Transverse Spin Fluctuations Research Articles

The squeezed dark nuclear spin state in lead halide perovskites

Coherent many-body states are highly promising for robust quantum information processing. While far-reaching theoretical predictions have been made for various implementations, direct experimental evidence of their appealing properties can be challenging. Here, we demonstrate optical manipulation of the nuclear spin ensemble in the lead halide perovskite semiconductor FAPbBr3 (FA = formamidinium), targeting a long-postulated collective dark state that is insensitive to optical pumping after its build-up. Via optical orientation of localized hole spins we drive the nuclear many-body system into this entangled state, requiring a weak magnetic field of only a few milli-Tesla strength at cryogenic temperatures. During its fast establishment, the nuclear polarization along the optical axis remains small, while the transverse nuclear spin fluctuations are strongly reduced, corresponding to spin squeezing as evidenced by a strong violation of the generalized nuclear squeezing-inequality with ξs < 0.5. The dark state corresponds to an ~35-body entanglement between the nuclei. Dark nuclear spin states can be exploited to store quantum information benefiting from their long-lived many-body coherence and to perform quantum measurements with a precision beyond the standard limit.

Temperature Variation of Gilbert Damping Constant in 3d Transition Metals from First Principles

A theoretical investigation of temperature-dependent Gilbert damping is presented. We evaluate the Gilbert damping constant α (and the corresponding Landau frequency λ) at a finite temperature for hcp-Co, fcc-Ni, and Cu-doped fcc-Ni from first principles by combining the torque correlation model and the disordered local moment scheme, in which the finite-temperature effect is included as the transverse spin fluctuation. The calculated λ has, from the viewpoint of the material dependence, well reproduced the experimental results, but quantitatively, these values are more underestimated than the experimental values. A comparison with the lifetime approximation results reveals that a change in the electronic structure due to the spin fluctuation affects λ for Co and Ni but not for Fe. On the basis of the variation of the local magnetic moment of Co and Ni at finite temperature, we conclude that these differences in λ are due to the difference in the degree of itinerancy of spins.

Effect of Dzyaloshinskii-Moriya Interaction on Heisenberg Antiferromagnetic Spin Chain in the Presence of a Longitudinal Magnetic Field

Using functional integral method for the Heisenberg antiferromagnetic spin chain with the added Dzyaloshinskii-Moriya Interaction in the presence of the longitudinal magnetic field, we find out expression for free energy of the spin chain via spin fluctuations, from which quantities characterize the antiferromagnetic order and phase transition such as staggered and total magnetizations derived. From that, we deduce the significant effect of the Dzyaloshinskii-Moriya interaction on the reduction of the antiferromagnetic order and show that the total magnetization can be deviated from the initial one under the influence of canting of the spins due to a combination of the Dzyaloshinskii-Moriya interaction and the magnetic field. Besides, the remarkable role of the transverse spin fluctuations due to the above factors on the antiferromagnetic behaviours of the spin chain is also indicated.

Persistence of Ising-like easy-axis spin correlations in the paramagnetic state of the spin-1 chain compound NiTe2O5

A $^{125}$Te nuclear magnetic resonance (NMR) study was carried out in the paramagnetic state of the recently discovered quasi-one-dimensional spin-1 chain compound NiTe$_2$O$_5$. We observed that the $^{125}$Te NMR spectrum splits into two in a magnetic field applied along the $c$ axis. Based on the strong temperature variation of the relative intensity ratio of the split lines, we infer that the line splitting arises from the two sublattice susceptibilities induced in opposite directions along the chains. In great support of this interpretation, a quantitative analysis of the spin-lattice relaxation rate $T_1^{-1}$ and the Knight shift data unravels dominant transverse spin fluctuations. We conclude that Ising-like uniaxial spin correlations persist up to surprisingly high temperatures compared to the exchange energy scales. Spin-charge coupling mechanism via a self-doping effect may be important.

First-principles calculations for Gilbert damping constant at finite temperature

We propose a first-principles calculation method for the Gilbert damping constants α at finite temperature. α is described by the torque correlation model in which the electronic structure is computed by the tight-binding linear muffin-tin orbital method. We include the finite-temperature effect as the transverse spin fluctuation in the disordered local moment picture within the coherent potential approximation. Applying the present method to bcc-Fe and L10-FePt, we demonstrate this temperature-dependent α. By comparing our calculated results with experimental results, we find the calculated values are less than half of the experimental values, reflecting the characteristics of the torque correlation model.

Odd-parity spin-loop-current order mediated by transverse spin fluctuations in cuprates and related electron systems

Unconventional symmetry-breaking phenomena due to nontrivial order parameters attract increasing attention in strongly correlated electron systems. Here, we predict theoretically the occurrence of nanoscale spontaneous spin-current, called the spin loop-current (sLC) order, as a promising origin of the pseudogap and electronic nematicity in cuprates. We reveal that the sLC is driven by the odd-parity electron-hole condensation that are mediated by transverse spin fluctuations around the pseudogap temperature $T^*$. At the same temperature, odd-parity magnon pair condensation occurs. The sLC order is "hidden" in that neither internal magnetic field nor charge density modulation is induced, whereas the predicted sLC with finite wavenumber naturally gives the Fermi arc structure. In addition, the fluctuations of sLC order work as attractive pairing interaction between adjacent hot spots, which enlarges the d-wave superconducting transition temperature $T_c$. The sLC state will be a key ingredient in understanding the pseudogap, electronic nematicity as well as superconductivity in cuprates and other strongly correlated metals.

Magnetism and magneto-optical effects in bulk and few-layer CrI3: a theoretical GGA + U study

The latest discovery of ferromagnetism in atomically thin films of semiconductors Cr2Ge2Te6 and CrI3 has unleashed numerous opportunities for fundamental physics of magnetism in two-dimensional (2D) limit and also for technological applications based on 2D magnetic materials. To exploit these 2D magnetic materials, however, the mechanisms that control their physical properties should be thoroughly understood. In this paper, we present a comprehensive theoretical study of the magnetic, electronic, optical and magneto-optical (MO) properties of multilayers (monolayer (ML), bilayer (BL) and trilayer) as well as bulk CrI3, based on the density functional theory with the generalized gradient approximation plus on-site Coulomb repulsion scheme. Interestingly, all the structures except the BL, are found to be single-spin ferromagnetic semiconductors. They all have a large out-of-plane magnetic anisotropy energy (MAE) of ∼0.5 meV/Cr, in contrast to the significantly thickness-dependent MAE in multilayers of Cr2Ge2Te6. These large MAEs suppress transverse spin fluctuations and thus stabilize long-range magnetic orders at finite temperatures down to the ML limit. They also exhibit strong MO effects with their Kerr and Faraday rotation angles being comparable to that of best-known bulk MO materials. The shape and position of the main features in the optical and MO spectra are found to be nearly thickness-independent although the magnitude of Kerr rotation angles increases monotonically with the film thickness. Magnetic transition temperatures estimated based on calculated exchange coupling parameters, calculated optical conductivity spectra, MO Kerr and Faraday rotation angles agree quite well with available experimental data. The calculated MAE as well as optical and MO properties are analyzed in terms of the calculated orbital-decomposed densities of states, band state symmetries and dipole selection rules. Our findings of large out-of-plane MAEs and strong MO effects in these single-spin ferromagnetic semiconducting CrI3 ultrathin films suggest that they will find valuable applications in semiconductor MO and spintronic nanodevices.

Charge-spin response and collective excitations in Weyl semimetals

Weyl semimetals are characterized by unconventional electromagnetic response. We present analytical expressions for all components of the frequency- and wave-vector-dependent charge-spin linear-response tensor of Weyl fermions. The spin-momentum locking of the Weyl Hamiltonian leads to a coupling between charge and longitudinal spin fluctuations, while transverse spin fluctuations remain decoupled from the charge. A real Weyl semimetal with multiple Weyl nodes can show this charge-spin coupling in equilibrium if its crystal symmetry is sufficiently low. All Weyl semimetals are expected to show this coupling if they are driven into a non-equilibrium stationary state with different occupations of Weyl nodes, for example by exploiting the chiral anomaly. Based on the response tensor, we investigate the low-energy collective excitations of interacting Weyl fermions. For a local Hubbard interaction, the charge-spin coupling leads to a dramatic change of the zero-sound dispersion: its velocity becomes independent of the interaction strength and the chemical potential and is given solely by the Fermi velocity. In the presence of long-range Coulomb interactions, the coupling transforms the plasmon modes into spin plasmons. For real Weyl semimetals with multiple Weyl nodes, the collective modes are strongly affected by the presence of parallel static electric and magnetic fields, due to the chiral anomaly. In particular, the zero-sound frequency at fixed momentum and the spin content of the spin plasmons go through cusp singularities as the chemical potential of one of the Weyl cones is tuned through the Weyl node. We discuss possible experiments that could provide smoking-gun evidence for Weyl physics.

Theoretical study of anisotropy in orbital and antiferromagnetic spin orderings in CMR manganites

We report here a tight binding model for doped rare earth manganites consisting of Kubo-Ohata type double exchange (DE) interaction between the eg and t2g band electron spins of same site. A Heisenberg type antiferromagnetic spin-spin interaction is considered among the core band electrons. Both nearest and next nearest neighbouring interactions are taken in the Heisenberg coupling and kinetic energy interaction. The presence of DE interaction induces antiferromagnetism (AFM) in eg band. The Jahn-Teller (JT) distortion leads to anisotropy in the manganite systems. We have considered JT distortion as an extra mechanism. The model Hamiltonian is solved using Zubarev's Green's function technique. The interplay between temperature dependent lattice strain and transverse spin fluctuations is studied. We have studied the in-plane anisotropy observed in the AFM spin fluctuation and its effect on the lattice strain.

From Ising Resonant Fluctuations to Static Uniaxial Order in Antiferromagnetic and Weakly Superconducting CeCo(In_{1-x}Hg_{x})_{5}(x=0.01).

CeCo(In_{0.990}Hg_{0.010})_{5} is a charge doped variant of the d-wave CoCoIn_{5} superconductor with coexistent antiferromagnetic and superconducting transitions occurring at T_{N}=3.4 and T_{c}=1.4 K, respectively. We use neutron diffraction and spectroscopy to show that the magnetic resonant fluctuations present in the parent superconducting phase are replaced by collinear c-axis magnetic order with three-dimensional Ising critical fluctuations. No low-energy transverse spin fluctuations are observable in this doping-induced antiferromagnetic phase and the dynamic resonant spectral weight predominately shifts to the elastic channel. Static (τ>0.2 ns) collinear Ising order is proximate to superconductivity in CeCoIn_{5} and is stabilized through hole doping with Hg.

High-temperature thermophysical properties of γ - and δ -Mn from first principles

Thermophysical properties of $\ensuremath{\gamma}$- and $\ensuremath{\delta}$-Mn phases have been investigated using first-principles calculations in their thermodynamically stable temperature range. An adiabatic approximation is used for partitioning of the Helmholtz free energy into electronic, magnetic, and vibrational contributions from the corresponding temperature induced excitations, where the fastest degree of freedom has been included in the slower ones. Namely, electronic excitations (on a one-electron level) have been included directly in the first-principles calculations at the corresponding temperatures. Magnetic excitations in the paramagnetic state then have been taken into consideration in the two opposite limits: localized, considering only transverse spin fluctuations (TSF), and itinerant, allowing for the full coupling of transverse and longitudinal spin fluctuations (LSF). Magnetic contribution to the free energy has been included in the calculations of the vibrational one, which has been obtained within the Debye-Gr\"uneisen model. The calculated thermophysical properties such as lattice constance, thermal lattice expansion, and heat capacity are in good agreement with available experimental data, especially in the case when the itinerant magnetic model is chosen. We also present our results for elastic properties at high temperatures.

133Cs-NMR study on aligned powder of competing spin chain compound Cs2Cu2Mo3O12

S = 1/2 competing spin chain compound Cs2Cu2Mo3O12 has two dominant exchange interactions of the nearest neighbouring ferromagnetic J1 = 93 K and the second nearest neighbouring antiferromagnetic J2 = +33 K, and is expected to show the nematic Tomonaga-Luttinger liquid (TLL) state under high magnetic field region. The recent theoretical study by Sato et al. has shown that in the nematic TLL state, the spin fluctuations are expected to be highly anisotropic, that is, its transverse component is suppressed. Our previous NMR study on the present system showed that the dominant contribution to nuclear spin relaxation comes from the longitudinal component. In order to conclude that the transverse component of spin fluctuations is suppressed, the knowledge of hyperfine coupling is indispensable. This article is solely devoted to investigate the hyperfine coupling of 133Cs-NMR site to prove that the anisotropic part of hyperfine coupling, which connects the nuclear spin relaxation with the transverse spin fluctuations is considerably large to be Aan = +770 Oe/μB.

Cooper Pairing in A Doped 2D Antiferromagnet with Spin-Orbit Coupling

We study the two-dimensional Hubbard model with the Rashba type spin-orbit coupling within and beyond the mean-field theory. The antiferromagnetic ground state for the model at half-filling and the Cooper pairing induced by antiferromagnetic spin fluctuations near half-filling are examined based on the random-phase approximation. We show that the antiferromagnetic order is suppressed and the magnetic susceptibility turns out to be anisotropic in the presence of the spin-orbit coupling. Energy spectrums of transverse spin fluctuations are obtained and the effective interactions between holes mediated by antiferromagnetic spin fluctuations are deduced in the case of low hole doping. It seems that the spin-orbit coupling tends to form s+p-wave Cooper pairs, while the s+d-wave pairing is dominant when the spin-orbit coupling is absent.

Thermodynamic properties of paramagnetic α - and β−Mn from first principles: The effect of transverse spin fluctuations

First-principles-based thermodynamic modeling of cubic $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases of Mn represent a challenge due to their structural complexity and the necessity of simultaneous treatment of several types of disorder (electronic, magnetic, and vibrational) that have very different characteristic time scales. Here we employ mean-field theoretical models to describe the different types of disorder and then we connect each layer of theory to the others using the adiabatic principle of separating faster and slower degrees of freedom. The slowest (vibrational) degrees of freedom are treated using the Moruzzi, Janak, and Schwarz formalism [Phys. Rev. B 37, 790 (1988)] of the Debye-Gr\uneisen model parametrized based on the first-principles calculated equation of state which includes the free-energy contributions due to the fast (electronic and magnetic) degrees of freedom via the Fermi-Dirac distribution function and a mean-field theory of transverse spin fluctuations. The magnetic contribution due to transverse spin fluctuations has been computed self-consistently within the disordered local moment picture of the paramagnetic state. The obtained results for thermodynamic properties such as lattice parameter, linear thermal expansion coefficient, and heat capacity of both phases show a good agreement with available experimental data. We also tested the assumption about the nature (localized versus delocalized) of magnetic moment on site IV in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Mn}$ and site I in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Mn}$ on the thermodynamic properties of these two phases. Similar to the findings of experimental studies, we conclude that magnetic moment on site IV in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Mn}$ is not of a localized character. However, a similar analysis suggests that the magnetic moment of site I in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Mn}$ should be treated as localized.

First-principles modeling of the Invar effect in Fe65Ni35 by the spin-wave method

Thermal lattice expansion of the Invar Fe65Ni35 alloy is investigated in first-principles calculations using the spin-wave method, which is generalized here for the ferromagnetic state with short range order. It is shown that magnetic short-range order effects make substantial contribution to the equilibrium lattice constant and cannot be neglected in the accurate ab initio modeling of the thermal expansion in Fe-Ni alloys. We also demonstrate that at high temperatures, close and above the magnetic transition, magnetic entropy associated with transverse and longitudinal spin fluctuations yields a noticeable contribution to the equilibrium lattice constant. The obtained theoretical results for the temperature dependent lattice constant are in semiquantitative agreement with the experimental data apart from the region close the magnetic transition.

Charge pumping driven by the laser-induced dynamics of the exchange splitting

We show that electric currents are induced in inversion asymmetric ferromagnets if the exchange splitting varies in time after excitation by laser pulses. We interpret this phenomenon as the magnetic variant of the inverse Edelstein effect. Based on \textit{ab initio} calculations we determine the size of this effect in Co/Pt(111) and Mn/W(001) magnetic bilayer systems and investigate its dependence on the magnetization direction. The comparison of our theoretical results to experiments measuring the THz signal emitted after laser excitation suggests that ultrafast demagnetization in 3$d$ transition metal ferromagnets is dominated by transverse spin fluctuations rather than by a reduction of the exchange splitting.

Pairing Mechanism of Unconventional Superconductivity in Doped Kane–Mele Model

We study the pairing symmetry of a doped Kane-Mele model on a honeycomb lattice with on-site Coulomb interaction. The pairing instability of Cooper pair is calculated based on the linearized Eliashberg equation within the random phase approximation (RPA). When the magnitude of the spin-orbit coupling is weak, even-frequency spin-singlet even-parity (ESE) pairing is dominant. On the other hand, with the increase of the spin-orbit coupling, we show that the even-frequency spin-triplet odd-parity (ETO) f-wave pairing exceeds ESE one. ETO f-wave pairing is supported by the longitudinal spin fluctuation. Since the transverse spin fluctuation is strongly suppressed by spin-orbit coupling, ETO f-wave pairing becomes dominant for large magnitude of spin-orbit coupling.

Superconducting phase diagram of itinerant antiferromagnets

We study the phase diagram of the Hubbard model in the weak-coupling limit for coexisting spin-density-wave order and spin-fluctuation-mediated superconductivity. Both longitudinal and transverse spin fluctuations contribute significantly to the effective interaction potential, which creates Cooper pairs of the quasi-particles of the antiferromagnetic metallic state. We find a dominant $d_{x^2-y^2}$-wave solution in both electron- and hole-doped cases. In the quasi-spin triplet channel, the longitudinal fluctuations give rise to an effective attraction supporting a $p$-wave gap, but are overcome by repulsive contributions from the transverse fluctuations which disfavor $p$-wave pairing compared to $d_{x^2-y^2}$. The sub-leading pair instability is found to be in the $g$-wave channel, but complex admixtures of $d$ and $g$ are not energetically favored since their nodal structures coincide. Inclusion of interband pairing, in which each fermion in the Cooper pair belongs to a different spin-density-wave band, is considered for a range of electron dopings in the regime of well-developed magnetic order. We demonstrate that these interband pairing gaps, which are non-zero in the magnetic state, must have the same parity under inversion as the normal intraband gaps. The self-consistent solution to the full system of five coupled gap equations give intraband and interband pairing gaps of $d_{x^2-y^2}$ structure and similar gap magnitude. In conclusion, the $d_{x^2-y^2}$ gap dominates for both hole and electron doping inside the spin-density-wave phase.

Phase transitions and order in two-dimensional generalized nonlinear σ models.

We study phase transitions and the nature of order in a class of classical generalized O(N) nonlinear σ models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising ferromagnetic spins, (ii) an advective Stokesian velocity, and (iii) multiplicative noises. In examples (i) and (ii), and also (iii) with the associated multiplicative noise being not sufficiently long-ranged, we show that the models may display a class of unusual phase transitions between stiff and soft phases, where the effective spin stiffness respectively diverges and vanishes in the long wavelength limit at two dimensions (2D), unlike in pure NLS. In the stiff phase, in the thermodynamic limit the variance of the transverse spin (or, the Goldstone mode) fluctuations are found to scale with the system size L in 2D as lnlnL with a model-dependent amplitude, which is markedly weaker than the well-known lnL dependence of the variance of the broken symmetry modes in models that display quasi-long-range order in 2D. Equivalently, for N=2 at 2D the equal-time spin-spin correlations decay in powers of inverse logarithm of the spatial separation with model-dependent exponents. These transitions are controlled by the model parameters those couple the O(N) spins with the additional variables. In the presence of long-range noises in example (iii), true long-range order may set in 2D, depending upon the specific details of the underlying dynamics. Our results should be useful in understanding phase transitions in equilibrium and nonequilibrium low-dimensional systems with continuous symmetries in general.

Noncollinear spin-fluctuation theory of transition-metal magnetism: Role of transverse spin fluctuations in Fe

A local electronic theory of transition-metal magnetism at finite temperatures is presented, which takes into account longitudinal and transverse spin fluctuations on the same footing. The magnetic properties are determined in the framework of a rotational-invariant $d$-band model Hamiltonian by applying a four-field Hubbard-Stratonovich functional-integral method in the static approximation. The role of transverse spin excitations on the temperature-dependent magnetic properties is investigated by performing alloy averages in the single-site virtual crystal approximation. Bulk Fe is considered as the representative example for the applications. Results are given for the average magnetization $M$, for the spin-excitation energies, and for the transverse and longitudinal contributions to the local magnetic moments ${\ensuremath{\mu}}_{l}$ at atom $l$. The importance of noncollinear spin excitations is quantified by comparison with the corresponding collinear calculations. An important reduction of about 33% of the calculated Curie temperature ${T}_{\mathrm{C}}$ is obtained, which now amounts to 1250 K and is thus relatively close to the experimental value. The longitudinal (transverse) components of ${\ensuremath{\mu}}_{l}$ are found to decrease (increase) as a function of temperature until the full rotational symmetry is reached at ${T}_{C}$. This reflects the increasing importance of the transverse spin fluctuations. The origin of the temperature dependence of $M$ and ${\ensuremath{\mu}}_{l}$ is analyzed in terms of the local spin-fluctuation energies.