Orbital current signature using neutron diffraction

Abstract

We review the hallmarks of orbital loop currents in various correlated electron materials and how they have been evidenced using polarized neutron diffraction. Over the last 20 years, loop current signatures have been observed in high temperature copper oxide superconductors, iridates, copper oxides spin ladders and recently kagome vanadate superconductors. Such currents induce orbital magnetic moments within the unit cell of these quantum materials that can be detected through their interaction with the neutron spin. In addition to the usual description of orbital moments using point-like local magnetic moments, we here show an alternative description of the neutron magnetic cross-section involving the microscopic currents running between different atomic orbitals. We discuss the corresponding magnetic structure factors and the resulting quantitative differences between both approaches.

Figures (7)

• Figure 1: High-$\rm T_C$ superconducting (SC) cuprates phase diagram versus hole concentration showing broken symmetries at the pseudogap (PG) temperature, T$^*$, that can be accounted for by loop currents: (a) for $\rm YBa_2Cu_3O_{6+x}$ (YBCO) bilayer system and (b) for the single layer material $\rm HgBa_2CuO_{4+\delta}$ (Hg1201). The figures are adapted fromBourges21 where the ${\bf q}=0$ intra unit cell (IUC) magnetism was reviewed along with other techniques which reported broken symmetries at T$^*$ (see text). AF and CDW refer to antiferromagnetism and charge density wave, respectively. Data for the ${\bf q}=1/2$ magnetism in YBCO are included fromBounoua22Bounoua23. Absence of ${\bf q}=0$ IUC magnetism at low doping in Hg1201 has been recently reportedAnderson24.
• Figure 2: Temperature dependence:(a) Comparison of the temperature dependence in the same YBCO$_{6.6}$ sample of the total magnetic signal at (0.5,0,0) (${\bf q}=1/2$) as extracted from XYZ polarization analysis (XYZ-PA) (fromBounoua22) and the ${\bf q}=0$ IUC magnetic order measured at the (1,0,0) Bragg peak and represented by the inverse of the flipping ratio $1/FR$ (fromMangin17). (b) Comparison of the temperature dependence in YBCO$_{6.9}$ of the total magnetic signal at (0.5,0,0) (${\bf q}=1/2$) as extracted from XYZ-PA (fromBounoua23) and the one of the intra unit cell magnetic order (${\bf q}=0$) measured at the (1,0,0.25) Q-position measured for a similar doping (fromMangin15).
• Figure 3: $L$-dependence:(a)$L$-dependence of the ${\bf q}=0$ magnetism measured on four cuprate families (fromdeAlmeida12). The plot is made versus the wavevector $Q_L=\frac{2\pi}{c} L$ in order to compare the four different cuprates. (b)$L$-dependence of the ${\bf q}=1/2$ magnetism measured on two YBCO samples (fromBounoua23). The point at $Q_L \sim 0.15$Å$^{-1}$ is lower due to extra $L$ structure factor dependence. The same form factor is obtained for both signals corresponding to the same grey full line.
• Figure 4: Orbital loop currents phases: (a) Four different degenerated loop currents states. Each spontaneous circulating currents (black arrows) comprises two loops circulating clockwise (in gray) and anti-clockwise (in purple) leading to two magnetic moments along the c axis perpendicular to the CuO$_2$ planes. The 4 possible patterns are characterized by horizontal colored arrows, corresponding to 4 distinct anapole polar vectors centered at the Cu-site. (b) Uniform pattern of one anapole state with 20x20 CuO$_2$ unit cells, (c) Anapole vortex pattern of the 4 anapoles as proposed by VarmaVarma19 and (d) 2D magnetic texture with 20x20 unit cells paved by the 4 anapoles. The central cluster reproduces the ${\bf q}=1/2$ magnetism with 2x2 loop current patterns binding large ferro-anapolar domains corresponding to the ${\bf q}=0$ magnetism (fromBounoua22Bounoua23).
• Figure 5: Magnetic structure factors: Magnetic moment distribution for two ground states with (a) the anapole along x+y (pattern $\mathcal{P}_a$) and (d) the anapole along x-y (pattern $\mathcal{P}_b$). Magnetic structure factors calculated for point-like moment located at the center of the loop triangle: (b) for anapole along x+y (pattern $\mathcal{P}_a$) and (e) for anapole along x-y (pattern $\mathcal{P}_b$). Magnetic structure factors calculated from the currents: (c) for the anapole along x+y (pattern $\mathcal{P}_a$) and (f) for the anapole along x-y (pattern $\mathcal{P}_b$). The form factor $f(Q)$ is not included in the calculations. $(\hat{x},\hat{y},\hat{z})$ defines an orthonormal coordinate system for the tetragonal lattice of cuprates.