Metallic Spin Glasses Research Articles

Electronic 1/f noise as a probe of dimensional effects on spin-glass dynamics

Over the past decade, spin-glass simulations have improved to the point that they now access time- and length-scales comparable to experiments at the mesoscale. A recent series of thin-film field-cooled/zero-field-cooled magnetization (FC/ZFC) experiments demonstrated activated spin dynamics, with a temperature-independent activation energy proportional to the logarithm of the film thickness and with coefficients in remarkable agreement with the simulation. These measurements require the application of small magnetic fields, which has been shown to affect the spin-glass energy landscape. Measurements of the 1/f noise in metallic spin-glasses have been previously shown to be a sensitive probe of the spin dynamics, and the measurements can be made without applying a magnetic field. In this mini-review, we review these techniques and discuss how transport measurements can fit into the current landscape of spin-glass measurements. We compare previous measurements to more recent measurements on similar films, made with ostensibly different cooling protocols, and compare both the previous and recent measurements to the magnetometry. The transport measurements—taken over a wider range of temperature than magnetometry—suggest that the maximum spin-glass energy barrier height is temperature-dependent, not fixed, possibly due to two-dimensional dynamics. We discuss this possibility, along with future measurements, which may be able to resolve this mystery.

Exact Numerical Solution of the Fully Connected Classical and Quantum Heisenberg Spin Glass.

We present the mean field solution of the quantum and classical Heisenberg spin glasses, using the combination of a high precision numerical solution of the Parisi full replica symmetry breaking equations and a continuous time quantum MonteCarlo algorithm. We characterize the spin glass order and its low-energy excitations down to zero temperature. The Heisenberg spin glass has a rougher energy landscape than its Ising analog, and exhibits a very slow temperature evolution of its dynamical properties. We extend our analysis to the doped, metallic Heisenberg spin glass, which displays unexpectedly slow spin dynamics, reflecting the proximity to the melting quantum critical point and its associated Sachdev-Ye-Kitaev Planckian dynamics.

Superposition principle and nonlinear response in spin glasses

The extended principle of superposition has been a touchstone of spin-glass dynamics for almost 30 years. The Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields H up to 10 Oe at the reduced temperature Tr=T/Tg=0.95, where Tg is the spin-glass condensation temperature. For H>10 Oe, they observe a departure from linear response which they ascribe to the development of nonlinear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin-glass correlation length, ξ(t,tw;H). Here, t is the time after H changes, and tw is the time from the quench for T>Tg to the working temperature T until H changes. We connect the growth of ξ(t,tw;H) to the barrier heights Δ(tw) that set the dynamics. The effect of H on the magnitude of Δ(tw) is responsible for affecting differently the two dynamical protocols associated with turning H off (TRM, or thermoremanent magnetization) or on (ZFC, or zero-field-cooled magnetization). This difference is a consequence of nonlinearity based on the effect of H on Δ(tw). Superposition is preserved if Δ(tw) is linear in the Hamming distance Hd (proportional to the difference between the self-overlap qEA and the overlap q[Δ(tw)]). However, superposition is violated if Δ(tw) increases faster than linear in Hd. We have previously shown, through experiment and simulation, that the barriers Δ(tw) do increase more rapidly than linearly with Hd through the observation that the growth of ξ(t,tw;H) slows down as ξ(t,tw;H) increases. In this paper, we display the difference between the zero-field-cooled ξZFC(t,tw;H) and the thermoremanent magnetization ξTRM(t,tw;H) correlation lengths as H increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.11 MoreReceived 22 July 2022Revised 18 May 2023Accepted 31 May 2023DOI:https://doi.org/10.1103/PhysRevB.107.214436©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMagnetismPhysical SystemsMetallic glassesSpin glassesTechniquesCritical phenomenaCondensed Matter, Materials & Applied Physics

Critical metallic phase in the overdoped random t-J model

We investigate a model of electrons with random and all-to-all hopping and spin exchange interactions, with a constraint of no double occupancy. The model is studied in a Sachdev-Ye-Kitaev-like large-M limit with SU(M) spin symmetry. The saddle-point equations of this model are similar to approximate dynamic mean-field equations of realistic, nonrandom, t-J models. We use numerical studies on both real and imaginary frequency axes, along with asymptotic analyses, to establish the existence of a critical non-Fermi-liquid metallic ground state at large doping, with the spin correlation exponent varying with doping. This critical solution possesses a time-reparameterization symmetry, akin to Sachdev-Ye-Kitaev (SYK) models, which contributes a linear-in-temperature resistivity over the full range of doping where the solution is present. It is therefore an attractive mean-field description of the overdoped region of cuprates, where experiments have observed a linear-T resistivity in a broad region. The critical metal also displays a strong particle-hole asymmetry, which is relevant to Seebeck coefficient measurements. We show that the critical metal has an instability to a low-doping spin-glass phase and compute a critical doping value. We also describe the properties of this metallic spin-glass phase.

Quantum Phase Transition at Nonzero Doping in a Random t-J Model.

We present exact diagonalization results on finite clusters of a t-J model of spin-1/2 electrons with random all-to-all hopping and exchange interactions. We argue that such random models capture qualitatively the strong local correlations needed to describe the cuprates and related compounds, while avoiding lattice space group symmetry breaking orders. The previously known spin glass ordered phase in the insulator at doping p=0 extends to a metallic spin glass phase up to a transition p=p_{c}≈1/3. The dynamic spin susceptibility shows signatures of the spectrum of the Sachdev-Ye-Kitaev models near p_{c}. We also find signs of the phase transition in the entropy, entanglement entropy, and compressibility, all of which exhibit a maximum near p_{c}. The electron energy distribution function in the metallic phase is consistent with a disordered extension of the Luttinger-volume Fermi surface for p>p_{c}, while this breaks down for p<p_{c}.

Deconfined Critical Point in a Doped Random Quantum Heisenberg Magnet

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interaction between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a nonzero critical value pc of the hole doping p away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point pc is flanked by confining phases: a disordered Fermi liquid with carrier density 1+p for p>pc and a metallic spin glass with carrier density p for p<pc. Additional evidence for the critical behavior is obtained from a large-M analysis of a model which extends the SU(2) spin symmetry to SU(M). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.6 MoreReceived 24 December 2019Revised 18 February 2020Accepted 23 March 2020DOI:https://doi.org/10.1103/PhysRevX.10.021033Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum criticalityQuantum phase transitionsPhysical SystemsCupratesTechniquesSachdev-Ye-Kitaev modelCondensed Matter, Materials & Applied Physics

Metal-insulator transition in a random Hubbard model

We examine the metal-insulator transition in a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange, and an on-site nonrandom repulsion, the Hubbard $U$. We argue that recent numerical results of Cha et al. [arXiv:2002.07181] can be understood in terms of a deconfined critical point between a disordered Fermi liquid and an insulating spin glass. We find a deconfined critical point in a previously proposed large $M$ theory, which generalizes the SU(2) spin symmetry to $\mathrm{SU}(M)$ and obtains exponents for the electron and spin correlators which agree with those of Cha et al. This critical point is expected to have the maximal quantum Lyapunov exponent. We also present a renormalization group analysis, and argue for the presence of an additional metallic spin glass phase at half-filling and small $U$.

Probing and dressing magnetic impurities in a superconductor

We propose a method to probe and control the interactions between an ensemble of magnetic impurities in a superconductor via microwave radiation. Our method relies upon the presence of sub-gap Yu-Shiba-Rusinov (YSR) states associated with the impurities. Depending on the sign of the detuning, radiation generates either a ferro- or antiferromagnetic contribution to the exchange interaction. This contribution can bias the statistics of the random exchange constants stemming from the RKKY interaction. Moreover, by measuring the microwave response at the YSR resonance, one gains information about the magnetic order of the impurities. To this end, we estimate the absorption coefficient as well as the achievable strength of the microwave-induced YSR-interactions using off-resonant radiation. The ability to utilize microwave fields to both probe and control impurity spins in a superconducting host may open new paths to studying metallic spin glasses.

Magnetic states of Ni-Mn-Sn based shape memory alloy: A combined muon spin relaxation and neutron diffraction study

The fascinating multiple magnetic states observed in the Ni-Mn-Sn based metamagnetic shape memory alloy are addressed through a combined muon spin relaxation (muSR) and neutron powder diffraction studies. The material used in the present investigation is an off-stoichiometric alloy of nominal composition, Ni[2.04]Mn[1.4]Sn[0.56]. This prototypical alloy, similar to other members in the Ni-Mn-Sn series, orders ferromagnetically below T[CA] (= 320 K), and undergoes martensitic type structural transition at T[MS] (= 290 K), which is associated with the sudden loss of magnetization. The sample regains its magnetization below another magnetic transition at T[CM] = 260 K. Eventually, the composition shows a step-like anomaly at T[B] = 120 K, which is found to coincide with the blocking temperature of exchange bias effect observed in the alloy. In our study, the initial asymmetry A_[10] ) of the $\mu$SR data falls rapidly below T[CA], indicating the onset of bulk magnetic order. A[10] regains its full asymmetry value below T[MS] suggesting the collapse of the ferromagnetic order into a fully disordered paramagnetic state. Below the second magnetic transition at T[CM], asymmetry drops again, confirming the re-entrance of a long range ordered state. Interestingly, A[10] increases sluggishly below T[B], indicating that the system attains a disordered/glassy magnetic phase below T[B], which is responsible for the exchange bias and frequency dispersion in the ac susceptibility data as previously reported. The neutron powder diffraction data do not show any magnetic superlattice reflections, ruling out the possibility of a long range antiferromagnetic state at low temperatures. The ground state is likely to be comprised of a concentrated metallic spin-glass in the backdrop of an ordered ferromagnetic state.

Pressure-tuned Frustration of Magnetic Coupling in Elemental Europium.

Applying linear response and the magnetic force theorem in correlated density functional theory, the intersublattice exchange constants of antiferromagnetic Eu are calculated and found to vanish near the pressure of P_{c}=82 GPa, just where magnetic order is observed experimentally to be lost. The Eu 4f^{7} moment remains unchanged at high pressure, again in agreement with spectroscopic measurements, leaving the picture of perfect frustration of interatomic Ruderman-Kittel-Kasuya-Yoshida couplings in a broad metallic background, leaving a state of electrons strongly exchange coupled to arbitrarily oriented, possibly quasistatic local moments. This strongly frustrated state gives way to superconductivity at T_{c}=1.7 K, observed experimentally. These phenomena, and free energy considerations related to correlations, suggest an unusual phase of matter that is discussed within the scenarios of the Doniach Kondo lattice phase diagram, the metallic spin glass class, and itinerant spin liquid or spin gas systems.

Magnetic impurity bands in Ga1−xMnxS : Towards understanding the anomalous spin-glass transition

We report on the magnetic and electronic properties of single-crystalline ${\mathrm{Ga}}_{0.91}{\mathrm{Mn}}_{0.09}\mathrm{S}$, which is a quasi-two-dimensional diluted magnetic semiconductor (DMS). Through an analysis of magnetization data, we show the existence of an anomalously high spin-glass transition temperature at 11.2 K. Using density functional theory (DFT), we characterize the properties contributing to the spin-glass transition through an examination of the electronic and magnetic properties for ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{S}$ with $x$ varying from 0.00 to 0.18 by randomly substituting Mn atoms into the gallium (Ga) lattice sites. We show that the presence of magnetic atoms produces impurity bands in the electronic structure, where an analysis of the density of states shows an increase in magnetic impurity bands at the Fermi level that lowers the semiconducting gap and is consistent with diluted magnetic semiconductors. Furthermore, this indicates that the spin-glass transition in ${\mathrm{Ga}}_{0.91}{\mathrm{Mn}}_{0.09}\mathrm{S}$ is similar to other DMS materials, where the primary mechanism is likely through magnetic exchange. However, the increased electron density in the system with Mn doping could explain the anomalously higher spin-glass transition temperature in ${\mathrm{Ga}}_{0.91}{\mathrm{Mn}}_{0.09}\mathrm{S}$. In comparison with the substantially lower transition temperatures in related II-VI based systems (i.e., ${\mathrm{Zn}}_{1\ensuremath{-}x}\mathrm{Mn}{}_{x}\mathrm{Te}$), the high transition temperature is associated with more metallic spin-glass systems that interact through RKKY exchange, which leads to the conclusion that there may be a combination of interactions occurring in these systems. Further measurements on the other substitution percentages will hopefully clarify these interactions.

Magnetism of Bi2Se3 thin films with Eu-rich flat inclusions

We report the results of experimental and theoretical studies of Eu-doped Bi2Se3 thin films with extremely inhomogeneous distribution of magnetic component. The obtained electron microscopy images suggest that Eu atoms are concentrated within platelet-like nanoinclusions. The number of inclusions grows with the increase in Eu content, x. Moreover, at relatively high x values, the stacks of platelets (inclusions located one under another) become rather frequent. A comparative analysis of magnetic properties of the films under study reveals no pronounced changes of their temperature dependence with the increase in x, which, however, leads to the decrease in the average magnetic moment per Eu atom. A theoretical analysis of different mechanisms contributing to a possible magnetic ordering in the Eu-doped films demonstrates that at small distances (i.e. within a platelet) a dominant contribution is related to the RKKY interaction via electrons in the bulk, while the ordering at inter-platelet distances is governed by magnetic dipole–dipole interaction. The latter implies the antiferromagnetic ordering within the stacks of platelets explaining a drop of per Eu atom. We employ the model of a metallic spin glass to estimate the transition temperature, characterising the interaction within the ensemble of randomly distributed magnetic platelets. This estimate gives satisfactory agreement with the experiment, even if we take into account a finite film thickness, thus, neglecting the interaction anisotropy and including only the antiferromagnetism related to the stacking. While the overall contribution of interface Dirac electrons is damped in the systems under study, we argue that the obtained results can be used for the investigation of ultrathin films with analogous impurity profile, where this contribution should be clearly pronounced.

Investigation of magnetic properties on spin-ordering effects of FeGa2S4 and FeIn2S4

We have studied crystal and magnetic properties of chalcogenides FeGa2S4 and FeIn2S4 with X-ray diffractometer (XRD), magnetic property measurement system (MPMS), magnetometer, physical property measurement system (PPMS), and Mössbauer spectrometer. The crystal structure has 2-dimension triangular lattice structure with P-3m1 of FeGa2S4, while FeIn2S4 has inverse spinel with space group Fd3m. The AC magnetic susceptibility measurements show that FeGa2S4 is an insulating spin glass material, exhibiting geometrical frustration, unlike in the antiferromagnetic [AFM] metallic spin glass FeIn2S4. From hysteresis (M-H) curves at 4.2K, FeGa2S4 has spin-flop behavior with an angle of 120° of triangle, as against linear slope of FeIn2S4 due to anti-parallel spin. The gap energy by splitting of 5T2g, Δ1 and electric quadrupole splitting ΔEQ of FeIn2S4 are much higher than that of FeGa2S4 at 4.2K because FeGa2S4 is geometrically frustrated magnet having degenerate ground state at low temperature.

Skew Scattering from Correlated Systems: Impurities and Collective Excitations in the Spin Hall Effect

The spin Hall effect is affected by the Coulomb interaction as well as spin–spin correlations in metals. Here we examine the enhancement in the effect caused by resonant skew scattering induced by electron correlations. For single-impurity scattering, local Coulomb correlations may significantly change the observed spin Hall angle. There may be additional effects because of the special atomic environment close to a surface — extra degeneracies compared to the bulk, enhanced correlations that move the relative d- or f-levels, and interference effects coming from the lower local dimension. Our results may explain the very large spin Hall angle observed in CuBi alloys. We discuss the impact on the spin Hall effect from cooperative effects, firstly in an itinerant ferromagnet where there is an anomaly near the Curie temperature originating from high-order spin fluctuations. The second case considered is a metallic spin glass, where exchange via slowly fluctuating magnetic moments may lead to the precession of...

Insulating and metallic spin glass in Ni-dopedKxFe2−ySe2single crystals

We report electron doping effects by Ni in K$_{x}$Fe$_{2-\delta-y}$Ni$_{y}$Se$_{2}$ (0.06 $\leq$ $y$ $\leq$ 1.44) single crystal alloys. A rich ground state phase diagram is observed. Small amount of Ni ($\sim$ 4\%) suppressed superconductivity below 1.8 K, inducing insulating spin glass magnetic ground state for higher Ni content. With further Ni substitution, metallic resistivity is restored. For high Ni concentration in the lattice the unit cell symmetry is high symmetry $I4/mmm$ with no phase separation whereas both $I4/m + I4/mmm$ space groups were detected in the phase separated crystals when concentration of Ni $<$ Fe. The absence of superconductivity coincides with the absence of crystalline Fe vacancy order.

Memory effects and magnetic relaxation in single-crystallineLa0.9Sr0.1CoO3

We report a detailed investigation of magnetic relaxation and memory effects in ${\mathrm{La}}_{0.9}$${\mathrm{Sr}}_{0.1}$${\mathrm{CoO}}_{3}$ single crystal from dc magnetization measurements. The analysis of magnetic relaxation at different temperatures and magnetic fields below the freezing temperature ${T}_{f}$ reveals the characteristics of the spin-glass phase. Below ${T}_{f}$, striking memory effects have been clearly observed in different experimental protocols. The memory effect in the zero-field-cooled magnetization further establishes that the glassy magnetic state arises from the cooperative spin-spin interaction but not due to the independent relaxation of metastable phase clusters. The asymmetric response with respect to negative and positive temperature changes favors the hierarchical model of memory effects rather than the droplet model discussed in other works for different insulating and metallic Heisenberg spin glasses.

Magnetic Dephasing in Mesoscopic Spin Glasses

We have measured universal conductance fluctuations in the metallic spin glass Ag:Mn as a function of temperature and magnetic field. From this measurement, we can access the phase coherence time of the electrons in the spin glass. We show that this phase coherence time increases with both the inverse of the temperature and the magnetic field. From this, we deduce that decoherence mechanisms are still active even deep in the spin glass phase.

Neutron Depolarization from Reentrant Spin Glasses

The reentrant spin glass study was elucidated for the first time by means of the novel method of neutron depolarization. The wavelength dependent neutron depolarization senses the magnetic induction in mesoscopic scale inside the magnetic material. It was demonstrat­ ed that the domain distribution in the ferromagnet could be determined by the careful depolarization study of the magnetization process. This method has been applied to the reentrant spin glass problem, and the observation of the mesoscopic magnetic field gives a significant experimental fact to evince the reentrant transition from the ferromagnetic order. The quite recent experiments are reviewed in this paper, which contains many new results from various metallic reentrant spin glasses. The reentrant behavior is concluded to be governed by the degree of the frustration.

Metallic spin-glasses beyond mean-field: an approach to the impurity-concentration dependence of the freezing temperature

A relation between the freezing temperature () and the exchange couplings () in metallic spin-glasses is derived, taking the spin correlations () into account. This approach does not involve a disorder average. The expansion of the correlations to first order in leads to the molecular-field result from Thouless–Anderson–Palmer. Employing the current theory for the spin interaction in disordered metals, an equation for as a function of the concentration of impurities is obtained, which reproduces the available data from AuFe, AgMn, and CuMn alloys well.

The Magnetic Behaviors of Spin-Glass $\hbox{FeGa}_{2}\hbox{O}_{4}$ System

We present the investigation of magnetic properties of spin-glass FeGa2O4 system. From X-ray diffraction patterns of FeGa2O4, refined with Rietveld's refinement method, its structure is determined to be cubic spinel with space group Fd - 3m and the lattice parameter of α0 = 8.385 Å. From temperature-dependent magnetization curves under 1000 Oe, the Neel temperature is found to be TN = 14 K, which coincides with the value obtained from the Mossbauer spectrum. The freezing temperature Tf of the sample shifts to higher temperature with increasing frequency, as seen in conventional metallic spin glasses. Also, we have determined the small activation energy, Ea of 1.04266 × 10-4 meV from Arrhenius law v = v0 exp(-En/kBTf), where kB is Boltzmann constant, and Ea is activation energy. The Mossbauer spectrum at 4.2 K shows severely distorted 8-line shape coming from frozen spin-disorder state and an incommensurate spin structure, as in spin glasses. The change in the electric quadrupole shift above Tf is caused by the presence of the maximum electric dipole interaction among frozen disordered spins around Tf as in spin-glass material, and charge re-distribution from spin-relocation arising above TN.