Specific heat and electron spin resonance of ErxLa1−xBe13

SPECIFIC HEAT A N D E L E C T R O N SPIN R E S O N A N C E OF ErxLa l_xBen3

H. W. M. VAN D E R L I N D E N , G. J. N I E U W E N H U Y S , H. D. D O K T E R Kamerlingh Onnes Laboratorium der Rijks-Universiteit, Leiden, The Netherlands

D. D A V I D O V and I. F E L N E R The Racah Institute of Physics, Hebrew University, Jerusalem, Israel

We have measured the specific heat and the ESR of ErxLa I xBet3 (x = 0, 0.04, 0.05, 0.06, 0.08, 0.09) in a temperature range 1.3 < T < 12 K. We describe the results with the L e a - L e a s k - W o l f crystalline electric field (CEF) Hamiltonian. The C E F groundstate was determined to be F7, with a I~ ~) first excited state at (10.2 _+ 0.4) K, a n d an overall splitting of (48 +_ 4) K.

Er in ErBel3 or diluted in LaBel3 experiences a cubic crystalline electric field which, due to the nearly spherical surrounding of 24 Be atoms has rather small gradients. F r o m E P R and susceptibility [ 1, 2] the groundstate is found to be a F 7, while a F s state at about l0 K separation is suggested. In order to determine the energy level scheme more accurately we have measured the specific heat of ErxLa~_xBel3, and extended our ESR measurements by analyzing the ESR signal intensity. We measured the specific heat of Er~Lal_xBel3 (x -- 0, 0.04, 0.05, 0.09) in zero magnetic field and also for x = 0.04 in a field of 1 T in the temperature range 1.3 < T < 12 K. The heat contact was made by electrolytically plating the sample with a thin layer of copper on which the copper bodies of the heater and thermometer were pressed. We use low percentages of Er diluted in LaBel3 to avoid a possible contribution of direct Er spin-spin interactions to the specific heat. In view of the simple cubic coordination of the rare earth atoms their interactions may play a role for the x = 0.09 sample, although its magnetic specific scales with the results of the lower concentrated samples. Therefore, attention will be focussed on the more dilute samples. The magnetic specific heat, AC, is defined as the total specific heat minus the specific heat of the non-magnetic LaBel3. Use of the coefficients V and fl for the electron and phonon contributions to the specific heat of LaBel3 as reported in literature [1] led to a magnetic specific heat that increased with increasing temperature and yielded an entropy content much larger than xR In (2J + 1) (with J = ~ for Er3+). In view of this result and after carefully checking the experimental procedures we were forced to conclude that the coefficients y and fl given in [1] are questionable and a new measure-

ment of LaBel3 was necessary. We could then describe the specific heat, C, of LaBel3 with C = y T + fiT 3, with y = ( l l __ 2) mJ mol - I K -2 and /3 = (0.16 _+ 0.04) m K mo1-1 K -4. In fig. l and fig. 2 AC of ErxLal_xBel3 (x = 0.04 and 0.05 respectively) is shown as a function of T. The results in zero external field have been analyzed through a computer diagonalization of the L e a - L e a s k - W o l f crystalline field Hamiltonian 0 6

by adjusting X and W in a least square procedure. The fit to our results yielded two sets parameters,

t,, C J~ 40C

,#

Illl

m -m

-a I \

i'

30C

~ p '

20C // 'OC ! ¢ i I

•

H

~;, <

i

• !t "" <~'~ ,

i

.

Fig. I. DifferenceAC of total specific heat and specific heat of the non-magnetic LaBel3 , versus T for Ero.04Lao.96Bem3 in zero magnetic field and in a magnetic field of 10 kG.

Journal of Magnetism and Magnetic Materials 15-18 (1980) 42-4z" ©North Holland

42

H. W. M. Van der Linden et a l . / Specific heat and E S R of E r x L a I _ x B e l 3 I

I

~ - -

~

l

T T T

I --

I

T~ IO

500

C rn../too

K)

43

Er'oc 5 Lao95 Be,?

Er'~ La 1 x B%3

2

100 "~ o x = 008

\

1

o × = o.o6

400 -

300

to:ooooo -

:

! 200 --

~

i 2

I

I 4

I

i

/ 1O 0 -

Fig. oe

N

/

/

I 2

l

l

t

l

4

_

~ 6

l

[ 8

i 10

_t 12 K

F i g . 2. A C v e r s u s T f o r Er0.05La0.95Be13 i n z e r o m a g n e t i c field.

X = 0 . 3 6 3 , W = 0 . 1 1 9 K and X = 0 . 3 1 8 , W = 0.099 K for the compounds with 4% and 5% Er, respectively. Both sets of parameters yield the energy level sequence to be F 7-- F O) 8 -- r (2) 8 -- F 6-- F (3) 8 with a F7-F(s l) splitting of (10.2 -4- 0.4) K and an overall splitting of (48 _+ 4) K. The specific heat of Er0.0n Lao.96Bet3 in an external field of l T was calculated by adding a Zeeman term gj/tBH- J to eq. (1) using the above sets of X and W values. These calculated curves are also shown in fig. 1. As can be seen, good agreement with the experiment is obtained. The above described CEF level scheme is consistent with ESR linewidth and g-value measurements [2]. Additional and independent information could be obtained by analyzing the ESR signal intensity. Generally, the intensity I of an ESR signal from the transition between states a and b is proportional to

Icc p(a)

-

Z

3. ESR

signal

I 6

I

l I I I 8 10 temper~tut~ (K)

intensity

of

b 12

k

I 14

I

c

/

16

Erxgat_xBe~3

(x =

0.05, 0.06, 0 . 0 8 ) a s a f u n c t i o n o f T.

H=0kG x =0.318 W= 0 . 0 9 9

....

I~

I' 0 : 0 T

2 L O

p(b) i(bl%p,,rtla)12.

(2)

Here, p(a) is the occupation probability of [a). For a system in thermodynamic equilibrium p(a) is prescribed by a Boltzmann factor, and the partition function z = 51, e x p ( i

where i runs over the (2J + I) CEF split levels.

~pert is the time-dependent perturbation Hamiltonian originating with the microwave field. The experimental signal intensity is proportional to the area A under a resonance absorption line. A has been deduced from the measured first derivative lines by taking the product of (AH) 2 and the peakto-peak distance, with consideration of a correction for the dispersive part. The ESR signal intensity of Er.,Lal_xBela (x = 0.05, 0.06, 0.08) as a function of T is shown in fig. 3. The solid lines in fig. 3 are fits to expression (2). As we were dealing with polycrystalline samples, some simplifications were made. Firstly, the matrix element in (2) was assumed to be independent of the direction of the magnetic field with respect to the crystalline axis. Secondly, Z was calculated with the level scheme as obtained from the specific heat measurements, neglecting the Zeeman splittings of all the levels other than the I" 7 ground doublet. Actually, in the temperature range of the measurements the fitting was only sensitive to the value of the FT-F(gl) energy separation, A 1. We found 8 < A1/k B < 10 K. Computer calculations of (2) were performed to confirm the validity of the above simplified procedure. A total Hamiltonian, including a CEF and a Zeeman term was diagonalized for several orientations of the external field, to check the.importance of the anisotropy of the F 8 levels. The above X and W parameters were used. The resulting temperature dependence of the signal intensity coincides far within experimental error with the solid curves in fig. 3. For comparison, the signal intensity of a thermally isolated doublet is also shown in fig. 3 (dotted lines). The usefulness of the ESR signal intensity as a tool to investigate CEF effects is clearly illustrated

44

H. W. M. Van der Linden et a L / Specific heat and ESR of ErxLal_xBel3

by the data on Ero.osLao.92Be13. The ESR linewidth analysis of this compound is complicated due to the effect of direct Er spin-spin interactions, and can only be performed once the energy level scheme of the Er is known [2]. However, the ESR signal intensity depends only on the thermodynamical population of the levels, and will therefore, in a first order approximation, not be affected by interactions.

This work was supported by the Stichting voor Fundamenteel Onderzoek der Materie ( F O M TNO).

References [1] E. Bucher, J. P. Maita, G. W. Hull, R. C. Fulton and A. S. Cooper, Phys. Rev. BI 1 (1975) 440. [2] H. D. Dokter, D. Davidov, J. M. Bloch, I. Felner and D. Shaltiel, J. Magn. Magn. Mat. 7 (1978) 78.