Elastocaloric Effect Probes -Wave Altermagnetic Criticality in MnF at Finite Temperature

Scientists are increasingly interested in altermagnets , exotic materials exhibiting order without conventional magnetisation. Rahel Ohlendorf (Max Planck Institute for Chemical Physics of Solids, Technische Universität Dresden), Luca Buiarelli (University of Minnesota) and Hilary M. L. Noad (Max Planck Institute for Chemical Physics of Solids) et al. have now demonstrated a novel method to probe the elusive altermagnetic critical point in manganese fluoride (MnF) using the elastocaloric effect under strain. Their combined approach, incorporating experiments, modelling and first-principles calculations, confirms theoretical predictions and establishes a crucial pathway for investigating altermagnetic behaviour in this and future materials , potentially revolutionising our understanding of complex magnetic orders.

The research team combined elastocaloric experiments, free-energy modelling, and first-principles calculations to establish a sensitive method for detecting the finite-temperature altermagnetic critical point. This breakthrough reveals how applying strain to MnF2 induces a measurable temperature change, the elastocaloric effect, directly linked to the unique Symmetry breaking characteristic of altermagnets. Specifically, the study focused on d-wave altermagnets, where the order parameter mirrors magnetic multipoles and couples to both a magnetic field and uniaxial strain, allowing for thermodynamic characterisation.

Experiments show that the elastocaloric effect serves as a powerful tool for probing the unconventional symmetry breaking in altermagnets, offering fundamental insights into their thermodynamic properties. The team meticulously explored the relationship between applied strain and temperature changes in MnF2, confirming predictions of a crossover from a sharp phase transition to a smoother transition at finite strain levels. Free-energy modelling and density functional theory calculations corroborated the experimental findings, revealing a weakly spin-orbit-coupled altermagnetic insulator with a small degree of off-stoichiometry as the underlying microscopic mechanism. This work establishes a clear link between the observed elastocaloric response and the emergent ferroic time-reversal symmetry breaking octupolar order present in MnF2.
The study unveils a scaling relation between the crossover temperature and the applied conjugate field, demonstrating a T∗−Tc ∝ h1/(βδ) behaviour, where β and δ represent critical exponents. Furthermore, researchers observed a peak in entropy near the critical temperature, decreasing predictably with increasing conjugate field, validating key theoretical predictions. By identifying a combination of magnetic field and strain as the relevant conjugate field (h = μBεxyμ0Hz), the team enabled thermodynamic measurements that directly reveal the nature of the broken symmetry in the ordered state. These results pave the way for exploring altermagnetic quantum criticality in both insulating and metallic materials, opening exciting possibilities for novel spintronic devices.

This research establishes a roadmap for future investigations of strain-tuned altermagnets, providing a sensitive thermodynamic probe for understanding their complex behaviour. The successful application of the elastocaloric effect to MnF2 demonstrates its potential for characterising multipolar order in a wide range of materials, extending beyond the rutile structure investigated here. The team’s findings not only confirm theoretical predictions but also provide a microscopic understanding of the observed thermodynamic response, solidifying the connection between symmetry breaking and measurable physical properties. Ultimately, this work advances the field of condensed matter physics and offers a pathway towards harnessing the unique functionalities of altermagnetic materials for technological applications.

Elastocaloric effect probes altermagnetic phase transition temperatures

Scientists investigated altermagnetic (AM) phenomena in MnF2, employing a combined methodology of elastocaloric experiments, free-energy modelling, and first-principles calculations to probe the predicted finite-temperature altermagnetic critical point. The research team focused on the elastocaloric effect (ECE), quantifying the adiabatic temperature change induced by strain, defined as ηij = ∂T/∂εijS = −T Cεij ∂S/∂εijT, where Cεij represents the specific heat at constant strain. This approach leverages the ECE’s sensitivity to symmetry breaking, facilitated by recent advances in in situ-tunable uniaxial pressure cells, to explore AM thermodynamics. Experiments employed MnF2 due to its well-characterized magnetic order below 67.5 K, known piezomagnetism, evidence of aspherical magnetization density, and observed AM magnon splitting.

To induce strain, researchers applied a uniaxial stress along the σ110 crystallographic direction, generating both symmetry-breaking εxy and a fully symmetric component. Knowing the Poisson’s ratio, ν, the team accounted for the symmetric component, recognising that it linearly shifts the critical temperature, Tc, alongside any field-induced shifts. This allowed construction of an extended AM free energy, expressed as f = kB/2 (T −Tc) Φ2 + u/4 Φ4 −λhΦ, where Φ is the AM order parameter and λ is the dimensionless coupling constant. The study pioneered the use of ECE to identify crossover lines in MnF2, experimentally determining T∗ − Tc as a function of the conjugate field h = μBμ0Hzεxy.

ECE data, ηxy, were collected as a function of relative temperature, T − Tc, at μ0Hz = 0 T and 6.44 T, revealing features traced to identify the AM critical point. Data analysis yielded T∗ = Tc + Tc λh / (kBTc)1/(βδ), aligning with expectations for an AM critical point at μBμ0Hzεxy = 0, and fitting well with a mean-field exponent of 1/(βδ) = 2/3. Furthermore, scientists performed density functional theory (DFT) calculations, demonstrating that the observed thermodynamic response is microscopically explained by a weakly spin, orbit-coupled AM insulator with a small degree of off-stoichiometry.

Elastocaloric Effect Probes Altermagnetic Symmetry Breaking in materials

Scientists have established a thermodynamic probe of the finite-temperature altermagnetic critical point using elastocaloric experiments, free-energy modeling, and first-principles calculations on MnF2. The work verifies key thermodynamic predictions resulting from symmetry breaking in a d-wave altermagnet, demonstrating a novel approach to understanding these materials. Researchers identified a conjugate field, h, as a combination of a magnetic field and shear strain, specifically defined as h = μBεxyμ0Hz, enabling thermodynamic measurements to reveal the nature of broken symmetry. Experiments focused on the elastocaloric effect (ECE), the adiabatic temperature change induced by strain, quantified by ηij = ∂T/∂εijS = −TCεij∂S/∂εijT, where Cεij represents the specific heat at constant strain.

The team measured the ECE to explore the thermodynamics of altermagnets, leveraging advances in in-situ tunable uniaxial pressure cells. Results demonstrate a clear connection between the ECE and the altermagnetic susceptibility, a relationship previously predicted theoretically but not yet experimentally verified. Measurements on MnF2, a well-characterized magnetic material with a transition temperature of Tc = 67.5 K, revealed experimental identification of predicted crossover lines. Scientists recorded signatures of entropy accumulation near the transition temperature, confirming theoretical expectations for altermagnetic systems.

Density functional theory (DFT) calculations further supported these findings, explaining the observed thermodynamic response through a weakly spin-orbit-coupled altermagnetic insulator with slight off-stoichiometry. The breakthrough delivers a roadmap for future thermodynamic investigations of strain-tuned altermagnets, particularly for exploring altermagnetic quantum criticality in both insulating and metallic materials. Measurements confirm the sensitivity of the ECE to altermagnetic symmetries, providing a powerful tool for characterizing these complex magnetic orders. Tests prove the validity of the theoretical framework connecting ECE to the altermagnetic susceptibility, opening new avenues for materials discovery and fundamental understanding.

Elastocaloric probing reveals altermagnetic order details in rare-earth

Scientists have demonstrated a novel thermodynamic measurement of the octupolar symmetry present in the altermagnetic (AM) order parameter of MnF2. By utilising the elastocaloric effect (ECE) as a sensitive probe, researchers have investigated the strain and field dependence of the AM free energy, revealing a cusp-shaped dependence of the crossover scale T* at the AM phase transition as a function of the field conjugate to the AM order parameter. This approach allows observation of the otherwise hidden AM order parameter, even in systems where the product of polarization, magnetisation (PZM) coupling is weak. The findings establish that even small deviations from stoichiometry can significantly influence the magnitude of λ in AM insulators, potentially explaining discrepancies in earlier studies of MnF2.

The authors acknowledge that the sensitivity to stoichiometry and experimental factors like background signals represent limitations to consider. Future research should apply this ECE methodology to other AM candidates with varying λ, potentially revealing substantial ECE signatures at finite fields and enabling the determination of AM susceptibility at temperatures much greater than the critical temperature. Furthermore, extending these measurements to metallic d-wave AMs, such as KV2Se2O, and higher-order g-wave AMs like hematite, could prove particularly powerful, given the influence of spin-orbit coupling. This work positions the ECE approach as a valuable tool for investigating AM fluctuations near quantum critical points and exploring the potential link between AM order and superconductivity.