I am a condensed matter theorist at Iowa State University, working on various problems in strongly correlated electronic systems. I tend to be interested in translating abstract theoretical ideas to real materials, and vice versa. I was an undergraduate in physics at Caltech, a graduate student in the condensed matter theory group at Rutgers University and most recently a Simons Postdoctoral Fellow in the condensed matter theory group at MIT. My curriculum vitae. |
The search for fundamentally new states of matter is a major driving force in condensed matter, and the peculiar regime between local and itinerant physics is one of the most fruitful places to look. Here, strong electronic correlations realize exotic phases not simply related to free electrons or their Fermi surface instabilities. Instead, these phases are characterized by new broken symmetries or even topological order, and these materials can carry low energy collective modes that fractionalize the electron's charge and spin. For example, spin liquids are magnetic states that break no symmetries, and yet form a highly correlated topologically ordered state with neutral spin 1/2 excitations. There are now several good spin liquid candidates, but it is necessary to examine how realistic models affect the spin liquid physics. Currently, I am interested in using the stuffed honeycomb generalization of the J_{1}-J_{2} honeycomb and triangular lattices to stabilize and study potential spin liquids in both limits. Heavy fermion materials also realize a variety of exotic phases; these materials combine electrons from the two extremes: localized electrons, which form magnetic moments or spins, and itinerant electrons, which form a metallic band. At low temperatures, these two species become strongly entangled as the itinerant electrons screen the local moments, effectively melting the spins to form a heavy Fermi liquid. When there are two, competing screening channels instead of one, the two channels ultimately cooperate to melt the spins into an exotic symmetry-breaking phase composite pair superconductivity, which is a purely local mechanism for d-wave superconductivity relevant to the 115 materials, and hastatic order, a time-reversal symmetry breaking phase without any large moments that may describe the hidden order in URu_{2}Si_{2}. Recently, I have studied how hastatic order can manifest in cubic Pr-based materials, motivated by materials like PrV_{2}Al_{20} and PrIr_{2}Zn_{20}, and I am generally interested in the generalization of the Doniach phase diagram to materials with even numbers of f-electrons and non-Kramers doublet ground states. |
Materials with non-Kramers doublet ground states naturally manifest the two-channel Kondo effect, as the valence fluctuations are from a non-Kramers doublet ground state to an excited Kramers doublet. Here, the development of a heavy Fermi liquid requires a channel symmetry breaking spinorial hybridization that breaks both single and double time-reversal symmetry, and is known as hastatic order. Motivated by cubic Pr-based materials with Î“3 non-Kramers ground state doublets, this paper provides a survey of cubic hastatic order using the simple two-channel Kondo-Heisenberg model. Hastatic order necessarily breaks time-reversal symmetry, but the spatial arrangement of the hybridization spinor can be either uniform (ferrohastatic) or break additional lattice symmetries (antiferrohastatic). The experimental signatures of both orders are presented in detail, and include tiny conduction electron magnetic moments. Interestingly, there can be several distinct antiferrohastatic orders with the same moment pattern that break different lattice symmetries, revealing a potential experimental route to detect the spinorial nature of the hybridization. We employ an SU(N) fermionic mean-field treatment on square and simple cubic lattices, and examine how the nature and stability of hastatic order varies as we vary the Heisenberg coupling, conduction electron density, band degeneracies, and apply both channel and spin symmetry breaking fields. We find that both ferrohastatic and several types of antiferrohastatic orders are stabilized in different regions of the mean-field phase diagram, and evolve differently in strain and magnetic fields. |
We investigate the classical phase diagram of the stuffed honeycomb Heisenberg lattice, which consists of a honeycomb lattice with a superimposed triangular lattice formed by sites at the center of each hexagon. This lattice encompasses and interpolates between the honeycomb, triangular and dice lattices, preserving the hexagonal symmetry while expanding the phase space for potential spin liquids. We use a combination of iterative minimization, classical Monte Carlo and analytical techniques to determine the complete ground state phase diagram. It is quite rich, with a variety of non-coplanar and non-collinear phases not found in the previously studied limits. In particular, our analysis reveals the triangular lattice critical point to be a multicritical point with two new phases vanishing via second order transitions at the critical point. We analyze these phases within linear spin wave theory and discuss consequences for the S = 1/2 spin liquid. |
Cubic Pr-based compounds with non-Kramers doublet ground states can realize a novel heavy Fermi liquid with spinorial hybridization ('hastatic' order) that breaks both single- and double-time reversal. Several Pr-"1-2-20" materials exhibit a suggestive heavy Fermi liquid stabilized in intermediate magnetic fields; these provide key insight into the quadrupolar Kondo lattice. We develop a simple, yet realistic model of ferrohastatic order, and elaborate its experimental signatures and behavior in field, where it is a good candidate to explain the observed heavy Fermi liquids. |
We have performed inelastic neutron scattering measurements on powder samples of the quasicrystal approximant, TbCd6, grown using isotopically enriched 112Cd. Both quasielastic scattering and distinct inelastic excitations were observed below 3 meV. The intensity of the quasielastic scattering measured in the paramagnetic phase diverges as TNâˆ¼22 K is approached from above. The inelastic excitations, and their evolution with temperature, are well characterized by the leading term, B02 O02, of the crystal electric field (CEF) level scheme for local pentagonal symmetry for the rare-earth ions [S. Jazbec et al., Phys. Rev. B 93, 054208 (2016)] indicating that the Tb moment is directed primarily along the unique local pseudofivefold axis of the Tsai-type clusters. We also find good agreement between the inverse susceptibility determined from magnetization measurements using a magnetically diluted Tb0.05Y0.95Cd6 sample and that calculated using the CEF level scheme determined from the neutron measurements. |
Double-stripe magnetism [Q=(Ï€/2,Ï€/2)] has been proposed as the magnetic ground state for both the iron-telluride and BaTi2Sb2O families of superconductors. Double-stripe order is captured within a J1âˆ’J2âˆ’J3 Heisenberg model in the regime J3â‰«J2â‰«J1. Intriguingly, besides breaking spin-rotational symmetry, the ground state manifold has three additional Ising degrees of freedom associated with bond-ordering. Via their coupling to the lattice, they give rise to an orthorhombic distortion and to two non-uniform lattice distortions with wave-vector (Ï€,Ï€). Because the ground state is four-fold degenerate, modulo rotations in spin space, only two of these Ising bond order parameters are independent. Here we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order, and solve it within a large-N limit. All three transitions, corresponding to the condensations of two Ising bond order parameters and one magnetic order parameter are simultaneous and first order in three dimensions, but lower dimensionality, or equivalently weaker interlayer coupling, and weaker magnetoelastic coupling can split the three transitions, and in some cases allows for two separate Ising phase transitions above the magnetic one. |
Spin-driven nematicity, or the breaking of the point-group symmetry of the lattice without long-range magnetic order, is clearly quite important in iron-based superconductors. From a symmetry point of view, nematic order can be described as a coherent locking of spin fluctuations in two interpenetrating N\'eel sublattices with ensuing nearest-neighbor bond order and an absence of static magnetism. Here, we argue that the low-temperature state of the recently discovered superconductor BaTi2Sb2O is a strong candidate for a more exotic form of spin-driven nematic order, in which fluctuations occurring in four N\'eel sublattices promote both nearest- and next-nearest neighbor bond order. We develop a low-energy field theory of this state and show that it can have, as a function of temperature, up to two separate bond-order phase transitions -- namely, one that breaks rotation symmetry and one that breaks reflection and translation symmetries of the lattice. The resulting state has an orthorhombic lattice distortion, an intra-unit-cell charge density wave, and no long-range magnetic order, all consistent with reported measurements of the low-temperature phase of BaTi2Sb2O. We then use density functional theory calculations to extract exchange parameters to confirm that the model is applicable to BaTi2Sb2O. |
The heavy fermion compound URu2Si2 continues to attract great interest due to the unidentified hidden order it develops below 17.5K. The unique Ising character of the spin fluctuations and low temperature quasiparticles is well established. We present detailed measurements of the angular anisotropy of the nonlinear magnetization that reveal a cos4Î¸ Ising anisotropy both at and above the ordering transition. With Landau theory, we show this implies a strongly Ising character of the itinerant hidden order parameter. |
Single crystals of RMg2Cu9 (R=Y, Ce-Nd, Gd-Dy, Yb) were grown using a high-temperature solution growth technique and were characterized by measurements of room-temperature x-ray diffraction, temperature-dependent specific heat and temperature-, field-dependent resistivity and anisotropic magnetization. YMg2Cu9 is a non-local-moment-bearing metal with an electronic specific heat coefficient, Î³âˆ¼ 15 mJ/mol K2. Yb is divalent and basically non-moment bearing in YbMg2Cu9. Ce is trivalent in CeMg2Cu9 with two magnetic transitions being observed at 2.1 K and 1.5 K. PrMg2Cu9 does not exhibit any magnetic phase transition down to 0.5 K. The other members being studied (R=Nd, Gd-Dy) all exhibits antiferromagnetic transitions at low-temperatures ranging from 3.2 K for NdMg2Cu9 to 11.9 K for TbMg2Cu9. Whereas GdMg2Cu9 is isotropic in its paramagnetic state due to zero angular momentum (L=0), all the other local-moment-bearing members manifest an anisotropic, planar magnetization in their paramagnetic states. To further study this planar anisotropy, detailed angular-dependent magnetization was carried out on magnetically diluted (Y0.99Tb0.01)Mg2Cu9 and (Y0.99Dy0.01)Mg2Cu9. Despite the strong, planar magnetization anisotropy, the in-plane magnetic anisotropy is weak and field-dependent. A set of crystal electric field parameters are proposed to explain the observed magnetic anisotropy. |
We use angle resolved photoemission spectroscopy, Raman spectroscopy, low energy electron diffraction, and x-ray scattering to reveal an unusual electronically mediated charge density wave (CDW) in K0.9Mo6O17. Not only does K0.9Mo6O17 lack signatures of electron-phonon coupling, but it also hosts an extraordinary surface CDW, with TS_CDW=220K nearly twice that of the bulk CDW, TB_CDW=115K. While the bulk CDW has a BCS-like gap of 12 meV, the surface gap is 10 times larger and well in the strong coupling regime. Strong coupling behavior combined with the absence of signatures of strong electron-phonon coupling indicates that the CDW is likely mediated by electronic interactions enhanced by low dimensionality. |
A rare combination of strong spinÃ¢â‚¬â€œorbit coupling and electron-electron correlations makes the iridate Mott insulator Sr2IrO4 a promising host for novel electronic phases of matter. The resemblance of its crystallographic, magnetic and electronic structures to La2CuO4, as well as the emergence on doping of a pseudogap region and a low-temperature d-wave gap, has particularly strengthened analogies to cuprate high-Tc superconductors. However, unlike the cuprate phase diagram, which features a plethora of broken symmetry phases in a pseudogap region that includes charge density wave, stripe, nematic and possibly intra-unit-cell loop-current orders, no broken symmetry phases proximate to the parent antiferromagnetic Mott insulating phase in Sr2IrO4 have been observed so far, making the comparison of iridate to cuprate phenomenology incomplete. Using optical second-harmonic generation, we report evidence of a hidden non-dipolar magnetic order in Sr2IrO4 that breaks both the spatial inversion and rotational symmetries of the underlying tetragonal lattice. Four distinct domain types corresponding to discrete 90Ã‚Â°-rotated orientations of a pseudovector order parameter are identified using nonlinear optical microscopy, which is expected from an electronic phase that possesses the symmetries of a magneto-electric loop-current order. The onset temperature of this phase is monotonically suppressed with bulk hole doping, albeit much more weakly than the NÃƒÂ©el temperature, revealing an extended region of the phase diagram with purely hidden order. Driving this hidden phase to its quantum critical point may be a path to realizing superconductivity in Sr2IrO4. |
We present magnetic susceptibility, resistivity, specific heat, and thermoelectric power measurements on (Ce1âˆ’xLax)Cu2Ge2 single crystals (0â‰¤xâ‰¤1). With La substitution, the antiferromagnetic temperature TN is suppressed in an almost linear fashion and moves below 0.36 K, the base temperature of our measurements for x>0.8. Surprisingly, in addition to robust antiferromagnetism, the system also shows low temperature coherent scattering below Tcoh up to âˆ¼0.9 of La, indicating a small percolation limit âˆ¼9% of Ce. Tcoh as a function of magnetic field was found to have different behavior for x<0.9 and x>0.9. Remarkably, (Tcoh)^2 at H=0 was found to be linearly proportional to TN. The jump in the magnetic specific heat Î´Cm at TN as a function of TK/TN for (Ce1âˆ’xLax)Cu2Ge2 follows the theoretical prediction based on the molecular field calculation for the S=1/2 resonant level model. |
The broken symmetry that develops below 17.5K in the heavy fermion compound URu2Si2 has long eluded identification. Here we argue that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor hybridization order parameter that breaks double time-reversal symmetry by mixing states of integer and half-integer spin. Such "hastatic order" (hasta:[Latin]spear) hybridizes Kramers conduction electrons with Ising, non-Kramers 5f2 states of the uranium atoms to produce Ising quasiparticles. The development of a spinorial hybridization at 17.5K accounts for both the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. This paper develops the theory of hastatic order in detail, providing the mathematical development of its key concepts. Hastatic order predicts a tiny transverse moment in the conduction sea, a collosal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant energy-dependent nematicity in the tunneling density of states. |
We use a tunable laser angle-resolved photoemission spectroscopy to study the electronic properties of the prototypical multiband BCS superconductor MgB2. Our data reveal a strong renormalization of the dispersion (kink) at Ã¢Ë†Â¼65meV, which is caused by the coupling of electrons to the E2g phonon mode. In contrast to cuprates, the 65 meV kink in MgB2 does not change significantly across Tc. More interestingly, we observe strong coupling to a second, lower energy collective mode at a binding energy of 10 meV. This excitation vanishes above Tc and is likely a signature of the elusive Leggett mode. |
The recent observation of fully-gapped superconductivity in Yb doped CeCoIn_{5} poses a paradox, for the disappearance of nodes suggests that they are accidental, yet d-wave symmetry with protected nodes is well established by experiment. Here, we show that composite pairing provides a natural resolution: in this scenario, Yb doping drives a Lifshitz transition of the nodal Fermi surface, forming a fully-gapped d-wave molecular superfluid of composite pairs. The T^{4} dependence of the penetration depth associated with the sound mode of this condensate is in accord with observation. |
The London penetration depth, lambda(T) was measured in single crystals of Ce_{1-x}R_{x}CoIn_{5}, R=La, Nd and Yb down to Tmin = 50 mK (Tc/Tmin > 50) using a tunnel-diode resonator. In the cleanest samples lambda(T) is best described by the power law, lambda(T) , with n = 1, consistent with line nodes. Substitutions of Ce with La, Nd and Yb lead to similar monotonic suppressions of Tc, however the effects on lambda(T) differ. While La and Nd doping results in an increase of the exponent to n = 2, as expected for a dirty nodal superconductor, Yb doping leads to n>3, inconsistent with nodes, suggesting a change from nodal to nodeless superconductivity where Fermi surface topology changes were reported, implying that the nodal structure and Fermi surface topology are closely linked. |
The observation of Ising quasiparticles is a signatory feature of the hidden order phase of URu2Si2. In this paper we discuss its nature and the strong constraints it places on current theories of the hidden order. In the hastatic theory such anisotropic quasiparticles are naturally described described by resonant scattering between half-integer spin conduction electrons and integer-spin Ising moments. The hybridization that mixes states of different Kramers parity is spinorial; its role as an symmetry-breaking order parameter is consistent with optical and tunnelling probes that indicate its sudden development at the hidden order transition. We discuss the microscopic origin of hastatic order, identifying it as a fractionalization of three body bound-states into integer spin fermions and half-integer spin bosons. After reviewing key features of hastatic order and their broader implications, we discuss our predictions for experiment and recent measurements. We end with challenges both for hastatic order and more generally for any theory of the hidden order state in URu2Si2. |
The hidden order developing below 17.5K in the heavy fermion material URu2Si2 has eluded identification for over twenty five years. This paper will review the recent theory of ``hastatic order,'' a novel two-component order parameter capturing the hybridization between half-integer spin (Kramers) conduction electrons and the non-Kramers 5f^2 Ising local moments, as strongly indicated by the observation of Ising quasiparticles in de Haas-van Alphen measurements. Hastatic order differs from conventional magnetism as it is a spinor order that breaks both single and double time-reversal symmetry by mixing states of different Kramers parity. The broken time-reversal symmetry simply explains both the pseudo-Goldstone mode between the hidden order and antiferromagnetic phases and the nematic order seen in torque magnetometry. The spinorial nature of the hybridization also explains how the Kondo effect gives a phase transition, with the hybridization gap turning on at the hidden order transition as seen in scanning tunneling microscopy. Hastatic order also has a number of new predictions: a basal-plane magnetic moment of order .01\mu_B, a gap to longitudinal spin fluctuations that vanishes continuously at the first order antiferromagnetic transition and a narrow resonant nematic feature in the scanning tunneling spectra. |
Adding a second Kondo channel to heavy fermion materials reveals new exotic symmetry breaking phases associated with the development of Kondo coherence. In this paper, we review two such phases, the "hastatic order" associated with non-Kramers doublet ground states, where the two-channel nature of the Kondo coupling is guaranteed by virtual valence fluctuations to an excited Kramers doublet, and "composite pair superconductivity," where the two channels differ by charge 2e and can be thought of as virtual valence fluctuations to a pseudo-isospin doublet. The similarities and differences between these two orders will be discussed, along with possible realizations in actinide and rare earth materials like URu2Si2 and NpPd5Al2. |
We introduce the idea of emergent lattices, where a simple lattice decouples into two weakly-coupled lattices as a way to stabilize spin liquids. In LiZn2Mo3O8, the disappearance of 2/3rds of the spins at low temperatures suggests that its triangular lattice decouples into an emergent honeycomb lattice weakly coupled to the remaining spins, and we suggest several ways to test this proposal. We show that these orphan spins act to stabilize the spin-liquid in the J_{1}-J_{2} honeycomb model and also discuss a possible 3D analogue, Ba2MoYO6 that may form a "depleted fcc lattice." * Editor's suggestion |
Motivated by the potential chiral spin liquid in the metallic spin ice Pr_{2}Ir_{2}O_{7}, we consider how such a chiral state might be selected from the spin ice manifold. We propose that chiral fluctuations of the conducting Ir moments promote ferro-chiral couplings between the local Pr moments, as a chiral analogue of the magnetic RKKY effect. Pr_{2}Ir_{2}O_{7} provides an ideal setting to explore such a chiral RKKY effect, given the inherent chirality of the spin-ice manifold. We use a slave-rotor calculation on the pyrochlore lattice to estimate the sign and magnitude of the chiral coupling, and find it can easily explain the 1.5K transition to a ferro-chiral state. * Editor's Suggestion |
The development of collective long-range order via phase transitions occurs by the spontaneous breaking of fundamental symmetries. Magnetism is a consequence of broken time-reversal symmetry while superfluidity results from broken gauge invariance. The broken symmetry that develops below 17.5K in the heavy fermion compound URu_{2}Si_{2} has long eluded such identification. Here we show that the recent observation of Ising quasiparticles in URu_{2}Si_{2} results from a spinor order parameter that breaks double time-reversal symmetry, mixing states of integer and half-integer spin. Such hastatic order hybridizes conduction electrons with Ising 5f^{2} states of the uranium atoms to produce Ising quasiparticles; it accounts for the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. Hastatic order predicts a tiny transverse moment in the conduction sea, a collosal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant energy-dependent nematicity in the tunneling density of states. |
The microscopic nature of the hidden order state in URu_{2}Si_{2} is dependent on the low-energy configurations of the uranium ions, and there is currently no consensus on whether it is predominantly 5f^{2} or 5f^{3}. Here we show that measurement of the basal-plane nonlinear susceptibility can resolve this issue; its sign at low-temperatures is a distinguishing factor. We calculate the linear and nonlinear susceptibilities for specific 5f^{2} and 5f^{3} crystal-field schemes that are consistent with current experiment. Because of its dual magnetic and orbital character, a Gamma_{5} magnetic non-Kramers doublet ground-state of the U ion can be identified by chi_{3}^{ab}(T) where we have determined the constant of proportionality for URu_{2}Si_{2}. |
Motivated by recent quantum oscillations experiments on URu_{2}Si_{2}, we discuss the microscopic origin of the large anisotropy observed many years ago in the anomaly of the nonlinear susceptibility in this same material. We show that the magnitude of this anomaly emerges naturally from hastatic order, a proposal for hidden order that is a two-component spinor arising from the hybridization of a non-Kramers Gamma_{5} doublet with Kramers conduction electrons. A prediction is made for the angular anisotropy of the nonlinear susceptibility anomaly as a test of this proposed order parameter for URu_{2}Si_{2}. |
The possible discovery of s_{Ãƒâ€šÃ‚Â±} superconducting gaps in the moderately correlated iron-based superconductors has raised the question of how to properly treat s_{Ãƒâ€šÃ‚Â±} gaps in strongly correlated superconductors. Unlike the d-wave cuprates, the Coulomb repulsion does not vanish by symmetry, and a careful treatment is essential. Thus far, only the weak correlation approaches have included this Coulomb pseudopotential, so here we introduce a symplectic N treatment of the t-J model that incorporates the strong Coulomb repulsion through the complete elimination of on-site pairing. Through a proper extension of time-reversal symmetry to the large N limit, symplectic-N is the first superconducting large N solution of the t-J model. For d-wave superconductors, the previous uncontrolled mean field solutions are reproduced, while for s_{Ãƒâ€šÃ‚Â±} superconductors, the SU(2) constraint enforcing single occupancy acts as a pair chemical potential adjusting the location of the gap nodes. This adjustment can capture the wide variety of gaps proposed for the iron based superconductors: line and point nodes, as well as two different, but related full gaps on different Fermi surfaces. |
Using a two-channel Anderson model, we develop a theory of composite pairing in the 115 family of heavy fermion superconductors that incorporates the effects of f-electron valence fluctuations. Our calculations introduce ÃƒÂ¢Ã¢â€šÂ¬Ã…â€œsymplectic Hubbard operators" an extension of the slave boson Hubbard operators that preserves both spin rotation and time-reversal symmetry in a large N expansion, permitting a unified treatment of anisotropic singlet pairing and valence fluctuations. We find that the development of composite pairing in the presence of valence fluctuations manifests itself as a phase-coherent mixing of the empty and doubly occupied configurations of the mixed valent ion. This effect redistributes the f-electron charge within the unit cell. Our theory predicts a sharp superconducting shift in the nuclear quadrupole resonance frequency associated with this redistribution. We calculate the magnitude and sign of the predicted shift expected in CeCoIn_{5}. |
We consider the internal structure of a d-wave heavy-fermion superconducting condensate, showing that it necessarily contains two components condensed in tandem: pairs of quasiparticles on neighboring sites and composite pairs consisting of two electrons bound to a single local moment. These two components draw upon the antiferromagnetic and Kondo interactions to cooperatively enhance the superconducting transition temperature. This tandem condensate is electrostatically active, with an electric quadrupole moment predicted to lead to a superconducting shift in the nuclear quadrupole resonance frequency. |
Here, we introduce a new class of large-N expansion that uses symplectic symmetry to protect the odd time-reversal parity of spin and sustain Cooper pairs as well-defined singlets. We show that when a lattice of magnetic ions exchange spin with their metallic environment in two distinct symmetry channels, they can simultaneously satisfy both channels by forming a condensate of composite pairs between local moments and electrons. We then discuss the application of this two channel Kondo model to the heavy fermion superconductors, PuCoGa_{5} and NpPd_{5}Al_{2}. The inclusion of spin-orbit coupling and the crystal fields predicts a g-wave superconducting order parameter. |
In this paper, we develop a new large N treatment of the Heisenberg model based on symplectic-N, represent the spins by Schwinger bosons, which allows us study the boundaries between short-range and long-range order. This limit treats ferromagnetic and antiferromagnetic correlations simultaneously, exacting an energy cost for frustrating antiferromagnetic bonds. As an example, we treated the two dimensional J1-J2 model, where the symplectic-N phase diagram improves over previous large N treatments both at zero and finite temperatures. |
Ca_{3}Co_{2-x}Mn_{x}O_{6}(x ~ 0.96) is a multiferroic with spin-chains of alternating Co^{2+} and Mn^{4+} ions. The spin state of Co^{2+} remains unresolved, as there is a discrepancy between high temperature X-ray absorption (S= 3/2) and low temperature neutron (S= 1/2) measurements. Here we study the high-field magnetization using magnetic modeling and confirm the small Co moment. With crystal-field analysis, we show that neither spin orbit coupling nor Jahn-Teller distortions yield a small effective moment with large anisotropy at low temperatures within the high spin (S = 3/2) scenario, while the low spin (S=1/2) can explain both the small moment and large anisotropy. In order to unify the experimental results, we propose a spin-state crossover, and make a number of specific predictions for experiment. |
Strongly correlated electrons provide a unique challenge to theorists as they sit at the intersection of the kinetic and potential energy scales, where traditional, perturbative many body techniques fail. To make progress, we must develop non-perturbative methods. One method that has had some success here is large N theory, which generalizes the number of components of the electron spin from 2 to N, providing an artificial perturbation expansion about a strongly correlated state which, if chosen properly, captures the essential physics. Large N has been heavily used in both the Kondo lattice and in frustrated magnetism, where SU(2N) is the traditional generalization of the electron spin group, SU(2). In choosing the large N group, we chose which symmetries to preserve and which to discard. Unfortunately, SU(2N) inadvertently loses the time inversion and charge conjugation properties of SU(2); while some generators invert under time reversal like spins, $\vec{S} \rightarrow -\vec{S}$, and remain neutral under charge conjugation, the others behave more like electric dipoles: neutral under time reversal and flipped by charge conjugation. To treat phenomena like frustrated magnetism and superconductivity, which relies on the formation of Cooper pairs, we must restrict ourselves to the subgroup of spin-like generators, SP(2N), a large N limit we call symplectic-N. This limit differs from the SP(2N) limit introduced by Sachdev and Read, which breaks the SU(2N) symmetry of the Hamiltonian down to SP(2N) in that the interaction Hamiltonian is constricted solely from symplectic spins. Symplectic-N has been successfully applied to frustrated magnetism, where it treats ferromagnetic and antiferromagnetic correlations simultaneously, and to the two channel Kondo model, where it treats the Kondo effect and superconductivity simultaneously. We are currently working to develop symplectic-N Hubbard operators to treat the t-J and Anderson models. |