Incommensurate Spin Density Wave Research Articles

Transition from an incommensurate spin density wave to a commensurate magnetic order in a triangular lattice compound Ho2PdAl6Ge4

Rare-earth (RE) intermetallics on a triangular lattice are promising candidates for generating interesting magnetic phases due to the complex interplay between Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction and geometrical frustration. Here we report the exotic magnetic structure of a layered compound Ho2PdAl6Ge4 with triangular lanthanide nets. Magnetization and heat capacity measurements in zero magnetic field reveal two magnetic phase transitions at TN1 = 10.8 K and TN2 = 6.0 K. Neutron powder diffraction demonstrates a commensurate antiferromagnetic phase with k1 = (0, 0, 1.5) below TN2. With increasing temperature, another incommensurate vector appears and therefore, the magnetic structure of the intermediate state is identified as an unusual incommensurate spin density wave with two propagation vectors k1 = (0, 0, 1.5) and k2 = (0.0492, 0.0492, 1.5). The magnetic moments in the intermediate state rotate continuously and form an unusual S-shaped wave arrangement in the ab plane, sharing similarities with typical cycloid and helix magnetic orders. These results identify Ho2PdAl6Ge4 as a candidate for exploring field-induced topological magnetic phases such as skyrmions, opening the way for further investigations on the family of RE2PdAl6Ge4 materials.

Incommensurate Spin Density Wave in Antiferromagnetic RuO_{2} Evinced by Abnormal Spin Splitting Torque.

Since the discovery of antiferromagnetism, metallic oxide RuO_{2} has exhibited numerous intriguing spintronics properties such as the anomalous Hall effect and anisotropic spin splitting effect. However, the microscopic origin of its antiferromagnetism remains unclear. By investigating the spin splitting torque in RuO_{2}/Py, we found that metallic RuO_{2} exhibits a spatially periodic spin structure which interacts with the spin waves in Py through interfacial exchange coupling. The wavelength of such structure is evaluated within 14-20nm depending on the temperature, which is evidence of an incommensurate spin density wave state in RuO_{2}. Our work not only provides a dynamics approach to characterize the antiferromagnetic ordering in RuO_{2}, but also offers fundamental insights into the spin current generation due to anisotropic spin splitting effect associated with spin density wave.

Multi- k magnetic structure and large anomalous Hall effect in candidate magnetic Weyl semimetal NdAlGe

The magnetic structure, magnetoresistance (MR), and Hall effect of the noncentrosymmetric magnetic semimetal NdAlGe are investigated, revealing an unusual magnetic state and anomalous transport properties that are associated with the electronic structure of this compound. The magnetization and MR measurements are both highly anisotropic and indicate an Ising-like magnetic system. The magnetic structure is complex in that it involves two magnetic ordering vectors, including an incommensurate spin density wave and commensurate ferrimagnetic state in zero field. We have discovered a large anomalous Hall conductivity that reaches $\ensuremath{\approx}430\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.28em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, implying that it originates from an intrinsic Berry curvature effect stemming from Weyl nodes found in the electronic structure. These electronic structure calculations indicate the presence of nested Fermi surface pockets with nesting wave vectors like the measured magnetic ordering wave vector and the presence of Weyl nodes in proximity to the Fermi surface. We associate the incommensurate magnetic structure with the large anomalous Hall response to be the result of the combination of Fermi surface nesting and the Berry curvature associated with Weyl nodes.

Kramers nodal lines and Weyl fermions in SmAlSi

Kramers nodal lines (KNLs) have recently been proposed theoretically as a special type of Weyl line degeneracy connecting time-reversal invariant momenta. KNLs are robust to spin orbit coupling and are inherent to all non-centrosymmetric achiral crystal structures, leading to unusual spin, magneto-electric, and optical properties. However, their existence in in real quantum materials has not been experimentally established. Here we gather the experimental evidence pointing at the presence of KNLs in SmAlSi, a non-centrosymmetric metal that develops incommensurate spin density wave order at low temperature. Using angle-resolved photoemission spectroscopy, density functional theory calculations, and magneto-transport methods, we provide evidence suggesting the presence of KNLs, together with observing Weyl fermions under the broken inversion symmetry in the paramagnetic phase of SmAlSi. We discuss the nesting possibilities regarding the emergent magnetic orders in SmAlSi. Our results provide a solid basis of experimental observations for exploring correlated topology in SmAlSi

Stripe helical magnetism and two regimes of anomalous Hall effect in NdAlGe

We report the magnetic and electronic transport properties of the inversion and time-reversal symmetry breaking Weyl semimetal NdAlGe. This material is analogous to NdAlSi, whose helical magnetism presents a rare example of a Weyl-mediated collective phenomenon, but with a larger spin-orbit coupling. Our neutron diffraction experiments revealed that NdAlGe, similar to NdAlSi, supports an incommensurate Ising spin density wave ($T_{\text{inc}}=6.8$ K) with a small helical spin canting of 3$^\circ$ and a long-wavelength of $\sim$ 35 nm, which transitions to a commensurate ferrimagnetic state below $T_{\text{com}}=5.1$ K. Using small-angle neutron scattering, we showed that the zero-field cooled ferrimagnetic domains form stripes in real space with characteristic length scales of 18 nm and 72 nm parallel and perpendicular to the [110] direction, respectively. Interestingly, for the transport properties, NdAlSi does not exhibit an anomalous Hall effect (AHE) that is commonly observed in magnetic Weyl semimetals. In contrast to NdAlSi, we identify two different AHE regimes in NdAlGe that are respectively governed by intrinsic Berry curvature and extrinsic disorders/spin fluctuations. Our study suggests that Weyl-mediated magnetism prevails in this group of noncentrosymmetric magnetic Weyl semimetals NdAl$X$, but transport properties including AHE are affected by material-specific extrinsic effects such as disorders, despite the presence of prominent Berry curvature.

Hall coefficient of (Cr100−xAlx)95Mo5 alloy system

The temperature dependence of the Hall coefficient, RH, for the (Cr100−xAlx)95Mo5 alloy system with 0 ≤ x ≤ 8.6, in the temperature range 2 K ≤ T ≤ 380 K and in a magnetic field of 4.5 T is reported. Anomalies in the form of an upturn were observed just below the Néel transition temperature, TN, for the incommensurate (I) spin density wave (SDW) alloys with x ≤ 1.3 and commensurate (C) spin density wave (SDW) alloys with x ≥ 5.3. In addition to these anomalies, alloys with x = 0, 0.5, 0.9 and 8.6 show a peculiar behaviour below TN, in which RH increases and then decreases depicting a hump on further cooling. Remarkably RH for the alloy with x = 0 shows a sign reversal of majority charge carriers from holes to electrons on cooling below 120 K. The crossover of majority charge carriers disappears by the addition of just 0.5 at.% Al into the base alloy with x = 0. The behaviour of the Hall coefficient for the alloys with x = 0, 0.5, 0.9 and 8.6, is explained in terms of the simple two band model in which both charge carriers contribute to magneto-transport properties. The relative magnetic contribution to the Hall coefficient, ΔRH(2K)/RH(2K), indicate a suppression of antiferromagnetism in the concentration range 1.7 ≤ x ≤ 4.7.

Functional renormalization group study of the two-dimensional Su-Schrieffer-Heeger-Hubbard model

We study the Hubbard model on the square lattice coupled in addition to the optical Su-Schrieffer-Heeger (SSH) phonons, using the singular-mode functional renormalization group method. At half-filling and in the absence of the Hubbard interaction $U$, we find the degenerate spin-density-wave (SDW)/charge-density-wave (CDW)/s-wave superconductivity (sSC) state at smaller electron-phonon coupling strength $\lambda$ and higher phonon frequency $\omega$, and the valence bond solid (VBS) state at larger $\lambda$ and lower $\omega$. After switching on a positive $U$, the VBS state is suppressed, while the SDW state is enhanced. At finite doping, the SSH phonon is found to favor sSC at $U=0$. With increasing positive $U$, we find d-wave superconductivity (dSC) and incommensurate SDW states. In a narrow window of moderate $U$ and $\lambda$, we also find the incommensurate VBS state. The sSC and dSC here can be naturally related to the CDW and SDW fluctuations, both of which can be triggered by the SSH phonons. In contrast, the repulsive interaction $U$ enhances SDW but suppresses CDW fluctuations. Our results at half filling are consistent with quantum Monte Carlo (QMC), and provide insights at finite doping where QMC may suffer from the minus sign problem.

Spin-density-wave order controlled by uniaxial stress in CeAuSb2

The tetragonal heavy fermion compound CeAuSb$_2$ (space group $P4/nmm$) exhibits incommensurate spin density wave (SDW) order below $T_{N}\approx6.5~K$ with the propagation vector $\mathbf{q}_A = (\delta_A,\delta_A,1/2)$. The application uniaxial stress along the [010] direction induces a sudden change in the resistivity ratio $\rho_a/\rho_b$ at a compressive strain of $\epsilon \approx -0.5$\%. Here we use neutron scattering to show that the uniaxial stress induces a first-order transition to a SDW state with a different propagation vector $(0,\delta_B,1/2)$ with $\delta_B=0.25$. The magnetic structure of the new (B) phase consists of Ce layers with ordered moments alternating with layers with zero moment stacked along the $c$-axis. The ordered layers have an up-up-down-down configuration along the $b$-axis. This is an unusual situation in which the loss of spatial inversion is driven by itinerant magnetic order. We argue that the change in SDW wavevector leads to a concomitant Fermi surface reconstruction, similar to other materials where a SDW can be controlled by uniaxial stress or magnetic field such as Sr$_3$Ru$_2$O$_7$.

Spin and charge density waves in quasi-one-dimensional KMn6Bi5

AMn6Bi5 materials (A = Na, K, Rb and Cs) consisting of unique Mn-cluster chains emerge as a new family of superconductors with the suppression of their antiferromagnetic (AFM) order under high pressures. Here, we report transverse incommensurate spin density waves (SDWs) for the Mn atoms with a propagating direction along the chain axes as a ground state for KMn6Bi5 by single crystal neutron diffraction. The SDWs have a refined amplitude of ~2.46 Bohr magnetons for the Mn atoms in the pentagons and ~0.29 Bohr magnetons with a large standard deviation for Mn atoms in the center between the pentagons. AFM dominate both the nearest-neighbor Mn-Mn interactions within the pentagon and next-nearest-neighbor Mn-Mn interactions out of the pentagon (along the propagating wave). The SDWs exhibit both local and itinerant characteristics probably formed by a cooperative interaction between local magnetic exchange and conduction electrons. A significant magnetoelastic effect during the AFM transition, especially along the chain direction, has been demonstrated by temperature-dependent x-ray powder diffraction. Single crystal x-ray diffraction below the AFM transition revealed satellite peaks originating from charge density waves along the chain direction with a q-vector twice as large as the SDW one, pointing to a strong real space coupling between them. Our work not only manifests a fascinating interplay among spin, charge, lattice and one dimensionality to trigger intertwined orders in KMn6Bi5 but also provides important piece of information for the magnetic structure of the parent compound to understand the mechanism of superconductivity in this new family.

Incommensurate spin density wave and magnetocaloric effect in the metallic triangular lattice HoAl2Ge2

We report the magnetic structure and the magnetocaloric effect (MCE) of the ternary compound $\mathrm{Ho}{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ with a trigonal ${\mathrm{CaAl}}_{2}{\mathrm{Si}}_{2}$-type crystal structure. A neutron powder diffraction experiment reveals that $\mathrm{Ho}{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ exhibits an incommensurate spin density wave (SDW) with a propagation vector $\mathbit{k}=(0.23,\phantom{\rule{0.28em}{0ex}}0,\phantom{\rule{0.28em}{0ex}}0.06)$. The special arrangement of magnetic moments in $\mathrm{Ho}{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ induces interesting physical phenomena and large magnetocaloric effects. The rise in resistivity at low temperatures indicates the effect of the SDW state in the electronic transport. The maximum magnetic-entropy change is $\ensuremath{-}16.1\phantom{\rule{0.16em}{0ex}}\mathrm{J}/\mathrm{kg}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ under a magnetic field change of 0--70 kOe for an isotropic $\mathrm{Ho}{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ powder and it increases to $\ensuremath{-}17.9\phantom{\rule{0.16em}{0ex}}\mathrm{J}/\mathrm{kg}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for a single crystal when the magnetic field ($H$) is applied parallel to the $ab$ plane. A large rotating magnetic-entropy change of $\ensuremath{-}5.1\phantom{\rule{0.16em}{0ex}}\mathrm{J}/\mathrm{kg}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for $H=20\phantom{\rule{0.16em}{0ex}}\mathrm{kOe}$ in a $\mathrm{Ho}{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ single crystal is obtained, which is closely associated to the magnetic anisotropy of the SDW order and its response to the external magnetic field. We discuss the large MCE in terms of the field-induced metamagnetic transition from the incommensurate SDW order to the ferromagnetic order. Our study establishes the triangular lattice $R{\mathrm{Al}}_{2}{\mathrm{Ge}}_{2}$ ($R$ = rare-earth elements) as a unique family of compounds to explore the existence of the incommensurate spin density waves and the correlated physical properties.

Evaluating Second-Order Phase Transitions with Diagrammatic Monte Carlo: Néel Transition in the Doped Three-Dimensional Hubbard Model

Diagrammatic MonteCarlo-the technique for the numerically exact summation of all Feynman diagrams to high orders-offers a unique unbiased probe of continuous phase transitions. Being formulated directly in the thermodynamic limit, the diagrammatic series is bound to diverge and is not resummable at the transition due to the nonanalyticity of physical observables. This enables the detection of the transition with controlled error bars from an analysis of the series coefficients alone, avoiding the challenge of evaluating physical observables near the transition. We demonstrate this technique by the example of the Néel transition in the 3D Hubbard model. At half filling and higher temperatures, the method matches the accuracy of state-of-the-art finite-size techniques, but surpasses it at low temperatures and allows us to map the phase diagram in the doped regime, where finite-size techniques struggle from the fermion sign problem. At low temperatures and sufficient doping, the transition to an incommensurate spin density wave state is observed.

Spin Density Wave versus Fractional Magnetization Plateau in a Triangular Antiferromagnet.

We report an excellent realization of the highly nonclassical incommensurate spin-density wave (SDW) state in the quantum frustrated antiferromagnetic insulator Cs_{2}CoBr_{4}. In contrast to the well-known Ising spin chain case, here the SDW is stabilized by virtue of competing planar in-chain anisotropies and frustrated interchain exchange. Adjacent to the SDW phase is a broad m=1/3 magnetization plateau that can be seen as a commensurate locking of the SDW state into the up-up-down (UUD) spin structure. This represents the first example of the long-sought SDW-UUD transition in triangular-type quantum magnets.

Real-space observation of incommensurate spin density wave and coexisting charge density wave on Cr (001) surface

In itinerant magnetic systems, a spin density wave (SDW) state can be induced by Fermi surface nesting and electron-electron interaction. It may intertwine with other orders such as charge density wave (CDW), while their relation is still yet to be understood. Here via spin-polarized scanning tunneling microscopy, we directly observed long-range spin modulation on Cr(001) surface, which corresponds to the well-known incommensurate SDW of bulk Cr. It displays 6.0 nm in-plane period and anti-phase behavior between adjacent (001) planes. Meanwhile, we simultaneously observed the coexisting CDW with half the period of SDW. Such SDW/CDW have highly correlated domain structures and are in-phase. Surprisingly, the CDW displays a contrast inversion around a density-of-states dip at −22 meV, indicating an anomalous CDW gap opened below EF. These observations support that the CDW is a secondary order driven by SDW. Our work is not only a real-space characterization of incommensurate SDW, but also provides insights on how SDW and CDW coexist.

Altering the magnetic ordering of Fe3Ga4 via thermal annealing and hydrostatic pressure

The effects of post-synthesis annealing temperature on arc-melted samples of Fe3Ga4 has been studied to investigate changes in crystallographic and magnetic properties induced by annealing. Results show a significant trend in the evolution of the (incommensurate spin density wave) ISDW-FM (ferromagnetic) transition temperature as a function of the refined unit cell volume in annealed samples. Strikingly, this trend allowed for the tuning of the transition temperature down to room-temperature (300 K) whilst maintaining a sharp transition in temperature, opening the door to the use of Fe3Ga4 in functional devices. Crystallographic analysis through Rietveld refinement of high-resolution x-ray diffraction data has showed that arc-melted stoichiometric Fe3Ga4 is multi-phase regardless of annealing temperature with a minor phase of FeGa3 decreasing in phase fraction at higher annealing temperature. In order to validate the trend in ISDW-FM transition temperature with regard to unit cell volume, high pressure magnetometry was performed. This showed that the FM-ISDW (~ 68 K) and ISDW-FM (~ 360 K) transition temperatures could be tuned, increased and decreased respectively, linearly with external pressure. Thus, external pressure and the ensuing crystallographic changes minimize the temperature range of the stability of the ISDW pointing toward the importance of structural properties on the mechanism for the formation of the intermediate ISDW phase. These results show how this model system can be tuned as well as highlighting the need for future high-pressure crystallography and related single crystal measurements to understand the mechanism and nature of the intermediate ISDW phase to be exploited in future devices.

Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature

The interplay between thermal and quantum fluctuations controls the competition between phases of matter in strongly correlated electron systems. We study finite-temperature properties of the strongly coupled two-dimensional doped Hubbard model using the minimally-entangled typical thermal states (METTS) method on width $4$ cylinders. We discover that a phase characterized by commensurate short-range antiferromagnetic correlations and no charge ordering occurs at temperatures above the half-filled stripe phase extending to zero temperature. The transition from the antiferromagnetic phase to the stripe phase takes place at temperature $T/t \approx 0.05$ and is accompanied by a step-like feature of the specific heat. We find the single-particle gap to be smallest close to the nodal point at $\mathbf{k}=(\pi/2, \pi/2)$ and detect a maximum in the magnetic susceptibility. These features bear a strong resemblance to the pseudogap phase of high-temperature cuprate superconductors. The simulations are verified using a variety of different unbiased numerical methods in the three limiting cases of zero temperature, small lattice sizes, and half-filling. Moreover, we compare to and confirm previous determinantal quantum Monte Carlo results on incommensurate spin-density waves at finite doping and temperature.

Multiple fermion scattering in the weakly coupled spin-chain compound YbAlO3

The Heisenberg antiferromagnetic spin-1/2 chain, originally introduced almost a century ago, is one of the best studied models in quantum mechanics due to its exact solution, but nevertheless it continues to present new discoveries. Its low-energy physics is described by the Tomonaga-Luttinger liquid of spinless fermions, similar to the conduction electrons in one-dimensional metals. In this work we investigate the Heisenberg spin-chain compound YbAlO3 and show that the weak interchain coupling causes Umklapp scattering between the left- and right-moving fermions and stabilizes an incommensurate spin-density wave order at q = 2kF under finite magnetic fields. These Umklapp processes open a route to multiple coherent scattering of fermions, which results in the formation of satellites at integer multiples of the incommensurate fundamental wavevector Q = nq. Our work provides surprising and profound insight into bandstructure control for emergent fermions in quantum materials, and shows how neutron diffraction can be applied to investigate the phenomenon of coherent multiple scattering in metals through the proxy of quantum magnetic systems.

Impurity-induced magnetic ordering in Sr2RuO4

Ti substituting Ru in Sr$_2$RuO$_4$ in small concentrations induces incommensurate spin density wave order with a wave vector $\boldsymbol{Q} \simeq (2 \pi /3, 2 \pi /3)$ corresponding to the nesting vector of two out of three Fermi surface sheets. We consider a microscopic model for these two bands and analyze the correlation effects leading to magnetic order through non-magnetic Ti-doping. For this purpose we use a position dependent mean field approximation for the microscopic model and a phenomenological Ginzburg-Landau approach, which both deliver consistent results and allow us to examine the inhomogeneous magnetic order. Spin-orbit coupling additionally leads to spin currents around each impurity, which in combination with the magnetic polarization produce a charge current pattern. This is also discussed within a gauge field theory in both charge and spin channel. This spin-orbit coupling effect causes an interesting modification of the magnetic structure, if currents run through the system. Our findings allow a more detailed analysis of the experimental data for Sr$_{2}$Ru$_{1-x}$Ti$_{x}$O$_{4}$. In particular, we find that the available measurements are consistent with our theoretical predictions.

Efficient magnetic superstructure optimization with [formula omitted

Simulating the incommensurate spin density waves (ISDW) states is not a simple task within the standard ab initio methods. Moreover, in the context of new material discovery, there is a need for fast and reliable tool capable to scan and optimize the total energy as a function of the pitch vector, thus allowing to automatize the search for new materials. In this paper we show how the ISDW can be efficiently obtained within the recently released ΘΦ program. We illustrate this on an example of the single orbital Hubbard model and of γ-Fe, where the ISDW emerge within the mean-field approximation and by using the twisted boundary conditions. We show the excellent agreement of the ΘΦ with the previously published ones and discuss possible extensions. Finally, we generalize the previously given framework for spin quantization axis rotation to the most general case of spin-dependent hopping matrix elements.

Phase diagram and quantum criticality of Heisenberg spin chains with Ising anisotropic interchain couplings

Motivated by recent progress on field-induced phase transitions in quasi-one-dimensional quantum antiferromagnets, we study the phase diagram of $S=1/2$ antiferromagnetic Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations. The interchain interactions is shown to enhance longitudinal spin correlations to stabilize an incommensurate longitudinal spin density wave order at low temperatures. With increasing field the ground state changes to a canted antiferromagnetic order until the magnetization fully saturates above a quantum critical point controlled by the $(3+2)$D XY universality. Increasing temperature in the quantum critical regime the system experiences a fascinating dimension crossover to a universal Tomonaga-Luttinger liquid. The calculated NMR relaxation rate $1/T_1$ indicates this Luttinger liquid behavior survives a broad field and temperature regime. Our results determine the global phase diagram and quantitative features of quantum criticality of a general model for quasi-one-dimensional spin chain compounds, and thus lay down a concrete ground to the study on these materials.

Tomonaga-Luttinger Liquid Spin Dynamics in the Quasi-One-Dimensional Ising-Like Antiferromagnet BaCo_{2}V_{2}O_{8}.

Combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising anisotropic quantum antiferromagnet BaCo_{2}V_{2}O_{8} in a longitudinal magnetic field. This material shows a quantum phase transition from a Néel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8T. Concomitantly, the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnetic chains.