A crystal structure that cannot be superposed on its mirror image by any combination of rotations and translations is classified as chiral. Such crystal structures have gained importance in recent years since they are prone to host unconventional magnetic orders and to exhibit topological magnetic textures. These properties result from the Dzyaloshinskii-Moriya antisymmetric exchange interaction which is authorized when space inversion is broken. While recent reports have shown the muon spin rotation and relaxation technique to provide unique information about structural and dynamical properties which are specific to chiral magnets in their ordered phase, the question here is whether this technique is sensitive to paramagnetic chiral correlations that are observed in neutron scattering experiments above the critical temperature. In the relevant long wavelength limit, it is shown that they do not contribute to the relaxation rate, which in turn only probes non-chiral correlations.
Positive-muon ($μ^+$) Knight shifts have been measured in the paramagnetic states of Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$ alloys, where $x =$ 0, 0.25, 0.45, 0.50, 0.55, 0.75, and 1.00. In Pr-substituted NdOs$_4$Sb$_{12}$ ($x \le$ 0.75), but not in NdOs$_4$Sb$_{12}$, Clogston-Jaccarino plots of $μ^+$ Knight shift~$K$ versus magnetic susceptibility~$χ$ exhibit an anomalous saturation of $K(χ)$ at $\sim-$0.5% for large susceptibilities (low temperatures), indicating a reduction of the coupling strength between $μ^+$ spins and $4f$ paramagnetism for temperatures $\lesssim$ 15~K. We speculate that itine…
The insulating pyrochlore compound Nd2Sn2O7 has been shown to undergo a second order magnetic phase transition at Tc ~ 0.91 K to a noncoplanar all-in--all-out magnetic structure of the Nd3+ magnetic moments. An anomalously slow paramagnetic spin dynamics has been evidenced from neutron backscattering and muon spin relaxation (muSR). In the case of muSR this has been revealed through the strong effect of a 50 mT longitudinal field on the spin-lattice relaxation rate. Here, motivated by a recent successful work performed for Yb2Ti2O7 and Yb2Sn2O7, analyzing the shape of the muSR longitudinal pol…
We report muon spin rotation measurements of the local magnetic susceptibility around a positive muon in the paramagnetic state of the quasi one-dimensional spin 1/2 antiferromagnet dichlorobis (pyridine) copper (II). Signals from three distinct sites are resolved and have a temperature dependent frequency shift which is significantly different than the magnetic susceptibility. This difference is attributed to a muon induced perturbation of the spin 1/2 chain. The obtained frequency shifts are compared with Transfer Matrix DMRG numerical simulations.
The magnetic and quadrupolar ordered states of polycrystalline YbRu2Ge2 have been investigated using zero-field muon spin relaxation (μSR) and neutron diffraction measurements. Specific heat measurements show three successive phase transitions, with decreasing temperature from a paramagnetic to a quadrupolar state at T0 ~ 10 K, from the quadrupolar to a magnetic state at T1 ~ 6.5 K and a possible change in the magnetic ground state at T2 ~ 5.5 K. Clear evidence for the magnetic transition below 7 K (spectrum at 8 K reveals paramagnetic state) and a likely change in the magnetic structure near …
Muon spin relaxation on Nd$_2$Ti$_2$O$_7$ (NTO) and NdLaTi$_2$O$_7$ (NLTO) compounds are presented. The time spectra for both compounds are as expected for the paramagnetic state at high temperatures, but deviate from the exponential function below about 100 K. The muon spin relaxation rate increases with decreasing temperature firstly, and then levels off below about 10 K, which is reminiscent of the frustrated systems. An enhancement of the relaxation rate by a longitudinal field in the paramagnetic state is observed for NTO, and eliminated by a magnetic dilution for the NLTO sample. This su…
The cubic double perovskite Ba$_2$YIrO$_6$ has been investigated by the local probe techniques nuclear magnetic resonance ($^{89}$Y NMR) and muon spin rotation (muSR). Both methods confirm the absence of magnetic long-range order in this compound but find evidence for diluted localized paramagnetic moments. NMR spin-lattice relaxation rate 1/T1 measurements suggest a slowing down of localized spin moments at low temperatures. An increase of the muSR spin-lattice relaxation rate lambda confirms the presence of weak magnetism in Ba$_2$YIrO$_6$ . However, these findings cannot be explained by the…
Magnetic systems with spins sitting on a lattice of corner sharing regular tetrahedra have been particularly prolific for the discovery of new magnetic states for the last two decades. The pyrochlore compounds have offered the playground for these studies, while little attention has been comparatively devoted to other compounds where the rare earth R occupies the same sub-lattice, e.g. the spinel chalcogenides CdR2X4 (X = S, Se). Here we report measurements performed on powder samples of this series with R = Yb using specific heat, magnetic susceptibility, neutron diffraction and muon-spin-rel…
We present a detailed study of the magnetic properties of weakly ferromagnetic/quantum critical Nb$_{1-y}$Fe$_{2+y}$ using muon spin rotation and relaxation ($μ$SR). By means of an angular dependent study of the muon spin rotation signal in applied magnetic fields on a single crystal in the paramagnetic state we establish the muon stopping site in the crystallographic lattice of NbFe$_2$. With this knowledge we develop models to describe the muon spin rotation and relaxation signals in the weakly ferromagnetic, spin density wave and quantum critical phases of Nb$_{1-y}$Fe$_{2+y}$ and fit the c…
We report measurements performed on a polycrystalline sample of the pyrochlore compound Nd2Sn2O7. It undergoes a second order magnetic phase transition at Tc ~ 0.91 K to a noncoplanar all-in-all-out magnetic structure of the Nd3+ magnetic moments. The thermal behavior of the low temperature specific heat fingerprints excitations with linear dispersion in a three-dimensional lattice. The temperature independent spin-lattice relaxation rate measured below Tc and the anomalously slow paramagnetic spin dynamics detected up to ~ 30 Tc are suggested to be due to magnetic short-range correlations in …
The recently synthesized MgFeGe compound is isostructural and isoelectronic with superconducting LiFeAs. Both materials are paramagnetic metals at room temperature. Inspection of their electronic structures without spin polarization reveals hardly any difference between the two. This fact was interpreted as evidence against popular theories relating superconductivity in Fe-based materials with spin fluctuations. We show that in the magnetic domain the two compounds are dramatically different, and the fact that MgFeGe does not superconduct, is, on the contrary, a strong argument in favor of the…
We report muon spin rotation measurements of the local magnetic susceptibility around a positive muon in the paramagnetic state of the quasi one-dimensional spin 1/2 antiferromagnet KCuF$_3$. Signals from two distinct sites are resolved which have a temperature dependent frequency shift which is different than the magnetic susceptibility. This difference is attributed to a muon induced perturbation of the spin 1/2 chain.
We present a muon spin relaxation study on the Ising pyrochlore Nd$_2$Zr$_2$O$_7$ which develops an "all-in-all-out" magnetic order below 0.4~K. At 20~mK far below the ordering transition temperature, the zero-field muon spin relaxation spectra show no static features and can be well described by a dynamical Gaussian-broadened Gaussian Kubo-Toyabe function indicating strong fluctuations of the ordered state. The spectra of the paramagnetic state (below 4.2~K) reveal anomalously slow paramagnetic spin dynamics and show only small difference with the spectra of the ordered state. We find that th…
We report a muon spin rotation/relaxation ($μ$SR) study of single-crystalline samples of the $α$-RuCl$_3$ honeycomb magnet, which is presumed to be a model compound for the Kitaev-Heisenberg interaction. It is inferred from magnetic susceptibility and specific-heat measurements that the present samples exhibit successive magnetic transitions at different critical temperatures $T_{\rm N}$ with decreasing temperature, eventually falling into the $T_{\rm N}=7$ K antiferromagnetic (7 K) phase that has been observed in only single-crystalline specimens with the least stacking fault. Via $μ$SR measu…
Transition metal oxides of the $4d$ and $5d$ block have recently become the targets of materials discovery, largely due to their strong spin-orbit coupling that can generate exotic magnetic and electronic states. Here we report the high pressure synthesis of Lu$_2$Rh$_2$O$_7$, a new cubic pyrochlore oxide based on $4d^5$ Rh$^{4+}$ and characterizations via thermodynamic, electrical transport, and muon spin relaxation measurements. Magnetic susceptibility measurements reveal a large temperature-independent Pauli paramagnetic contribution, while heat capacity shows an enhanced Sommerfeld coeffic…
Muon Knight shift as a precise probe of the superconducting symmetry of Sr$_2$RuO$_4$
Toyota Riken–Kyoto University Research Center (TRiKUC), Kyoto University（丰田理研-京都大学研究中心）；Institute for Chemical Research, Kyoto University（京都大学化学研究所）；PSI Center for Neutron and Muon Sciences CNM（保罗谢尔研究所中子与缪子科学中心）；Institute for Solid State Physics, the University of Tokyo（东京大学固体物理研究所）；Department of Physics, University of British Columbia（不列颠哥伦比亚大学物理系）；Department of Electronic Science and Engineering, Graduate School of Engineering, Kyoto University（京都大学大学院工学研究科电子科学与工程系）
We report on zero-field muon spin rotation, electron spin resonance and polarized Raman scattering measurements of the coupled quantum spin ladder Ba2CuTeO6. Zero-field muon spin rotation and electron spin resonance probes disclose a successive crossover from a paramagnetic through a spin-liquid-like into a magnetically ordered state with decreasing temperature. More significantly, the two-magnon Raman response obeys a T-linear scaling relation in its peak energy, linewidth and intensity. This critical scaling behavior presents an experimental signature of proximity to a quantum critical point…
We report muon-spin rotation, heat capacity, magnetization, and ac magnetic susceptibility measurements of the layered spin-1/2 antiferromagnet NaNiO2. These show the onset of long-range magnetic order below T_N = 19.5K. Rapid muon depolarization persisting to about 5K above T_N is consistent with the presence of short-range magnetic order. The temperature and frequency dependence of the ac susceptibility suggests that magnetic clusters persist above 25K in the paramagnetic state and that their volume fraction decreases with increasing temperature. A frequency dependent peak in the ac magnetic…
The magnetic nature of low dimensional compound, CrCl$_3$, was investigated by muon spin rotation, relaxation and resonance ($μ^+$SR). The $μ^+$SR measurements revealed three distinct phases as a function of temperature: an antiferromagnetic state (AF) for $T\leq T_{\rm N}=14.32(6)$~K, a ferromagnetic short range ordered state (FM-SRO) for $T_{\rm N}<T<\sim18$~K and a paramagnetic phase (PM) above $\sim18$~K. Moreover, the AF state exhibits appreciable spin dynamics, which increases with decreasing temperature below $T_{\rm N}$. These dynamics originate from out of plane fluctuations, which se…
The magnetic ground state of double perovskite Sr2DyRuO6 has been investigated using muon spin rotation and relaxation (muSR), neutron powder diffraction (NPD) and inelastic neutron scattering (INS), in addition to heat capacity and magnetic susceptibility (ac and dc) measurements. A clear signature of a long-range ordered magnetic ground state has been observed in the heat capacity data, which exhibit two sharp anomalies at 39.5 and 36 K found as well in the magnetic data. Further confirmation of long-range magnetic ordering comes from a sharp drop in the muon initial asymmetry and a peak in …
Two phase transitions in the tetragonal strongly correlated electron system CeNiAsO were probed by neutron scattering and zero field muon spin rotation. For $T <T_{N1}$ = 8.7(3) K, a second order phase transition yields an incommensurate spin density wave with wave vector $\textbf{k} = (0.44(4), 0, 0)$. For $T < T_{N2}$ = 7.6(3) K, we find co-planar commensurate order with a moment of $0.37(5)~μ_B$, reduced to $30 \%$ of the saturation moment of the $|\pm\frac{1}{2}\rangle$ Kramers doublet ground state, which we establish by inelastic neutron scattering. Muon spin rotation in $\rm CeNiAs_{1-x}…
We demonstrate via a muon spin rotation experiment that the electronic ground state of the iridium spinel compound, CuIr$_2$S$_4$, is not the presumed spin-singlet state but a novel paramagnetic state, showing a quasistatic spin glass-like magnetism below ~100 K. Considering the earlier indication that IrS$_6$ octahedra exhibit dimerization associated with the metal-to-insulator transition below 230 K, the present result suggests that a strong spin-orbit interaction may be playing an important role in determining the ground state that accompanies magnetic frustration.
The high field superconducting state in CeCoIn5 has been studied by transverse field muon spin rotation measurements with an applied field parallel to the crystallographic c-axis close to the upper critical field Hc2 = 4.97 T. At magnetic fields >= 4.8 T the muon Knight shift is enhanced and the superconducting transition changes from second order towards first order as predicted for Pauli-limited superconductors. The field and temperature dependence of the transverse muon spin relaxation rate sigma reveal paramagnetic spin fluctuations in the field regime from 2 T < H < 4.8 T. In the normal s…
The fascinating multiple magnetic states observed in the Ni-Mn-Sn based metamagnetic shape memory alloy are addressed through a combined muon spin relaxation (muSR) and neutron powder diffraction studies. The material used in the present investigation is an off-stoichiometric alloy of nominal composition, Ni[2.04]Mn[1.4]Sn[0.56]. This prototypical alloy, similar to other members in the Ni-Mn-Sn series, orders ferromagnetically below T[CA] (= 320 K), and undergoes martensitic type structural transition at T[MS] (= 290 K), which is associated with the sudden loss of magnetization. The sample reg…
We have investigated the non-centrosymmetric tetragonal heavy-fermion compound CeAuAl3 using muon spin rotation (muSR), neutron diffraction (ND) and inelastic neutron scattering (INS) measurements. We have also revisited the magnetic, transport and thermal properties. The magnetic susceptibility reveals an antiferromagnetic transition at 1.1 K with a possibility of another magnetic transition near 0.18 K. The heat capacity shows a sharp lambda-type anomaly at 1.1 K in zero-filed, which broadens and moves to higher temperature in applied magnetic field. Our zero-field muSR and ND measurements c…
The magnetic ground state of oxynitride pyrochlore Lu$_2$Mo$_2$O$_{5-y}$N$_2$, a candidate compound for the quantum spin liquid ($S=1/2$, Mo$^{5+}$), was studied by muon spin rotation/relaxation experiment. In contrast to Lu$_2$Mo$_2$O$_7$ ($S=1$, Mo$^{4+}$) which exhibits the spin-glass behavior with a freezing temperature $T_g\simeq16$ K, no such spin freezing or long range magnetic order was observed down to 0.3 K. Moreover, two separate magnetic domains were detected below $\sim$13 K, which were characterized by differences in spin dynamics. The first is the "sporadic" spin fluctuation see…
Investigations of the spin dynamics of the geometrically frustrated pyrochlore (Tb_pY_{1-p})_2Ti_2O_7, using muon spin relaxation and neutron spin echo, as a function of magnetic coverage p, have been carried out. Our major finding is that paramagnetic fluctuations prevail as T->0 for all values of p, and that they are sensitive to dilution, indicating a cooperative spin motion. However, the percolation threshold p_c is not a critical point for the fluctuations. We also find that the low temperatures spectral density has a 1/f behavior, and that dilution slows down the spin fluctuations.
We have performed muon spin rotation/relaxation (muSR) measurements on single crystals of the chiral helimagnet Cr1/3NbS2 at zero to low magnetic field. The transition from the paramagnetic to helical magnetically ordered phase at zero field is marked by the onset of a coherent oscillation of the zero-field muon spin polarization below a critical temperature Tc. An enhancement of the muon spin precession frequency is observed below T ~ 50K, where anomalous behavior has been observed in bulk transport measurements. The enhanced precession frequency indicates a low-temperature modification of th…
We report the local magnetic response of an electron-doped cuprate superconductor, Pr$_{0.89}$LaCe$_{0.11}$CuO$_{4}$ ($T_c\simeq26$ K), studied by muon spin rotation (\msr) over a field range from 200 Oe to 50 kOe. In the paramagnetic state, the muon Knight shift along the crystal c-axis ($K_μ^z$) is proportional to the in-plane susceptibility $χ_{ab}$. More surprisingly, $K_μ^z$ is strongly enhanced by the occurrence of superconductivity (below $\sim$40 kOe), changing its sign from positive to negative around $\sim1$ kOe with increasing field. This finding can be understood by considering the…
We have investigated polycrystalline samples of the zigzag chain system BaTb$_2$O$_4$ with a combination of magnetic susceptibility, heat capacity, neutron powder diffraction, and muon spin relaxation measurements. Despite the onset of Tb$^{3+}$ short-range antiferromagnetic correlations at $|θ_{CW}|$ $=$ 18.5 K and a very large effective moment, our combined measurements indicate that BaTb$_2$O$_4$ remains paramagnetic down to 0.095 K. The magnetic properties of this material show striking similarities to the pyrochlore antiferromagnet Tb$_2$Ti$_2$O$_7$, and therefore we propose that BaTb$_2$…
We have carried out muon spin relaxation (muSR), neutron diffraction and inelastic neutron scattering (INS) investigations on polycrystalline samples of Ce(Ru1-xFex)2Al10 (x=0, 0.3, 0.5, 0.8 and 1) to investigate the nature of the ground state (magnetic ordered versus paramagnetic) and the origin of the spin gap formation as evident from the bulk measurements in the end members. Our zero-field muSR spectra clearly reveal coherent two-frequency oscillations at low temperature in x=0, 0.3 and 0.5 samples, which confirms the long-range magnetic ordering of the Ce-moment with TN=27, 26 and 21 K re…
In the quasi-1D heavy-fermion system YbNi$_4$(P$_{1-x}$As$_x$)$_2$ the presence of a ferromagnetic (FM) quantum critical point (QCP) at $x_c$ $\approx 0.1$ with unconventional quantum critical exponents in the thermodynamic properties has been recently reported. Here, we present muon-spin relaxation ($μ$SR) experiments on polycrystals of this series to study the magnetic order and the low energy 4$f$-electronic spin dynamics across the FM QCP. The zero field $μ$SR measurements on pure YbNi$_4$(P$_{2}$ proved static long range magnetic order and suggested a strongly reduced ordered Yb moment of…
Effects of the magnetic impurity Ni on the Cu-spin dynamics and superconductivity have been studied in La_2-x_Sr_x_Cu_1-y_Ni_y_O_4_ with x = 0.13 changing y finely up to 0.10. Compared with the case of the nonmagnetic impurity Zn, it has been found from the muon-spin-relaxation measurements that a large amount of Ni is required to stabilize a magnetic order of Cu spins. However, the evolution toward the stabilization of the magnetic order with increasing impurity concentration is qualitatively similar to each other. The area of the non-superconducting and slowly fluctuating or static region of…
Using local-probe magnetic-characterization techniques of muon spin relaxation ($μ$SR) and electron spin resonance (ESR) we have investigated the Mn-induced magnetism of the wide-bandgap perovskite SrTiO$_3$. Our results clearly demonstrate that this diluted magnetic oxide (DMO) remains paramagnetic down to low temperatures for both doping cases, i.e., when Mn substitutes for Sr or Ti. In addition, both experimental techniques have unveiled that the distribution of individual Mn$^{2+}$ and Mn$^{4+}$ ions is nonrandom, as these ions partially aggregate into nanosized clusters.
Longitudinal-field muon spin relaxation experiments have been carried out in the paramagnetic state of single-crystal Gd_2Ti_2O_7 just above the phase transition at T_m = 1.0 K. At high applied fields the exponential relaxation time T_1 is proportional to field, whereas T_1 saturates below a crossover field B_c that is ~2.5 T at 1.5 K and decreases as T_m is approached. At low fields the relaxation rate increases markedly as the freezing temperature is approached, as expected for critical slowing down of the spin fluctuations, but the increase is suppressed by applied field. This behavior is c…
Er2Ti2O7 is believed to be a realization of an XY antiferromagnet on a frustrated lattice of corner-sharing regular tetrahedra. It is presented as an example of the order-by-disorder mechanism in which fluctuations lift the degeneracy of the ground state, leading to an ordered state. Here we report detailed measurements of the low temperature magnetic properties of Er2Ti2O7, which displays a second-order phase transition at T_N \simeq 1.2 K with coexisting short- and long-range orders. Magnetic-susceptibility studies show that there is no spin-glass-like irreversible effect. Heat-capacity meas…
The SrCr$\_{9p}$Ga$\_{12-9p}$O$\_{19}$ and Ba$\_{2}$Sn$\_{2}$ZnGa$\_{10-7p}$Cr$\_{7p}$O$\_{22}$ compounds are two highly-frustrated magnets possessing a quasi-two-dimensional Kagomé bilayer of spin 3/2 chromium ions with antiferromagnetic interactions. Their magnetic susceptibility was measured by local Nuclear Magnetic Resonance and non-local (SQUID) techniques, and their low-temperature spin dynamics by Muon Spin Resonance. Consistent with the theoretical picture drawn for geometrically frustrated systems, the Kagomé bilayer is shown here to exhibit: (i) short range spin-spin correlations do…
Magnetism of layered cobaltites Na$_x$CoO$_2$ with $x$ = 0.6 and 0.9 has been investigated by a positive muon spin rotation and relaxation ($μ^+$SR) spectroscopy together with magnetic susceptibility and specific heat measurements, using single crystal samples in the temperature range between 250 and 1.8 K. Zero-field (ZF-) $μ^+$SR measurements on Na$_{0.9}$CoO$_2$ indicates a transition from a paramagnetic to an incommensurate spin density wave state at 19 K(=$T_{\sf SDW}$). The anisotropic ZF-$μ^+$SR spectra suggest that the oscillating moments of the {\sf IC-SDW} directs along the c-axis. S…
We report x-ray diffraction, magnetic susceptibility, heat capacity, $^{1}$H nuclear magnetic resonance (NMR), and muon spin relaxation ($μ$SR) measurements, as well as density-functional band-structure calculations for the frustrated $S=3/2$ triangular lattice Heisenberg antiferromagnet (TLHAF) $α$-HCrO$_{2}$ (trigonal, space group: $R\bar{3}m$). This compound undergoes a clear magnetic transition at $T_{\rm N} \simeq 22.5$~K, as seen from the drop in the muon paramagnetic fraction and concurrent anomalies in the magnetic susceptibility and specific heat. Local probes (NMR and $μ$SR) reveal a…
Local electronic structure and dynamics of hydrogen in $\text{CeO}_2$
High Energy Accelerator Research Organization (KEK-IMSS)（高能加速器研究机构）；The Graduate University for Advanced Studies (Sokendai)（高级研究院）；Japan Atomic Energy Agency（日本原子能研究开发机构）
Two B-site ordered double perovskites, La2LiMoO6 and Ba2YMoO6, based on the S = 1/2 ion, Mo5+, have been investigated in the context of geometric magnetic frustration. Powder neutron diffraction, heat capacity, susceptibility, muon spin relaxation(_SR), and 89Y NMR- including MAS NMR- data have been collected. La2LiMoO6 deviates strongly from simple Curie-Weiss paramagnetic behavior below 150K and zero-field cooled/ field cooled (ZFC/FC)irreversibility occurs below 20K with a weak, broad susceptibility maximum near 5K in the ZFC data. A Curie-Weiss fit shows a reduced mu_eff=1.42μ_B, (spin onl…
We report a comprehensive electronic structure investigation of the paramagnetic (PM), the large moment antiferromagnetic (LMAF), and the hidden order (HO) phases of URu$_2$Si$_2$. We have performed relativistic full-potential calculations on the basis of the density functional theory (DFT), employing different exchange-correlation functionals to treat electron correlations within the open $5f$-shell of uranium. Specifically, we investigate---through a comparison between calculated and low-temperature experimental properties---whether the $5f$ electrons are localized or delocalized in URu$_2$S…
We report on systematic muon-spin rotation and relaxation ($μ$SR) studies of the magnetic properties of EuAl$_4$ and EuGa$_4$ single crystals at a microscopic level. Transverse-field $μ$SR measurements, spanning a wide temperature range (from 1.5 to 50 K), show clear bulk AFM transitions, with an almost 100% magnetic volume fraction in both cases. Zero-field $μ$SR measurements, covering both the AFM and the paramagnetic (PM) states, reveal internal magnetic fields $B_\mathrm{int}(0) = 0.33$ T and 0.89 T in EuAl$_4$ and EuGa$_4$, respectively. The transverse muon-spin relaxation rate $λ_\mathrm…
We have used neutron scattering and muon spin relaxation (muSR) to investigate the structural and magnetic properties of the beta-phase of elemental manganese doped with dilute amounts of indium. beta-Mn is an example of a topologically frustrated antiferromagnetically correlated metal - but which remains paramagnetic at all temperatures. The addition of In to beta-Mn results in a vast volume expansion of the lattice, and would therefore be expected to have a major effect on the stability and localization of the Mn moment - as observed in, for example, Ru and Al doped beta-Mn alloys. We find t…
The tunable magnetism at graphene edges with lengths of up to 48 unit cells is analyzed by an exact diagonalization technique. For this we use a generalized interacting one-dimensional model which can be tuned continuously from a limit describing graphene zigzag edge states with a ferromagnetic phase, to a limit equivalent to a Hubbard chain, which does not allow ferromagnetism. This analysis sheds light onto the question why the edge states have a ferromagnetic ground state, while a usual one-dimensional metal does not. Essentially we find that there are two important features of edge states:…
3d Conformal Field Theories via Fuzzy Sphere Algebra
Walter Burke Institute for Theoretical Physics and Department of Physics, California Institute of Technology（加州理工学院沃尔特·伯克理论物理研究所和物理系）；Department of Mathematics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校数学系）
