Turn-on of Current-Induced Spin Torque upon Noncollinear Antiferromagnetic Ordering in Delafossite PdCrO2

Abstract

We report measurements of the current-induced spin torque produced by the delafossite antiferromagnet PdCrO2 and acting on an adjacent ferromagnetic permalloy layer. The spin torque increases strongly as the temperature is reduced through the Neel temperature, when the PdCrO2 transitions from a paramagnetic phase to a noncollinear antiferromagnetic state. This result is qualitatively consistent with density functional theory calculations regarding how spin-current generation changes upon antiferromagnetic ordering in PdCrO2.

Figures (4)

• Figure 1: Structural, electronic and magnetic properties of PdCrO$_2$ samples. a, Schematic depicting the crystal structure of PdCrO$_2$. The material consists of alternating atomic planes occupied of chromium atoms in green and palladium atoms in red separated by oxygen atoms in black. The arrows represent spin orientations in the Cr layers. b, Angle-resolved photoemission spectroscopy intensity maps of the Fermi surface of a $3$ nm PdCrO$_2$ sample collected using $21.2$ eV photons at $6$ K. c, Temperature-dependent resistivity of a $7$ nm thick PdCrO$_2$ sample. d, First derivative of resistance with respect to temperature for a $7$ nm thick PdCrO$_2$ film. e, Hall response as a function of temperature for the $7$ nm thick PdCrO$_2$ film. A dc current of $100 \mu$A is applied and the magnetic field is swept out of the plane.
• Figure 2: Second harmonic Hall measurements on PdCrO$_2$ ($7$ nm) / Py ($5$ nm). a, Schematic for the Hall devices containing a PdCrO$_2$ / Py bilayer. For second-harmonic Hall measurements, the external magnetic field is applied in plane at an angle $\phi$ relative to the applied electric field $E$. The PdCrO$_2$ and Py layers are shown in teal and red, respectively. b, Second harmonic Hall voltage as a function of $\phi$ at $10$ K. The strength of the magnetic field is $800$ Oe. The $\cos\phi$ ($D_Y$) and $\cos\phi \cos2\phi$ ($F_Y$) components are shown in red and blue, respectively. A $sin2\phi$ component caused is shown in purple. c, Magnetic-field dependence of the $\cos\phi$ component of the second harmonic Hall voltage ($V_{XY}^{2\omega}$) at $10$ K. The solid curve in teal is a sum of voltages from damping-like torque (orange), the ordinary Nernst effect (blue) and the spin Seebeck effect (a constant term). d, Magnetic field dependence of the $\cos\phi \cos2\phi$ contribution to the second harmonic Hall voltage as a function of $1/B_{ext}$ at $10$ K. e, Magnetic field dependence of the $\cos\phi$ component of the second harmonic Hall voltage ($V_{XY}^{2\omega}$) at $50$ K. The solid curve in teal is a linear fit to the $D_Y$ component at $50$ K. f, Magnetic field dependence of the $\cos\phi \cos2\phi$ contribution to the second harmonic Hall voltage as a function of $1/B_{ext}$ at $50$ K.
• Figure 3: Spin-orbit-torque generation in PdCrO$_2$ ($2.7$ nm) / Py ($5$ nm) thin film measured with longitudinal ST-FMR. a, An example ST-FMR scan at $10$ K, where the longitudinal mixing voltage ($V_{mix}$) is plotted against external magnetic field ($H_{ext}$). Symmetric and anti-symmetric components are represented by red and blue curves, respectively. The microwave current applied has a frequency of $9$ GHz and a power of $18$ dBm. The external magnetic field is oriented at $45^\circ$ to the current. b, Anti-symmetric mixing voltage ($V_A$) and symmetric mixing voltage ($V_S$) as a function of magnetic field angle ($\phi$). Blue and red curves are fits to $\sin2\phi \cos\phi$. c, In plane damping-like spin-orbit-torque efficiency ratio ($\xi_{DL}/\xi_{FL}$) from STFMR as a function of temperature. d, Spin-orbit-torque efficiency from second harmonic Hall measurements as a function of temperature for PdCrO$_2$ of various thicknesses.
• Figure 4: Electronic structure for PdCrO$_2$. a, Electronic band structure of paramagnetic PdCrO$_2$. b, Spin-resolved electronic band structure of antiferromagnetic PdCrO$_2$. Red and blue represent positive and negative spin orientations, respectively. c, Electronic band structure of the enclosed rectangular area in b. d, Spin Berry curvature distribution in the plane formed by $k_x$ and $k_y$ at $k_z$ = 0 for the paramagnetic phase. e, Spin Berry curvature distribution in the plane formed by $k_x$ and $k_y$ at $k_z$ = 0 for the antiferromagnetic phase.