Large-moment Antiferromagnetism Research Articles

In-Plane Anisotropic Response to Uniaxial Pressure in the Hidden Order State of URu2Si2

We investigate the uniaxial-pressure dependence of resistivity for URu2−x Fe x Si2 samples with x = 0 and 0.2, which host a hidden order (HO) and a large-moment antiferromagnetic (LMAFM) phase, respectively. For both samples, the elastoresistivity ζ shows a seemingly divergent behavior above the transition temperature T 0 and a quick decrease below it. We find that the temperature dependence of ζ for both samples can be well described by assuming the uniaxial pressure effect on the gap or certain energy scale except for ζ (110) of the x = 0 sample, which exhibits a nonzero residual value at 0 K. We show that this provides a qualitative difference between the HO and LMAFM phases. Our results suggest that there is an in-plane anisotropic response to the uniaxial pressure that only exists in the hidden order state without necessarily breaking the rotational lattice symmetry.

Isoelectronic perturbations to f-d-electron hybridization and the enhancement of hidden order in URu2Si2

Electrical resistivity measurements were performed on single crystals of URu2-x Os x Si2 up to x = 0.28 under hydrostatic pressure up to P = 2 GPa. As the Os concentration, x, is increased, 1) the lattice expands, creating an effective negative chemical pressure Pch(x); 2) the hidden-order (HO) phase is enhanced and the system is driven toward a large-moment antiferromagnetic (LMAFM) phase; and 3) less external pressure Pc is required to induce the HO→LMAFM phase transition. We compare the behavior of the T(x, P) phase boundary reported here for the URu2-x Os x Si2 system with previous reports of enhanced HO in URu2Si2 upon tuning with P or similarly in URu2-x Fe x Si2 upon tuning with positive Pch(x). It is noteworthy that pressure, Fe substitution, and Os substitution are the only known perturbations that enhance the HO phase and induce the first-order transition to the LMAFM phase in URu2Si2 We present a scenario in which the application of pressure or the isoelectronic substitution of Fe and Os ions for Ru results in an increase in the hybridization of the U-5f-electron and transition metal d-electron states which leads to electronic instability in the paramagnetic phase and the concurrent formation of HO (and LMAFM) in URu2Si2 Calculations in the tight-binding approximation are included to determine the strength of hybridization between the U-5f-electron states and the d-electron states of Ru and its isoelectronic Fe and Os substituents in URu2Si2.

Anisotropic resonance modes emerging in an antiferromagnetic superconducting state

Two strong arguments in favor of magnetically driven unconventional superconductivity arise from the coexistence and closeness of superconducting and magnetically ordered phases on the one hand, and from the emergence of magnetic spin-resonance modes at the superconducting transition on the other hand. Combining these two arguments one may ask about the nature of superconducting spin-resonance modes occurring in an antiferromagnetic state. This problem can be studied in underdoped BaFe2 As2, for which the local coexistence of large moment antiferromagnetism and superconductivity is well established by local probes. However, polarized neutron scattering experiments are required to identify the nature of the resonance modes. In the normal state of Co underdoped BaFe2 As2 the antiferromagnetic order results in broad magnetic gaps opening in all three spin directions that are reminiscent of the magnetic response in the parent compound. In the superconducting state two distinct anisotropic resonance excitations emerge, but in contrast to numerous studies on optimum and over-doped BaFe2 As2 there is no isotropic resonance excitation. The two anisotropic resonance modes appearing within the antiferromagnetic phase are attributed to a band selective superconducting state, in which longitudinal magnetic excitations are gapped by antiferromagnetic order with sizable moment.

Phase diagram of URu2–xFexSi2 in high magnetic fields

Electrical transport measurements were performed on URu2 - x Fe x Si2 single-crystal specimens in high magnetic fields up to 45 T (DC fields) and 60 T (pulsed fields). We observed a systematic evolution of the critical fields for both the hidden-order (HO) and large-moment antiferromagnetic (LMAFM) phases and established the 3D phase diagram of T-H-x In the HO phase, H/H0 scales with T/T0 and collapses onto a single curve. However, in the LMAFM phase, this single scaling relation is not satisfied. Within a certain range of x values, the HO phase reenters after the LMAFM phase is suppressed by the magnetic field, similar to the behavior observed for URu2Si2 within a certain range of pressures.

Phase diagram and thermal expansion measurements on the system URu2−xFexSi2

Thermal expansion, electrical resistivity, magnetization, and specific heat measurements were performed on URu2-xFexSi2 single crystals for various values of Fe concentration x in both the hidden-order (HO) and large-moment antiferromagnetic (LMAFM) regions of the phase diagram. Our results show that the paramagnetic (PM) to HO and LMAFM phase transitions are manifested differently in the thermal expansion coefficient. The uniaxial pressure derivatives of the HO/LMAFM transition temperature T0 change dramatically when crossing from the HO to the LMAFM phase. The energy gap also changes consistently when crossing the phase boundary. In addition, for Fe concentrations at xc ≈ 0.1, we observe two features in the thermal expansion upon cooling, one that appears to be associated with the transition from the PM to the HO phase and another one at lower temperature that may be due to the transition from the HO to the LMAFM phase.

Evolution of critical pressure with increasing Fe substitution in the heavy-fermion systemURu2−xFexSi2

Measurements of electrical resistivity, $\ensuremath{\rho}(T)$, were performed under quasihydrostatic pressure up to $P\ensuremath{\sim}2.2$ GPa to determine the pressure dependence of the so-called hidden order (HO) and large-moment antiferromagnetic (LMAFM) phases for the ${\mathrm{URu}}_{2\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{Si}}_{2}$ system with $x$ = 0.025, 0.05, 0.10, 0.15, and 0.20. As the Fe concentration ($x$) is increased, we observed that a smaller amount of external pressure, ${P}_{c}$, is required to induce the HO $\ensuremath{\rightarrow}$ LMAFM phase transition. A critical pressure of ${P}_{c}\ensuremath{\sim}1.2$ GPa at $x=0.025$ reduces to ${P}_{c}\ensuremath{\sim}0$ at $x=0.15$, suggesting the ${\mathrm{URu}}_{2\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{Si}}_{2}$ system is fully expressed in the LMAFM phase for $x\phantom{\rule{4pt}{0ex}}\ensuremath{\ge}\phantom{\rule{4pt}{0ex}}{x}_{c}^{*}=0.15$, where ${x}_{c}^{*}$ denotes the ambient pressure critical concentration of Fe. Using a bulk modulus calculation to convert $x$ to chemical pressure, ${P}_{\mathrm{ch}}(x)$, we consistently found that the induced HO $\ensuremath{\rightarrow}$ LMAFM phase transition occurred at various combinations of ${x}_{c}$ and ${P}_{c}$ such that ${P}_{\mathrm{ch}}({x}_{c})+{P}_{c}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}1.5$ GPa, where ${x}_{c}$ denotes those critical concentrations of Fe that induce the HO $\ensuremath{\rightarrow}$ LMAFM phase transition for the ${\mathrm{URu}}_{2\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{Si}}_{2}$ compounds under pressure. We performed exponential fits of $\ensuremath{\rho}(T)$ in the HO and LMAFM phases in order to determine the pressure dependence of the energy gap, $\mathrm{\ensuremath{\Delta}}$, that opens over part of the Fermi surface in the transition from the paramagnetic (PM) phase to the HO/LMAFM phase at the transition temperature, ${T}_{0}$. The change in the pressure variation of $\mathrm{\ensuremath{\Delta}}(P)$ at the HO $\ensuremath{\rightarrow}$ LMAFM phase transition is consistent with the values of ${P}_{c}$ determined from the ${T}_{0}(P)$ phase lines at the PM $\ensuremath{\rightarrow}$ HO/LMAFM transition.

Role of commensurate and incommensurate low-energy excitations in the paramagnetic to hidden-order transition ofURu2Si2

We report low-energy inelastic neutron scattering data of the paramagnetic (PM) to hidden-order (HO) phase transition at $T_0=17.5\,{\rm K}$ in URu$_2$Si$_2$. While confirming previous results for the HO and PM phases, our data reveal a pronounced wavevector dependence of low-energy excitations across the phase transition. To analyze the energy scans we employ a damped harmonic oscillator model containing a fit parameter $1/\Gamma$ which is expected to diverge at a second-order phase transition. Counter to expectations the excitations at $\vec{Q}_1=(1.44,0,0)$ show an abrupt step-like suppression of $1/\Gamma$ below $T_0$, whereas excitations at $\vec{Q}_0=(1,0,0)$, associated with large-moment antiferromagnetism (LMAF) under pressure, show an enhancement and a pronounced peak of $1/\Gamma$ at $T_0$. Therefore, at the critical HO temperature $T_0$, LMAF fluctuations become nearly critical as well. This is the behavior expected of a super-vector order parameter with nearly degenerate components for the HO and LMAF leading to nearly isotropic fluctuations in the combined order-parameter space.

Chemical pressure tuning ofURu2Si2via isoelectronic substitution of Ru with Fe

We have used specific heat and neutron diffraction measurements on single crystals of URu$_{2-x}$Fe$_x$Si$_2$ for Fe concentrations $x$ $\leq$ 0.7 to establish that chemical substitution of Ru with Fe acts as "chemical pressure" $P_{ch}$ as previously proposed by Kanchanavatee et al. [Phys. Rev. B {\bf 84}, 245122 (2011)] based on bulk measurements on polycrystalline samples. Notably, neutron diffraction reveals a sharp increase of the uranium magnetic moment at $x=0.1$, reminiscent of the behavior at the "hidden order" (HO) to large moment antiferromagnetic (LMAFM) phase transition observed at a pressure $P_x\approx$ 0.5-0.7~GPa in URu$_2$Si$_2$. Using the unit cell volume determined from our measurements and an isothermal compressibility $\kappa_{T} = 5.2 \times 10^{-3}$ GPa$^{-1}$ for URu$_2$Si$_2$, we determine the chemical pressure $P_{ch}$ in URu$_{2-x}$Fe$_x$Si$_2$ as a function of $x$. The resulting temperature $T$-chemical pressure $P_{ch}$ phase diagram for URu$_{2-x}$Fe$_x$Si$_2$ is in agreement with the established temperature $T$-external pressure $P$ phase diagram of URu$_2$Si$_2$.

Scaling relation found in anomalous electrical transport and superconductivity of heavy fermion superconductor URu2Si2

The pressure dependent electrical resistivity of URu2Si2 has been studied at high pressure across the first order phase boundary of Px where the ground state switches under pressure from “hidden order” (HO) to large moment antiferromagnetic (LAFM) states. We have measured an ultra-clean single crystal whose quality is the highest among those used in previous studies. We have previously analyzed the resistivity data with the generalized power law ρ = ρ0 + AnTn. It was found that the electric transport property deviates from Fermi liquid theory in the HO phase but obeys the theory well above Px. In this paper, we re-analyze the data using the polynomial in T expression ρ = ρ0 + α1T + α2T2. The analysis finds the relation α1/α2 α Tsc in the HO phase. While the pressure dependence of α2 is very weak, α1 is roughly proportional to Tsc. This suggests a strong correlation between the anomalous quasiparticle scattering and the superconductivity and that both have a common origin. The present study clarifies a universality of the HO phase inherent in strongly correlated electron superconductors near quantum criticality.

Strong correlation between anomalous quasiparticle scattering and unconventional superconductivity in the hidden-order phase of URu2Si2

The pressure dependent electrical resistivity of URu${}_{2}$Si${}_{2}$ has been studied at high pressure across the first order phase boundary of ${P}_{x}$ where the ground state switches under pressure from ``hidden order'' (HO) to large moment antiferromagnetic (LAFM) states. The electrical transport in URu${}_{2}$Si${}_{2}$ at low temperatures shows a strong sample dependence. We have measured an ultraclean single crystal whose quality is the highest among those used in previous studies. The generalized power law $\ensuremath{\rho}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}{\ensuremath{\rho}}_{0}+\phantom{\rule{0.16em}{0ex}}{A}_{n}T{}^{n}$ analysis finds that the electric transport property deviates from Fermi liquid theory in the HO phase but obeys the theory well above ${P}_{x}$. The analysis using the polynomial in $T$ expression $\ensuremath{\rho}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}{\ensuremath{\rho}}_{0}+\phantom{\rule{0.16em}{0ex}}{\ensuremath{\alpha}}_{1}T+\phantom{\rule{0.16em}{0ex}}{\ensuremath{\alpha}}_{2}T{}^{2}$ reveals the relation ${\ensuremath{\alpha}}_{1}/{\ensuremath{\alpha}}_{2}$ $\ensuremath{\propto}$ ${T}_{\text{sc}}$ in the HO phase. While the pressure dependence of ${\ensuremath{\alpha}}_{2}$ is very weak, ${\ensuremath{\alpha}}_{1}$ is roughly proportional to ${T}_{\text{sc}}$. This suggests a strong correlation between the anomalous quasiparticle scattering and the superconductivity and that both have a common origin. The present study clarifies a universality of the HO phase inherent in strongly correlated electron superconductors near quantum criticality.

Pressure-tuned point-contact spectroscopy of URu2Si2from hidden order to antiferromagnetic states: Similarity of the Fermi surface gapping

We report soft point-contact spectroscopy studies of URu${}_{2}$Si${}_{2}$ both in the hidder order (HO) and the large-moment antiferromagnetic (LMAF) states accessed by pressure. In the HO state at ambient pressure, the spectroscopy shows two asymmetric peaks around the Fermi energy that emerge below the hidden order temperature ${T}_{\mathrm{HO}}$. In the LMAF state at higher pressures, the spectra are remarkably similar to those in the HO state, indicating a similar Fermi-surface gapping in the HO and LMAF states and providing a clue to unraveling the puzzling HO state.

Twofold enhancement of the hidden-order/large-moment antiferromagnetic phase boundary in the URu2−xFexSi2system

Electrical resistivity, specific heat, and magnetization measurements on URu${}_{2\ensuremath{-}x}$Fe${}_{x}$Si${}_{2}$ reveal a twofold enhancement of the ``hidden-order'' (HO)/large-moment antiferromagnetic (LMAFM) phase boundary ${T}_{0}(x)$. The ${T}_{0}({P}_{\text{ch}})$ curve, obtained by converting $x$ to ``chemical pressure'' ${P}_{\text{ch}}$, is strikingly similar to the ${T}_{0}(P)$ curve, where $P$ is applied pressure, for URu${}_{2}$Si${}_{2}$ both exhibit a ``kink'' at 1.5 GPa and a maximum at $\ensuremath{\sim}$7 GPa. This similarity suggests that the HO-LMAFM transition at 1.5 GPa in URu${}_{2}$Si${}_{2}$ occurs at $x$ $\ensuremath{\approx}$ 0.2 (${P}_{\text{ch}}\ensuremath{\approx}1.5$ GPa) in URu${}_{2\ensuremath{-}x}$Fe${}_{x}$Si${}_{2}$. URu${}_{2\ensuremath{-}x}$Fe${}_{x}$Si${}_{2}$ provides an opportunity for studying the HO and LMAFM phases with methods that probe the electronic structure [e.g., scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES), and point-contact spectroscopy (PCS)] but cannot be used under pressure.

Electronic structure theory of the hidden-order materialURu2Si2

We report a comprehensive electronic structure investigation of the paramagnetic (PM), the large moment antiferromagnetic (LMAF), and the hidden order (HO) phases of ${\text{URu}}_{2}{\text{Si}}_{2}$. We have performed relativistic full-potential calculations on the basis of the density-functional theory, employing different exchange-correlation functionals to treat electron correlations within the open $5f$ shell of uranium. Specifically, we investigate---through a comparison between calculated and low-temperature experimental properties---whether the $5f$ electrons are localized or delocalized in ${\text{URu}}_{2}{\text{Si}}_{2}$. The local spin-density approximation (LSDA) and generalized gradient approximation (GGA) are adopted to explore itinerant $5f$ behavior, the GGA plus additional strong Coulomb interaction ($\text{GGA}+U$ approach) is used to approximate moderately localized $5f$ states, and the $5f$-core approximation is applied to probe potential properties of completely localized uranium $5f$ states. We also performed local-density approximation plus dynamical mean-field theory calculations (DMFT) to investigate the temperature evolution of the quasiparticle states at 100 K and above, unveiling a progressive opening of a quasiparticle gap at the chemical potential when temperature is reduced. A detailed comparison of calculated properties with known experimental data demonstrates that the LSDA and GGA approaches, in which the uranium $5f$ electrons are treated as itinerant, provide an excellent explanation of the available low-temperature experimental data of the PM and LMAF phases. We show furthermore that due to a material-specific Fermi-surface instability a large, but partial, Fermi-surface gapping of up to 750 K occurs upon antiferromagnetic symmetry breaking. The occurrence of the HO phase is explained through dynamical symmetry breaking induced by a mode of long-lived antiferromagnetic spin fluctuations. This dynamical symmetry breaking model explains why the Fermi-surface gapping in the HO phase is similar but smaller than that in the LMAF phase and it also explains why the HO and LMAF phases have the same Fermi surfaces yet different order parameters. A suitable order parameter for the HO is proposed to be the Fermi-surface gap, and the dynamic spin-spin correlation function is further suggested as a secondary order parameter.

Parasitic Small-Moment Antiferromagnetism and Nonlinear Coupling of Hidden Order and Antiferromagnetism inURu2Si2Observed by Larmor Diffraction

We report for the first time simultaneous microscopic measurements of the lattice constants, the distribution of the lattice constants, and the antiferromagnetic moment in high-purity URu(2)Si(2), combining Larmor and conventional neutron diffraction at low temperatures and pressures up to 18 kbar. Our data demonstrate quantitatively that the small moment in the hidden order (HO) of URu(2)Si(2) is purely parasitic. The excellent experimental conditions we achieve allow us to resolve that the transition line between HO and large-moment antiferromagnetism (LMAF), which stabilizes under pressure, is intrinsically first order and ends in a bicritical point. Therefore, the HO and LMAF must have different symmetry, which supports exotic scenarios of the HO such as orbital currents, helicity order, or multipolar order.

Heavy holes as a precursor to superconductivity in antiferromagnetic CeIn 3

Numerous phenomenological parallels have been drawn between f- and d-electron systems in an attempt to understand their display of unconventional superconductivity. The microscopics of how electrons evolve from participation in large moment antiferromagnetism to superconductivity in these systems, however, remains a mystery. Knowing the origin of Cooper paired electrons in momentum space is a crucial prerequisite for understanding the pairing mechanism. Of special interest are pressure-induced superconductors CeIn(3) and CeRhIn(5) in which disparate magnetic and superconducting orders apparently coexist-arising from within the same f-electron degrees of freedom. Here, we present ambient pressure quantum oscillation measurements on CeIn(3) that crucially identify the electronic structure-potentially similar to high-temperature superconductors. Heavy hole pockets of f-character are revealed in CeIn(3), undergoing an unexpected effective mass divergence well before the antiferromagnetic critical field. We thus uncover the softening of a branch of quasiparticle excitations located away from the traditional spin fluctuation-dominated antiferromagnetic quantum critical point. The observed Fermi surface of dispersive f-electrons in CeIn(3) could potentially explain the emergence of Cooper pairs from within a strong moment antiferromagnet.

Temperature-pressure phase diagram ofURu2Si2from resistivity measurements and ac calorimetry: Hidden order and Fermi-surface nesting

By performing combined resistivity and calorimetric experiments under pressure, we have determined a precise temperature-pressure $(T,P)$ phase diagram of the heavy fermion compound $\mathrm{U}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$. It will be compared with previous diagrams determined by elastic neutron diffraction and strain gauge techniques. At first glance, the low-pressure ordered phase referred to as hidden order is dominated by Fermi-surface nesting, which has strong consequences on the localized spin dynamics. The high-pressure phase is dominated by large moment antiferromagnetism (LMAF) coexisting with at least dynamical nesting needed to restore on cooling a local moment behavior. ac calorimetry confirms unambiguously that bulk superconductivity does not coexist with LMAF. $\mathrm{U}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$ is one of the most spectacular examples of the dual itinerant and local character of uranium-based heavy fermion compounds.

Interplay between different states in heavy-fermion physics

Calorimetry experiments under high pressure were used to clarify the interplay between different states such as superconductivity (SC) and antiferromagnetism (AF) in CeRhIn 5 , spin density wave (SDW) and large moment antiferromagnetism (LMAF) in URu 2 Si 2 . Evidences are given on the reentrance of AF under magnetic field in the SC phase of CeRhIn 5 up to p c = 2.5 GPa where the Néel temperature will collapse in the absence of SC. For URu 2 Si 2 measurements up to 10 GPa support strongly the coexistence of SDW and LMAF at high pressures.

Pressure dependence of the magnetization ofURu2Si2

The ground state of URu2Si2 changes from so-called hidden order (HO) to large-moment antiferromagnetism (LMAF) upon applying hydrostatic pressure in excess of 14 kbar. We report the dc-magnetization M(B,T,p) of URu2Si2 for magnetic fields B up to 12 T, temperatures T in the range 2 to 100 K, and pressure p up to 17 kbar. Remarkably, characteristic scales such as the coherence temperature T*, the transition temperature T0, and the anisotropy in the magnetization depend only weakly on the applied pressure. However, the discontinuity in dM/dT at T0, which measures the magnetocaloric effect, decreases nearly 50 % upon applying 17 kbar for M and B parallel to the tetragonal c-axis, while it increases 15-fold for the a-axis. Our findings suggest that the HO and LMAF phases have an astonishing degree of similarity in their physical properties, but a key difference is the magnetocaloric effect near T0 in the basal plane.

Inhomogeneous magnetic order in Th-doped UPt 3 detected by μSR

We report on a μSR study of U 1− x Th x Pt 3 ( 0 ⩽ x ⩽ 0.05 ) conducted to investigate the onset of “large-moment antiferromagnetism” (LMAF). At low Th content ( x ⩽ 0.002 ) magnetic ordering on the time scale of the μSR experiment (10 −8 s) is not detected. For x = 0.005 a weak magnetic signal appears below T = 2 K , while for 0.006 ⩽ x ⩽ 0.05 , spontaneous oscillations in the μSR spectra signal the presence of the LMAF phase. Analysis of the μSR spectra with a three-component depolarization function reveals that the magnetic phase transition is quite broad. The broadening may be the effect of disorder on the fluctuation spectrum of the small-moment antiferromagnetic state reported for UPt 3 below T N ∼ 6 K .

Group theory and octupolar order inURu2Si2

Recent experiments on URu2Si2 show that the low-pressure hidden order is non-magnetic but it breaks time reversal invariance. Restricting our attention to local order parameters of 5f2 shells, we find that the best candidate for hidden order is staggered order of either Tz(beta) or Txyz octupoles. Group theoretical arguments for the effect of symmetry-lowering perturbations (magnetic field, mechanical stress) predict behavior in good overall agreement with observations. We illustrate our general arguments on the example of a five-state crystal field model which differs in several details from models discussed in the literature. The general appearance of the mean field phase diagram agrees with the experimental results. In particular, we find that a) at zero magnetic field, there is a first-order phase boundary between octupolar order and large-moment antiferromagnetism with increasing hydrostatic pressure; b) arbitrarily weak uniaxial pressure induces staggered magnetic moments in the octupolar phase; and c) a new phase with different symmetry appears at large magnetic fields.