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Some reflections from the 1950s
Solid State Sciences 7 (2005) 642–644 www.elsevier.com/locate/ssscie
Some reflections from the 1950s John B. Goodenough Texas Materials Institute, ETC 9.102, University of Texas at Austin, Austin, TX 78712, USA Received 4 November 2004; accepted 9 November 2004 Available online 18 April 2005
The 1950s was a decade of intense interest in the field of transition-metal oxides because of the pioneering work in Holland and France during World War II that led to the formulation by Louis Néel of the two-sublattice model of antiferromagnetism and ferrimagnetism. The ferrimagnetic insulators were of great technical interest, and the advent of neutron diffraction made possible the direct observation of magnetic order. In Grenoble, a remarkable collaboration between the theorist, Louis Néel, the X-ray diffraction insights of Erwin Felix Levy Bertaut, and the experimental magnetician, René Pauthenet, was laying much of the groundwork for the revolution in magnetism taking place in that era and was planting scientific seeds that would bloom into the magnificent facilities now existing at the Institut Laue Langevin in Grenoble. My friendship with Erwin Felix Levy Bertaut began with our first meeting in Grenoble in the summer of 1954. In the autumn of 1952, I joined a group at the MIT Lincoln Laboratory that had been charged with the responsibility to develop a square B–H hysteresis loop in polycrystalline ferrospinels for a random access memory of the digital computer. The leading magneticians of the day were convinced that such a task was not possible since the square B–H loops of Deltamax and Permalloy tapes were achieved by rolling the alloys so as to align the easy magnetization axes of the grains. Nevertheless, development of the semiautomatic ground environment (SAGE) air-defense system of that day depended upon development of the random-access memory with a read-rewrite switching speed of under 6 µs. Our empirical studies of the ferrospinels relied heavily on the work of Bertaut, who had developed criteria for determining from X-ray diffraction patterns the cation distribution between the tetrahedral A sites and the octahedral B sites of the A[B2 ]O4 spinels. We also relied on the Néel theory of ferrimagnetism, which is applicable to the ferrospinels, and on the magnetic measurements of Pauthenet. It was, therefore, natural that, while vacationing in Europe in the summer of 1954, I would 1293-2558/2005 Published by Elsevier SAS. doi:10.1016/j.solidstatesciences.2004.11.009
visit Grenoble where Louis Néel, René Pauthenet, and Erwin Felix Bertaut were continuing their remarkable collaboration begum during the years of World War II. It was only after the Liberation of France that Bertaut was able to use his surname Levy; the people of the Vallée d’Isère have a proud history of sheltering their Jewish colleagues, of providing an underground passage for downed allies airmen to return to England, and for a sustained resistance to the German occupation. My work on the square B–H loop problem had begum with an analysis of the role of magnetic poles at grain boundaries in the nucleation of domains of reverse magnetization on reversing the applied magnetic field H. I was able to show that the smaller magnetization of a ferrimagnet compared to that of a ferromagnet alleviated the problem of misaligned grains in the ferrospinels; a sufficiently square B–H loop in a polycrystalline ceramic was not theoretically impossible! I was also able to point out that the switching speed of a magnetic core in the memory is restricted by a driving field that is limited to twice the coercivity, by an intrinsic relaxation time, and by the size of the core. However, the analysis showed that in order to achieve a square B–H loop with a sufficiently large coercivity, it would be necessary to build in a subtle defect that would act in a reverse field as a nucleation center for a domain of reverse magnetization; once nucleated the domain should grow away from the center to switch the magnetization direction. While this analysis was being made, others in the group were making a systematic study of the Fe3 O4 –Mn3 O4 – MgFe2 O4 phase diagram under different thermal treatments to adjust the degree of cation ordering between tetrahedral and octahedral sites. By mapping the structural and B-H characteristics of this phase diagram, I found that the presence of a sufficient concentration of Mn3+ ions on the octahedral sites resulted in a distortion from cubic to tetragonal symmetry; I also noted that Cu2+ ions on the octahedral sites had the same effect. Therefore, before the summer of
J.B. Goodenough / Solid State Sciences 7 (2005) 642–644
1954 I had deduced that the distortion to tetragonal symmetry was due to a cooperation orbital ordering that removes the twofold orbital degeneracy at octahedral-site Mn3+ and Cu2+ ions. (I had not yet heard of the Jahn–Teller theorem for molecules with orbital degeneracies and therefore had modeled the problems with the language of Linus Pauling.) Consequently, I felt emboldened in the summer of 1954 to visit Grenoble to tell Bertaut about my deduction and to meet his two colleagues, René Pauthenet, and Louis Néel. The three of them gave me a warm welcome, and thus began an enduring friendship with all three that lasted until each of their passings. The systematic empiricism of the other members of our group resulted in realization of the needed square B–H loop in a ceramic ferrospinel, and my mapping revealed that the magnetic cores with the desired properties had compositions that were cubic, but contained a Mn3+ -ion concentration that approached the threshold for long-range cooperative orbital ordering. However, It was not until several years later that I was able to argue from indirect evidence that dynamic, short-range orbital ordering induced formation of Mn3+ -rich regions within the cubic spinels in order to lower the elastic strain energy associated with local orbital fluctuations; these chemical inhomogeneities provide the subtle centers for nucleation of reverse domains that would grow away from them. By empiricism, carefully programmed annealing procedures had been developed that created the required chemical inhomogeneities. In the 1950s, Bertaut and Pauthenet were also exploring the magnetic properties of the perovskites and the garnets; the garnet Y3 Fe5 O12 offered a low-loss microwave ferrite. However, the transition-metal perovskites have had a more enduring fascination. By 1951, metallic conductivity in the Nax WO3 bronzes and in the ferromagnetic phase of the La1−x Srx MnO3 system had startled a theoretical community accustomed to thinking that oxides are ionic compounds with localized d-electron configurations having their orbital manifold split by electrostatic crystalline fields. It would take over a decade to demonstrate the fallacy of this mind-set and the possibility of exploring in the perovskites the crossover from localized to itinerant d-electron behavior without interference from overlapping, broad s-p bands. My interest in the perovskites was triggered by a presentation of Wollan and Koehler in the spring of 1954 on a neutron-diffraction study of the LaMO3 perovskites with M = Cr, Mn, Fe, and Ni. Antiferromagnetic order between all Cr3+ and Fe3+ nearest neighbors in LaCrO3 and LaFeO3 was understandable with the P.W. Anderson theory of superexchange, but LaNiO3 showed no long-range magnetic order and LaMnO3 had anisotropic Mn–O–Mn interactions, ferromagnetic (001) planes coupling antiparallel to one another along the c-axis. This anisotropic magnetic coupling could not be accounted for with existing theory, and it suggested to me that a cooperative orbital ordering at the Mn3+ O6/2 sites must be responsible. This observation allowed me to deduce the antiferrodistortive nature of the orbital ordering and to
643
formulate the rules for the sign of the spin-spin superexchange interactions that are now known as the Goodenough– Kanamori rules. Moreover, Koehler and Wollan had also observed ferromagnetic zig-zag chains coupled antiparallel to one another in the (001) planes of La0.5 Ca0.5 MnO3 , an observation I could rationalize with long-range ordering of Mn4+ and Mn3+ ions together with long-range orbital ordering on the Mn3+ ions and the rules for the sign of the spin-spin interactions. However, the lack of any long-range magnetic or orbital ordering in LaNiO3 remained a puzzle even though I recognized that the Ni3+ ions must be in their low-spin state. In 1958, Dzialoshimskii pointed out that an antisymmetric spin-spin interaction Dij · Si × Sj would be allowed under certain symmetry conditions and that this interaction could account for an intrinsic, weak ferromagnetism found in several antiferromagnetic oxides. The mismatch of the (A–O) and (M–O) equilibrium bond lengths in an AMO3 perovskite is given by the√deviation from unity of the tolerance factor t ≡ (A–O)/[ 2(M–O)]. The internal stresses induced by a t < 1 are relieved by a cooperative rotation of the corner-shared MO6/2 octahedra. A rotation about a ¯ axis gives orthorhombic Pbnm (or Pnma) symmetry, [110] and an intrinsic weak ferromagnetism was found in the orthorhombic perovskites that reflected both an antisymmetric exchange and a local site anisotropy. Bertaut immediately worked out from symmetry arguments the allowed magnetic components along the crystal axes for all possible types of antiferromagnetic order that could be envisaged at that time for an orthorhombic perovskite. Another topic of interest in the 1950s was the influence of competing spin-spin interactions on the long-range magnetic order. For example, in 1958 competitive interactions were shown to be responsible for helical spin configurations in three different compounds quite independently by Yoshimori in Japan, Villain in France, and Kaplan in my group. Tom Kaplan et al. went on to determine the ground-state magnetic order for the cubic A[B2 ]O4 spinels with competitive B–B and A–B interactions as in Mn[Cr2 ]O4 . They predicted a complex spin configuration consisting of canted B-site spins having a ferromagnetic component antiparallel to that of the A site with a helical rotation of the triangular configuration about an independent axis; the spiral propagated along a [110] axis. This prediction allowed Corliss and Hastings to interpret a neutron-diffraction pattern that had not previously been solved. Meanwhile, Bertaut quite independently had developed the same mathematical formulism in order to be able to solve complex spin configurations obtained from neutron-diffraction data. It was a striking example of Bertaut’s analytical ability that he applied so effectively to diffraction problems. I had also noted that metal–metal interactions across a shared octahedral-site face or edge could be strong enough to transform d electrons from a localized to an itinerant character and that at the crossover, a narrow d band is commonly transformed at lower temperatures into a charge-
644
J.B. Goodenough / Solid State Sciences 7 (2005) 642–644
density wave by the formation of metal–metal bonds as occurs in VO2 . Therefore, while contemplating the metallic character of MoO2 , which like VO2 distorts the rutile structure by forming metal–metal c-axis dimers, I realized that the second 4d electron of the Mo4+ ion must by responsible for the metallic conductivity; but this electron could only interact with neighboring Mo4+ ions across an oxide ion. At last it was clear to me that the covalent bonding between oxygen and transition-metal d states could make the 180◦ Ni–O–Ni interactions in single-valent LaNiO3 strong enough to make itinerant the single σ -bonding e-electron of low-spin Ni3+ . Paul Raccah had just joined my group, and I told him to measure the electronic conductivity of LaNiO3 as I was sure he would find it to be metallic. This measurement resolved the origin of metallic conductivity associated with itinerant d electrons in perovskites and it led me to substantiate its implications by mapping out perovskites with localized versus itinerant d electrons; the mapping showed that the σ -bonding e orbitals become itinerant before the π -bonding t orbitals, thus clarifying the coexistence of itinerant e electrons in the presence of a localized t3 configuration with spin S = 3/2 as assumed by de Gennes in his double-exchange model of ferromagnetic La1−x Srx MnO3 . My attempts to monitor the transition from localized to itinerant electronic behavior in the perovskites in the 1960s were frustrated by separations into two phases, one with itinerant and the other with localized d electrons. High-level
administrative decisions at the Lincoln Laboratory stopped these investigations, so I turned to energy problems and accepted an offer to head the Inorganic Chemistry Laboratory at the University of Oxford in the 1970s. Nevertheless, I was alerted to the fact that the transition from localized to itinerant electronic behavior must be first-order, a deduction I would rationalize on the basis of the virial theorem on my return to the US and to the problem in 1986 at the moment of the discovery of high-temperature superconductivity in the copper oxides. It led to my formulation of bond-length fluctuations in the superconductive phase and of a spinodal phase segregation into the superconductive phase and an antiferromagnetic parent phase in the underdoped region, the superconductive phase and a metallic phase in the overdoped region of the phase diagram. My colleague J.-S. Zhou and I have recently demonstrated bond-length fluctuations in the RNiO3 family and shown that a first-order insulator-metal transition resulting from ordering of these fluctuations in PrNiO3 decreases under increasing pressure until it terminates in a non-Fermi-liquid phase at a quantum critical point. The attached picture shows Bertaut just before his tragic accident discussing with me in Grenoble our evidence for bond-length fluctuations in the perovskites and their implications for high-temperature superconductivity in the copper oxides and the colossal magnetoresistance (CMR) phenomenon in the manganites. He kept a keen and critical interest in the properties of transition-metal compounds until the very end.
Some reflections from the 1950s John B. Goodenough Texas Materials Institute, ETC 9.102, University of Texas at Austin, Austin, TX 78712, USA Received 4 November 2004; accepted 9 November 2004 Available online 18 April 2005
The 1950s was a decade of intense interest in the field of transition-metal oxides because of the pioneering work in Holland and France during World War II that led to the formulation by Louis Néel of the two-sublattice model of antiferromagnetism and ferrimagnetism. The ferrimagnetic insulators were of great technical interest, and the advent of neutron diffraction made possible the direct observation of magnetic order. In Grenoble, a remarkable collaboration between the theorist, Louis Néel, the X-ray diffraction insights of Erwin Felix Levy Bertaut, and the experimental magnetician, René Pauthenet, was laying much of the groundwork for the revolution in magnetism taking place in that era and was planting scientific seeds that would bloom into the magnificent facilities now existing at the Institut Laue Langevin in Grenoble. My friendship with Erwin Felix Levy Bertaut began with our first meeting in Grenoble in the summer of 1954. In the autumn of 1952, I joined a group at the MIT Lincoln Laboratory that had been charged with the responsibility to develop a square B–H hysteresis loop in polycrystalline ferrospinels for a random access memory of the digital computer. The leading magneticians of the day were convinced that such a task was not possible since the square B–H loops of Deltamax and Permalloy tapes were achieved by rolling the alloys so as to align the easy magnetization axes of the grains. Nevertheless, development of the semiautomatic ground environment (SAGE) air-defense system of that day depended upon development of the random-access memory with a read-rewrite switching speed of under 6 µs. Our empirical studies of the ferrospinels relied heavily on the work of Bertaut, who had developed criteria for determining from X-ray diffraction patterns the cation distribution between the tetrahedral A sites and the octahedral B sites of the A[B2 ]O4 spinels. We also relied on the Néel theory of ferrimagnetism, which is applicable to the ferrospinels, and on the magnetic measurements of Pauthenet. It was, therefore, natural that, while vacationing in Europe in the summer of 1954, I would 1293-2558/2005 Published by Elsevier SAS. doi:10.1016/j.solidstatesciences.2004.11.009
visit Grenoble where Louis Néel, René Pauthenet, and Erwin Felix Bertaut were continuing their remarkable collaboration begum during the years of World War II. It was only after the Liberation of France that Bertaut was able to use his surname Levy; the people of the Vallée d’Isère have a proud history of sheltering their Jewish colleagues, of providing an underground passage for downed allies airmen to return to England, and for a sustained resistance to the German occupation. My work on the square B–H loop problem had begum with an analysis of the role of magnetic poles at grain boundaries in the nucleation of domains of reverse magnetization on reversing the applied magnetic field H. I was able to show that the smaller magnetization of a ferrimagnet compared to that of a ferromagnet alleviated the problem of misaligned grains in the ferrospinels; a sufficiently square B–H loop in a polycrystalline ceramic was not theoretically impossible! I was also able to point out that the switching speed of a magnetic core in the memory is restricted by a driving field that is limited to twice the coercivity, by an intrinsic relaxation time, and by the size of the core. However, the analysis showed that in order to achieve a square B–H loop with a sufficiently large coercivity, it would be necessary to build in a subtle defect that would act in a reverse field as a nucleation center for a domain of reverse magnetization; once nucleated the domain should grow away from the center to switch the magnetization direction. While this analysis was being made, others in the group were making a systematic study of the Fe3 O4 –Mn3 O4 – MgFe2 O4 phase diagram under different thermal treatments to adjust the degree of cation ordering between tetrahedral and octahedral sites. By mapping the structural and B-H characteristics of this phase diagram, I found that the presence of a sufficient concentration of Mn3+ ions on the octahedral sites resulted in a distortion from cubic to tetragonal symmetry; I also noted that Cu2+ ions on the octahedral sites had the same effect. Therefore, before the summer of
J.B. Goodenough / Solid State Sciences 7 (2005) 642–644
1954 I had deduced that the distortion to tetragonal symmetry was due to a cooperation orbital ordering that removes the twofold orbital degeneracy at octahedral-site Mn3+ and Cu2+ ions. (I had not yet heard of the Jahn–Teller theorem for molecules with orbital degeneracies and therefore had modeled the problems with the language of Linus Pauling.) Consequently, I felt emboldened in the summer of 1954 to visit Grenoble to tell Bertaut about my deduction and to meet his two colleagues, René Pauthenet, and Louis Néel. The three of them gave me a warm welcome, and thus began an enduring friendship with all three that lasted until each of their passings. The systematic empiricism of the other members of our group resulted in realization of the needed square B–H loop in a ceramic ferrospinel, and my mapping revealed that the magnetic cores with the desired properties had compositions that were cubic, but contained a Mn3+ -ion concentration that approached the threshold for long-range cooperative orbital ordering. However, It was not until several years later that I was able to argue from indirect evidence that dynamic, short-range orbital ordering induced formation of Mn3+ -rich regions within the cubic spinels in order to lower the elastic strain energy associated with local orbital fluctuations; these chemical inhomogeneities provide the subtle centers for nucleation of reverse domains that would grow away from them. By empiricism, carefully programmed annealing procedures had been developed that created the required chemical inhomogeneities. In the 1950s, Bertaut and Pauthenet were also exploring the magnetic properties of the perovskites and the garnets; the garnet Y3 Fe5 O12 offered a low-loss microwave ferrite. However, the transition-metal perovskites have had a more enduring fascination. By 1951, metallic conductivity in the Nax WO3 bronzes and in the ferromagnetic phase of the La1−x Srx MnO3 system had startled a theoretical community accustomed to thinking that oxides are ionic compounds with localized d-electron configurations having their orbital manifold split by electrostatic crystalline fields. It would take over a decade to demonstrate the fallacy of this mind-set and the possibility of exploring in the perovskites the crossover from localized to itinerant d-electron behavior without interference from overlapping, broad s-p bands. My interest in the perovskites was triggered by a presentation of Wollan and Koehler in the spring of 1954 on a neutron-diffraction study of the LaMO3 perovskites with M = Cr, Mn, Fe, and Ni. Antiferromagnetic order between all Cr3+ and Fe3+ nearest neighbors in LaCrO3 and LaFeO3 was understandable with the P.W. Anderson theory of superexchange, but LaNiO3 showed no long-range magnetic order and LaMnO3 had anisotropic Mn–O–Mn interactions, ferromagnetic (001) planes coupling antiparallel to one another along the c-axis. This anisotropic magnetic coupling could not be accounted for with existing theory, and it suggested to me that a cooperative orbital ordering at the Mn3+ O6/2 sites must be responsible. This observation allowed me to deduce the antiferrodistortive nature of the orbital ordering and to
643
formulate the rules for the sign of the spin-spin superexchange interactions that are now known as the Goodenough– Kanamori rules. Moreover, Koehler and Wollan had also observed ferromagnetic zig-zag chains coupled antiparallel to one another in the (001) planes of La0.5 Ca0.5 MnO3 , an observation I could rationalize with long-range ordering of Mn4+ and Mn3+ ions together with long-range orbital ordering on the Mn3+ ions and the rules for the sign of the spin-spin interactions. However, the lack of any long-range magnetic or orbital ordering in LaNiO3 remained a puzzle even though I recognized that the Ni3+ ions must be in their low-spin state. In 1958, Dzialoshimskii pointed out that an antisymmetric spin-spin interaction Dij · Si × Sj would be allowed under certain symmetry conditions and that this interaction could account for an intrinsic, weak ferromagnetism found in several antiferromagnetic oxides. The mismatch of the (A–O) and (M–O) equilibrium bond lengths in an AMO3 perovskite is given by the√deviation from unity of the tolerance factor t ≡ (A–O)/[ 2(M–O)]. The internal stresses induced by a t < 1 are relieved by a cooperative rotation of the corner-shared MO6/2 octahedra. A rotation about a ¯ axis gives orthorhombic Pbnm (or Pnma) symmetry, [110] and an intrinsic weak ferromagnetism was found in the orthorhombic perovskites that reflected both an antisymmetric exchange and a local site anisotropy. Bertaut immediately worked out from symmetry arguments the allowed magnetic components along the crystal axes for all possible types of antiferromagnetic order that could be envisaged at that time for an orthorhombic perovskite. Another topic of interest in the 1950s was the influence of competing spin-spin interactions on the long-range magnetic order. For example, in 1958 competitive interactions were shown to be responsible for helical spin configurations in three different compounds quite independently by Yoshimori in Japan, Villain in France, and Kaplan in my group. Tom Kaplan et al. went on to determine the ground-state magnetic order for the cubic A[B2 ]O4 spinels with competitive B–B and A–B interactions as in Mn[Cr2 ]O4 . They predicted a complex spin configuration consisting of canted B-site spins having a ferromagnetic component antiparallel to that of the A site with a helical rotation of the triangular configuration about an independent axis; the spiral propagated along a [110] axis. This prediction allowed Corliss and Hastings to interpret a neutron-diffraction pattern that had not previously been solved. Meanwhile, Bertaut quite independently had developed the same mathematical formulism in order to be able to solve complex spin configurations obtained from neutron-diffraction data. It was a striking example of Bertaut’s analytical ability that he applied so effectively to diffraction problems. I had also noted that metal–metal interactions across a shared octahedral-site face or edge could be strong enough to transform d electrons from a localized to an itinerant character and that at the crossover, a narrow d band is commonly transformed at lower temperatures into a charge-
644
J.B. Goodenough / Solid State Sciences 7 (2005) 642–644
density wave by the formation of metal–metal bonds as occurs in VO2 . Therefore, while contemplating the metallic character of MoO2 , which like VO2 distorts the rutile structure by forming metal–metal c-axis dimers, I realized that the second 4d electron of the Mo4+ ion must by responsible for the metallic conductivity; but this electron could only interact with neighboring Mo4+ ions across an oxide ion. At last it was clear to me that the covalent bonding between oxygen and transition-metal d states could make the 180◦ Ni–O–Ni interactions in single-valent LaNiO3 strong enough to make itinerant the single σ -bonding e-electron of low-spin Ni3+ . Paul Raccah had just joined my group, and I told him to measure the electronic conductivity of LaNiO3 as I was sure he would find it to be metallic. This measurement resolved the origin of metallic conductivity associated with itinerant d electrons in perovskites and it led me to substantiate its implications by mapping out perovskites with localized versus itinerant d electrons; the mapping showed that the σ -bonding e orbitals become itinerant before the π -bonding t orbitals, thus clarifying the coexistence of itinerant e electrons in the presence of a localized t3 configuration with spin S = 3/2 as assumed by de Gennes in his double-exchange model of ferromagnetic La1−x Srx MnO3 . My attempts to monitor the transition from localized to itinerant electronic behavior in the perovskites in the 1960s were frustrated by separations into two phases, one with itinerant and the other with localized d electrons. High-level
administrative decisions at the Lincoln Laboratory stopped these investigations, so I turned to energy problems and accepted an offer to head the Inorganic Chemistry Laboratory at the University of Oxford in the 1970s. Nevertheless, I was alerted to the fact that the transition from localized to itinerant electronic behavior must be first-order, a deduction I would rationalize on the basis of the virial theorem on my return to the US and to the problem in 1986 at the moment of the discovery of high-temperature superconductivity in the copper oxides. It led to my formulation of bond-length fluctuations in the superconductive phase and of a spinodal phase segregation into the superconductive phase and an antiferromagnetic parent phase in the underdoped region, the superconductive phase and a metallic phase in the overdoped region of the phase diagram. My colleague J.-S. Zhou and I have recently demonstrated bond-length fluctuations in the RNiO3 family and shown that a first-order insulator-metal transition resulting from ordering of these fluctuations in PrNiO3 decreases under increasing pressure until it terminates in a non-Fermi-liquid phase at a quantum critical point. The attached picture shows Bertaut just before his tragic accident discussing with me in Grenoble our evidence for bond-length fluctuations in the perovskites and their implications for high-temperature superconductivity in the copper oxides and the colossal magnetoresistance (CMR) phenomenon in the manganites. He kept a keen and critical interest in the properties of transition-metal compounds until the very end.