MULTIPLE PHASE-TRANSITIONS IN RARE-EARTH TETRABORIDES AT LOW-TEMPERATURE

Abstract We report the temperature dependence of the magnetic susceptibility of single crystals of PrB 4 , GdB 4 , TbB 4 , HoB 4 and TmB 4 , both parallel and perpendicular to the tetragonal c-axis. We also present low temperature resistance measurements on crytals of GdB 4 through TmB 4 . Two magnetic phase transitions are found for TbB 4 , DyB 4 , HoB 4 and TmB 4 . For the latter two compounds, the lower transitions appear to be first order. For HoB 4 , we have measured the low temperature specific heat. The lower transition in TbB 4 and HoB 4 is rapidly depressed upon dilution with YB 4 .


Introduction
All the rare earth elements, except Eu, form isostructural, metallic tetraborides (RB4) crystallizing in the tetragonal space group P4/ mbm.
There are four equivalent rare earth sites per unit cell with site symmetry ram.
Buschow 1 has reviewed the magnetic data on the tetraborldes.
Almost all of these data are for polycrystalline material.
For the heavy rare earth tetraborides, the Curie-Weiss temperatures (8) approximately follow the deGermes factor, but the ordering temperatures do not. The RB 4 compounds, NdB 4 through TmB 4, order antiferromagnetically.
PrB 4 is anomalous in that it orders ferromagneticall 7. 2 SchEfer et al. 3 have studied the low temperature magnetic structure of ErB 4 and DyB 4. They find simple commensurate antiferromagnetic ordering for both compounds with the R moments aligned along the c-axis.
Small single crystals of RB 4 suitable for magnetic and electrical measurements can be easily grown. 4 It is the purpose of this communication to report on the anisotropic magnetic susceptibilities and/or resistivities of PrB 4 and GdB 4 through TmB 4, and on the presence of a Research supported by NSF Contract No. NSF / DMR77 -0846 9.
Research supported by DOE Contract No. DOE/AT03-76-R-70ZZ7. second low temperature phase transition in TbB 4, DyB 4, HoB 4 and Trod 4. This second transition in DyB 4 and HoB 4 was seen previously by E. Biicher5 in crystals grown by Fisk and Schmidt. This work was not published.

Experimental Details
RB 4 crystals were grown from molten A1, except for PrB 4. The flux used in this case was Pr3Co, the Pr3Co plus PrB 4 being cooled slowly from 1200°C in a sealed 3/8" diameter Ta tube. Pr3Co dissolves rapidly in HC1, and the much slower attack on PrB 4 allowed crystals with sizes up to 4ram× 4ram× 1 mmtobe isolated. Some of the crystals were grown with Benriched liB: these are so indicated.
Resistivity measurements were made between 1.6 K and 300 K using a 4-probe ac technique at 220 Hz. A Faraday magnetometer was used for the magnetic measurements between 1.4 K and 300 K. The c-axis of the crystals was determined by Lane photographs, and magnetic measurements were made parallel and perpendicular to this direction.
The specific heat measurements were made with a pulse method in a semi-adiabatic 3He calorimeter. 6 A large number of small crystals were packed tightly in a copper cup and the heat capacity of the assembly was measured.
The data presented are, of course, corrected for the contribution of the addenda.

Results and Discussion
Our susceptibility (X) results for the PrB 4, GdB4, TbB4, HoB 4 and TmB 4 are shown in Figs. I and 3. Figure 2 displays low temperature resistance data on the heavy rare earth RB 4 compounds.
All resistance measurements presented are ilc-axis, except for GdB 4, where we give the results for a plane Ic-axis: other measurements show no qualitative differences for the resistivity measured perpendicular to the direction shown. The small size of the crystals only allowed an approximate determination of the absolute value of the electrical resistivity, so that we have plotted the data on an arbitrary resistance scale which varies from sample to sample.
For GdB 4, the spin disorder contribution to the resistivity Qm is ~ 15 ~{~cm, while for HoB 4, the total Pm (from both transitions) is ~ 0.75 U~] -cm. The data are summarized in Table I. The compounds GdB 4 and ErB 4 appear to have only a single, second order phase transition, while TbB 4 and DyB 4 appear to have two second order phase transitions. The compounds Hob 4 and TmB 4 both appear to have a second order phase transition followed by a first order transition at lower tempe rature.
Some features which stand out are (i) the susceptibility of GdB 4 is not anisotropic above the N~el temperature (TN); (ii) the susceptibilities of PrB 4, TbB 4 and TmB 4 are markedly anisotropic; and (iii) the R magnetic moments appear to align along the c-axis, except in the case of GdB 4 and TmB 4, as judged by the behavior of X below T N .
These materials are all good metals, and the crystals typically have resistance ratios of 50 or better. Point (i) above indicates that the anisotropbr present for a number of the heavy rare earth tetraborides is not due to anisotropy in the conduction bands being reflected in the RKKY interaction. The anisotropy is probably not purely a single ion anisotropy due~to crystal field effects either since in this case a variation in the magnetic moment ordering direction (point (iii)) would be expected between rare earths to the left of and including Ho and to the right of and including Er: the 41 quadrupole moment has opposite sign for these two groups. It seems likely, however, that the cause of the multiple phase transitions is related to this anisotropy.
We have examined Hob 4 in further detail.  heat results. The data indicate a second order transition at the upper T N, followed by a first order spike which seems to be superimposed on the smoothly decreasing heat capacity arising from the second order transition.
The total molar entropy under the curve to the upper N~el temperature is R ~ i. 77, the contribution under the spike being only R~ I. Ii. The site syzrn~etry of the rare earth here is ram. The crystal field can therefore lift all the degeneracy of the 558 4f I0 Ho ground state• The fact that the entropy to the upper T N is somewhat less than R ~n 2 makes it possible that Ho here has two nearby singlets lying lowest.
A few mixed crystals of Ho I_XYXB4 were grown. We find that the upper T N is nearly linear in x, extrapolating to T N = 0 for x = I. The lower T N falls off much faster and is below 1.7 K at x = 0.3. This is the kind of behavior that might be expected if the lower transition is driven by the internal field associated with the (c) Low temperature specific heat C vs ternperature T of HoB 4. upper T N. We note that a measurement made on a crystal of Tb0.74Y0. z1B4 only revealed one low temperature transition. W. C. Koehler 7 has made a detailed study of some of our HoB 4 crystals using neutron diffraction. He finds a very complicated incommensurate phase between the upper and lower TN'S and there is possibly a ferromagnetic component to the lowest temperature magnetic phase. I-le v~11 report these results separately.   (C)Not Curie-Weiss.

II
Our results suggest that in a number of RB 4 compounds, the anisotropy energy is comparable to the exchange energy. PrB 4 is an extreme case in that the anisotropy is sufficient to give large 8's of opposite sign for X parallel and perpendicular to the c-axis. These results on the uniaxial character of PrB 4 are in agreement with those of Berrada et al. 8 on crystals of PrB 4 made below the Curie temperature.