Magnetic and Structural Phase Transitions in Thulium under High Pressures and Low Temperatures

The nature of 4f electrons in many rare earth metals and compounds may be broadly characterized as being either “localized” or “itinerant”, and is held responsible for a wide range of physical and chemical properties. The pressure variable has a very dramatic effect on the electronic structure of rare earth metals which in turn drives a sequence of structural and magnetic transitions. We have carried out four-probe electrical resistance measurements on rare earth metal Thulium (Tm) under high pressures to 33 GPa and low temperatures to 10 K to monitor the magnetic ordering transition. These studies are complemented by angle dispersive x-ray diffraction studies to monitor crystallographic phase transitions at high pressures and low temperatures. We observe an abrupt increase in magnetic ordering temperature in Tm at a pressure of 17 GPa on phase transition from ambient pressure hcp-phase to α-Sm phase transition. In addition, measured equation of state (EOS) at low temperatures show anomalously low thermal expansion coefficients likely linked to magnetic transitions.


Introduction
The localized state in rare earth metals is marked by tightly bound shells or narrow bands of highly correlated electrons near the Fermi level with localized magnetic moments for all of the rare earth elements. The regular trivalent rare earth structural sequence, observed at low pressures for La through Lu excepting Eu and Yb as a function of increasing pressure or decreasing atomic number, typifies this behaviour [1]. The structures are all close packed and of high symmetry, and the sequence hexagonal close packed (hcp) → α-Sm → double hexagonal close packed (dhcp) → face centered cubic (fcc) may be reproduced solely by transfer of sp electrons to the d-band. The f-delocalization transition is of first order, and may be accompanied by a discontinuous drop in volume, loss of magnetic moment on the 4f-shell, a lowering of electrical resistivity, and a stiffening of the crystalline lattice. The magnetic ordering temperatures at high pressures and low temperatures in heavy lanthanides have been investigated using magnetic susceptibility measurements and it was reported that magnetic transition disappear at pressures above 5-10 GPa [2]. Recently, it has been shown that electrical transport measurements is a very sensitive technique in measuring magnetic ordering temperatures in rare earth metal terbium and these measurements have been validated by direct observation of magnetic ordering by neutron diffraction studies [3].

Experimental Methods
High pressure electrical resistance measurements were made by employing an eight-probe designer diamond anvil cell in a four-probe configuration to pressures up to 33 GPa and temperatures to 10 K. The eight tungsten microprobes were encapsulated in a homoepitaxial diamond film and were exposed only near the tip of the diamond in order to make electrical contact with the Thulium (Tm) sample at high pressures and low temperatures. Two electrical leads were used to pass a dc current through the sample and two additional leads were used to monitor the voltage across the sample. The sample was cut from a 0.1-mm thick foil of polycrystalline Tm and loaded into the cell along with a ruby pressure marker. The pressure was monitored by the ruby fluorescence technique and care was taken to calibrate the ruby R 1 emission at low temperatures as described in an earlier publication [4]. The electrical resistance of the Tm sample was measured with increasing pressure, and the sample was then decompressed, and measured again during a second compression in order to verify if the magnetic transition could be recovered. The electrical resistance measurements were complemented by angledispersive image plate x-ray diffraction on Tm to high pressures and liquid helium temperatures (4 K). X-ray diffraction was then performed on sample pressurized at the HPCAT 16 ID-B beamline at the Advanced Photon Source at Argonne National Laboratories in Chicago, Illinois. A 30.494 keV beam of x-rays was collimated to a spot size with Full Width at Half Maximum (FWHM) of 5x7 µm and scanned across the sample area while spectra were collected to pressure up to 36 GPa and low temperatures to 4 K.

Results and Discussion
The following sequence of phase transitions are known in Tm from hcp to Sm-type at 17 GPa, Sm-type to dhcp phase at 32 GPa, and dhcp to hR24 phase at 61 GPa, and hR24 phase to monoclinic C2/m phase at 124 GPa [5]. At ambient pressure, Tm shows a c-axis sinusoidal Anti-Ferromagnetic (AFM) phase at Néel Temperature T N = 56 K followed by a modulated Ferromagnetic (FM) phase at T C = 25 K. The AFM transition temperature T N was tracked in an earlier magnetic susceptibility measurement on Tm to a pressure 12 GPa and T N was found to show a decrease with increasing pressure [2]. Figure  1 shows the four probe electrical resistance (R) for Tm as a function of temperature at a pressure of 7 GPa exhibiting anomalous behaviour near 50 K. The temperature derivative of electrical resistance (dR/dT) is also shown in figure 1 where the magnetic transition T N is clearly evident as a minimum at 52.5 K for 7 GPa. The procedure shown in figure 1 was utilized for all data points in the hcp-phase below 17 GPa. In pressure range above 17 GPa for the α-Sm phase, the electrical resistance changes are more gradual as shown in figure 2. In these cases, the temperature derivative of electrical resistance (dR/dT) shows a change in slope at the magnetic transition T N of 131.8 K at a pressure of 17.6 GPa (figure 2).
The magnetic transition temperature T N data for both the hcp-phase and α-Sm phases are combined and are shown as a function of pressure in figure 3. The three independent experiments that were performed on Tm show remarkable consistency with each other. The magnetic transition temperature T N for the hcp-phase was observed to decrease gradually first to 7 GPa and then at a faster rate till transition to α-Sm Phase at 17 GPa. There is an abrupt increase in T N by as much as 100 K on transition from the hcp-phase to α-Sm phase at 17 GPa (figure 3). On increasing pressure beyond 17 GPa till 33 GPa, the magnetic transition temperature T N was found to be relatively insensitive to changes in pressure. It is to be noted that additional changes in T N are anticipated when Tm transforms finally to dhcp and other high phases above 30 GPa [5].  The integrated image plate x-ray diffraction data is shown in figure 4 for the hcp phase at 4 GPa and 7 K as well as for the α-Sm Phase at 36 GPa and 20 K. The wavelength for x-ray beam is λ = 0.4066 Å for both spectra shown in figure 4. The pressure was measured by ruby-fluorescence at low temperatures. The measured Pressure-Volume (P-V) data or equation of state is shown in figure 5 at various temperatures to a pressure of 36 GPa. There are two important conclusions to be drawn from figure 5; the first is that there is no discernible volume change on phase transition from hcp-Sm-type phase transition at all temperatures. This is consistent with the EOS data obtained at ambient temperature. The second important conclusion is that there is no discernible volume contraction measured on cooling at various pressures. The measured EOS at various temperatures between 10 K to 200 K for Tm basically overlap with each other indicating that any volume contraction on cooling is basically countered by slight volume increase on magnetic ordering.

Conclusions
The four probe electrical resistance measurements have been carried out on heavy rare earth metal Thulium to 33 GPa and 10 K using a designer diamond anvil cell. The electrical resistance measurements are complemented by angle dispersive x-ray diffraction measurements at high pressures and low temperatures using a synchrotron source. The paramagnetic to anti-ferromagnetic transition is readily detected in electrical resistance measurements and the Néel Temperature T N is observed to decrease gradually in the hcp-phase till the transition pressure of 17 GPa to the α-Sm phase. The transformation to the α-Sm phase results in an abrupt increase in T N by as much as 100 K. The