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In this dissertation, we investigate the stabilization and dynamics of chiral domain walls and skyrmions in several ferromagnet/heavy metal thin-film multilayers. In each material system, the ferromagnet/heavy metal interfaces were engineered to give rise to an interfacial Dzyaloshinskii-Moriya interaction (iDMI) – a spin-orbit coupling mediated effect known to promote the formation of chiral magnetic textures. Throughout several comprehensive studies (presented herein as separate chapters), we explore the stabilization and dynamics of skyrmions in three distinct types of material systems: Thin-films close to experiencing a spin-reorientation transition, ultrathin films with low ferromagnetic exchange and high perpendicular magnetic anisotropy, and thick multilayers with large perpendicular magnetic anisotropy. Through experimental and theoretical studies, we explore the processes by which skyrmions can be created and moved in response to both quasi-static and transient electrical currents, magnetic fields, and temperature changes. In all cases, the systematic variation of material properties and experimental conditions to better understand and control the mechanisms by which skyrmions are stabilized is a key underlying theme. In another thrust, we have studied the field-driven dynamics of chiral domain walls and have characterized a new effect in which magnetic stripe domains with chiral domain walls unidirectionally expand in response to applied magnetic fields, with growth symmetries that cannot be understood from the static energy frameworks typically employed to understand the impact of the interfacial Dzyaloshinskii-Moriya interaction in thin-film systems. Using analytical models, we have found that the in-plane torques generated by perpendicular magnetic fields stabilize steady-state domain wall magnetization profiles that are highly asymmetric in elastic energy, resulting in abnormal growth behaviors that are in line with the experimental findings. Building on this understanding of the field-driven dynamics of stripe domains, we expand this understanding to the growth directionalities observed when stripe domain motion is induced by spin-orbit torque.

We have performed an experimental and modeling-based study of the spin-orbit torque-induced growth of magnetic stripe domains in heavy metal/ferromagnet thin-film heterostructures that possess chiral N\'eel-type domain walls due to an interfacial Dzyaloshinskii-Moriya interaction. In agreement with previous reports, the stripe domains stabilized in these systems exhibit a significant transverse growth velocity relative to the applied current axis. This behavior has previously been attributed to the Magnus force-like skyrmion Hall effect of the stripe domain spin topology, which is analogous to that of a half-skyrmion. However, through analytic modeling of the in-plane torques generated by spin-orbit torque, we find that a dynamical reconfiguration of the domain wall magnetization profile is expected to occur - promoting motion with similar directionality and symmetry as the skyrmion Hall effect. These results further highlight the sensitivity of spin-orbit torque to the local orientation of the domain wall magnetization profile and its contribution to domain growth directionality., Comment: 21 pages, 4 figures, 3 supplementary figures

Time-resolved ultrafast EUV magnetic scattering was used to test a recent prediction of >10 km/s domain wall speeds by optically exciting a magnetic sample with a nanoscale labyrinthine domain pattern. Ultrafast distortion of the diffraction pattern was observed at markedly different timescales compared to the magnetization quenching. The diffraction pattern distortion shows a threshold-dependence with laser fluence, not seen for magnetization quenching, consistent with a picture of domain wall motion with pinning sites. Supported by simulations, we show that a speed of $\approx$ 66 km/s for highly curved domain walls can explain the experimental data. While our data agree with the prediction of extreme, non-equilibrium wall speeds locally, it differs from the details of the theory, suggesting that additional mechanisms are required to fully understand these effects., 5 pages, 4 figures; Supplemental Material: 9 pages, 9 figures

Science advances 8(13), eabn0523 (2022). doi:10.1126/sciadv.abn0523, Magnetic nanoparticles such as FePt in the L10 phase are the bedrock of our current data storage technology. As the grains become smaller to keep up with technological demands, the superparamagnetic limit calls for materials with higher magnetocrystalline anisotropy. This, in turn, reduces the magnetic exchange length to just a few nanometers, enabling magnetic structures to be induced within the nanoparticles. Here, we describe the existence of spin-wave solitons, dynamic localized bound states of spin-wave excitations, in FePt nanoparticles. We show with time-resolved x-ray diffraction and micromagnetic modeling that spin-wave solitons of sub–10 nm sizes form out of the demagnetized state following femtosecond laser excitation. The measured soliton spin precession frequency of 0.1 THz positions this system as a platform to develop novel miniature devices., Published by Assoc., Washington, DC [u.a.]

In this paper, we use the Weil-Petersson gradient flow for renormalized volume to study the space $CC(N;S,X)$ of convex cocompact hyperbolic structures on the relatively acylindrical 3-manifold $(N;S)$. Among the cases of interest are the deformation space of an acylindrical manifold and the Bers slice of quasi-Fuchsian space associated to a fixed surface. To treat the possibility of degeneration along flow-lines to peripherally cusped structures, we introduce a surgery procedure to yield a surgered gradient flow that limits to the unique structure $M_{\rm geod} \in CC(N;S,X)$ with totally geodesic convex core boundary facing $S$. Analyzing the geometry of structures along a flow line, we show that if $V_R(M)$ is the renormalized volume of $M$, then $V_R(M)-V_R(M_{\rm geod})$ is bounded below by a linear function of the Weil-Petersson distance $d_{\rm WP}(\partial_c M, \partial_c M_{\rm geod})$, with constants depending only on the topology of $S$. The surgered flow gives a unified approach to a number of problems in the study of hyperbolic 3-manifolds, providing new proofs and generalizations of well-known theorems such as Storm's result that $M_{\rm geod}$ has minimal volume for $N$ acylindrical and the second author's result comparing convex core volume and Weil-Petersson distance for quasifuchsian manifolds.

In this paper we construct examples of Weil-Petersson geodesics with nonminimal ending laminations which have 1-dimensional limit sets in the Thurston compactification of Teichm\"{u}ller space., Comment: 27 pages, 4 figures; the paper was revised, in particular some pictures were added to section 3 to illustrate the construction. Also, Theorem 2.3 about the combinatorial estimate for the hyperbolic length of a curve on a Riemann surface is included. The paper will appear in J. Topol. Anal

In this paper we prove that the limit set of any Weil-Petersson geodesic ray with uniquely ergodic ending lamination is a single point in the Thurston compactification of Teichm\"uller space. On the other hand, we construct examples of Weil-Petersson geodesics with minimal nonuniquely ergodic ending laminations and limit set a circle in the Thurston compactification., Comment: 46 pages, 3 figures, v3: some minor additions and corrections were made. The paper will appear in Int. Math. Res. Not. (IMRN)

We give a generalization of Thurston's Bounded Image Theorem for skinning maps, which applies to pared 3-manifolds with incompressible boundary that are not necessarily acylindrical. Along the way we study properties of divergent sequences in the deformation space of such a manifold, establishing the existence of compact cores satisfying a certain notion of uniform geometry., 41 pages, 5 figures. v2 contains new Theorem 4.9 which gives a finer model core statement in the convergent case

Given a sequence of curves on a surface, we provide conditions which ensure that (1) the sequence is an infinite quasi-geodesic in the curve complex, (2) the limit in the Gromov boundary is represented by a nonuniquely ergodic ending lamination, and (3) the sequence divides into a finite set of subsequences, each of which projectively converges to one of the ergodic measures on the ending lamination. The conditions are sufficiently robust, allowing us to construct sequences on a closed surface of genus $g$ for which the space of measures has the maximal dimension $3g-3$, for example. We also study the limit sets in the Thurston boundary of Teichm\"uller geodesic rays defined by quadratic differentials whose vertical foliations are obtained from the constructions mentioned above. We prove that such examples exist for which the limit is a cycle in the $1$-skeleton of the simplex of projective classes of measures visiting every vertex., Comment: 71 pages, 4 figures. v2: Some revisions and additions have been made. An example before the description of property P in section 3 was added. Section 6 was rewritten to address a mistake in the proof of Theorem 6.5 (called Theorem 6.7 in v1). Accepted for publication in J. Reine Angew Math

A recent preprint of S. Kojima and G. McShane [KM] observes a beautiful explicit connection between Teichm\"uller translation distance and hyperbolic volume. It relies on a key estimate which we supply here: using geometric inflexibility of hyperbolic 3-manifolds, we show that for $S$ a closed surface, and $\psi \in \text{Mod}(S)$ pseudo-Anosov, the double iteration $Q(\psi^{-n}(X),\psi^n(X))$ has convex core volume differing from $2n \text{vol}(M_\psi)$ by a uniform additive constant, where $M_\psi$ is the hyperbolic mapping torus for $\psi$. We combine this estimate with work of Schlenker, and a branched covering argument to obtain an explicit lower bound on Weil-Petersson translation distance of a pseudo-Anosov $\psi \in \text{Mod}(S)$ for general compact $S$ of genus $g$ with $n$ boundary components: we have $$ \text{vol}(M_\psi) \le 3 \sqrt{\pi/2(2g - 2 +n)} \, \| \psi \|_{WP}.$$ This gives the first explicit estimates on the Weil-Petersson systoles of moduli space, of the minimal distance between nodal surfaces in the completion of Teichm\"uller space, and explicit lower bounds to the Weil-Petersson diameter of the moduli space via [CP]. In the process, we recover the estimates of [KM] on Teichm\"uller translation distance via a Cauchy-Schwarz estimate (see [Lin])., Comment: 17 pages, 2 figures - incorporated corrections and comments

We use ending laminations for Weil-Petersson geodesics to establish that bounded geometry is equivalent to bounded combinatorics for Weil-Petersson geodesic segments, rays, and lines. Further, a more general notion of non-annular bounded combinatorics, which allows arbitrarily large Dehn-twisting, corresponds to an equivalent condition for Weil-Petersson geodesics. As an application, we show the Weil-Petersson geodesic flow has compact invariant subsets with arbitrarily large topological entropy., 39 Pages, 3 figures. Minor revisions

We define an ending lamination for a Weil-Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil-Petersson metric, these ending laminations provide an effective boundary theory that encodes much of its asymptotic CAT(0) geometry. In particular, we prove an ending lamination theorem (Theorem 1.1) for the full-measure set of rays that recur to the thick part, and we show that the association of an ending lamination embeds asymptote classes of recurrent rays into the Gromov-boundary of the curve complex. As an application, we establish fundamentals of the topological dynamics of the Weil-Petersson geodesic flow, showing density of closed orbits and topological transitivity., To appear, Geom. & Funct. Anal., referee's comments incorporated for final version

Given a closed hyperbolic 3-manifold T_\psi that fibers over the circle with monodromy \psi : S -> S, the monodromy $\psi$ determines an isometry of Teichmuller space with its Weil-Petersson metric whose translation distance ||\psi||_WP is positive. We show there is a constant K >= 1 depending only on the topology of S so that the volume of T_\psi satisfies ||\psi||_WP/K, Comment: 10 pages, 2 figures

Let S be a surface with genus g and n boundary components and let d(S) = 3g-3+n denote the number of curves in any pants decomposition of S. We employ metric properties of the graph of pants decompositions CP(S) prove that the Weil-Petersson metric on Teichmuller space Teich(S) is Gromov-hyperbolic if and only if d(S) = 3 the Weil-Petersson metric has higher rank in the sense of Gromov (it admits a quasi-isometric embedding of R^k, k >= 2); when d(S) = 3, and that no complete Riemannian metric of pinched negative curvature exists on Moduli space M(S) when d(S) >= 2., Comment: 23 pages, 1 figure