Diagnosing phases of magnetic insulators via noise magnetometry with spin qubits

Two-dimensional magnetic insulators exhibit a plethora of competing ground states, such as ordered (anti)ferromagnets, exotic quantum spin liquid states with topological order and anyonic excitations, and random singlet phases emerging in highly disordered frustrated magnets. Here we show how single-spin qubits, which interact directly with the low-energy excitations of magnetic insulators, can be used as a diagnostic of magnetic ground states. Experimentally tunable parameters, such as qubit level splitting, sample temperature, and qubit-sample distance, can be used to measure spin correlations with energy and wave-vector resolution. Such resolution can be exploited, for instance, to distinguish between fractionalized excitations in spin liquids and spin waves in magnetically ordered states, or to detect anyonic statistics in gapped systems.

Figure 1

(a) Experimental setup showing a spin qubit located at a distance $d$ from a two-dimensional magnetic insulator. (b) Detection of low-energy $S=1$ excitations in magnetically ordered phases using a single-spin qubit. (c) Schematic depiction of the detection of $S=1/2$ fractionalized excitations in spin liquids. (d) Detection of low-energy excitations in disordered valence bond solids.

Figure 2

The honeycomb lattice of the Kitaev model. ${\mathbf{n}}_1$ and ${\mathbf{n}}_2$ are the two Bravais lattice vectors, and ${\delta }_i(i=1,2,3)$ indicate nearest neighbors. The orange and gray circles correspond to the two sublattices. The rounded triangle at each site shows the four Majorana fermions used to write the Pauli spin operators. The free $c$ Majorana fermion is indicated by the brown dot. The red, green, and blue dots refer to $b_i^x, b_i^y$, and $b_i^z$ Majorana fermions, and the corresponding bonds denote the bond variables $u_{ij}^{\mu }$ along the $x,y$, and $z$ links, respectively. $W_p$ is the flux operator defined in the main text, $W_p=-1$ correspond to gapped vison excitations.

Figure 3

Schematic diagram indicating different regimes for $1/T_1$ as a function of $d, T$, and $\omega$ valid for Dirac spinons, see Eqs. (25) and (26), and spinon Fermi surfaces, see Eqs. (28) and (30).

Figure 4

The power-law distribution of couplings $J$, with the level structures of a pair of weakly coupled impurity spins at $J>h$ and $J<h$ showing the transitions that contribute to the dynamic spin-structure factor.