Recent results
Quantum many-body theory group
Quantum many-body theory group
National Institute of Science Education and Research (NISER), India
Hybridization-induced Mott insulator in strongly correlated ABO3 systems:
Hybridization-induced Mott insulator in strongly correlated ABO3 systems:
Model phase diagram for pressure induced Mott to metal transition in ABO3 where A site is a valence skipping element, e. g. in BiNiO3. A-O lattice stiffness (κ) vs charge transfer energy between O and B site variation mimics pressure effects as determined from DFT calculations. (a) For U/tB =6.5, decreasing (εB −εOx) leads to a transition from a lattice distorted insulator (DI) to an undistorted metal (UM). The phase diagram is obtained by a slave rotor mean field theory for treating the large correlation strength on B site. The B-O model with interaction on the B site in 3D is coupled to the A sites in a rock salt structure (cubic perovskite) to start with. The hybridization modulation between alternating A site and its nearest 12 Oxygen is treated as a variational parameter. In the Mott state, the 12 Ox around the A site is alternatively collapsed leading to a doubling of the unit cell.
Model phase diagram for pressure induced Mott to metal transition in ABO3 where A site is a valence skipping element, e. g. in BiNiO3. A-O lattice stiffness (κ) vs charge transfer energy between O and B site variation mimics pressure effects as determined from DFT calculations. (a) For U/tB =6.5, decreasing (εB −εOx) leads to a transition from a lattice distorted insulator (DI) to an undistorted metal (UM). The phase diagram is obtained by a slave rotor mean field theory for treating the large correlation strength on B site. The B-O model with interaction on the B site in 3D is coupled to the A sites in a rock salt structure (cubic perovskite) to start with. The hybridization modulation between alternating A site and its nearest 12 Oxygen is treated as a variational parameter. In the Mott state, the 12 Ox around the A site is alternatively collapsed leading to a doubling of the unit cell.
If the local charge transfer energy between B and O sites is large and the A-O lattice stiffness is small, we find that the system is a Mott insulator. However, on increasing the energy level difference between B and O sites and increasing the lattice stiffness, we get a phase transition to a metal. This mimics the ambient pressure Mott insulator to a metal (at high pressure) transition in BiNiO3. The model calculation for the first time (along with DFT support) indicates the crucial role played by A site and shows a need to include the A site charge transfer energy relative to oxygen in the Zaanen-Allen-Sawatzky (ZSA) classification of metals and insulators. The later is required because at its heart, the A site energy level controls the NI or B site valency. When it becomes half filled the Mott state is stabilized. Pressure increase destabilizes the Mott state by changing the NI local occupation.Thus the A site physics indirectly stabilizes both the Mott phase and the insulator to metal transition. On a side issue, perhaps the correct terminology of the insulator here is a charge transfer insulators as the lowest particle excitation are dominated by Oxygen states, while the lowest hole line excitations are dominated by d like states. The A site DOS lies close below the Ox DOS in the Mott state and it would be of interest to see if the high energy excitation spectra can capture this contribution.
If the local charge transfer energy between B and O sites is large and the A-O lattice stiffness is small, we find that the system is a Mott insulator. However, on increasing the energy level difference between B and O sites and increasing the lattice stiffness, we get a phase transition to a metal. This mimics the ambient pressure Mott insulator to a metal (at high pressure) transition in BiNiO3. The model calculation for the first time (along with DFT support) indicates the crucial role played by A site and shows a need to include the A site charge transfer energy relative to oxygen in the Zaanen-Allen-Sawatzky (ZSA) classification of metals and insulators. The later is required because at its heart, the A site energy level controls the NI or B site valency. When it becomes half filled the Mott state is stabilized. Pressure increase destabilizes the Mott state by changing the NI local occupation.Thus the A site physics indirectly stabilizes both the Mott phase and the insulator to metal transition. On a side issue, perhaps the correct terminology of the insulator here is a charge transfer insulators as the lowest particle excitation are dominated by Oxygen states, while the lowest hole line excitations are dominated by d like states. The A site DOS lies close below the Ox DOS in the Mott state and it would be of interest to see if the high energy excitation spectra can capture this contribution.
Papers: arXiv:1801.08152
Disorder-induced non-Fermi liquid state in a Mott insulator:
Disorder-induced non-Fermi liquid state in a Mott insulator:
Phase diagram of the Anderson-Hubbard model at half filling. The data is shown for a fixed U and varying box disorder (V) and temperature. At T=0 earlier work had discovered that there could be a metallic window between the low disorder Mott insulator (M-I) and the large disorder correlated Anderson insulator (CA-I). In our recent work, we have established the above phase diagram by studying the evolution of the T=0 phases with temperature. The grey region is the paramagnetic metal PM-M. We have shown that the scaling of both the resistivity and the specific heat with temperature can be tuned by using different combinations of U and V that keeps the system in a metallic state. For small U and V the resistivity scales linearly with T, and the T^{\alpha} changes gradually with increasing U and V. Note that the metal at T=0 occurs for U~V, up to V=U=5t. Finally, we show that the tunability is related to clusters of charges in the metal whose sizes change with changing U and V. Thus, within a single model linear resistivity as seen in cuprate strange metal, tunability of resistivity scaling exponent as observed in heavy fermion systems and charge cluster non-Fermi liquid metal as found in 2DEG, can be captured. While obviously, the mechanisms of each these materials are very different, we have shown that nonetheless, we can capture different features of NFL states within a unified framework.
Phase diagram of the Anderson-Hubbard model at half filling. The data is shown for a fixed U and varying box disorder (V) and temperature. At T=0 earlier work had discovered that there could be a metallic window between the low disorder Mott insulator (M-I) and the large disorder correlated Anderson insulator (CA-I). In our recent work, we have established the above phase diagram by studying the evolution of the T=0 phases with temperature. The grey region is the paramagnetic metal PM-M. We have shown that the scaling of both the resistivity and the specific heat with temperature can be tuned by using different combinations of U and V that keeps the system in a metallic state. For small U and V the resistivity scales linearly with T, and the T^{\alpha} changes gradually with increasing U and V. Note that the metal at T=0 occurs for U~V, up to V=U=5t. Finally, we show that the tunability is related to clusters of charges in the metal whose sizes change with changing U and V. Thus, within a single model linear resistivity as seen in cuprate strange metal, tunability of resistivity scaling exponent as observed in heavy fermion systems and charge cluster non-Fermi liquid metal as found in 2DEG, can be captured. While obviously, the mechanisms of each these materials are very different, we have shown that nonetheless, we can capture different features of NFL states within a unified framework.
Papers: Phys. Rev. Lett. 119, 086601 (2017)
Magnetism & Nematicity in Fe based superconductors:
Magnetism & Nematicity in Fe based superconductors:
Phase diagram of two-band Hubbard model relevant to the undoped Fe based superconductor compound. We capture the AF-M_1 (\pi,0) AF metallic phase with anisotropic conductivity, a new AF-metal which conducts only along the AF direction (AF-M_2) and a (\pi,0) AF insulating phase at large U/W. We find a sliver of a nematic phase at the boundary between magnetic order and paramagnetic phases. Finally, the grey region shows the regime of local moments in the PM phase. The dashed line in the crossover between small and large local moments in the PM phase. Pnictides in the above phase diagram would lie around U/W=0.5. All temperature-induced transitions are either second order or possibly weakly first order. We have generalized a recently developed tool, 'Monte Carlo-Mean field' approach for multiband Hubbard models, that allows controlled access to zero and finite T phases. The phase diagram is an example of the application of this approach.
Phase diagram of two-band Hubbard model relevant to the undoped Fe based superconductor compound. We capture the AF-M_1 (\pi,0) AF metallic phase with anisotropic conductivity, a new AF-metal which conducts only along the AF direction (AF-M_2) and a (\pi,0) AF insulating phase at large U/W. We find a sliver of a nematic phase at the boundary between magnetic order and paramagnetic phases. Finally, the grey region shows the regime of local moments in the PM phase. The dashed line in the crossover between small and large local moments in the PM phase. Pnictides in the above phase diagram would lie around U/W=0.5. All temperature-induced transitions are either second order or possibly weakly first order. We have generalized a recently developed tool, 'Monte Carlo-Mean field' approach for multiband Hubbard models, that allows controlled access to zero and finite T phases. The phase diagram is an example of the application of this approach.
Papers: Phys. Rev. B 93, 085144 (2016)
Negative charge transfer oxides: Novel charge ordering
Negative charge transfer oxides: Novel charge ordering
Rare earth Nickelates, Ferrates and Cobaltates, exhibit a host of poorly understood phenomena. The central issue being large transition metal-oxygen hybridization. The lack of clear understanding of the role of oxygen has translated into hotly debated phenomenon such as the cause of metal-insulator transition in the Nickelates and the origin and doping dependence of magnetism in the Cobaltates. A number of recent theoretical studies, including ours, have predicted a novel route for metal-insulator transition in the rare earth Nickelates(ANiO3). Here instead of the expected Ni+4-Ni+2 type charge order accompanied by Jahn-Teller distortion, a breathing mode distortion along with weak charge order involving both Ni and oxygen, has been shown to cause the metal-insulator transition. This is shown in the picture below. The strong Ni-O hybridization causes a Ni (d7) to (d8L) transition, which removes the odd occupation of the degenerate orbitals and suppresses the Jahn-Teller ordering tendency, where L denotes an (oxygen) ligand hole.
Rare earth Nickelates, Ferrates and Cobaltates, exhibit a host of poorly understood phenomena. The central issue being large transition metal-oxygen hybridization. The lack of clear understanding of the role of oxygen has translated into hotly debated phenomenon such as the cause of metal-insulator transition in the Nickelates and the origin and doping dependence of magnetism in the Cobaltates. A number of recent theoretical studies, including ours, have predicted a novel route for metal-insulator transition in the rare earth Nickelates(ANiO3). Here instead of the expected Ni+4-Ni+2 type charge order accompanied by Jahn-Teller distortion, a breathing mode distortion along with weak charge order involving both Ni and oxygen, has been shown to cause the metal-insulator transition. This is shown in the picture below. The strong Ni-O hybridization causes a Ni (d7) to (d8L) transition, which removes the odd occupation of the degenerate orbitals and suppresses the Jahn-Teller ordering tendency, where L denotes an (oxygen) ligand hole.
Figure: Breathing mode distortion accompanying the charge ordering transition in the rare earth Nickelates.
Half metals:
Half metals:
Strain effects in the manganites:
Strain effects in the manganites:
Recent experiments have shown that epitaxial strain can increase the thermal stability for both FM-metallic and AF- insulating phases in the manganites. Our aim was to understand the underlying mechanism for this and the ensuing material systematics. For this we studied the effect of strain on the AF-charge-orbital ordered insulating (AF-CO-I) state and FM metallic states at half doping, within a strong electron-phonon coupled two orbital model, using ED+MC. We reproduced the experimental results for the AF-CO-I state in Pr0.5Sr0.5MnO3, where tensile strain enhances TN. We have provided detailed real space evolution of spin, charge and orbital variables under strain and have shown that the generic reason for such response is a competition between strain induced 'orbital bias' and 'anisotropic enhancement of hybridization'. Finally, we demonstrate, by transport calculations, strain induced conversion of FM metal to AF-insulator at half doping which then shows large magnetoresistance. In fact, our results show that strain engineering on thin manganite films can allow control of %MR in ferromagnetic metals, generate CMR in otherwise robust insulators and even allow routes to raise CMR temperatures.
Recent experiments have shown that epitaxial strain can increase the thermal stability for both FM-metallic and AF- insulating phases in the manganites. Our aim was to understand the underlying mechanism for this and the ensuing material systematics. For this we studied the effect of strain on the AF-charge-orbital ordered insulating (AF-CO-I) state and FM metallic states at half doping, within a strong electron-phonon coupled two orbital model, using ED+MC. We reproduced the experimental results for the AF-CO-I state in Pr0.5Sr0.5MnO3, where tensile strain enhances TN. We have provided detailed real space evolution of spin, charge and orbital variables under strain and have shown that the generic reason for such response is a competition between strain induced 'orbital bias' and 'anisotropic enhancement of hybridization'. Finally, we demonstrate, by transport calculations, strain induced conversion of FM metal to AF-insulator at half doping which then shows large magnetoresistance. In fact, our results show that strain engineering on thin manganite films can allow control of %MR in ferromagnetic metals, generate CMR in otherwise robust insulators and even allow routes to raise CMR temperatures.
Figure: Starting from an insulating parameter point, it is possible to apply compressive strain to convert it to a F-M; in(a) we show the resistivity of the resulting F-M as a function of temperature for various values of compression (color coded with the double arrows in the inset). There is a pronounced peak which systematically shifts to higher temperatures with increasing compression. (b) Temperature at resistance peak TCMR (left axis), which increases with increasing compression, and %MR (right axis) as a function of strain, which decreases as compression is increased. The %MR does not decrease drastically at first, and there is a region where TCMR can be enhanced without losing the large %MR.
Double Perovskites:
Double Perovskites:
(i) Stability of magnetic phases: SFMO has large S=5/2 spins on the Fe sites with intervening nonmagnetic Mo sites. The large Fe 'core' spins are treated classically in theory and provide a static background for the itinerant electrons. It has been shown theoretically that such the magnetic-nonmagnetic structure allows for itinerancy driven AF states for some doping ranges. But these AF states have not been seen in the experiments. By studying the stability of variational states of the Fe core spin in presence of direct hopping in the Mo sub-lattice and Coulomb correlations within Hartree approximation, we have shown that for realistic parameter regimes for materials like SFMO, the FM phase is the only stable state.
(i) Stability of magnetic phases: SFMO has large S=5/2 spins on the Fe sites with intervening nonmagnetic Mo sites. The large Fe 'core' spins are treated classically in theory and provide a static background for the itinerant electrons. It has been shown theoretically that such the magnetic-nonmagnetic structure allows for itinerancy driven AF states for some doping ranges. But these AF states have not been seen in the experiments. By studying the stability of variational states of the Fe core spin in presence of direct hopping in the Mo sub-lattice and Coulomb correlations within Hartree approximation, we have shown that for realistic parameter regimes for materials like SFMO, the FM phase is the only stable state.
(ii) Effective spin model & disorder effects: These materials have a notorious tendency of alloying the B and B' sites. Such stoichiometric antisite disorder, along with excess B(=Fe) or excess B'(=Mo) types of disorder are unavoidable. Thus it is crucial to study the stability of the classical model through the model parameters. These parameters are determined by fitting the spin-wave spectrum of quantum Hamiltonian about an FM core spin background, with that of the classical model. We have benchmarked the classical model against ED+MC on 82 clusters by comparing temperature dependence of between the itinerant electron polarization at the chemical potential and the core spin magnetization allowed us to study the classical spin only model and infer about half-metallicity. MC simulations on our classical model allowed us to study disorder effects in 3D, perform finite-size scaling to extract Tc and do adequate disorder averaging. For excess Fe/Mo FM state and the half-metallic nature in the presence of disorder. For this, we derived an effective classical model for the B-site spins by generalizing the Anderson-Hasegawa treatment for DE model. Doping enters our magnetization. Further, the one to one correspondence disorder we found the observed reduction in Tc (see the dashed line and solid symbols in Figure).
(ii) Effective spin model & disorder effects: These materials have a notorious tendency of alloying the B and B' sites. Such stoichiometric antisite disorder, along with excess B(=Fe) or excess B'(=Mo) types of disorder are unavoidable. Thus it is crucial to study the stability of the classical model through the model parameters. These parameters are determined by fitting the spin-wave spectrum of quantum Hamiltonian about an FM core spin background, with that of the classical model. We have benchmarked the classical model against ED+MC on 82 clusters by comparing temperature dependence of between the itinerant electron polarization at the chemical potential and the core spin magnetization allowed us to study the classical spin only model and infer about half-metallicity. MC simulations on our classical model allowed us to study disorder effects in 3D, perform finite-size scaling to extract Tc and do adequate disorder averaging. For excess Fe/Mo FM state and the half-metallic nature in the presence of disorder. For this, we derived an effective classical model for the B-site spins by generalizing the Anderson-Hasegawa treatment for DE model. Doping enters our magnetization. Further, the one to one correspondence disorder we found the observed reduction in Tc (see the dashed line and solid symbols in Figure).
(iii) Route to raise Tc: Excess Fe introduces strong AF Fe-Fe nearest neighbors that pin the FM sublattice and tends to raise Tc, however it also reduces the doping which would suppress Tc. We show that valence compensation, e.g. by La doping, would allow for a disorder enhancement of Tc (solid line in Figure). We back up these conclusions, of enhanced Tc and its one to one correspondence to half-metallicity, with a rather expensive 3D (83) cluster calculations employing a variant of ED+MC at a few parameter points for the quantum Hamiltonian.
(iii) Route to raise Tc: Excess Fe introduces strong AF Fe-Fe nearest neighbors that pin the FM sublattice and tends to raise Tc, however it also reduces the doping which would suppress Tc. We show that valence compensation, e.g. by La doping, would allow for a disorder enhancement of Tc (solid line in Figure). We back up these conclusions, of enhanced Tc and its one to one correspondence to half-metallicity, with a rather expensive 3D (83) cluster calculations employing a variant of ED+MC at a few parameter points for the quantum Hamiltonian.
Papers: Phys. Rev. Lett. 107, 257201 (2011), Phys. Rev. B 87, 165104 (2013), Phys. Rev. B 87, 165105 (2013)
Figure: Variation of Tc (normalized to 420K, the Tc for SFMO) with excess Fe and excess Mo disorder in Sr2Fe1+yMo1-yO6. Dashed line, Monte Carlo results from the classical model, show the the fall in Tc due to excess Fe and excess Mo. Results are shown for parameters typical to SFMO. Solid symbols are experimental results from D. Topwal, et. al., PRB 73, 094419 (2006). We show, with the solid line, that valence compensation, say, by La doping for Sr, enhances Tc by about 100K for 20% excess Fe.
Older results:
Older results:
Field melting of spin-charge-orbital ordered state in the manganites:
Field melting of spin-charge-orbital ordered state in the manganites:
One of the themes of our research was to clarify the physics of the magnetic field induced melting of the charge ordered state at half doping in the manganites, where such non-equilibrium phenomena play an important role. Among the several unexplained issues, it was particularly puzzling that if phase competition is governed by electronic bandwidth, why do materials with same bandwidths have very different melting fields? It was also unclear that if the field melted state is homogeneous or or a percolative metal. We employed a newly developed real space, exact diagonalization based Monte Carlo (ED-MC) technique called 'Travelling Cluster Approximation'(TCA), that allows one to handle fermions in the background of strong spatial fluctuations. It also allows one to track the spatial evolution of the spin, charge and orbital degrees of freedom as the system undergoes a phase transition. Since spatial coexistence and percolation are vital in these studies, it is pertinent to perform simulations on large system sizes. It is here that TCA is greatly advantageous, allowing access to system sizes (~40^2), as opposed to (~8^2), in conventional ED-MC. We could map out the bandwidth variation of the hysteretic response to magnetic field sweeps and explain the reason for the striking difference between the melting field of materials with same bandwidths. Ability to calculate transport properties in conjunction with real space analysis allowed us to predict that the field melted state is an inhomogeneous metal even in the absence of disorder, which stands as a testable prediction. Further, we have also provided a single framework that unifies the response of the charge ordered state to applied fields both of the clean and the disordered system.
One of the themes of our research was to clarify the physics of the magnetic field induced melting of the charge ordered state at half doping in the manganites, where such non-equilibrium phenomena play an important role. Among the several unexplained issues, it was particularly puzzling that if phase competition is governed by electronic bandwidth, why do materials with same bandwidths have very different melting fields? It was also unclear that if the field melted state is homogeneous or or a percolative metal. We employed a newly developed real space, exact diagonalization based Monte Carlo (ED-MC) technique called 'Travelling Cluster Approximation'(TCA), that allows one to handle fermions in the background of strong spatial fluctuations. It also allows one to track the spatial evolution of the spin, charge and orbital degrees of freedom as the system undergoes a phase transition. Since spatial coexistence and percolation are vital in these studies, it is pertinent to perform simulations on large system sizes. It is here that TCA is greatly advantageous, allowing access to system sizes (~40^2), as opposed to (~8^2), in conventional ED-MC. We could map out the bandwidth variation of the hysteretic response to magnetic field sweeps and explain the reason for the striking difference between the melting field of materials with same bandwidths. Ability to calculate transport properties in conjunction with real space analysis allowed us to predict that the field melted state is an inhomogeneous metal even in the absence of disorder, which stands as a testable prediction. Further, we have also provided a single framework that unifies the response of the charge ordered state to applied fields both of the clean and the disordered system.
Papers: Europhys. Lett. 86, 27003 (2009), Euro. Phys. J. B 87 238 (2014), Euro. Phys. J. B 87 239 (2014)
Figure: Hysteresis and reentrant features in the field response of half doped charge ordered manganites. The top panel is from experiments, the lower panel are our results. The two columns are for situations at different electronic bandwidths.
Disorder effects in the manganites:
Disorder effects in the manganites:
The manganites have a structure ABO3, where A is the cation site and B is the Mn site. The most common disorder in such correlated transition metal oxides is ‘A site’ cation disorder due to dopants introduced for hole doping. The primary effect of such disorder is suppression of long-range order and increase in the resistivity. Remarkably, low-density substitution on the ‘B site’ has rather strange effects. These include the metallization of insulators, the emergence of charge order from a homogeneous system, and conversion of antiferromagnets to ferromagnets. Prior to our work, there had been no theoretical attempts to understand these issues which are of great relevance to disorder assisted controlling of transport responses in these materials. TCA we studied a wide range of ‘disorder’ effects arising from the deliberate substitution of dopants on the ‘B site’ of the manganites. We were able to identify a general principle dictating the apparently diverse experimental results, provide a detailed spatial picture of the states that emerge and make suggestions for further use of B site disorder as a tool for electronic phase control. Using TCA we studied a wide range of ‘disorder’ effects.
The manganites have a structure ABO3, where A is the cation site and B is the Mn site. The most common disorder in such correlated transition metal oxides is ‘A site’ cation disorder due to dopants introduced for hole doping. The primary effect of such disorder is suppression of long-range order and increase in the resistivity. Remarkably, low-density substitution on the ‘B site’ has rather strange effects. These include the metallization of insulators, the emergence of charge order from a homogeneous system, and conversion of antiferromagnets to ferromagnets. Prior to our work, there had been no theoretical attempts to understand these issues which are of great relevance to disorder assisted controlling of transport responses in these materials. TCA we studied a wide range of ‘disorder’ effects arising from the deliberate substitution of dopants on the ‘B site’ of the manganites. We were able to identify a general principle dictating the apparently diverse experimental results, provide a detailed spatial picture of the states that emerge and make suggestions for further use of B site disorder as a tool for electronic phase control. Using TCA we studied a wide range of ‘disorder’ effects.
Papers: Phys. Rev. Lett. 99, 147206 (2007), Europhys. Lett. Vol 84, 37007 (2008)
Figure: Real space snapshots from our simulations depicting disorder assisted formation of checkerboard charge ordered insulator out of an uniform metal. To the benign metal with uniform electronic density (left), when B-site disorder is added in small quantities (the middle panel dots indicate their spatial locations), the system becomes a weakly insulating charge ordered material (right) with large magneto-resistance.