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DOE OSTI2020

Determining topological order from infinite projected entangled pair states

In this work, we present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered systems, the iPEPS wrapped on a torus becomes a superposition of degenerate, locally indistinguishable ground states. Projectors in the form of infinite matrix product operators onto states with well-defined anyon flux are used to compute topological S and T matrices (encoding mutual and self-statistics of emergent anyons). The algorithm is shown to be robust against a perturbation driving string-net toric code across a phase transition to a ferromagnetic phase. Our approach provides accurate results near quantum phase transition, where the correlation length is prohibitively large for other numerical methods. Moreover, we used numerically optimized iPEPS describing the ground state of the Kitaev honeycomb model in the toric code phase and obtained topological data in excellent agreement with theoretical prediction.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Axion insulator state in ferromagnetically ordered CrI 3 /Bi 2 Se 3 /MnBi 2 Se 4 heterostructures

Ferromagnetic (FM) axion insulators may greatly simplify experimental explorations of the topological magnetoelectric effect, as the FM ordering can be stable in a broad range of magnetic field. Through density functional theory calculations and four-band model studies, we find that two-dimensional van der Waals FM CrI 3 and MnBi 2 Se 4 overlayers induce opposite-sign exchange fields in the topological surface states of Bi 2 Se 3 film when they are ferromagnetically ordered. As a consequence, the CrI 3 /Bi 2 Se 3 /MnBi 2 Se 4 heterostructure is a robust FM axion insulator, according to surface-resolved Berry curvature calculations. Our work opens up opportunities for the design of materials with the topological magnetoelectric effect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model

In this work, we study an effective spin model derived perturbatively from a random transverse-field Ising model on the pyrochlore lattice. The model consists of spin configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization up to N=64 site systems. Furthermore, we calculate spin-glass correlation functions and local entanglement entropy S T between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where S T =ln 6. Increasing randomness, at low transverse fields, first leads to a frozen phase, with long-range spin-glass order and S T =ln 2 corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Absence of μ SR evidence for magnetic order in the pseudogap phase of Bi 2 + x Sr 2 - x CaCu 2 O 8 + δ

We present an extended zero-field muon spin relaxation (ZF-$µSR$) study of overdoped $Bi_{2+x}Sr_{2-x}\,CaCu_2O_{8+δ}$ (Bi2212) single crystals, intended to elucidate the origin of weak quasistatic magnetism previously detected by $µSR$ in the superconducting and normal states of optimallydoped and overdoped samples. New results on heavily-overdoped single crystals show a similar monotonically decreasing ZF-$µSR$ relaxation rate with increasing temperature that persists above the pseudogap (PG) temperature $T^*$ and does not evolve with hole doping ($p$). Additional measurements using an ultra-low background apparatus confirm that this behavior is an intrinsic property of Bi2212, which cannot be due to magnetic order associated with the PG phase. Instead we show that the temperature-dependent relaxation rate is most likely caused by structural changes that modify the contribution of the nuclear dipole fields to the ZF-$µSR$ signal. Finally, our results for Bi2212 emphasize the importance of not assuming the nuclear-dipole field contribution is independent of temperature in ZF-$µSR$ studies of high-temperature (high-$T_c$) cuprate superconductors, and do not support a recent $µSR$ study of $YBa_2Cu_3O_{6+x}$ that claims to detect magnetic order in the PG phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Unveiling the medium-range order in glass models and its role in glass formation

The correlation between structure and glass formability in glassy systems is a long-standing puzzle. To solve this puzzle, many descriptors based on the short-range order (SRO) have been proposed. In this paper we show that the SRO, however, offers little help in explaining the glass formability and stability; instead it is the formation of medium-range order that stabilizes the glass against crystallization by suppressing the atomic rearrangement and compositional change. Our results provide a perspective for understanding the correlation between structure and stability in glasses.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Doping-dependent phonon anomaly and charge-order phenomena in the HgBa 2 CuO 4 + δ and HgBa 2 CaCu 2 O 6 + δ superconductors

Using resonant x-ray diffraction and Raman spectroscopy, we study charge correlations and lattice dynamics in two model cuprates, HgBa 2 CuO 4 + δ and HgBa 2 CaCu 2 O 6 + δ . We observe a maximum of the characteristic charge order temperature around the same hole concentration (p ≈ 0.09) in both compounds, and concomitant pronounced anomalies in the lattice dynamics that involve the motion of atoms in and/or adjacent to the CuO 2 layers. These anomalies are already present at room temperature, and therefore precede the formation of the static charge correlations, and we attribute them to an instability of the CuO 2 layers. Our finding implies that the charge order in the cuprates is an emergent phenomenon, driven by a fundamental variation in both lattice and electronic properties as a function of doping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

First-order magnetic phase transition in P r 2 In with negligible thermomagnetic hysteresis

Magnetic first-order phase transitions are key for the emergence of functionalities of fundamental and applied significance, including magnetic shape memory as well as magnetostrictive and magnetocaloric effects. Such transitions are usually associated with thermomagnetic hysteresis. In this paper we report the observation of a firstorder transition in Pr 2 In from a paramagnetic to a ferromagnetic state at $T_C$ = 57K without a detectable thermomagnetic hysteresis, which is also accompanied by a large magnetocaloric effect. The peculiar electronic structure of Pr2In exhibiting a large density of states near the Fermi energy explains the highly responsive magnetic behavior of the material. The magnetic properties of Pr 2 In are reported, including observation of another (second-order) magnetic transition at 35 K.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Theory of strain-induced magnetic order and splitting of $T_c$ and $T_{\text{TRSB}}$ in Sr 2 RuO 4

The internal structure of the superconducting state in Sr 2 RuO 4 remains elusive at present, and exhibits evidence for time-reversal symmetry breaking. Recent muon spin relaxation measurements under uniaxial strain have revealed an increasing splitting between the superconducting critical temperature $T_c$ and the onset of time-reversal symmetry breaking $T_{\text{TRSB}}$ with applied strain. In addition, static magnetic order is induced by the uniaxial strain beyond ~1 GPa, indicating that unstrained Sr 2 RuO 4 is close to a magnetic quantum critical point. Here we perform a theoretical study of the magnetic susceptibility and the associated pairing structure as a function of uniaxial strain. In this work, it is found that the recent muon relaxation data can be qualitatively explained from the perspective of spin-fluctuation mediated pairing and the associated strain dependence of accidentally degenerate pair states in unstrained Sr 2 RuO 4 . In addition, while unstrained Sr 2 RuO 4 features mainly (2π /3, 2π /3) magnetic fluctuations, uniaxial strain promotes (π, ±π /2) magnetic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Laser pulse driven control of charge and spin order in the two-dimensional Kondo lattice

Fast and dynamical control of quantum phases is highly desired in the application of quantum phenomena in devices. On the experimental side, ultrafast laser pulses provide an ideal platform to induce femtosecond dynamics in a variety of materials. Here we show that a laser pulse driven heavy fermion system can be tuned to dynamically evolve into a phase, which is not present in equilibrium. Using the state-of-the-art time-dependent variational Monte Carlo method, we perform numerical simulations of realistic laser pulses applied to the Kondo lattice model. By tracking spin and charge degrees of freedom we identify a dynamical phase transition, within the partially Kondo screened phase, from a charge ordered into a metallic state, while preserving the spin order of the system. Furthermore, we propose using high-harmonic generation and nonequilibrium optical conductivity to identify the dynamical phase transition in an ultrafast experiment.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Measurement of Ehrlich-Schwoebel barrier contribution to the self-organized formation of ordered surface patterns on Ge(001)

Normal-incidence 1-keV Ar + ion bombardment leads to amorphization and ultrasmoothing of Ge at room temperature, but at elevated temperatures the Ge surface remains crystalline and is unstable to the formation of self-organized nanoscale patterns of ordered pyramid-shaped pits. The physical phenomenon distinguishing the high-temperature patterning from room-temperature ultrasmoothing is believed to be a surface instability due to the Ehrlich-Schwoebel barrier for diffusing vacancies and adatoms, which is not present on the amorphous material. This real-time grazing-incidence small-angle x-ray scattering study compares smoothing of a prepatterned Ge sample at room temperature with patterning of an initially flat Ge sample at an elevated temperature. In both experiments, when the nanoscale structures are relatively small in height, the average kinetics can be explained by a linear theory. Furthermore, the linear theory coefficients, indicating surface stability or instability, were extracted for both experiments. A comparison between the two measurements allows estimation of the contribution of the Ehrlich-Schwoebel barrier to the self-organized formation of ordered nanoscale patterns on crystalline Ge surfaces.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Noncollinear antiferromagnetic order in the buckled honeycomb lattice of magnetoelectric Co 4 Ta 2 O 9 determined by single-crystal neutron diffraction

Co 4 Ta 2 O 9 exhibits a three-dimensional magnetic lattice based on the buckled honeycomb motif. It shows unusual magnetoelectric effects, including the sign change and nonlinearity. These effects cannot be understood without the detailed knowledge of the magnetic structure. Herein, we report neutron diffraction and direction-dependent magnetic susceptibility measurements on Co 4 Ta 2 O 9 single crystals. In this work, below 20.3 K, we find a long-range antiferromagnetic order in the alternating buckled and flat honeycomb layers of Co 2+ ions stacked along the c axis. Within experimental accuracy, the magnetic moments lie in the ab plane. They form a canted antiferromagnetic structure with a tilt angle of ~14° at 15 K in the buckled layers, while the magnetic moments in each flat layer are collinear. This is directly evidenced by a finite (0, 0, 3) magnetic Bragg peak intensity, which would be absent in the collinear magnetic order. The magnetic space group is C2/c'. It is different from the previously reported C2/c' group, also found in the isostructural Co 4 Nb 2 O 9 . The revised magnetic structure successfully explains the major features of the magnetoelectric tensor of Co 4 Ta 2 O 9 within the framework of the spin-flop model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Influence of hydrostatic pressure on hidden order, the Kondo lattice, and magnetism in URu 2 Si 2-x P x

Within the chemical substitution series URu 2 Si 2-x P x , there is an evolution in the ground-state behavior from hidden ordered (HO) for x ≲ 0.03, to Kondo lattice behavior with no ordering (NO) for 0.03 ≲ x ≲ 0.26, to antiferromagnetism (AFM-2) for 0.26 ≲ x ≲ 0.5 [A. Gallagher et al., Nat. Commun. 7, 10712 (2016); A. Gallagher et al., J. Phys.: Condens. Matter 29, 024004 (2016)]. To better understand what factors control this behavior, temperature-dependent electrical resistivity measurements are performed for this series under applied pressures P up to 20.5 kbar. Specimens in the HO x region show similarities to the parent compound, where HO transforms into antiferromagnetism (AFM-1) at a critical pressure (P c ). P c decreases with increasing x and collapses towards P = 0 near x ≈ 0.03, suggesting that AFM-1 occurs at ambient pressure for this concentration. No pressure-induced phase transitions are observed in the NO x region and the AFM-2 state is only weakly suppressed by P. Measurements further reveal that AFM-1 and AFM-2 are distinct from each other. Calculations of the wave functions using the tight-binding Hartree-Fock approximation are performed and show (i) that the radial probability distributions for the phosphorus ions are more tightly bound than those for the silicon and (ii) that the energy difference between the orbitals decreases with increasing x. The cumulative effect of these two factors is that Si → P substitution decreases the hybridization strength, which correlates with the weakening of HO. At large x, additional effects such as electrical charge tuning also play an important role in determining the ground-state

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Effect of surface steps on chemical ordering in the subsurface of Cu(Au) solid solutions

Atomic steps are typically assumed to only influence surface phenomena of solids. In contrast, in this paper we show, using in-situ atomic-resolution electron microscopy observations and atomistic modeling, the pronounced effect from surface stepsin inducing compositional and structural evolution in the subsurface of a Cu(Au) solid solution. We find that Au surface segregation results in a stacked sequence of Cu-Au ordered phases in the subsurface. The presence of a monatomic step at the surface induces the formation of an anti-phase boundary that extends from the surface step to deeper layers by maintaining the same composition profile associated with each terrace. The bunching of surface steps induces chemical disordering of the Cu-Au ordered phases in the subsurface region of the bunched steps. These results demonstrate the instant propagation of surface dynamics of atomic steps into the subsurface region and can find broader applicability in utilizing surface defects to tune the composition and structure in the subsurface of alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Antiferromagnetic ordering and possible lattice response to dynamic uranium valence in U 3 O 8

Determining the correct electronic structure of U 3 O 8 remains a formidable experimental and theoretical challenge. In the low-temperature phase, two crystallographic U sites are separated into a distinct 2U(V)+1U(VI) oxidation configuration. At low temperatures, the U(V) sites form a distorted honeycomb lattice, but the U(VI) sit on a triangular sublattice, suggesting potential for magnetic frustration effects. The spin configuration of the unpaired f electrons on the U(V) sites is likely antiferromagnetic (AFM) from susceptibility measurements, but this has not been confirmed. Here in this paper, we present a neutron scattering investigation of the structure and dynamics of U 3 O 8 from 1.7 to 600 K. We confirm static AFM ordering onset at between 22 and 25 K, which is present down to at least 1.7 K with AFM peaks corresponding to [0.5 1 1] and [0.5 2 2] in the orthorhombic phase. These measurements rule out static AFM order along the a axis of the Amm2 phase, a configuration previously suggested by theory. Above 100 K a quasielastic scattering channel opens that we speculate arises from a lattice relaxation response to thermally activated electron hopping. This term does not conform to a magnetic form factor, so it is not related to spin relaxations. If correct, this mechanism stabilizes a continuous valence transition from 2U(V)+1U(VI) in the low-temperature (T<600 K) orthorhombic phase to the hexagonal phase that contains only one degenerate U site, wherein the U valence can be dynamically stabilized between U(V)↔U(VI) by phonon-assisted electron hopping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Direct imaging of electrical switching of antiferromagnetic Néel order in α-Fe 2 O 3 epitaxial films

In this work, we report the direct observation of switching of the Néel vector of antiferromagnetic (AFM) domains in response to electrical pulses in micron-scale Pt/α-Fe 2 O 3 Hall bars using photoemission electron microscopy. Current pulses lead to reversible and repeatable switching with the current direction determining the final state, consistent with Hall effect experiments that probe only the spatially averaged response. Current pulses also produce irreversible changes in domain structure, in and even outside the current path. In both cases only a fraction of the domains switch in response to pulses. Furthermore, the analysis of images taken with different x-ray polarizations shows that the AFM Néel order has an out-of-plane component in equilibrium that is important to consider in analyzing the switching data. These results show that—in addition to effects associated with spin-orbit torques from the Pt layer, which can produce reversible switching—changes in AFM order can be induced by purely thermal effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Lattice symmetry breaking transition and critical size limit for ferroic orders in nanophase BiFeO3

Finite size effects on the ferroic orders in BiFeO 3 are studied by atomic pair distribution function analysis and magnetic measurements. While bulk rhombohedral BiFeO 3 exhibits ferroelectricity and antiferromagnetism with a cycloidal magnetic moment arrangement leading to zero magnetization and weak magnetoelectric coupling, BiFeO 3 nanoparticles with a size smaller than the spin cycloid period of 62 nm preserve their polar rhombohedral structure and develop ferromagnetism, thus exhibiting coexisting polarization and nonzero magnetization that enhances the magnetoelectric coupling. When the nanoparticles become smaller than 17 nm, however, their crystal lattice expands and becomes nonpolar cubic. They also become superparamagnetic and thus simultaneously cease exhibiting both ferroelectricity and ferromagnetism. Our findings shed light on the interaction between the lattice structure and ferroic orders in nanophase perovskites and also provide a rare example of a lattice symmetry breaking phase transition that determines their critical size.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Ubiquity of amplitude-modulated magnetic ordering in the H - T phase diagram of the frustrated non-Fermi-liquid YbAgGe

YbAgGe contains a magnetic geometrically frustrated kagome-like lattice that also features significant local single-ion anisotropy. The electronic state is established by hybridization of 4f and conduction electrons leading to heavy electronic masses. The competition between these various interactions leads to nontrivial behavior under external magnetic field, including a sequence of magnetic phase transitions, non-Fermi-liquid states, and possibly a quantum critical point. We present a series of neutron diffraction experiments performed in the mK temperature range and under magnetic fields up to 8 T in the hexagonal plane, revealing the microscopic nature of the first four subsequent magnetic states of this phase diagram. The magnetic phases are associated with the propagation vectors K 1 =($\frac{1}{3}$ 0 $\frac{1}{3}$) for H < 2 T, K 2 = (0 0 0.32) for 2 T < H < 3 T, K 1 = ($\frac{1}{3}$ 0 $\frac{1}{3}$) for 3 T < H < 4.5 T and k 3 = (0.195 0.195 0.38) for 4.5 T < H < 7 T. Our structural refinements reveal a strong modulation of the magnetic moment amplitude in all phases. We observe that the ordered moments of the three magnetically different Yb sites become increasingly different in field, which complies with the principle local anisotropy directions relative to the field direction. While the ordered moments are aligned predominantly in the hexagonal plane, we also find a significant out-of-plane component and a ferromagnetic contribution above 2 T. Here we discuss possible scenarios that may evolve around the phase boundary at 4.5 T, which is associated with putative quantum criticality as identified by various bulk probes. We propose further steps that are required to better understand the microscopic interactions in this material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Beyond magnons in Nd 2 ScNbO 7 : An Ising pyrochlore antiferromagnet with all-in–all-out order and random fields

We report the low-temperature magnetic properties of Nd 3+ pyrochlore Nd 2 ScNbO 7 . Susceptibility and magnetization show an easy-axis moment, and heat capacity reveals a phase transition to long-range order at T N =371(2) mK with a fully recovered ΔS=Rln(2), 53% of it recovered for T>T N . Elastic neutron scattering shows a long-range all-in all-out magnetic order with low-Q diffuse elastic scattering. Inelastic neutron scattering shows a low-energy flat band, indicating a magnetic Hamiltonian similar to Nd 2 Zr 2 O 7 . Nuclear hyperfine excitations measured by ultra-high-resolution neutron backscattering indicate a distribution of static electronic moments below T N , which may be due to B-site disorder influencing Nd crystal electric fields. Analysis of heat-capacity data shows an unexpected T-linear or T 3/2 term which is inconsistent with conventional magnon quasiparticles, but is consistent with fractionalized spinons or gapless local spin excitations. We use legacy data to show similar behavior in Nd 2 Zr 2 O 7 . Comparing local static moments also reveals a suppression of the nuclear Schottky anomaly in temperature, evidencing a fraction of Nd sites with nearly zero static moment, consistent with exchange-disorder-induced random singlet formation. Finally, taken together, these measurements suggest an unusual fluctuating magnetic ground state which mimics a spin liquid, but may not actually be one.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗