Thermal Spin Fluctuations Research Articles

Thermally induced localization of dopants in a magnetic spin ladder

I unveil an emergent localization phenomenon pertaining to the motion of a dopant in a thermal spin lattice. This is rendered localized by thermal spin fluctuations, whereby it is in stark constrast to the intrinsic origin of Anderson localization for quenched disorder. The system of interest consists of spin-1/2 particles organized in a two-leg ladder with nearest-neighbor Ising interactions J. The motion of a hole—the dopant—is initialized by suddenly removing a spin from the thermal spin ensemble, which then moves along the ladder via nearest-neighbor hopping t. I find that the hole remains for all values of J/t and for nonzero temperatures. The origin is an effective disorder potential seen by the hole and induced by thermal spin fluctuations. Its length scale is found to match with the underlying spin-spin correlation length at low temperatures. For ferromagnetic couplings (J<0), the associated localization length of the hole increases with decreasing temperature and becomes proportional to the correlation length at low temperatures, asymptotically delocalizing at low temperatures. For antiferromagnetic couplings (J>0), there is a smooth crossover between thermal localization at high temperatures to localization driven by the antiferromagnetic order at low temperatures. At infinite temperatures, the dynamics becomes independent of the sign of the spin coupling, whereby the localization length is a universal function of |J|/t, diverging as (t/J)2 for |J|≪t. Finally, I analyze a setup with Rydberg-dressed atoms, which naturally realizes finite-range Ising interactions, accessible in current experimental setups. I show that the discovered localization phenomenon can be probed on experimentally accessible length- and timescales, providing a strong testing ground for my predictions. Published by the American Physical Society 2024

Spin-fluctuation-induced sign reversal of the spin Hall angle in Pt100−x Co x alloys near the Curie temperature

The spin Hall effect (SHE), typically emerging in non-magnetic metals with strong spin-orbit couplings, has attracted significant attention for its ability to convert a charge current into a spin current, a key feature in power-efficient spintronic devices. Recently, an enhanced SHE has been detected in the magnetic alloys, where the spin Hall conductivity is strongly modified by the dynamical and thermal spin fluctuations. We find that the spin Hall angle ( θSH ) in Pt100−x Co x alloys dramatically changes at the Curie temperature, which is positive in the paramagnetic phase akin to Pt, while negative in the ferromagnetic phase. Such intriguing behavior of θSH stemming from individual and collective fluctuations in the magnetic moments is further substantiated with the full-fledged Monte Carlo simulations. Our work broadens insights into the SHE and highlights the importance of spin fluctuations for the spin-current generation near the ferromagnetic instability point of magnetic alloys.

Theoretical determination of Ising-type transition by using the Self-Consistent Harmonic Approximation

Over the years, the Self-Consistent Harmonic Approximation (SCHA) has been successfully utilized to determine the transition temperature of many different magnetic models, particularly the Berezinskii–Thouless–Kosterlitz transition in two-dimensional ferromagnets. More recently, the SCHA has found application in describing ferromagnetic samples in spintronic experiments. In such a case, the SCHA has proven to be an efficient formalism for representing the coherent state in the ferromagnetic resonance state. One of the main advantages of using the SCHA is the quadratic Hamiltonian, which incorporates thermal spin fluctuations through renormalization parameters, keeping the description simple while providing excellent agreement with experimental data. In this article, we investigate the SCHA application in easy-axis magnetic models, a subject that has not been adequately explored to date. We obtain both semiclassical and quantum approaches of the SCHA for a general anisotropic magnetic model and employ them to determine various quantities such as the transition temperature, spin-wave energy spectrum, magnetization, and critical exponents. To verify the accuracy of the method, we compare the SCHA results with experimental and Monte Carlo simulation data for many distinct well-known magnetic materials.

First-Principles Studies on Spin-Dependent Transport of Magnetic Junctions with Half-Metallic Heusler Compounds

Two types of magnetoresistance (MR), i.e., tunnel magnetoresistance (TMR) and current perpendicular to plane giant magnetoresistance (CPP-GMR), are theoretically discussed for systems with half-metallic (HFM) Co-based full Heusler compounds. In TMR, the non-collinear spin structure at the Co2MnSi(CMS)/MgO(001) interface that results from thermal spin fluctuations significantly reduced the TMR ratio at room temperature (RT). Enhancement of the exchange stiffness of CMS/MgO was essential to suppress the reduction in TMR at RT. Furthermore, it is proposed that inserting of a B2-CoFe layer between CMS and MgO is a promising way to enhance the interface exchange stiffness constant. In CPP-GMR, the interface spin asymmetry γ in the Valet-Fert model was essential to enhance GMR at RT, because the temperature dependence of γ in experiments was much larger than that of the bulk spin asymmetry β. I showed that the experimental CPP-GMR ratio increases with the decrease in the theoretical resistance-area product RPA, which is roughly consistent with the RP dependence of γ. This means that matching of the conductive channel between HMF and a non-magnetic metallic spacer is a key parameter to enhance γ. These findings will be very important for room temperature spintronics devices applied in future artificial intelligence hardware.

Possible Origin of Low-Frequency Magnetic Flux Noise in Superconducting Devices

The magnetic flux noise caused by surface spin fluctuations in superconducting quantum interference devices (SQUIDs) limits their development. In this work, we report that different adsorbents such as H, O2, NO, and NO2 that adsorb on the surfaces of Mg-based and Pb-based SQUIDs, respectively, producing large local magnetic moments ranging from 0.7-1.6 μB, with energy barriers for thermal spin fluctuation as low as 10-30 mK. Moreover, we observe that the presence of H atoms on the surface of MgO can cause the coadsorption of other molecules, which generates additional spin sources. Monte Carlo simulations of the weakly coupled spin on a two-dimensional square lattice produce a low-frequency flux noise spectrum. We suggest eliminating the surface magnetism by coating the surface with monolayer indium phosphide or protecting the surface from other molecules by nonmagnetic preoccupants with a larger adsorption energy. The work provides important physical insights and feasible strategies for reducing magnetic noise sources in superconducting circuits.

Magnetic and magnetotransport properties of MnSb polycrystals near equatomic composition

In this work, we studied properties of the MnSb polycrystalline samples synthesized from a melt of high-purity elements. We observed the presence of a ferromagnetic state with Curie temperature significantly higher than room temperature (Tc≈568 K). The results of structural and magnetic studies suggest the presence of a slight deviation from the equatomic composition towards the small excess of Mn (∼ 1 at.%). It was found that the studied sample have high resistivity (up to 425 μΩ⋅cm) at room temperature, however, it significantly decreases upon cooling, breaking the Mooij correlation. The magnetoresistance of the MnSb polycrystal is positive at low temperatures and does not get saturated in studied magnetic field range (≤40 kOe), which suggests that this contribution stems from the classical Lorenz mechanism. Negative magnetoresistance contribution, associated with the suppression of thermal spin fluctuations by external magnetic field, becomes dominant at higher temperatures (T≥74 K). The normal Hall effect coefficient is positive and significantly increases upon heating, which indicates a substantial variation of delocalized holes density with temperature. The anomalous Hall effect coefficient is also positive, and its temperature dependence suggests that the skew scattering mechanism provides a considerable contribution at low temperatures.

Spin-tunable thermoelectric performance in monolayer chromium pnictides

Historically, finding two-dimensional (2D) magnets is well known to be a difficult task due to the instability against thermal spin fluctuations. Metals are also normally considered poor thermoelectric (TE) materials. Combining intrinsic magnetism in two dimensions with conducting properties, one may expect to get the worst for thermoelectrics. However, we will show this is not always the case. Here, we investigate the spin-dependent TE properties of monolayer chromium pnictides ($\mathrm{Cr}X$, where $X=\text{P}$, As, Sb, and Bi) using first-principles calculations of electron- and phonon-energy dispersion, along with the Boltzmann transport formalism under an energy-dependent relaxation time approximation. All the $\mathrm{Cr}X$ monolayers are dynamically stable and they also exhibit half metallicity with ferromagnetic ordering. Using the spin-valve setup with an antiparallel spin configuration, the half metallicity and ferromagnetism in monolayer $\mathrm{Cr}X$ enable the manipulation of spin degrees of freedom to tune the TE figure of merit $(ZT)$. At an optimized chemical potential and operating temperature of 500 K, the maximum $ZT$ values ($\ensuremath{\approx}0.22$, 0.12, and 0.09) with the antiparallel spin-valve setup in CrAs, CrSb, and CrBi improve up to almost twice the original values ($ZT\ensuremath{\approx}0.12$, 0.08, and 0.05) without the spin-valve configuration. Only in CrP, which is the lightest species and less spin polarized among $\mathrm{Cr}X$, the maximum $ZT$ $(\ensuremath{\approx}0.34)$ without the spin-valve configuration is larger than that $(\ensuremath{\approx}0.19)$ with the spin-valve one. We also find that, at 500 K, all the $\mathrm{Cr}X$ monolayers possess exceptional TE power factors of about 0.02--0.08 W/m ${\mathrm{K}}^{2}$, which could be one of the best values among 2D conductors.

Slow spin dynamics in the hyperhoneycomb lattice [(C2H5)3NH]2Cu2(C2O4)3 revealed by H1 NMR studies

We report the results of magnetic susceptibility $\chi$ and $^1$H nuclear magnetic resonance (NMR) measurements on a three-dimensional hyper-honeycomb lattice compound [(C$_2$H$_5$)$_3$NH]$_2$Cu$_2$(C$_2$O$_4$)$_3$ (CCCO). The average value of the antiferromagnetic (AFM) exchange coupling between the Cu$^{2+}$ ($S$ = 1/2) spins was determined to be $J$~$\sim$~50 K from the $\chi$ measurements. No long-range magnetic ordering has been observed down to $T$ = 50 mK, although NMR lines become slightly broader at low temperatures below 1 K. The broadening of the NMR spectrum observed below 1 K reveals that the Cu spin moments remain at this temperature, suggesting a non-spin-singlet ground state. The temperature and magnetic field dependence of 1/$T_1$ at temperatures above 20 K is well explained by paramagnetic thermal spin fluctuations where the fluctuation frequency of Cu$^{2+}$ spins is higher than the NMR frequency of the order of MHz. However, a clear signature of the slowing down of the Cu$^{2+}$ spin fluctuations was observed at low temperatures where 1/$T_1$ shows a thermally-activated behavior. The magnetic field dependence of the magnitude of the spin excitation gap suggests that the magnetic behaviors of CCCO are characterized as an AFM chain at low temperatures.

Spontaneous creation and annihilation dynamics of magnetic skyrmions at elevated temperature

Skyrmions are topologically protected nanoscale magnetic structures with a wide range of potential applications. Here we determine the life cycle of skyrmions from their creation to their intrinsic dynamics and thermal stability to their eventual thermodynamic demise. Using atomistic simulations of Ir/Co/Pt, parameterized from ab initio calculations, we demonstrate the thermal phase transition to a skyrmion state under application of a perpendicular magnetic field. The created skyrmions exhibit Brownian particlelike dynamics driven by the underlying thermal spin fluctuations. At an elevated temperature window well below the Curie temperature, the skyrmions are metastable and can collapse to a uniform magnetic state. With application of an external magnetic field, the intrinsic local thermal spin fluctuations at this elevated temperature window are sufficiently large to allow the spontaneous formation of new skyrmions in thermodynamic equilibrium analogous to a spontaneous skyrmion gas. Such a system could be used to implement a skyrmion-based true random number generator.

Generic Seebeck effect from spin entropy

How magnetism affects the Seebeck effect is an important issue of wide concern in the thermoelectric community but remains elusive. Based on a thermodynamic analysis of spin degrees of freedom on varied d-electron-based ferromagnets and antiferromagnets, we demonstrate that in itinerant or partially itinerant magnetic compounds there exists a generic spin contribution to the Seebeck effect over an extended temperature range from slightly below to well above the magnetic transition temperature. This contribution is interpreted as resulting from transport spin entropy of (partially) delocalized conducting d electrons with strong thermal spin fluctuations, even semiquantitatively in a single-band case, in addition to the conventional diffusion part arising from their kinetic degrees of freedom. As a highly generic effect, the spin-dependent Seebeck effect might pave a feasible way toward efficient “magnetic thermoelectrics.”

Spin Fluctuations in Quantized Transport of Magnetic Topological Insulators.

In magnetic topological insulators, quantized electronic transport is intertwined with spontaneous magnetic ordering, as magnetization controls band gaps, hence band topology, through the exchange interaction. We show that considering the exchange gaps at the mean-field level is inadequate to predict phase transitions between electronic states of distinct topology. Thermal spin fluctuations disturbing the magnetization can act as frozen disorders that strongly scatter electrons, reducing the onset temperature of quantized transport appreciably even in the absence of structural impurities. This effect, which has hitherto been overlooked, provides an alternative explanation of recent experiments on magnetic topological insulators.

Magnetic properties and spin wave spectra of a ferromagnetic monolayer with 2D tetragonal structure: An application for Co2S2 monolayer

In this paper, the magnetic properties, thermal spin fluctuation and the spin wave spectra of a 2D tetragonal ferromagnetic monolayer with Heisenberg model including single-ion anisotropy are studied using functional integral method. Influence of exchange interaction at edge on these properties of the monolayer is also considered. The model is applied for a new robust ferromagnetic monolayer with the 2D tetragonal structure, Co2S2, in which the exchange interaction between magnetic atoms and non-magnetic atoms is included due to hybridization between Co 3d states and S 3p states.

Effects of intrinsic defects and alloying with Fe on the half-metallicity of Co2MnSi

The electronic structure and half-metallic gap of Co$_{2}$MnSi in the presence of crystallographic defects, partial Fe substitution for Mn, and thermal spin fluctuations are studied using the coherent potential approximation and the disordered local moment method. In the presence of 5\% Co or Mn vacancies the Fermi level shifts down to the minority-spin valence-band maximum. In contrast to NiMnSb, both types of Mn antisite defects in Co$_{2}$MnSi are strongly exchange-coupled to the host magnetization, and thermal spin fluctuations do not strongly affect the half-metallic gap. Partial substitution of Mn by Fe results in considerable changes in the Bloch spectral function near the Fermi level, which strongly deviate from the rigid-band picture. In particular, a light band with the Fe character crosses the Fermi level at about 50\% concentration. At room temperature, Fe substitution of up to 30\% slightly increases the spin polarization at the Fermi level.

Anisotropic field-induced ordering in the triangular-lattice quantum spin liquid NaYbSe2

High-quality single crystals of NaYbSe$_2$, which resembles a perfect triangular-lattice antiferromagnet without the intrinsic disorder, are investigated by magnetization and specific heat, as well as the local probe techniques nuclear magnetic resonance (NMR) and electron spin resonance (ESR). The low-field measurements confirm the absence of any spin freezing or long-range magnetic order down to 50~mK, which suggests a quantum spin liquid ground (QSL) state with gapless excitations. The instability of the QSL state is observed upon applying magnetic fields. For the $H\bot c$ direction, a field-induced magnetic phase transition is observed above 2~T from the $C_{\rm p}(T)$ data, agreeing with a clear $\frac{M_s}{3}$ plateau of $M(H)$, which is associated with an up-up-down (uud) spin arrangement. For the $H\|c$ direction, a field-induced transition could be evidenced at a much higher field range (9 - 21~T). The $^{23}$Na NMR measurements provide microscopic evidence for field-induced ordering for both directions. A reentrant behavior of $T_{\rm N}$, originating from the thermal and quantum spin fluctuations, is observed for both directions. The anisotropic exchange interactions $J_{\perp}\simeq$ 4.7~K and $J_z\simeq$2.33~K are extracted from the modified bond-dependent XXZ model for the spin-$\frac{1}{2}$ triangular-lattice antiferromagnet. The absence of magnetic long-range order at zero fields is assigned to the effect of strong bond-frustration, arising from the complex spin-orbit entangled $4f$ ground state. Finally, we derive the highly anisotropic magnetic phase diagram, which is discussed in comparison with the existing theoretical models for spin-$\frac{1}{2}$ triangular-lattice antiferromagnets.

Temperature and Thickness Dependence of Statistical Fluctuations of the Gilbert Damping in Co - Fe - B / MgO Bilayers

We theoretically investigate the temperature and thickness dependence of the effective Gilbert damping constant (α) in the Co-Fe-B/MgO system using atomistic spin dynamics. We consider a high damping constant at the interface layer and a low damping constant for the bulklike layers due to large interfacial spin-orbit coupling. We find a strong dependence of the effective Gilbert damping with the film thickness, in quantitative agreement with experimental data. The temperature dependence of the effective damping arising from thermal-spin fluctuations up to temperatures of 400 K is weak, with no apparent change over the studied temperature range. Interestingly, we find that the temperature produces a different effect: a statistical fluctuation of the Gilbert damping parameter for a given relaxation induced solely from the finite size of the system. This statistical variation of the Gilbert damping is an intrinsic effect and is important for spintronic devices operating at gigahertz frequencies, where the dynamic response must be carefully controlled.

Grüneisen parameter and thermal expansion near magnetic quantum critical points in itinerant electron systems

Complete expressions of the thermal-expansion coefficient $\alpha$ and the Gr\"{u}neisen parameter $\Gamma$ are derived on the basis of the self-consistent renormalization (SCR) theory. By considering zero-point as well as thermal spin fluctuation under the stationary condition, the specific heat for each class of the magnetic quantum critical point (QCP) specified by the dynamical exponent $z=3$ (FM) and $z=2$ (AFM) and the spatial dimension ($d=3$ and $2$) is shown to be expressed as $C_{V}=C_a-C_b$, where $C_a$ is dominant at low temperatures, reproducing the past SCR criticality endorsed by the renormalization group theory. Starting from the explicit form of the entropy and using the Maxwell relation, $\alpha=\alpha_a+\alpha_b$ (with $\alpha_a$ and $\alpha_b$ being related to $C_a$ and $C_b$, respectively) is derived, which is proven to be equivalent to $\alpha$ derived from the free energy. The temperature-dependent coefficient found to exist in $\alpha_b$, which is dominant at low temperatures, contributes to the crossover from the quantum-critical regime to the Curie-Weiss regime and even affects the quantum criticality at 2d AFM QCP. Based on these correctly calculated $C_{V}$ and $\alpha$, Gr\"{u}neisen parameter $\Gamma=\Gamma_a+\Gamma_b$ is derived, where $\Gamma_a$ and $\Gamma_b$ contain $\alpha_a$ and $\alpha_b$, respectively. The inverse susceptibility coupled to the volume $V$ in $\Gamma_b$ gives rise to divergence of $\Gamma$ at the QCP for each class even though characteristic energy scale of spin fluctuation $T_0$ is finite at the QCP, which gives a finite contribution in $\Gamma_a=-\frac{V}{T_0}\left(\frac{\partial T_0}{\partial V}\right)_{T=0}$. General properties of $\alpha$ and $\Gamma$ including their signs as well as the relation to $T_0$ and the Kondo temperature in temperature-pressure phase diagrams of Ce- and Yb-based heavy electron systems are discussed.

Magnetic Susceptibility and Spin Fluctuations in the Nonsuperconducting Phase of PuCoGa5

Within the Hubbard model with allowance for Hund’s and spin–orbit interactions, the concepts of thermal spin fluctuations in a strongly correlated system of f electrons in PuCoGa5 are developed. The effect of fluctuations of the spin magnetic moments of different orbitals on the spin–orbit splitting of the f electron spectrum is considered. The mean square magnetic moment obtained in this case makes it possible to describe the observed temperature dependence of the magnetic susceptibility (χ(T)) of PuCoGa5 near and above the electron pairing temperature. Estimates of the radius of spin correlations correspond in order of magnitude to the sizes of Cooper pairs in superconductors with the d symmetry of the order parameter. In the high-temperature region, the magnetic susceptibility obeys the Curie–Weiss law. With decreasing temperature, when approaching the pairing temperature, the ferromagnetic instability is suppressed and the temperature maximum of χ(T) appears.

Prediction of the phase stability and elastic property of ϵ-Pu at high temperature from theoretical study

The phase stability and elastic property of ϵ-Pu at 800 K are predicted through systematically theoretical calculations, by taking the temperature-dependent phonon smearing, spin fluctuation, phonon vibration, and volume expansion effects into account. Dominated by the phonon smearing at 800 K, ϵ-Pu is thermodynamically stabilized in the paramagnetic state with the absolute value of the local magnetic moment (μPu) about 3.8 μB, being smaller than the 0 K value (about 5.0 μB). The resulted thermal spin fluctuation, which prefers the δ−ϵ phase transition, greatly decreases the volume (V) and the shear elastic constants (C′ and C44) of the ϵ phase. However, the phonon smearing itself prefers the expansion of V and also the increase of C′ and C44. Besides the influence of the spin fluctuation and phonon smearing at 800 K, the equilibrium V of ϵ-Pu seems to be dominated by the phonon vibration, and the lattice thermal expansion also further increases C′ whereas decreases C44. The determined V as well as C′ and C44 of ϵ-Pu at 800 K is reasonable in comparison with the previous studies. This insight provides a good understanding of the physical mechanisms driving the thermodynamical stability of ϵ-Pu at high temperature.

Plastic deformation modes in paramagnetic γ-Fe from longitudinal spin fluctuation theory

Using an efficient first-principles computational scheme, we calculate the intrinsic stacking fault energy (γisf) and the unstable stacking fault energy (γusf) of paramagnetic γ-Fe as a function of temperature. The formation energies are derived from free energies accounting for thermal longitudinal spin fluctuations (LSFs). LSFs are demonstrated to be important for the accurate description of the temperature-dependent magnetism, intrinsic and unstable stacking fault energies, and have a comparatively large effect on γisf of γ-Fe. Dominated by the magneto-volume coupling at thermal excitations, γisf of γ-Fe exhibits a positive correlation with temperature, while γusf declines with increasing temperature. The predicted stacking fault energy of γ-Fe is negative at static condition, crosses zero around 540 K, and reaches 71.0 mJ m−2 at 1373 K, which is in good agreement with the experimental value. According to the plasticity theory formulated in terms of the intrinsic and unstable stacking fault energies, twinning remains a possible deformation mode even at elevated temperatures. Both the large positive temperature slope of γisf and the predicted high-temperature twinning are observed in the case of austenitic stainless steels.

Ultrafast demagnetization at high temperatures

Time-resolved pump-probe measurements were made at variable heat accumulation in Co/Pd superlattices. Heat accumulation increases the baseline temperature and decreases the equilibrium magnetization. Transient ultrafast demagnetization first develops with higher fluence in parallel with strong equilibrium thermal spin fluctuations. The ultrafast demagnetization is then gradually removed as the equilibrium temperature approaches the Curie temperature. The transient magnetization time-dependence is well fit with the spin-flip scattering model.