Frustrated magnets exhibit novel and useful properties, including dramatic field-sensitive properties and suppressed magnetic ordering temperatures. To elucidate the microscopic origins of this behavior we (i) grew the prototypical spinel material, Mn 3 O 4, in our laboratory and (ii) studied it with temperature- and field-dependent light scattering. There are several key results of our study ((M. Kim et al., Phys. Rev. Lett. 104, (2010)) : (1). A phonon mode splitting at the 33 K ferrimagnetic transition in Mn 3 O 4 (Fig. (a)) indicates that magnetic frustration in Mn 3 O 4 is resolved via a tetragonal-to-monoclinic structural transition. (2). The spin frustrated phase was recovered below 33 K in Mn 3 O 4 by applying a magnetic field transverse to the ordered moment (Fig. (b)), revealing a quantum phase transition to a rare state of matter that remains disordered down to T=0K. (3). The structural distortions in Mn 3 O 4 can be controlled with an applied field (Fig. (c)), which may have use in field-tuned “shape memory” devices. Our results show the important role of spin-lattice coupling in governing the novel magnetic phases and properties of magnetically frustrated materials (a) Temperature dependent light scattering intensity of the 295 cm - 1 phonon mode in Mn 3 O 4, showing a tetragonal-to-monoclinic distortion near 33K. (b) Field-dependence of 295 cm -1 phonon intensity at T=3K, showing that the spin-frustrated tetragonal phase can be recovered by applying a magnetic field transverse to the magnetic ordering direction. (c) Field-temperature phase diagram of Mn 3 O 4 inferred from these data for H || [1-10]. monoclinic ferrimagnet Energy Shift (cm -1 ) H (T) Energy Shift (cm -1 ) Temperature (K) T 2 =33K (a) (b) (c) T (K) H || [1-10] monoclinic ferrimagnet tetragonal spin-disordered Field-tuning magnetic frustration in the magneto-dielectric spinel Mn 3 O 4 S. Lance Cooper, U. of Illinois at Urbana-Champaign, DMR

The research supported by this grant has had several noteworthy “broader impacts” this year: (1). Single-crystal growth and distribution - We have used floating zone methods to grow high quality single crystal samples of the spinel material Mn 3 O 4 (Fig. (a)), which we have distributed to many other groups in the condensed matter community, including Prof. Peter Abbamonte, U. of Illinois (temperature-dependent X-ray), Dr. Christie Nelson, Brookhaven National Laboratory (magnetic-field-dependent X- ray), Prof. Gang Cao, U. of Kentucky (magnetic susceptibility), and Prof. Raffi Budakian, U. of Illinois (magnetic force resonance microscopy). (2). Student training - This grant supported the PhD thesis work of two female graduate students from the U. of Illinois (Fig. (b)), Minjung Kim and Yewon Gim, and a Research Experience for Undergraduates (REU) student, Jake Seeley (Haverford College). These students learned a variety of techniques, including single crystal growth, X-ray diffraction and magnetic characterization, cryogenics, high pressure- and magnetic-field methods, and optical spectroscopic methods. Further, these students had extensive practice giving scientific presentations via group meetings and conference presentations. (3). Outreach activities (Fig. (c)) – To encourage their interest in science, on June 24, 2010, I led a tour of our high-field/pressure optical spectroscopy laboratory to K-12 students as part of the Math Science Partnership (EnLiST) program. In July 2010, I gave a presentation on our NSF supported work, “Controlling exotic matter at extreme temperatures, pressures, and magnetic fields,” to REU students. Grad student Minjung Kim Large single crystal rod of Mn 3 O 4 grown in our lab using a floating zone method REU student Jake Seeley (a) (b) Grad student Yewon Gim PI Cooper giving a tour of our high-field, high-pressure optical spectroscopy laboratory to students, parents, and teachers (c) Field-tuning magnetic frustration in the magneto-dielectric spinel Mn 3 O 4 S. Lance Cooper, U. of Illinois at Urbana-Champaign, DMR