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Competing interactions in frustrated magnets can give rise to highly degenerate ground states from which correlated liquid-like states of matter often emerge. The scaling of this degeneracy influences the ultimate ground state, with extensive degeneracies potentially yielding quantum spin liquids, while sub-extensive or smaller degeneracies yield static orders. A longstanding problem is to understand how ordered states precipitate from this degenerate manifold and what echoes of the degeneracy survive ordering. Here, we use neutron scattering to experimentally demonstrate a new "nodal line" spin liquid, where spins collectively fluctuate within a sub-extensive manifold spanning one-dimensional lines in reciprocal space. Realized in the spin-orbit coupled, face-centered cubic iridate K$_2$IrCl$_6$, we show that the sub-extensive degeneracy is robust, but remains susceptible to fluctuations or longer range interactions which cooperate to select a magnetic order at low temperatures. Proximity to the nodal line spin liquid influences the ordered state, enhancing the effects of quantum fluctuations and stabilizing it through the opening of a large spin-wave gap. Our results demonstrate quantum fluctuations can act counter-intuitively in frustrated materials: instead of destabilizing ordering, at the brink of the nodal spin liquid they can act to stabilize it and dictate its low-energy physics., Comment: Main article: 9 pages, 3 figures. Supplemental material: 22 pages, 15 figures

The pyrochlore iridates have become ideal platforms to unravel fascinating correlated and topolog?ical phenomena that stem from the intricate interplay among strong spin-orbit coupling, electronic correlations, lattice with geometric frustration, and itinerancy of the 5d electrons. The all-in-all?out antiferromagnetic state, commonly considered as the magnetic ground state, can be dramatically altered in reduced dimensionality, leading to exotic or hidden quantum states inaccessible in bulk. Here, by means of magnetotransport, resonant elastic and inelastic x-ray scattering experiments, we discover an emergent quantum disordered state in (111) Y2Ir2O7 thin films (thickness less than 30 nm) per?sisting down to 5 K, characterized by dispersionless magnetic excitations. The anomalous Hall effect observed below an onset temperature near 135 K corroborates the presence of chiral short-range spin configurations expressed in non-zero scalar spin chirality, breaking the macroscopic time-reversal symmetry. The origin of this chiral state is ascribed to the restoration of magnetic frustration on the pyrochlore lattice in lower dimensionality, where the competing exchange interactions together with enhanced quantum fluctuations suppress any long-range order and trigger spin-liquid-like behavior with degenerate ground-state manifold.

The iron-based high-$T_c$ superconductors exhibit rich phase diagrams with intertwined phases, including magnetism, nematicity and superconductivity. The superconducting $T_c$ in many of these materials is maximized in the regime of strong nematic fluctuations, making the role of nematicity in influencing the superconductivity a topic of intense research. Here, we use the AC elastocaloric effect (ECE) to map out the phase diagram of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ near optimal doping. The ECE signature at $T_c$ on the overdoped side, where superconductivity condenses without any nematic order, is quantitatively consistent with other thermodynamic probes that indicate a single-component superconducting state. In contrast, on the slightly underdoped side, where superconductivity condenses within the nematic phase, ECE reveals a second thermodynamic transition proximate to and below $T_c$. We rule out magnetism and re-entrant tetragonality as the origin of this transition, and find that our observations strongly suggest a phase transition into a multicomponent superconducting state. This implies the existence of a sub-dominant pairing instability that competes strongly with the dominant $s^\pm$ instability. Our results thus motivate a re-examination of the pairing state and its interplay with nematicity in this extensively studied iron-based superconductor, while also demonstrating the power of ECE in uncovering strain-tuned phase diagrams of quantum materials.

The Fe intercalated transition metal dichalcogenide (TMD), Fe$_{1/3}$NbS$_2$, exhibits remarkable resistance switching properties and highly tunable spin ordering phases due to magnetic defects. We conduct synchrotron X-ray scattering measurements on both under-intercalated ($x$ = 0.32) and over-intercalated ($x$ = 0.35) samples. We discover a new charge order phase in the over-intercalated sample, where the excess Fe atoms lead to a zigzag antiferromagnetic order. The agreement between the charge and magnetic ordering temperatures, as well as their intensity relationship, suggests a strong magnetoelastic coupling as the mechanism for the charge ordering. Our results reveal the first example of a charge order phase among the intercalated TMD family and demonstrate the ability to stabilize charge modulation by introducing electronic correlations, where the charge order is absent in bulk 2H-NbS$_2$ compared to other pristine TMDs.

We report the single crystal growth and characterization of EuIn$_2$, a magnetic topological semimetal candidate according to our density functional theory (DFT) calculations. We present results from electrical resistance, magnetization, M\"ossbauer spectroscopy, and X-ray resonant magnetic scattering (XRMS) measurements. We observe three magnetic transitions at $T_{\text{N}1}\sim 14.2~$K, $T_{\text{N}2}\sim12.8~$K and $T_{\text{N}3}\sim 11~$K, signatures of which are consistently seen in anisotropic temperature dependent magnetic susceptibility and electrical resistance data. M\"ossbauer spectroscopy measurements on ground crystals suggest an incommensurate sinusoidally modulated magnetic structure below the transition at $T_{\text{N}1}\sim 14~$K, followed by the appearance of higher harmonics in the modulation on further cooling roughly below $T_{\text{N}2}\sim13~$K, before the moment distribution squaring up below the lowest transition around $T_{\text{N}3}\sim 11~$K. XRMS measurements showed the appearance of magnetic Bragg peaks below $T_{\text{N}1}\sim14~$K, with a propagation vector of $\bm{\tau}$ $=(\tau_h,\bar{\tau}_h,0)$, with $\tau_h$varying with temperature, and showing a jump at $T_{\text{N}3}\sim11$~K. The temperature dependence of $\tau_h$ between $\sim11$~K and $14$~K shows incommensurate values consistent with the M\"{o}ssbauer data. XRMS data indicate that $\tau_h$ remains incommensurate at low temperatures and locks into $\tau_h=0.3443(1)$.

The origin of nematicity in FeSe remains a critical outstanding question towards understanding unconventional superconductivity in proximity to nematic order. To understand what drives the nematicity, it is essential to determine which electronic degree of freedom admits a spontaneous order parameter independent from the structural distortion. Here, we use X-ray linear dichroism at the Fe K pre-edge to measure the anisotropy of the 3d orbital occupation as a function of in situ applied stress and temperature across the nematic transition. Along with X-ray diffraction to precisely quantify the strain state, we reveal a lattice-independent, spontaneously-ordered orbital polarization within the nematic phase, as well as an orbital polarizability that diverges as the transition is approached from above. These results provide strong evidence that spontaneous orbital polarization serves as the primary order parameter of the nematic phase., Comment: Main: 22 pages, 4 figures. Supp: 32 pages, 18 figures

Symmetry plays a key role in determining the physical properties of materials. By Neumann's principle, the properties of a material are invariant under the symmetry operations of the space group to which the material belongs. Continuous phase transitions are associated with a spontaneous reduction in symmetry. (For example, the onset of ferromagnetism spontaneously breaks time reversal symmetry.) Much less common are examples where proximity to a continuous phase transition leads to an increase in symmetry. Here, we find an emergent tetragonal symmetry close to an apparent charge density wave (CDW) bicritical point in a fundamentally orthorhombic material, ErTe$_3$, for which the CDW phase transitions are tuned via anisotropic strain. The underlying structure of the material remains orthorhombic for all applied strains, including at the bicritical point, due to a glide plane symmetry in the crystal structure. Nevertheless, the observation of a divergence in the anisotropy of the in-plane elastoresistivity reveals an emergent electronic tetragonality near the bicritical point.

Field-induced superconductivity is a rare phenomenon where an applied magnetic field enhances or induces superconductivity. This fascinating effect arises from a complex interplay between magnetism and superconductivity, and it offers the tantalizing technological possibility of an infinite magnetoresistance superconducting spin valve. Here, we demonstrate field-induced superconductivity at a record-high temperature of T=9K in two samples of the ferromagnetic superconductor Eu(Fe$_{0.88}$Co$_{0.12}$)$_{2}$As$_{2}$. We combine tunable uniaxial stress and applied magnetic field to shift the temperature range of the zero-resistance state between 4K and 10K. We use x-ray diffraction and spectroscopy measurements under stress and field to demonstrate that stress tuning of the nematic order and field tuning of the ferromagnetism act as independent tuning knobs of the superconductivity. Finally, DFT calculations and analysis of the Eu dipole field reveal the electromagnetic mechanism of the field-induced superconductivity., Comment: Main text: 15 pages, 5 figures; Supplement: 15 pages, 10 supplementary figures

We investigate an experimental toy-model system of a pseudospin-half square-lattice Hubbard Hamiltonian in [(SrIrO3)1/(CaTiO3)1] to include both nontrivial complex hopping and moderate electronic correlation. While the former induces electronic Berry phases as anticipated from the weak-coupling limit, the later stabilizes an antiferromagnetic (AFM) Mott insulator ground state in analogous to the strong-coupling limit. Their combined results in the real system are found to be an anomalous Hall effect with a non-monotonic temperature dependence due to the self-competition of the electron-hole pairing in the Mott state, and an exceptionally large Ising anisotropy that is captured as a giant magnon gap beyond the superexchange approach. The unusual phenomena highlight the rich interplay of electronic topology and electronic correlation in the intermediate-coupling regime that is largely unexplored and challenging in theoretical modelling., Comment: Accepted by Phys. Rev. X

The number of atomic layers confined in a two-dimensional structure is crucial for the electronic and magnetic properties. Single-layer and bilayer $J_{\rm eff} = 1/2$ square lattices are well-known examples where the presence of the extra layer turns the XY-anisotropy to the $c$-axis anisotropy. We report on experimental realization of a hybrid SrIrO$_3$/SrTiO$_3$ superlattice that integrates monolayer and bilayer square lattices in one layered structure. By synchrotron x-ray diffraction, resonant x-ray magnetic scattering, magnetization, and resistivity measurements, we found that the hybrid superlattice exhibits properties that are distinct from both the single-layer and bilayer systems and cannot be explained by a simple addition of them. In particular, the entire hybrid superlattice orders simultaneously through a single antiferromagnetic transition at temperatures similar to the bilayer system but with all the $J_{\rm eff} = 1/2$ moments mainly pointing in the $ab$-plane similar to the single-layer system. The results show that bringing monolayer and bilayer with orthogonal properties in proximity to each other in a hybrid superlattice structure is a powerful way to stabilize a unique state not obtainable in a uniform structure.

Electronic nematicity in iron pnictide materials has been extensively studied by various experimental techniques, yet its heat capacity anomaly at the phase transition has not been examined quantitatively. In this work we review the thermodynamic description of nematicity in $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ using the Landau free energy, which defines the behavior of three thermodynamic quantities: the structural orthorhombicity that develops below the nematic transition, the softening shear modulus above the transition, and the discontinuous heat capacity at the transition. We derive a quantitative relationship between these three quantities, which is found to hold for a range of dopings. This result shows that the nematic transition is exceedingly well described by a mean-field model in the underdoped regime of the phase diagram.

Emergent superconductivity is strongly correlated with the symmetry of local atomic configuration in the parent compounds of iron-based superconductors. While chemical doping or hydrostatic pressure can change the local geometry, these conventional approaches do not provide a clear pathway in tuning the detailed atomic arrangement predictably, due to the parent compounds complicated structural deformation in the presence of the tetragonal-to-orthorhombic phase transition. Here, we demonstrate a systematic approach to manipulate the local structural configurations in BaFe2As2 epitaxial thin films by controlling two independent structural factors orthorhombicity (in-plane anisotropy) and tetragonality (out-of-plane/in-plane balance) from lattice parameters. We tune superconductivity without chemical doping utilizing both structural factors separately, controlling local tetrahedral coordination in designed thin film heterostructures with substrate clamping and bi-axial strain. We further show that this allows quantitative control of both the structural phase transition, associated magnetism, and superconductivity in the parent material BaFe2As2. This approach will advance the development of tunable thin film superconductors in reduced dimension.

The interplay between electronic interactions and strong spin-orbit coupling is expected to create a plethora of fascinating correlated topological states of quantum matter. Of particular interest are magnetic Weyl semimetals originally proposed in the pyrochlore iridates, which are only expected to reveal their topological nature in thin film form. To date, however, direct experimental demonstrations of these exotic phases remain elusive, due to the lack of usable single crystals and the insufficient quality of available films. Here, we report on the discovery of the long-sought magnetic Weyl semi-metallic phase in (111)-oriented Eu$_2$Ir$_2$O$_7$ high-quality epitaxial thin films. The topological magnetic state shows an intrinsic anomalous Hall effect with colossal coercivity but vanishing net magnetization, which emerges below the onset of a peculiar magnetic phase with all-in-all-out antiferromagnetic ordering. The observed anomalous Hall conductivity arises from the non-zero Berry curvature emanated by Weyl node pairs near the Fermi level that act as sources and sinks of Berry flux, activated by broken cubic crystal symmetry at the top and bottom terminations of the thin film.

Materials with strong magnetoresistive responses are the backbone of spintronic technology, magnetic sensors, and hard drives. Among them, manganese oxides with a mixed valence and a cubic perovskite structure stand out due to their colossal magnetoresistance (CMR). A double exchange interaction underlies the CMR in manganates, whereby charge transport is enhanced when the spins on neighboring Mn3+ and Mn4+ ions are parallel. Prior efforts to find different materials or mechanisms for CMR resulted in a much smaller effect. Here we show an enormous CMR at low temperatures in EuCd2P2 without manganese, oxygen, mixed valence, or cubic perovskite structure. EuCd2P2 has a layered trigonal lattice and exhibits antiferromagnetic ordering at 11 K. The magnitude of CMR (104 percent) in as-grown crystals of EuCd2P2 rivals the magnitude in optimized thin films of manganates. Our magnetization, transport, and synchrotron X-ray data suggest that strong magnetic fluctuations are responsible for this phenomenon. The realization of CMR at low temperatures without heterovalency leads to a new regime for materials and technologies related to antiferromagnetic spintronics.

Of all parent compounds of iron-based high-temperature superconductors, EuFe2As2 exhibits by far the largest magnetostructural coupling due to the sizable biquadratic interaction between Eu and Fe moments. While the coupling between Eu antiferromagnetic order and Fe structural/antiferromagnetic domains enables rapid field detwinning, this prevents simple magnetometry measurements from extracting the critical fields of the Eu metamagnetic transition. Here we measure these critical fields by combining x-ray magnetic circular dichroism spectroscopy with in-situ tunable uniaxial stress and applied magnetic field. The combination of two tuning knobs allows us to separate the stress-detwinning of structural domains from the field-induced reorientation of Eu moments. Intriguingly, we find a spin-flip transition which can only result from a strongly anisotropic interaction between Eu planes. We argue that this anisotropic exchange is a consequence of the strong anisotropy in the magnetically ordered Fe layer, which presents a new form of higher-order coupling between Eu and Fe magnetism., Comment: Main text: 11 pages 5 figures

We describe a novel approach for the rational design and synthesis of self-assembled periodic nanostructures using martensitic phase transformations. We demonstrate this approach in a thin film of perovskite SrSnO3 with reconfigurable periodic nanostructures consisting of regularly spaced regions of sharply contrasted dielectric properties. The films can be designed to have different periodicities and relative phase fractions via chemical doping or strain engineering. The dielectric contrast within a single film can be tuned using temperature and laser wavelength, effectively creating a variable photonic crystal. Our results show the realistic possibility of designing large-area self-assembled periodic structures using martensitic phase transformations with the potential of implementing "built-to-order" nanostructures for tailored optoelectronic functionalities., Comment: 13 pages, 5 figures

Electronic nematicity in iron pnictide materials is coupled to both the lattice and the conducting electrons, which allows both structural and transport observables to probe nematic fluctuations and the order parameter. Here we combine simultaneous transport and x-ray diffraction measurements with in-situ tunable strain (elasto-XRD) to measure the temperature dependence of the shear modulus and elastoresistivity above the nematic transition and the spontaneous orthorhombicity and resistivity anisotropy below the nematic transition, all within a single sample of $Ba(Fe_{0.96}Co_{0.04})_{2} As_{2}$. The ratio of transport to structural quantities is nearly temperature-independent over a 74 K range and agrees between the ordered and disordered phases. These results show that elasto-XRD is a powerful technique to probe the nemato-elastic and nemato-transport couplings, which have important implications to the nearby superconductivity. It also enables the measurement in the large strain limit, where the breakdown of mean field description reveals the intertwined nature of nematicity., Comment: Main text 10 pages, 4 figures

We report on the epitaxial strain-driven electronic and antiferromagnetic modulations of a pseudospin-half square lattice realized in superlattices of (SrIrO3)1/(SrTiO3)1. With increasing compressive strain, we find the low-temperature insulating behavior to be strongly suppressed with a corresponding systematic reduction of both the Neel temperature and the staggered moment. However, despite such a suppression, the system remains weakly insulating above the Neel transition. The emergence of metallicity is observed under large compressive strain but only at temperatures far above the N\'eel transition. These behaviors are characteristics of the Slater-Mott crossover regime, providing a unique experimental model system of the spin-half Hubbard Hamiltonian with a tunable intermediate coupling strength.

Rare earth pyrochlore Iridates (RE2Ir2O7) consist of two interpenetrating cation sublattices, the RE with highly-frustrated magnetic moments, and the Iridium with extended conduction orbitals significantly mixed by spin-orbit interactions. The coexistence and coupling of these two sublattices create a landscape for discovery and manipulation of quantum phenomena such as the topological Hall effect, massless conduction bands, and quantum criticality. Thin films allow extended control of the material system via symmetry-lowering effects such as strain. While bulk Pr2Ir2O7 shows a spontaneous hysteretic Hall effect below 1.5K, we observe the effect at elevated temperatures up to 15K in epitaxial thin films on (111) YSZ substrates synthesized via solid phase epitaxy. Similar to the bulk, the lack of observable long-range magnetic order in the thin films points to a topological origin. We use synchrotron-based element-specific x-ray diffraction (XRD) and x-ray magnetic circular dichroism (XMCD) to compare powders and thin films to attribute the spontaneous Hall effect in the films to localization of the Ir moments. We link the thin film Ir local moments to lattice distortions absent in the bulk-like powders. We conclude that the elevated-temperature spontaneous Hall effect is caused by the topological effect originating either from the Ir or Pr sublattice, with interaction strength enhanced by the Ir local moments. This spontaneous Hall effect with weak net moment highlights the effect of vanishingly small lattice distortions as a means to discover topological phenomena in metallic frustrated magnetic materials.

5d iridates have shown vast emergent phenomena due to a strong interplay among its lattice, charge and spin degrees of freedom, because of which the potential in spintronic application of the thin-film form is highly leveraged. Here we have epitaxially stabilized perovskite SrIr$_{0.8}$Sn$_{0.2}$O$_3$ on [001] SrTiO$_3$ substrates through pulsed laser deposition and systematically characterized the structural, electronic and magnetic properties. Physical properties measurements unravel an insulating ground state with a weak ferromagnetism in the compressively strained epitaxial film. The octahedral rotation pattern is identified by synchrotron x-ray diffraction, resolving a mix of $a^+b^-c^-$ and $a^-b^+c^-$ domains. X-ray magnetic resonant scattering directly demonstrates a G-type antiferromagnetic structure of the magnetic order and the spin canting nature of the weak ferromagnetism., Comment: Accepted by Physical Review Material

High temperature superconductivity emerges in the vicinity of competing strongly correlated phases. In the iron-based superconductor $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$, the superconducting state shares the composition-temperature phase diagram with an electronic nematic phase and an antiferromagnetic phase that break the crystalline rotational symmetry. Symmetry considerations suggest that anisotropic strain can enhance these competing phases and thus suppress the superconductivity. Here we study the effect of anisotropic strain on the superconducting transition in single crystals of $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ through electrical transport, magnetic susceptibility, and x-ray diffraction measurements. We find that in the underdoped and near-optimally doped regions of the phase diagram, the superconducting critical temperature is rapidly suppressed by both compressive and tensile stress, and in the underdoped case this suppression is enough to induce a strain-tuned superconductor to metal quantum phase transition., Comment: Main Text: 8 pages + 3 figures Supplementary: 8 pages +7 figures + 3 tables

As a hallmark of electronic correlation, spin-charge interplay underlies many emergent phenomena in doped Mott insulators, such as high-temperature superconductivity, whereas the half-filled parent state is usually electronically frozen with an antiferromagnetic order that resists external control. We report on the observation of a new positive magnetoresistance that probes the staggered susceptibility of a pseudospin-half square-lattice Mott insulator built as an artificial SrIrO3/SrTiO3 superlattice. Its size is particularly large in the high-temperature insulating paramagnetic phase near the N\'eel transition. This novel magnetoresistance originates from a collective charge response to the large longitudinal spin fluctuations under a linear coupling between the external magnetic field and the staggered magnetization enabled by strong spin-orbit interaction. Our results demonstrate a magnetic control of the binding energy of the fluctuating particle-hole pairs in the Slater-Mott crossover regime analogous to the BCS-to-Bose-Einstein condensation crossover of ultracold-superfluids., Comment: Accepted by Nature communications

A fundamental difference between antiferromagnets and ferromagnets is the lack of linear coupling to a uniform magnetic field due to the staggered order parameter. Such coupling is possible via the Dzyaloshinskii-Moriya (DM) interaction but at the expense of reduced antiferromagnetic (AFM) susceptibility due to the canting-induced spin anisotropy. We solve this long-standing problem with a top-down approach that utilizes spin-orbit coupling in the presence of a hidden SU(2) symmetry. We demonstrate giant AFM responses to sub-Tesla external fields by exploiting the extremely strong two-dimensional critical fluctuations preserved under a symmetry-invariant exchange anisotropy, which is built into a square-lattice artificially synthesized as a superlattice of SrIrO3 and SrTiO3. The observed field-induced logarithmic increase of the ordering temperature enables highly efficient control of the AFM order. As antiferromagnets promise to afford switching speed and storage security far beyond ferromagnets, our symmetry-invariant approach unleashes the great potential of functional antiferromagnets., Comment: 3 figures

Searching for new functionality in next generation electronic devices is a principal driver of material physics research. Multiferroics simultaneously exhibit electric and magnetic order parameters that may be coupled through magnetoelectric (ME) effects. In single-phase materials the ME effect arises from one of three known mechanisms: inverse Dzyaloshinskii-Moriya (IDM) interaction, spin dependent ligand-metal (p-d) orbital hybridization, and exchange striction. However, the coupling among these mechanisms remains largely unexplored despite envisioned potential capabilities. Here, we present cooperative tuning between both IDM interaction and p-d hybridization that leads to discrete ME states in Ba0.5Sr2.5Co2Fe24O41. In-situ x-ray diffraction exposes the microscopic interplay between these two mechanisms, marked by a unique ME susceptibility upon electric and magnetic fields. The entangled multi-ME coupling phenomenon observed in this room-temperature ME hexaferrite offers a pathway to novel functional control for ME device applications.

Ordered electronic phases are intimately related to emerging phenomena such as high Tc superconductivity and colossal magnetoresistance. The coupling of electronic charge with other degrees of freedom such as lattice and spin are of central interest in correlated systems. Their correlations have been intensively studied from femtosecond to picosecond time scales, while the dynamics of ordered electronic phases beyond nanoseconds are usually assumed to follow a trivia thermally driven recovery. Here, we report an unusual slowing down of the recovery of an electronic phase across a first-order phase transition, far beyond thermal relaxation time. Following optical excitation, the recovery time of both transient optical reflectivity and x-ray diffraction intensity from a charge-ordered superstructure in a La$_{1/3}$Sr$_{2/3}$FeO$_3$ thin film increases by orders of magnitude longer than the independently measured lattice cooling time when the sample temperature approaches the phase transition temperature. The combined experimental and theoretical investigations show that the slowing down of electronic recovery corresponds to the pseudo-critical dynamics that originates from magnetic interactions close to a weakly first-order phase transition. This extraordinary long electronic recovery time exemplifies an interplay of ordered electronic phases with magnetism beyond thermal processes in correlated systems.

Elastic strain is potentially an important approach in tuning the properties of the improperly multiferroic hexagonal ferrites, the details of which have however been elusive due to the experimental difficulties. Employing the method of restrained thermal expansion, we have studied the effect of isothermal biaxial strain in the basal plane of h-LuFeO3 (001) films. The results indicate that a compressive biaxial strain significantly enhances the ferrodistortion, and the effect is larger at higher temperatures. The compressive biaxial strain and the enhanced ferrodistortion together, cause an increase in the electric polarization and a reduction in the canting of the weak ferromagnetic moments in h-LuFeO3, according to our first principle calculations. These findings are important for understanding the strain effect as well as the coupling between the lattice and the improper multiferroicity in h-LuFeO3. The experimental elucidation of the strain effect in h-LuFeO3 films also suggests that the restrained thermal expansion can be a viable method to unravel the strain effect in many other epitaxial thin film materials.