Infrared reflectivity investigation of the phase transition sequence in Pr0.5Ca0.5MnO3

Journal of Magnetism and Magnetic Materials 408 (2016) 81–88

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Infrared reflectivity investigation of the phase transition sequence in Pr0.5Ca0.5MnO3 J.L. Ribeiro a,n, L.G. Vieira a, I.T. Gomes a,b, J.P. Araújo b, P. Tavares c, B.G. Almeida a a

Centro and Departamento de Física da Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal IFIMUP and IN - Institute of Nanoscience and Nanotechnology, Departamento de Física e Astronomia da Faculdade de Ciências da Universidade do Porto, R. do Campo Alegre, 687, 4769-007 Porto, Portugal c Centro de Química – Vila Real, Universidade de Trás-os-Montes e Alto Douro, 5001-801 Vila Real, Portugal b

art ic l e i nf o

a b s t r a c t

Article history: Received 12 October 2015 Received in revised form 29 December 2015 Accepted 8 February 2016 Available online 9 February 2016

This work reports an infrared reflectivity study of the phase transition sequence observed in Pr0.5Ca0.5MnO3. The need to measure over an extended spectral range in order to properly take into account the effects of the high frequency polaronic absorption is circumvented by adopting a simple approximate method, based on the asymmetry present in the Kramers Kronig inversion of the phonon spectrum. The temperature dependence of the phonon optical conductivity is then investigated by monitoring the behavior of three relevant spectral moments of the optical conductivity. This combined methodology allows us to disclose subtle effects of the orbital, charge and magnetic orders on the lattice dynamics of the compound. The characteristic transition temperatures inferred from the spectroscopic measurements are compared and correlated with those obtained from the temperature dependence of the induced magnetization and electrical resistivity. & 2016 Elsevier B.V. All rights reserved.

Keywords: Ferromagnetism and anti-ferromagnetism Orbital order Spin–lattice coupling Optical conductivity Infrared spectroscopy

1. Introduction The RE1
xAExMnO3 perovskite compounds (RE being a trivalent rare-earth and AE a divalent alkaline earth) form a family of materials with strongly correlated electrons and subtle interplays between magnetic, charge and orbital orders [1–7]. In this class of compounds, the eg manganese orbitals form a narrow band allowing electrons to hop among the two (x 2 − y2 ) and (3z 2 − r 2) states, while the three t2g electrons remain localized and ferromagnetically aligned, as expected from the usual Hund`s rules. Because the probability of hopping of the eg electrons between neighbor Mn ions critically depends on the relative orientation of their spins, there is a strong correlation between the type of magnetic ordering established at low temperatures and the metallic or insulator character adopted by the system. Hence, conductivity can be potentially switched on (off) by stabilizing a ferromagnetic (antiferromagnetic) state, giving eventually rise to colossal magneto-resistances. In these systems, the eg electrons are extended in the basal (010) plane, and are strongly hybridized with the oxygen p-orbitals. This yields a dominant ferromagnetic coupling between the eg electron spins via double exchange. In contrast, the localized t2g n

Corresponding author. E-mail address: jlr@fisica.uminho.pt (J.L. Ribeiro).

http://dx.doi.org/10.1016/j.jmmm.2016.02.026 0304-8853/& 2016 Elsevier B.V. All rights reserved.

electrons couple via the usual superexchange antiferromagnetic mechanism. Therefore, there is a strong potential competition between these two magnetic orders, which may lead to the stabilization of complex spin arrangements. Small changes in some parameters, such as the Mn–O–Mn bonding angle and bonding length (which are defined, to a large extent, by the size of the A-site ions), or the application of an external magnetic field, may dictate both the type of the magnetic order established and the magnitude of the conductivity in the system [8–11]. The Pr1
xCaxMnO3 is one of the most interesting and more deeply investigated members of this family [12–14]. Since Pr and Ca have similar sizes (c.a. 1.18 Α), there is a very low mismatch over the entire composition range 0 ox o1 [15]. The solid solution remains insulating over the entire compositional range, even if different magnetic ground states are observed in different ranges [12–14,16]. PrMnO3 orders in A-type AFM structure, with a pseudo-proper magnetization induced by a Dzyaloshinskii-Moriya mechanism [16]. That canted spin arrangement is maintained in Pr1
xCaxMnO3 for 0 ox o0.15 (TN∼80 K), while for 0.15o xo 0.3, the solid solutions enter into a ferromagnetic insulator state with Tc ≈ 100 K − 140 K . In the range 0.3 ox o0.8, a structural instability gives rise to the onset of orbital and charge ordered states ( 250K > Too − co > 180K ). For this large compositional range, different types of AFM orders are observed at lower temperatures (TN ≤ Too − co ; CE-AFM for 0.3 o xo 0.7; C-AFM for 0.7 ox o0.8), and the ferromagnetic insulating state is strongly destabilized

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( Tc < 10K ). Finally, in the Mn4 þ rich side, x ≈ 0.9 a G-type AFM structure appears ( TN ≈ 90K ) with a strong FM component, giving rise to a metallic cluster glass state. The half-doped system Pr0.5Ca0.5MnO3 is particularly interesting due to its lowest order commensurate filling. For this composition, the observed phase sequence reflects the competition between primary order parameters of different symmetries, namely a spontaneous canted magnetization of symmetry mΓ4 + , an AFM arrangement of symmetry m (U1 + U4 ) + , and a structural distortion of symmetry X1 that leads to the orbital and charge ordered states [17].1 The separate nature of these primary order parameters makes it hard to detect the stability ranges of different phases by relying on a single technique, due to the difficulty in finding a single unique probe capable of an efficient coupling to all of them. In this work we take advantage of the strong responsiveness of the lattice dynamics to the charge, orbital and magnetic ordering processes, and show that simple infrared reflectivity measurements may allow a detailed mapping of the phase sequence details, providing that adequate methods of spectral analysis are employed. This paper is organized as follows. The experimental details of the study are described in Section 2. In Section 3, the method used for decoupling the contributions of phonons and polarons to the optical conductivity in the far infrared range is discussed, and the spectral functions that will be subsequently used are defined. In Section 4, the essential set of experimental results of FIR reflectivity (complemented with auxiliary measurements of d.c. resistivity and induced magnetization) are presented, and the mapping of the phase sequence thus obtained is briefly discussed. Finally, Section 5 presents a few concluding remarks.

2. Experimental details Polycrystalline Pr0.5Ca0.5MnO3 samples have been prepared by solid state reaction of Pr6O11, CaO, and MnO2 weighted in stoichiometric proportions. This mixture was first heated twice at 950 °C with intermediate grindings to achieve complete decarbonatation. The powder was then uniaxially pressed under 100 MPa in the form of pellets and sintered at 1500 °C for 12 h in air. The pellets were finally cooled down to 800 °C at 5 °C/min and quenched to room temperature. The morphology and microstructure of the samples have been determined by scanning electron microscopy. Fig. 1a) shows a typical SEM micrograph obtained on the surface of a fractured sample. The samples were composed by grains with dimensions of order of 1μm. The estimated relative densities are of the order of ρr∼92%. The crystallographic structure has been investigated at room temperature by powder X-ray diffraction (XRD; PANalytical X'Pert Pro), using Cu Kα radiation (λ ¼0.15418 nm) and the Bragg– Brentano θ/2θ geometry. The diffractogram, shown in Fig. 1b, revealed a single orthorhombic Pnma phase (JCPDS card number 56290), with lattice parameters a ¼5.38, b¼7.61, and c ¼5.39 A, in good agreement with lattice parameters obtained in Pr0.5Ca0.5MnO3 single crystals. The dc resistivity of the samples was measured with a fourprobe method, in polished pellets, with dc- sputtered gold electrodes. The measurements were made in the temperature range 5 oT o300 K at a controlled rate of 1 K/min. The magnetization induced by a magnetic field of 1.5 Tesla has been studied as function of temperature (10 KoT o380 K) with a superconducting 1 Here, the symmetry of the order parameter is labeled by the irreducible representation (irrep) according to which it transforms under the parent phase space group. Magnetic irreps (odd under time reversal) are labeled by a prefix m.

quantum interference device (SQUID) MPMS magnetometer from Quantum Design. The temperature dependence (10–290 K) of the infrared reflectance spectra of the polycrystalline samples were measured at near normal incidence (angle of incidence α E 11°) with a Bruker IFS 66 V spectrometer and a closed cycle helium cryostat Advanced Research Systems (coupled to an ARS-2HW helium compressor). The wavenumber range of 100–3000 cm
1 was scanned with different light sources, beam splitters and detectors. A Globar source, a KBr beam splitter, and a DTGS detector with a KBr window were used to cover the middle infrared (MIR) region (500–3000 cm
1). The far infrared (FIR) region was studied with an Hg lamp, 6μ-M8 Mylar beam splitter, and a DTGS detector with a polyethylene window. The resolution for the FIR and MIR spectral ranges was better than 2 and 4 cm
1, respectively.

3. Methodology 3.1. The method of spectral inversion In general, the optical response of polycrystalline samples of anisotropic materials is difficult to describe. If the domains are very small compared with the radiation wavelength, or if the degree of optical anisotropy of the randomly oriented crystallites is not very strong, then the polycrystalline response can be well described by an effective scalar dielectric function [18–24]. However, if the optical domains are large (compared with the radiation wavelength) and markedly anisotropic, then the optical response of the polycrystalline medium may be very complex. For example, non-zero cross polarization reflectivity may occur, a Brewster angle may no longer be identified for parallel polarized incident light, and the reflectance for s-polarized light may eventually be smaller than the reflectance for p-polarized light [25,26]. Obviously, these effects cannot be described by assuming an effective scalar dielectric function. A simple empirical criterion for the applicability of the effective medium approximation in highly anisotropic crystallites [24] requires that 10d o λ, where λ is the vacuum radiation wavelength and d the typical size of the crystallites. In the present case, since the samples investigated have typical domains of the order of 1 mm, that condition is verified for wavenumbers smaller than 1000 cm
1. That is, the effective medium approximation can in principle be used over the whole range of the phonon spectrum, even in the case of a high optical anisotropy. Fig. 2 shows the room temperature infrared reflectivity spectrum of a polycrystalline sample of Pr0.5Ca0.5MnO3 measured in the range 100–3000 cm
1. As can be seen, the reflectivity R(ω) displays a clear frequency independent plateau near 2500 cm
1. The inset of that figure shows the real (ε1) and imaginary (ε2) parts of the dielectric function obtained from Kramers–Kronig inversion of R(ω), assuming that this function remained frequency independent above 2700 cm
1. Besides three main effective phonon bands that are reminiscent of the three phonon modes present in a cubic perovskite (more of which will be discussed below), there is one important feature: contrary to the case of pure polariton modes, the reflectivity spectrum lies in an almost flat, slightly deformed baseline. The reflectivity rises at small frequencies and decreases smoothly as the frequency increases, in such a way that typical minimum reflectance points, such as the Christiansens' point are erased. This deformation, also seen in ε2 (ω), tends to disappear as the temperature decreases from room temperature. Spectroscopic measurements carried out over an extended frequency range (100–16,000 cm
1) have disclosed, at higher frequencies, broad reflectivity band whose origin has been

J.L. Ribeiro et al. / Journal of Magnetism and Magnetic Materials 408 (2016) 81–88

83

a)

20

40

(313) (204) , (402) , (161)

(004),(400),(242) (410)

(114)

(123),(321),(042),(240)

60

(331)

(222),(141) (311)

(202),(040)

(131)

(212),(230)

(221)

(022)

(002),(200),(121)

(210) (112)

(011) (101),(020) (111)

Intensity (a.u.)

b)

80

2 (degrees) Fig. 1. Scanning electron micrograph of a polycrystalline sample of Pr0.5Ca0.5MnO3 (a), and the corresponding powder X-ray diffractogram (b). The vertical lines mark the positions of the bulk peaks. ∞

2 σ1 (ω) = σ 0+ 7 π

∫

ω′σ 2 ( ω′) 2

dω′

ω′ − ω2

0

(1)

∞

2ω σ 2 (ω) = − 7 π

∫

0

Fig. 2. Room temperature reflectivity of polycrystalline Pr1/2Ca1/2MnO3. The inset shows the real (ε1) and imaginary (ε2) parts of dielectric function obtained by Kramers–Kronig inversion.

ascribed to Jahn–Teller polaronic conductivity. The low frequency tail of this band can be clearly seen in the rise of R(ω) observed in Fig. 2 above 2500 cm
1 (at room temperature, that band is centered at about 8000 cm
1 [27–31] ). It is the presence of this band (and of the related finite conductivity) the cause of the deformed background seen at lower energies. The fact that the polaronic band occurs at frequencies that are much higher (∼8000 cm
1) than the typical phonon frequencies (o 700 cm
1) enables us to use a simple Kramers–Kronig transformation to separate both contributions. In fact, if we neglect the frequency dependence of the polaronic conductivity tail over the entire phonon frequency range, we have essentially an additional constant contribution that is similar to that of a Drude conductivity in the limiting case ωτ < < 1 (where τ is the electronic relaxation time). One important effect of this nearly frequency independent conductivity (s0) is that the symmetry of the Kramers–Kronig transformation calculated over the phonon frequency range is broken [32]. That is, due to the constant conductivity s0, the real and imaginary parts of the optical conductivity σ1 (ω) + iσ 2 (ω) are no longer the Kramers–Kronig transform of each other because the Hilbert transform of s2(ω) now equals σ1 (ω) − σ0 . That is:

σ1 (ω′) 2

ω′ − ω2

dω′ (2)

Therefore, it is possible to estimate σ0 by just subtracting the Hilbert transform of σ 2 (ω) from the σ1 (ω) that results from a direct Kramers–Kronig inversion of the power reflectivity. As shown in Fig. 3, the suppression of the flat background and the estimation of the phonon optical conductivity spectrum at room temperature can be reasonably achieved in this way. The inset in Fig. 3 shows how s0 varies with temperature. As expected, this conductivity decreases with temperature as the polaronic band shifts towards higher frequencies. Interestingly, the rate at which s0(T) decreases is markedly different over different temperature ranges. In particular, there is a clear plateau between Too ≈ 250K (temperature that can be identified with the orbital ordering transition, see below) and TN ≈ 180 K , followed by a drastic decreasing below TN . Given the strong correlation between

Fig. 3. Original and corrected optical conductivity spectra of polycrystalline Pr0.5Ca0.5MnO3 at room temperature. s0 is the subtraction constant used to perform the correction. The inset shows the temperature evolution of the correction constant conductivity s0 as a function of temperature. A sharp decreasing of s0 at about TN ≈ 180K indicates the onset of the CE-type AFM ordering.

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J.L. Ribeiro et al. / Journal of Magnetism and Magnetic Materials 408 (2016) 81–88

the electronic hopping probability and the magnetic state that is characteristic of this type of materials, one can interpret this latter temperature as the Néel temperature marking the onset of the CEAFM phase, in agreement with [14]. We have therefore obtained a first relevant information on the phase diagram of the material by employing this simple methodology for decoupling the contribution of phonons and the polarons to the measured spectra: the location of the AFM phase transition.

shown in the next section, the temperature dependence of these functions reflect remarkably well the details of the phase diagram of the compound.

3.2. The method of spectral analysis

The magnitude and the temperature dependence of the electrical resistivity of the samples are entirely similar to those measured in single crystals [37,38] or polycrystalline samples with good oxygen stoichiometry [39]. The resistivity ρ shows a typical thermally activated behavior (see Fig. 4), with relatively low values near room temperature. Above 250 K, ln (ρ) varies linearly with T
1, with a slope that corresponds to an effective activation energy of the order of Ea ¼0.180 eV. In the range 1804 T4 110 K, the activation energy reduces to 0.150 eV. The transition between these two regimes extends over the wide temperature range 180o To250 K. At lower temperatures ( T < T * ≈ 110 K ) the data departs from this simple activation law. Fig. 5 displays the magnetization induced by a magnetic field B¼ 1.5T. The magnetization shows a maximum at Too ≈ 254 K , a decrease on cooling in the range 254 K > T > 110 K , and a sharp

ωn =

∫0

∞

ωn

σ dω . ε0 ε∞ ω2

(3)

Let us consider some specific examples. The second order moment defines the spectral weight:

ω2 =

∫0

∞

σ dω . ε0 ε∞

4.1. Electrical resistivity and magnetization

5

10

resistivity (a.u.)

The phonon optical conductivity obtained above from the power reflectivity of polycrystalline samples must be seen as macroscopic response function of an effective medium. The intrinsic optical anisotropy and the overlap of reflectivity bands of different symmetries give rise to effective reflection bands with complex shapes. As a result, a detailed description of that shape via the fitting of a particular model is of limited interest because the parameters of that model have no well-defined physical meaning, and different sets of parameters may yield identical fittings of the data. A better approach consists of adopting a spectral analysis based on quantities that describe the global features of the measured spectrum, over large frequency ranges, and without relying on specific models for the effective dielectric function. One example of such an approach is the analysis of the spectral moments, which are defined on the basis of very basic causal constraints or sum rules [33–35]. These spectroscopic functions have recently proven to be remarkably responsive to the subtle changes induced by the magnetic ordering on vibrational spectra of EuMnO3 [26]. The n-order spectral moment is defined with respect to a given spectral density function. If the conductivity function is considered, the corresponding n-th order moment can be defined as

4. Results and discussion

σ dω . ε0 ε∞ ω2

(5)

One can also define the n-order weighted moment as the ratio between the n-order and the zero order moments [35]. The second order weighted moment ∞

Ω2

T

=

∫0

∞

∫0

σ dω ε 0 ε∞ σ

ε 0 ε∞ ω 2

dω

(6)

is particularly useful since it may define a characteristic frequency of the whole spectrum, ΩT =[ Ω2 T ]1/2 . Also, the damping of that effective mode can be estimated from the rms width of the tranverse loss function [36]:

δ T =⎡⎣ Ω2

T

1/2 − Ω 2T ⎤⎦ ,

2

10

1

10

0

10

-1

50

(4)

(7)

where Ω2 T and Ω 2T are the second order weighted moment and the squared first order weighted moment, respectively. Similar expressions can be obtained for a characteristic longitudinal frequency and damping by replacing in the formulae above the transversal loss function by the longitudinal loss function. As

5

10

resistivity (a.u.)

∫0

∞

3

10

10

The dielectric strength, defined as the difference between the static and the high frequency dielectric response, Δε = ε (0)−ε∞, is proportional to the zero order moment [33]

2 ∆ε = ε∞ π

4

10

4

10

100

250 K 200 K

150

200

T (K)

250

300

110 K

3

10

2

10

1

10

0

10

-1

10

0.004 0.006 0.008 0.010 0.012 -1

1/T (K ) Fig. 4. (a) Temperature dependence of the dc resistivity ( ρ ) of a ceramic sample of PrxCa1
xMnO3 (in arbitrary logarithm units); (b) The plot of ln (ρ) as a function of T
1 shows four distinct temperature ranges: a linear behavior corresponding to an activation energy Ea ¼0.180 eV (T 4250 K), an extended transition region (250 Ko T o 200 K), a second linear regime with Ea ¼0.150 eV (200 K 4T 4110 K), and finally, for T o 110 K, a region where ln (ρ) shows a non-linear dependence on T
1.

J.L. Ribeiro et al. / Journal of Magnetism and Magnetic Materials 408 (2016) 81–88

Fig. 5. (a) Induced magnetization M (T ) (in arbitrary units) measured on a cooling run under an applied field of 1.5 T; (b) The temperature derivative dM (T ) measured dT in the range 4o T o 350 K.

85

behavior that χ −1 (T ) exhibits in the paramagnetic phase) may not be completely suppressed. Since early stages, it is known that the magnetic phase diagram of the Pr1
xCaxMnO3 system is complex [40–45]. As reported in [39,45], the phase diagram obtained for polycrystalline solid solutions of Pr1
xCaxMnO3 includes, for compositions in the range x o0.3, a low temperature ferromagnetic insulating phase, that extends beyond x ¼0.3 for very low temperatures. The nature of this phase and its range of stability seem to depend on the oxygen stoichiometry of the samples [39]. For x ¼0.3, for instance, a collinear CE-type AFM structure (TN  130 K) is reported to be succeeded by a canted ferromagnetic structure, together with an antiferromagnetic component of the CE type (TCA∼115 K) [14,46]. It is possible that that canted ferromagnetic structure may still be detectable in polycrystalline samples, at very low temperatures for nearly half-filled compositions. The resilience of the ferromagnetic order may be enhanced by disorder effects. Monte Carlo studies performed on CE-AFM/OO phase in a 3-dim lattice with an open surface reveal that an increase in charge density due to the unscreened Coulomb interactions drives the surface layer from an AFM/CO to a phase-separated state and provides the FM tendency at the surface, while the inner core remains in a stable CE-type CO state [47]. This effect would give rise to an exchange bias effect at the interface of the FM and AFM components, whose magnitude may depend on the thickness of the AFM and FM layers and on the grain size [48]. This exchange bias effect may eventually stabilize different local spin configurations, and lead to glassy and non-ergodic behavior [48]. 4.2. Infrared spectra

Fig. 6. The anomaly in the susceptibility near the orbital ordering transition is well described by assuming a biquadratic coupling γη2M2 between the magnetization M and the orbital order parameter η , with γ > 0 . In the disordered phase (T > Too ), the C susceptibility follows a Curie–Weiss law, χ (T ) = , with Tc ≈ 200 K . The “kink” T − TC observed in χ −1 (T ) results from the appearance of an additional contribution 2 −1 Δχ ∝ η . Below Too , that additional contribution can be fitted to a mean field law 1 Δχ −1 ∝ (Too − T )2β with β = . 2

increase at about Tc ≈ 40 K . The anomaly seen at Too is depicted with more detail in Fig. 6. At high temperatures, T > 300 K , the 1 M susceptibility χ = B follows a Curie–Weiss law χ −1 = C (T − θ ), with θ ≈ 200 K . The process of stabilization of a magnetic order with a ferromagnetic component (which is anticipated by this behavior of the paramagnetic susceptibility) is, however, aborted by the condensation of the orbital ordering at Too . The shape of the anomaly observed in M (T ) at this structural transition is characteristic of the dominant symmetry allowed biquadratic coupling γM2η2 between the magnetization M and the orbital ordering parameter η , if γ > 0. In that case, that coupling originates a reduction of the induced magnetization below the orbital ordering transition at Too (as observed), due to the ap1 χ −1 = C (T − θ ) for T 4Too, and pearance of η ≠ 0 [that is,

We can now consider the temperature dependence of the FIR reflectivity spectra of the compound. Fig. 7 shows the real part of the phonon conductivity spectra (estimated by the method described in Section 3), for different temperatures in the range 10 KoT o280 K. These functions show three main bands, centered around 200, 340, and 570 cm
1 at room temperature, which are reminiscent of the three F1u infrared active modes characteristic of a cubic perovskite. For a cubic structure, the lowest frequency band originates from the external modes that correspond to the vibration of the Pr or Ca ions against the MnO6 octahedra, the middle band relates to the bending mode due to the internal vibration of both Mn and apical oxygen ions against planar oxygens, and the higher band to the stretching mode of the Mn ion against the O6 octahedra. Note that both the bending and the

1

χ −1 = C (T − θ ) + 2γη2 for T oToo] 2. The anomaly observed at Tc ≈ 40K suggests that the weak ferromagnetic instability (which, as seen, is anticipated by the 2 This biquadratic coupling term also explains why the onset of the orbital order destabilizes the ferromagnetic state (by increasing its energy), making possible the condensation of the competing AFM phase. The connection between orbital order and antiferromagnetism results therefore from a combination between symmetry constraints and thermodynamics ( γ > 0 ).

Fig. 7. Optical conductivity spectra (real part) of polycrystalline Pr0.5Ca0.5MnO3 for selected temperatures. The optical conductivities below 280 K are shifted in intensity.

dT

onset of a weak magnetization (Tc ¼ 40 K), and the orbital–ordering transition (Too ¼254 K). The temperatures T* ¼120 K and TN ¼ 180 K identify the temperatures at which dM changes sign and the andT

tiferromagnetic order is established (see Section 3), respectively. Finally, the temperature TL ≈ 210 K corresponds to the temperature at which clear anomalies in the temperature dependence of the spectral moments are observed: ΩT (T ) exhibits here a clear cusp, the effective damping δT enters into a quasi-plateau (see Fig. 8c; on cooling, this plateau lasts down to TN ≈ 180 K ), and the temperature dependence of Δε becomes steeper (on cooling; see Fig. 8d) Given that the structural order parameter leading to the orbital ordered state belongs to the X-point of the Brillouin zone, for which a Lifshitz invariant is allowed by symmetry, it seems plausible to interpret TL as the temperature at which the orbital order → 1 locks at k = ( 2 , 0, 0), and a full charge order state of symmetry Γ4 + is finally established. In fact, diffraction data do disclose a lock-in transition in the range TN oT oToo for Pr0.5Ca0.5MnO3, [37,50,51], at a temperature that may depend on the sample preparation. The infrared data suggests therefore that, in our samples, the stability range of the incommensurate orbital order (with → 1 k = ( 2 − ε, 0, 0)) is T00 = 254K < T < TL = 210 K . Over this temperature range, the modulated orbital order would be accom→ panied by an incommensurate charge wave with k = (2ε, 0, 0). Since commensurate order parameter is labeled by the irrep X1, then that incommensurate orbital ordering would be labeled either by the irrep mΣ1 or mΣ3; see [52]. In both cases, the expected symmetry of the incommensurate phase is described by the superspace group Pmcn1′ (00γ ) 0000. Only below TL the full charge

TC

TN TL

T*

TOO

0.05 (a) 0.00

-1

(cm )

-0.05

(b)

170 165 160

-1

stretching modes are expected to depend on the distortion of the MnO6 octahedra. Thus, the bending and stretching modes should be affected by modifications of the Mn–O–Mn bond angle and bond-lengths, respectively [49], parameters that play important parts in defining the magnitude of the competing magnetic interactions present in the system. Conversely, a magnetic phase transition is likely to affect these vibrational modes, since the changing of the magnetic couplings is bound to modify the structural parameters of a Jahn–Teller system. The orthorhombic symmetry of the paramagnetic phase is signaled by the complex structure of the reflectivity bands due to the superposition of different modes (group theoretical site-symmetry analysis of the system predicts 25 infrared active modes for the Pnma structure: 9B1u þ7B2u þ 9B3u). Below the orbital ordering phase transition (Too ¼254 K), which leads to a multiple unit cell, a low frequency mode emerges at around 160 cm
1 (clearly in the range of the external modes). There is also an important temperature dependence of the position of the middle effective band, which shifts towards lower frequencies as the temperature decreases. A more quantitative insight of how the infrared spectra map the phase transition sequence can be gained by looking at the detailed temperature dependence of some global spectroscopic moments. In the following, we will focus on the moments ΩT , δT , and Δε (see Section 3), calculated over the three spectral ranges of the main effective bands. In each case, the temperature dependence of the derivative of the induced magnetization will also be displayed for comparison and easy reference. Let us start with the lower energy effective band mainly originated in the external modes (lattice modes). Fig. 8 shows the temperature dependence of ΩT , δT , and Δε , calculated for this band over the range 120–224 cm
1. The five vertical lines shown in the figure identify the temperatures Tc ¼40 K, T* ¼ 120 K, TN ¼180 K, TL ¼210 K, and Too ¼ 254 K. As seen, the temperatures Tc ¼ 40 K and Too ¼254 K correspond to the two anomalies in dM that mark the

dM(T ) /dT(a.u.)

J.L. Ribeiro et al. / Journal of Magnetism and Magnetic Materials 408 (2016) 81–88

(cm ) T

86

(c)

28 26 24

200 (d) 150 100 50 0

50

100

150

200

250

300

T (K) Fig. 8. (a) Temperature derivative of the induced magnetization (dM /dT ) ; (b) Characteristic transverse frequency ΩT =[ Ω2 ]1/2 (see Eq. (6)) for the lower T frequency effective band (120–224 cm
1); (c) variance of the frequency in the
1 range 120–224 cm (see Eq. (7)) ; (d) zero order moment (dielectric strength; see Eq. (5)) for the lower frequency band (120–224 cm
1). The vertical lines identify the different critical temperatures discussed in the text. Magnetic and spectroscopic measurements were performed in the same sample.

ordered state would be established as a secondary effect of a 2 commensurate orbital ordering of symmetry P m1 1′ . A second temperature disclosed by the infrared data is T * ≈ 120 K . In the spectroscopic data T * clearly marks a change in the regime of δT (T ), a parameter that measures the anharmonicity of the lattice modes. That is, the rise of the induced magnetization on cooling is accompanied by the increase of the non-harmonic effects that affect that lattice modes as a whole. A similar behavior is disclosed by the same functions when calculated for the intermediate and higher frequency effective bands (see Figs. 9 and 10). The middle frequency effective band (which, as seen, is dominated by the bending modes due to the internal vibrations of both Mn and apical oxygen ions against planar oxygen) shows an impressive softening of ΩT , whose value decreases from about 302 cm
1 at room temperature to 278 cm
1 near T*. This softening is accompanied by a decreasing of the average damping, as measured by the r.m.s parameter δT . No exuberant anomalies are seen at the transition points. The transitions from the parent Pnma phase to the orbital ordered incommensurate phase, at Too ¼254 K, and from that phase to the charge and commensurate orbital ordered phase (at TL ≈ 180 K ) are marked by subtle changes of slope, both in ΩT (T ) and δT (T ). Over this temperature range, the dielectric strength Δε (T ) of the

TC

T*

TN TL

TOO

dM(T) /dT (a.u.)

dM(T) /dT (a.u.)

J.L. Ribeiro et al. / Journal of Magnetism and Magnetic Materials 408 (2016) 81–88

0.05 0.00

-0.05

TC

87

TN TL

T*

TOO

0.05 0.00 -0.05 560

300 290

550

280 60

40

55

35

50

30

45 40

80

6

60

5

40

4

20

0

50

100

150

200

250

300

3

0

effective band increases on cooling from room temperature down to T*. This behavior suggests that the temperature dependence of structural parameters, such as the Mn–O–Mn bond angle, are only slightly affected by the transitions from the parent phase to the orbital and charge ordered CE-AFM phase. But, as shown in Fig. 9, the behavior of the spectroscopic parameters is drastically altered on crossing T*. Below this temperature,the rising of the induced magnetization on cooling (see Fig. 5) is accompanied by the rising of δT , the hardening of ΩT , and the saturation of the dielectric strength of the middle effective band. This behavior seems consistent with the increasing of disorder and the breakdown of the ergodic behavior, possibly triggered by the nucleation and growth of random ferromagnetic domains within a CE-AFM phase. Particularly impressive, however, is the sharp responsiveness of the higher frequency band to the phase transition sequence (see Fig. 10). As seen, this band mainly originates from the internal stretching modes of the Mn ions against the oxygen octahedra, being therefore an excellent probe to the change of the Mn–O–Mn bond length. The decreasing of ΩT (T ) and δT (T ) observed in the parent phase on cooling is clearly altered as the system enters the incommensurate orbital ordered phase at Too. Below this temperature, these functions show a quasi-plateau down to circa 230 K, followed by an almost linear decreasing as the system

100

150

200

250

300

T (K)

T (K) Fig. 9. (a) Temperature derivative of the induced magnetization; (b) Characteristic transverse frequency ΩT =[ Ω2 ]1/2 ( see Eq. (6)) for the lower frequency effective T band (224–370 cm
1); (c) variance of the frequency in the range 224–370 cm
1 (see Eq. (7)) ; (d) zero order moment (dielectric strength; see Eq. (5)) for the lower frequency band (224–370 cm
1). The vertical lines identify the different critical temperatures discussed in the text. Magnetic and spectroscopic measurements were performed in the same sample.

50

Fig. 10. (a) Temperature derivative of the induced magnetization; (b) Characteristic transverse frequency ΩT =[ Ω2 ]1/2 (see Eq. (6)) for the lower frequency effective T band (470–700 cm
1); (c) variance of the frequency in the range 470–700 cm
1 (see Eq. (7)) ; (d) zero order moment (dielectric strength; see Eq. (5)) for the lower frequency band (470–700 cm
1). The vertical lines identify the different critical temperatures discussed in the text. Magnetic and spectroscopic measurements were performed in the same sample.

crosses the lock-in transition. In the temperature range 180 Ko To200 K, that is, as the system approaches the AFM order, there is a very steep increase of all the spectroscopic functions (on cooling). This increase is then stopped at the AFM phase transition. In other words, the onset of the AFM phase is accompanied (in the paramagnetic side) by important changes in the rigidity and length of the Mn–O–Mn bonds. Below TN, these changes disappear, and all the studied functions exhibit nearly temperature independent values in the range T* oT oTN. Interestingly, T* is clearly marked by discontinuities in the temperature dependence of ΩT (T ), δT (T ) and Δε (T ).

5. Conclusion The combined use of a simple approximate method for decoupling the contribution of phonons and polarons to the optical conductivity with a global spectral analysis based on the moment representation allowed us to disclose subtle effects of the orbital, charge and magnetic orders in the lattice dynamics of the compound. We have shown that the different spectral moments of the phonon optical conductivity display clear anomalies at the transitions points of a phase sequence that includes an incommensurate

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orbital ordered sate, a commensurate orbital order phase (accompanied by homogeneous charge order), and an antiferromagnetic state. Evidence of disorder effects and possible ergodicity breakdown due to the nucleation of random ferromagnetic domains could also be inferred from the spectroscopic data. The transition temperatures obtained from the reflectivity data (Too ¼254 K, TL ¼210 K, TN ¼180 K, T*¼ 120 K and Tc ¼40 K) correlate rather well with the values estimated from magnetization and dc conductivity measurements performed in the same samples. The strength and the average transverse frequency of the effective band related with the lattice modes were found to be particularly affected by the transition from incommensurate to commensurate orbital order, and by the consequent onset of the full charge ordered state. Also, the increase of the width of the transverse loss function δT (T ) observed below T* for these modes indicates that the growth of the induced magnetization is clearly accompanied by an increase of the lattice anharmonicity, an effect that is likely related with the disorder induced by the growth of local ferromagnetic domains. Precursor effects of the magnetic ordering have been clearly observed over the range TN oT oTL, both in the hardening of the average transverse frequency, and in the increase of the effective damping and strength of the higher frequency effective band. The temperature range in which these effects were observed, and the nature of the modes involved, suggest that the lock-in of the orbital order at the X-point of the Brillouin zone plays a crucial part in the stabilization of the antiferromagnetic state, by triggering a process that involve significant Jahn–Teller distortions and changes of the Mn–O–Mn bond lengths.

Acknowledgments This work was supported by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Projects of CFUM [PEst-C/FIS/UI0607/2013 (F-COMP-01-0124FEDER-022711)].

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