta Li ne ar fi t

M ( T)/

M ( 5 K )

T

( K

)

B = 5.9 7 ´ 10

K

Figure

0 1 0 0 2 0 0 3 0 0 4 0 0 0. 000

0. 002

0. 004

0. 006

0. 008 Experi m ent al dat a Fer ro m agnet ic fi t Par am agnet ic fi t Per col at ion theor y fi t

Res ist ivi ty W ( .cm )

T (K )

Figure

0 100 200 300 400

0. 2

0. 4

0. 6

0. 8

1. 0

f

T (K)

Figure