Bypassing Dynamical Freezing in Artificial Kagome Ice

V. Schánilec, B. Canals, V. Uhlíř, L. Flajšman, J. Sadílek, T. Šikola, and N. Rougemaille

Phys. Rev. Lett. 125, 057203 – Published 31 July 2020

Abstract

Spin liquids are correlated, disordered states of matter that fluctuate even at low temperatures. Experimentally, the extensive degeneracy characterizing their low-energy manifold is expected to be lifted, for example, because of dipolar interactions, leading to an ordered ground state at absolute zero. However, this is not what is usually observed, and many systems, whether they are chemically synthesized or nanofabricated, dynamically freeze before magnetic ordering sets in. In artificial realizations of highly frustrated magnets, ground state configurations, and even low-energy manifolds, thus remain out of reach for practical reasons. Here, we show how dynamical freezing can be bypassed in an artificial kagome ice. We illustrate the efficiency of our method by demonstrating that the a priori dynamically inaccessible ordered ground state and fragmented spin liquid configurations can be obtained reproducibly, imaged in real space at room temperature, and studied conveniently. We then identify the mechanism by which dynamical freezing occurs in the dipolar kagome ice.

Received 21 February 2020
Revised 1 July 2020
Accepted 10 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.057203

Physics Subject Headings (PhySH)

Frustrated magnetism Spin ice Spin liquid

Kagome lattice

Magnetic force microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

V. Schánilec ^1,2, B. Canals¹, V. Uhlíř ², L. Flajšman², J. Sadílek², T. Šikola^2,3, and N. Rougemaille ¹

¹Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
²Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
³Institute of Physical Engineering, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, Brno, 616 69, Czech Republic

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 125, Iss. 5 — 31 July 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) The top and bottom panels represent the spin and charge states in each of the four phases, averaged over a large number of equilibrated spin configurations. In the top panel, the length of the arrows represents the mean value of the spins after averaging. This length is zero in the PM and SL1 phases, exactly $1 / 3$ in the SL2 manifold, and 1 in the LRO ground state. The shaded triangles give the spin unit cell. In the bottom panel, the blue and red dots represent the mean value of the magnetic charges after averaging (blue codes for $- 1$ and red for $+ 1$ ). In the PM and SL1 phases, the average charge is zero everywhere, whereas it is $\pm 1$ in the SL2 and LRO phases. (b) Schematics of the spin dynamics involved in the SL1 and SL2 phases. Examples of possible spin flips and loop moves are highlighted in blue.
Reuse & Permissions
Figure 2
(a) Schematics illustrating how a notch located at a kagome vertex lifts the sixfold degeneracy between ice rule states. The two vertices in blue have a lower energy than the four red vertices. (b) Variation of the energy gap $E_{2} - E_{1}$ as a function of the depth of the notch for 5-, 10-, and 25-nm-thick nanomagnets. The vertex energy is given in arbitrary units (a.u.).
Reuse & Permissions
Figure 3
(a) Electron micrograph of a lattice showing the positions of the notches. (b),(c) Magnetic image and resulting spin-charge configuration for a LRO imprinted state and a notch size of 200 nm (b) and 100 nm (c). The two lattices have undergone the exact same demagnetization procedure. In the spin-charge configurations, the spins are represented by black arrows, the vertex charge by a red or blue dot, and the charge domains appear in white or green. 7% (b) and 39% (c) of the vertices break the notch rule. Scale bar is $6 μ m$ . (d) Temperature dependence of the first seven spin-spin correlators. The dots are deduced from the experimental images reported in (b) and (c), illustrating how the effective temperature is affected by the notch size. Insets show the magnetic structure factors associated to the two experimental spin configurations. $J_{1}$ is the coupling strength between two nanomagnets not sharing the notch; see Supplemental Material [46].
Reuse & Permissions
Figure 4
(a),(b) Magnetic image and resulting spin-charge configuration for a LRO imprinted state and a notch size of 200 nm (a), and for a lattice with no notch (b). Color code is the same as in Fig. 3. Comparing the two magnetic images reveals the efficiency of the notch strategy. In (a), 4% of the vertices break the notch rule (positions are indicated by a circle).
Reuse & Permissions

Physical Review Letters