~ Solid State Communications, Vol.46,No.], pp.33-35, |983. OO38-IO98/83/]3OO33-O3503.OO/O Printed in Great Britain. Pergamon Press Ltd.

LOW TEMPERATURE THERMOELECTRIC POWER OF LaBs, PrBs and NdBs

Naushad All and S.B. Woods

Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2Jl

(Received by M. F. Collins, December 24, 1982)

We have measured the thermoelectric power of LaBs, PrBs and NdBs in the temperature range 2-20K. PrBs and NdB6 order antiferromagnetlcally at T N = 6.99K and 7.74K respectively, whereas LaBs is non-magnetlc. The thermoelectric power data have a negative maximum near 5.5K in all three hexaborldes. This negative peak is thought to be mainly due to phonon drag in LaBs. In PrBs and NdB s there is an additional contribution due to magnon drag. It is expected that the high temperature thermoelectric power is mainly due to an electron diffusion term and a contribution due to spin disorder scattering. The thermoelectric power and the resisti- vity have been compared in the vicinity of T N. A qualitative similarity in the temperature derivatives of these two quantities has been found for PrB6 and NdB6 near T N.

Recently there has been considerable interest in understanding the magnetic and transport properties of rare-earth hexaboride (REB6) compounds. The magnetic properties of REBs vary from the dense Kondo behaviour of CeB6 through antiferromagnetic PrBs, NdBs, GdBs and DyBs to the mixed valence SmBs. The REBs compounds have a cubic crystal structure of the CsCI type with a rare-earth ion at each corner of the cube and a boron octahedron at the body centre. I The trlvalent REBs compounds are believed to be monovalent metals from Fermi surface information and band structure calcula- tions. 2

Lanthanum hexaboride is non-magnetic, and becomes superconducting below ~ 2K, while PrBs and NdBs order antiferromagnetlcally at N~el temperatures T N = 6.99K and 7.74K respectively. 3 A recent neutron diffraction study ~ shows two low temperature phase transitions in PrBs at 6.9K and 4.2K. Below 6.9K a phase that is incommensurate with the X-ray lattice appears and a second commensurate phase appears at ~ 4.2K co-exlsting with the incommensurate phase. At lower temperatures only the commen- surate phase remains. Only a commensurate antiferromagnetic phase has been found in NdBs. s

The thermoelectric power of a magnetic metal can he written:

S = S + S + S (1) e g m

where S e is the thermoelectric power due to electron diffusion, Sg is the phonon drag contribution and S m is the contribution due to magnon drag. At low temperatures phonon and magnon drag can make significant contributions. Theoretical studies of the phonon drag s'7 contribution to the thermoelectric power find it to vary as T 3, that is, it is proportional to the lattice specific heat. The sign of Sg can be negative or positive depending on whether the electron-phonon interaction is predominantly of normal or Umklapp character. The magnon drag contribution S m has the same temperature dependence s as Sg. Hence it is

obvious that the different contributions to S are very difficult to separate. At higher temperatures the electron diffusion contribution is expected to dominate. At the same time there will be a thermoelectric power Ss_ d due to spin-

P disorder scattering above the magnetic transi- tion temperature. 9 To our knowledge there has not been a theoretical calculation for Ssp d.

However, Gratz 9 has been able to show empirically for GdCu, GdNi and GdAI2 that • .S spd is linear in temperature with the sign Delng negative for some materials and positive for others.

Now we turn our attention to the thermo- electrle power near the N~el (or critical) temperature. Recent theoretical studies I° have shown for ferromagnetic (F) and antiferromag- netic (AF) metals that the temperature deriva- tive of the resistivity has the same temperature dependence as that of the magnetic specific heat (Cm) • i.e.

d_~= C = t -~ dt m (2)

in the vicinity of T N (or T C), where u is the critical index and t = I(T-TN)/TNI or I(T-Tc)/TcI. From eq. (2) one expects a sharp maximum in dp/dt at T N or (Tc). Such a behaviour has been found for a number of F and AFmaterials. It has also been shown theoretically 11 that

dS dp d-T ~ d-~ ~ Cm (3)

for F and AF metals and there is some experi- mental evidence for such behaviour. 12

Single crystals of NdBs and PrB6 were grown by a floating zone method. Polycrystalline LaB6 was made by melting LaBs powder. The electrical resistance was measured using a con- ventional four terminal method with a current of 20mA and a detection sensitivity of I0 -s volts. The thermoelectric voltage was measured using a potentiometer and a galvanometer ampli- fier with a sensitivity of ~ 2x10 -9 volts. The

33

34 LOW TEMPERATURE THERMOELECTRIC

temperature difference across the sample was measured using a calibrated AuFe thermocouple. The thermoelectric power of the leads was obtained using V3Ga (superconducting transition at ~ 17K) and lead (Pb) as specimens. This enabled us to find the absolute thermoelectric power of our specimens.

The thermoelectric powers of LAB6, PrB6 and NdB s are shown in Fig. I as a function of temperature. The thermoelectric power of non- magnetic LaB6 has a negative maximum at ~ 5.5K.

0.6

04

02

0

-02

S -0.4 ~v

De0.-o.6

-0.8

-10

-12

-14

-1.6

0

I I I I I 1 I I I 4 ,

z~

8 ~ P r B 6 [ 1 1 0 ]

8 % A o %0

~... t,,~.~ oO o o = "',,~. o A ~ 4 A °Oooo

~aA~,,~A~ az, LaB6 Ooo

~. oo o ~ ° o

\ \ J ,, s. . t

.%

; • %

% . , . . , , " •

m• I e

I I I I I I ] / I 2 4 6 8 10 12 14 16 18

T(K)

Fig. i. Absolute thermoelectric power (S) of LAB6, PrB6 and NdB6 as a function of temperature (T).

It remains negative up to ~ 12K above which it becomes increasingly positive. The electron diffusion term which is present at all tempera- tures and becomes linear in T for T ~ eD, where e D is the Debye temperature, is believed to be dominant at high temperatures. At sufficiently low temperatures S e is very small and once again becomes linear in T. It is probable that most of the thermoelectric power below 10K, particularly in the very non-linear region is due to the phonon drag contribution (Sg). Normal electron-phonon scattering processes at the lowest temperatures would give a negative Sg proportional to T 3 while above 5.5 K, as UNklapp processes become dominant, after an initial increase of an approximately exponential nature Sg should once again show a T 3 dependence but now with a positive sign. The competing effects of these contributions to the thermo- electric power would then produce the negative peak that is observed at 5.5K.

First we note that LAB6, PrB6 and NdB6 are iso-structural compounds with lattice dimensions, a o = 4.153 A °, 4.133A ° and 4.126 ° respectively and specific heat measurements 13'I~ have been interpreted in terms of the non-magnetic lattice

POWER OF LAB6, PrB 6 and NdB 6 Vol. 46, No. ]

specific heat being the same for each at low temperatures. The negative peak in the thermo- electric power at ~ 5.5K is -0.28 ~V/deg in height for LaB6 whereas it is -0.55 DV/deg for PrB6 and -1.15 ~V/deg for NdB6. It is reason- able to assume that the phonon drag contribution to the peak is nearly the same in each compound and the increased height in PrB6 and NdB6 is due to magnon drag. These two contributions to S have the same temperature dependence when considered separately but when both are present the situation may be more complicated. In the temperature region just below the N~el tempera- ture the electrical resistivity of PrB6 and NdB6, which is shown in Fig. 2 and is discussed at more length by Ali and Woods, 3 varies as T 4 and is attributed to electron-spin wave scatter- ing. The details of the spin wave spectra are still unknown and because of the cross- interactions eq. (i) may not be a good approxi- mation here.

90

85

30

0

0

o 20 x

I i i

LaB6

L PrB6[110] i ~ NdB61110]

Y - - o o o o

/ %

Y I 5

i i

/

P o °l~9~p PrB61110 ]

T(K)

I ] 10 ~5

T(K)

lo o

40

3O

20

10

20

Fig. 2. Normalized resistance (r = Rx/Rs), where R x is specimen resistance and R S = 0.1~, as a function of tempera- ture (T) for LAB6, PrB6 and NdB6. The insert is a magnified curve for

the normalized resistance of PrB6 in the temperature range 3-5K.

There is a sharp increase in the thermo- electric power near the N~el temperatures

6.9K and ~ 7.7K for PrB6 and NdB6 respectively. Similar behaviour is found in the resistivity data in Fig. 2 and PrB6 and NdB6. Above T N the thermoelectric power decreases monotonically with temperature. Well above T N a linear contribution to S is expected due to spin disorder scattering (Sspd) along with the elec- tron diffusion term. A quantitative analysis of the temperature derivative of S and r (resistance) in the vicinity of T N (Fig. 3) shows that a linear relationship between dS/dT

o

Vol. 46, No. !

13!

1.0

S'

K2

0.5

o 5o"

o ' , - 25 x

LOW TEMPERATURE THERMOELECTRIC

~u u

f:. m ,

I ,

i i

e.@.o_~ j_.o-- 4"/

PrB6[1 1 O] ~ . . e . . . . e . . . o . o . o _ ,. °

:÷

o .

:4 ?:

j o ooo oooooooo°O i

~ oo ooOooo oo

I I I 6 7 8

T(K)

Fig. 3. The temperature derivative of the resistance (r') and thermoelectric power (S') as a function of tempera- ture (T) for PrB6.

REFERENCES

I. V.I. Matkovich (ed.), Boron and Refractory Borides (Springer Berlin, 1977), Chapters III, IX and XV.

2. Y. Ishizawa, T. Tanaka, E. Banni and S. Kawal, J. Phys. Soc. Japan 42, 112 (1977).

3. N. Ali and S.B. Woods, J. Appl. Phys. 53, 7905 (1982).

4. C.M. McCarthy, C.W. Tompson, R.J. Graves, H.W. White, Z. Fisk and H.R. Ott, Solid State Commun. 36, 861 (1980).

5. C.M. McCarthy and C.W. Tompson, J. Phys. Chem. Solids 41, 1319 (1980).

6. A.M. Gu~nault, J. Phys. F ~, 373 (1971). 7. M. Bailyn, Phys. Rev. 157, 480 (1967). 8. M. Bailyn, Phys. Rev. 126, 2040 (1962). 9. E. Gratz, J. Magn. Magn. Mater. 24, 1-6

(1981). i0. M.E. Fisher and J.S. Langer, Phys. Rev.

Lett. 20, 660 (1968), T.G. Richard and

POWER OF LAB6, PrB 6 and NdB 6 35

and dr/dT exists. This is in accordance with the recent theoretical calculations, 11 that all transport properties have the same temperature dependence near the critical temperature.

At ~ 3.5K we observe a positive contrlbu- tion to the thermoelectric power in PrBs which is associated with the appearance of the low temperature commensurate phase. The resistivity data in Fig. 2 show a thermal hysteresis associated with this phase.

Acknowledgements: The authors are thankful to Dr. T. Kamatsubara for providing the samples, and the technical assistance of Mr. T. Vallan is gratefully acknowledged. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.

D.J.W. Geldart, Phys. Rev. B 15, 1502 (1977), D.J.W. Geldart and T.G. Richard, Phys. Rev. B 12, 5175 (1975) and S.A. Alexander, J.S. Helman and I. Balberg, Phys. Rev. B 13, 304 (1976).

ii. M. Ausloos, Solid State Commun. 21, 373 (1977).

12. J.B. Souse, R.P. Pinto, M.M. Amado, J.M. Moreira, M.E. Braga, P. Morin and M. Ausloos, J. Phys. F i0, 1809 (1980), J.B. Sousa, R.P. Pinto, M.M. Amado, J.M. Moreira and M.E. Braga, Solid State Commun. 31, 209 (1979).

13. K.N. Lee, R. Bachmann, T.H. Beballe and J.P. Maita, Phys. Rev. B 2, 4580 (1970).

14. E.F. Westrum, J.R., H.L. Clever and G. Feick, Rare Earth Research (edited by L. Eyring), p. 597, vol. III, Gordon and Breach, New York (1966).