Lattice effects on the dHvA oscillations and magnetic breakdown in quasi-two dimensional organic conductors

ELSEVIER

Lattice

Synthetic Metals 86 (1997) 22 19-2220

effects

on the dHvA oscillations and magnetic breakdown dimensional organic conductors

in quasi-two

P.S. Sandhu’ and J.S. Brooks2 1Physics Deparlment, Boston University, Boston MA 02215, USA 2 National

High Magnetic Field Laboratory,

Florida State University Tallahassee

FL 323 10, USA

Abstract We describe

a theoretical

approach

to investigate

the effect

of the lattice

potential

on the dHvA

oscillations

and

magnetic breakdown in quasi-two dimensional organic metals such as a-(BEDT_lTF)2KHg(SCN)4. We construct a tight binding Hamiltonian based on the extended Huckel approximation to describe these systems which can then be numerically solved to obtain the energy spectrum as a function of magnetic field. Results on the field dependence of the chemical potential and thermodynamic potential are presented. Key words: Organic conductors,

1.

magnetic

Introduction The quasi two dimensional

breakdown,

(2D) organic

chemical

metals of

the family a-(BEDT-TTF)2X form a unique class of materials with an interesting set of properties: they have simple Fermi surfaces (FS) and yield high quality quantum oscillations. These features make them ideal test systems to investigate novel aspects of electron dynamics in a metal. One puzzling feature of these materials is the behavior of magnetic breakdown which is inconsistent with semiclassical theories [1,2]. In addition to the fundamental frequency and the spectrum

a associated

with the closed pockets

magnetic breakdown frequency of these salts shows several

6, the dHvA combination

2.

Theoretical details Our aim is to understand the effect of the magnetic field on the realistic band structure obtained by the extended Huckel tight-binding approach. The relevant interactions in the model are between pairs of adjacent o3796779/97/%17.000

molecules in the 2D conducting (ac) plane of the crystal (Fig. 1). This leads to a tight binding model in which the hopping amplitudes between adjacent sites are determined by the transfer integrals calculated in the extended Huckel approximation. There are 7 different hopping amplitudes between sites denoted by cl, c2, c3 and pl, p2, p3, p4 corresponding to the 7 distinct transfer integrals in the extended f-luckel calculation [6].

I

I

1997 Ekevier Science S.A All rights reserved 10-2

I

.

in the FS,

frequencies such as 6 - a [3]. This frequency has previously been observed in transport measurements where it can be understood as arising from the so-called Stark interference effect [4]. However this interference effect is not expected to occur in the magnetization and hence the presence of additional difference frequencies in the dHvA spectrum is not clearly understood within the framework of the semi-classical theory . It is therefore important to calculate the magnetization of these systems in a fully quantummechanical approach [5] in order to determine the origin of the difference frequency and to possibly shed light on a new mechanism for magnetic breakdown. We construct a tightbinding Hamiltonian to describe this system based on the previously determined band structure [6] which is in good agreement with experiment. In this paper we focus on describing the steps involved in the calculation and argue that this provides a useful approach to understand the details of the magnetization behaviour in this material. We also present some results on the field-dependence of the chemical potential and thermodynamic potential.

PII SO3794779(96)048

potential

__

I i_

_

.:

.

‘I

kt:.{L

,-i,

??

I 1

,’ tg/&‘%

-

1

te.2 !

;I

I.

I T I

.

I T

!.,

I

I

IT .

I

i

Figure 1. A view of the unit cell in the ac conducting of the a-(BEDT_TTF)2KHg(SCN)4 molecule hopping amplitudes between different sites lattice. In a magnetic

field B, the Hamiltonian

I

TI

plane

showing the in the crystal

for a 2D lattice

is

given by H=rijC~c:cj(2xi~~.~)+H.c.] where tQ refers to G the hopping amplitudes beiween sites i and j [7]. Here the effect of the magnetic field is included by making the Peierls substitution where -A’=-B(y,O,O) is the vector potential chosen in the Landau gauge. The smallest plaquette in the unit cell is the triangle of area 0’ / 16 where a is the lattice constant and we define the flux through the plaquette as

2220

P.S. Sandhu. J.S. Brooks /Synthetic Metals 86 (1997 2219-2220

@= Ba2 / 16 in units of @c, the flux quantum.

Summing

up

all the terms in the above equation, calculating the phase factors corresponding to each and then transforming to Fourier space we obtain the k-space representation of the Hamiltonian as a 4q dimensional matrix for each value of q. determined by @I@, = p/q (where p,q are integers). The energy spectrum is then calculated for each value of the magnetic field by diagonalizing the Hamiltonian numerically.For each value of q, 4q eigenvalues are obtained:

All the calculations are done at a small but finite value of temperature close to T = 0, in order to achieve the physical requirement that the thermal broadening be smaller than the separation between magnetic subbands. The chemical potential and thermodynamic potential calculated using the above procedure are plotted in Fig.2 and Fig.3. A clear oscillatory behaviour of both these quantities is evident.

Ei , i = 1,2...4q which are automatically grouped into separate magnetic subbands. Knowing the energy spectrum, at each value of field, the corresponding thermodynamic quantities can be calculated. The chemical potential is obtained by inverting the equation subject k

that N,,

to the

constraint

i exp[P(4hPa)+l]

= ‘2x21 k

and $-=:. n-lax

i

12 2.0 20

iii' .= 5i +j s 3_

40

80~10-~

Magnetic Field (Q/B,) Figure 3.. Thermodynamic . _ magnetic field for 7- - 0.

1.5

potential

as a function

of

3.

I

80~10-~

Magnetic Field (wD,) Figure 2. Chemical field for T - 0.

potential

as a function

of magnetic

(Since there are 6 electrons per unit cell distributed among 4 bands, the total occupancy is 314th). Once the chemical potential is known it’s value can be inserted into the following equation to determine the thermodynamic potential at the same value of magnetic field:

Results and conclusions We have calculated the field-dependence of the chemical potential and thermodynamic potential for the system a-(BEDT-TTF)2KHg(SCN)4, based on its previously determined band-structure. From these quantities it is possible to calculate the magnetization of the system as a function of magnetic field. Analysis of the Fourier spectrum of the oscillatory magnetization is expected to yield valuable information about the magnetic breakdown behaviour. Work to understand these aspects of the problem is currently in progress. This work was supported under grant # NSF-DMR-95610247. We thank Ju Kim for valuable guidance. References [l] A. B. Pippard, Philos. Trans. R. Sot. A256, 317 (1964) [2]. L. M. Falicov and H. Stachoviak, Phys. Rev. 147, 505 (1966) [3] S. Uji et a/. (this conference) [4] D. Shoenberg, Magnetic Oscillations in Metals (Cambridge Univ. Press, 1984) [5] K. Machida et a/., Phys. Rev. B, 51, 8946 (1995), K. Kishigi et al., J. Phys. Sot. Jpn. 64, 3043 (1995) [6] C. E. Campos et a/.,Phys. Rev. B, 53, 12725 (1996) [7] Ju H. Kim and I. D. Vagner, Phys. Rev. 8, 48, 16564 (1993)