# Pressure strain-tuned Kondo in Heusler

V. Tzanos, Angel Arevalo-Lopez, C. L. Bull, C. J. Ridley, A. Mehrnejat, A. F.

Kusmartseva

► To cite this version:

V. Tzanos, Angel Arevalo-Lopez, C. L. Bull, C. J. Ridley, A. Mehrnejat, et al., Pressure strain-tuned Kondo in Heusler. Materials Science and Engineering: B, 2024, Mater. Sci. Eng. B-Adv. Funct. Solid-State Mater., 307, 10.1016/j.mseb.2024.117484. hal-05264459

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Submitted on 17 Sep 2025

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# Pressure-induced, strain-tuned Kondo response in Pd₂MnIn Heusler alloy

V. Tzanos<sup>a</sup>, A.M. Arevalo-Lopez<sup>b</sup>, C.L. Bull<sup>c,d</sup>, C.J. Ridley<sup>c</sup>, A. Mehrnejat<sup>a</sup>, A.F. Kusmartseva<sup>a,*</sup>

## ARTICLE INFO

**Keywords:**

Spintronic materials

Kondo response

Heusler alloys

High-pressure phases

Half-metals

## ABSTRACT

Over the past few decades Heusler alloys have provided a rich ground for exploration and discovery of half-metal candidates resulting in the progress of diverse spintronic applications. The current investigation in Heusler alloy Pd₂MnIn demonstrates how the application of pressure could be used to introduce local deformational strain into the lattice and its effect of magneto-electronic properties in these systems. The results, showcasing high-pressure neutron diffraction experiments, X-ray diffraction and magnetisation studies, indicate that cycling to ~70 kbar irreversibly locally deforms the crystal lattice leading to the formation of ferromagnetic, glassy Kondo islands that persist up to high temperatures and ambient pressure conditions. The newly discovered strain-driven Kondo response could lead to breakthroughs in the search for half-metals, Kondo metals and other unconventional spintronic materials.

## 1. Introduction

Recent decades have seen a rapid surge in the discovery of half-metal systems underpinned by the expanding growth in the field of spintronics. Half-metal materials, where one spin channel of the conduction electrons is metallic and the other semiconducting are attractive candidates for the creation of spin polarised charge carriers and highly relevant in spintronic applications. Half-metal properties would enable manipulation of the spin degree of freedom in logical devices, as well as the development of novel spin valves for spin injections. Heusler alloys, specifically half Heusler [1] and inverse Heusler [2] materials have provided a fruitful ground in the theoretically-driven search for half-metals. Recent computational studies have predicted that Co₂Mn-based Heuslers could provide multiple viable half-metal candidates [3, 4]. However, most known Heusler half-metals are ferromagnetic [5–7] and have insufficiently high spin polarisation at room temperature to be viable in device applications. Attempts to address this challenge have prompted interest in 2D materials and Heusler nanos-structures [8,9]. Additionally, a relatively unexplored avenue relates to antiferromagnetic Heusler alloys.

The Heusler alloys are ternary intermetallics with composition X₂YZ where X and Y atoms are chosen from the transition metal elements and Z atoms are chosen from one of the B subgroups 3, 4, and 5. Full Heusler alloys typically crystallise in a Cu₂MnAl cubic L2₁ structure with space group Fm$\bar{3}$m. The most common form of disorder present in full Heusler alloys is B₂ and relates to when Y and Z atoms become

interchangeable [7]. Palladium based full Heusler alloy Pd₂MnIn is an antiferromagnet with transition temperature T_N = 145 K and a magnetic moment of 4μ_B on the Mn site [10,11]. The antiferromagnetism is Pd₂MnIn is highly sensitive to chemical doping [12,13], magnetic field [14] and lattice disorder [11]. Specifically, chemical doping on both the X and Z sites can tune the antiferromagnetism in this system towards ferromagnetism [12,13]. Application of a high magnetic field exceeding B = 6T can induce a metamagnetic transition in this material into a more ordered magnetic state at low temperatures [14].

The malleability of the magnetism in Pd₂MnIn may be related to its position in the Slater–Pauling (SP) phase diagram, where it lies close to the half-metallic properties line (M_t = Z_t - 24, Z_t = 30 and M_t = 4μ_B) calculated for full Heuslers [15]. One approach to bridge the gap between the Pd₂MnIn and the half-metallic SP line, to induce half-metallic characteristics in this system, would be to increase its total magnetic moment M_t. The magnetism in this material arises due to unoccupied minority (Mn d) bands, and could, therefore, be strengthened by increasing the hybridisation between the occupied Mn d and empty In sp states. This could be achieved by application of external pressure or strain [16]. For these reasons, it is plausible to assume that with the application of external pressure (or strain) could be used to tune Pd₂MnIn towards exhibiting promising half-metal behaviour.

<footnote><sup>a</sup>Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom</footnote>

<footnote><sup>b</sup>Unite de Catalyse et Chimie du Solide (UCCS), Universite de Lille, Lille, F-59000, France</footnote>

<footnote><sup>c</sup>ISIS Facility, Rutherford Appleton Laboratory, Didcot, OX11 0QC, UK</footnote>

<footnote><sup>d</sup>EaStCHEM School of Chemistry, The University of Edinburgh, Kings Buildings, David Brewster Road, Edinburgh EH9 3FJ, UK</footnote>

<footnote>* Corresponding author.
E-mail address: A.Kusmartseva@lboro.ac.uk (A.F. Kusmartseva).</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** High-pressure setup for electrical and magnetic studies in Pd₂MnIn. (a) High-pressure setup for electrical resistivity ρ measurements inside a Bridgman-type pressure cell with accessible pressures 0–100 kbar: (i) photographic image showing the sample space, containing pyrophilite gasket, steatite medium, Pd₂MnIn sample, Pb pressure gauge and Au wires for electrical connections; (ii) Schematic labelled diagram of the sample space: V and I are used to measure sample resistance to determine ρ, and Vp_b measured across the Pb pressure gauge is used to determine the pressure. (b) High-pressure setup for neutron diffraction experiments: (i) single toroidal zirconia-toughened alumina (ZTA) ceramic anvil on a B₄C epoxy coated WC seat; (ii) single-toroidal Ti–Zr alloy gasket to contain the powder Pd₂MnIn sample; (iii) gasket, anvil and seat combined assembly to be inserted into a V3 Paris-Edinburgh (PE) press to generate pressures 0–280 kbar. The incident and scattering neutron beam orientations for transverse and longitudinal diffraction measurements across the PE press are shown [17].</figcaption></figure>

This study conducts an investigation into the electronic transport and magnetic properties in polycrystalline Pd₂MnIn samples in the pressure range 0–70 kbar. Measurements of electrical resistivity and powder neutron diffraction were carried out at high pressures. Supplementary X-ray diffraction experiments and magnetisation measurements were performed at ambient pressure to ascertain the sample quality and the effect of internal strain.

## 2. Methods

A slug sample of Pd₂MnIn was prepared by melting the appropriate quantities of the high-purity constituent elements in an Ar (argon) arc furnace. The evacuated quartz ampoule was subsequently annealed at 1000 K for 48 h and cooled at a slow rate of 1 Kh⁻¹ to below the order–disorder transition temperature at 880 K. From 880 K the sample was cooled at a faster rate of 1 Kmin⁻¹ to room temperature. The synthesis recipe has previously shown to produce ordered cubic L2₁ structure [11,18]. The crystallographic structure was verified by powder X-ray diffraction methods.

For high-pressure electrical resistivity ρ measurements Pd₂MnIn platelets of approximate dimensions 300 µm × 500 µm were polished to an approximate thickness of ~100 µm with a high-grade silicon carbide polishing paper (Fig. 1a, (i)). Pressure was generated inside Bridgman cells using tungsten carbide (WC) anvils with culet sizes 3.50 mm and accessible pressures 0 - 100 kbar. The sample space was set up similar to examples in published literature [19]. Pyrophilite gaskets were polished to a thickness of ~ 200 µm and two steatite discs of approximate thickness ~ 90 µm provided the quasi-hydrostatic pressure medium by sandwiching the assembly (Fig. 1a, (i)). Au wires with 25 µm diameter were inserted into the sample space through fine-cut

channels in the gasket, 4 of which were arranged in a linear configuration to determine the resistivity ρ of the sample. The superconducting transition of the Pb pressure gauge was used to estimate the pressure inside the cell, with the width of the transition providing an estimation of its uncertainty. The Pd₂MnIn sample was touching the Pb gauge inside the sample space to reduce the number of Au wires, but the Pb gauge was measured independently from the sample. Stanford Research SR830 Lock-in amplifier was used to provide the current *I* = 1mA and determine minute electrical voltage signals *V* and *Vp_b* across the sample and Pb gauge respectively (Fig. 1a, (ii)). The measurements were obtained at a frequency of *f* = 31.317 Hz and the signal to noise ratio was improved using a room temperature transformer with gain *G* = 100.

High-pressure neutron diffraction experiments on powder Pd₂MnIn were conducted at the PEARL beamline at the ISIS Pulsed Neutron and Muon source. The pressure was generated using a V3 Paris-Edinburgh (PE) press with single toroidal zirconia-toughened alumina (ZTA) ceramic anvils (Fig. 1b, (i)) to access pressures 0–100 kbar [20]. The PE press was set up in accordance with published literature [17]. Pd₂MnIn powder was enclosed inside a single-toroidal Ti-Zr alloy gasket allowing sample volumes of ~100 mm³ (Fig. 1b, (ii)). NaCl powder was mixed together with Pd₂MnIn to act as a pressure gauge. The PE press was inserted into a vacuum tank and cooled down with liquid nitrogen N₂ [20] to a measurement temperature of 100 K. Neutron diffraction data was collected both in transverse and longitudinal configuration, allowing for the incident and scattering neutron beam to pass through the gasket and obtaining results at higher scattering angles corresponding to a longer d–spacings up to 12.5 Å(see, Fig. 1b, (iii)) [17]. At each pressure point the counts were collected for 24 h once the PE press
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Pd₂MnIn resistivity temperature dependence in the pressure range 0–70 kbar. Electrical resistivity follows metallic-like behaviour over the temperature range 3–270 K at lowest pressure of 17 kbar (black curve). As the pressure is increased incrementally to 70 kbar the temperature-dependent character of the resistivity changes from metallic to semiconductor-like at high temperatures — as shown by the cyan curve at 70kbar. At higher pressures the resistivity manifests a broad peak around $T_{peak} \sim 100$ K and demonstrates positive pressure dependence. Notably, upon pressure release to 0 kbar the metallic behaviour in the resistivity is not recovered and the broad peak around $\sim 150$ K, as well as semiconductor-like behaviour at high temperatures, remain (see, grey curve).</figcaption></figure>

has been cooled down to a temperature of 100 K, to ensure reliable statistics.

Powder X-ray diffraction (XRD) measurements were collected using a Bruker D2 Phaser diffractometer. Bruker 2D Phaser uses a Copper (Cu) target to generate K-α₁,₂ X-rays with wavelengths of 1.5 Å and energies 8.04 keV. The crystallographic data was collected in a Bragg-Brentano geometry at room temperature. The results were analysed in FullProf Rietveld refinement.

Magnetisation measurements were conducted using a standard Vibrating Sample Magnetometer (VSM) option inside a Cryogenics Ltd. Cryogen Free Measurement System (CFMS). All results were normalised to the sample mass used. Sample masses were 167 mg and 253 mg for the strained and unstrained Pd₂MnIn powder samples, respectively. The magnetisation as a function of temperature was collected in an applied field of 30 mT. Data was obtained both under zero-field cooling (ZFC) and field cooling (FC) conditions. All data was measured during the warm-up between 3–200 K at a steady rate of 1K/min. The dependence of magnetisation on the applied magnetic field $B= \pm 1$T was collected at select temperatures $T = 50$ K, 100 K and 150 K during the warm-up after cooling down in zero applied magnetic field.

### 3. Results

Electrical resistivity in Pd₂MnIn shows substantial pressure dependence in the range 0–70 kbar (Fig. 2). The values of resistivity increase gradually as the pressure is increased. The resistivity at $P = 70$ kbar exceeds the resistivity at $P = 17$ kbar by approximately 50% of its room temperature value. Furthermore, at low pressures ($P = 17$ kbar) the resistivity across the entire temperature range 3–270 K shows a positive temperature coefficient, comparable to a metallic system. As the pressure is increased above $P > 20$ kbar the temperature coefficient at high temperatures ($T > 150$ K) changes sign, leading to the emergence of a broad peak anomaly around $T_{peak} \sim 100–150$ K. Notably,

the overall temperature dependence of the resistivity becomes flatter with applied pressure, as demonstrated by a reduction in the relative normalised change in the resistivity $\Delta\rho_{norm} = \frac{\rho_{max} - \rho_{min}}{\rho(270K)} = 14\pm1\%$ and $\Delta\rho_{norm} = 9\pm1\%$ at low and high pressure respectively. This type of temperature dependence properties is reminiscent of half-metallic systems [5]. Importantly, as the pressure is released back to ambient value of $P = 0$ kbar after reaching pressures up to $P = 70$ kbar, the original temperature behaviour, observed initially at low pressures, is not recovered (Fig. 2, grey line). Upon return from high pressures, the resistivity retains high room-temperature values, negative temperature coefficient at high temperatures ($T > 150$ K) and the broad peak anomaly around $T_{peak} \sim 150$ K. The behaviour is indicative of irreversible pressure-induced changes arising in Pd₂MnIn, which may be potentially similar to those found in shape memory Heusler alloys [21].

The irreversible pressure-induced behaviour is most notable when the low and ambient pressure resistivities, obtained on pressure increase and release respectively, are compared directly (see, Fig. 3). The ambient ($P = 0$ kbar), post high-pressure resistivity (Fig. 3, grey line) has been shifted down by ~50% of its room temperature ($T = 270$ K) value to coincide with low-pressure ($P = 17$ kbar) resistivity (Fig. 3, black line) measured during pressure increase. The post high-pressure ambient resistivity shows a negative temperature coefficient in its temperature dependence at high temperatures ($T > 150$ K). There is also a characteristic broad peak anomaly emerging around $T_{peak} \sim 150$ K.

The key parameters to define the broad peak-like anomaly in electrical resistivity in Pd₂MnIn are the temperature at which the peak is observed $T_{peak}$ and the normalised peak resistivity value $\rho_{peak}/\rho(270K)$. The peak temperature $T_{peak}$ is determined visually from the temperature dependence in $\rho$ and its uncertainty estimated from the derivative $\frac{d\rho}{dT}$. The pressure dependence of the peak temperature $T_{peak}$ is shown in Fig. 4(a). The peak temperature $T_{peak}$ decreases as the pressure is increased reaching a pressure-independent value of $T_{peak} = 113 \pm 5$ K.
<figure><img src="image_6.png" /><figcaption>Fig. 3. Pressure effect on the temperature dependent resistivity in Pd₂MnIn after pressure increase to 70 kbar. The resistivity at low pressures (17 kbar) upon pressure increase shows metallic temperature dependence with no obvious peak and remaining flat at high temperatures (see, black curve). The resistivity when the pressure is released back to 0 kbar from 70 kbar shows a clear broad peak anomaly around 150 K as well as negative temperature coefficient in its temperature dependence at high temperatures (see, grey curve). The grey curve is shifted down by approximately ~ 50% of its room temperature value to coincide with the black curve values.</figcaption></figure>

after P > 40 kbar (see, Fig. 4a) black circles). Upon pressure release back to 0 kbar the peak temperature increases to T<sub>peak</sub> = 154 ± 5K (see, Fig. 4a) pink triangle). Conversely, the normalised peak resistivity value increases as the pressure is increased and saturates at a plateau ρ<sub>peak</sub>/ρ(270K) = 107 ± 2% after P > 50 kbar (see, Fig. 4b) black squares). This indicates that the peak in the resistivity becomes more pronounced as the pressure is increased. As the pressure is released back to 0 kbar the normalised peak resistivity decreases to ρ<sub>peak</sub>/ρ(270K) = 103 ± 1% (see, Fig. 4b) pink star). Thus, pressure cycling to 70 kbar introduces a broad peak anomaly into the resistivity at T<sub>peak</sub> = 154 ± 5K and flat high-temperature resistivity variation ~3% across the 150–270 K temperature range.

Negative temperature coefficients in the resistivity temperature dependencies are usually expected in semiconductors due to the presence of a band gap in the electronic spectrum. In these type of systems the negative temperature coefficient becomes increasingly stronger as the temperature is lowered. However, this behaviour would be at odds with the positive temperature coefficient in Pd₂MnIn resistivity at low temperatures T < 100 K. An alternative description for negative temperature coefficient in resistivity in metals would arise due to the Kondo effect, which occurs when dilute magnetic impurities interact with conduction electrons [22–24]. Kondo theory and Hamann equation predict a logarithmic variation in the temperature dependence of the resistivity Eq. (1), when the phonon contribution to the conductivity is negligible:

$$ \rho = \rho_0 + B \times \ln \left( \frac{T}{T_K} \right) \quad (1) $$

where ρ₀ is the residual resistivity, T_K is the Kondo temperature and B is a parameter that is, nominally, proportional to the concentration of the Kondo impurities [22,23].

To test the premise, the high-temperature resistivity in Pd₂MnIn at select pressure points has been fitted with the Kondo model, as described by Eq. (1) across the temperature 150–250 K and pressure 17–70 kbar ranges (Fig. 5). Resistivity at the intermediate pressure (P = 47 kbar) is well described by the Kondo model and Hamann equation in the temperature range 170–220 K (see, Fig. 5, black squares on the left side of the double y plot). Resistivity at high pressure (P = 70 kbar) shows an equally good Kondo model fit extended to wider temperatures 180–250 K (see, Fig. 5, black circles on the right side of the double y plot). The Kondo model fit is shown as a red solid line in Fig. 5. For clarity, only 1 point in a 1000 is shown on the resistivity curves. This behaviour confirms that the Kondo model is suitable to describe the high-temperature behaviour of the resistivity in Pd₂MnIn across the pressure range of interest 0–70 kbar.

Within the Kondo model the Kondo temperature T_K is related to the magnetic coupling J between the dilute magnetic impurities [24] as shown by Eq. (2):

$$ T_K = \frac{1}{n_{\text{DOS}}} \exp \left( -\frac{1}{J \times n_{\text{DOS}}} \right) \quad (2) $$

where n_DOS is the density of states and J is the magnetic coupling. Under the conditions where the variations in the density of states are negligible n_DOS ≈ const. Eq. (2) can be further simplified to Eq. (3):

$$ \ln(T_K) \sim -\frac{1}{J} \quad (3) $$

whereby the logarithm of the Kondo temperature Ln(T_K) becomes proportional to the inverse of the magnetic coupling J between the dilute magnetic impurities.

High-temperature electrical resistivity in Pd₂MnIn has been fitted with the Kondo model (Eq. (1)) across the temperatures 170–250 K at all measured pressures 0–70 kbar. The pressure evolution of the
<figure><img src="image_7.png" /><figcaption>Fig. 4. Pressure effect on the peak behaviour in the resistivity in Pd$_{2}$MnIn. The peak temperature $T_{\text{peak}}$ in the resistivity was determined visually from the temperature dependence in $\rho$. The error in the peak temperature was determined from the derivative $d\rho/dT$. The error in the pressure determination was obtained from the width of the superconducting transition temperature of the Pb pressure gauge. Black points were obtained during pressure increase (black arrow). Pink point was obtained after pressure release (pink arrow) to 0 kbar. (a) The peak temperature $T_{\text{peak}}$ decreases as the pressure is increased and becomes pressure-independent after $P > 40$ kbar (see, black circles). Upon pressure release back to 0 kbar the peak temperature $T_{\text{peak}}$ increases to ~ 150 K (see, pink triangle). (b) The normalised peak resistivity value defined as $\rho_{\text{peak}}/\rho_{\text{at 270K}}$ increases as the pressure is increased and saturates at a ~107% plateau after $P > 50$ kbar (see, black squares). This indicates that the peak in resistivity becomes more pronounced as the pressure is increased. As the pressure is released back to 0 kbar the normalised peak resistivity decreases (see, pink star). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Examples of the Kondo model fits to the resistivity in Pd₂MnIn in the pressure range 17–70 kbar. The Kondo model fit is shown as a red solid line. For clarity, only 1 point in a 1000 is shown on the resistivity curves. Resistivity at intermediate pressures of 47 kbar follows a Kondo model behaviour in the temperature range 170–220 K (see, black squares on the left side of the double y plot). Resistivity at high pressures of 70 kbar shows an equally good Kondo model fit expanded to wider temperatures 180–250 K (see, black circles on the right side of the double y plot).</figcaption></figure>

relevant Kondo parameters Ln($T_K$) and $\frac{1}{B}$ are shown in Fig. 6. The left side of the double y plot shows the pressure dependence of Ln($T_K$) (see, Fig. 6, black solid pentagons). Ln($T_K$) decreases by several orders of magnitude in the pressure range 17–70 kbar and reaches a saturating value for pressure exceeding $P > 50$ kbar. Notably, upon pressure release to 0 kbar Ln($T_K$) remains low, close to its high-pressure saturating value (see, Fig. 6, pink partially filled pentagon). Ln($T_K$) is inversely proportional to the magnetic coupling $J$ between the magnetic scattering centres/impurities. Notably, the relation implies that the magnetic coupling $J$ becomes stronger by several orders of magnitude as the pressure is increased and is stabilised by pressure cycling to 70 kbar.

The right side of the double y plot shows the pressure dependence of the inverse of the $B$ parameter which is proportional to the concentration of the magnetic scattering centres/impurities (see, Fig. 6, black partially crossed diamonds). $\frac{1}{B}$ decreases as the pressure is increased. The low pressure value of $\frac{1}{B}$ is not recovered upon pressure release to 0 kbar (see, Fig. 6, pink partially filled diamond). The results suggest that the concentration of the magnetic scattering centres/impurities is decreased as the pressure increased and is reduced by pressure cycling to 70 kbar. The error bars in Ln($T_K$) and $\frac{1}{B}$ were calculated by shifting the fitted temperature ranges by $\pm 5$ K on either side. The remarkable result that the Kondo response is observed in paramagnetic Pd₂MnIn under pressure in the absence of chemical doping with magnetic impurities and is retained, to some extent, when the pressure is removed raises questions as to its origin.

Here, it is important to note that the generation of pressure inside a Bridgman cell is invariably accompanied by spatial pressure gradients and strain inside the sample space. The pressure medium is pressed steatite powder and is, therefore, quasi-hydrostatic. The evidence for strain inside the sample space is most strongly confirmed by the broad width of the superconducting transition at low temperature in the Pb pressure gauge (Fig. 1a, i)). This results in an uncertainty in the estimation of the pressure inside the cell as $\pm 5$ kbar as well as corroborates

the presence of internal strain. The amount of strain present in the sample space would be correlated with the width of the superconducting transition in the Pb gauge. To shed light on the conundrum of the observed Kondo response in the high-temperature resistivity of Pd₂MnIn, powder neutron diffraction experiments were conducted at high pressures and low temperatures (see, Fig. 7). The neutron diffraction measurements were performed in a Paris-Edinburgh (PE) press as described in the Methods section. It is important to note, that the creation of pressure in a PE press results in internal strain gradients, similar to the Bridgman cell. This is because the pressure medium inside the PE press is the sample powder itself, which is also quasi-hydrostatic. It is fair to assume, that when the sample is at 0 kbar there is not internal strain in the sample space. Powder neutron diffraction time-of-flight (TOF) measurements in Pd₂MnIn were performed at 100 K temperature in the pressure range 0–40 kbar at the PEARL beamline (Fig. 7). Sample at $P = 0$ kbar has no internal strain and shows a broad peak in the TOF results characteristic of type 2 antiferromagnetism (AFM) along the (111) crystallographic direction (see, Fig. 7, black line and points). The peak is fitted with a Gaussian function (Fig. 7, red line). The peak intensity is significantly attenuated due to the intrinsic In neutron scattering absorption. As the pressure is increased ($P \neq 0$ kbar), internal strain arising in the sample due to pressure gradients inside the pressure cell leads to the complete disappearance of the type 2 AFM peak at the temperature of 100 K (see, Fig. 7, blue, pink, green and yellow lines and points. For clarity, non-zero pressure results are shifted along the y-axis. The neutron diffraction results indicate that Pd₂MnIn is no longer antiferromagnetic at a temperature of 100 K, due to the presence of internal strain introduced with the application of external pressure. Consequently, this implies that magnetism in Pd₂MnIn is extremely sensitive to lattice strain, which would explain the significant reported variations in the antiferromagnetic transition temperature $T_N \sim 120–150$ K found in the literature [10,11,14].

To corroborate these findings, the crystallographic structures of two Pd₂MnIn powder samples collected before and after the high-pressure neutron diffraction experiments were compared using X-ray
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** The pressure evolution of the Kondo model fit parameters across the pressure range 0–70 kbar in Pd₂MnIn. Black points were obtained upon pressure increase, pink points were obtained at pressure release. The left side of the double y plot shows the pressure dependence of Ln(Tₖ) (see, black solid pentagons). Ln(Tₖ) decreases by several orders of magnitude in the pressure range 17–70 kbar and reaches a saturating value for pressure exceeding P > 50 kbar. Notably, upon pressure release to 0 kbar Ln(Tₖ) remains low, close to its high-pressure saturating value (see, pink partially filled pentagon). The right side of the double y plot shows the pressure dependence of the inverse of the B parameter which is proportional to the concentration of the magnetic scattering centres. 1/B decreases as the pressure is increased (see, black partially crossed diamonds). The low pressure value of 1/B is not recovered upon pressure release to 0 kbar (see, pink partially filled diamond). The error bars in Ln(Tₖ) and 1/B were calculated by shifting the fitted temperature range by ±5 K on either side. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Powder neutron diffraction time-of-flight (TOF) measurements in Pd₂MnIn at 100 K temperature in the pressure range 0–40 kbar at the PEARL beamline. Sample at 0 kbar has no internal strain and shows a broad peak in the TOF results characteristic of type 2 antiferromagnetism (AFM) along the (111) crystallographic direction (see, black line and points). The peak is fitted with a Gaussian function (see, red line). As the pressure is increased, internal strain arising in the sample due to pressure gradients inside the pressure cell leads to the complete disappearance of the type 2 AFM peak at the temperature of 100 K (see, blue, pink, green and yellow lines and points. For clarity, non-zero pressure results are shifted along the y-axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Powder X-ray diffraction measurements of Pd₂MnIn at room temperature. The sample containing no strain (see, solid black squares) shows narrow XRD peaks coinciding well with the model simulation (see, solid red line). Prominent peaks are indexed. The intensities across different datasets are normalised to the maximum intensity of the (220) peak. The sample recovered after the high-pressure neutron diffraction experiment at PEARL shows significant peak broadening (see, open squares), which is indicative of the presence of internal strain. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

diffraction (XRD) measurements at room temperature (see, Fig. 8). The sample before the high-pressure neutron diffraction experiments contained no internal strain and showed narrow XRD peaks that coincide well with the model simulation (see, Fig. 8 solid squares and solid red line, respectively). Prominent peaks are indexed using Fullprof Rietveld refinement. Whereas, the sample recovered after the high-pressure neutron diffraction experiment at PEARL shows significant peak broadening (see, Fig. 8 open squares), which is indicative of the presence of internal strain. The intensities across different datasets are normalised to the maximum intensity of the (220) index peak.

Finally, magnetisation measurements were conducted on two Pd₂MnIn powder samples collected before and after the high-pressure neutron diffraction experiments, without and with strain respectively. Magnetisation *M* was measured as a function of temperature in an external magnetic field of *B* = 30mT both under zero-field cooled (ZFC) and field cooled (FC) conditions as described in the Methods section (Fig. 9). All data was normalised to sample mass. The ZFC and FC magnetisations in a sample without strain show an antiferromagnetic transition temperature *T*<sub>N</sub> ~ 120 K (see, Fig. 9, black solid and open squares). The ZFC and FC magnetisations begin to deviate at temperatures below *T* < 80 K when frozen glass effects are observed. These results are consistent with findings obtained for crystallographically ordered Pd₂MnIn samples from published literature [10,11,14]. On the other hand, the ZFC and FC magnetisations in the strained sample (recovered from PEARL) show an antiferromagnetic transition at much lower temperatures *T*<sub>N</sub> ~ 40 K (see, Fig. 9, blue solid and open circles) and glassy effects appearing near *T*~ 100 K. Notably, similar temperature dependencies in the magnetisation were observed in crystallographically disordered, quenched Pd₂MnIn samples [11]. These results explain the absence of antiferromagnetic order at a temperature of *T* = 100 K in high-pressure neutron diffraction experiments at PEARL. The presence of internal strain due to generation of pressure has suppressed the antiferromagnetic transition to lower temperatures.

Interestingly, the strain dependence of the magnetic isotherms *M* as a function of magnetic field (B= ±1T) at select temperatures in the range 50–150 K has revealed unexpected behaviour. The sample without strain shows linear magnetic isotherms as a function of magnetic field at 50 K (Fig. 10a, solid blue triangles), 100 K (Fig. 10a, solid red circles) and 150 K (Fig. 10a, solid black squares). This type of field dependence is expected for paramagnetic and antiferromagnetic materials. On the other hand, strained sample (recovered from PEARL) shows a ferromagnetic (FM) anomaly superposed on top of the expected linear field dependence in the magnetic isotherms at all measured temperatures (see, Fig. 10 b), partially filled blue triangles, red circles and black squares respectively). The observed FM signal appears to be strongly sensitive to internal strain inside the sample and could be consistent with the presence of strain-formed ferromagnetic glassy inclusions in Pd₂MnIn. The FM glassy inclusions interacting with itinerant conduction electrons in Pd₂MnIn may be the origin of the observed Kondo response observed in the electrical resistivity.

## 4. Discussion and conclusion

To summarise, the temperature dependence of electrical resistivity ρ(T) in paramagnetic Pd₂MnIn has revealed unexpected signatures of the Kondo effect under high pressure in the absence of chemical doping (see, Fig. 2). Neutron and X-ray diffraction measurements (see, Figs. 7, 8) have confirmed that the origin of the Kondo response in the resistivity is most likely linked to the formation of strain-induced islands of local lattice deformation. The strain arises due to pressure gradients resulting from the application of pressure across quasi-hydrostatic pressure medium. Magnetisation measurements and comparisons between samples with different amounts of strain have confirmed that the Kondo islands are probably ferromagnetic and glassy and exist at all temperatures (see, Fig. 10). The Kondo response in the resistivity occurs when the conduction electrons in Pd₂MnIn interact with the ferromagnetic (FM), glassy Kondo islands. Likely, the Kondo
<figure><img src="image_12.png" /><figcaption>Fig. 9. Temperature dependence of the magnetisation *M* in Pd<sub>2</sub>MnIn samples with and without strain in an external magnetic field of 30 mT. All data is normalised to sample mass. Zero-field cooled (ZFC) and field cooled (FC) magnetisations in a sample without strain show an antiferromagnetic transition temperature T<sub>N</sub> ~ 120 K (see, black solid and open squares). The ZFC and FC magnetisations begin to deviate below T < 80 K when frozen glass effects are observed. ZFC and FC magnetisations in the strained sample (recovered from PEARL) show an antiferromagnetic transition at much lower temperatures T<sub>N</sub> ~ 40 K (see, blue solid and open circles) and glassy effects appearing near T~ 100 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

response becomes masked when Pd<sub>2</sub>MnIn becomes antiferromagnetic at low temperatures (T < 50 K) which would lead to the observed metallic behaviours in the resistivity.

In addition, it was shown that the Kondo response is strengthened by the application of pressure. This is demonstrated by the simultaneous logarithmic decrease in the Kondo temperature T<sub>K</sub> and the 1/B parameter in the Hamann equation Eq. (1) with the application of pressure (see, Fig. 6). Physically this could be interpreted as a pressure-induced increase in the magnetic coupling constant *J* between the glassy, FM Kondo islands accompanied by a decrease in their concentration density. Therefore, a combination of these findings implies that as the pressure (and strain) is increased the FM Kondo islands are perceived to grow in size and interact more strongly with the delocalised conduction electrons. A schematic way how such processes could arise are depicted in Fig. 11(a).

The present discovery of strain and pressure-controlled Kondo island effect in Pd<sub>2</sub>MnIn could be used to fabricate Heusler-alloy based metamaterials with nanoscale magnetic striations for a variety of technological applications in memory and spintronic valves and switching devices. The strain can be reliably introduced into Heusler alloy thin films by controlling the substrate texture on the nanoscale ~100 nm as shown in Fig. 11(b). The impact of strain is expected to be most significant when the Heusler film thickness is reduced to a fraction of the size of the texturing parameter. Thus, for a substrate texture variation of the order of ~100 nm the Heusler thin film thickness should approach ~10 nm for maximal local strain formation.

The correlation between the presence of the Kondo effect and
half-metallic properties is not an isolated incident. For example, ferro-
magnetic Kondo-lattice models have frequently been used to describe
the spin-polarisation and magnetisation properties in half-metals [25].

Heusler thin-films, particular the Co₂Mn-based systems, have demon-
strated Kondo effect at low temperatures [3,4], which may have rel-
evance to their unconventional spin polarisation behaviours. The im-
portance of the Kondo effect has also been shown in various 2D
materials, such as Dirac and Weyl semimetals and their nanostructures
that have been proposed as half-metal candidates [8,9,26,27]. Notably,
recent studies on two-dimensional electron system (2DES) found at the
LaAlO₃/SrTiO₃ interfaces have discovered emerging Kondo effect due
to orbital selection by electrical gating in the complete absence of mag-
netic impurities [28]. In these types of low-dimensional materials the
presence of an electrical field may often be mimicked by locally varying
lattice strain, which could be effectively used to control the spin po-
larisation and magnetisation [29]. The more broad implications would
suggest that by locally varying strain inside a 3D bulk material Kondo-
like properties may also be induced and potentially bring the system
closer to half-metallic characteristics. This is potentially what has been
observed in the present high-pressure study on polycrystalline Pd₂MnIn
bulk samples. The emergence of strain-related Kondo signatures have
been irreversibly induced in Pd₂MnIn by cycling it to high pressures of
P = 70 kbar and coincide with near temperature-independent features
in electrical conductivity, reminiscent of a half-metal. In-depth theo-
retical studies may confirm whether the high-temperature Kondo effect
properties seen in strained Pd₂MnIn could indeed be an indication of
half-metallic behaviour.

The present findings could mean significant breakthroughs in the
fields of half-metals and spintronic systems. The ability to manipulate
magnetic and electronic properties through strain-controlled Kondo
response is an attractive approach to engineer and design novel ma-
terials for spintronic and related applications. The implications of this
discovery reach far beyond the field of Heusler alloys and could be
particularly relevant in low-dimensional materials, their derivatives
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** The strain dependence of the magnetic isotherms *M* in Pd<sub>2</sub>MnIn at select temperatures in the range 50–150 K and magnetic fields *B*= ±1T. (a) Sample without strain shows linear magnetic isotherms at 50 K (solid blue triangles), 100 K (solid red circles) and 150 K (solid black squares). This behaviour is expected for paramagnetic and antiferromagnetic materials. (b) Strained sample (recovered from PEARL) shows a near temperature-independent ferromagnetic (FM) anomaly superposed on top of the expected linear magnetic isotherms at 50 K, 100 K and 150 K (see, partially filled blue triangles, red circles and black squares respectively). The FM signal could be consistent with the presence of strain-formed ferromagnetic Kondo glassy inclusions in Pd<sub>2</sub>MnIn. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

and nanostructures which are, due to their reduced dimensionality,
more susceptible to strain and deformation. Utilising strain-controlled
magneto-electric-elastic phenomena may create a road map towards
innovative technological applications to help address the global chal-
lenges that we face today.

Declaration of competing interest

The authors declare the following financial interests/personal rela-
tionships which may be considered as potential competing interests:
Anna Kusmartseva reports financial support was provided by The Royal
Society. If there are other authors, they declare that they have no

known competing financial interests or personal relationships that
could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgments

This publication is based upon work supported by the Royal Society
of London No. 21-52-10015. A.K. acknowledges the support from the
Royal Society, United Kingdom, grant numbers IEC/R2/202314 and
IEC/R2/202164.
<figure><img src="image_14.png" /><figcaption>**Fig. 11.** A schematic diagram to illustrate the formation of pressure-induced, strain-controlled Kondo islands in paramagnetic $Pd_2MnIn$. (a) The increase in deformational strain as quasi-hydrostatic pressure is applied to $Pd_2MnIn$ creates ferromagnetic (FM) glassy regions (blue shaded regions) across the sample, where magnetic coupling *J* arises between the neighbouring Mn atoms (shown in purple). The conduction electrons exhibit Kondo-like responses upon interaction with the FM glassy islands. As the pressure (and strain) increases the FM glassy islands grow in size and the magnetic coupling *J* inside the islands becomes stronger. (b) Potential applications of the strain-controlled Kondo effect in $Pd_2MnIn$ could be used to fabricate metamaterials with nanoscale magnetic striations for memory devices. As an example, this could be achieved by growing Heusler thinfilms on a nano-textured substrate and introducing strain on the nanoscale ~100 nm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

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