Phototunable Magnetism in Copper Octacyanomolybdate

We introduce copper molybdenum cyanides of general formula Cu2[Mo(CN)8]·nH2O, which can serve as optofunctional magnetic devices. Their ground states generally stay paramagnetic down to temperatures of the K order but exhibit a spontaneous magnetization upon photoirradiation usually below a few tens of K. To interest us still further, such a ferromagnetic stateinduced by blue-laser irradiation is demagnetized step by step through further application of red or near-infrared laser pulses. We solve this intriguing photomagnetism. The ground-state properties are fully revealed by means of a group-theoretical technique. Taking account of experimental observations, we simulate applying pump laser pulses to a likely ground state and successfully reproduce both the magnetization and demagnetization dynamics. We monitor the photorelaxation process through angle-resolved photoemission spectroscopy. Electrons are fully itinerant in any of the photoinduced steady states, forming a striking contrast to the initial equilibrium state of atomic aspect. The fully demagnetized final steady state looks completely different from the initial paramagnetism but bears good analogy to one of the possible ground states available with the Coulomb repulsion on Cu sites suppressed.


Introduction
Photomanipulation of magnetism in metal-based molecular systems is one of the most challenging themes in the fields of synthetic chemistry, solid-state physics, and engineering. Many efforts to developments of new materials and measurement techniques have been devoted to an achievement of the purpose. Prussian-blue analogues which involve hexacyanometalates [M(CN) 6 ] − ( : 3 transition metals) are widely known as phototunable magnets [1][2][3][4]. In the ironcobalt analogues, photoirradiation triggers the transition from the low-spin configuration, Fe II ( = 0)-CN-Co III ( = 0), to the high-spin configuration, Fe III ( = 1/2)-CN-Co II ( = 3/2) [5][6][7]. Such a photoredox reaction, which is induced by the charge-transfer excitation between cyano-bridged metals, is one of the key ingredients of photomagnetism in metal-based molecular systems [8]. For the purpose of designing and constructing new photoswitchable magnets based on the octacyanometalates [ (CN) 8 ] − ( = Mo, W), the chemical explorations of various cationic precursor complexes have made remarkable progress in the past decade [9,10].
Octa-coordinated complexes are rich in configuration and such a geometric variety is characteristic of transition metals of the second and third rows [11]. The octacyano-bridged systems possess various charge-transfer and magnetic-exchange pathways and the resultant conducting and magnetic properties. Paramagnetic [12,13], ferromagnetic [14][15][16], and antiferromagnetic [17][18][19] assemblies have been actually synthesized. Among others, octacyanomolybdates of [Mo IV (CN) 8 ] 4− -based coordination networks are much interesting, where the anionic precursor as a building block takes the square antiprism (SAPR-8) configuration [20,21]. Recently, remarkable phototunable magnetism of the copper-molybdenum bimetallic assemblies Cu 2 [Mo(CN) 8 ] ⋅ H 2 O [22 -25] has been reported. Ohkoshi et al. [26] observed details of the photoinduced magnetization and demagnetization of Cu 2 [Mo(CN) 8  low temperature 3 K, irradiation of a paramagnetic ground state with a laser light of 473 nm induces a macroscopic magnetization. Subsequent irradiation with another laser light of 658 nm conversely reduces the produced magnetization. When the sample is further irradiated with 785 nm and 840 nm laser lights successively, the magnetization gets smaller and smaller. The photoinduced magnetization is stable for hours up to 100 K or more and the photoconversion, both magnetization and demagnetization, is repeatable. In spite of such intriguing observations, neither the photoexcitation mechanism nor the ground-state magnetism has been interpreted yet beyond a phenomenological understanding. As is shown in Figure 1, the mixed-valent bimetallic compound Cu II 2 [Mo IV (CN) 8 ] crystallizes in the 4/ tetragonal space group with C 4ℎ point, where each constituent ion [Mo IV (CN) 8 ] 4− takes the SAPR-8 configuration with D 4 point symmetry. Fully filled 4 2 orbitals on Mo IV sites and half-filled 3 / orbitals on Cu II sites are physically active due to the crystalline-field splitting. The supramolecular coordination network based on octacyanomolybdates of the SAPR-8 configuration gives unique hopping paths and they must play a major role in realizing the photoreversible ferromagnetism.
We reveal possible magnetic and nonmagnetic states by making good use of a group-theoretical analysis on the 4/ cyano-bridged bimetallic assembly and simulate photoirradiation of the equilibrium states by numerically solving the time-dependent Schrödinger equation.

Model Hamiltonian and Its Symmetry Properties
We describe the supramolecular coordination network comprising divalent copper and tetravalent molybdenum ions in terms of a three-band extended Hubbard Hamiltonian [27,28] Figure 1. An on-site Coulomb repulsion and an orbital energy on the Cu(Mo) site are described as Cu(Mo) and Cu(Mo) , respectively. ∑ ⟨n,m, , ⟩ and ∑ ⟨n ̸ = m⟩ ∑ 4 =1 mean the sums all over nearest neighboring copper and molybdenum sites and nearest neighboring copper sites, respectively. The electron hoppings MoCu/CuCu , the intermetallic Coulomb repulsions MoCu/CuCu , the exchange interactions MoCu/CuCu , and the pair-hopping interactions MoCu/CuCu are considered. All the two-body terms are treated within the Hartree-Fock (HF) scheme.
Unless the gauge symmetry is broken, the symmetry group of any electron system can be written as [29,30] The Scientific World Journal 3  where P, S, and T are the groups of space, spin rotation, and time reversal, respectively. The space group is further decomposed as which read { a + b + c; , , ∈ Z} ≡ L and { , 4 , 2 , −1 4 , , 4 , 2 ≡ ℎ , −1 4 } ≡ C 4ℎ , respectively. An irreducible representation of G over the real number field, which is referred to as, consists of those of P, S, and T:̆=̆⊗̆⊗. Once a wave vector Q is fixed, the relevant little group D(Q) is given.̆is therefore labeled as Q(Q). Since cell doubling along the and directions is expected under the present lattice structure, we consider Q = ( / , / , 0) as well as Q = 0, which are referred to as M and Γ, respectively, whose little groups are C 4ℎ in itself. A spin rotation by around an axis e (|e| = 1), (e, ) ∈ S, is represented as The space groups of the former two and the latter two turn out to be L 1 ∧ C 4ℎ and L 2 ∧ C 4ℎ , respectively, where L 1 = L and L 2 = {( + + − )a + ( + − − )b + c; + , − , ∈ }. We explain them in Table 1 and Figure 2. Here, the twodimensional representations and , generally available in a C 4ℎ Hamiltonian, are discarded, because they have no axial isotropy subgroup [31,32]. Every irreducible representation is guaranteed to yield a stable solution only when its isotropy subgroup possesses a one-dimensional fixed point subspace [33].
As is shown in Figure   The Scientific World Journal

Competing Ground States
We have calculated the ground-state phase diagram at the sufficiently low temperature B = 0.001 MoCu . In Figure 3 (1) and (2), respectively. Phase boundaries drawn in black and red denote transitions of the first and second order, respectively. We calculate optical properties of the PM state labeled ×. The CDP state labeled ∘ is discussed later in connection with photoexcitation of the PM state.
positive MoCu . On the other hand, the direct Cu-Cu exchange interaction CuCu is taken to be negative. The magnitude of the exchange interactions in the transfer-integral unit is comparable to that in typical cyano-bridged transition-metal complexes [37][38][39]. The pair-hopping correlation MoCu set positive indirectly supports FM, destabilizing any other phase [27]. On the other hand, CuCu set negative favors PM and M-MoCu-CDW because the pair hoppings between Cu sites are possible in them. PM and FM are sitting adjacently on the phase diagrams, and, therefore, a photoinduced phase transition between them is promising. With the experimental observations [26] in mind, we choose Cu = Mo = 3.2 MoCu and CuCu = 2.4 MoCu as standard parameters for Cu II 2 [Mo IV (CN) 8 ], which is indicated by × in Figure 3. On this parameter point, we can well reproduce the valences of Mo IV and Cu II in the paramagnetic ground state. Another nonmagnetic and uniform state, referred to as CDP, can be stabilized in a Mo ≫ Cu region. In contrast with PM, CDP shows localization of electrons on Cu orbitals. The PM and CDP states belong to the same irreducible representation but their electronic structures are quite different from each other. The details of CDP are discussed later.
In Figure 4(a), we present a band structure of the PM state. Hereafter, the transfer integral MoCu is set equal to 0.7 eV, which is comparable to the intermetallic transfer integrals in typical Prussian-blue analogues [7,40]. In the PM state, bands for the up-and down-spin electrons are degenerate and the Fermi level lies in the band gap of 0.35 eV. Thus it exhibits insulating behavior. In the PM state, the Cu orbitals contribute to both the occupied and unoccupied bands, whereas the Mo orbitals contribute only to the occupied bands. One can easily understand these differences by considering the valences of Cu and Mo ions in the PM state.
We further calculate the polarized optical conductivity defined as with the relevant current operator equal to |a|. The Drude spectral weight [41,42] in (4) is given by with the kinetic-energy operator We define the ground state | 0 ⟩ as where |0⟩ is the true electron vacuum, F is the Fermi energy, and † k( ) creates an electron of spin in the HF eigenstate with an eigenvalue k( ) ( = 1, 2, . . . , 12). Excited states can be calculated within the HF scheme, being generally defined as where k( ) ≤ F < k(]) . Every excited state of the HF type is a single Slater determinant. The thus-calculated absorption spectra are shown in Figure 4(b), where every spectral line is Lorentzianbroadened by a width of 0.1 MoCu . The PM state shows gap-full structures in the ⊥ and ‖ spectra. A major absorption in ‖ is attributed to electron excitations from the highest-occupied molecular orbital (HOMO) to the lowestunoccupied molecular orbital (LUMO) at point Γ, while a broad absorption band in ⊥ is due to the HOMO-LUMO interband transitions at around points Γ, M, and A. ⊥ has a larger oscillator strength than that of ‖ by the Cu-to-Cu electron transfers in the -plane.

Phototunable Magnetism
Here we investigate effects of photoirradiation of the PM ground state. The photoinduced magnetization is hardly detectable at zero magnetic field, while it rapidly increases just The Scientific World Journal as an external field is applied [22]. With this in mind, we apply a moderate field to the system as follows: where = 2.5 T. Now the spin degeneracy is lifted and higher-lying down-spin electrons may selectively be excited into conduction bands. We describe such photoexcitations by multiplying the hopping term  [26] in mind, we set the pumping photon energy ℎ 0 equal to 2.6 eV unless otherwise noted, which is indicated by the vertical arrow in Figure 4. Another key ingredient of the photomagnetization is a spin-mixing interaction. In an attempt at breaking the conservation law for the total magnetization, we introduce Dzyaloshinskii-Moriya (DM) interactions: Once we start the time integration ( > 0), Ψ( ) deviates from the eigenvectors of H HF ( ) in general. Pump laser pulses are described by the vector potential, In Figure 5, we study DM interaction effects on the photomagnetism, before entering into detailed discussions of Both the -and -axis-polarized photons indeed induce magnetization and demagnetization of the system. The macroscopic magnetizations are induced by the first pulses and they are erased successively by the second, third, and fourth pulses. The induced magnetizations by the -axis-polarized photons are slightly larger than those by the -axis-polarized ones. Even though varies over three orders of magnitude (0.07-70 meV), the induced magnetizations take almost the same value and the following demagnetization processes hardly vary. Depending on the value of , the global magnetization occurs at different points in time, but these differences are at most 9 fs and 14 fs in the cases of A 0 ‖ a and A 0 ‖ c, respectively. Of course, in the absence of the DM interaction, photoirradiation never induces a net magnetization. Thus, the DM interaction plays an important role to bring the magnetic relaxation but does not so strongly affect the performances of the photomagnets. Hereafter, we set the magnitude of the DM vector equal to 0.7 meV, which is comparable to that in typical transition-metal oxides [46,47].
In Figure 6, we present details of the photoinduced dynamics, where the increase of the electronic energy, and the magnetization, M, are monitored. We first focus on the dynamics induced by the -axis-polarized photons. The irradiation with ℎ 0 photons first induces electron transfers from Mo to Cu sites. The electronic energy nonmonotonically increases with a time passage through instantaneous stagnation in the photoabsorption, which is seen at around the center of the pulse. Δ upon the first photoirradiation reads as a double-stepped function of time. The occurrence of the significant magnetization looks simultaneous with the second step of Δ ( ). The thus-induced magnetization is decreased by the second irradiation with 0.75ℎ 0 photons. Even in this demagnetization process, electrons further transfer from Mo to Cu sites. This means that the demagnetization process cannot be interpreted as a simple reverse process of the magnetization. The magnetization gets smaller and smaller by the second, third, and fourth pulses; that is, the photoinduced ferromagnetic state comes back to a nonmagnetic state finally. Next, we discuss the case of A 0 ‖ c. We obtain qualitatively the same results with A 0 ‖ a, upon the first photoirradiation.
However, the absorbed energy is slightly smaller than that in the case of A 0 ‖ a. Given the larger magnetization than that induced by the -axis-polarized photons, the -axis-polarized ones are more effective for photomagnetization than theaxis-polarized ones. Electron transfers upon the subsequent photoirradiation are insignificant in comparison with those in the case of A 0 ‖ a, where the electrons transiently come back to Mo sites only by the third photoirradiation. However, step-by-step demagnetization, observed in the case of A 0 ‖ a as well, is clearly seen. Thus, the dynamics induced by theand -axis-polarized photons are similar to each other. Even if we consider superposition of the two excited states which are induced by photons polarized in the and directions (see the right panels of Figure 6), the above magnetic features are retained. The tunable photomagnetism we revealed here agrees with the polycrystalline-sample measurements [26]. We further present , , and corresponding to the -, -, and -direction components of M, respectively, in Figure 6(c). In both the cases of A 0 ‖ a and A 0 ‖ c, photoirradiation does not induce . While rotating in the -plane, the induced magnetizations disappear. Here, we emphasize that the thus-demagnetized states by the photoirradiation differ from the initial stationary PM state in the valence arrangement. The electron densities on both Cu and Mo sites come close to the average value 16/12 = 1.33.
Photon-energy dependences of the magnetization and demagnetization dynamics are shown in Figure 7. In the case of A 0 ‖ a, the induced magnetization value decreases with decreasing irradiated photon energy. However, the magnetization values in the final steady states at 3.0 ps seem to be unaffected by the photon energy ℎ 0 . The same tendency is seen in the dynamics induced by the -axis-polarized photons. Here, we recall the ground-state optical conductivity of PM shown in Figure 4(b). In the ‖ spectrum, an absorption at 2.0 eV is smaller than that at 2.6 eV, whereas, in the ⊥ spectrum, the former is larger than the latter. Despite such differences between ⊥ and ‖ , the magnetic responses to the -and -axis-polarized photons resemble each other in the photon-energy dependence. The photoinduced ferromagnetism is strongly affected by the photon energy itself rather than the intensity of the corresponding photon absorption. We will thus be able to control a sensitivity of the photomagnetism by tuning a wavelength of the irradiation light.
In order to see changes in the electronic structures in more detail, we calculate one-particle spectral functions [48]: with the electron part The Scientific World Journal Here,̃ † k(]) creates an electron in the eigenstate of energy k(]) for the instantaneous Hamiltonian H HF ( ) and the delta function is Lorentzian-broadened with a width of 0.1 MoCu . Figure 8 visualizes ( ; k, ) corresponding to "momentumresolved" density of states in the cases of irradiating the PM state with the pulsed laser lights polarized parallel to the crystalline axes and , which correspond to the time variations in Figure 6. They demonstrate time evolutions of the band structure of the PM state shown in Figure 4(a). As is shown in Figure 8, band structure changes in the cases of A 0 ‖ a and A 0 ‖ c resemble each other. In the photoinduced FM states at = 0.75 ps, the degeneracy between up and down spins in the initial stationary PM state is so lifted as to induce a net magnetization. The band splitting caused by the -axis-polarized photons is more noticeable than that by the -axis-polarized ones. That is why the larger magnetization is induced by the -axis-polarized photons. In the subsequent demagnetization processes, the up-and down-spin bands intend to converge, where we find stimulated photon emission as well as photon absorption, which is never seen in the magnetization processes. A significant decrease of the band splitting is induced by the second pulse irradiation with -axis-polarized photons, which corresponds to the remarkable demagnetization shown in Figure 6(c). The induced magnetizations decrease with decreasing band splitting, by the third and fourth photoirradiation. The thusdemagnetized final steady states at = 3.00 ps show an entirely different band structure from that of the initial stationary PM state.

Summary and Discussion
We have revealed phototunable magnetism in the cyano-bridged copper-molybdenum bimetallic assembly Cu 2 [Mo(CN) 8 ], where the coordination geometry of every molybdenum complex ion is square antiprism. Indeed the magnetization is both induced and erased optically, but the present reversible magnetism does not necessarily mean a round trip of electrons. Divalent copper ions are reduced into monovalent ones during magnetization, while reoxidation of these photoexcited copper ions is of rare occurrence during demagnetization. Electrons of Cu character and those of Mo character are both fully itinerant in any of the photoinduced steady states and look different from rather atomic ones in the initial equilibrium paramagnetic state. In this context we may be reminded of the thus-called hidden states [49].  Figure 9: (a) The one-particle spectral functions ( ; k, ), ( ; k, ), and ( ; k, ) at = 3.00 ps in the case of A 0 ‖ a in Figure 6. (b) A band structure of the CDP state labeled ∘ in Figure 3. The Fermi energy F is indicated by a dotted horizontal line. steady state at = 3.00 ps. This band structure looks very similar to that of the equilibrium CDP state shown in Figure 9(b). The CDP state exhibits insulating behavior due to the energy gap of 0.88 eV, where the Cu and Mo orbitals contribute to the occupied and unoccupied bands, respectively, because all the electrons are localized on Cu sites. On the other hand, the final steady state has no well-defined electron and hole bands anymore due to the photoirradiation, which are clearly seen in ( ; k, ) and ( ; k, ), and therefore this state is metallic. Electron transfers from Cu to Mo sites in the equilibrium CDP state can lead to situation just like Figure 9(a). Thus the final steady state may read as a CDP state which has the different electron distribution from that in the equilibrium situation. The photoconverted FM state from the PM state is further optically converted to such a "nonequilibrium" CDP state. In the ground-state phase diagram, the CDP phase as well as the PM phase is indeed located adjacent to the FM phase (cf. Figure 3(b)). Such a relationship among three phases may be a key ingredient of the tunable photomagnetism. In order to improve a performance of the photomagnets, it is also necessary to clarify thermal and chemical-doping effects on the phase competition. Modern experiments enable us to directly observe femtosecond electron transfer dynamics [50][51][52][53][54]. For example, time-resolved optical measurements can detect the metallic conductivity of the photoexcited states and time-and angleresolved photoemission measurements can directly observe the changes in the band structures shown in Figure 8. We hope the present calculations will stimulate such ultrafast pump-probe experiments on the cyano-bridged coppermolybdenum bimetallic assemblies.