Sensor free, self regulating thermal switching via anomalous Ettingshausen effect and spin reorientation in DyCo5

Abstract

We propose a sensor free, self regulating thermal switch that combines the anomalous Ettingshausen effect (AEE) with a temperature driven spin reorientation transition (SRT) in the rare earth cobalt compound DyCo$_5$. Using density functional theory and the Kubo linear-response formalism, we compute the anomalous Hall conductivity $σ_{xy}(\varepsilon)$ and the finite temperature anomalous Nernst conductivity $α_{xy}(T)$ for two magnetization directions, magnetization parallel and perpendicular to the crystallographic c axis. While the intrinsic $σ_{xy}$ at the Fermi level remains sizable for both orientations, $α_{xy}$ exhibits an about two orders of magnitude contrast in the SRT temperature window. This contrast is consistent with the low temperature Mott relation through the energy slope $\partial_\varepsilon σ_{xy}(\varepsilon)\rvert_{E_{\mathrm F}}$ and is traced to strongly peaked Berry curvature hot spots generated by spin orbit coupling induced avoided crossings of Co $3d$ bands. Combining $α_{xy}$ with longitudinal transport coefficients, we estimate device level metrics, namely the anomalous Nernst thermopower $S_{\mathrm{ANE}}$ and the Ettingshausen coefficient $Π_{\mathrm{AEE}}=T S_{\mathrm{ANE}}$, and demonstrate robust orientation controlled switching under a fixed in plane bias current. These results establish a materials based route to compact thermal control without external sensors or feedback electronics and provide a concrete example that the proposed principle can be realized in an existing ferromagnet.

Figures (3)

• Figure 1: Schematic of a self regulating thermal control device based on the anomalous Ettingshausen effect (AEE) and a spin reorientation transition (SRT). Here, $T$ denotes temperature, $\bm{M}$ magnetization, $\bm{J}_c$ charge current density, and $\bm{J}_q$ heat current density. (1) Initial state: the device is in contact with the object; both are at temperature $T$. Under a constant in plane $\bm{J}_c$, AEE generates a transverse $\bm{J}_q$ set by $\bm{M}$. (2) Object heated: the object temperature increases to $T+\delta T$. (3) Entering the SRT range: the device also warms toward $T+\delta T$; within the SRT interval $\bm{M}$ reorients ($\parallel c \leftrightarrow \perp c$), reversing or redirecting $\bm{J}_q$ so that heat is drawn from the object. (4) Negative feedback: cooling reduces $\delta T$ and the system relaxes toward $T$, achieving self regulated operation without external sensing.
• Figure 2: Transport coefficients of DyCo$_5$ as functions of the chemical potential $\mu$ for two magnetization directions, $\bm{M}\parallel(100)$ and $\bm{M}\parallel(001)$. The chemical potential is varied within a rigid band approximation to indicate the carrier doping trend, and $\mu=0$ corresponds to the Fermi level ($E_F$). (a) Anomalous Hall conductivity (AHC) $\sigma_{xy}(\mu)$ in units of $10^{4}$ S/m. (b) Anomalous Nernst conductivity (ANC) $\alpha_{xy}(\mu)$ in units of A m$^{-1}$ K$^{-1}$. (c) Longitudinal conductivity shown as $\sigma_{yy}(\mu)/\tau$ in units of $10^{20}$ S m$^{-1}$ s$^{-1}$, where $\tau$ is the relaxation time. (d) Longitudinal Seebeck coefficient $S_{yy}(\mu)$ in units of $\mu$V/K. Panels (c) and (d) provide the longitudinal inputs required to evaluate the transverse thermopower due to ANE, $S_{\mathrm{ANE}}$, via Eq. \ref{['eq:sane_smallangle']}. A common color scheme is used across panels to distinguish $\bm{M}\parallel(100)$ and $\bm{M}\parallel(001)$.
• Figure 3: Band dispersion and Berry curvature of DyCo$_5$ along the high symmetry path $\Gamma \to M \to K \to \Gamma \to A$ within the energy window $-0.5$ eV $<E<0.5$ eV. The upper panels show the band dispersion, while the lower panels plot the Berry curvature summed over occupied states, $\Omega_{z}(\bm{k})=\sum_{n} f(\varepsilon_{n\bm{k}})\,\Omega_{n,z}(\bm{k})$, which corresponds to the integrand of the intrinsic anomalous Hall conductivity up to a constant prefactor. (a) $\bm{M}\parallel c$ and (b) $\bm{M}\perp c$. In both cases $\Omega_{z}(\bm{k})$ is nearly zero over most of the path but exhibits two sharply peaked hot spots along $\Gamma \to A$, with opposite signs near $\Gamma$ and near $A$. Upon reorienting $\bm{M}$, the hot spot positions shift slightly along $\Gamma \to A$, resulting in a modest change in the separation between the two peaks. These hot spots coincide with band (avoided) crossings of Co $3d$ states in the dispersion, indicating that the orientation dependence of the thermoelectric Hall response originates from Berry curvature hot spots generated by spin orbit coupling near band degeneracies.