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Ab initio study of the optical phonons in one-dimensional antiferromagnetCa2CuO3 Center for Materials Science, Vietnam National University, 334 Nguyen Trai, Hanoi 10000, Vietnam 共Receive

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Ab initio study of the optical phonons in one-dimensional antiferromagnet Ca 2 CuO 3

Nam Nhat Hoang, Thu Hang Nguyen, and Chau Nguyen

Citation: Journal of Applied Physics 103, 093524 (2008); doi: 10.1063/1.2917061

View online: http://dx.doi.org/10.1063/1.2917061

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Ab initio study of the optical phonons in one-dimensional antiferromagnet

Ca2CuO3

Center for Materials Science, Vietnam National University, 334 Nguyen Trai, Hanoi 10000, Vietnam

共Received 3 November 2007; accepted 2 March 2008; published online 8 May 2008兲

We present the cluster-model ab initio study of the optical phonons in the one-dimensional

antiferromagnet Ca2CuO3 based on the Hartree–Fock self-consistent field calculation with the

3-21G basis set The obtained results showed very good agreement with the observed data The

composed of the vibrations of the oxygen in static host lattice, whereas the Cu movements only

happened in the collective lattice vibrations An almost complete classification of the forbidden

I INTRODUCTION

The importance of the low dimensional system A2CuO3

共A=Sr,Ca兲 in both practical and fundamental aspects has

attracted much attention from scientists during the past few

decades This system exhibits various properties associated

with its low dimensionality, such as the covalent insulation,1

the Van Hove singularity on the spin Fermi surface,2and the

spin-charge separation.3,4 The structure of Ca2CuO3

关sche-matically featured in Fig 1共a兲兴 is very similar to the

two-dimensional superconducting La2CuO4 There is only

oxy-gen lacking which perpendicularly connects two parallel

Cu-O chains Some compounds with the Ca2CuO3structure,

e.g., an oxygen excessive Sr2CuO3.1, can transform their

structure under pressure into the La2CuO4type structure and

become the high T c superconductors 共the Sr2CuO3.1 has T c

= 70 K兲.5

The A2CuO3 exhibits a strong spin 1/2

chains The intrachain exchange integral J储⬇0.6 eV,

esti-mated on the basis of the t-J model, shows a record high

value among the 1D systems and is about 300 times greater

than the interchain coupling J⬜.6 9With this observation, the

structure of Raman-active phonons along the Cu-O共2兲 chain

direction is enriched by features that are normally forbidden,

while in the other two directions, only two A g-mode phonons

are visible The first experimental study of the optical

phonons in Ca2CuO3was presented by Yoshida et al.10 and

Zlateva et al.11 and later by Bobovich et al.12 and Hoang et

al.13 The first two studies reported the measurement on the

single crystals, whereas the last two reported on the powder

samples Despite differences in the chemical contents of the

samples, which followed either from the differences in

preparation routes or from the doping of further elements

共e.g., Sr or U兲, the discussed phonon structures agreed quite

well with each other There are also two theoretical results

available for the undoped Ca2CuO3 One is from the lattice

dynamic calculation11 and the other from the tight-binding

approach.14As these studies showed, there was a strong

cou-pling between the forbidden phonons and the intrachain

charge-transfer process mediated by the electrons excited by light Although several observed features have their correct explanation, the problem still remains for the assignment of Cu–O bands and the majority of overtones It is also worth-while to mention that not all phonons can be classified as originating from the pure Ca2CuO3 phase Recent studies have shown that there was always a recognizable amount of the CuO phase presented in the final Ca2CuO3 samples that have been prepared by the ceramic technology.12,13,15,16

II OBSERVED OPTICAL PHONONS IN

Ca 2 CuO 3

For the pure and the Sr-doped, U-doped Ca2CuO3, sev-eral Raman studies are available.10–14 Figure 2 共upper part兲 shows the measured data using the light from He–Ne laser with␭=623.8 nm 关共i.e., 1.96 eV, note that the maximal scat-tering output occurs at 2.0 eV共Ref 10兲兴 From Fig.2, the peaks are seen at 200, 280, 307, 467, 530, 663, 890, 942,

1142, 1217, and 1337 cm−1 This structure represents the most complete picture of all observed Raman-active optical

a兲Electronic mail: namnhat@gmail.com.

FIG 1. 共Color online兲 The packing structure of three unit cells 共a⫻3b

⫻c兲 for Ca2 CuO3共a兲 and the model cluster Ca 18 Cu8O28used in the ab initio

calculation of vibrational states 共b兲.

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phonons in the Ca2CuO3 For the scattering light from

1.17 eV兲, some peaks disappeared 共i.e., 200, 467, and

942 cm−1兲 but the main features remained the same.12 , 13

It is obvious that the structure of the Raman spectra depends on

energy of the excitation light and for our case the He–Ne

laser provided a more complete set of scattering lines In

共D 2h25兲, the optical phonons at the ⌫ point 共k=0兲 compose of

six Raman active modes共2A g + 2B 1g + 2B 2g兲 and nine IR

ac-tive modes共3B 1u + 3B 2u + 3B 3u 兲 The A g -, B 1g -, and B 2g-mode

C22 兲 of the Ca and O共1兲, so with the vibrations of these

atoms along axis c 共A g 兲 and a and b 共B 1g and B 2g兲 The

A g-mode phonons are active in the 共a,a兲, 共b,b兲, and 共c,c兲

geometry and the B 1g - and B 2g-mode phonons are allowed

only in the共a,c兲 and 共b,c兲 settings By performing the

scat-tering measurement in these exact configurations with some

single crystal pieces, the A g -, B 1g -, and B 2g-mode phonons

can be determined Indeed, Yoshida et al.10has identified the

A g-mode phonons to be 306 cm−1共assigned to the Ca

These two phonons were the sole phonons in the c共a,a兲c¯ and

phonons were experimentally observed in the respective scattering configurations.10,11

The rich features only appeared for the a共b,b兲a¯ configu-ration, i.e., when the light polarization was parallel to axis b Yoshida et al.10 reported the following lines: 235, 306, 440,

500, 690, 880, 940, 1140, 1200, and 1330 cm−1 All these peaks, except the one at 500 cm−1共not seen in Refs.11and

12兲, have their counterparts in the spectra in Fig 2 共upper part兲 The weak features that were also visible 共but not dis-cussed兲 in Ref.10closely correspond to 200, 470, 640, 1000, and 1390 cm−1 The first two of them were also reported in Ref.11 This peak structure is richer than that offered by the symmetry analysis Among them, the 440, 500, and

phonon scatterings.10Since the 440 and 690 cm−1lines were

and 670 cm−1in Ref.12, 430 and 690 cm−1in Ref.11, and

430 and 670 cm−1in Ref.13兲 Zlateva et al.11

suggested that all extra lines in the Raman spectra are due to the high-order scattering This consideration resources in the finite and seg-mented Cu–O共2兲 chains of different lengths in the real poly-crystalline samples, which expectedly leads to the overtones

It may, however, result from the impure phases presented as

phases from the final product by means of the ceramic and oxalate coprecipitation techniques.15,16

The B 1u -, B 2u -, and B 3u-mode phonons, associated with

Cu, 2a of O 共2兲, and 4f of Ca and O共1兲兴, correspond to the vibration of these atoms along the crystallographic axis c, b, and a respectively As these modes are IR active, they can be

observed in the reflectivity measurement for light

measurement.11The following lines were reported in Ref.10

共TO phonons兲: 215, 340, and 660 cm−1共B 2u兲, 260, 410, 460, and 580 cm−1 共B 1u and B 3u兲 The additional structures were found at 350 and 540 cm−1 and were ascribed as the B 1u

-and B 3u-mode phonons in Ref.11 Most of these peaks are reproduced in Fig.2共lower part兲

III DEFINITION OF CLUSTER MODELS AND OTHER SETTINGS

For the purpose of classification of all the vibrational

states, we performed the ab initio study on the model cluster

illustrated in Fig 1共b兲 with the GAUSSIAN 2003 software.17 This is a medium sized layer model stacking one Cu–O layer between the other two Ca–O layers One of the difficulties with the cluster model, besides the usual convergence prob-lems and vast computational costs, is that the symmetry of the local models is not the same as that of the real com-pound This introduces several additional model-specific lines into the output spectra Those “phantom lines” can be partly identified by investigating various models of different

FIG 2 The Raman scattering spectra 共upper兲 and the FTIR transmission

spectra 共lower兲 of the pure Ca 2 CuO3 The Raman lines selected for listing in

Table I are denoted by the arrows The data for the graphs were taken from

Ref 13 with the permission from those authors.

093524-2 Hoang, Nguyen, and Nguyen J Appl Phys 103, 093524共2008兲

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shapes and sizes, but they cannot be avoided in principle Six

different clusters were involved in the calculation:共1兲

Start-ing from the Ca4Cu2O8cluster by adding a unit Ca2Cu2O6to

form the twofold and threefold structures Ca6Cu4O14 and

Ca18Cu8O28 关Fig.1共b兲兴 by adding a unit Ca6Cu4O12 to form

the ninefold and twelvefold structures Ca24Cu12O40 and

Ca30Cu16O52 The largest cluster contains 938 basis functions

关molecular orbitals 共MOs兲兴 for the UHF/STO-3G setting

共746 paired electron occupied MOs and 192 unoccupied

MOs兲 It is reasonable that the higher level theories can be

used for the smaller clusters, such as the density functional

theory with some larger basis sets However, for the larger

clusters 共sixfold and above兲, the calculation was performed

method with the unrestricted spin model共UHF兲 on the 3-21G

wave function basis set The more compact restricted spin

HF model共RHF兲 was successful in the so-called single point

energy calculation 共integral accuracy reduced to 10−5兲 but usually failed in the second derivatives calculation共when the integral accuracy increased to 10−8兲 For the smaller clusters, the stability tests showed that there was a transition from the RHF to UHF, i.e., the UHF wave functions usually provided the lower energy minimum With the increase in cluster size, there was a considerable difference in the output spectra when the smaller STO-3G set was substituted for the 3-21G set However, the difference was not large if the 6-31G set replaced the 3-21G set It is preferably to chose the larger sets but for the relatively large sizes of the studied clusters, the 3-21G set provided optimal computational efficiency at the present time Larger settings, e.g., the DFT/6-31G re-quired an extra amount of storage which exceeded the 4 GB limit for the file size in most file systems The frequency computation was accomplished with the Mulliken charge analysis and the thermochemistry analysis for the vibrational states

TABLE I The Raman and IR frequencies 共cm −1 兲 for Ca 2 CuO3 Comparisons are given to the pure Ca2CuO3 共Ref 11 兲, the Sr-doped Ca 2 CuO3共Refs 10 and 11 兲 and to the theoretical values obtained by the lattice dynamic calculation 共Refs 11 兲 and the tight-binding approach 共Ref 14 兲 For the Raman-forbidden lines, the values presented in parentheses correspond to the additional features visible in Fig 4 in Ref 10 but not reported by its authors.

Optical phonons in Ca2CuO3 Assignment

共BV=breathing vibration兲

Refs 10 and 11 This work Ref 10 Ref 11 Ref 13 Ref 11 Ref 14 This work

A g-mode phonons 共Raman active兲共c axis兲

B 2u-mode phonons共IR active兲共b axis兲

B 1u - and B 3u-mode phonons共IR active兲共c and a axes兲

Cu共B 1u兲 Cu, Ca 储a + BV 共B 1u兲 260 278 272 291 265

O共1兲, O共2兲共B 3u兲 O 共2兲,O共1兲储a 共B 3u兲 350 354 350 337 351

O共1兲共B 1u兲 O 共1兲储c 共B 1u兲 410 412 415 400 410

O共2兲共B 3u兲 O 共1兲储a 共B 3u兲 460 457 453 424 450 457

O共2兲共B 1u兲 O 共2兲储c 共B 1u兲 540 530 532 548

The Raman-forbidden lines

? O 共2兲储a + BV 共200兲 203 200 211

Cu O 共2兲储a + Ca 僆共b,c兲 235 231

T-point O共2兲 O 共1兲储c + BV 440 430 419 440 235+ 235 O 共1兲储c + O共2兲储b + BV 共470兲 472 467 461

O 共1兲, O共2兲 O 共1兲储a + O 共2兲僆共a,b兲 500 505 512

? O 共2兲储b + CuO? 共640兲 630

Two phonon 500+ 500 or CaO? 共1000兲

Three phonon 440+ 440+ 440 1330 1337 Two phonon 690+ 690 共1390兲

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IV PHONONS FROM THE AB INITIO CALCULATION

Excluding the vibrations that are specifically associated

with the atoms lying at the cluster boundary, the final

calcu-lated Raman and IR spectra are shown in Fig.3 These

spec-tra belong to the medium sized cluster Ca18Cu8O28

From the analysis of simulated vibrational states three

corre-spond to the vibration of Cu, O共1兲, and O共2兲 along b axis

These lines have been assigned in Ref 10 to the same atoms,

however, the ab initio results show some slight movement of

Ca with the 210 cm−1 line The B 3uphonon at 351 and the

B 1uphonons at 548 and 589 cm−1 associate with the

vibra-tion of O共2兲 along axis a and c respectively The O共1兲 atoms

also participate in the 351 line The assignment here is again

the same as in Ref.10 The other B 1uphonon at 410 cm−1

and B 3uphonon at 457 cm−1originate in the moving of O共1兲

along c or a In Refs.10and11, the O共2兲 movement along

axis a has been assigned to the 457 cm−1line The rest peak,

i.e., the B 1u phonon seen at 265 cm−1, follows from the

breathing vibration involving both Cu and Ca transition

along axis a This peak has been considered as resulting from

the sole movement of Cu in the previous studies.10,11

phonons 306 and 528 cm−1are the same as in Ref.10 These

phonons are caused by the moving of the Ca and O共1兲 along

axis c in nearly static host lattice.

Among the Raman-forbidden lines that were considered

as the overtones in the previous studies,10,11the peaks at 211,

O共2兲 along axis a 共288 line兲 plus the breathing vibration

共211兲 or the movement of Ca in 共b,c兲 plane 共231兲 The peaks

440 and 461 cm−1originate from the vibration of O共1兲 along

c 共440兲 plus O共2兲 along b 共461兲 The shift at 512 cm−1

关ob-served also in the Sr-doped Ca2CuO3 共Refs 10 and11兲兴 is

due to the displacement of both O共1兲 along axis a and O共2兲

in共a,b兲 plane The sole O共2兲 stretching motion along axis b

is responsible for the 630 cm−1forbidden line The

illustra-tion is given in Fig.4for the 211 and 512 cm−1 lines

It is worth noting that in Ca2CuO3, the Cu–O共2兲 bands showed the lower frequencies in comparison with the Cu–O

632 cm−1 This agrees with the smaller force constant for the Cu-O bonding in Ca2CuO3, which is partly demonstrated by the longer average bond distance, 1.889 Å in Ca2CuO3 ver-sus 1.875 Å in CuO From the charge analysis, the valence distributed within the Cu–O bonds in the pure CuO is also a little higher than in the Ca2CuO3

For the shifts associated with the Ca–O bands, two lines

peak is suggested as the two phonon scattering from the

500 cm−1 line, there is no reason to exclude it from being considered as originating from the impure CaO

For the Raman shifts which correspond to the vibration

of the Cu, the ab initio results showed that there was no

simple vibration of Cu in the static host lattice All vibrations involving the Cu atoms are mainly the collective lattice vi-brations in which the O共2兲 atoms participate 共e.g., the

211 cm−1line兲 This observation agrees well with the struc-tural analysis of rigidity of the Cu–O共2兲 bonds 共axis b兲

cou-pling of phonons in the 1D Cu–O共2兲 chain with electron-hole pairs created during excitation by light.10,14Such coupling is

a very typical phenomenon in the superconducting cuprates The doping in Ca2CuO3seems to have only a little effect on

Sr-doped10,11and U-doped13兲 did not show any new features

FIG 3 The simulated IR and Raman spectra for the Ca18Cu8O28cluster as

obtained from the ab initio calculation using the unrestricted spin HF SCF

model with 3-21G basis set.

FIG 4.共Color online兲 Two phases of the O共2兲 vibration along axis a in the

forbidden 211 cm −1 Raman shift 共a兲 and the phases of the O共1兲 parallel

movement along a together with the O 共2兲 stretching motion in 共a,b兲 plane

in 512 cm −1 shift 共b兲.

093524-4 Hoang, Nguyen, and Nguyen J Appl Phys 103, 093524共2008兲

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V CONCLUSION

From the analysis given, the Cu–O共2兲 bands in Ca2CuO3

are strongly coupled with the collective lattice breathing

vi-brations while most of the rest of the phonons originates

from the sole vibrations of the oxygen in nearly static host

lattice For more accurate results, the density functional

theory calculation should be involved with some larger basis

sets such as the 6-31G Considering computational costs at

the present time, we leave this for the future

ACKNOWLEDGMENTS

The authors would like to thank Project Nos QG-07-02

共Vietnam National Univeristy兲 and DTCB 405 506 共Ministry

of Science and Technology, Vietnam兲 for the financial

sup-ports

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