Unconventional magnetism represents a paradigm shift in condensed matter physics, effectively bridging the fast, high-density advantages of antiferromagnets with the facile read-write capability of ferromagnets. Recent developments in spin space group theory have established a systematic methodology to decouple magnetic geometry from relativistic spin-orbit coupling, driving the exploration of unconventional magnets that exhibit compensated magnetization with time-reversal-odd responses. Here, we review unconventional magnetism across three pivotal facets in momentum space: spin textures, quantum geometry, and emergent quasiparticles. From the perspective of symmetry analysis, we elucidate the mechanisms underlying time-reversal-odd physical responses, including non-relativistic spin splitting, anomalous and nonlinear Hall effects, and exotic electronic and magnonic topological phases. Finally, we provide a forward-looking perspective on coupling unconventional magnetism with ferroelectricity, superconductivity, and moiré engineering. By exploiting symmetry-driven insights, this review highlights the functional potential of unconventional magnets in developing next-generation, high
Unconventional superconductivity is a desirable state of matter due to its potential for high transition temperatures $T_{\mathrm{c}}$ and associated favorable superconducting properties. However, the sign-changing nature of the order parameter of unconventional superconductors renders their condensates fragile to disorder, an inevitability in real materials. We uncover the generic properties of electronic band structures and associated Bloch weights able to support robust unconventional superconductivity. We demonstrate this property in several case studies of the kagome and Lieb lattices, showing how unconventional superconductors exhibit unusually weak $T_{\mathrm{c}}$ suppression by disorder, despite featuring fully compensated sign-changing order parameters. We contrast these results with those for unconventional superconductivity on the square and honeycomb lattices, which are unable to protect the condensates from disorder. Finally, we discuss material candidates for which this effect may be realized.
Unconventional magnetism including altermagnetism and unconventional compensated magnetism, characterized by its duality of real-space antiferromagnetic alignment and momentum-space spin splitting, has garnered widespread attention. While altermagnetism has been extensively studied, research on unconventional compensated magnetism remains very rare. In particular, unconventional compensated magnetic materials are only theoretically predicted and have not yet been synthesized experimentally. In this study, based on symmetry analysis and the first-principles electronic structure calculations, we predict that LaMn$_2$SbO$_6$ is a unconventional compensated magnetic semiconductor. Given that the Mn ions at opposite spin lattice cannot be connected by any symmetry, the spin splitting in LaMn$_2$SbO$_6$ is isotropic. More importantly, LaMn$_2$SbO$_6$ has already been synthesized experimentally, and its magnetic structure has been confirmed by neutron scattering experiments. Therefore, LaMn$_2$SbO$_6$ serves as an excellent material platform for investigating the novel physical properties of unconventional compensated magnetic materials.
The recently predicted unconventional magnets offer a new ground for exploring the formation of nontrivial spin states due to their inherent nonrelativistic momentum-dependent spin splitting. In this work, we consider unconventional magnets with $d$- and $p$-wave parities, and investigate the effect of time-periodic light drives for inducing the formation of spin-triplet phases in the normal and superconducting states. In particular, we consider unconventional magnets without and with conventional superconductivity under linearly and circularly polarized light drives and treat the time-dependent problem within Floquet formalism, which naturally unveils photon processes and Floquet bands determining the emergent phenomena. We demonstrate that the interplay between unconventional magnetism and light gives rise to a non-trivial light-matter coupling which governs the emergence of Floquet spin-triplet states with and without superconductivity that are absent otherwise. We find that photon-assisted processes promote the formation of spin-triplet densities and spin-triplet Cooper pairs between different Floquet sidebands. More precisely, the Floquet sidebands offer an additional quantum
In this work, we prove that linear bounded operators $T$ on a Banach space $X$ allowing spectral cuts along rectifiable Jordan curves meeting their spectrum are related to classes of operators admitting an unconventional functional calculus. We identify several such classes and address the consequences regarding the existence of non-trivial closed invariant subspaces, extending previous results of Chalendar. Furthermore, we establish that every operator belonging to a broad subclass of compact perturbations of diagonalizable normal operators on separable Hilbert spaces, namely, trace-class perturbations, possesses an unconventional functional calculus and is super-decomposable, thereby extending earlier results obtained by the authors.
In this work we review the recent advances on superconducting phenomena in junctions formed by superconductors and unconventional magnets. Conventional magnets, such as ferromagnets and antiferromagnets, are characterized by broken time-reversal symmetry but only ferromagnets produce a finite net magnetization due to parallel spin alignment and spin-split bands in momentum. Very recently, a new type of magnets has been reported and here we refer to them as unconventional magnets because they exhibit special properties of both ferromagnets and antiferromagnets: they exhibit zero net magnetization (like antiferromagnets) and a nonrelativistic spin splitting of energy bands (like ferromagnets), both leading to anisotropic spin-polarized Fermi surfaces. An interesting property of unconventional magnets is that their magnetic order can be even or odd with respect to momentum, where $d$-wave altermagnets and $p$-wave magnets are the most representative examples. In this regard, $d$-wave altermagnets and $p$-wave magnets are seen as counterparts in magnetism of the unconventional $d$- and $p$-wave superconducting states, respectively. While the impact of conventional magnetism on supercon
We consider unconventional magnets with proximity-induced superconductivity and investigate the emergence of superconducting correlations by carrying out a full classification of allowed Cooper pair symmetries. In particular, we focus on $d$-wave altermagnets and $p$-wave magnets under the influence of spin-singlet and spin-triplet superconductivity induced by proximity effect. Under generic conditions, we find that unconventional magnets not only drive a spin-singlet to spin-triplet conversion but also they transfer their parity symmetry that induces superconducting correlations with higher angular momentum. For instance, a conventional spin-singlet $s$-wave superconductor with $d$-wave altermagnetism is able to host odd-frequency mixed spin-triplet $d$-wave superconducting pair amplitudes, while when combining with $p$-wave magnetism the emerging superconducting pairing acquires an even-frequency mixed spin-triplet $p$-wave symmetry. We further demonstrate that unconventional magnetism produces even more exotic superconducting correlations in spin-singlet $d$-wave superconductors, where odd-frequency mixed spin-triplet $g$-wave and even-frequency mixed spin-triplet $f$-wave pair
Nonreciprocal devices, allowing to manipulate one-way signals, are crucial to quantum information processing and quantum network. Here we propose a nonlinear cavity-magnon system, consisting of a microwave cavity coupled to one or two yttrium-iron-garnet (YIG) spheres supporting magnons with Kerr nonlinearity, to investigate nonreciprocal unconventional photon blockade. The nonreciprocity originates from the direction-dependent Kerr effect, distinctly different from previous proposals with spinning cavities and dissipative couplings. For a single sphere case, nonreciprocal unconventional photon blockade can be realized by manipulating the nonreciprocal destructive interference between two active paths, via vary the Kerr coefficient from positive to negative, or vice versa. By optimizing the system parameters, the perfect and well-tuned nonreciprocal unconventional photon blockade can be predicted. For the case of two spheres with opposite Kerr effects, only reciprocal unconventional photon blockade can be observed when two cavity-magnon coupling strengths Kerr strengths are symmetric. However, when coupling strengths or Kerr strengths become asymmetric, nonreciprocal unconventional
In this work, we carry out a systematic investigation of the coherence peak in unconventional superconductors as they transition into the superconducting phase at $T_c$. Using $d$-wave cuprates as an example, we reveal the presence of a coherence peak below $T_c$ in the charge channel. The nuclear quadrupole relaxation rate is shown to be an effective method for detecting this unconventional coherence peak, with the superconducting coherence factor playing a pivotal role in its emergence. Additionally, we explore the influence of correlation effects, which further enhance this phenomenon. Extending our analysis, we demonstrate the existence of a similar coherence peak in ultrasonic attenuation and iron-based superconductors. Our findings offer a fresh perspective on probing superconducting gap symmetry in unconventional superconductors.
In this work, we consider the analytical properties and the efficient numerical solution of the Bardeen-Cooper-Schrieffer equation for unconventional superconductivity incorporating long-range power-law electron-electron interactions within a tight-binding model on a $d$-dimensional lattice. It is a nonlinear convolution equation for the complex matrix-valued superconducting gap under symmetry constraints imposed by the fermionic anticommutation rules. The long-range interaction enters in momentum space in the form of the now efficiently computable Epstein zeta function, which exhibits a power-law singularity at zero momentum. This needs to be accounted when evaluating the convolution. After a brief overview of some of the equation's analytical properties, we discuss its efficient numerical solution using a Galerkin method with B-splines. We present numerical results for a nodal superconductor on a two-dimensional square lattice.
The topological semimetal CrPt$_3$ has potential for generating unconventional spin torques due to its ferrimagnetic ordering, topological band structure, and high anomalous Hall effect. CrPt$_3$ exhibits ferrimagnetic behavior only in its chemically ordered phase and is paramagnetic in its chemically disordered phase. By controlling the growth and annealing temperatures, epitaxial films of both chemically ordered and disordered phases of CrPt$_3$ are prepared allowing us to investigate the role of magnetic ordering on unconventional torque generation. We use angle dependent spin-torque ferromagnetic resonance and second harmonic Hall measurements to probe the spin torques generated from epitaxial CrPt$_3$ in CrPt$_3$/Cu/Ni$_{81}$Fe$_{19}$ heterostructures. With current applied along specific directions with respect to the crystal order we reveal unconventional spin torques in both ordered and disordered films. When current flows parallel to the $[1\overline{1}1]$ and $[\overline{1}11]$ directions we observe an unconventional field-like torque that is opposite in sign for the two directions. Our calculations reveal that this unconventional torque originates from an indirect nonloca
``Unconventional magnetism" was proposed to describe the exotic states arising from Landau-Pomeranchuk instabilities in the spin channel nearly two decades ago. Its odd-partial-wave-channel (e.g. $p$-wave) states break parity giving rise to the dynamic generation of spin-orbit coupling, while its even-partial-wave-channel (e.g. $d$-wave) states break time-reversal symmetry. Both types of states can exhibit collinear and non-collinear spin configurations over Fermi surfaces with the former and latter termed as the $α$ and $β$-phases, respectively. The collinear states in even partial-wave channels are in the same symmetry class of ``altermagnetism". In this work, we investigate unconventional magnetism in both $p$- and $d$-wave channels within spin-orbit coupled systems with parity and time-reversal symmetries maintained. Based on the Ginzburg-Landau free energy analysis, the $p$-wave channel yields the gyrotropic, Rashba, Dresselhaus-type spin-orbit couplings. They compete and mix evolving from the $β$-phase to the $α$-phase with various types of spin-momentum lockings. Analyses are performed in parallel for the $d$-wave unconventional magnetism. We emphasize that the single-partic
We perform a theoretical investigation of the spin susceptibility of unconventional superconductivity on the kagome lattice. Despite the existence of a sign-changing gap structure, which sums to zero over the Fermi surface, we show that such unconventional pairing states may exhibit a Hebel-Slichter peak in the temperature-dependent spin-lattice relaxation rate. It originates from destructive sublattice interference effects. For the same reason, unconventional pairing states on the kagome lattice tend not to exhibit a neutron resonance peak. These results supplement previous theoretical studies of the surprising robustness of sign-changing gap structures to disorder on the kagome lattice. Taken together these findings imply that unconventional superconductivity on the kagome lattice is deceptive in the sense that its properties may appear similar to conventional non-sign-changing superconductivity. These results may be of relevance to the superconducting state of the kagome superconductors $A$V$_3$Sb$_5$ ($A$: K, Rb, Cs) and CsTi$_3$Bi$_5$.
New unconventional compensated magnets with a $p$-wave spin polarization protected by a composite time-reversal translation symmetry have been proposed in the wake of altermagnets. To facilitate the experimental discovery and applications of these unconventional magnets, we construct an effective analytical model. The effective model is based on a minimal tight-binding model for unconventional $p$-wave magnets that clarifies the relation to other magnets with $p$-wave spin-polarized bands. One of the most prominent advantages of our analytical model is the possibility to employ various analytical approaches while capturing essential features of $p$-wave magnets. We illustrate the effective model by evaluating the tunneling conductance in junctions with $p$-wave magnets, revealing a large magnetoresistance, spin filtering, and anisotropic bulk spin conductivity beyond linear response despite the absence of a net magnetization. These results show that unconventional $p$-wave magnets offer several useful functionalities, broadening the material selection for spintronics devices.
Based on the elementary band representations (EBR), some topologically trivial materials are classified as unconventional ones (obstructed atomic limit), where the EBR decomposition of electronic states is not consistent with the atomic valence-electron band representations. In the work, we identify that the unconventional nature can also exist in phonon spectra, where the EBR decomposition of the phonon modes is not consistent with atomic vibration band representations (ABR). The unconventionality has two types: type I is on an empty site; type II is on an atom site with non-atomic vibration orbitals. Our detailed calculations show that black phosphorus (BP) and 1H-MoSe2 have unconventional both phonon spectra and electronic band structures. The BP has the type-I unconventional phonon spectrum, while 1H-MoSe2 has the type-II one. The obstructed phonon modes are obtained for two types of unconventional phonon spectra.
The control of unconventional magnetism, which displays ferromagnetism-like properties with compensated magnetization, has drawn intense attention for advancing antiferromagnetic spintronics. Here, through symmetry analysis, we propose a general stacking rule, characterized by a connection operator linking two stacked bilayers, for controlling unconventional magnetism via sliding ferroelectricity. Such rule enables the simultaneous switching of both electric polarization and nonrelativistic spin splitting or anomalous Hall effect in altermagnets, a class of collinear unconventional magnets. By comprehensively surveying the 80 layer groups, we identify all the stacking orders that allow for such two types of simultaneous switching. Furthermore, we extend the stacking rule to collinear compensated ferrimagnets, where the opposite-spin sublattices are not connected by any symmetry operator, yet the net magnetization remains zero. Combined with first-principles calculations, we demonstrate the sliding ferroelectric control of spin polarization and anomalous Hall effect in the altermagnetic AgF2 and Fe2MoSe4 bilayers. Our work provides a symmetry strategy for achieving ferroelectric con
To economically produce from very low permeability shale formations, hydraulic fracturing stimulation is typically used to improve their conductivity. This process deforms and breaks the rock, hence requires the geomechanics data and calculation. The development of unconventional reservoirs requires large geomechanical data, and geomechanics has involved in all calculations of the unconventional reservoir projects. Geomechanics has numerous contributions to the development of unconventional reservoirs from reservoir characterization and well construction to hydraulic fracturing and reservoir modeling as well as environmental aspect. This paper reviews and highlights some important aspects of geomechanics on the successful development of unconventional reservoirs as well as outlines the recent development in unconventional reservoir geomechanics. The main objective is to emphasize the importance of geomechanical data and geomechanics and how they are being used in in all aspects of unconventional reservoir projects.
The ideal altermagnets are a class of collinear, crystal-symmetry-enforced fully compensated magnets with nonrelativistic spin-split bands, in which contributions from Berry curvature to magneto-optical effects (MOEs) are strictly forbidden by an effective time-reversal symmetry. Here we show that, in such systems, MOEs are exclusively induced by the quantum metric and, in realistic altermagnets, are typically dominated by it. We refer to Berry-curvature-induced MOEs as conventional MOEs and to quantum-metric-dominated MOEs as unconventional MOEs. We derive general formulas that incorporate both Berry curvature and quantum metric for unconventional MOEs in altermagnets, enabling a quantitative evaluation of their respective contributions. Through symmetry analysis, we prove that ideal altermagnets are constrained to exhibit only unconventional MOEs. Using the three-dimensional canonical altermagnet MnTe and the emerging two-dimensional bilayer twisted altermagnet CrSBr as illustrative examples, we demonstrate that unconventional MOEs are prevalent in altermagnets. Our results establish altermagnets as a natural platform for quantum-metric-driven optical phenomena, substantially bro
Many unconventional computing models, including some that appear to be quite different from traditional ones such as Turing machines, happen to characterise either the complexity class P or PSPACE when working in deterministic polynomial time (and in the maximally parallel way, where this applies). We discuss variants of cellular automata and membrane systems that escape this dichotomy and characterise intermediate complexity classes, usually defined in terms of Turing machines with oracles, as well as some possible reasons why this happens.
Based on first-principles calculations, we demonstrate that 1H/2H-phase transition metal dichalcogenides MX2 (M=Nb,Ta; X=S,Se,Te) are unconventional metals, which have an empty-site band of $A_1'@1e$ elementary band representation at the Fermi level. The computed phonon dispersions indicate the stability of the system at high temperatures, while the presence of the soft phonon mode suggests a phase transition to the charge density wave state at low temperatures. Based on the Bardeen-Cooper-Schrieffer theory and computed electron-phonon coupling, our calculations show that the superconductivity (SC) in NbSe2 is mainly attributed to the soft phonon mode due to the half filling of the empty-site band. Accordingly, the SC has been predicted in unconventional metals TaNS monolayer and 2H-TaN2 bulk with computed $T_C=$ 10 K and 26 K respectively. These results demonstrate that the unconventional metals with partial filling of the empty-site band offer an attractive platform to search for superconductors.