Muon Spin Relaxation Study of MnGe and Development of Pair Distribution Function Methods

The first half of the thesis presents our experimental study of a helical magnet MnGe. We apply μSR technique to study the dynamic as well as the static magnetism in MnGe. Our key findings are as follows. From the muon dynamic relaxation 1/T1 results, no apparent critical behavior or anomaly was observed at the boundary between param- agnetic and the induced-ferromagnetic regions. Our study revealed linear relation between the transverse field relaxation rate and the static magnetization. Furthermore, their ratio, which can be regarded a form of hyperfine coupling constant, is very similar in the induced ferromagnetic region and the paramagnetic region. This suggest that the Z component of the Mn moment is static in both regions. On the other hand, the single relaxation rate in the transverse spectra suggest that the internal field is highly homogeneous in the induced ferromagnetic region. We therefore speculate that the induced ferromagnetic region and the paramagnetic region are not separate phases, but rather a single phase with different tendencies as temperature decrease. With decreasing temperature, the paramagnetic region is marked with the winning of the tendency towards ferromagnetic ordering over random ordering, and the induced ferromagnetic region is marked with the winning of the tendency towards the helical order over ferromagnetic order.At lower temperature, we observed dynamic critical behavior in the boundary between the induced ferromagnetic region and the Skyrmion region. Specifically, in low fields, the 1/T1 relaxation rate behaves qualitatively different from the prediction of SCR theory for itinerant ferromagnet for large temperature regime above Tc. In high fields, on the other hand, the system recovers the SCR itinerant ferromagnetic behavior. Through analyzing field effect on spin fluctuation and phase transition in the low and high field regimes, we speculate that this could be due to the suppression of helical fluctuation into ferromagnetic-like fluc- tuation by large magnetic fields. Our μSR results, which show 2nd order signature for the transition between the induced ferromagnetic region into the Skyrmion region, is consistent with considerations based on the topology of the magnetic structure in each phase. At low temperatures within the Skyrmion region of MnGe, our analysis of the transverse field data shows that all the three components of the Mn moment is frozen. The quadratic tempera- ture dependence of 1/T1 at low temperatures suggest the two-magnon spin wave to be the dominant spin excitation in the Skyrmion region. This is similar to those seen in local- ized moment magnets and is qualitatively different from the linear temperature dependence predicted from SCR theory for itinerant ferromagnets. The second half of the thesis present our derivation of the structure function and the pair distribution function (PDF) for textured materials. We also derive the analytical form of the PDF for a few special cases of texture. In this study, we start from the general form of a 3D structure function and derive the general and orientationally averaged form of the structure function and PDF for textured samples. In particular for a thin film sample with fibre texture, our formalism gives the result known as the 2 dimensional PDF. We developed open-software that calculates the 2 dimensional PDF for a textured thin film, and showed that the experimental PDF was well fitted using the model. On the other hand, the PDF method could be extended to an energy-dependent form, which could reveal explicitly the effect of lattice dynamics on the local arrangement of the atoms. This is usually called the dynamic PDF method. In this thesis we derive the analytical form of the dynamic PDF for a simple molecule that contains two identical atoms. And we interpret the mathematical results with physical consideration of the lattice dynamics. In addition, we also propose a new definition for the dynamic PDF which can be shown to reduce to the atomic PDF by integrating over energy. This new definition of the dynamic PDF incorporates the contribution from multi-phonon scattering effects, and can be computed conveniently from inelastic neutron scattering

Muon Spin Relaxation Study of MnGe and Development of Pair Distribution Function Methods

The first half of the thesis presents our experimental study of a helical magnet MnGe. We apply μSR technique to study the dynamic as well as the static magnetism in MnGe. Our key findings are as follows. From the muon dynamic relaxation 1/T1 results, no apparent critical behavior or anomaly was observed at the boundary between param- agnetic and the induced-ferromagnetic regions. Our study revealed linear relation between the transverse field relaxation rate and the static magnetization. Furthermore, their ratio, which can be regarded a form of hyperfine coupling constant, is very similar in the induced ferromagnetic region and the paramagnetic region. This suggest that the Z component of the Mn moment is static in both regions. On the other hand, the single relaxation rate in the transverse spectra suggest that the internal field is highly homogeneous in the induced ferromagnetic region. We therefore speculate that the induced ferromagnetic region and the paramagnetic region are not separate phases, but rather a single phase with different tendencies as temperature decrease. With decreasing temperature, the paramagnetic region is marked with the winning of the tendency towards ferromagnetic ordering over random ordering, and the induced ferromagnetic region is marked with the winning of the tendency towards the helical order over ferromagnetic order.At lower temperature, we observed dynamic critical behavior in the boundary between the induced ferromagnetic region and the Skyrmion region. Specifically, in low fields, the 1/T1 relaxation rate behaves qualitatively different from the prediction of SCR theory for itinerant ferromagnet for large temperature regime above Tc. In high fields, on the other hand, the system recovers the SCR itinerant ferromagnetic behavior. Through analyzing field effect on spin fluctuation and phase transition in the low and high field regimes, we speculate that this could be due to the suppression of helical fluctuation into ferromagnetic-like fluc- tuation by large magnetic fields. Our μSR results, which show 2nd order signature for the transition between the induced ferromagnetic region into the Skyrmion region, is consistent with considerations based on the topology of the magnetic structure in each phase. At low temperatures within the Skyrmion region of MnGe, our analysis of the transverse field data shows that all the three components of the Mn moment is frozen. The quadratic tempera- ture dependence of 1/T1 at low temperatures suggest the two-magnon spin wave to be the dominant spin excitation in the Skyrmion region. This is similar to those seen in local- ized moment magnets and is qualitatively different from the linear temperature dependence predicted from SCR theory for itinerant ferromagnets. The second half of the thesis present our derivation of the structure function and the pair distribution function (PDF) for textured materials. We also derive the analytical form of the PDF for a few special cases of texture. In this study, we start from the general form of a 3D structure function and derive the general and orientationally averaged form of the structure function and PDF for textured samples. In particular for a thin film sample with fibre texture, our formalism gives the result known as the 2 dimensional PDF. We developed open-software that calculates the 2 dimensional PDF for a textured thin film, and showed that the experimental PDF was well fitted using the model. On the other hand, the PDF method could be extended to an energy-dependent form, which could reveal explicitly the effect of lattice dynamics on the local arrangement of the atoms. This is usually called the dynamic PDF method. In this thesis we derive the analytical form of the dynamic PDF for a simple molecule that contains two identical atoms. And we interpret the mathematical results with physical consideration of the lattice dynamics. In addition, we also propose a new definition for the dynamic PDF which can be shown to reduce to the atomic PDF by integrating over energy. This new definition of the dynamic PDF incorporates the contribution from multi-phonon scattering effects, and can be computed conveniently from inelastic neutron scattering

Local atomic and magnetic structure of dilute magnetic semiconductor (Ba,K)(Zn,Mn)2_2As2_2

We have studied the atomic and magnetic structure of the dilute ferromagnetic semiconductor system (Ba,K)(Zn,Mn)$_2$As$_2$ through atomic and magnetic pair distribution function analysis of temperature-dependent x-ray and neutron total scattering data. We detected a change in curvature of the temperature-dependent unit cell volume of the average tetragonal crystallographic structure at a temperature coinciding with the onset of ferromagnetic order. We also observed the existence of a well-defined local orthorhombic structure on a short length scale of $\lesssim 5$ \AA, resulting in a rather asymmetrical local environment of the Mn and As ions. Finally, the magnetic PDF revealed ferromagnetic alignment of Mn spins along the crystallographic $c$-axis, with robust nearest-neighbor ferromagnetic correlations that exist even above the ferromagnetic ordering temperature. We discuss these results in the context of other experiments and theoretical studies on this system

muSR and Magnetometry Study of the Type-I Superconductor BeAu

We present muon spin rotation and relaxation (muSR) measurements as well as demagnetising field corrected magnetisation measurements on polycrystalline samples of the noncentrosymmetric superconductor BeAu. From muSR measurements in a transverse field, we determine that BeAu is a type-I superconductor with Hc = 256 Oe, amending the previous understanding of the compound as a type-II superconductor. To account for demagnetising effects in magnetisation measurements, we produce an ellipsoidal sample, for which a demagnetisation factor can be calculated. After correcting for demagnetising effects, our magnetisation results are in agreement with our muSR measurements. Using both types of measurements we construct a phase diagram from T = 30 mK to Tc = 3.25 K. We then study the effect of hydrostatic pressure and find that 450 MPa decreases Tc by 34 mK, comparable to the change seen in type-I elemental superconductors Sn, In and Ta, suggesting BeAu is far from a quantum critical point accessible by the application of pressure.Comment: 10 pages, 8 figure

Disentangling superconducting and magnetic orders in NaFe_1-xNi_xAs using muon spin rotation

Muon spin rotation and relaxation studies have been performed on a "111" family of iron-based superconductors NaFe_1-xNi_xAs. Static magnetic order was characterized by obtaining the temperature and doping dependences of the local ordered magnetic moment size and the volume fraction of the magnetically ordered regions. For x = 0 and 0.4 %, a transition to a nearly-homogeneous long range magnetically ordered state is observed, while for higher x than 0.4 % magnetic order becomes more disordered and is completely suppressed for x = 1.5 %. The magnetic volume fraction continuously decreases with increasing x. The combination of magnetic and superconducting volumes implies that a spatially-overlapping coexistence of magnetism and superconductivity spans a large region of the T-x phase diagram for NaFe_1-xNi_xAs . A strong reduction of both the ordered moment size and the volume fraction is observed below the superconducting T_C for x = 0.6, 1.0, and 1.3 %, in contrast to other iron pnictides in which one of these two parameters exhibits a reduction below TC, but not both. The suppression of magnetic order is further enhanced with increased Ni doping, leading to a reentrant non-magnetic state below T_C for x = 1.3 %. The reentrant behavior indicates an interplay between antiferromagnetism and superconductivity involving competition for the same electrons. These observations are consistent with the sign-changing s-wave superconducting state, which is expected to appear on the verge of microscopic coexistence and phase separation with magnetism. We also present a universal linear relationship between the local ordered moment size and the antiferromagnetic ordering temperature TN across a variety of iron-based superconductors. We argue that this linear relationship is consistent with an itinerant-electron approach, in which Fermi surface nesting drives antiferromagnetic ordering.Comment: 20 pages, 14 figures, Correspondence should be addressed to Prof. Yasutomo Uemura: [email protected]

Real-space texture and pole-figure analysis using the 3D pair distribution function on a platinum thin film

An approach is described for studying texture in nanostructured materials. The approach implements the real-space texture pair distribution function (PDF), txPDF, laid out by Gong & Billinge {(2018[Gong, Z. & Billinge, S. J. L. (2018). arXiv:1805.10342 [cond-mat].]). arXiv:1805.10342 [cond-mat]}. It is demonstrated on a fiber-textured polycrystalline Pt thin film. The approach uses 3D PDF methods to reconstruct the orientation distribution function of the powder crystallites from a set of diffraction patterns, taken at different tilt angles of the substrate with respect to the incident beam, directly from the 3D PDF of the sample. A real-space equivalent of the reciprocal-space pole figure is defined in terms of interatomic vectors in the PDF and computed for various interatomic vectors in the Pt film. Furthermore, it is shown how a valid isotropic PDF may be obtained from a weighted average over the tilt series, including the measurement conditions for the best approximant to the isotropic PDF from a single exposure, which for the case of the fiber-textured film was in a nearly grazing incidence orientation of ∼10°. Finally, an open-source Python software package, FouriGUI, is described that may be used to help in studies of texture from 3D reciprocal-space data, and indeed for Fourier transforming and visualizing 3D PDF data in general

Interfacial Charge Transfer Circumventing Momentum Mismatch at Two-Dimensional van der Waals Heterojunctions

Interfacial charge separation and recombination at heterojunctions of monolayer transition metal dichalcogenides (TMDCs) are of interest to two-dimensional optoelectronic technologies. These processes can involve large changes in parallel momentum vector due to the confinement of electrons and holes to the K valleys in each layer. Because these high-momentum valleys are usually not aligned across the interface of two TMDC monolayers, how parallel momentum is conserved in the charge separation or recombination process becomes a key question. Here we probe this question using the model system of a type-II heterojunction formed by MoS₂ and WSe₂ monolayers and the experimental technique of femtosecond pump–probe spectroscopy. Upon photoexcitation specifically of WSe₂ at the heterojunction, we observe ultrafast (<40 fs) electron transfer from WSe₂ to MoS₂, independent of the angular alignment and thus momentum mismatch between the two TMDCs. The resulting interlayer charge transfer exciton decays via nonradiative recombination with rates varying by up to three-orders of magnitude from sample to sample but with no correlation with interlayer angular alignment. We suggest that the initial interfacial charge separation and the subsequent interfacial charge recombination processes circumvent momentum mismatch via excess electronic energy and via defect-mediated recombination, respectively