Daniel Khomskii

Daniel Khomskii, an outstanding physicist and materials scientist and an author of several revolutionary concepts in condensed-matter physics, passed away peacefully in Cologne, Germany, on 12 August 2024, at the age of 85, in the wake of a horrible road accident two years ago. His scientific expertise as well as his flamboyant personality will live forever in our memory.

Daniel has lived through turbulent years both in science and in everyday life. He was born in Leningrad, then in the USSR, in 1938, the peak year of Stalin’s terror. He would live through a world war, the demise of Stalin’s regime, the rise of antisemitism in the Soviet Union, the disintegration of the USSR, as well as through the greatest discovery in physics. He studied at Moscow State University from 1956 till 1962, had a short spell at the Moscow Institute of Physical Chemistry, and in 1965, moved to the famous Lebedev Physical Institute in Moscow, specifically to the theoretical department, led at that time by Nobel laureate Igor Tamm, first as a graduate student, and then as a staff researcher, advancing from a junior to a senior researcher and to leading scientist, under the auspices of Vitaly Ginzburg, another future Nobel Prize winner.

In 1969, Daniel received the degree of “Science Candidate” (equivalent to a PhD) for his dissertation entitled “Electronic structure and properties of crystals with strong electron correlations.” This would remain his most favorite field (despite excursions into other parts of theoretical physics, as described below) and the subject of several seminal books and several hundred journal articles. In 1982, he was awarded the second-level scientific degree (no analogue in the US), “Science Doctor.” In 1990, he moved to West Germany, to the University of Cologne; in 1992, he accepted a professor’s position at the University of Groningen in the Netherlands; and in 2003, he returned to the University of Cologne, where he stayed till the accident in 2022.

An interesting aspect of Daniel’s scientific biography is that he started, as an undergraduate student, with elementary particles theory. Maybe that was a reason for his broad perspective in condensed-matter theory, which he was famous for. In particular, among his many discoveries in physics of strongly correlated systems was “confinement” in the Hubbard model, a series of papers in 1967–68 in which he studied hole motion in the Hubbard model and showed how a moving hole leaves behind a string of flipped spin (analogous to the gluon field strings in color confinement) and thus generates a distance-independent force between the holes. Two decades later, this construction would become highly popular among high-T_c theorists.

Arguably the most popular discovery associated with his name is the Kugel–Khomskii model of 1972 (Klim Kugel was one of the first graduate students of Daniel’s), which spawned a whole new branch of condensed-matter physics, the concept of orbital ordering (which can be viewed as the third class of ordering phenomena in condensed matter, after charge and spin ordering). It took about two decades to pick up speed, but since 1993, more than 3000 articles explicitly mention orbital order (about 2000 of them cite his original papers).

Some other critical concepts that Daniel was fully or partially responsible for include multiferroics, excitonic correlations in mixed valence and heavy fermion systems, and the dielectric formalism in the theory of superconductivity. (Few people know that it was Khomskii and co-workers who first showed, in 1970, that the T_c prefactor in the theory of superconductivity is the logarithmically averaged phonon frequency, and not Debye or mean squared frequency.)

Last, but not least, Daniel’s uplifting personality and enthusiasm were legendary in our condensed-matter community. His door was always open for experimentalists with new results, for theorists with new ideas, for computational scientists with new methods. And his input was always valuable, sometimes instrumental, for further progress. His knowledge of the universe of strongly correlated materials was astounding—behind his back, people used to refer to him as a walking encyclopedia, even as he was well past 80. His comprehensive 500-page book Transition Metal Compounds was but a small fraction of the wealth of knowledge he had in his head.

We, his students, collaborators, and friends, will always hold his memory deep in our hearts.

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