Session Z54: Magnetic Domains and Domain Walls

Surface acoustic waves assisted domain wall depinning from patterned notches in micron sized wires.

Surface acoustic waves (SAW) create high frequency strain fields that interact with ferromagnetic (FM) thin films via the magneto-strictive coefficients. SAW decrease the coercive field, change magnetization direction, boost domain wall (DW) velocities, drive precessional switching and substantially increase the depinning probability of DW from randomly distributed pinning sites. Here, we investigate SAW induced depinning of DWs in periodic notches, positioned at nodes and antinodes of the SAW, in a [Co(0.4nm)/Pt(0.6nm)]₅ multilayer using both magneto-optical Kerr effect (MOKE) microscopy and scanning MOKE. These notches act as pinning potential barriers for the DW motion. Characterizing the individual pinning parameters of each notch, specifically the energy barrier (E₀) and intrinsic critical field (H₀), we then turn to the effect of high frequency SAW on these well characterized pinning sites. We find the depinning probability doubles at SAW excitations of 2.5V (corresponding to a strain amplitude of ~1.4×10^-4) in most of the pinning sites and a 4-10 fold increase at 4V excitation. We model this behavior by taking into account the SAW induced changes in the anisotropy and the SAW induced effective magnetic field.      

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The spin-orbit torque (SOT) generated when a charge current is passed through a heavy metal with sizeable spin-orbit coupling [1] has attracted significant research interest, given that it gives rise to the efficient movement of novel magnetic textures, such as chiral domain walls and skyrmions. Here, we discuss an experimental study of the SOT-induced motion of magnetic stripe domains in Pt/Co/Pt and Pt/Co/Ni/Pt thin-film heterostructures that possess an interfacial Dzyaloshinskii-Moriya interaction that favors the formation of chiral Neel-type domain walls [2]. In agreement with previous reports, we find that the domains exhibit a significant transverse velocity relative to driving force of the SOT. In these past works, this behavior was attributed to the Magnus force-like skyrmion Hall effect exhibited by the stripe domain topology (equivalent to that of a half-skyrmion) [3-5]. However, magnetometry and ferromagnetic resonance spectroscopy measurements suggest that the theoretically predicted transverse motion of stripe domains in our samples may be too large to be explained by the skyrmion Hall effect. Analytically modeling the steady-state dynamical reconfiguration of the half-skyrmion profile induced by SOT, we demonstrate how motion with similar directionality and symmetry as the skyrmion Hall effect can originate – further highlighting the sensitivity of SOT to the local orientation of the domain wall magnetization profile. 

[1] M.I. Dyakonov and V.I. Perel, JTEP Lett. 13, 467 (1971).

[2] A. Fert, Mat. Sci. Form. 59-60, 439 (1990)

[3] S. Zhang, X. Zhang, et al., Sci. Adv. 6, 1876 (2020).

[4] S. Yang, K.-W. Moon, et al., Adv. Quant. Tech. 4, 2000060 (2021).   

Unraveling the solitonic nature of spin-stripes to skyrmion transition in a Fe/Gd thin film.

Understanding phase-transition of one-dimensional spin-stripes to two-dimensional skyrmions in magnetic thin films exhibiting enigmatic display of soliton physics, is essential for the development of both fundamental and applied sciences. Unlike in antisymmetric Dzylozhinskii-Moriya interaction (DMI) materials of fixed chirality, the field evolution of stripe-structures in dipolar interaction mediated thin-films has remained unresolved and is a topic of great potential for future research. Herein we observe using X-ray resonant scattering that stripes in a dipolar interaction dominant Fe/Gd film behave like finite-sized chiral soliton lattice (CSL) exhibiting discrete jumps in periodicity with applied field. Our results also show absence of discrete jumps after CSL-to-skyrmion transition thus providing insights into the the role of chirality and dimensionality in different topological magnetic structures.   

Nitrogen-vacancy center-based spin-echo measurement protocol to detect magnetic domain wall dynamics

The nitrogen-vacancy (NV) center in diamond is an atomic defect comprised of a vacancy adjacent to a substitutional nitrogen. The electronic spin of the negatively charged NV center (NV[-]) has widely been used in sensing and imaging magnetic fields optically. The NV[-] center electronic spin state can be initialized optically and its spin-dependent photoluminescence sensitively measured. The NV[-] spin exhibits a long coherence time even at room temperature. The spin decoherence time is mainly limited by the inhomogeneous and time-varying magnetic fields generated by surrounding paramagnetic spins and ¹³C nuclear spins. The low-frequency dephasing can be eliminated by using the Hahn spin-echo protocol. An NV[-] center close to a magnetic domain wall (DW) in a ferromagnet experiences a constant dipolar field if the DW is static throughout the Hahn echo sequence with respect to the NV[-] center. However, a moving/oscillating DW will create time-varying dipolar field sensed by the NV[-] spin. This time-varying field will cause dephasing of NV[-] spin thereby decreasing the spin-echo amplitude. A spin-echo experiment synchronized to the motion of a DW induced by a pulsed current enables the measurement of a rapidly moving magnetic texture. This method can also characterize the pinning potential through the measurement of the thermally excited dynamics of the pinned DW.   

Nonlinear Optical Studies of Neel Order and Magnetic Domain Structure in Antiferromagnetic RuO2

A challenge in antiferromagnetic (AF) spintronics is the lack of suitable table-top techniques to determine spin orientations and magnetic domain structure. RuO2, a collinear AF, has been recently theoretically predicted to exhibit unexpected properties such as anomalous Hall effect [1] and a linear magneto-optical effect [2] that arise from the fact that opposite magnetic sublattices in RuO2 are connected by a combination of time reversal and rotation operations.  We use a modified Onsager’s relation suitable for AF materials to show that the same symmetry property results in a symmetric second order optical susceptibility tensor. We use optical second harmonic generation (SHG) to study Neel order and spin domains in thin RuO2 films. Our results show that spins are oriented along the c-axis, resulting in magnetic space group P4₂’/mnm’. However, small canting of the spins is seen in thin films. Interestingly, strain is seen to play an important role in the AF domain size. Whereas AF domain sizes in RuO2 grown on TiO2 substrates are as small as few tens of nm, domain sizes in films grown on r-Al2O3 are much larger than a micron. We will discuss results from linear magneto-optical imaging of spin domains in RuO2. [1] Sci. Adv. 6, eaaz8809 (2020) [2] Phys. Rev. B 104, 024401(2021).   

Controlling magnetic configuration in soft-hard bilayers probed by polarized neutron reflectometry

Hard/soft magnetic bilayer thin films have been widely used in data storage technologies and permanent magnet applications. The magnetic configuration and response to temperatures and magnetic fields in these heterostructures are considered to be highly dependent on the interfacial coupling. However, the intrinsic properties of each of the layers, such as the saturation magnetization and layer thickness, also strongly influence the magnetic configuration. Changing these parameters provides an effective method to tailor magnetic properties in composite magnets. Here, we use polarized neutron reflectometry (PNR) to experimentally probe the interfacial magnetic configurations in hard/soft bilayer thin films: L1₀-FePt/A1-FePt, [Co/Pd] /CoPd, [Co/Pt] /FeNi and L1₀-FePt/Fe at room temperature, which all have a perpendicular magnetic anisotropy in the hard layer. These films were designed with different soft and hard layer thicknesses ( and ) and saturation magnetization ( and ), respectively. The influences of an in-plane magnetic field () and temperature (T) are also studied using a L1₀‑FePt/A1-FePt bilayer sample. Comparing the PNR results to micromagnetic simulations reveals that the interfacial magnetic configuration is highly dependent on ,  and the external factors ( and T), and has a relatively weak dependence on  and . Key among these results, for thin , the hard and soft layers are rigidly coupled in the out-of-plane direction, then undergo a transition to relax in-plane. This transition can be delayed to larger  by decreasing  Understanding the influence of these parameters on the magnetic configuration is critical to designing functional composite magnets for applications.   

Formation of Domains and magnetic Reversal in the canted Antiferromagnet α-Fe2O3

Antiferromagnets are at the forefront of research in spintronics and demonstrate high potential for revolutionizing memory technologies. Here, we study the canted antiferromagnet α-Fe₂O₃ using imaging based on x-ray magnetic linear dichroism (XMLD) and spin Hall magnetoresistance (SMR) measurements in α-Fe₂O₃/Pt Hall cross devices.

The domain structure forms a multi-domain state at zero field and depends strongly on the magnetic field. Combining angle-dependent SMR and XMLD measurements, we can find, that the internal destressing fields driving the formation of domains do not follow the hexagonal crystal symmetry of α-Fe₂O₃. Furthermore, the canting induces a weak ferromagnetic moment which lifts the degeneracy of the sublattices and consequently the orientation of the Néel vector with respect to the field resulting in hysteresis. The irreversibility upon switching the polarity of the field elucidates the formation of antiferromagnetic as well as ferromagnetic domain walls at low magnetic fields. These insights serve as a foundation for further studies of electrical and optical manipulation of the domain structure of canted antiferromagnets.   

Resistance of single magnetic domain walls and its size effect in half-metallic CrO2 epitaxial nanostructures

Magnetic domain walls can be used to induce large magnetoresistance (MR) and hence are viewed as active electron transport agents, particularly in half-metallic solids with 100% spin polarization. In this talk, we will report a study of the size effect on excess resistance induced by a single magnetic domain wall in a one-dimensional half-metallic CrO₂ nanoscale conductor. We grow an asymmetric built-in constriction whose channel width (d) ranges from 30 to 200 nm and measure their MR. We observe repeatable and reversible MR jumps by sweeping a magnetic field. The MR jumps are interpreted as the domain-wall resistance (DMR) induced by the creation and annihilation of a single magnetic domain wall near the constricted neck. We confirm the field dependence of the magnetic configuration through micromagnetic simulation studies. Our results suggest a large size effect of d on the DMR, as the DMR scales with d as d^-1.87±0.32. Accordingly, we predict that the MR ratio of a simple CrO₂ nanowire impregnated with a constriction at a 150 nm² cross section could reach 100%. This large MR far exceeds that of a conventional ferromagnetic nanowire, confirming the role of half metallicity on enhanced magneto transport. The large DMR can be taken advantage of in the construction of spintronic devices such as magnetic sensing or memory.

    

Ultrashort Spin Waves Emission by an Antiferromagnetic Domain Wall Driven by Spin Current

Antiferromagnets (AFMs) have great benefits for spintronic applications [1] such as high frequencies (up to THz) [2], high speeds (up to tens of km/s) of magnetic excitations, and field-free operation. Advanced devices will require high-speed propagating spin waves (SWs) as signal carriers, i.e. SWs with high k-vectors, the excitations of which remain challenging.

We show that a domain wall (DW) in AFM with an anisotropy or DMI, driven by spin current, can be a source of such propagating SWs with high frequencies and shorter wavelengths, comparable to the exchange length of the AFM. In the proposed generator, the spin current, with polarization directed along the principal crystal axis, excites the precession of the Néel vector within the DW. The threshold current is defined by the value of the in-plane anisotropy, and the frequency of the DW precession is tuneable by the strength of the spin current. We show that the above precession of the DW leads to robust emission of high-frequency propagating SWs into the AFM strip with very short wavelengths comparable to the exchange length, which is hard to achieve by any other method.

[1] O. Gomonay et al., Nat. Physics 14, 213 (2018)

[2] R. Khymyn et al., Sci. Rep. 7, 43705 (2017); O. Sulymenko et al., Phys. Rev. Appl. 8, 064007 (2017)   

Resistance fluctuations probing the magnetic polaron state in the antiferromagnetic insulator Eu5In2Sb6

We investigate the nonsymmorphic Zintl semiconductor Eu₅In₂Sb₆. Zintl phases are valence precise intermetallic phases formed by cations and covalently bonded (poly)anionic structures containing post-transition metals. The electron transfer between those two entities gives rise to an insulating state, whereas the inclusion of rare-earth elements allows for magnetism that may promote new quantum ground states. Eu₅In₂Sb₆ is a rare example of an antiferromagnet exhibiting a colossal magnetoresistance (CMR) effect, which may be driven by the presence of magnetic polarons. Upon cooling, a magnetic transition occurs at the Neel temperature T_N1 = 14 K, which can be suppressed by a magnetic field. While the negative MR is small at room temperature, it rapidly increases with decreasing temperature and ultimately peaks at -99.999% for B  = 9 T at T_N1, which is one of the largest observed CMR in a stoichiometric antiferromagnet [1]. The magnetic ground state below another transition temperature T_N2 = 7 K, however, is complex and yet to be fully understood. As a powerful probe to test possible scenarios for explaining the CMR effect, we employ resistance fluctuation (noise) spectroscopy and analyze the observed generic 1/f-type noise in terms of a model of magnetic polarons.

[1] P. Rosa et al., npj Quantum Mater. 5, 52 (2020)   

Magnetic Domain Structures on Gd(0001)/W(110) Films

Due to their partially filled 4f shell which are coupled by the RKKY interaction, rare earth metals exhibit long-range magnetic order. Depending on the sign of the RKKY coupling and details of the sample geometry many different domain structures have been observed. For example, spin-resolved STM studies of Dy(0001) thin films on W(110) revealed a six-fold symmetric magnetic domain structure [1]. Here we report on similar experiments on Gadolinium (Gd) films epitaxially grown on W(110). Gd is a ferromagnetic metal with a Curie temperature of 293 K.  Its half-filled 4f shell results in an almost spherical charge distribution and therefore a rather small magnetic anisotropy in comparison other rare earth metals [2].

Earlier spatially averaging experiments [2] suggest that Gd(0001) films on W(110) exhibit a thickness-dependent spin reorientation transition at around 40 nm from in-plane at thin films to out-of-plane for thicker. Our investigation on Gd(0001) films grown on W(110) indeed show a rather rich spin structure in STM/STS studies. For rather thin film thicknesses we observe large in-plane domains (several µm large) oriented along the [1-10] direction of the W(110) substrate. Above approximately 100 atomic layers, a significant contribution of the out-of-plane magnetization emerges. This leads to spin spiral-like magnetic domains with in-plane as well as out-of-plane components. The periodicity of these zig-zag stripe domains increases with increasing film thickness from (50 ± 10) nm up to (120 ± 40) nm. We will discuss the transition of the magnetic structure in dependence of the Gd film thickness.

[1] Berbil-Bautista et. al., Phys. Rev. B 76, 064411 (2007)

[2] Berger et. al., PhysRevB.52.1078 (1995)   

Antiferromagnetic coupling of anti-phase domains

NiMn-based Heusler compounds show a variety of interesting functional properties such as the ferromagnetic shape memory effect or the magnetocaloric effect. Since the magnetic properties are very sensitive to the degree of structural order in these systems [1], understanding the correlation of these two ordering parameters is crucial.

In these systems the magnetic moments are mainly carried by the Mn atoms, which interact ferromagnetically in the L2₁-ordered state and antiferromagnetically for neighbouring Mn spins. Using TEM and Lorentz TEM a reversal of magnetization at structural anti-phase domain boundaries (APBs) has been observed in Ni₂MnAl_0.5Ga_0.5 implying that structural and magnetic domains are identical [2]. To clarify the reason of this relation and to study the mechanism of coupling of ferromagnetic domains across APBs, we investigated Ni₂MnAl and Ni₂MnAl_0.5Ga_0.5 powder samples in distinct ordering states via magnetic small-angle neutron scattering, giving access to the magnetization microstructure. With an external magnetic field applied we observe a redistribution of intensity along the field direction, implying that the domains couple antiferromagnetically.

[1] P. Neibecker et al., Appl. Phys. Lett. 105, 261904 (2014)

[2] H. Ishikawa, Acta Mater. 56, 4789 (2008)   

The domain-wall motion driven by a rotating field in a ferrimagnet

We theoretically study a ferrimagnetic domain-wall motion driven by a rotating magnetic field. We find the dynamics of a ferrimagnetic domain wall can be classified into two regimes. When the frequency is lower than a certain critical frequency set by the field magnitude, there is a stationary solution for the domain-wall dynamics, where a domain-wall in-plane magnetization rotates in-phase with the external field. The field-induced precession of the domain wall gives rise to the translational motion of the domain wall via the gyrotropic coupling between the domain-wall angle and position. In this phase- locking regime, a domain-wall velocity increases as the frequency increases. When the frequency exceeds the critical frequency, a domain-wall angle precession is not synchronous with the applied field. In this phase-unlocking regime, a domain wall velocity decreases as the frequency increases. Moreover, the direction of the domain-wall motion is found to be reversed across the angular compensation point where the net spin density of the ferrimagnet changes its sign. Our work suggests that the dynamics of magnetic solitons under time-varying biases may serve as platform to study critical phenomena.   

Magneto-transport and magnetic textures in Ho/FeCoGd/β-W multilayers with additive chiral exchange

Here we report on the evaluation of interface-driven magnetic interactions in a uniquely designed multilayer where each magnetic layer of two antiferromagnetically coupled sublattices of 3d and 4f moments is sandwiched between the layers of β-tungsten and holmium whose spin Hall angles are large but opposite in sign. The atomic and magnetic periodicity of these multilayers is established by polarized neutron reflectivity measurements and the presence of a stripe domain spin texture of zero remanence with x-ray photoelectron microscopy. Measurements of the Hall resistivity (ρ_xy(T, H))  together with static magnetization (M(T,H)) over a broad range of temperature (T) and magnetic field (H) indicate impending compensation between 3d and 4f sublattices at T > 350 K and a distinct topological contribution to ρ_xy. It is argued that this topological effect draws its strength from the interfacial Dzyaloshinskii – Moriya Interaction.   

A $J_1-J_3$ Heisenberg kagome lattice with an order by disorder induced Potts order

Motivated by the physical properties of Vesignieite BaCu$_3$V$_2$O$_8$(OH)$_2$, we study the $J_1-J_3$ Heisenberg model on the kagome lattice, that is proposed to describe this compound for $J_1<0$ and $J_3\gg|J_1|$. The nature of the classical ground state and the possible phase transitions are investigated through analytical calculations and parallel tempering Monte Carlo simulations. For $J_1<0$ and $J_3>\frac{1+\sqrt{5}}4|J_1|$, the ground states are not all related by an Hamiltonian symmetry. Order appears at low temperature via the order by disorder mechanism, favoring collinear configurations and leading to an emergent $q=4$ Potts parameter to a finite temperature phase transition. For $J_3$ between $\frac14|J_1|$ and $\frac{1+\sqrt{5}}4|J_1|$, the ground state goes through a succession of semi-spiral states, possibly giving rise to multiple phase transitions at low temperatures. Effect of quantum fluctuations are studied through linear spin wave approximation and high temperature expansions of the $S=1/2$ model.