Magnetic, transport, and thermal properties of ferromagnetic EuB 6

Magnetic rneasuremcnts on Al-Ou„ grown EuB 6 crystals show that this material orders ferromagnetically with a transition temperature Tc = 13.7 K. The effective moment derive<I rrom paramagnetic susceptibility measurements gives J.l.c« = 7.76 µ 8, and the saturation magnetization extrapolated to 0 K is within 10% of the theoretical value of 7 µ 8 expected for Eu+ 2• The magnetic order, however, cannot be that or a simple colinear ferromagnet because the magnetic specific heat in zero applied magnetic field shows a broad maximum centered about 9 K rather than the expected 1.-like anomaly at 13.7 K. Finally, transport measurements suggest that EuB 6 is an intrinsic semimental.


INTRODUCTION
EuB 6 is a cubic material crysta 0 1lizing in a structure which may be regarded as a CsCl-type array of Eu atoms and 8 6 octahedra.
Recently. lsikawa et a l. ( 1) have reported measurements on EuBI> single crystals prepared by flou-zontng. These measurements indicated that EuB 6 is scmi-metallic, contains some Eu+ 3 and becomes antiferrom agnetic with T N = 5-6 K . A recent investiga· tion of carbon substituted Eu B 6 indicates, howeve r, chat both the lattice constant and ehe paramagnetic Curie temperature diminish smoothly with increasing carbon content [2), that the order c hanges from ferro 10 antiferromagnetic [31. and that the Eu is divalent throughout the series; Kasaya, et al. [2] suggest that the earlier finding o f an tiferromagnetism f l] may be due to carbon con1amination. Sincc it has long been believed that EuB 6 is a semi· conductor which orders fcrromagnetically 14] (T, = 8 K ) and contains only Eu+ 2 [5,61. we feit it worthwhile to check these results o n crystals prepared by grow th from molten Al. We present our findings below. along with a few cornparative measurement~ on crystals grown from molten Eu metal.

C RYSTAL GROWTH AN D LATTICE PARAMETER
Most of our measurements were made on crystals precipita ted from molten Al [7J. 1.49 g of 99.9% Research Chemical Eu (this is excess Eu) and 0.282 g of 99.9995% Eagle-Picher B were placed in a recrystallized covcred alumina crucible along with 71.1 g of 99. 999% Al bar. This crucible was placed in a vertical tube furnact: through which an argon flow was maintained. Tbe load was soaked at 1450°C for 12 hrs .• followed by a cool-down at 6°C/hr to 670°C. The crystals were then separated by dissolving the Al in hot NaOH sol ution.
Smalh:r crystals were also grown by heating boron in excess Eu s ealed in a Ta tube to 1550°C for 10 minutes in an induction coil. The crystals were then separated by leaching in HCI.
The lattice parameter of ou r Al -grown material was found to be a 0 -4 . 1850 ± .0003 A; for an Eu-growo c rystal, a 0 ~ 4. 183 8 ± .0003 Ä. The detailcd study of Etoumcau, e t al. [8) showed that ThB 6 has a considerable rangc of stoichiometry corresponding to variable Th vacancics, and that the vacancies are larger than the occupied Th sites. We thcrefore infer from our Jattice parameter measurements that the Al-grown material is Eu-deficient. This conclus1on is based on the assumption that our Eu-grown material is stoichiomctric. as its method of preparauon would seem to favor .
A rough interpo!ation from the results of Ref. 8 suggests as much as 10% Eu vacancies in the Al -grown material, a va lue which is consistcnt with estimates presented below.

HAL L EFFECT AN O ELECTRICAL RESISTIVITY
Hall e ffect measurements at both room temperature and 77 K gave the sa me negative Hall constant for the Al-grown crystals. which c orresponded to between 3.7 x 10 1 9 Figure 1 shows the electrical resistivity for a typical Al-grown crystal in the temperature range below 220 K. The average room temperature resistivity for some 10 samples is approximately 700 µ!!-cm . A minimum at -30 K suggests the onset of short range magnetic order, followed by long range ordering at 14 K. The spin disorder term is approximately 300 µSl-cm [9] .
The fact that our room temperature electrical res1s11v1ty is some 7 times the value given in Ref. 1 is consistent with our carrier concentration being smaller by about this same factor of 7. However, tbere is no !arge spin disorder term below the ordering temperature for the float-zoned crystal, and its high residual resistivity (-100 µ!! -cm) is hard to understand.
The size of the lattice term at room temperature for our crystal is some 300 µ.ll-cm. This lattice term for LaB 6 is approximately 7 µ.fl -cm. This suggests about 2% carriers, which corresponds to -3 x 10 20 carriers/ cm 3 . A further estimate for the carrier concentration of Al-grown EuB 6 can be obtained from the magnitude of the spin disorder resistivity. This resistivity, on a free electron model, should vary as (g-1)2J(J+ 1 )/ z213, where Z is the number of conduction electrons per atom [ 1 O]. Utilizing our measured value for EuB 6 and the known magnitude of the spin disorder term in NdB 6 [I 1] leads to Z = 0.08 for our Al-grown sample.

MAGNETIC SUSCEPTrBILITY AND HEAT CAPACITY
Figures 2 and 3 sbow our susceptibility results for Al-grown crystals of EuB 6 . Tbc high temperature data (Fig. 2) can be fitted with a Curie-Weiss law, yielding an effective moment of 7.76 11 8 per Eu ion, assuming an exact EuB 6 composition; this value is 2.3% lower thao expected for stoicbiometric EuB 6 containing only Eu+ 2 . Assuming that the concentration of Eu+ 3 is negligible (see below), the low effective moment'corresponds to a formula Eu(n 7 Ho. l3B6. This 13 % Eu vacancy concentration for the AJ-grown material is consistent with, albeit higher than, our other estimates. However, the puzzle remains that the negative Hall constant suggests electrons as the carriers, whereas band structure considerations [ 12, 13] au poiot to vacancies as leading to hole carriers. The x(T) data below 70 K are plotted in Fig. 3; these data as well as saturation magnetization data obtained from Arrott plots (sec insert, Fig. 3) indicate that the Al-grown material orders ferromagnetically at 13. 7 K.  th.e accuracy of th.e latter measurements is limited by the 20% accuracy of the sample mass measurement.
Th.e total h.eat capacity between 1.4 and 26 K for the same 5.7 mg sample used in the low field susceptibility measurements is plotted in Fig. 4. The dashed line indicates our estimate of the lattice specific heat (8 0 "' 293 K). lt is immediately apparent that the magnetic specific heat anomaly (the difference between the dashed line and the data) does not correspond to the usual second· order transition. In fact, a broad maximum occurs al about 9 K, whereas Tc = 13.7 K. The magnetic order, therefore, cannot be that of a simple colinear ferromagnet. The magnetic entropy given up below 20 K is 17 .1 ± 1. 7 J/ mK, nearly the full value expected for Eu+ 2 and consistent with our estimates of the vacancy concentration.  We have not as yet performed a complete set of measurements on the Eu-grown EuB 6 • However, from ac-susceptibility measurements we find that the material orders ferromagnetically at 7 K. DISCUSSION R . L. Cohen l 14] has performed Mossbauer measurements on our Al-grown EuB~ crystals and found an extrt!mely clea n E u+ 2 spectrum. with less than 0.5 % Eu+ 3 possible. Therefore, the Eu+ 3 concentration appears to bc much smaller than our various estimates of the Eu vacancy conce ntration and will not be considered further in ou r discussion.
Thc important experimental points 10 be explai ned are t he following: (i) th e Hall effect indic.:ates elec.;1ron conduction whilc the band structure considerations point to hole conduc.:tion for Eu vac:ancies; (i i) the specifi c hcat anomaly is not that of a simple ferromagnet; and (iii) the magnetization does no1 sa1ura1e in 20 kOe at 4.2 K.
In regards to point (i). it seems like ly to us that EuH 1 , is a semi-me tal in which a s light band overlap produces the sma ll carrier conc.:en trat ion observed; an elect ron mobility higher than th e hole mobility would account for the negative sign of the Hall con-Stanl. Th e fact that our Al-grown material is off-stoichiometry does not alter this qualitative conclusion. In spite of the fact that the magnetic propenies indicate well behaved fe rromagneti c order, our thermal data shows that the order is more com plicated. This observation is consistent with earlier data obtaincd on polycrystal· linc samples r 1s1. The exchange mechanism and therefore the t ype of magnetic order are obviously very sensitive to carricr concentration 12. l 6, I 7 J and perhaps to th e rati o of e lectro n to hole conduction. None the less. the detailed nature of these mechanisms is not presently understood.
In conclusion. we have found for single c rysta l EuBh the occu· rence of ferromagnctism in contrast to the results of Ref. 1. although the thermal properties suggest that the ordcr is not colinear. We further conclude from ou r measurements that EuH 6 is an intrinsic semi-metal. in agreement with the hypothesis of lsikawa, et al.