Research Article: Spin Solid versus Magnetic Charge Ordered State in Artificial Honeycomb Lattice of Connected Elements

Date Published: January 04, 2018

Publisher: John Wiley and Sons Inc.

Author(s): Artur Glavic, Brock Summers, Ashutosh Dahal, Joseph Kline, Walter Van Herck, Alexander Sukhov, Arthur Ernst, Deepak K. Singh.


The nature of magnetic correlation at low temperature in two‐dimensional artificial magnetic honeycomb lattice is a strongly debated issue. While theoretical researches suggest that the system will develop a novel zero entropy spin solid state as T → 0 K, a confirmation to this effect in artificial honeycomb lattice of connected elements is lacking. This study reports on the investigation of magnetic correlation in newly designed artificial permalloy honeycomb lattice of ultrasmall elements, with a typical length of ≈12 nm, using neutron scattering measurements and temperature‐dependent micromagnetic simulations. Numerical modeling of the polarized neutron reflectometry data elucidates the temperature‐dependent evolution of spin correlation in this system. As temperature reduces to ≈7 K, the system tends to develop novel spin solid state, manifested by the alternating distribution of magnetic vortex loops of opposite chiralities. Experimental results are complemented by temperature‐dependent micromagnetic simulations that confirm the dominance of spin solid state over local magnetic charge ordered state in the artificial honeycomb lattice with connected elements. These results enable a direct investigation of novel spin solid correlation in the connected honeycomb geometry of 2D artificial structure.

Partial Text

Two dimensional artificial honeycomb lattice provides a facile platform to explore many novel properties of magnetic materials in one system.1, 2 It includes the ice analog of magnetism, spin ice, spin liquid, and an unusual spin solid state, depicted by the distribution of magnetic vortex loops of opposite chiralities.3, 4 The complex variety of entropy controlled magnetic phases that are predicted to arise in an artificial honeycomb lattice as a function of reducing temperature cannot be realized in a “3D” bulk material of geometrically frustrated origin. According to recent theoretical reports, the honeycomb lattice behaves as a paramagnet at high temperature, corresponding to a gas of ±1 and ±3 magnetic charges.5, 6 As temperature is reduced, the system crosses over into a spin‐ice type state, manifested by “two‐in & one‐out” (or vice‐versa) configuration where two of the moments along the honeycomb element point to the vertex and one points away from the vertex (or vice‐versa). At further reduction in temperature, a new ordering regime, characterized by the topological “charge order” of ±1 magnetic charges, develops (depicted in Figure 3). Thermal energy is expected to be comparable to the strength of the dipolar interaction (≈D) in the charge ordered regime. The transition from a local spin ice to the charge ordered state is chiral in nature, as a number of mobile closed loops of each chirality develop.3, 5, 6 At much lower temperature, the system is predicted to evolve into a “spin‐ordered” state of chiral vortex loops with zero entropy density, also called the “spin solid” state. It represents a novel phase of magnetic matter with zero entropy and magnetization.7

The fabrication of artificial honeycomb lattice samples involved the synthesis of hexagonal diblock copolymer templates and near parallel deposition of permalloy material on top of the honeycomb structured silicon substrates in an ultrahigh vacuum chamber. Similar diblock copolymer templates are extensively used to fabricate nanostructured materials.15 Under suitable physical conditions, a diblock copolymer tends to self‐assemble where one component tends to develop long‐range periodic structures.16, 17 Additionally, the flexibility in tuning the structural properties and lattice parameters, by simply varying the composition and molecular weight of the diblock copolymer, allow to create a plethora of nanomaterials.18, 19 Some of the notable examples include the fabrication of nanodot, nanoring, and nanoparticle assemblies.15, 17, 19, 20 More recently, researchers have used diblock templates and glancing angle deposition to create directional hierarchical structures of metal nanoparticles.17 An atomic force microscopy image of a typical honeycomb sample is shown in Figure1a (see the Experimental Section for detail). A small angle X‐ray scattering measurement in the grazing incidence angle configuration (GISAXS) confirms the high structural quality of the sample. GISAXS measurements can provide information about the structural properties of a system.21, 22, 23 The GISAXS measurements were performed using a Ga Kα source with a wavelength of 1.34 Å at an incident angle of 0.15°. A 1 mm thick stainless steel foil was used to attenuate the reflected beam. As shown in Figure 1b, GISAXS measurements show a primary spacing of 31 nm, which is consistent with the atomic force microscopy image within the calibration error. The second and third peaks visible in the scattering pattern occur at multiples of 3 and 2 of the primary peak, corresponding to a 2D hexagonal lattice. The higher order peaks seem to be overshadowed by the background in the data, which is most likely arising due to the possible inhomogeneity in the sample. The dimension of the constituting element of the honeycomb lattice is not perfect, rather varies a little bit from the average size of 12 nm in length and 5 nm in width. However, the small variation in the element size is not expected to affect the underlying physics much, as the interelemental energy will only change marginally (less than 2 K for a variation of up to 2 nm). From the modeling of the GISAXS data, the large domain size of long‐range structural order in the honeycomb lattice was confirmed (paracrystal correlation length of 250 nm).

In summary, we have presented experimental investigation of magnetic correlations at low temperature in newly designed artificial honeycomb lattice. The experimental results were independently verified by the temperature‐dependent micromagnetic simulations. Among the various magnetic phases that are expected to arise as a function of reducing temperature in artificial honeycomb lattice, magnetic charge ordered state and spin solid state hold greater significances.37 Both states are somewhat unique to this 2D structure that involve chiral vortex loops. While the charge ordered state is expected to develop below magnetostatic dipolar interaction temperature, given by D ≈ kBT, the spin solid state arises as T → 0 K. Based on our experimental and theoretical researches, we infer that the magnetic moments along the honeycomb element in the newly fabricated honeycomb lattice tend to develop the spin solid state, compared to magnetic charge ordered state (ice‐2 phase), as temperature reduces below the interelemental energy, T ≈ 12 K. Our results also suggest the highly competing nature of novel magnetic phases in artificial honeycomb lattice of connected elements. Future experimental researches, such as the estimation of entropy per element, are desirable to further understand the development of the spin solid state6, 7 A real time imaging technique, such as Lorentz microscopy, can provide direct evidence of spin solid state in this system. Future efforts in this regard are specially desirable.

Sample Fabrication and Characterizations: Fabrication of artificial honeycomb lattice involves the synthesis of porous hexagonal diblock template on top of a silicon substrate, calibrated reactive ion etching using CF4 gas to transfer the hexagonal pattern to the underlying silicon substrate, and the deposition of magnetic material (permalloy) on top of the uniformly rotating substrate in near‐parallel configuration (≈1°) to achieve the 2D character of the system. The sample fabrication process utilized diblock copolymer polystyrene(PS)‐b‐poly‐4‐vinyl pyridine (P4VP) of molecular weight 23K Dalton with the volume fraction of 70% PS and 30% P4VP. The self‐assembly of diblock copolymer was driven by microphase separation arising from the immiscibility of the polymer blocks. A microphase separated diblock copolymer film can take various forms from spherical to cylindrical to lamellar, depending upon the volume fraction of each block. At this volume fraction, the diblock copolymer tends to self‐assemble, under right condition, in a hexagonal cylindrical structure of P4VP in the matrix PS.38 A 0.5% PS‐b‐P4VP copolymer solution in toluene was spin casted onto cleaned silicon wafers at 2500 rpm for 30 s and placed in vacuum for 12 h to dry. The samples were solvent annealed at 25 °C for 12 h in a mixture of THF/toluene (80:20 v/v) environment. The process results in the self‐assembly of P4VP cylinders in a hexagonal pattern within a PS matrix. The average diameter of a P4VP cylinder was ≈ 12 nm and the center‐to‐center distance between two cylinders was ≈ 30 nm, also consistent with that reported by Park et al.38 Submerging the samples in ethanol for 20 min releases the P4VP cylinders yielding a porous hexagonal template. The diblock template was used as a mask to transfer the topographical pattern to the underlying silicon substrate. The top surface of the reactively etched silicon substrate resembles a honeycomb lattice pattern. This property is exploited to create metallic honeycomb lattice by depositing permalloy, Ni0.81Fe0.19, in near parallel configuration in an electron‐beam evaporation. For this purpose, a new sample holder was designed and setup inside the e‐beam chamber. The substrate was rotated uniformly about its axis during the deposition to create uniformity. This allowed evaporated permalloy to coat the top surface of the honeycomb only, producing the desired magnetic honeycomb lattice with a typical element size of 12 nm (length) × 5 nm (width) × 8 nm (thickness). Atomic force microscopy image of a typical honeycomb lattice is shown in Figure 1a (also see Figure S6 in the Supporting Information where it is shown that the average roughness in the thickness of a honeycomb element is less than 0.5 nm). The center‐to‐center spacing between neighboring honeycombs is ≈ 30 nm. Thus, each honeycomb is about 30 nm wide. Further details about the fabrication procedure can be found somewhere else. GISAXS, at an incident angle of 0.15o, confirmed the good structural quality of the sample.

The authors declare no conflict of interest.




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