Orphan Spins Research Articles

Random singlet-like state in the dimer-based triangular antiferromagnet Ba6Y2Rh2Ti2O17−δ

We present the magnetic, thermodynamic, and muon spin relaxation (μSR) results of the dimer-based triangular antiferromagnet Ba6Y2Rh2Ti2O17−δ. The magnetic susceptibility data show the sub-Curie-Weiss behavior χ(T)∝T−αχ below 100 K, suggesting random magnetism. The isothermal magnetization results reveal the presence of weakly interacting structural orphan spins about 6.1% at 2 K, arising from the oxygen deficiency. The comprehensive μSR experiments exhibit the coexisting relaxing and nonrelaxing components along with the thermally activated behavior in the muon spin relaxation rate, reflecting the fluctuating orphan spins in the dimer singlet background. In addition, we observe the scaling behavior of M(H,T) in H/T and Pz(t) in t/HLF with the scaling exponents αχ=αM=0.75 and αμ=0.72, respectively, but not for the magnetic specific heat data. The failure of the scaling relation in Cm(H,T)/T implies low-energy excitations dressed by the conventional orphan spins. Based on these observations, we find that the magnetic ground state resembles random singlets and discuss the possible configurations of the spin dimer unit Rh2O9. Our results shed light on the role of quenched disorder in the dimer-based frustrated magnets. Published by the American Physical Society 2024

Heat transport of the kagome Heisenberg quantum spin liquid candidate YCu3(OH)6.5Br2.5 : Localized magnetic excitations and a putative spin gap

The spin-1/2 kagom\'{e} Heisenberg antiferromagnet is generally accepted as one of the most promising two-dimensional models to realize a quantum spin liquid state. Previous experimental efforts were almost exclusively on only one archetypal material, the herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, which unfortunately suffers from the notorious orphan spins problem caused by magnetic disorders. Here we turn to YCu$_3$(OH)$_{6.5}$Br$_{2.5}$, recently recognized as another host of a globally undistorted kagom\'{e} Cu$^{2+}$ lattice free from the orphan spins, thus a more feasible system for studying the intrinsic kagom\'{e} quantum spin liquid physics. Our high-resolution low-temperature thermal conductivity measurements yield a vanishing small residual linear term of $\kappa/T$ ($T\rightarrow 0$), and thus clearly rule out itinerant gapless fermionic excitations. Unusual scattering of phonons grows exponentially with temperature, suggesting thermally activated phonon-spin scattering and hence a gapped magnetic excitation, consistent with a $\mathbb{Z}_2$ quantum spin liquid ground state. Additionally, the analysis of magnetic field impact on the thermal conductivity reveals a field closing of the spin gap, while the excitations remain localized.

Universal scaling of specific heat in the S=12 quantum kagome antiferromagnet herbertsmithite

Despite tremendous investigations, a quantum spin liquid (QSL) state realized in a spin-1/2 kagome Heisenberg antiferromagnet remains largely elusive. In herbertsmithite $\mathrm{Zn}{\mathrm{Cu}}_{3}{(\mathrm{O}\mathrm{H})}_{6}{\mathrm{Cl}}_{2}$, a quantum spin liquid candidate on the perfect kagome lattice, precisely characterizing the intrinsic physics of the kagome layers is extremely challenging due to the presence of interlayer Cu/Zn antisite disorder within its crystal structure. Here we measured the specific heat and thermal conductivity of single-crystal herbertsmithite in magnetic fields with high resolution. Strikingly, intrinsic magnetic specific heat contribution arising from the kagome layers exhibits excellent scaling collapse as a function of $T/H$ (temperature/magnetic field). In addition, no residual linear term in the thermal conductivity $\ensuremath{\kappa}/T(T\ensuremath{\rightarrow}0)$ is observed in zero and applied magnetic fields, indicating the absence of itinerant gapless excitations. These results capture a new essential feature of the QSL state of the kagome layers; localized orphan spins are induced by exchange bond randomness, surrounded by a nonitinerant QSL.

Gapless spin liquid behavior in a kagome Heisenberg antiferromagnet with randomly distributed hexagons of alternate bonds

We demonstrate that the new single crystal of YCu$_3$[OH(D)]$_{6.5}$Br$_{2.5}$ (YCOB) is a kagome Heisenberg antiferromagnet (KHA) without evident orphan spins ($\ll$ 0.8\%). The site mixing between polar OH$^-$ and non-polar Br$^-$ causes local distortions of Cu-O-Cu exchange paths, and gives rise to 70(2)\% of randomly distributed hexagons of alternate bonds ($\sim$ $J_1-\Delta J$ and $J_1+\Delta J$) and the rest of almost uniform hexagons ($\sim$ $J_1$) on the kagome lattice. Simulations of the random exchange model with $\Delta J$/$J_1$ = 0.7(1) show good agreement with the experimental observations, including the weak upturn seen in susceptibility and the slight polarization in magnetization. Despite the average antiferromagnetic coupling of $J_1$ $\sim$ 60 K, no conventional freezing is observed down to $T$ $\sim$ 0.001$J_1$, and the raw specific heat exhibits a nearly quadratic temperature dependence below 1 K $\sim$ 0.02$J_1$, phenomenologically consistent with a gapless (spin gap $\leq$ 0.025$J_1$) Dirac quantum spin liquid (QSL). Our result sheds new light on the theoretical understanding of the randomness-relevant gapless QSL behavior in YCOB, as well as in other relevant materials.

Orphan spin operator diagonal suppression

We report the suppression of diagonal signals in (H)N(H)(H)NH spectra through the use of untransferred signals (orphan spin operators) from cross polarization steps. In contrast to most diagonal suppression methods, there is no loss of sensitivity for cross-peaks at ultrafast MAS. For the proton-detected (H)N(H)(H)NH sequence, recorded with 55 kHz MAS, we observed approximately 50% suppression of diagonal signal after 1.08 ms mixing. A similar construction for CHHC spectra at 13 kHz MAS suppresses both the diagonal and cross-peaks, and simulations suggest proton assisted recoupling (PAR) is responsible. Alternatively, a combined PAR+CHHC spectrum can be recorded.

Nature of the randomness-induced quantum spin liquids in two dimensions

The nature of the randomness-induced quantum spin liquid state, the random-singlet state, is investigated in two dimensions (2D) by means of the exact-diagonalization and the Hams-de Raedt methods for several frustrated lattices, e.g. the triangular, the kagome and the J1-J2 square lattices. Properties of the ground state, the low-energy excitations and the finite-temperature thermodynamic quantities are investigated. The ground state and the low-lying excited states consist of nearly isolated singlet-dimers, clusters of resonating singlet-dimers, and orphan spins. Low-energy excitations are either singlet-to-triplet excitations, diffusion of orphan spins accompanied by the recombination of nearby singlet-dimers, creation or destruction of resonating singlet-dimers clusters. The latter two excitations give enhanced dynamical ‘liquid-like’ features to the 2D random-singlet state. Comparison is made with the random-singlet state in a 1D chain without frustration, the similarity and the difference between in 1D and in 2D being highlighted. Frustration in a wide sense, not only the geometrical one but also including the one arising from the competition between distinct types of interactions, play an essential role in stabilizing this frustrated random singlet state. Recent experimental situations on both organic and inorganic materials are reviewed and discussed.

Dynamic magnetism in the disordered hexagonal double perovskite BaTi1/2Mn1/2O3

Magnetic frustration and disorder are key ingredients to prevent the onset of magnetic order. In the disordered hexagonal double perovskite BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$, Mn$^{4+}$ cations, with $S=3/2$ spins, can either form highly correlated states of magnetic trimers or dimers or remain as weakly interacting orphan spins. At low temperature ($T$), the dimer response is negligible, and magnetism is dominated by the trimers and orphans. To explore the role of magnetic frustration, disorder and possibly of quantum fluctuations, the low-$T$ magnetic properties of the remaining magnetic degrees of freedom of BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$ are investigated. Heat-capacity data and magnetic susceptibility display no evidence for a phase transition to a magnetically ordered phase but indicate the formation of a correlated spin state. The low-temperature spin dynamics of this state is then explored by $\mu$SR experiments. The zero field $\mu^{+}$ relaxation rate data show no static magnetism down to $T=19$ mK and longitudinal field experiments support as well that dynamic magnetism persists at low $T$. Our results are interpreted in terms of a spin glass state which stems from a disordered lattice of orphans spins and trimers. A spin liquid state in BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$, however, is not excluded and is also discussed.

Fractionalized Z_{2} Classical Heisenberg Spin Liquids.

Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalized spin liquid phase, the so-called Coulomb or U(1) spin liquid, has until recently been identified: This exhibits algebraic spin correlations and impurity moments, "orphan spins," whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalization in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z_{2} spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavor.

Multiple acquisitions via sequential transfer of orphan spin polarization (MAeSTOSO): How far can we push residual spin polarization in solid-state NMR?

Conventional multidimensional magic angle spinning (MAS) solid-state NMR (ssNMR) experiments detect the signal arising from the decay of a single coherence transfer pathway (FID), resulting in one spectrum per acquisition time. Recently, we introduced two new strategies, namely DUMAS (DUal acquisition Magic Angle Spinning) and MEIOSIS (Multiple ExperIments via Orphan SpIn operatorS), that enable the simultaneous acquisitions of multidimensional ssNMR experiments using multiple coherence transfer pathways. Here, we combined the main elements of DUMAS and MEIOSIS to harness both orphan spin operators and residual polarization and increase the number of simultaneous acquisitions. We show that it is possible to acquire up to eight two-dimensional experiments using four acquisition periods per each scan. This new suite of pulse sequences, called MAeSTOSO for Multiple Acquisitions via Sequential Transfer of Orphan Spin pOlarization, relies on residual polarization of both 13C and 15N pathways and combines low- and high-sensitivity experiments into a single pulse sequence using one receiver and commercial ssNMR probes. The acquisition of multiple experiments does not affect the sensitivity of the main experiment; rather it recovers the lost coherences that are discarded, resulting in a significant gain in experimental time. Both merits and limitations of this approach are discussed.

Orphan spin polarization: A catalyst for high-throughput solid-state NMR spectroscopy of proteins.

Magic angle spinning solid-state NMR (MAS ssNMR) spectroscopy is a powerful method for structure determination of biomacromolecules that are recalcitrant to crystallization (membrane proteins and fibrils). Conventional multidimensional ssNMR methods acquire one experiment at a time. This approach is time consuming and discards orphan (unused) spin operators. Relatively low sensitivity and poor resolution of protein samples require long acquisition times for multidimensional ssNMR experiments. Here, we describe our recent progress in the development of multiple acquisition solid-state NMR methods for protein structure determination. A family of experiments called Polarization Optimized Experiments (POE) were designed, in which we utilized the orphan spin operators that are discarded in classical multidimensional NMR experiments, recovering them to allow simultaneous acquisition of multiple 2D and 3D experiments, all while using conventional probes with spectrometers equipped with one receiver. Three strategies namely, DUMAS, MEIOSIS, and MAeSTOSO were used for the concatenation of various 2D and 3D experiments. These methods open up new avenues for reducing the acquisition times of multidimensional experiments for biomolecular ssNMR spectroscopy.

Disorder-Driven Spin-Orbital Liquid Behavior in the Ba3XSb2O9 Materials.

Recent experiments on the Ba(3)XSb(2)O(9) family have revealed materials that potentially realize spin- and spin-orbital liquid physics. However, the lattice structure of these materials is complicated due to the presence of charged X(2+)-Sb(5+) dumbbells, with two possible orientations. To model the lattice structure, we consider a frustrated model of charged dumbbells on the triangular lattice, with long-range Coulomb interactions. We study this model using Monte Carlo simulation, and find a freezing temperature, T(frz), at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba(3)CuSb(2)O(9). At T=T(frz) we find a complicated "branching" structure of superexchange-linked X(2+) clusters, which form a fractal pattern with fractal dimension d(f)=1.90. We show that this gives a natural explanation for the presence of orphan spins. Finally we provide a plausible mechanism by which such dumbbell disorder can promote a spin-orbital resonant state with delocalized orphan spins.

Magnetic dimers and trimers in the disorderedS=32spin systemBaTi1/2Mn1/2O3

We report a structural-magnetic investigation by x-ray absorption spectroscopy (XAS), neutron diffraction, dc susceptibility $({\ensuremath{\chi}}_{\text{dc}})$, and electron spin resonance (ESR) of the 12R-type perovskite ${\text{BaTi}}_{1/2}{\text{Mn}}_{1/2}{\text{O}}_{3}$. Our structural analysis by neutron diffraction supports the existence of structural trimers with chemically disordered occupancy of ${\text{Mn}}^{4+}$ and ${\text{Ti}}^{4+}$ ions, with the valence of the Mn ions confirmed by the XAS measurements. The magnetic properties are explored by combining dc-susceptibility and $X$-band (9.4 GHz) electron spin resonance, both in the temperature interval of $2\ensuremath{\le}T\ensuremath{\le}1000$ K. A scenario is presented under which the magnetism is explained by considering magnetic dimers and trimers, with exchange constants ${J}_{a}/{k}_{B}=200\phantom{\rule{0.16em}{0ex}}(2)$ K and ${J}_{b}/{k}_{B}=130\phantom{\rule{0.16em}{0ex}}(10)$ K, and orphan spins. Thus, ${\text{BaTi}}_{1/2}{\text{Mn}}_{1/2}{\text{O}}_{3}$ is proposed as a rare case of an intrinsically disordered $S=\frac{3}{2}$ spin gap system with a frustrated ground state.

Multiple acquisition of magic angle spinning solid-state NMR experiments using one receiver: Application to microcrystalline and membrane protein preparations

Solid-state NMR spectroscopy of proteins is a notoriously low-throughput technique. Relatively low-sensitivity and poor resolution of protein samples require long acquisition times for multidimensional NMR experiments. To speed up data acquisition, we developed a family of experiments called Polarization Optimized Experiments (POE), in which we utilized the orphan spin operators that are discarded in classical multidimensional NMR experiments, recovering them to allow simultaneous acquisition of multiple 2D and 3D experiments, all while using conventional probes with spectrometers equipped with one receiver. POE allow the concatenation of multiple 2D or 3D pulse sequences into a single experiment, thus potentially combining all of the aforementioned advances, boosting the capability of ssNMR spectrometers at least two-fold without the addition of any hardware. In this perspective, we describe the first generation of POE, such as dual acquisition MAS (or DUMAS) methods, and then illustrate the evolution of these experiments into MEIOSIS, a method that enables the simultaneous acquisition of multiple 2D and 3D spectra. Using these new pulse schemes for the solid-state NMR investigation of biopolymers makes it possible to obtain sequential resonance assignments, as well as distance restraints, in about half the experimental time. While designed for acquisition of heteronuclei, these new experiments can be easily implemented for proton detection and coupled with other recent advancements, such as dynamic nuclear polarization (DNP), to improve signal to noise. Finally, we illustrate the application of these methods to microcrystalline protein preparations as well as single and multi-span membrane proteins reconstituted in lipid membranes.

Orphan spin operators enable the acquisition of multiple 2D and 3D magic angle spinning solid-state NMR spectra

We propose a general method that enables the acquisition of multiple 2D and 3D solid-state NMR spectra for U-(13)C, (15)N-labeled proteins. This method, called MEIOSIS (Multiple ExperIments via Orphan SpIn operatorS), makes it possible to detect four coherence transfer pathways simultaneously, utilizing orphan (i.e., neglected) spin operators of nuclear spin polarization generated during (15)N-(13)C cross polarization (CP). In the MEIOSIS experiments, two phase-encoded free-induction decays are decoded into independent nuclear polarization pathways using Hadamard transformations. As a proof of principle, we show the acquisition of multiple 2D and 3D spectra of U-(13)C, (15)N-labeled microcrystalline ubiquitin. Hadamard decoding of CP coherences into multiple independent spin operators is a new concept in solid-state NMR and is extendable to many other multidimensional experiments. The MEIOSIS method will increase the throughput of solid-state NMR techniques for microcrystalline proteins, membrane proteins, and protein fibrils.

Vacancy-induced spin textures and their interactions in a classical spin liquid

Motivated by experiments on the archetypal frustrated magnet SrCr$_{9p}$Ga$_{12-9p}$O$_{19}$ (SCGO), we study the classical Heisenberg model on the pyrochlore slab (Kagom\'e bilayer) lattice with site-dilution $x=1-p$. This allows us to address generic aspects of the physics of non-magnetic vacancies in a classical spin liquid. We explicitly demonstrate that the pure ($x=0$) system remains a spin-liquid down to the lowest temperatures, with an unusual {\em non-monotonic} temperature dependence of the susceptibility, which even turns diamagnetic for the apical spins between the two kagome layers. For $x> 0$ but small, the low temperature magnetic response of the system is most naturally described in terms of the properties of spatially extended spin textures that cloak an "orphan" $S=3/2$ Cr$^{3+}$ spin in direct proximity to a pair of missing sites belonging to the same triangular simplex. In the $T \rightarrow 0$ limit, these orphan-texture complexes each carry a net magnetization that is exactly half the magnetic moment of an individual spin of the undiluted system. Furthermore, we demonstrate that they interact via an entropic {\em temperature dependent} {\em pair-wise exchange interaction} $J_{eff}(T,\vec{r}) \sim T {\mathcal J} (\vec{r} \sqrt{T})$ that has a logarithmic form at short-distances and decays exponentially beyond a thermal correlation length $\xi(T) \sim 1/\sqrt{T}$. The sign of $J_{eff}$ depends on whether the two orphan spins belong to the same Kagome layer or not. We provide a detailed analytical account of these properties using an effective field theory approach specifically tailored for the problem at hand. These results are in quantitative agreement with large-scale Monte Carlo numerics.