🔬 materials science

Observation of in-plane anomalous Nernst effect

This paper reports the discovery of a robust in-plane anomalous Nernst effect in symmetry-tailored ultrathin ferromagnetic oxide films, demonstrating that the effect can arise from spontaneous in-plane magnetization and out-of-plane orbital magnetization, thereby overcoming the traditional orthogonality constraint and enabling more flexible magnetothermoelectric device designs.

Original authors: Tadashi Yoneda, Shinichi Nishihaya, Markus Kriener, Haruto Kaminakamura, Ming-Chun Jiang, Naohiro Tezuka, Yoshiya Murakami, Ryotaro Arita, Hiroaki Ishizuka, Masaki Uchida

Published 2026-08-17

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Tadashi Yoneda, Shinichi Nishihaya, Markus Kriener, Haruto Kaminakamura, Ming-Chun Jiang, Naohiro Tezuka, Yoshiya Murakami, Ryotaro Arita, Hiroaki Ishizuka, Masaki Uchida

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to catch a fish with a net. In the world of electronics, scientists have long known a very specific rule about how to catch "heat" and turn it into electricity. They call this the Nernst effect. Think of it like a magical river: if you push a river of heat in one direction and apply a magnetic field from above (like a giant magnet hovering over the water), the river doesn't just flow forward; it gets pushed sideways, creating a voltage you can use. For decades, the rule was strict: the magnet had to be perpendicular to the river and the sideways voltage. It was like saying, "You can only catch fish if the net is held at a perfect 90-degree angle." If you tried to hold the net sideways, the fish would just swim right through, and you'd get nothing. This rule made designing devices tricky, because you couldn't just stack things up however you wanted; you were forced into a rigid, cross-shaped layout.

But what if the river could be tricked into flowing sideways even when the magnet is lying flat? That is the big question this paper tackles. The researchers are working in the field of thermoelectrics, which is all about turning temperature differences into electrical power. They are looking at a special type of material called a ferromagnet, which is a metal that acts like a permanent magnet. Usually, scientists thought that to get this sideways voltage (the Nernst effect), the magnetic "spin" inside the metal had to point straight up or down, perpendicular to the flow of heat. However, a new theory suggested that maybe, just maybe, the electrons inside these materials have a secret trick. They might be able to generate a sideways voltage even if the magnetic spin is lying flat, parallel to the heat flow, as long as some other invisible property (called orbital magnetization) is doing the heavy lifting.

Here is where the story gets exciting. The authors of this paper decided to test this theory using a very thin film of a material called Strontium Ruthenate ( $SrRuO_3$ ). They didn't just look at the material; they put it on a special stage where they could rotate the magnetic field in every possible direction, like a globe spinning in a spotlight. They wanted to see what happened when they pointed the magnetic field right along the flat surface of the film, parallel to the heat flow.

The result was a surprise that breaks the old rules. They found that even when the magnetic field was lying flat on the table, the material still produced a strong sideways voltage. It was as if the fish were jumping into the net even though the net wasn't held at the "correct" 90-degree angle. The voltage they measured was huge—about 40% as strong as the voltage they got when they used the traditional, perpendicular magnetic field. This proves that the old "orthogonality rule" (the requirement for everything to be at right angles) is not a hard law of nature, but just a limitation of the materials we used to study.

The paper explains that this happens because of a hidden partnership inside the atoms. Even though the main magnetic spin is lying flat, the way the electrons orbit the nucleus creates a tiny, invisible magnetic push that points straight up. This "orbital magnetization" acts like a secret agent, doing the job of the perpendicular magnet that we thought was necessary. The researchers confirmed this by doing complex computer simulations that showed the electrons' orbits indeed create this upward push when the main spin is flat.

So, what does this mean for the future? The authors suggest that this discovery opens the door to much more flexible designs for energy-harvesting devices. Imagine building a tiny power generator that fits into a curved surface or a very thin strip of metal. Before, the magnetic parts had to be stacked in a way that made the device bulky or hard to make. Now, because the magnetic field can lie flat and still work, engineers can design these devices to be smaller, thinner, and fit into places they never could before. The paper doesn't claim to have built a working device yet, but it has proven the physics works, suggesting that the next generation of thermal energy harvesters could be far more versatile than we ever imagined.

Technical Summary: Observation of In-Plane Anomalous Nernst Effect

Problem Statement
The Nernst effect, which converts a heat current into a transverse voltage under a magnetic field or spin magnetization, is a promising mechanism for energy harvesting and thermal management. However, the conventional anomalous Nernst effect (ANE) is fundamentally constrained by an orthogonality requirement: the spontaneous spin magnetization must be perpendicular to the plane defined by the temperature gradient and the induced voltage. This geometric constraint limits the flexibility of device layouts in practical applications. While the anomalous Hall effect (AHE) has recently been demonstrated to occur with in-plane spin magnetization through mechanisms involving Berry curvature and spin-orbit coupling, it remains unclear if the same physics applies to the ANE, given that ANE is governed by the energy derivative of the Hall conductivity (via Mott's formula) rather than the integrated Berry curvature of occupied bands.

Methodology
The authors investigated this phenomenon using ultrathin films of the prototypical ferromagnetic oxide, strontium ruthenate (SrRuO $_3$ ), grown on (111) SrTiO $_3$ substrates. These films possess a trigonal distortion with compressive epitaxial strain, creating a magnetic point group ( $2'/m'$ ) that satisfies the symmetry requirements for an in-plane ANE response.

The experimental approach involved systematic magnetothermoelectric and magnetotransport measurements under spherical rotations of the magnetic field:

Sample Preparation: (111)-oriented SrRuO $_3$ films (~4 nm thick) were fabricated via molecular beam epitaxy.
Field Rotation: Measurements were conducted by rotating the magnetic field both azimuthally (within the (111) plane) and polarly (from out-of-plane [111] to in-plane [11 $\bar{2}$ ] directions) up to 9 T.
Signal Extraction: To isolate the intrinsic in-plane ANE from extrinsic contributions (such as field misalignment or out-of-plane temperature gradients), the authors employed antisymmetrization of raw data and subtracted one-fold symmetric components ( $S_{yx, C1, B}$ and $S_{yx, C1, T}$ ).
Theoretical Modeling: First-principles calculations were performed using the DFT+U framework (VASP) combined with Wannier tight-binding models to compute Berry curvature, orbital magnetization, and thermoelectric conductivity for specific in-plane spin magnetization states.

Key Results

Emergence of In-Plane ANE: The study demonstrates a pronounced Nernst signal ( $S_{yx}$ ) when the magnetic field and spontaneous spin magnetization lie entirely within the plane defined by the temperature gradient and voltage. This signal persists at zero magnetic field and exhibits a large hysteresis, confirming its origin in spontaneous ferromagnetic ordering.
Magnitude and Symmetry: The in-plane ANE signal reaches approximately 40% of the magnitude observed under out-of-plane spin magnetization. The signal exhibits a three-fold rotational symmetry consistent with the crystal structure of the (111) SrRuO $_3$ film, with distinct behaviors observed at $\phi = 0^\circ$ and $\phi = 60^\circ$ .
Temperature Dependence: The transverse thermoelectric conductivity ( $\alpha_{xy}$ ) shows a non-monotonic temperature dependence, peaking around 80 K and decreasing at lower temperatures. This contrasts with the monotonic increase of the anomalous Hall resistivity ( $\rho_{yx}$ ) as temperature decreases, reflecting the Mott relation where the Nernst effect is proportional to the energy derivative of the Hall conductivity.
Mechanism Identification: The results indicate that the in-plane ANE arises from an off-diagonal coupling between in-plane spin magnetization and out-of-plane orbital magnetization. First-principles calculations confirm that in-plane spin magnetization (specifically along the [11 $\bar{2}$ ] direction) induces a finite out-of-plane orbital magnetization ( $M_{orb}^z$ ) and a non-zero $\alpha_{xy}$ , whereas magnetization along the [1 $\bar{1}$ 0] direction yields zero response.

Significance and Claims
The paper claims to have experimentally observed the in-plane anomalous Nernst effect, demonstrating that the effect is no longer limited by the conventional orthogonality condition requiring spin magnetization to be perpendicular to the temperature gradient-voltage plane.

The authors assert that this finding:

Broadens the Design Space: It lifts the geometric restriction on spin magnetization, allowing for more flexible designs of magnetothermoelectric materials and devices. Specifically, it suggests that thermopile structures could be optimized by aligning spin magnetization along the stripes (rather than perpendicular to them), potentially enabling smaller device footprints.
Offers New Control Mechanisms: The ability to control the sign of the ANE through crystal symmetry engineering (e.g., domain engineering or heterostructuring) provides a new approach to polarity control beyond conventional Fermi level tuning.
Validates Theoretical Predictions: The observation confirms that intrinsic coupling between in-plane spin and out-of-plane orbital magnetization can generate significant thermoelectric responses, extending the understanding of Berry-curvature-related quantum geometry in thermoelectric phenomena.

The authors conclude that while this work focuses on SrRuO $_3$ , the phenomenon is expected to be observable in a broader class of materials with large intrinsic ANE derived from Berry curvature hot spots or Weyl points, provided the symmetry requirements are met.

Technical Summary: Observation of In-Plane Anomalous Nernst Effect

More like this