Research Article

Deep melting reveals liquid structural memory and anomalous ferromagnetism in bismuth

Yu Shu, Dongli Yu, Wentao Hu, Yanbin Wang, Guoyin Shen, Yoshio Kono, Bo Xu, Julong He, Zhongyuan Liu, and Yongjun Tian
PNAS March 28, 2017 114 (13) 3375-3380; first published March 13, 2017; https://doi.org/10.1073/pnas.1615874114

  1. Edited by Kamran Behnia, École Supérieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI), Paris, France, and accepted by Editorial Board Member Zachary Fisk February 13, 2017 (received for review September 23, 2016)

Significance

Condensed matter physics owes much of its development to bismuth (Bi). It was the first metal with a Fermi surface that was experimentally identified. Many intriguing phenomena were first discovered in Bi, such as the large magnetoresistance and the propagations of microwaves. For over a century, Bi has been known to be diamagnetic. We have observed an unusual ferromagnetism in pure Bi samples after treatments under certain pathways of pressure and temperature conditions. The ferromagnetism is found to be associated with a surprising structural memory effect in the molten state and the ability for solid Bi to “remember” its liquid structural motifs. This structural memory effect may present an important route in defect engineering for creating materials.

Abstract

As an archetypal semimetal with complex and anisotropic Fermi surface and unusual electric properties (e.g., high electrical resistance, large magnetoresistance, and giant Hall effect), bismuth (Bi) has played a critical role in metal physics. In general, Bi displays diamagnetism with a high volumetric susceptibility (∼10−4). Here, we report unusual ferromagnetism in bulk Bi samples recovered from a molten state at pressures of 1.4–2.5 GPa and temperatures above ∼1,250 K. The ferromagnetism is associated with a surprising structural memory effect in the molten state. On heating, low-temperature Bi liquid (L) transforms to a more randomly disordered high-temperature liquid (L′) around 1,250 K. By cooling from above 1,250 K, certain structural characteristics of liquid L′ are preserved in L. Bi clusters with characteristics of the liquid L′ motifs are further preserved through solidification into the Bi-II phase across the pressure-independent melting curve, which may be responsible for the observed ferromagnetism.

Bismuth (Bi) has played important roles in metal and condensed matter physics. The extremely low carrier density of Bi allows quantum limits of the Landau level to be studied under high magnetic field (1) and quantum size effects to be observed at ∼100-nm length scale (2). At ambient condition, Bi is known to crystallize in the rhombohedral A-7 type structure (space group R-3m, D3d5), with the primitive unit cell containing two atoms at positions (u,u,u) and (−u,−u,−u). Each atom has three equidistant nearest neighbors tightly bonded at a distance of ∼3.062 Å (3). The Bi4 motifs form puckered bilayers (Fig. S1A) with a thickness of 1.59 Å stacked along the rhombohedral [111] direction. The distance between adjacent bilayers is 2.35 Å (4), slightly smaller than the next nearest distance of 3.512 Å (5). Each atom’s next nearest neighbors are in the adjacent bilayers, and the bonding within each bilayer is much stronger than the interbilayer bonding. As such, Bi exhibits rather complex interatomic binding, with coexisting covalent (within the bilayers), metallic, and weaker van der Waals-like (between bilayers) bonding (4).

Fig. S1.
Fig. S1.

Layered characteristics of (A) rhombohedral A-7 Bi and (B) pressure-induced monoclinic Bi-II.

The phase diagram of Bi is rich and complex (Fig. 1). At ambient pressure, Bi melts at 544 K (6) with a liquid–liquid transition at 1,010 K (7). With increasing pressure, Bi undergoes structural transitions in both solid and liquid states. The A-7 structured Bi-I phase transforms successively into the monoclinic (Bi-II), incommensurate host–guest (Bi-III), and body-centered cubic (Bi-V) phases (8⇓–10) with increasing pressure to ∼6 GPa. On pressure release, these high-pressure metallic crystalline phases are unstable and revert to the Bi-I phase. Below ∼1.6 GPa, the melting temperature of Bi-I decreases with increasing pressure, a behavior similar to that of ice. Between 1.6 and 2.4 GPa (11), the solid just below melting is the Bi-II phase, which has a similar bilayer structure to that of Bi-I, except that the distance between adjacent bilayers is reduced to ∼2.17 Å and the bilayer thickness is reduced to 0.92 Å, because the Bi4 motifs are flattened and devoid of the threefold rotational symmetry as present in the A-7 structure (Fig. S1B). Bi-II is stable in a narrow pressure–temperature range and characterized by a flat melting curve virtually independent of pressure (Fig. 1). Above 2.4 GPa, the melting curve of Bi-V exhibits a steep positive slope. An electrical resistivity and thermobaric study (12) claims that molten Bi has several liquid phases up to 6 GPa. However, no structural studies have been reported to confirm these phases. Our own structural study, presented later in this paper, shows evidence of one structural transition in liquid Bi at ∼1,250 K between 2 and 4 GPa. This transition is in general agreement with the ambient pressure liquid transition at 1,010 K (7), with transition temperature having a weakly positive pressure dependence. Hereafter, we denote the two liquids as L and L′ for the low- and high-temperature liquids, respectively (Fig. 1)

Fig. 1.
Fig. 1.

Schematic illustration of evolution of Bi liquid structure under high pressures and magnetic properties of recovered Bi samples. The star (⋆) represents a liquid–liquid transition at ambient pressure (7). Circles (●) are our observed liquid–liquid transitions at 2 and 4 GPa. The pressure–temperature phase diagram is redrawn according to the results of a number reports. In a narrow pressure range between ∼1.6 and ∼2.4 GPa, melting of Bi involves no change in density. Within this narrow pressure range, “deep” melt of Bi above ∼1,250 K exhibits irreversible structural changes with cooling (dashed line labeled as irreversible). At higher pressures or lower temperatures, only reversible behavior is observed (thin black lines labeled as reversible). A surprising weak ferromagnetism is observed in Bi samples quenched from the deep melt state within the said narrow pressure range.

The complex bonding characteristics of Bi-I result in striking differences in material properties between surface and bulk in the A-7 structure. Bulk Bi-I possesses rich unusual electronic properties, such as high electrical resistance (13, 14), large magnetoresistance (15⇓–17), and unusually great Hall effect (18⇓–20). Together with its low melting point (6, 11), these properties make Bi an important material with wide industrial and engineering applications. The surfaces of Bi-I single crystals are a much better metal than the bulk because of the existence of electronic surface states crossing the Fermi level (21). Under ambient pressure, bulk Bi-I is not superconducting (14), but superconductivity has been reported in twisted Bi-I bicrystals (22⇓–24), Bi-I single crystalline and granular nanowires by electrochemically depositing Bi into porous polycarbonate membrane (25⇓–27), and granular films of Bi clusters (28, 29). These observed superconducting behaviors are related to either surface, such as grain boundaries (25⇓–27) and twisted interfaces (22⇓–24), or electronic properties of nanometer-sized Bi clusters (29).

Here, we report unusual ferromagnetism in bulk Bi samples recovered from a deep molten state at temperatures above ∼1,250 K and pressures of 1.4–2.5 GPa. In an effort to understand this surprising ferromagnetism in association with melting, we discover another surprise of liquid Bi. When liquid L′ is cooled to below 1,250 K, certain structural characteristics of liquid L′ are preserved in L. Bi clusters with characteristics of the liquid L′ motifs are further preserved through solidification into the Bi-II phase across the pressure-independent melting curve. To our knowledge, such a “memory effect” in the liquid state has never been reported before. We attribute the unusual ferromagnetism to the structure memory effect: clusters of Bi in configurations similar to the structural motifs of liquid L′ are preserved through quenching across liquid L into the solid state (Bi-II). These clusters, which possess magnetic moments as have been shown by experiments and theoretical simulations (30⇓–32), are responsible for the ferromagnetism in the bulk samples.

Results

Ferromagnetism in Bi After High-Pressure Deep Melting.

Bulk Bi samples were compressed to pressures of 1–4 GPa and heated to temperatures up to 2,373 K for a dwelling time of 30 min, and then, they were quenched (Materials and Methods and cell assemblies used are shown in Fig. S2). Experimental conditions are given in Table S1. Hereafter, samples treated at high pressure and temperature are denoted as Bi(P, T), where P and T indicate the applied pressure (in gigapascals) and temperature (in Kelvin), respectively, from which the sample was quenched. Fig. 2A shows measured magnetization (M) as a function of magnetic field (H) for a series of samples Bi(P, 2,173), with P= 1.4–3.0 GPa. The measured M contains a large diamagnetic contribution as exemplified by sample Bi(3, 2,173), which is purely diamagnetic. Superimposed on the diamagnetic background, anomalous ferromagnetism with small hysteresis is observed. By subtracting the diamagnetic background, saturation magnetization (MS) is obtained (Fig. 2A, Inset). MS is present only in samples treated at pressures from 1.4 to 2.5 GPa, peaking around 2 GPa. Outside this narrow pressure range, no ferromagnetism is observed (MS = 0). This pressure window coincides with the span of the flat melting curve of Bi-II (Fig. 1).

Fig. 2.
Fig. 2.

Ferromagnetism measured in Bi samples quenched from deep melting. (A) M vs. H curves for Bi(P, 2,073) samples. (B) M vs. H curves for Bi(2, T) samples. Insets show the determined ferromagnetic saturation magnetization (MS) after subtraction of the diamagnetic contribution. (C) M vs. H curves for Bi(2, 2,273) samples obtained in the Kawai-type apparatus by rapid quenching (red curve) and slow cooling (black line). The rates of temperature changes in quenching and slow cooling are shown in Insets in the upper right and the lower left, respectively.

Fig. S2.
Fig. S2.

Schematic assemblies of Bi samples in (A) cubic anvil and (B) Kawai-type apparatus presses for heat treatments under high pressure.

View this table:
Table S1.

Experimental conditions under which heat treatments have been performed and recovered Bi samples

The appearance of ferromagnetism also depends on temperature. Fig. 2B shows the M vs. H curves for samples Bi(2, T), and Fig. 2B, Inset gives the determined MS, which decreases rapidly with decreasing temperature from 2,273 K and disappears completely below 1,273 K. Similar measurements on the as-received samples show a strong diamagnetic behavior (Fig. S3A), consistent with previous reports (33). Note that the melting temperatures in these experiments are much lower than the estimated boiling temperature (1,837 K at 1 atm and increases sharply with pressure) of Bi.

Fig. S3.
Fig. S3.

(A) M vs. H curve for the as-received starting Bi sample showing a normal diamagnetic behavior of rhombohedral Bi. M vs. H curves for the Bi(P, 2,273) samples obtained after the heat treatments in the (B) cubic and (C) Kawai presses. Insets in the lower right show the saturation magnetization of MS determined by subtraction of the diamagnetic contribution and its dependence on the applied pressure, and Insets in upper left show the drop of temperature with time after shutting off the heating current.

More than 20 samples were treated in two different high-pressure devices (Materials and Methods and SI Text). Fig. S3 B and C shows measurements on two series of samples Bi(P, 2,173): one conducted in the cubic anvil press, and the other conducted in the Kawai-type apparatus. The agreement in the general pressure dependence is excellent. The results confirm that this surprising ferromagnetism is present only in samples treated at pressures between 1.4 and 2.5 GPa and temperatures above 1,273 K. However, exact values of saturation magnetization and coercivity can be somewhat different because of many factors, such as cooling rate, different pressure media, heater and capsule materials, and assembly preparation procedures. Among these factors, cooling rate is the most critical. Fig. 2C shows M vs. H curves for two Bi(2, 2,273) samples obtained by quenching or cooling slowly to room temperature in the Kawai-type apparatus. No ferromagnetism is observed in the sample that was slowly cooled to room temperature.

Structure of Bi Liquid at High Pressures and Temperatures.

High-pressure, high-temperature liquid structure study was carried out on bulk Bi using a multiangle energy-dispersive X-ray diffraction (EDXRD) technique at the 16-BM-B beamline at the Advanced Photon Source (34) (Materials and Methods and the cell assembly used is shown in Fig. S4). Fig. S5 displays obtained structural factors, S(q), of Bi liquid at 2 and 4 GPa up to 2,000 K. On heating to 1,050 K, all S(q) data contain a well-resolved small peak (q1′) around 2.9 Å−1 (corresponding to an interatomic spacing of ∼2.2 Å) on the high-q side of the first sharp diffraction peak (FSDP) near 2.5 Å−1. This small peak has been observed in previous structural studies on Bi liquid at ambient pressure as a shoulder next to the FSDP (7, 35, 36). At 2 GPa, the small peak shifts on heating toward lower q, with diminishing intensity, until about 1,500 K, where it merges into the tail of the FSDP, becoming nonresolvable (Fig. S5A). On cooling from 2,000 to 650 K, the peak does not return to its original position and intensity (Fig. S5A).

Fig. S4.
Fig. S4.

Cross-section of the cell assembly used for in situ EDXRD experiments. Inset in the upper right shows the Bi foil being sandwiched by two half-cylinders of BN. The foils was perpendicular to the incident X-ray beam in multiangle EDXRD experiments.

Fig. S5.
Fig. S5.

Structural factors S(q) of liquid Bi at various pressure and temperature conditions. Here, q=4πsinθ/λ is the momentum transfer, with θ being the diffraction angle and λ being the wavelength. Red solid curves are structural factors obtained on heating (from 650 K). Black dotted curves are those obtained on cooling from maximum temperature as indicated: (A) 2 GPa up to 2,000 K [note irreversible changes in S(q) through the heating/cooling cycle], (B) 2 GPa up to 1,000 K [S(q) is completely reversible], and (C) 4 GPa up to 2,000 K [S(q) are reversible].

After determining the positions for the second main peak (q2) and the FSDP (q1), we plot the ratio q2/q1 in Fig. S6. At 2 GPa, a discontinuity is observed in q2/q1 near 1,250 K on heating. On cooling from 2,000 K, the ratio decreases continuously until 1,250 K and then remains roughly constant at lower temperatures, suggesting that the liquid structural change is not reversible. However, when the liquid is heated to 1,000 K and cooled back down at 2.0 GPa (○ in Fig. S6), the ratio is completely reversible. At 4 GPa, the ratio shows a jump in its temperature dependence near 1,250 K, but the behavior is completely reversible with heating/cooling cycles up to 2,000 K (Fig. S6).

Fig. S6.
Fig. S6.

Ratio of q2/q1 in S(q) on heating (red) and cooling (black). Here, q1,2 are positions of the FSDP and the second main peak around 4.5 Å−1, respectively. Red and black symbols represent data obtained with increasing and decreasing temperature, respectively. Data from two heating and cooling cycles are shown at 2 GPa: one up to 2,000 K (open triangles) and the other up to 1,000 K (open circles). Ratio for the 1,000-K cycle is completely reversible. At 4 GPa, the ratio (solid triangles) exhibits a significant jump in the slope of the q2/q1 vs. temperature curve at 1,250 K, but the behavior is completely reversible between 650 and 2,000 K.

Pair distribution functions, g(r), are calculated from the structure factors. Density information is required for these calculations. We used the liquid density data up to 800 K measured at ambient pressure (7) and extrapolated them to 2,000 K (Fig. S7A, red line). To check the pressure effect on density, we also calculated liquid density based on the equations of state of crystalline Bi-I at 2 GPa (37) (Fig. S7A, black line). These two datasets may be considered as bounds. Although a change in g(r) is visible using the two density datasets, the changes in peak positions of r1 and r2 are within experimental errors (Fig. S7B). Therefore, within a reasonable uncertainty, density is not sensitive to the peak positions of r1 and r2. The obtained g(r) shows a prominent, albeit small, peak near 5 Å at 2 GPa and 2,000 K between the first and second main peaks that are centered around 3.5 and 6.5 Å, respectively (Fig. 3A). With decreasing temperature from 2,000 K, the small peak remains until about 1,250 K, below which it becomes nonresolvable as a shoulder begins to grow on the right-hand side of the first main peak. With further decrease in temperature, the shoulder grows stronger, so that the 650-K g(r) curve obtained on cooling becomes significantly different from that obtained on heating. This temperature-induced change in g(r) is sensitive to both pressure and temperature. At the same pressure of 2 GP, heating liquid Bi to 1,000 K and then cooling down do not induce observable changes in g(r) (Fig. 3B). At a higher pressure of 4 GPa, heating liquid Bi to 2,000 K and then cooling down do not induce any observable change either (Fig. 3C).

Fig. 3.
Fig. 3.

Pair distribution functions g(r) of liquid Bi at various pressure and temperature conditions calculated from the corresponding structural factors S(q) given in Fig. S6. Curves obtained during heating and cooling are colored red and black, respectively. (A) Heating and cooling cycle between 650 and 2,000 K at 2 GPa. The 2,000-K curve shows a small peak near 5 Å, which persists on cooling to about 1,250 K. Note also the irreversible change in g(r) at 650 K on heating and after cooling. (B) Heating and cooling cycle between 650 and 1,000 K at 2 GPa. The g(r) curves are completely reversible. (C) Heating and cooling cycle between 650 and 2,000 K at 4 GPa. The g(r) curves are also reversible.

Fig. S7.
Fig. S7.

Effect of density on g(r) for liquid Bi. (A) Density of liquid Bi as a function of temperature. Black circles are density data calculated according to equation of state (EOS) data of crystalline Bi-I at 2 GPa (40), whereas red circles are experimental (labeled as EXP) data obtained at ambient pressure (7). (B) Pair distribution functions g(r) of liquid Bi at 2 GPa and 2,000 K using the different density data in A. The peak positions of r1 and r2 are not affected by the choice of initial density data.

Fig. 4 summarizes the positions of the first (r1) and second (r2) main peaks in g(r) through the different heating and cooling cycles at 2 and 4 GPa. Both r1 and r2 decrease with increasing temperature from 650 K. For r1, the rate of decrease exhibits a discontinuity at 1,250 K, so that above 1,250 K, r1 remains constant. The overall behavior is reversible on cooling (Fig. 4A). However, r2 shows a significant jump at 1,250 K on heating. This discontinuity is irreversible on cooling (Fig. 4A). When heating is limited to below 1,250 K, both r1 and r2 show no irreversible behavior at 2 GPa (Fig. 4B). At 4 GPa, r2 exhibits a similar jump near 1,250 K, but the behavior is reversible on cooling from 2,000 K (Fig. 4C). These results clearly show that, around 2 GPa, Bi liquid under deep melt conditions (T>1,250K) exhibits irreversible structural changes when cooled back down to below 1,250 K.

Fig. 4.
Fig. 4.

Positions of the first (r1) and second (r2) peaks in pair distribution functions g(r) of liquid Bi at various pressures and temperatures: (A) 2 GPa up to 2,000 K (note the obvious irreversible changes in r2 through the heating/cooling cycle), (B) 2 GPa up to 1,000 K (both r1 and r2 are reversible), and (C) 4 GPa up to 2,000 K (r1 and r2 are also reversible).

Transmission EM on Recovered Samples.

High-resolution transmission EM (HRTEM) on samples quenched from deep melt around 2 GPa reveals evidence of defects. In the 30×30-nm2 area shown in Fig. S8, numerous domains of various polytypes are observed that have close similarity to the A-7 structure (38). Crystal lattice varies smoothly across the domains with poorly defined domain boundaries. Thickness of the transition layers across nanometric crystalline domains in HRTEM images is typically 2–3 nm. Such fuzzy boundary layers are ubiquitous throughout samples quenched from deep melt around 2 GPa. In addition, crystals recovered from melts at high pressure exhibit strikingly different melting points under a transmission electron microscope (39), suggesting highly defective crystal structures.

Fig. S8.
Fig. S8.

HRTEM images obtained from the recovered sample Bi(2, 2,273). (A) Fast Fourier transform (FFT)-filtered HRTEM image and (Inset) the corresponding FFT pattern viewed along the [100] zone axis. Note the mottled appearance of the entire area. The area contains numerous small domains of different polytypes, but no domain boundaries can be clearly defined. (B and C) Enlarged HRTEM images of selected areas marked by the red rectangles in A. Schematics (blue dots) in B show ideal arrangement of atoms within the bilayers in the A-7 structure. Note deviation of local structures from rhombohedral A-7 by various extents and the obvious deviation in some local areas outlined by red circles in B and C.

Discussion

Structural Transition and Memory Effect in Liquid Bi.

We interpret the discontinuities in structural factors (Fig. S6) and pair distribution functions (Fig. 4) as caused by a structural change in Bi liquid through deep melting. The temperatures at which structural discontinuities are observed on heating at 2 and 4 GPa are plotted as blue dots in Fig. 1. No other structural changes were observed. The transition temperatures are in general agreement with the transition observed at 1 atm (∼1,010 K) (7). The disappearance of the small peak at ∼2.9 Å−1 above ∼1,250 K (Fig. 3 B and C) is also consistent with the proposed liquid–liquid transition. The small peak q1′ at ∼2.9 Å−1 was previously interpreted as a signature of a short-lived diatomic molecular unit (Bi2) in liquid state according to ab initio molecular dynamics calculations on small clusters of Bi atoms at 600 K (40). However, if the formation of the Bi2 units were caused by the breakup of larger structural units (such as the bilayers), which are related to the low-temperature crystalline phase, then the population of Bi2 should increase with temperature, because the liquid is expected to be more disordered. This assumption is not the case according to our observations (Fig. 3), which show that the intensity of the small peak continues to decrease with increasing temperature. We note that this peak, ∼2.2 Å in real space, is virtually identical to the distance between the bilayers in the Bi-II phase (Fig. S1).

Based on the complex interatomic binding in rhombohedral Bi-I, the 1-atm melting process has been postulated to occur in two discrete steps (41). The first step involves loosening of the adjacent bilayers, leading to a liquid crystal-like (or “smectic-like”) liquid (L) near 544 K, while retaining the threefold rotational symmetry in the Bi4 motifs in the bilayers. With increasing temperature, the bilayers gradually loosen their bond coherence. When temperature is sufficiently high (>1,010 K), the bond-orientational ordering of the Bi4 motifs disappears, resulting in a more randomly disordered liquid (L′). Two pieces of experimental evidence support the notion that the structure of L is unusual. (i) Molten Bi just above 544 K exhibits a peculiar memory effect, with solidified melt “remembering” the crystallographic orientation of the crystals before melting (42). (ii) Ambient pressure sound velocity of Bi is reported to remain constant across melting for a range of 60 K into the melt (43). The structural similarity between Bi-I and Bi-II (Fig. S1) further suggests that the two-step melting model (41) is applicable to Bi-II melting. The fact that Bi-II melts independent of pressure (i.e., melting is associated with no change in density) further suggests that liquid L is structurally more closely related to Bi-II than Bi-I. Indeed, undercooled liquid L by droplet emulsion forms metastable crystals at ambient condition with structure that is distinct from that of Bi-I but similar to that of the monoclinic Bi-II phase (44). It is, therefore, likely that this peak represents a remnant of the bilayer-like units in liquid L, consistent with the two-step liquid model (41). The irreversible liquid structure change above ∼1,250 K at 2.0 GPa indicates that, around this pressure and at temperatures deep in the liquid state, Bi possesses certain “memory” of the L′ structural units on cooling. Note that the cooling rate in the liquid structure experiments was very slow, because each diffraction pattern in Fig. 3 required 2 h to acquire. Even at such a slow cooling rate, certain characteristics of L′ were still preserved in liquid L. If Bi is cooled rapidly from L′, more structural units of L′ are likely to be preserved in liquid L. Unfortunately, an attempt to study liquid structure by rapid cooling was unsuccessful, because a significant pressure drop was encountered. To our knowledge, Bi is the first elemental material to show the ability to “remember” its liquid structural motifs when crossing a pressure-independent melting line into crystalline field (Bi-II). The physical origin of this surprising behavior requires additional investigation.

Origin of Ferromagnetism in Bi.

The conditions of irreversible structural change in Bi liquid correlate remarkably well with those under which the anomalous ferromagnetism appears in quenched crystalline bulk Bi. This coincidence strongly suggests that the anomalous ferromagnetism is related to deep melting of Bi. HRTEM imaging reveals fuzzy boundaries across crystalline domains in Bi quenched from melting. These boundaries, being 2 to 3 nm thick with poorly defined lattice structure, may be considered as formed by various Bi clusters. For liquid Bi at 2 GPa, a small peak near 5 Å is observed in the g(r) at 2,000 K and the subsequent pair distribution functions down to 1,250 K (Fig. 3A). According to density functional/molecular dynamics simulations (30), this small peak corresponds to the species with CN≈12 in liquid Bi determined with bond distance cutoffs around 5 Å. Various sizes of Bi clusters have been reported. In Bi thin films, Bi clusters exhibit a critical linear size (l) on the order of 4 nm, below which Bi clusters are amorphous-like with strongly increased conduction electron density and density of states at the Fermi energy (29). It has also been reported that Bi clusters with well-defined size l exhibit superconductivity, with superconducting transition temperature (TC) dependent on l: TC decreases from 4.3 K for l∼5 nm to < 2 K for l∼20 nm (28). Although detailed structural properties of such clusters are unknown, first principles calculations (31) on BiN and BiN − clusters (with N from 2 to 13) show that many clusters have ground-state free energies very close to that of the A-7 structure, suggesting that these clusters coexist with the Bi-I phase at ambient condition. Furthermore, individual BiN clusters with N being odd have been shown to exhibit paramagnetism with magnetic moments <3 μB according to Stern–Gerlach deflection measurements at low temperature (32).

At nanoscale, broken bonds and nonbonding electrons may become dominant, with emerging new physical properties in many single-element materials. Noble metals Au, Pt, and Rh change from conductors to insulators and from nonmagnetic to magnetic (45, 46); ferromagnetism is observed in room temperature graphene and attributed to nanometer-sized defects (47). First principles calculations support the notion that single-atom defects can induce ferromagnetism in graphene (48). These results combined with evidence of Bi clusters led us to speculate that the unusual ferromagnetism in Bi recovered from deep melt originates from cluster-like disordered Bi layers across crystalline domains. These layers are likely preserved from liquid L′ during quenching, because samples quenched from liquid L do not exhibit ferromagnetism. However, a complete picture of the origin of ferromagnetism in Bi requires additional investigations to determine the exact kinds (and sizes) of clusters that are responsible for the ferromagnetism. Other possible mechanisms, such as topological electronic states of Bi, may also play roles in the origin of ferromagnetism.

In conclusion, the anomalous ferromagnetism in solid Bi quenched from the deep melt is closely correlated with the structural memory effects of liquid Bi. The ability for solid Bi to remember liquid structure motifs seems to be related to structural similarities between the solid and liquid around 2 GPa, where melting temperature is pressure-independent (i.e., no discontinuity in specific volume or density across the melting line). Using flat melting curves as a rough guideline (49), we speculate that similar effects may be present in other elements, such as Sb, Te, Ce, Pu, and Te, etc., when quenched from a deeply molten state. Such effects should be considered as a pathway in tailoring physical properties of these and related materials.

Materials and Methods

In Situ EDXRD Experiments.

The in situ EDXRD experiments were performed using a VX-3 Paris–Edinburgh press at the white X-ray beamline 16-BM-B (High Pressure Collaborative Access Team at the Advanced Photon Source, Argonne National Laboratory). The sample cell assemblages, which are optimized to maintain sufficient vertical access for the X-ray beam, are illustrated in Fig. S4. In both the melt study and the high-pressure, high-temperature treatment for magnetic measurements, starting material was Bi granules purchased from Alfa Aesar (purity of 99.999%). For melt structure study, a slice of Bi 50 μm in thickness, 1.8 mm in length, and 1.0 mm in width was loaded in a boron nitride (BN) capsule, which is surrounded by a cylindrical graphite heater. The pressure was determined from the thermal equation of the state of the magnesium oxide (MgO) pressure-transmitting media (50), and the estimated errors in pressure were ±0.2 GPa. The temperature was determined using the power–temperature curves calibrated in an identical cell assembly (34). The incident white X-ray beam was collimated to a size of 0.3 mm (vertical) × 0.1 mm (horizontal) using two sets of tungsten slits. The sample was first compressed to a desired pressure at room temperature and then increased to high temperature above the melting curve. The X-ray diffraction patterns of the liquid sample were collected by a Ge solid-state detector at 10 different 2θ angles (3∘, 4∘, 5∘, 7∘, 9∘, 11∘, 14∘, 17∘, 21∘, and 25∘) to cover a large range in Q space (Q = 4πEsinθ/12.398, where E is the X-ray energy up to 100 keV). The typical time for collecting one set of diffraction patterns of 10 angles was 2 h. Details of the EDXRD measurement and data analysis method are described elsewhere (34).

Heat Treatments of Bulk Bi Under High-Temperature, High-Pressure Condition.

The high-temperature, high-pressure (HTHP) treatments of Bi cylinder were performed in two types of press equipment: one is a dominantly used large-volume cubic press of six tungsten carbide (WC) anvils (cubic anvil), and the other is a cubic press of eight WC anvils (Kawai-type apparatus; T25). The Bi cylinders were used for the HTHP treatments, and they were initially formed by compressing the as-received Bi granules. The schematic illustration in Fig. S2A displays the assembly of a Bi cylinder for the dominant HTHP treatments in the six-anvil cubic press. A Bi cylinder of 6 mm in diameter and 6 mm in height was wrapped by a BN capsule of 8-mm o.d. and inserted into a graphite tube heater of 8-mm i.d. and 10-mm o.d.; then, they were placed into a pyrophyllite cube of 49 mm in length. A zirconia tube was used between the graphite tube and the pyrophyllite cube. The pyrophyllite cube served as both pressure medium and gasket in the six-anvil cubic press. For the HTHP treatments in the eight-anvil press, the similar assembly of a Bi cylinder of 2.8 mm in diameter and 3.5 mm in height was made as schematically shown in Fig. S2B, but a magnesia octahedron was used to replace the pyrophyllite cube. In all of the performed HTHP treatments, the Bi sample was heated at a rate of 100∘C/min via current to a desired high temperature under an applied high pressure. After a dwelling time of 30 min at the desired temperature, the heating current was immediately shut off for quenching the Bi sample to room temperature, and then, the applied pressure was released. During the HTHP treatment, the temperature was in situ-monitored with a type C thermocouple (W5/Re26), and the pressure was estimated from a calibration curve of pressure based on the electrical resistance changes during the phase transitions of Bi at room temperature.

SI Text

Measurements of Selected Area Electron Diffraction, High-Resolution Transmission Electron Microscopy (HRTEM), and Bulk Magnetization.

The as-received Bi granules and the HTHP-treated Bi samples were ground in an agate mortar with a pestle for the measurements of selected area electron diffraction (SAED) and high-resolution transmission electron microscopy (HRTEM). The SAED and HRTEM measurements were carried out in JEM-2010 at an accelerating voltage of 200 kV, during which the low-intensity electron beam was used by narrowing the diaphragm to block most of the electron beam (about 80–90%). Bulk magnetization was measured in a vibrating sample magnetometer attached to the physical property measurement system (PPMS-9; Quantum Design).

Error Analysis.

The errors of q1 and q2 have been estimated from error sources in experimental measurements and data processing. In data processing, we mainly consider the uncertainties in q values obtained by using different energy windows in the raw data from the multiangle EDXRD measurements. Because of the absorption of the cell assembly and the use of tungsten in the collimation system (34), we find it necessary to select an effective window for data analysis. However, the cutoff channels (low and high) may vary a little. The average deviations in q are found to be about 0.004–0.008 Å−1 (∼0.1–0.3%), even with the most extreme window selections in our data analysis. In peak position determination, we use an interpolation approach, which typically gives an uncertainty in q of less than 0.005 Å−1. Among experimental errors, the largest error comes from the effect of pressure deviation on q. In our in situ experiments, the pressure deviation is about ±0.2GPa, which results in about 0.7% volume change and an error in q of 0.2% (about 0.004 Å−1) to our samples. Therefore, we estimated the errors of q2/q1 of about 0.008–0.011 calculated byEr(q2q1)=±(1q1)2Δq22+(q2q12)2Δq12≈±0.009.Because these errors are not statistical numbers from multiple measurements, we apply this estimation for all data points at different temperature and pressure conditions.

For peak position determination in g(r), we use the interpolation approach. For all of the g(r) data, the deviations of r1 and r2 are about 0.002 and 0.005 Å, respectively. Combined with the errors in S(q) (∼0.3–0.5%), the errors in r are about 0.009–0.02 Å for all g(r) curves.

Acknowledgments

We thank Curtis Kenney-Benson for assistance in experiments. We appreciate the financial support of National Natural Science Foundations of China Grants 51421091, 51332005, and 51025103 and Ministry of Science and Technology of China Grant 2011CB808205. Y.W. acknowledges support from US National Science Foundation (NSF) Grants EAR-1214376, 1361276, and 1620548. G.S. acknowledges the support of Department of Energy (DOE)-Basic Energy Sciences (BES), Division of Materials Science and Engineering Award DE-FG02-99ER45775. High Pressure Collaborative Access Team operations are supported by DOE-National Nuclear Security Administration (NNSA) Award DE-NA0001974 and DOE-BES Award DE-FG02-99ER45775, with partial instrumentation funding by the NSF. The Advanced Photon Source is a US DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357.

Footnotes

  • ↵1Y.S. and D.Y. contributed equally to this work.

  • ↵2To whom correspondence may be addressed. Email: wang{at}cars.uchicago.edu or gshen{at}carnegiescience.edu.

  • Author contributions: Y.S., D.Y., Y.W., G.S., B.X., J.H., Z.L., and Y.T. designed research; Y.S., D.Y., W.H., and Y.K. performed research; W.H. and Y.K. contributed new reagents/analytic tools; Y.S., D.Y., W.H., Y.W., G.S., Y.K., and Z.L. analyzed data; and Y.S., D.Y., Y.W., G.S., and Z.L. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission. K.B. is a Guest Editor invited by the Editorial Board.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1615874114/-/DCSupplemental.

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Liquid structural memory and ferromagnetism in Bi
Yu Shu, Dongli Yu, Wentao Hu, Yanbin Wang, Guoyin Shen, Yoshio Kono, Bo Xu, Julong He, Zhongyuan Liu, Yongjun Tian
Proceedings of the National Academy of Sciences Mar 2017, 114 (13) 3375-3380; DOI: 10.1073/pnas.1615874114
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Proceedings of the National Academy of Sciences: 114 (13)
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