Enhanced magnetic ordering in Sm metal under extreme pressure

TL;DR

This study investigates how extreme pressure influences the magnetic ordering temperature of Sm metal, revealing a significant increase above 85 GPa and suggesting a transition to a highly correlated electron state similar to a Kondo lattice.

Contribution

It provides new insights into the pressure-induced magnetic behavior of Sm metal and its comparison with other lanthanides, highlighting the emergence of a Kondo lattice state at high pressures.

Findings

Magnetic ordering temperature of Sm increases sharply above 85 GPa.

Sm exhibits a Kondo lattice-like state under extreme pressure.

Comparison with Nd, Tb, Dy reveals similar pressure-dependent magnetic phenomena.

Abstract

The dependence of the magnetic ordering temperature To of Sm metal was determined through four-point electrical resistivity measurements to pressures as high as 150 GPa. A strong increase in To with pressure is observed above 85 GPa. In this pressure range Sm ions alloyed in dilute concentration with superconducting Y exhibit giant Kondo pair breaking. Taken together, these results suggest that for pressures above 85 GPa Sm is in a highly correlated electron state, like a Kondo lattice, with an unusually high value of To. A detailed comparison is made with similar results obtained earlier on Nd, Tb and Dy and their dilute magnetic alloys with superconducting Y.

Full text

I

Introduction

Except for Ce, the local-moment magnetic state in elemental lanthanide metals is highly stable. Under the application of sufficient pressure, however, the magnetic state would be expected to destabilize. In recent studies on the trivalent lanthanide metals Nd song , Gd lim1 , Tb lim2 , and Dy lim1 the magnetic ordering temperature $T_{\text{o}}$, with the exception of Gd, was found to rise steeply to anomalously high values upon the application of extreme pressure. In the same pressure range, alloying Nd, Tb, and Dy in dilute concentration into superconducting Y resulted in a very large suppression of the superconducting transition temperature $T_{\text{c}}$, in the case of Y(Nd) the record value 39 K/(at.% Nd) song . Such high values are a signature of giant Kondo pair breaking, a sign that these lanthanides may be approaching a magnetic instability. The anomalous rise in $T_{\text{o}}$ and the giant pair breaking thus appear to be related.

It is interesting to note that in the Kondo lattice model described by the Doniach phase diagram doniach $T_{\text{o}}$ is expected to first increase with the magnitude of the negative covalent mixing exchange coupling $J_{-}$ schrieffer before passing through a maximum and falling rapidly to the quantum critical point at 0 K (see Fig 9 in the Discussion section). This occurs when the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction kittel is suppressed by Kondo spin screening. Since the magnitude of $J_{-}$ normally increases under pressure schilling1 , in the Doniach picture $T_{\text{o}}$ versus pressure should pass through a maximum and fall towards 0 K. This behavior was indeed recently observed for elemental Nd metal by Song et al. song . In contrast, due to the extreme stability of Gd’s magnetic state with its half-filled 4$f^{7}$ configuration, even pressures to 1 or 2 Mbar are not sufficient to bring Gd near a magnetic instability. Indeed, neither giant pair breaking in Y(Gd) nor an anomalous rise in $T_{\text{o}}$ for Gd are observed at extreme pressure lim1 ; fabbris .

In view of the intriguing magnetic behavior in trivalent Nd metal and Y(Nd) alloys at extreme pressure, an in-depth study of an additional light trivalent lanthanide Sm, both as elemental metal and in the dilute magnetic alloy Y(Sm), was undertaken. Sm metal crystallizes in the Sm-type ($\alpha$-Sm) structure at ambient pressure, transitioning to dhcp at 4 GPa, to fcc at 14 GPa, to hR24 (dfcc) at 19 GPa, to hP3 at 37 GPa, and finally to tI2 at 91 GPa zhao ; vohra . These structural transitions thus follow the regular trivalent lanthanide structure sequence under pressure: hcp$\rightarrow$Sm-type$\rightarrow$dhcp$\rightarrow$fcc$\rightarrow$dfcc, a sequence generated by the increasing $d$ character in the conduction band upon compression pettifor .

Trivalent Sm assumes the configuration [Xe]4$f^{5}$ yielding for the free Sm3+ ion in the ground state 6H5/2, with Landé $g$-factor $g_{J}$ = 2/7 and total angular momentum $J_{t}$ = 5/2. The effective magnetic moment of free Sm*3+*calculated from Hund’s rules is $p_{eff}=$ 0.85 $\mu_{\text{B. }}$ However, magnetic susceptibility measurements on paramagnetic Sm salts give $p_{eff}=$ 1.74 $\mu_{\text{B }}$blundell . The difference between the theoretical and experimental values is believed due to contributions from low-lying excited states with different $J_{t}$ values.

In Sm metal the situation is more complicated since the crystalline electric field and conduction-electron polarization significantly influence the magnetic state of Sm3+ adachi . As a result of this complexity, Sm metal exhibits a number of interesting physical phenomena. Both the temperature-dependent heat capacity jennings and electrical resistivity alstad have anomalies near 13 K and 106 K. The fact that the temperature-dependent magnetic susceptibility of Sm has peaks near these temperatures strongly suggests antiferromagnetic ordering mcewen . This was confirmed by Koehler and Moon from neutron diffraction experiments on single crystalline 154Sm koehler . They viewed the Sm-type structure with space group R$\overline{3}$m as a combination of hexagonal and cubic sites where Sm3+ ions at these sites magnetically order at 106 K and 14 K, respectively.

In temperature-dependent resistivity measurements $R(T)$ a knee is observed at the magnetic ordering temperature $T_{\text{o}}$ due to the loss of spin-disorder scattering upon cooling. Dong et al. dong measured resistivity on Sm to 43 GPa and found that the two ordering temperatures move toward each other with increasing pressure, finally merging together near 66 K at 8 GPa as Sm enters the dhcp phase. At higher pressures $T_{\text{o}}$ increases rapidly to 135 K at 43 GPa. Johnson et al. johnson measured $R(T)$ on Sm to 47 GPa. They find that the two ordering temperatures merge near 56 K at 10 GPa and increase slowly up to the (hR24$\rightarrow$hP3) phase transition at 34 GPa where a second ordering temperature reportedly appears.

In this work four-point dc resistivity measurements are carried out on pure Sm metal to $\sim$ 150 GPa using a diamond anvil cell. The two magnetic ordering temperatures merge at 13 GPa after which $T_{\text{o}}(P)$ increases gradually to a maximum at 53 GPa, but then decreases and passes through a minimum at 85 GPa followed by a sharp increase to $\sim$ 140 K at 150 GPa. Giant superconducting pair breaking is also observed in dilute Y(Sm) alloys. Taken together, both effects suggest that extreme pressure drives Sm to an unconventional magnetic state, a state likely related to that observed earlier in Nd, Tb, and Dy.

II

Experimental Techniques

Polycrystalline Sm samples for the high-pressure resistivity measurements were cut from a Sm ingot. The dilute magnetic alloys of Y(Sm) were made by argon arc-melting small amounts of Sm with Y (both Sm and Y 99.9 % pure, Ames Laboratory ames ). To enhance homogeneity the alloys were sealed in glass ampules under vacuum and annealed at 600${}^{\text{o}}$C for two weeks. The concentrations of Sm for the four alloys as determined from x-ray fluorescence analysis are: 0.15(2) at.%, 0.40(3) at.%, 0.83(4) at.%, and 1.16(6) at.%. Before arc-melting the nominal concentrations were 0.5 at.%, 1.0 at.%, 1.2 at.%, and 2 at.%, respectively. It follows that 30% to 70% of the Sm evaporated during arc-melting due to its relatively low boiling point.

A diamond anvil cell (DAC) made of conventional and binary CuBe schilling was used to reach pressures to $\sim$150 GPa between two opposed diamond anvils (1/6-carat, type Ia) with 0.18 mm diameter culets beveled at 7 degrees to 0.35 mm diameter. The force applied to the anvils was generated by a stainless-steel diaphragm filled with He gas daniels . The Re gasket (250 $\mu$m thick) was pre-indented to 30 $\mu$m and a 90 $\mu$m diameter hole drilled through the center of the pre-indentation area. A cBN-epoxy insulation layer was compressed onto the surface of the gasket. Four Pt strips (4 $\mu$m thick) were then placed on the insulation layer, acting as the electrical leads for the four-point resistivity measurement. The Sm or Y(Sm) sample with dimensions 40 $\times$ 40 $\times$ 4 $\mu$m3 was then placed on the Pt strips. Further details of the high-pressure resistivity techniques can be found elsewhere lim1 ; shimizu .

The DAC was inserted into an Oxford flow cryostat capable of varying temperature from ambient to 1.3 K. Pressure was determined at room temperature using the diamond vibron vibron . Earlier resistivity experiments by Song et al. song in an identical DAC using both vibron and ruby manometers revealed an approximately linear pressure increase of $\sim$ 30% on cooling from 295 to 4 K. In the present experiments this calibration allows an estimate of the pressure at the magnetic or superconducting transition temperatures from the vibron pressure at ambient temperature.

III Results of Experiment

Four-point resistance measurements $R(T)$ were carried out on Sm in two runs over the temperature and pressure ranges 1.3 - 295 K and 2 - 127 GPa (measured at room temperature), respectively. The data from run 1 are shown in Fig 1. For all pressures the resistance is seen to decrease upon cooling. A kink or knee appears in $R(T)$ in the lower temperature range that results from the progressive loss of spin-disorder scattering $R_{\text{sd}}(T)$ as Sm orders magnetically. At 2 and 4 GPa two kinks are visible in the $R(T)$ curves; at higher pressures only one kink or knee appears. With increasing pressure the knee is seen to shift in temperature and broaden; the broadening is due to the increasing pressure gradient across the sample in the non-hydrostatic pressure environment. The value of $T_{\text{o}}$ is determined from the intersection temperature of two straight lines tracking $R(T)$ above and below the knee region, as illustrated in Fig 1 for 27 GPa pressure. In most experiments the Sm sample was cooled to $\sim 4$ K; however, considering both runs, at pressures 2, 9, 25, 51, 60, 86, 93, 97, and 127 GPa the sample was cooled to 1.3 K. In no experiment on Sm was superconductivity, or even an onset to superconductivity, observed.

In Fig 2 the values of $T_{\text{o}}$ for Sm from runs 1 and 2 are plotted versus pressure and compared to previous results from Dong et al. dong to 43 GPa and Johnson et al. johnson to 47 GPa. In all experiments the two branches of $T_{\text{o}}$ are seen to merge near 13 GPa followed by an increase in $T_{\text{o}}$. In the present experiments $T_{\text{o}}(P)$ passes through a maximum near 53 GPa, gradually decreasing to $\sim 60$ K near 85 GPa, before rising sharply to $\sim 140$ K at 150 GPa. The report by Johnson et al. johnson that a second transition appears in the pressure range 35 - 50 GPa could not be confirmed.

Due to the broadening of the resistivity knee under nonhydrostatic pressure, the determination of the value of $T_{\text{o}}$ for Sm becomes progressively more difficult in the upper pressure range. The same was true for the other trivalent lanthanides Nd, Gd, Tb, and Dy studied previously song ; lim1 ; lim2 . In particular, as here for Sm, a rapid upward shift of the knee in $R(T)$ was also observed for Dy above 70 GPa pressure lim1 . That the knee for Dy does indeed result from magnetic ordering over the entire pressure range was recently confirmed by synchrotron Mössbauer spectroscopy (SMS) to 141 GPa bi .

Independent information on the origin of the resistivity knee in Sm can be gained by comparing the pressure dependence of the spin-disorder resistance $R_{\text{sd}}(P)$ for $T>T_{\text{o}}$ to that of $T_{\text{o}}(P)$ obtained from the resistivity knee. As discussed in Ref lim1 , both $T_{\text{o}}$ taylor and $R_{\text{sd}}$ daal are proportional to $J^{2}N(E_{\text{F}})$, where $J$ is the exchange interaction between local moment and conduction electrons and $N(E_{\text{F}})$ is the density of states at the Fermi energy. A similarity between the pressure dependences $T_{\text{o}}(P)$ and $R_{\text{sd}}(P)$ is anticipated for the trivalent lanthanide metals since their $spd$ conduction electron properties are closely related. This similarity was indeed observed for Nd song , Gd lim1 , Tb lim2 , and Dy lim1 ; it would be interesting to examine whether this also holds for Sm, together with Nd the second light lanthanide studied. From Fig 1 it is readily seen that where the resistivity knee shifts under pressure to higher temperatures the size of the resistivity drop-off below the knee also increases. A semi-quantitative estimate of $R_{\text{sd}}$ is now attempted.

The total measured resistance is the sum of three terms, $R(T)=R_{\text{d}}+R_{\text{ph}}(T)+R_{\text{sd}}(T),$ where $R_{\text{d}}=R(0$ K$)$ is the temperature-independent defect contribution. In the paramagnetic state in the temperature region above the resistance knee, $R_{\text{sd}}(T)$ is constant, taking on its maximum value $R_{\text{sd}}^{\text{max}}$, so that the only temperature dependence comes from the phonon resistance $R_{\text{ph}}(T)$. To estimate $R_{\text{sd}}^{\text{max}},$ Colvin et al. colvin assumed that $R_{\text{ph}}(T)$ depends linearly on temperature, and extended a straight line fit to $R(T)$ for $T>T_{\text{o}}$ to 0 K with intercept $R_{\text{int}}$ and then subtracted off $R_{\text{d}}$ from this intercept. An example for this estimate is given in Fig 1 at 27 GPa where $R_{\text{sd}}^{\text{max}}=[R_{\text{int}}-R_{\text{d}}]=(115-18)$ m$\Omega=97$ m$\Omega$.

In Fig 3 $R_{\text{sd}}^{\text{max}}$ is plotted as a function of pressure. Comparing Figs 2 and 3, a parallel behavior of the pressure dependences $T_{\text{o}}(P)$ and $R_{\text{sd}}^{\text{max}}(P)$ is indeed observed, thus supporting the identification of the resistance knee with the onset of magnetic ordering in Sm. Also included in Fig 3 is the quantity [$R$(290 K) – $R$(4 K)] that is seen to also qualitatively track $T_{\text{o}}$ versus pressure. This suggests that the resistance from electron-phonon scattering at room temperature does not change dramatically within the pressure range of these experiments.

To examine whether the rapid rise in $T_{\text{o}}$ for pressures above 85 GPa might be related to an approaching instability in Sm’s magnetic state, Sm is alloyed in dilute concentration with Y, a high-pressure superconductor having, compared to the trivalent lanthanides, closely similar conduction electron properties and structural sequence under pressure wittig2 . Under these circumstances the ability of the Sm ion to suppress Y’s superconductivity, the degree of pair breaking $\Delta T_{\text{c}}\equiv T_{\text{c}}$[Y] - $T_{\text{c}}$[Y(Sm)], can reveal valuable information about the magnetic state of the Sm ion itself. This general observation was emphasized for lanthanide ions by Maple maple .

In the present experiment Y(Sm) alloys with differing dilute Sm concentrations were studied at pressures to 180 GPa. Fig 4 shows the superconducting transitions in four-point resistance measurements on Y(0.15 at.% Sm) at selected pressures. As illustrated in this figure for the $R(T)$ data at 52 GPa, $T_{\text{c}}$ is defined as the temperature at which the resistance transition reaches the halfway mark, whereas the intersection point of two straight red lines defines $T_{\text{c}}^{\text{onset \ }}$, and $T_{\text{c}}^{\text{zero}}$ gives the temperature where the resistance disappears. The fact that a typical total transition width is less than 2 K gives evidence that the distribution of Sm ions in the alloys is homogeneous. As seen from the data in Fig 4, $T_{\text{c}}$ increases monotonically with pressure to 140 GPa, but then decreases to 180 GPa.

The dependence of $T_{\text{c}}$ on pressure for Y(Sm) alloys with Sm concentrations 0.15, 0.40, 0.83, and 1.16 at.% is shown in Fig 5. Below $\sim$ 40 GPa the $T_{\text{c}}(P)$ dependence for all four alloys tracks that for pure Y. However, above $\sim$ 40 GPa a strong suppression sets in. This suppression $\Delta T_{\text{c}}$ is so strong that for Y(1.16 at.% Sm) at pressures above 50 GPa $T_{\text{c}}$ lies below the temperature range of this experiment (1.3 K). For the more dilute Y(0.15 at.% Sm) and Y(0.40 at.% Sm) alloys, $T_{\text{c}}$ remains well above 1.3 K at all pressures.

To allow a more meaningful comparison of the degree of superconducting pair breaking $\Delta T_{\text{c}}$ for the different alloys, in Fig 6 $\Delta T_{\text{c}}$ is divided by the Sm concentration $c$ and then plotted versus pressure for all alloys measured. Where they can be compared, the individual $\Delta T_{\text{c}}/c$ curves agree reasonably well and increase monotonically with pressure, reaching the extremely high value of $\sim$ 40 K/at.% Sm at 180 GPa, a value slightly higher than that found earlier for Y(0.4 at.% Nd) song . Both the giant pair breaking in Y(Sm) and the remarkable increase of $T_{\text{o}}$ in Sm give evidence for unconventional physics in Sm above 85 GPa.

IV Discussion

The present results on Sm and Y(Sm) alloys will now be compared to those from earlier studies on the lanthanides Nd song , Gd lim1 , Tb lim2 , and Dy lim1 . Going from right to left across the lanthanide series (Lu to La) or by applying pressure, one finds with few exceptions samudrala the canonical rare-earth crystal structure sequence hcp$\rightarrow$Sm-type$\rightarrow$dhcp$\rightarrow$fcc$\rightarrow$hR24 believed to mainly arise from an increase in the number $n_{\text{d}}$ of $d$-electrons in the conduction band pettifor .

In the elemental lanthanide metals magnetic ordering arises from the indirect RKKY exchange interaction between the magnetic ions. For a conventional lanthanide metal with a stable magnetic moment, the magnetic ordering temperature $T_{\text{o}}$ is expected to scale with the de Gennes factor $(g-1)^{2}J_{t}(J_{t}+1)$, modulated by the prefactor $J^{2}N(E_{\text{F}})$, where $J$ is the exchange interaction between the 4$f$ ion and the conduction electrons, $N(E_{\text{F}})$ the density of states at the Fermi energy, $g$ the Landé-$g$ factor, and $J_{t}$ the total angular momentum quantum number taylor .

In Fig 7(a) the dependence of the magnetic ordering temperature $T_{\text{o}}$ on pressure is shown for the four lanthanide metals Nd, Sm, Tb, and Dy. Except for Nd, $T_{\text{o}}(P)$ is seen to initially decrease rapidly with pressure, but then pass through a minimum and rise. $T_{\text{o}}(P)$ for Gd lim1 also shows this same initial behavior. Since the de Gennes factor, in the absence of a magnetic instability or valence transition, is constant under pressure, the initial $T_{\text{o}}(P)$ dependence for the above lanthanides likely originates in the pressure dependence of the prefactor $J^{2}N(E_{\text{F}})$. Electronic structure calculations for Dy support this conclusion jackson1 ; fleming .

The strong initial decrease in $T_{\text{o}}$ with pressure in Sm (upper transition), Gd, Tb, and Dy occurs within the hcp and Sm-type phases. The minimum in $T_{\text{o}}(P)$ at approximately 20 GPa for Dy appears at somewhat lower pressures for Tb, Gd, and Sm, disappearing entirely for Nd. As discussed in some detail in Ref song , this is consistent with an increase in the number of d electrons in the conduction band going from Dy to Nd; the electronic structure and the crystal structures taken on by Nd resemble those of Dy but at a pressure approximately 30 - 40 GPa higher song . The systematic behavior for all five lanthanides Dy, Tb, Gd, Sm, and Nd in the region of pressure where the hcp, Sm-type, dhcp, and hR24 structures occur, gives evidence that changes in the magnetic ordering temperature in this region are mainly determined by corresponding changes in the properties of the conduction electrons that mediate the RKKY interactions between the magnetic lanthanide ions.

It would seem helpful to propose that the $T_{\text{o}}(P)$ curves for each element can be separated into two principal pressure regions: a “conventional” region at lower pressure governed by the electronic properties of the conduction electrons and normal positive exchange interactions $J_{+}$ between the lanthanide ion and the conduction electrons, and an “unconventional” region at higher pressures where exotic physics dominates leading to negative covalent-mixing exchange $J_{-}$ and associated anomalous magnetic properties. In the “conventional” region the observed variations in $T_{\text{o}}(P)$ would be principally caused by changes in the prefactor $N(E_{\text{F}})J^{2}_{+}$ with pressure. In the “unconventional” pressure region highly correlated electron effects dominate leading to anomalous magnetic properties, including anomalous $T_{\text{o}}(P)$ dependences and giant superconducting pair breaking in dilute magnetic alloys.

Although the properties of the conduction electrons and the magnetic state of the lanthanide ion are intertwinned, the “conventional” and “unconventional” regions represent different physics, the former being amenable through standard electronic structure calculations, whereas the latter is only accessible through consideration of strong highly correlated electron effects. The stability of the ion’s magnetic state is determined to a large extent by the exchange interactions within a given lanthanide ion (Hund’s rules). Once the “unconventional” rapid rise in $T_{\text{o}}$ with pressure sets in, it overpowers the “conventional” conduction electron behavior and determines $T_{\text{o}}(P)$. Since in Dy and Nd the “unconventional” region begins at a lower pressure, the rapid rise in $T_{\text{o}}$ may prevent the “conventional” second minimum seen in Sm and Tb from appearing in $T_{\text{o}}(P)$ for Dy or Nd.

A rough estimate of the boundary pressure where the “unconventional” $T_{\text{o}}(P)$ behavior may begin for a given lanthanide is indicated by a vertical tick mark in Fig 7(a). In the “unconventional” region itself the $T_{\text{o}}(P)$ data curves have been given double thickness. There is a good deal of arbitrariness for where this boundary is placed, particularly for Sm and Tb where the second $T_{\text{o}}(P)$ minimum may well belong to the “unconventional” region, instead of the “conventional” region, as indicated by the beginning of anomalous superconducting pair breaking in Y(Sm) or Y(Tb) near the pressure for the second minimum in $T_{\text{o}}(P)$.

Focussing now on the anomalous rise in $T_{\text{o}}$ with pressure in the “unconventional” region in Fig 7(a), we note that this rise is steepest for Nd but becomes progressively less steep for Dy, Tb, and Sm. At least part of this reduction in steepness has to do with the fact that the compressibility of the lanthanides decreases significantly as pressure is increased. To bring out the physics more clearly, $T_{\text{o}}$ in Fig 7(b) is replotted versus the relative volume $V/V_{\text{o}}$. Different features in the respective curves are shifted to new relative positions, but now it is seen that the sharp upturns in $T_{\text{o}}(P)$ have nearly the same slope and are much steeper relative to the changes in the “conventional” region at lower pressures. This points to a common mechanism for the upturn in these four lanthanides.

In Fig 8 the normalized pair breaking curve $\Delta T_{c}/c$ for Y(Sm) from Fig 6 is compared to those for the dilute magnetic alloys Y(Nd) song , Y(Tb) lim2 , and Y(Dy) lim1 . For Y(Sm) and Y(Nd) the pair breaking begins to increase rapidly at relatively low pressures compared to Y(Tb) and especially Y(Dy). At least part of the reason for this is that the Y host exerts lattice pressure on the light lanthanides Sm and Nd, but not on Tb and Dy. This can be seen by comparing the respective molar volumes in units of cm3/mol:  Y(19.88), Nd(20.58), Sm(19.98), Gd(19.90), Tb(19.30), Dy(19.01) singman . Without exception, the region of pressure where $T_{\text{o}}(P)$ increases rapidly lies within the region of pressure where the superconducting pair breaking $\Delta T_{c}/c$ in the corresponding dilute magnetic alloy with Y is anomalously large. Note also that the maximum value of the slope of $\Delta T_{c}/c$ versus pressure in Fig 8 is noticeably reduced for Y(Dy). At least part of this effect is due to the sizable reduction in the compressibility of Y at higher pressures.

For the dilute magnetic alloy Y(Nd) the normalized pair breaking data in Fig 8 are seen to be reduced ($\Delta T_{c}/c$ turns upwards) for pressures above 160 GPa. Presumably the same effect would also be observed in Y(Sm), Y(Tb), and Y(Dy) if the experiments were extended to even higher pressures. This reduction in giant pair breaking seen in Y(Nd) at the highest pressures was observed previously in dilute magnetic alloys La(Ce) wittig1 , La(Pr) wittig3 , and Y(Pr) fabbris ; wittig4 and can be readily accounted for in terms of Kondo pair-breaking theory zuckermann where the magnitude of the negative exchange interaction $J_{-}$ between the magnetic ions and the conduction electrons increases with pressure. The appearance of such Kondo physics in the dilute magnetic alloy suggests that the corresponding concentrated system will likely show Kondo lattice, heavy Fermion, and fluctuating valence behavior at higher pressures, eventually culminating in a full increase in valence whereby one 4$f$ electron completely leaves its orbital and joins the conduction band.

The well known Doniach model doniach is often cited to account for the dependence of the magnetic ordering temperature $T_{\text{o}}$ in a Kondo lattice as a function of the magnitude of the negative exchange parameter $J_{-}$ (see Fig 9). Whereas the upturn in $\Delta T_{c}/c$ occurs above 160 GPa for Y(Nd), the downturn in $T_{\text{o}}(P)$ begins above 80 GPa (see Fig 7(a)) for Nd in its “unconventional” pressure region (double line width). The rapid rise in $T_{\text{o}}(P)$ for Nd followed by its rapid downturn resembles the dependence anticipated from the Doniach model song . A similar $T_{\text{o}}(P)$ dependence would be expected for Sm, Tb and Dy if the experiments were extended to even higher pressures.

The values of the pair-breaking parameter $\Delta T_{c}/c$ for Nd and Sm impurities in Y are surprisingly large - in fact, to our knowledge, the largest ever reported. However, even more surprising is the sharp upturn in $T_{\text{o}}(P)$ where $T_{\text{o}}$ reaches values that appear to be much higher than would have been possible had “unconventional” physics, such as Kondo physics, not been operative. In the case of Dy, $T_{\text{o}}(P)$ extrapolates to values well above room temperature, higher than any known value for an elemental lanthanide metal at either ambient or high pressure lim1 .

In summary, the magnetic properties of the light lanthanide Sm have been studied to extreme pressure and found to parallel those of another light lanthanide, Nd, as well as the heavy lanthanides Gd, Tb, and Dy. It appears that the magnetic phase diagram can be separated into two regions: a low-pressure region where conventional changes in the electronic structure determine $T_{\text{o}}(P)$, and a high-pressure region where highly correlated electron effects dominate, leading to such anomalous phenomena as unexpectedly high magnetic ordering temperatures and giant superconducting pair-breaking. The authors hope that this and previous work will lead to increased theoretical activity in this area.

Acknowledgments. The authors would like to thank A. K. Gangopadhyay for his assistance in preparing the Y(Sm) alloys and R. A. Couture for carrying out the x-ray fluorescence determination of the Sm content in these alloys. Thanks are also due Daniel Haskel for his critical reading of the manuscript. This work was supported by the National Science Foundation (NSF) through Grant No. DMR-1104742 and No. DMR-1505345 as well as by the Carnegie/DOE Alliance Center (CDAC) through NNSA/DOE Grant No. DE-FC52-08NA28554.