Atomic-scale visualization of a cascade of magnetic orders in the layered antiferromagnet GdTe₃

Layered antiferromagnets are attracting significant interest due to their potential in spintronics and twistronics. Rare-earth tritellurides (RTe₃) are a class of van der Waals materials exhibiting a unidirectional incommensurate CDW, tunable by rare-earth substitution. Except for LaTe₃ and TmTe₃, all members are magnetic, with antiferromagnetic ordering above 2 K. While Fermi surface nesting was initially proposed to drive the CDW, recent studies suggest strong momentum-dependent electron-phonon coupling as the primary mechanism. The quasi-two-dimensional structure, with RTe blocks separated by Te planes, influences the electronic and magnetic properties. Itinerant electrons in Te planes initiate the CDW, while localized magnetic moments reside on the RTe blocks. This separation allows for multiple magnetic ground states and offers a valuable opportunity to study the interplay between charge and magnetic order. GdTe₃, exhibiting the highest mobility among van der Waals layered magnets, is of particular interest due to potential applications in low-temperature spintronics. It also shows superconductivity under pressure and a potentially unconventional CDW. Previous measurements revealed a cascade of low-temperature transitions in specific heat and resistivity around 12 K, 10 K, and 7 K, indicating a series of magnetic phases. However, the exact nature of these phases remained unknown due to challenges in neutron scattering measurements. This research utilizes SP-STM to investigate the low-temperature magnetic states and the interplay between CDW and magnetic order in GdTe₃.

Extensive research has been conducted on rare-earth tritellurides (RTe₃) for over two decades, focusing on their magnetic and electronic characteristics. Studies have explored the unidirectional incommensurate charge density wave (CDW) state with a wave vector qCDW = 1/5b (where b is the lattice constant) and its tunability through rare-earth element substitution. The CDW's origin has been debated, with early work attributing it to Fermi surface nesting, while more recent studies highlight the importance of strongly momentum-dependent electron-phonon coupling. The quasi-two-dimensional structure, consisting of RTe blocks separated by Te square-lattice sheets, significantly impacts the electronic and magnetic properties. Most RTe₃ compounds (excluding LaTe₃, TmTe₃, and ErTe₃) exhibit antiferromagnetic ordering below 2 K. GdTe₃ has drawn significant attention due to its exceptionally high mobility, opening up possibilities for low-temperature spintronics applications. The observation of superconductivity under pressure and the unconventional nature of its CDW have further fueled research efforts. Previous studies reported a cascade of low-temperature magnetic transitions in GdTe₃, observed in specific heat, resistivity, and magnetic susceptibility measurements. However, the lack of clear information on the precise nature of the magnetic ordering parameters motivated this investigation.

Single crystals of GdTe₃ were grown using a self-flux technique. Spin-polarized scanning tunneling microscopy (SP-STM) measurements were performed after cleaving the crystals at 77 K. Two types of tips were used: metallic W tips for imaging the charge density wave (CDW) and magnetic Cr tips for imaging the spin contrast. The spin polarization of the Cr tips was confirmed by imaging the antiferromagnetically ordered Fe₁.₀₃Te before GdTe₃ measurements. Fourier transforms (FTs) of STM topographies were obtained and analyzed. To analyze the magnetic phases, Fourier transforms of STM topographies obtained with spin-polarized tips were compared to those obtained with normal (spin-averaged) tips. New peaks in the spin-polarized data revealed magnetic ordering. Temperature-dependent measurements were conducted using Joule heating with a Cu coil. The temperature was controlled using a Lakeshore 340 controller. The temperature dependence of the CDW and AFM peak intensities in the Fourier transforms were carefully analyzed. A Ginzburg-Landau theory was developed to explain the observed phase transitions. The intensity of Fourier peaks was extracted by averaging the intensity of a 3x3 pixel area centered on each peak. Background intensity was determined by averaging the intensity in a 3x3 pixel area far from any peaks. In cases where the Fourier transforms were mirror-symmetrized, this step was explicitly noted in the figure caption. Scanning tunneling spectroscopy (dI/dV) measurements were also performed to investigate the electronic density of states.

SP-STM revealed a striped antiferromagnetic (AFM) phase below 7 K, with a wave vector qAFM = (±, 0), perpendicular to the CDW. The periodicity of this AFM phase is twice that of the Gd lattice. As temperature increases from 4K to 7.9 K, the AFM peaks weaken and disappear, suggesting a Néel temperature of ~7.5 K. Above 7 K, and up to 12 K an intermediate magnetic phase is present: a spin density wave (SDW) with the same wave vector as the CDW, qSDW ≈ qCDW. The SDW's existence is supported by the observation that the CDW peak intensity shows a significant temperature dependence only when measured with a spin-polarized Cr tip, exhibiting a maximum intensity at ~10 K before decreasing between 7 and 8 K. This intensity variation is not observed with non-magnetic W tips. dI/dV spectroscopy shows no significant change in the electronic density of states across these temperature regimes, indicating that the observed CDW behavior is magnetic in origin. The coexistence of a bidirectional CDW and AFM order near domain walls was also observed. The authors propose that the SDW arises as a daughter order resulting from the coupling of a c-axis AFM order (forming around 12 K) and the CDW. A Ginzburg-Landau model supports this hypothesis. The striped AFM order observed below 7 K could be attributed to a rotation of the c-axis AFM moments into the ab-plane, or a more complex transition involving a reentrant paramagnetic phase. Comparing temperature-dependent Fourier transform intensities from spin-polarized and spin-averaged STM tips allowed the detection of the hidden SDW order, having the same periodicity as the CDW.

This research provides a direct visualization of the complex interplay between charge and spin orders in GdTe₃, revealing a cascade of magnetic phases. The observation of a spin density wave (SDW) with the same wave vector as the charge density wave (CDW) is particularly significant, offering a compelling example of a daughter order driven by the interaction of a c-axis AFM order and CDW. The Landau free energy model successfully captures this interaction, highlighting the importance of considering the interplay between different ordering phenomena. The findings highlight the potential of SP-STM as a tool to unveil hidden magnetic orders that may possess the same periodicity as existing orders within a material. Future studies incorporating in-plane magnetic fields could further illuminate the intricate interplay between charge and magnetic orders in GdTe₃ and other rare-earth tritellurides.

This study successfully identified the in-plane low-temperature magnetic phases of GdTe₃ using spin-polarized scanning tunneling microscopy (SP-STM). Two distinct magnetic orders were found: a spin density wave (SDW) emerging near 12 K and a striped antiferromagnetic (AFM) order setting in around 7.5 K. The SDW is proposed to be a daughter order of an intermediate-temperature c-axis AFM phase and the CDW. The study demonstrates a novel method for detecting hidden spin orders with the same periodicity as other orders by comparing temperature-dependent Fourier transforms from spin-polarized and spin-averaged STM tips. Future experiments under in-plane magnetic fields could provide further insights into the interplay of magnetic and charge orders in this material class.

The study primarily focuses on the surface properties of GdTe₃, and the observed magnetic orders might not perfectly represent the bulk behavior. The Ginzburg-Landau model used to explain the SDW formation is a simplified representation of a complex system, and further theoretical work could be necessary to capture all nuances of the phase transitions. The interpretation of the bidirectional CDW and AFM orders near domain walls requires further investigation to fully understand their origin and significance.