Lattice dynamics in colossal magnetoresistance manganites

5ourna't ot Magnetism and Magnetic Materials 177-181 (1998) 881-883

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Lattice dynamics in colossal magnetoresistance manganites B.I. Min*, J.D. Lee, S.J. Youn Department of Physics, Pohang Universityof Science and Technology, Pohang 790-784, South Korea

Abstract

Based on the HamiItonian of small polarons with strong electron-phonon interaction, we have investigated anomalous behaviors of the sound velocity in colossal magnetoresistance (CMR) manganese oxides. In the low-doping metallic regime, the sound velocity has been found to be hardened below the ferromagnetic transition temperature Tc due to T-dependent electron screening coming from the double exchange (DE) interaction. On the contrary, in the high-doping regime (x > 0.5), the charge ordering (CO) interaction rather than the DE induces the hardening of the sound velocity by the ordering of localized polarons around the CO transition temperature T c o . © 1998 Elsevier Science B.V. All rights reserved.

Ke3~vords." Giant magnetoresistance; Electron-phonon interaction; Charge ordering; Transition-metaI oxides

Recently discovered 'colossal' magnetoresistance (CMR) manganites Rz-~A~MnO3 (R = La, Pr, Nd; A = Ca, Ba, Sr, Pb) have become a subject of intense investigations due to their unusual physical properties and very rich phase diagram [1, 23. Undoped RMnO3 is an antiferromagnetic (AFM) insulator, but for 0.2 < x < 0.5, the system becomes a ferromagnetic (FM) metal with the observed CMR. At higher doping (x > 0.5), the ground state becomes again an AFM insulator accompanied by the charge-ordered (CO) state [3-61. These novel features reveal that several interactions originating from the spin, the charge, and the lattice degree of freedom are competing. Hence, a phenomena at specific doping should be understood by a predominant interaction among those or the interplay of those interactions. For instance, the correlation between ferromagnetism and metallic conductivity for 0.2 < x < 0.5 was explained qualitatively in terms of the double-exchange (DE) mechanism [%9]. On the other hand, it has been proposed that JahnTeller polaron effects due to a strong electron-phonon interaction are responsible for anomalous properties

of manganites [10-13]. There are indeed many experimental evidences suggesting importance of the electron-lattice coupling in manganese oxides [14-18]. Near the magnetic and metallic transition, dramatic changes are observed in the lattice degree of freedom- the anomalous lattice expansion [14] and the shift of phonon frequency [15, 16], reflecting that the lattice is closely related to the electronic and magnetic properties. Also in insulating phase, the CO transition is accompanied by a dramatic increase (>~ 10%) in the sound velocity, implying a strong electron-phonon coupling [17]. In this paper, we have explored the origins of the renormalization of the phonon frequency in manganites both in metallic and in CO phases. First, to characterize the lattice dynamics in the metallic phase, we have considered the phonon degree of freedom in the presence of the DE interaction. Second, we have studied the CO effects on the lattice dynamics, taking into account the acoustic phonons coupled to the CO states. The effective Hamiltonian in the metallic phase incorporating the electron-phonon interaction is written as .H=t/cos~/

~
*Corresponding author. Tel.: + 82 562 279 2074; fax: + 82 562 279 3099; e-mail: [email protected]. 0304-8853/98/$19.00 ~) 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 53(97)008 3 5-4

c!cj+ ~ coqa~ae q

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B.L blin et aL /Journal of Magnetism and Magnetic Materials 177-181 (1998) 881-883 1.1

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o

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Fig. 1. The behaviors of the renormalized sound velocity ~"in the metallic (dashed line) and in the CO (x = 0.5, solid line) phase. In the metallic phase, we use fl = 0.07, and in the CO phase, we use g2(0) = 0.SzI7. where the first term corresponds to the DE Hamiltonian with 0u being the angle between nearest-neighbor spins. The DE plays a role, through - 7(T), of increasing the bandwidth below T¢, accompanied by ferromagnetic ordering. Phonon hardening occurs in the metallic region ( T < T¢), and thus it is expected that the hardening is due to the change in the electron screening in terms of the DE factor ?(T) ]-19]. The renormalized phonon frequency (Sq and the damping constants % can be obtained from the following equation [20"]:

((Dq -- igq) 2 = (0 2 -- 2COq[Mql2~7(q, (~-)q -t- i0+),

(5q>>%,

(2) where the electron screening function ~(q, e~q) includes 7(T). Taking the real part of Eq. (2) yields CSq= c%(t - J~/7(r)) z/2, where ficontains all the T-independent terms [19]. Here terms other than y(T) are assumed to have very weak temperature dependences. In Fig. 1, (Sq is plotted as a function of T. It is seen that the frequency becomes hardened with decreasing T, which is attributed to the ?(T) factor in DE. To investigate lattice dynamics near the CO transition, let us consider the following Hamiltonian d4"~¢pincorporating the electron-acoustic phonon coupling, cos

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Fig. 2. Sound velocity experiment reported by Ramirez et al.

[17]. repulsion of carriers, is expected to be the most dominant and relevant interaction in the CO phase, whereby the CO ordering phenomena can be explained in terms of the order-disorder transition of small potaron [21]. In our approach, the first term DE is no longer an interaction governing the physics of the CO formation, but should be treated just as a perturbation. This is on the basis of rather reasonable notion that the ordering of mixed MnS+/Mn 4+ atoms suppresses the DE [22]. Therefore, the DE term is safely neglected in studying lattice dynamics in the CO phase. By employing the canonical transformation, the electron-phonon coupling term can be decoupled. Then introducing the generalized susceptibility function, one can obtain the following renormalized sound velocity, g = so~,/1 + g2(O);(oJT), where x~jT) corresponds to the uniform A F M spin susceptibility of the Ising model with the exchange interaction ¼17 = ¼Y~(Vk 2g2(k))e - ~ " (3: nearest-neighbor vector). The AFM transition of the above Ising model corresponds to the CO transition, and thus below Tco, the real space ordering of Mna+/Mn 4+ species takes place, By using the uniform A F M spin susceptibility in the mean field approximation, the behavior of sound velocity g as a function of T can be obtained (see Fig. 1). The sound velocity is softened smoothly above Tco but becomes substantially hardened below Tco, which originates from the ;G,,(T). The behavior of the above sound velocity around Tco is qualitatively very similar to the observation of Ramirez et al. [17] for Lal-xCa~MnO3 (0.63 E x ~< 0.67) (Fig. 2). Note that the origin of hardening in this case is different from the case of low-doping metallic phase. We have seen that, in the low-doping case, the renormalization of the sound velocity occurs due to T-dependent electron screening coming from the 7(T) of DE interaction. On the contrary, in the high-doping case, the ordering of localized polarons is responsible for the renormalization. Accordingly, the sound velocity in the CO state will not be susceptible to the external magnetic field, because the DE interaction is not involved. This feature is consistent with the experiment [17].

B.I, Minet aI./ Journal of MagTzetism and Magnetic Materials 777-18I (1998) 881-883

This work was s u p p o r t e d by the P O S T E C H - B S R I p r o g r a m of the K M E and also in part by the K O S E F t h r o u g h the S R C p r o g r a m of S N U - C T P .

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