Journal of Magnetism and Magnetic Materials 140-144 (1995) 1653-1654

~ i~ Journal of magnetism and magnetic

ELSEVIER , ~ materials

ESR on the quasi-one-dimensional Heisenberg antiferromagnet Tetraphenylverdazyl

Bernd Pilawa *

Physikalisches Institut, Universitiit Karlsruhe (TH), PO Box 6980, D-76128 Karlsruhe, Germany

Abstract 1,3,5,6-Tetraphenylverdazyl (Ph-TPV) is an organic quasi-one-dimensional Heisenberg antiferromagnet (HAF). The

intrachain exchange constant is Jld = --16 K and the N6el temperature Tr~ = 0.92 K. By ESR an analysis of the one-dimensional properties of Ph-TPV was carried out. No anomalies of the ESR line width and line shape were observed at high temperatures.

1. Introduction

1,3,5,6-Tetraphenylverdazyl (Ph-TPV) is a new organic radical, which is obtained from the well known radical 1,3,5-Triphenylverdazyl (TPV) [1,2] by adding one addi- tional phenyl ring. Crystalline Ph-TPV (space group Pnma [3]) attracted our interest because of its excellent one-di- mensional magnetic properties. The antiferromagnetic ex- change along the crystallographic a-direction (Jld = --16 ___ 1 K) is roughly three times stronger than that of the related compound TPV (Jld = --4.7 K) [4]. By specific heat measurements the N6el temperature Trq = 0.92 K was determined [5]. The ratio of TN/2 I Jld i S(S + 1), which often is used to classify one-dimensional magnets, is even smaller for Ph-TPV than for inorganic one-dimensional spin S = 1 / 2 HAF (e.g. Ph-TPV, 0.036; C u ( N n 3 ) 4 S O 4 •

H20, 0.091; CuC12.2NCsHs, 0.056 [6]). By means of ESR at 9.47 GHz the correlation of the molecular spins was studied. The following results were obtained.

2. Intensity of the ESR signal

Fig. 1 shows the intensity of the observed ESR signal. According to the fluctuation-dissipation theorem foX"(to) d to should be proportional to the static magnetic susceptibility [7]. The experimental results obtained for a magnetic field applied parallel and perpendicular to the direction of the magnetic chains are compared in Fig. 1 with numerically calculated susceptibilities of spin S = 1 / 2 chains with periodic boundary conditions of 8 and 9 spins, respectively [8]. The ESR intensity is normalised at 200 K

* Fax: +49 721/608/6103; email: pilawa@pimajestix. physik.uni-karlsruhe.de.

0 I I ~ J I i I I I I I I I I

0 100 200 300 T (K)

Fig. 1. Intensity of the ESR absorption signal (full dots: H II a; open dots: H _1_ a) compared with the calculated static magnetic susceptibility of closed chains of N = 8 and 9 spins, respectively. The experimental susceptibility was normalized at 200 K to the calculated Curie-Weiss susceptibility for 0 = - 16 K.

to the value of the Curie-Weiss susceptibility with 0 = - 1 6 K. Experiment and theory agree down to 20 K. At lower temperatures the calculation fails, due to the small number of included spins. At T = 0 K, however, the extrapolated value of the measured intensity corresponds well to the prediction of Bonner and Fisher [8]: x ( T = 0 K) = O.05066NA(gtxa)2/IJ]dl = 4.75 × 10 -3 emu/mol . This observation, together with the fact that no difference between the static magnetic susceptibilities X II and X ± could be detected, indicates that the magnetic properties of Ph-TPV can be very well approximated by the isotropic Heisenberg exchange Hamiltonian.

3. Shift of the magnetic resonance field

The magnetic resonance field depends on the direction along which the field is applied. At room temperature the

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1654 B. Pilawa /Journal of Magnetism and Magnetic Materials 140-144 (1995) 1653-1654

difference between the magnetic field applied either paral- lel or perpendicular to the chain direction is 1.81 Oe. When the temperature is reduced this difference decreases to 0.33 Oe at 4.5 K. In order to account for this result, three contributions have to be considered. First, there is a small static anisotropy in g of the Ph-TPV molecule (e.g. due to spin-orbit interaction): (g II - g ±)/g = (1.16 _+ 0.08) X 10 -3. The shift is caused by the demagnetisation due to the non-spherical sample shape and also by a small anisotropy of the static magnetic susceptibility [9]:

HII-H± ( g ± - g l , x(N±-NI,)3XII-X-----------~x) H g 2 X '

(1)

where H, g, and X denote the mean values. With Nil = 0 and N± = 2"rr, for a needle-shaped crystal, one finds at temperatures above 50 K, that there is no anisotropy of X. Below that temperature XI I - X ± increases. At 4.5 K its value is (1.26 __. 0.1) × 10 -6 emu/mol. The error accounts for the uncertainty of the demagnetisation factors.

4. Line shape and line width

At all temperatures and all directions of the applied magnetic field a Lorentzian ESR line shape has been observed. The line width is 0 .90e (peak to peak) at room temperature and increases drastically below 15 K (see inset of Fig. 2). The width of exchange narrowed lines is

1 F(r ) dT

8h2kn T xT

The integral can be approximated by [7]:

a -~o ~ (~+ ('r)S"++ ~(r)$7(0)$7+ 1(0)) dz. (3) t,J

Fig. 2 shows the experimentally obtained temperature vari- ation of f~_ ~F(~-) d~" ct A HT x. The experiment agrees well with the numerically obtained temperature dependence of f~_~F(~') dr below 200 K. The calculation is carried out for independent chains with periodic boundary conditions of 8 and 9 spins, respectively.

Although the static magnetic susceptibility determined by ESR, the shift of the ESR line and the temperature-de- pendent variation of the ESR line width confirm that

1.2

0 8

~ 0 .4 - - l a l " "

. . o - - ( b ) 0 .8 . . . . . . . . . .

100 200 T (K )

0.0 100 200 300

T (K)

Fig. 2. Temperature dependence of AHT X (dots) compared with J+_~F('r) d~" calculated for closed chains of 8 spins (a) and 9 spins (b), respectively. All values are normalised to one at 200 K. Inset: line width (peak to peak).

Ph-TPV is a quasi-one-dimensional HAF, none of the anomalies of the ESR line shape and line width typical of one-dimensional HAFs have been observed. This shows that the interchain exchange interaction, although approxi- mately 300 times smaller than the intrachain exchange, is strong enough to prevent one-dimensional properties of the spin dynamic at high temperatures.

Acknowledgements: I am grateful to H. Benner, J.P. Boucher, E. Dormann, H. von L6hneysen and H. Winter for stimulating discussions and H. Naarmann for preparing the samples. This work was financially supported by the Bundesministerium fiir Forschung und Technologic as part of the project 03M4067-6.

References

[1] R. Kuhn and H. Trischmann, Angew. Chem. 75 (1963) 294. [2] R. Kuhn and H. Trischmann, Monatsh. Chem. 95 (1964) 457. [3] E. Dormann, H. Winter, W. Dyakonow, B. Gotschy, A. Lang,

H. Naarmann, B. Pilawa, N. Walker, Ber. Bunsenges. Phys. Chem. 96 (1992) 922.

[4] E. Dormann, W. Dyakonow, B. Gotschy, A. Lang, H. Naar- mann, B. Pilawa, N. Walker and H. Winter, Synth. Metals 55-57 (1993) 3273.

[5] B. Pilawa and U. Pietrus, to be published. [6] M.J. Hennessy, C.D. McElwee and P.M. Richards, Phys. Rev.

B7 (1973) 930. [7] M.J. Hennessy and P.M. Richards, Phys. Rev. B7 (1973)

4084. [8] J.C. Bonner and M.E. Fisher, Phys. Rev. 135 (1964) A640. [9] J.P. Boucher, J. Magn. Magn. Mater. 15-18 (1980) 687.