Impurity Spin Research Articles

Yu-Shiba-Rusinov states in real metals

Theoretical descriptions of Yu-Shiba-Rusinov (YSR) states induced by magnetic impurities inside the gap of a superconductor typically rely on a classical spin model or are restricted to spin-1/2 quantum spins. These models fail to account for important aspects of YSR states induced by transition-metal impurities, including the effects of higher quantum spins coupled to several conduction-electron channels, crystal or ligand-field effects, and magnetic anisotropy. We introduce and explore a zero-bandwidth model, which incorporates these aspects, is readily solved numerically, and analytically tractable in several limiting cases. The principal simplification of the model is to neglect Kondo renormalizations of the exchange couplings between impurity spin and conduction electrons. Nevertheless, we find excellent correspondence in those cases, in which we can compare our results to existing numerical-renormalization-group calculations. We apply the model to obtain and understand phase diagrams as a function of pairing strength and magnetic anisotropy as well as subgap excitation spectra. The single-channel case is most relevant for transition-metal impurities embedded into metallic coordination complexes on superconducting substrates, while the multi-channel case models transition-metal adatoms.

Influence Matrix Approach to Many-Body Floquet Dynamics

In this work, we introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional. Focusing on a family of interacting, Floquet spin chains, we consider a Keldysh path-integral description of the dynamics. The central object in our approach is the influence matrix (IM), which describes the effect of the system on the dynamics of a local subsystem. For translationally invariant models, we formulate a self-consistency equation for the influence matrix. For certain special values of the model parameters, we obtain an exact solution which represents a perfect dephaser (PD). Physically, a PD corresponds to a many-body system that acts as a perfectly Markovian bath on itself: at each period, it measures every spin. For the models considered here, we establish that PD points include dual-unitary circuits investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the IM temporal entanglement is low. A combination of analytical insights and MPS computations allows us to characterize the structure of the influence matrix in terms of an effective "statistical-mechanics" description. We finally illustrate the predictive power of this description by analytically computing how quickly an embedded impurity spin thermalizes. The influence matrix approach formulated here provides an intuitive view of the quantum many-body dynamics problem, opening a path to constructing models of thermalizing dynamics that are solvable or can be efficiently treated by MPS-based methods, and to further characterizing quantum ergodicity or lack thereof.

Radiofrequency spectroscopy of one-dimensional trapped Bose polarons: crossover from the adiabatic to the diabatic regime

We investigate the crossover of the impurity-induced dynamics, in trapped one-dimensional Bose polarons subject to radio frequency (RF) pulses of varying intensity, from an adiabatic to a diabatic regime. Utilizing adiabatic pulses for either weak repulsive or attractive impurity-medium interactions, a multitude of polaronic excitations or mode-couplings of the impurity-bath interaction with the collective breathing motion of the bosonic medium are spectrally resolved. We find that for strongly repulsive impurity-bath interactions, a temporal orthogonality catastrophe manifests in resonances in the excitation spectra where impurity coherence vanishes. When two impurities are introduced, impurity–impurity correlations, for either attractive or strong repulsive couplings, induce a spectral shift of the resonances with respect to the single impurity. For a heavy impurity, the polaronic peak is accompanied by a series of equidistant side-band resonances, related to interference of the impurity spin dynamics and the sound waves of the bath. In all cases, we enter the diabatic transfer regime for an increasing bare Rabi frequency of the RF field with a Lorentzian spectral shape featuring a single polaronic resonance. The findings in this work on the effects of external trap, RF pulse and impurity–impurity interaction should have implications for the new generations of cold-atom experiments.

From weak antilocalization to Kondo scattering in a magnetic complex oxide interface

Quantum corrections to electrical resistance can serve as sensitive probes of the magnetic landscape of a material. For example, interference between time-reversed electron paths gives rise to weak localization effects, which can provide information about the coupling between spins and orbital motion, while the Kondo effect is sensitive to the presence of spin impurities. Here we use low-temperature magnetotransport measurements to reveal a transition from weak antilocalization (WAL) to Kondo scattering in the quasi-two-dimensional electron gas formed at the interface between SrTiO$_3$ and the Mott insulator NdTiO$_3$. This transition occurs as the thickness of the NdTiO$_3$ layer is increased. Analysis of the Kondo scattering and WAL points to the presence of atomic-scale magnetic impurities coexisting with extended magnetic regions that affect transport via a strong magnetic exchange interaction. This leads to distinct magnetoresistance behaviors that can serve as a sensitive probe of magnetic properties in two dimensions.

Bound Soliton–Defect Spin States in Anisotropic Ferromagnetic Chains

The interaction of soliton with an impurity spin in a discrete anisotropic ferromagnetic chain is studied. The defect spin in our model is characterized by modification of the exchange interaction with its neighbors. A perturbed nonlinear Schrödinger (NLS) equation for the spin amplitude is derived on the basis of a semiclassical and a continuum approximation. A specific feature of this type of defect is that it leads to perturbations to all terms of the NLS equation. Localized soliton-defect spin solutions are obtained for the case of dark and bright solitons and their stability is analyzed.

Soliton Scattering on Impurities with Modified Exchange Interactions in Anisotropic Ferromagnetic Chains

The soliton propagation in an anisotropic ferromagnetic chain where the exchange interactions of an impurity spin with its neighbors are modified is investigated. We considered easy-axis anisotropy of the chain which leads to the formation of bright soliton solutions. The character of the soliton-impurity interaction is different when the exchange coupling of the spin is modified in the x,y-plane or in the z-direction. Our results show that the action of the defect depends on the soliton wave number in a complicated manner and for large velocities becomes significant. A comparison with the soliton dynamics in the presence of point defects is made.

Non-Hamiltonian dynamics of indirectly coupled classical impurity spins

We discuss the emergence of an effective low-energy theory for the real-time dynamics of two classical impurity spins within the framework of a prototypical and purely classical model of indirect magnetic exchange: Two classical impurity spins are embedded in a host system which consists of a finite number of classical spins localized on the sites of a lattice and interacting via a nearest-neighbor Heisenberg exchange. An effective low-energy theory for the slow impurity-spin dynamics is derived for the regime, where the local exchange coupling between impurity and host spins is weak. To this end we apply the recently developed adiabatic spin dynamics (ASD) theory. Besides the Hamiltonian-like classical spin torques, the ASD additionally accounts for a novel topological spin torque that originates as a holonomy effect in the close-to-adiabatic-dynamics regime. It is shown that the effective low-energy precession dynamics cannot be derived from an effective Hamilton function and is characterized by a non-vanishing precession frequency even if the initial state deviates only slightly from a ground state. The effective theory is compared to the fully numerical solution of the equations of motion for the whole system of impurity and host spins to identify the parameter regime where the adiabatic effective theory applies. Effective theories beyond the adiabatic approximation must necessarily include dynamic host degrees of freedom and go beyond the idea of a simple indirect magnetic exchange. We discuss an example of a generalized constrained spin dynamics which does improve the description but also fails for certain geometrical setups.

Crystalline electric field excitations in the quantum spin liquid candidate NaYbSe2

Very recently we revealed a large family of triangular lattice quantum spin liquid candidates named rare-earth chalcogenides, which features a high-symmetry structure without structural/charge disorders and spin impurities, and may serve as an ideal platform exploring spin liquid physics. The knowledge of crystalline electric-field (CEF) excitations is an essential step to explore the fundamental magnetism of rare-earth spin systems. Here we employed inelastic neutron scattering (INS) and Raman scattering (RS) to carry out a comprehensive CFE investigation on $NaYbSe_{2}$, a promising representative of the family. By comparison with its nonmagnetic compound $NaLuSe_{2}$, we are able to identify the CEF excitations at 15.8, 24.3 and 30.5 meV at 5K. The selected cuts of the INS spectra are well re-produced with a large anisotropy of $g$ factors ($g_{ab}:g_{c}\sim3:1$). Further, the CEF excitations are explained well by our calculations based on the point charge model. Interestingly, $NaYbSe_{2}$ exhibits an unusual CEF shift to higher energies with increasing temperatures, and the Raman mode close to the first CEF excitation shows an anomalously large softening with decreasing temperatures. The absence of the anomalies in $NaLuSe_{2}$ clearly demonstrates a CEF-phonon coupling not reported in the family. It can be understood in term of the weaker electronegativity of Se. The fact that the smallest first CEF excitation in the sub-family of $NaYbCh_{2}$ is $\sim$ 180K (Ch=O, S, Se), guarantees that the sub-family can be strictly described with an effective S=1/2 picture at sufficiently low temperatures. Interestingly the CEF-phonon coupling revealed here may present alternative possibilities to manipulate the spin systems.

Decay rates and decoherence of an interstitial two-level spin impurity in a ferromagnetic lattice

The decay rate of an interstitial two-level spin impurity, located in the center of a unit cell of an anisotropic ferromagnetic lattice subjected to an external magnetic field, is derived. The impurity is coupled to nearest-neighbor spins through a Heisenberg $XY$ interaction. By mapping the lattice spin operators using the Holstein-Primakoff transformation, we establish the similarity with the Fano-Anderson model at low temperatures, and we calculate the retarded Green's function in one and two dimensions analytically for arbitrary coupling strength. It is shown that the reduced density matrix of the impurity satisfies an exact master equation in Lindblad form, from which the decay rate and the Lamb shift are deduced. The evolution in time of the latter together with the excited-state occupation probability is investigated and its dependence on the applied magnetic field is discussed. It is found that there exists a critical resonance-like value of the magnetic field around which the behavior of the decay rate and the density matrix changes drastically. The Markovian decay law, as given by the Fermi golden rule, does not hold in the weak-coupling regime unless the magnetic field is weak, typically less than the critical value. The weak-coupling regime is further treated perturbatively up to second order, and the obtained results are compared with the exact solution. We also discuss the Zeno regime of the dynamics, where it is shown that, at short times, the effective decay rate is twice as small as the exact decay rate, and that when the impurity energy lies outside the lattice continuum, the measurement speeds up the decay of the survival probability.

Order parameter for the multichannel Kondo model at quantum criticality

A multichannel Kondo model, where two or more equivalent but independent channels of electrons compete to screen a spin-1/2 impurity, shows overcompensation of the impurity spin, leading to the non-Fermi-liquid behavior in various thermodynamic and transport properties. However, when the channel symmetry is broken, an impurity quantum phase transition can occur at zero temperature. Identification of an order parameter describing the impurity quantum phase transition is very difficult since it is beyond the conventional Landau-Ginzburg-Wilson theory. By employing the natural orbitals renormalization group method, we study both two-channel and threechannel Kondo models, from the perspective of spin correlation between the impurity and electrons in electronic channels. Here we demonstrate that by introducing the spin-correlation ratio as an order parameter we can characterize impurity quantum phase transitions driven by channel asymmetry. In particular, the universal critical exponents $\beta$ of the spin-correlation ratio and $\nu$ of the correlation length are explicitly determined by finite-sizescaling analysis, namely, $\beta = 0.10(1), \nu = 2.0(1)$, and $\beta = 0.10(1), \nu = 2.5(1)$ for the two-channel and three-channel Kondo models, respectively.

Magnetic field noise analyses generated by the interactions between a nitrogen vacancy center diamond and surface and bulk impurities

We investigated the mechanism of magnetic noise due to both surface and bulk impurities. For surface noise, we apply the Langevin method to spin fluctuation theory to calculate the noise for paramagnetic surface impurities absorbed in a thin layer of water. We find that the mechanisms generating noise are spin flip and spin precession which depend on impurity spin relaxation and spin precession time. For the bulk noise, we consider carbon-13 and nitrogen as impurities and employ the correlated-cluster expansion to calculate noise. Carbon-13 noise is a few orders of magnitude larger than nitrogen due to the higher impurity density in the typical NV center diamond system. We also find that the noise in the secular approximation underestimates noise under low applied magnetic field. Overall, the major source of magnetic field noise is spin precession noise, which is more than five orders of magnitude larger than the spin flip noise.

Interplay between Majorana fermion and impurity in thermal-driven transport model

In quantum transport, especially in spintronics, its central theme is to manipulate spin degrees of freedom in solid-state systems, to understand the interaction between the particle spin and its solid-state environments and to make useful devices. Recently, Majorana fermion has been introduced into quantum transport and received much attention. In this paper, we study a thermal-driven transport model which consists of a quantum dot coupled with two normal metal leads, a impurity spin (whose angular quantum number is more than or equal to one-half) and a Majorana fermion. We focus on the interplay between Majorana fermion and the impurity in this exactly solvable model. It is found that the system can generate thermal-induced spin current, and the currents are affected by Majorana fermion and impurity. With large temperature difference, the currents are sensitive to gate voltage, and the quantitative relation between spin-up current and gate voltage tends to be linear when the coupling between Majorana and quantum dot is strong, showing Majorana fermion's robustness. In addition, the spin current induced by Majorana fermion exhibits an oscillating antisymmetric structure around zero-bias point. This spin current’s zero point is related to the angular quantum number of impurity spin. These results are expected to be useful in thermal-electric conversion devices, and may be observed in future experiments.

Sensing chiral magnetic noise via quantum impurity relaxometry

We present a theory for quantum impurity relaxometry of magnons in thin films, exhibiting quantitative agreement with recent experiments without needing arbitrary scale factors used in theoretical models thus far. Our theory reveals that chiral coupling between prototypical spin>1/2 quantum impurities and magnons plays a central role in determining impurity relaxation, which is further corroborated by our experiments on nickel films interfaced with nitrogen-vacancy centers. Along with advancing magnonics and understanding decoherence in hybrid quantum platforms with magnets, the ability of a quantum impurity spin to sense chiral magnetic noise presents an opportunity to probe chiral phenomena in condensed matter.

Impurities in three-dimensional quadratic band-touching Luttinger semimetals: Friedel and RKKY oscillations

We investigate the response of 3D Luttinger semimetals to localized charge and spin impurities as a function of doping. The strong spin-orbit coupling of these materials strongly influences the Friedel oscillations and RKKY interactions. This can be seen at short distances with an $1/r^4$ divergence of the responses, and anisotropic behavior. Certain of the spin-orbital signatures are robust to temperature, even if the charge and spin oscillations are smeared out, and give an unusual diamagnetic Pauli susceptibility. We compare our results to the experimental literature on the bismuth-based half-Heuslers such as YPtBi and on the pyrochlore iridate Pr$_2$Ir$_2$O$_7$.

First principles investigations of Fe3+ impurity and Fe3+ + V−Cd complex in strongly confined CdSe quantum dot

Solitary dopant or defect in a semiconductor is the basis of the emerging field of optoelectronics known as solotronics. It has been shown that the spin of a single magnetic ion impurity can be manipulated optically. Among the magnetic ions, Fe3+ has been proposed as a primary candidate for the design of quantum dots (QDs) for solotronics because of its zero nuclear spin in contrast to Mn2+ and larger magnetic moment compared to Fe2+. In this work, we performed density function theory calculations to determine optimal parameters for the colloidal synthesis of single FeCd3+over FeCd2+ in CdSe of 1 nm in radius. We also investigated Fe3+ plus Cd vacancy complex (FeCd3++VCd−). Transition energy level calculations show FeCd3+ to be a deep-level donor and VCd− to be a shallow acceptor. Charge difference plots show that the charge of the ionized electron is localized around FeCd3+. Tetrahedral symmetry is retained at the FeCd3+ site. The magnetic moment of Fe3+ is almost the same in the core and at the surface and is equal to ∼4.27 μB for passivated QD. The large moment can be manipulated for spin control in conjunction with unoccupied vacancy states of the triplet t2 level of the shallow VCd acceptor to create a hole spin current in a lithographically patterned surface.

Anisotropic Kondo screening induced by spin-orbit coupling in quantum wires

Using the numerical renormalization group (NRG) method we study a magnetic impurity coupled to a quantum wire with Rashba and Dresselhaus spin-orbit coupling (SOC) in an external magnetic field. We consider the low-filling regime with the Fermi energy close to the bottom of the band and report the results for local static and dynamic properties in the Kondo regime. In the absence of the field, local impurity properties remain isotropic in spin space despite the SOC-induced magnetic anisotropy of the conduction band. In the presence of the field, clear fingerprints of anisotropy are revealed through the strong field-direction dependence of the impurity spin polarization and spectra, in particular of the Kondo peak height. The detailed behavior depends on the relative magnitudes of the impurity and band $g$-factors. For the case of impurity $g$-factor somewhat lower than the band $g$-factor, the maximal Kondo peak suppression is found for field oriented along the effective SOC field axis, while for a field perpendicular to this direction we observe a compensation effect (``revival of the Kondo peak''): the SOC counteracts the Kondo peak splitting effects of the local Zeeman field. We demonstrate that the SOC-induced anisotropy, measurable by tunneling spectroscopy techniques, can help to determine the ratio of Rashba and Dresselhaus SOC strengths in the wire.

Spin magnetometry as a probe of stripe superconductivity in twisted bilayer graphene

The discovery of alternating superconducting and insulating ground-states in magic angle graphene has suggested an intriguing analogy with cuprate high-$T_c$ materials. Here we argue that the network states of small angle twisted bilayer graphene (TBG) afford a further perspective on the cuprates by emulating their stripe-ordered phases, as in La$_{1.875}$Ba$_{0.125}$CuO$_4$. We show that the spin and valley quantum numbers of stripes in TBG graphene fractionalize, developing characteristic signatures in the tunneling density of states and the magnetic noise spectrum of impurity spins. By examining the coupling between the charge rivers we determine the superconducting transition temperature. Our study suggests that magic angle graphene can be used for a controlled emulation of stripe superconductivity and quantum sensing experiments of emergent anyonic excitations.

Thermodynamics and Screening in the Ising–Kondo Model

A simplification of the symmetric single‐impurity Kondo model is introduced and studied. In the Ising–Kondo model, host electrons scatter off a single magnetic impurity at the origin whose spin orientation is dynamically conserved. This reduces the problem to potential scattering of spinless fermions that can be solved exactly using the equation‐of‐motion technique. The Ising–Kondo model provides an example for static screening. At low temperatures, the thermodynamics at finite magnetic fields resembles that of a free spin‐1/2 in a reduced external field. Alternatively, the Curie law is interpreted in terms of an antiferromagnetically screened effective spin. The spin correlations decay algebraically to zero in the ground state and display commensurate Friedel oscillations. In contrast to the symmetric Kondo model, the impurity spin is not completely screened, i.e., the screening cloud contains less than a spin‐1/2 electron. At finite temperatures and weak interactions, the spin correlations decay to zero exponentially with correlation length ξ(T) = 1/(2πT).

Ultrafast molecular dynamics in terahertz-STM experiments: Theoretical analysis using the Anderson-Holstein model

We analyze ultrafast tunneling experiments in which electron transport through a localized orbital is induced by a single cycle THz pulse. We include both electron-electron and electron-phonon interactions on the localized orbital using the Anderson-Holstein model and consider two possible filling factors, the singly occupied Kondo regime and the doubly occupied regime relevant to recent experiments with a pentacene molecule. Our analysis is based on variational non-Gaussian states and provides the accurate description of the degrees of freedom at very different energies, from the high microscopic energy scales to the Kondo temperature $T_K$. To establish the validity of the new method we apply this formalism to study the Anderson model in the Kondo regime in the absence of coupling to phonons. We demonstrate that it correctly reproduces key properties of the model, including the screening of the impurity spin, formation of the resonance at the Fermi energy, and a linear conductance of $2e^2/h$. We discuss the suppression of the Kondo resonance by the electron-phonon interaction on the impurity site. When analyzing THz STM experiments we compute the time dependence of the key physical quantities, including current, the number of electrons on the localized orbital, and the number of excited phonons. We find long-lived oscillations of the phonon that persist long after the end of the pulse. We compare the results for the interacting system to the non-interacting resonant level model.

Uncovering Non-Fermi-Liquid Behavior in Hund Metals: Conformal Field Theory Analysis of an SU(2)×SU(3) Spin-Orbital Kondo Model

Hund metals have attracted attention in recent years due to their unconventional superconductivity, which supposedly originates from non-Fermi-liquid (NFL) properties of the normal state. When studying Hund metals using dynamical mean-field theory, one arrives at a self-consistent "Hund impurity problem" involving a multiorbital quantum impurity with nonzero Hund coupling interacting with a metallic bath. If its spin and orbital degrees of freedom are screened at different energy scales, $T_\mathrm{sp} < T_\mathrm{orb}$, the intermediate energy window is governed by a novel NFL fixed point, whose nature had not yet been clarified. We resolve this problem by providing an analytical solution of a paradigmatic example of a Hund impurity problem, involving two spin and three orbital degrees of freedom. To this end, we combine a state-of-the-art implementation of the numerical renormalization group, capable of exploiting non-Abelian symmetries, with a generalization of Affleck and Ludwig's conformal field theory (CFT) approach for multichannel Kondo models. We characterize the NFL fixed point of Hund metals in detail for a Kondo model with an impurity forming an SU(2)$\times$SU(3) spin-orbital multiplet, tuned such that the NFL energy window is very wide. The impurity's spin and orbital susceptibilities then exhibit striking power-law behavior, which we explain using CFT arguments. We find excellent agreement between CFT predictions and numerical renormalization group results. Our main physical conclusion is that the regime of spin-orbital separation, where orbital degrees of freedom have been screened but spin degrees of freedom have not, features anomalously strong local spin fluctuations: the impurity susceptibility increases as $\chi_\mathrm{sp}^\mathrm{imp} \sim \omega^{-\gamma}$, with $\gamma > 1$.